In this paper we prove that, within the framework of $\textsf{RCD}^\star(K,N)$ spaces with $N\<\infty$, the entropic cost (i.e. the minimal value of the Schr{\"o}dinger problem) admits:A threefold dynamical variational representation, in the spirit of the Benamou{\textendash}Brenier formula for the Wasserstein distance; A Hamilton{\textendash}Jacobi{\textendash}Bellman dual representation, in line with Bobkov{\textendash}Gentil{\textendash}Ledoux and Otto{\textendash}Villani results on the duality between Hamilton{\textendash}Jacobi and continuity equation for optimal transport;A Kantorovich-type duality formula, where the Hopf{\textendash}Lax semigroup is replaced by a suitable {\textquoteleft}entropic{\textquoteright} counterpart.We thus provide a complete and unifying picture of the equivalent variational representations of the Schr{\"o}dinger problem as well as a perfect parallelism with the analogous formulas for the Wasserstein distance. Riemannian manifolds with Ricci curvature bounded from below are a relevant class of $\textsf{RCD}^*(K,N)$ spaces and our results are new even in this setting.

}, issn = {1432-2064}, doi = {10.1007/s00440-019-00909-1}, url = {https://doi.org/10.1007/s00440-019-00909-1}, author = {Nicola Gigli and Luca Tamanini} } @article {GIULIANI2019324, title = {BlackNUFFT: Modular customizable black box hybrid parallelization of type 3 NUFFT in 3D}, journal = {Computer Physics Communications}, volume = {235}, year = {2019}, pages = {324 - 335}, abstract = {Many applications benefit from an efficient Discrete Fourier Transform (DFT) between arbitrarily spaced points. The Non Uniform Fast Fourier Transform reduces the computational cost of such operation from O(N2) to O(NlogN) exploiting gridding algorithms and a standard Fast Fourier Transform on an equi-spaced grid. The parallelization of the NUFFT of type 3 (between arbitrary points in space and frequency) still poses some challenges: we present a novel and flexible hybrid parallelization in a MPI-multithreaded environment exploiting existing HPC libraries on modern architectures. To ensure the reliability of the developed library, we exploit continuous integration strategies using Travis CI. We present performance analyses to prove the effectiveness of our implementation, possible extensions to the existing library, and an application of NUFFT type 3 to MRI image processing. Program summary Program Title: BlackNUFFT Program Files doi: http://dx.doi.org/10.17632/vxfj6x2p8x.1 Licensing provisions: LGPL Programming language: C++ External routines/libraries: deal.II , FFTW, PFFT Nature of problem: Provide a modular and extensible implementation of a parallel Non Uniform Fast Fourier Transform of type 3. Solution method: Use of hybrid shared distributed memory paradigm to achieve high level of efficiency. We exploit existing HPC library following best practices in scientific computing (as continuous integration via TravisCI) to reach higher complexities and guarantee the accuracy of the solution proposed.

}, keywords = {C++, Extensibility, FFT, Modularity, MPI, MRI image processing, NUFFT type 3, TBB}, issn = {0010-4655}, doi = {https://doi.org/10.1016/j.cpc.2018.10.005}, url = {http://www.sciencedirect.com/science/article/pii/S0010465518303539}, author = {Nicola Giuliani} } @conference {2019, title = {A complete data-driven framework for the efficient solution of parametric shape design and optimisation in naval engineering problems}, booktitle = {VIII International Conference on Computational Methods in Marine Engineering}, year = {2019}, abstract = {In the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples of the ROM application, in the naval field, can be found in [31, 24]. Mandatory ingredient for the ROM methods is the relation between the high-fidelity solutions and the parameters. Dealing with geometrical parameters, especially in the industrial context, this relation may be unknown and not trivial (simulations over hand morphed geometries) or very complex (high number of parameters or many nested morphing techniques). To overcome these scenarios, we propose in this contribution an efficient and complete data-driven framework involving ROM techniques for shape design and optimization, extending the pipeline presented in [7]. By applying the singular value decomposition (SVD) to the points coordinates defining the hull geometry {\textendash}- assuming the topology is inaltered by the deformation {\textendash}-, we are able to compute the optimal space which the deformed geometries belong to, hence using the modal coefficients as the new parameters we can reconstruct the parametric formulation of the domain. Finally the output of interest is approximated using the proper orthogonal decomposition with interpolation technique. To conclude, we apply this framework to a naval shape design problem where the bulbous bow is morphed to reduce the total resistance of the ship advancing in calm water.

}, author = {Nicola Demo and Marco Tezzele and Andrea Mola and Gianluigi Rozza} } @article {2019, title = {A continuous dependence result for a dynamic debonding model in dimension one}, number = {SISSA;05/2019/MATE}, year = {2019}, institution = {SISSA}, abstract = {In this paper we address the problem of continuous dependence on initial and boundary data for a one-dimensional debonding model describing a thin film peeled away from a substrate. The system underlying the process couples the weakly damped wave equation with a Griffith{\textquoteright}s criterion which rules the evolution of the debonded region. We show that under general convergence assumptions on the data the corresponding solutions converge to the limit one with respect to different natural topologies.

}, url = {http://preprints.sissa.it/xmlui/handle/1963/35329}, author = {Filippo Riva} } @article {GIGLI2019, title = {Differential structure associated to axiomatic Sobolev spaces}, journal = {Expositiones Mathematicae}, year = {2019}, abstract = {The aim of this note is to explain in which sense an axiomatic Sobolev space over a general metric measure space ({\`a} la Gol{\textquoteright}dshtein{\textendash}Troyanov) induces {\textendash} under suitable locality assumptions {\textendash} a first-order differential structure.

}, keywords = {Axiomatic Sobolev space, Cotangent module, Locality of differentials}, issn = {0723-0869}, doi = {https://doi.org/10.1016/j.exmath.2019.01.002}, url = {http://www.sciencedirect.com/science/article/pii/S0723086918300975}, author = {Nicola Gigli and Enrico Pasqualetto} } @article {2019, title = {A dynamic model for viscoelastic materials with prescribed growing cracks}, year = {2019}, abstract = {In this paper we prove the existence of solutions for a class of viscoelastic dynamic systems on time-dependent cracked domains, with possibly degenerate viscosity coefficients. Under stronger regularity assumptions we also show a uniqueness result. Finally, we exhibit an example where the energy-dissipation balance is not satisfied, showing there is an additional dissipation due to the crack growth.

}, url = {http://preprints.sissa.it:8180/xmlui/handle/1963/35334}, author = {Maicol Caponi and Francesco Sapio} } @conference {2019, title = {Efficient Reduction in Shape Parameter Space Dimension for Ship Propeller Blade Design}, booktitle = {VIII International Conference on Computational Methods in Marine Engineering}, year = {2019}, abstract = {In this work, we present the results of a ship propeller design optimization campaign carried out in the framework of the research project PRELICA, funded by the Friuli Venezia Giulia regional government. The main idea of this work is to operate on a multidisciplinary level to identify propeller shapes that lead to reduced tip vortex-induced pressure and increased efficiency without altering the thrust. First, a specific tool for the bottom-up construction of parameterized propeller blade geometries has been developed. The algorithm proposed operates with a user defined number of arbitrary shaped or NACA airfoil sections, and employs arbitrary degree NURBS to represent the chord, pitch, skew and rake distribution as a function of the blade radial coordinate. The control points of such curves have been modified to generate, in a fully automated way, a family of blade geometries depending on as many as 20 shape parameters. Such geometries have then been used to carry out potential flow simulations with the Boundary Element Method based software PROCAL. Given the high number of parameters considered, such a preliminary stage allowed for a fast evaluation of the performance of several hundreds of shapes. In addition, the data obtained from the potential flow simulation allowed for the application of a parameter space reduction methodology based on active subspaces (AS) property, which suggested that the main propeller performance indices are, at a first but rather accurate approximation, only depending on a single parameter which is a linear combination of all the original geometric ones. AS analysis has also been used to carry out a constrained optimization exploiting response surface method in the reduced parameter space, and a sensitivity analysis based on such surrogate model. The few selected shapes were finally used to set up high fidelity RANS simulations and select an optimal shape.

}, author = {Andrea Mola and Marco Tezzele and Mahmoud Gadalla and Valdenazzi, Federica and Grassi, Davide and Padovan, Roberta and Gianluigi Rozza} } @article {GENTIL2019, title = {An entropic interpolation proof of the HWI inequality}, journal = {Stochastic Processes and their Applications}, year = {2019}, abstract = {The HWI inequality is an {\textquotedblleft}interpolation{\textquotedblright}inequality between the Entropy H, the Fisher information I and the Wasserstein distance W. We present a pathwise proof of the HWI inequality which is obtained through a zero noise limit of the Schr{\"o}dinger problem. Our approach consists in making rigorous the Otto{\textendash}Villani heuristics in Otto and Villani (2000) taking advantage of the entropic interpolations, which are regular both in space and time, rather than the displacement ones.

}, keywords = {Entropic interpolations, Fisher information, Relative entropy, Schr{\"o}dinger problem, Wasserstein distance}, issn = {0304-4149}, doi = {https://doi.org/10.1016/j.spa.2019.04.002}, url = {http://www.sciencedirect.com/science/article/pii/S0304414918303454}, author = {Ivan Gentil and Christian L{\'e}onard and Luigia Ripani and Luca Tamanini} } @article {riccobelli2018constitutive, title = {On the existence of elastic minimizers for initially stressed materials}, journal = {Phil. Trans. R. Soc. A}, volume = {377}, number = {2144}, year = {2019}, publisher = {The Royal Society}, author = {Davide Riccobelli and A. Agosti and Pasquale Ciarletta} } @article {doi:10.1142/S0129055X19500053, title = {Ground state energy of mixture of Bose gases}, journal = {Reviews in Mathematical Physics}, volume = {31}, number = {02}, year = {2019}, pages = {1950005}, abstract = {We consider the asymptotic behavior of a system of multi-component trapped bosons, when the total particle number N becomes large. In the dilute regime, when the interaction potentials have the length scale of order O(N-1), we show that the leading order of the ground state energy is captured correctly by the Gross{\textendash}Pitaevskii energy functional and that the many-body ground state fully condensates on the Gross{\textendash}Pitaevskii minimizers. In the mean-field regime, when the interaction length scale is O(1), we are able to verify Bogoliubov{\textquoteright}s approximation and obtain the second order expansion of the ground state energy. While such asymptotic results have several precursors in the literature on one-component condensates, the adaptation to the multi-component setting is non-trivial in various respects and the analysis will be presented in detail.

}, doi = {10.1142/S0129055X19500053}, url = {https://doi.org/10.1142/S0129055X19500053}, author = {Alessandro Michelangeli and Phan Thanh Nam and Alessandro Olgiati} } @article {cotti2019, title = {Isomonodromy deformations at an irregular singularity with coalescing eigenvalues}, journal = {Duke Math. J.}, volume = {168}, number = {6}, year = {2019}, month = {04}, pages = {967{\textendash}1108}, publisher = {Duke University Press}, abstract = {We consider an n{\texttimes}n linear system of ODEs with an irregular singularity of Poincar\'e rank 1 at z=$\infty$, holomorphically depending on parameter t within a polydisc in Cn centred at t=0. The eigenvalues of the leading matrix at z=$\infty$ coalesce along a locus Δ contained in the polydisc, passing through t=0. Namely, z=$\infty$ is a resonant irregular singularity for t∈Δ. We analyse the case when the leading matrix remains diagonalisable at Δ. We discuss the existence of fundamental matrix solutions, their asymptotics, Stokes phenomenon and monodromy data as t varies in the polydisc, and their limits for t tending to points of Δ. When the deformation is isomonodromic away from Δ, it is well known that a fundamental matrix solution has singularities at Δ. When the system also has a Fuchsian singularity at z=0, we show under minimal vanishing conditions on the residue matrix at z=0 that isomonodromic deformations can be extended to the whole polydisc, including Δ, in such a way that the fundamental matrix solutions and the constant monodromy data are well defined in the whole polydisc. These data can be computed just by considering the system at fixed t=0. Conversely, if the t-dependent system is isomonodromic in a small domain contained in the polydisc not intersecting Δ, if the entries of the Stokes matrices with indices corresponding to coalescing eigenvalues vanish, then we show that Δ is not a branching locus for the fundamental matrix solutions. The importance of these results for the analytic theory of Frobenius Manifolds is explained. An application to Painlev\'e equations is discussed.

}, doi = {10.1215/00127094-2018-0059}, url = {https://doi.org/10.1215/00127094-2018-0059}, author = {Giordano Cotti and Boris Dubrovin and Davide Guzzetti} } @article {FEOLA2019119, title = {Local well-posedness for quasi-linear NLS with large Cauchy data on the circle}, journal = {Annales de l{\textquoteright}Institut Henri Poincar{\'e} C, Analyse non lin{\'e}aire}, volume = {36}, number = {1}, year = {2019}, pages = {119 - 164}, abstract = {We prove local in time well-posedness for a large class of quasilinear Hamiltonian, or parity preserving, Schr{\"o}dinger equations on the circle. After a paralinearization of the equation, we perform several paradifferential changes of coordinates in order to transform the system into a paradifferential one with symbols which, at the positive order, are constant and purely imaginary. This allows to obtain a priori energy estimates on the Sobolev norms of the solutions.

}, keywords = {Dispersive equations, Energy method, Local wellposedness, NLS, Para-differential calculus, Quasi-linear PDEs}, issn = {0294-1449}, doi = {https://doi.org/10.1016/j.anihpc.2018.04.003}, url = {http://www.sciencedirect.com/science/article/pii/S0294144918300428}, author = {Roberto Feola and Felice Iandoli} } @article {Bawane:2017gjf, title = {N=2 gauge theories on unoriented/open four-manifolds and their AGT counterparts}, journal = {JHEP}, volume = {07}, year = {2019}, pages = {040}, doi = {10.1007/JHEP07(2019)040}, url = {http://inspirehep.net/record/1631219/}, author = {Aditya Bawane and Benvenuti, Sergio and Giulio Bonelli and Muteeb, Nouman and Alessandro Tanzini} } @article {gigli_rigoni_2019, title = {A Note About the Strong Maximum Principle on RCD Spaces}, journal = {Canadian Mathematical Bulletin}, volume = {62}, number = {2}, year = {2019}, pages = {259{\textendash}266}, publisher = {Canadian Mathematical Society}, abstract = {We give a direct proof of the strong maximum principle on finite dimensional RCD spaces based on the Laplacian comparison of the squared distance.

}, doi = {10.4153/CMB-2018-022-9}, author = {Nicola Gigli and Chiara Rigoni} } @article {Kozhasov2019, title = {On the Number of Flats Tangent to Convex Hypersurfaces in Random Position}, journal = {Discrete \& Computational Geometry}, year = {2019}, month = {Mar}, issn = {1432-0444}, doi = {10.1007/s00454-019-00067-0}, url = {https://doi.org/10.1007/s00454-019-00067-0}, author = {Khazhgali Kozhasov and Antonio Lerario} } @article {AGOSTINELLI2019103702, title = {Nutations in growing plant shoots: The role of elastic deformations due to gravity loading}, journal = {Journal of the Mechanics and Physics of Solids}, year = {2019}, pages = {103702}, abstract = {The effect of elastic deformations induced by gravity loading on the active circumnutation movements of growing plant shoots is investigated. We consider first a discrete model (a gravitropic spring-pendulum system) and then a continuous rod model which is analyzed both analytically (under the assumption of small deformations) and numerically (in the large deformation regime). We find that, for a choice of material parameters consistent with values reported in the available literature on plant shoots, rods of sufficient length may exhibit lateral oscillations of increasing amplitude, which eventually converge to limit cycles. This behavior strongly suggests the occurrence of a Hopf bifurcation, just as for the gravitropic spring-pendulum system, for which this result is rigorously established. At least in this restricted set of material parameters, our analysis supports a view of Darwin{\textquoteright}s circumnutations as a biological analogue to structural systems exhibiting flutter instabilities, i.e., spontaneous oscillations away from equilibrium configurations driven by non-conservative loads. Here, in the context of nutation movements of growing plant shoots, the energy needed to sustain oscillations is continuously supplied to the system by the internal biochemical machinery presiding the capability of plants to maintain a vertical pose.

}, keywords = {Circumnutations, Flutter instability, Gravitropism, Hopf bifurcation}, issn = {0022-5096}, doi = {https://doi.org/10.1016/j.jmps.2019.103702}, url = {http://www.sciencedirect.com/science/article/pii/S0022509619306106}, author = {Daniele Agostinelli and Alessandro Lucantonio and Giovanni Noselli and Antonio DeSimone} } @article {Michelangeli2019, title = {Point-Like Perturbed Fractional Laplacians Through Shrinking Potentials of Finite Range}, journal = {Complex Analysis and Operator Theory}, year = {2019}, month = {May}, abstract = {We construct the rank-one, singular (point-like) perturbations of the d-dimensional fractional Laplacian in the physically meaningful norm-resolvent limit of fractional Schr{\"o}dinger operators with regular potentials centred around the perturbation point and shrinking to a delta-like shape. We analyse both possible regimes, the resonance-driven and the resonance-independent limit, depending on the power of the fractional Laplacian and the spatial dimension. To this aim, we also qualify the notion of zero-energy resonance for Schr{\"o}dinger operators formed by a fractional Laplacian and a regular potential.

}, issn = {1661-8262}, doi = {10.1007/s11785-019-00927-w}, url = {https://doi.org/10.1007/s11785-019-00927-w}, author = {Alessandro Michelangeli and Raffaele Scandone} } @article {1903.04302, title = {Quasi-continuous vector fields on RCD spaces}, year = {2019}, author = {Cl{\'e}ment Debin and Nicola Gigli and Enrico Pasqualetto} } @article {Beltr{\'a}n2019, title = {The Real Polynomial Eigenvalue Problem is Well Conditioned on the Average}, journal = {Foundations of Computational Mathematics}, year = {2019}, month = {May}, abstract = {We study the average condition number for polynomial eigenvalues of collections of matrices drawn from some random matrix ensembles. In particular, we prove that polynomial eigenvalue problems defined by matrices with random Gaussian entries are very well conditioned on the average.

}, issn = {1615-3383}, doi = {10.1007/s10208-019-09414-2}, url = {https://doi.org/10.1007/s10208-019-09414-2}, author = {Carlos Beltr{\'a}n and Khazhgali Kozhasov} } @article {FEOLA2019932, title = {Reducibility of first order linear operators on tori via Moser{\textquoteright}s theorem}, journal = {Journal of Functional Analysis}, volume = {276}, number = {3}, year = {2019}, pages = {932 - 970}, abstract = {In this paper we prove reducibility of a class of first order, quasi-linear, quasi-periodic time dependent PDEs on the torus∂tu+ζ.∂xu+a(ωt,x).∂xu=0,x∈Td,ζ∈Rd,ω∈Rν. As a consequence we deduce a stability result on the associated Cauchy problem in Sobolev spaces. By the identification between first order operators and vector fields this problem can be formulated as the problem of finding a change of coordinates which conjugates a weakly perturbed constant vector field on Tν+d to a constant diophantine flow. For this purpose we generalize Moser{\textquoteright}s straightening theorem: considering smooth perturbations we prove that the corresponding straightening torus diffeomorphism is smooth, under the assumption that the perturbation is small only in some given Sobolev norm and that the initial frequency belongs to some Cantor-like set. In view of applications in KAM theory for PDEs we provide also tame estimates on the change of variables.

}, keywords = {Hyperbolic PDEs, KAM theory, Nash{\textendash}Moser, Reducibility}, issn = {0022-1236}, doi = {https://doi.org/10.1016/j.jfa.2018.10.009}, url = {http://www.sciencedirect.com/science/article/pii/S0022123618303793}, author = {Roberto Feola and Filippo Giuliani and Riccardo Montalto and Michela Procesi} } @article {Bellettini2019, title = {On the relaxed area of the graph of discontinuous maps from the plane to the plane taking three values with no symmetry assumptions}, journal = {Annali di Matematica Pura ed Applicata (1923 -)}, year = {2019}, month = {Jul}, abstract = {In this paper, we estimate from above the area of the graph of a singular map u taking a disk to three vectors, the vertices of a triangle, and jumping along three $\mathcal{C}^2$-embedded curves that meet transversely at only one point of the disk. We show that the singular part of the relaxed area can be estimated from above by the solution of a Plateau-type problem involving three entangled nonparametric area-minimizing surfaces. The idea is to {\textquoteleft}{\textquoteleft}fill the hole{\textquoteright}{\textquoteright} in the graph of the singular map with a sequence of approximating smooth two-codimensional surfaces of graph-type, by imagining three minimal surfaces, placed vertically over the jump of u, coupled together via a triple point in the target triangle. Such a construction depends on the choice of a target triple point, and on a connection passing through it, which dictate the boundary condition for the three minimal surfaces. We show that the singular part of the relaxed area of u cannot be larger than what we obtain by minimizing over all possible target triple points and all corresponding connections.

}, issn = {1618-1891}, doi = {10.1007/s10231-019-00887-0}, url = {https://doi.org/10.1007/s10231-019-00887-0}, author = {Giovanni Bellettini and Alaa Elshorbagy and Maurizio Paolini and Riccardo Scala} } @article {Lu{\v c}i{\'c}2019, title = {The Serre{\textendash}Swan theorem for normed modules}, journal = {Rendiconti del Circolo Matematico di Palermo Series 2}, volume = {68}, number = {2}, year = {2019}, month = {Aug}, pages = {385{\textendash}404}, issn = {1973-4409}, doi = {10.1007/s12215-018-0366-6}, url = {https://doi.org/10.1007/s12215-018-0366-6}, author = {Danka Lu{\v c}i{\'c} and Enrico Pasqualetto} } @conference {2019, title = {Shape optimization through proper orthogonal decomposition with interpolation and dynamic mode decomposition enhanced by active subspaces}, booktitle = {VIII International Conference on Computational Methods in Marine Engineering}, year = {2019}, abstract = {We propose a numerical pipeline for shape optimization in naval engineering involving two different non-intrusive reduced order method (ROM) techniques. Such methods are proper orthogonal decomposition with interpolation (PODI) and dynamic mode decomposition (DMD). The ROM proposed will be enhanced by active subspaces (AS) as a pre-processing tool that reduce the parameter space dimension and suggest better sampling of the input space. We will focus on geometrical parameters describing the perturbation of a reference bulbous bow through the free form deformation (FFD) technique. The ROM are based on a finite volume method (FV) to simulate the multi-phase incompressible flow around the deformed hulls. In previous works we studied the reduction of the parameter space in naval engineering through AS [38, 10] focusing on different parts of the hull. PODI and DMD have been employed for the study of fast and reliable shape optimization cycles on a bulbous bow in [9]. The novelty of this work is the simultaneous reduction of both the input parameter space and the output fields of interest. In particular AS will be trained computing the total drag resistance of a hull advancing in calm water and its gradients with respect to the input parameters. DMD will improve the performance of each simulation of the campaign using only few snapshots of the solution fields in order to predict the regime state of the system. Finally PODI will interpolate the coefficients of the POD decomposition of the output fields for a fast approximation of all the fields at new untried parameters given by the optimization algorithm. This will result in a non-intrusive data-driven numerical optimization pipeline completely independent with respect to the full order solver used and it can be easily incorporated into existing numerical pipelines, from the reference CAD to the optimal shape.

}, author = {Marco Tezzele and Nicola Demo and Gianluigi Rozza} } @article {2019, title = {On the square distance function from a manifold with boundary}, year = {2019}, abstract = {We characterize arbitrary codimensional smooth manifolds $\mathcal{M}$ with boundary embedded in $\mathbb{R}^n$ using the square distance function and the signed distance function from $\mathcal{M}$ and from its boundary. The results are localized in an open set.

}, url = {http://cvgmt.sns.it/media/doc/paper/4260/manif_with_bound_dist.pdf}, author = {Giovanni Bellettini and Alaa Elshorbagy} } @article {2019, title = {Strong Novikov conjecture for low degree cohomology and exotic group C*-algebras}, journal = {arXiv e-prints}, year = {2019}, month = {May}, pages = {arXiv:1905.07730}, abstract = {We strengthen a result of Hanke{\textendash}Schick about the strong Novikov conjecture for low degree cohomology by showing that their non-vanishing result for the maximal group $C^*$-algebra even holds for the reduced group $C^*$-algebra. To achieve this we provide a Fell absorption principle for certain exotic crossed product functors.

}, keywords = {Mathematics - K-Theory and Homology, Mathematics - Operator Algebras}, author = {Paolo Antonini and Buss, Alcides and Engel, Alexander and Siebenand , Timo} } @article {2019, title = {On the topological degree of planar maps avoiding normal cones}, number = {SISSA;04/2019/MATE}, year = {2019}, institution = {SISSA}, abstract = {The classical Poincar{\'e}{\textendash}Bohl theorem provides the exis-tence of a zero for a function avoiding external rays. When the do-main is convex, the same holds true when avoiding normal cones. We consider here the possibility of dealing with nonconvex sets having in-ward corners or cusps, in which cases the normal cone vanishes. This allows us to deal with situations where the topological degree may be di˙erent from {\textpm}1.}, url = {http://preprints.sissa.it/handle/1963/35330}, author = {Alessandro Fonda and Giuliano Klun} } @article {Iraso2019, title = {Two-Dimensional Yang{\textendash}Mills Theory on Surfaces with Corners in Batalin{\textendash}Vilkovisky Formalism}, journal = {Communications in Mathematical Physics}, year = {2019}, month = {Mar}, abstract = {In this paper we recover the non-perturbative partition function of 2D Yang{\textendash}Mills theory from the perturbative path integral. To achieve this goal, we study the perturbative path integral quantization for 2D Yang{\textendash}Mills theory on surfaces with boundaries and corners in the Batalin{\textendash}Vilkovisky formalism (or, more precisely, in its adaptation to the setting with boundaries, compatible with gluing and cutting{\textendash}-the BV-BFV formalism). We prove that cutting a surface (e.g. a closed one) into simple enough pieces{\textendash}-building blocks{\textendash}-and choosing a convenient gauge-fixing on the pieces, and assembling back the partition function on the surface, one recovers the known non-perturbative answers for 2D Yang{\textendash}Mills theory.

}, issn = {1432-0916}, doi = {10.1007/s00220-019-03392-w}, url = {https://doi.org/10.1007/s00220-019-03392-w}, author = {Riccardo Iraso and Mnev, P.} } @article {1901.02449, title = {Zero modes and low-energy resolvent expansion for three dimensional Schrodinger operators with point interactions}, year = {2019}, url = {https://arxiv.org/abs/1901.02449}, author = {Raffaele Scandone} } @article {20.500.11767_81643, title = {Accelerating the iterative solution of convection-diffusion problems using singular value decomposition}, journal = {NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS}, year = {2018}, pages = {1{\textendash}21}, doi = {10.1002/nla.2211}, url = {https://arxiv.org/abs/1807.09467}, author = {Giuseppe Pitton and Luca Heltai} } @article {doi:10.1137/17M1147354, title = {Analysis of a Dynamic Peeling Test with Speed-Dependent Toughness}, journal = {SIAM Journal on Applied Mathematics}, volume = {78}, number = {2}, year = {2018}, pages = {1206-1227}, abstract = {We analyse a one-dimensional model of dynamic debonding for a thin film, where the local toughness of the glue between the film and the substrate also depends on the debonding speed. The wave equation on the debonded region is strongly coupled with Griffith{\textquoteright}s criterion for the evolution of the debonding front. We provide an existence and uniqueness result and find explicitly the solution in some concrete examples. We study the limit of solutions as inertia tends to zero, observing phases of unstable propagation, as well as time discontinuities, even though the toughness diverges at a limiting debonding speed.

}, doi = {10.1137/17M1147354}, url = {https://doi.org/10.1137/17M1147354}, author = {Giuliano Lazzaroni and Lorenzo Nardini} } @article {20.500.11767_81647, title = {An authenticated theoretical modeling of electrified fluid jet in core{\textendash}shell nanofibers production}, journal = {JOURNAL OF INDUSTRIAL TEXTILES}, volume = {47}, year = {2018}, pages = {1791{\textendash}1811}, doi = {10.1177/1528083717710711}, author = {Rafiei, S. and Noroozi, B. and Luca Heltai and Haghi, A. K.} } @article {2018arXiv180705892A, title = {The Baum{\textendash}Connes conjecture localised at the unit element of a discrete group}, journal = {ArXiv e-prints}, year = {2018}, keywords = {19K35, 46L80, 46L85, 58J22, Mathematics - K-Theory and Homology, Mathematics - Operator Algebras}, author = {Paolo Antonini and Azzali, S. and Skandalis, G.} } @article {2018, title = {Canonical Surfaces and Hypersurfaces in Abelian Varieties}, number = {arXiv:1808.05302}, year = {2018}, url = {https://arxiv.org/abs/1808.05302}, author = {Luca Cesarano} } @article {2018, title = {On the Cauchy problem for the wave equation on time-dependent domains}, number = {SISSA;19/2018/MATE}, year = {2018}, institution = {SISSA}, abstract = {We introduce a notion of solution to the wave equation on a suitable class of time-dependent domains and compare it with a previous de nition. We prove an existence result for the solution of the Cauchy problem and present some additional conditions which imply uniqueness.}, url = {http://preprints.sissa.it/handle/1963/35314}, author = {Gianni Dal Maso and Rodica Toader} } @article {2018, title = {Certified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models}, journal = {Journal of Scientific Computing}, volume = {74}, year = {2018}, pages = {197-219}, doi = {10.1007/s10915-017-0430-y}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85017156114\&doi=10.1007\%2fs10915-017-0430-y\&partnerID=40\&md5=023ef0bb95713f4442d1fa374c92a964}, author = {Immanuel Martini and Bernard Haasdonk and Gianluigi Rozza} } @article {2018, title = {Characteristic boundary layers for mixed hyperbolic systems in one space dimension and applications to the Navier-Stokes and MHD equations}, number = {SISSA;45/2018/MATE}, year = {2018}, institution = {SISSA}, abstract = {We provide a detailed analysis of the boundary layers for mixed hyperbolic-parabolic systems in one space dimension and small amplitude regimes. As an application of our results, we describe the solution of the so-called boundary Riemann problem recovered as the zero viscosity limit of the physical viscous approximation. In particular, we tackle the so called doubly characteristic case, which is considerably more demanding from the technical viewpoint and occurs when the boundary is characteristic for both the mixed hyperbolic-parabolic system and for the hyperbolic system obtained by neglecting the second order terms. Our analysis applies in particular to the compressible Navier-Stokes and MHD equations in Eulerian coordinates, with both positive and null conductivity. In these cases, the doubly characteristic case occurs when the velocity is close to 0. The analysis extends to non-conservative systems.}, url = {http://preprints.sissa.it/handle/1963/35325}, author = {Stefano Bianchini and Laura Spinolo} } @article {doi:10.1142/S0218202518500379, title = {Cohesive fracture with irreversibility: Quasistatic evolution for a model subject to fatigue}, journal = {Mathematical Models and Methods in Applied Sciences}, volume = {28}, number = {07}, year = {2018}, pages = {1371-1412}, abstract = {In this paper we prove the existence of quasistatic evolutions for a cohesive fracture on a prescribed crack surface, in small-strain antiplane elasticity. The main feature of the model is that the density of the energy dissipated in the fracture process depends on the total variation of the amplitude of the jump. Thus, any change in the crack opening entails a loss of energy, until the crack is complete. In particular this implies a fatigue phenomenon, i.e. a complete fracture may be produced by oscillation of small jumps. The first step of the existence proof is the construction of approximate evolutions obtained by solving discrete-time incremental minimum problems. The main difficulty in the passage to the continuous-time limit is that we lack of controls on the variations of the jump of the approximate evolutions. Therefore we resort to a weak formulation where the variation of the jump is replaced by a Young measure. Eventually, after proving the existence in this weak formulation, we improve the result by showing that the Young measure is concentrated on a function and coincides with the variation of the jump of the displacement.

}, doi = {10.1142/S0218202518500379}, url = {https://doi.org/10.1142/S0218202518500379}, author = {Vito Crismale and Giuliano Lazzaroni and Gianluca Orlando} } @inbook {tezzele2018combined, title = {Combined parameter and model reduction of cardiovascular problems by means of active subspaces and POD-Galerkin methods}, booktitle = {Mathematical and Numerical Modeling of the Cardiovascular System and Applications}, year = {2018}, pages = {185{\textendash}207}, publisher = {Springer}, organization = {Springer}, author = {Marco Tezzele and Francesco Ballarin and Gianluigi Rozza} } @article {giantesio2017comparison, title = {A Comparison Between Active Strain and Active Stress in Transversely Isotropic Hyperelastic Materials}, journal = {J. Elast.}, year = {2018}, publisher = {Springer Nature}, author = {Giulia Giantesio and Alessandro Musesti and Davide Riccobelli} } @inbook {AuricchioContiLefieuxMorgantiRealiRozzaVeneziani2018, title = {Computational methods in cardiovascular mechanics}, booktitle = {Cardiovascular Mechanics}, year = {2018}, pages = {54}, publisher = {CRC Press}, organization = {CRC Press}, chapter = {Computational methods in cardiovascular mechanics}, abstract = {The introduction of computational models in cardiovascular sciences has been progressively bringing new and unique tools for the investigation of the physiopathology. Together with the dramatic improvement of imaging and measuring devices on one side, and of computational architectures on the other one, mathematical and numerical models have provided a new, clearly noninvasive, approach for understanding not only basic mechanisms but also patient-specific conditions, and for supporting the design and the development of new therapeutic options. The terminology in silico is, nowadays, commonly accepted for indicating this new source of knowledge added to traditional in vitro and in vivo investigations. The advantages of in silico methodologies are basically the low cost in terms of infrastructures and facilities, the reduced invasiveness and, in general, the intrinsic predictive capabilities based on the use of mathematical models. The disadvantages are generally identified in the distance between the real cases and their virtual counterpart required by the conceptual modeling that can be detrimental for the reliability of numerical simulations.

}, url = {https://www.taylorfrancis.com/books/e/9781315280288/chapters/10.1201\%2Fb21917-5}, author = {Auricchio, Ferdinando and Conti, Michele and Lefieux, Adrian and Morganti, Simone and Alessandro Reali and Gianluigi Rozza and Veneziani, Alessandro}, editor = {Michel F. Labrosse} } @article {2018, title = {On the continuity of the trace operator in GSBV (Ω) and GSBD (Ω)}, number = {SISSA;39/2018/MATE}, year = {2018}, note = {27 pages}, abstract = {In this paper we present a new result of continuity for the trace operator acting on functions that might jump on a prescribed (n-1)-dimensional set Г, with the only hypothesis of being rectifiable and of finite measure. We also show an application of our result in relation to the variational model of elasticity with cracks, when the associated minimum problems are coupled with Dirichlet and Neumann boundary conditions.}, url = {http://preprints.sissa.it/handle/1963/35324}, author = {Emanuele Tasso} } @article {20.500.11767_83906, title = {deal2lkit: A toolkit library for high performance programming in deal.II}, journal = {SOFTWAREX}, volume = {7}, year = {2018}, pages = {318{\textendash}327}, doi = {10.1016/j.softx.2018.09.004}, author = {Alberto Sartori and Nicola Giuliani and Mauro Bardelloni and Luca Heltai} } @article {20.500.11767_81694, title = {The deal.II Library, Version 9.0}, journal = {JOURNAL OF NUMERICAL MATHEMATICS}, year = {2018}, doi = {10.1515/jnma-2018-0054}, url = {https://doi.org/10.1515/jnma-2018-0054}, author = {Giovanni Alzetta and Arndt, Daniel and W. Bangerth and Boddu, Vishal and Brands, Benjamin and Denis Davydov and Gassm{\"o}ller, Rene and Timo Heister and Luca Heltai and Kormann, Katharina and Martin Kronbichler and Matthias Maier and Pelteret, Jean-Paul and B. Turcksin and David Wells} } @article {1807.10063, title = {Differential of metric valued Sobolev maps}, year = {2018}, author = {Nicola Gigli and Enrico Pasqualetto and Elefterios Soultanis} } @article {1807.02060, title = {Dimension reduction for thin films with transversally varying prestrain: the oscillatory and the non-oscillatory case}, year = {2018}, author = {Marta Lewicka and Danka Lu{\v c}i{\'c}} } @article {TezzeleSalmoiraghiMolaRozza2018, title = {Dimension reduction in heterogeneous parametric spaces with application to naval engineering shape design problems}, journal = {Advanced Modeling and Simulation in Engineering Sciences}, volume = {5}, number = {1}, year = {2018}, month = {Sep}, pages = {25}, abstract = {We present the results of the first application in the naval architecture field of a methodology based on active subspaces properties for parameters space reduction. The physical problem considered is the one of the simulation of the hydrodynamic flow past the hull of a ship advancing in calm water. Such problem is extremely relevant at the preliminary stages of the ship design, when several flow simulations are typically carried out by the engineers to assess the dependence of the hull total resistance on the geometrical parameters of the hull, and others related with flows and hull properties. Given the high number of geometric and physical parameters which might affect the total ship drag, the main idea of this work is to employ the active subspaces properties to identify possible lower dimensional structures in the parameter space. Thus, a fully automated procedure has been implemented to produce several small shape perturbations of an original hull CAD geometry, in order to exploit the resulting shapes to run high fidelity flow simulations with different structural and physical parameters as well, and then collect data for the active subspaces analysis. The free form deformation procedure used to morph the hull shapes, the high fidelity solver based on potential flow theory with fully nonlinear free surface treatment, and the active subspaces analysis tool employed in this work have all been developed and integrated within SISSA mathLab as open source tools. The contribution will also discuss several details of the implementation of such tools, as well as the results of their application to the selected target engineering problem.

}, doi = {10.1186/s40323-018-0118-3}, author = {Marco Tezzele and Filippo Salmoiraghi and Andrea Mola and Gianluigi Rozza} } @article {MR3871555, title = {Discriminant circle bundles over local models of Strebel graphs and Boutroux curves}, journal = {Teoret. Mat. Fiz.}, volume = {197}, number = {2}, year = {2018}, pages = {163{\textendash}207}, issn = {0564-6162}, doi = {10.4213/tmf9513}, url = {https://doi.org/10.4213/tmf9513}, author = {Marco Bertola and Korotkin, D. A.} } @inbook {20.500.11767_86398, title = {A distributed lagrange formulation of the finite element immersed boundary method for fluids interacting with compressible solids}, booktitle = {Mathematical and Numerical Modeling of the Cardiovascular System and Applications}, volume = {16}, year = {2018}, pages = {1{\textendash}21}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, address = {Cham}, doi = {10.1007/978-3-319-96649-6_1}, url = {https://arxiv.org/abs/1712.02545v1}, author = {Boffi, Daniele and Gastaldi, Lucia and Luca Heltai} } @article {Michelangeli_2018, title = {Effective non-linear spinor dynamics in a spin-1 Bose{\textendash}Einstein condensate}, journal = {Journal of Physics A: Mathematical and Theoretical}, volume = {51}, number = {40}, year = {2018}, month = {sep}, pages = {405201}, publisher = {IOP Publishing}, abstract = {We derive from first principles the experimentally observed effective dynamics of a spinor Bose gas initially prepared as a Bose{\textendash}Einstein condensate and then left free to expand ballistically. In spinor condensates, which represent one of the recent frontiers in the manipulation of ultra-cold atoms, particles interact with a two-body spatial interaction and a spin{\textendash}spin interaction. The effective dynamics is well-known to be governed by a system of coupled semi-linear Schr{\"o}dinger equations: we recover this system, in the sense of marginals in the limit of infinitely many particles, with a mean-field re-scaling of the many-body Hamiltonian. When the resulting control of the dynamical persistence of condensation is quantified with the parameters of modern observations, we obtain a bound that remains quite accurate for the whole typical duration of the experiment.

}, doi = {10.1088/1751-8121/aadbc2}, url = {https://doi.org/10.1088\%2F1751-8121\%2Faadbc2}, author = {Alessandro Michelangeli and Alessandro Olgiati} } @proceedings {demo2018efficient, title = {An efficient shape parametrisation by free-form deformation enhanced by active subspace for hull hydrodynamic ship design problems in open source environment}, year = {2018}, publisher = {International Society of Offshore and Polar Engineers}, address = {Sapporo, Japan}, abstract = {In this contribution, we present the results of the application of a parameter space reduction methodology based on active subspaces to the hull hydrodynamic design problem. Several parametric deformations of an initial hull shape are considered to assess the influence of the shape parameters considered on the hull total drag. The hull resistance is typically computed by means of numerical simulations of the hydrodynamic flow past the ship. Given the high number of parameters involved - which might result in a high number of time consuming hydrodynamic simulations - assessing whether the parameters space can be reduced would lead to considerable computational cost reduction. Thus, the main idea of this work is to employ the active subspaces to identify possible lower dimensional structures in the parameter space, or to verify the parameter distribution in the position of the control points. To this end, a fully automated procedure has been implemented to produce several small shape perturbations of an original hull CAD geometry which are then used to carry out high-fidelity flow simulations and collect data for the active subspaces analysis. To achieve full automation of the open source pipeline described, both the free form deformation methodology employed for the hull perturbations and the solver based on unsteady potential flow theory, with fully nonlinear free surface treatment, are directly interfaced with CAD data structures and operate using IGES vendor-neutral file formats as input files. The computational cost of the fluid dynamic simulations is further reduced through the application of dynamic mode decomposition to reconstruct the steady state total drag value given only few initial snapshots of the simulation. The active subspaces analysis is here applied to the geometry of the DTMB-5415 naval combatant hull, which is which is a common benchmark in ship hydrodynamics simulations.}, keywords = {Active subspaces, Boundary element method, Dynamic mode decomposition, Fluid structure interaction, Free form deformation, Fully nonlinear potential, Numerical towing tank}, issn = {978-1-880653-87-6}, url = {https://www.onepetro.org/conference-paper/ISOPE-I-18-481}, author = {Nicola Demo and Marco Tezzele and Andrea Mola and Gianluigi Rozza} } @booklet {1807.11370, title = {The Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: from Laminar to Turbulent Flows}, year = {2018}, author = {Saddam Hijazi and Shafqat Ali and Giovanni Stabile and Francesco Ballarin and Gianluigi Rozza} } @article {2018, title = {Energy-dissipation balance of a smooth moving crack}, number = {SISSA;31/2018/MATE}, year = {2018}, abstract = {In this paper we provide necessary and sufficient conditions in order to guarantee the energy-dissipation balance of a Mode III crack, growing on a prescribed smooth path. Moreover, we characterize the singularity of the displacement near the crack tip, generalizing the result in [S. Nicaise, A.M. Sandig - J. Math. Anal. Appl., 2007] valid for straight fractures.}, url = {http://preprints.sissa.it/handle/1963/35320}, author = {Maicol Caponi and Ilaria Lucardesi and Emanuele Tasso} } @article {2018, title = {Existence and uniqueness of dynamic evolutions for a one dimensional debonding model with damping}, number = {SISSA;28/2018/MATE}, year = {2018}, abstract = {In this paper we analyse a one-dimensional debonding model for a thin film peeled from a substrate when friction is taken into account. It is described by the weakly damped wave equation whose domain, the debonded region, grows according to a Griffth{\textquoteright}s criterion. Firstly we prove that the equation admits a unique solution when the evolution of the debonding front is assigned. Finally we provide an existence and uniqueness result for the coupled problem given by the wave equation together with Griffth{\textquoteright}s criterion.

}, url = {http://preprints.sissa.it/xmlui/handle/1963/35319}, author = {Lorenzo Nardini and Filippo Riva} } @article {2018, title = {Existence for elastodynamic Griffith fracture with a weak maximal dissipation condition}, number = {SISSA;04/2018/MATE}, year = {2018}, abstract = {We consider a model of elastodynamics with fracture evolution, based on energy-dissipation balance and a maximal dissipation condition. We prove an existence result in the case of planar elasticity with a free crack path, where the maximal dissipation condition is satisfied among suitably regular competitor cracks.}, url = {http://preprints.sissa.it/handle/1963/35308}, author = {Gianni Dal Maso and Cristopher J. Larsen and Rodica Toader} } @article {2018, title = {Existence of solutions to a phase field model of dynamic fracture with a crack dependent dissipation}, number = {SISSA;06/2018/MATE}, year = {2018}, abstract = {We propose a phase-field model of dynamic crack propagation based on the Ambrosio-Tortorelli approximation, which takes in account dissipative effects due to the speed of the crack tips. In particular, adapting the time discretization scheme contained in [Bourdin et al., Int. J. Fracture 168 (2011), 133-143] and [Larsen et al., Math. Models Methods Appl. Sci. 20 (2010), 1021-1048], we show the existence of a dynamic crack evolution satisfying an energy dissipation balance, according to Griffith{\textquoteright}s criterion.}, url = {http://preprints.sissa.it/handle/1963/35307}, author = {Maicol Caponi} } @article {demo2018ezyrb, title = {EZyRB: Easy Reduced Basis method}, journal = {The Journal of Open Source Software}, volume = {3}, number = {24}, year = {2018}, pages = {661}, doi = {10.21105/joss.00661}, url = {https://joss.theoj.org/papers/10.21105/joss.00661}, author = {Nicola Demo and Marco Tezzele and Gianluigi Rozza} } @inbook {Bianchini2018, title = {Failure of the Chain Rule in the Non Steady Two-Dimensional Setting}, booktitle = {Current Research in Nonlinear Analysis: In Honor of Haim Brezis and Louis Nirenberg}, year = {2018}, pages = {33{\textendash}60}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, address = {Cham}, isbn = {978-3-319-89800-1}, doi = {10.1007/978-3-319-89800-1_2}, url = {https://doi.org/10.1007/978-3-319-89800-1_2}, author = {Stefano Bianchini and Paolo Bonicatto}, editor = {Rassias, Themistocles M.} } @article {Stabile2018_2, title = {Finite volume POD-Galerkin stabilised reduced order methods for the parametrised incompressible Navier-Stokes equations}, journal = {Computers \& Fluids}, year = {2018}, month = {feb}, publisher = {Elsevier {BV}}, doi = {10.1016/j.compfluid.2018.01.035}, url = {https://doi.org/10.1016/j.compfluid.2018.01.035}, author = {Giovanni Stabile and Gianluigi Rozza} } @article {agostiniani2018foldable, title = {Foldable structures made of hydrogel bilayers}, year = {2018}, author = {Virginia Agostiniani and Antonio DeSimone and Alessandro Lucantonio and Danka Lu{\v c}i{\'c}} } @article {doi:10.1063/1.5033856, title = {Fractional powers and singular perturbations of quantum differential Hamiltonians}, journal = {Journal of Mathematical Physics}, volume = {59}, number = {7}, year = {2018}, pages = {072106}, abstract = {We consider the fractional powers of singular (point-like) perturbations of the Laplacian and the singular perturbations of fractional powers of the Laplacian, and we compare two such constructions focusing on their perturbative structure for resolvents and on the local singularity structure of their domains. In application to the linear and non-linear Schr{\"o}dinger equations for the corresponding operators, we outline a programme of relevant questions that deserve being investigated.

}, doi = {10.1063/1.5033856}, url = {https://doi.org/10.1063/1.5033856}, author = {Alessandro Michelangeli and Andrea Ottolini and Raffaele Scandone} } @article {GEORGIEV20181551, title = {On fractional powers of singular perturbations of the Laplacian}, journal = {Journal of Functional Analysis}, volume = {275}, number = {6}, year = {2018}, pages = {1551 - 1602}, abstract = {We qualify a relevant range of fractional powers of the so-called Hamiltonian of point interaction in three dimensions, namely the singular perturbation of the negative Laplacian with a contact interaction supported at the origin. In particular we provide an explicit control of the domain of such a fractional operator and of its decomposition into regular and singular parts. We also qualify the norms of the resulting singular fractional Sobolev spaces and their mutual control with the corresponding classical Sobolev norms.

}, keywords = {Point interactions, Regular and singular component of a point-interaction operator, Singular perturbations of the Laplacian}, issn = {0022-1236}, doi = {https://doi.org/10.1016/j.jfa.2018.03.007}, url = {http://www.sciencedirect.com/science/article/pii/S0022123618301046}, author = {Vladimir Georgiev and Alessandro Michelangeli and Raffaele Scandone} } @article {doi:10.1142/S0129167X18500076, title = {Framed symplectic sheaves on surfaces}, journal = {International Journal of Mathematics}, volume = {29}, number = {01}, year = {2018}, pages = {1850007}, abstract = {A framed symplectic sheaf on a smooth projective surface $X$ is a torsion-free sheaf $E$ together with a trivialization on a divisor $D \subset X$ and a morphism $\Lambda^2 E \rightarrow \mathcal{O}_X$ satisfying some additional conditions. We construct a moduli space for framed symplectic sheaves on a surface, and present a detailed study for $X =\mathbb{P}_\mathbb{C}^2$. In this case, the moduli space is irreducible and admits an ADHM-type description and a birational proper map onto the space of framed symplectic ideal instantons.

}, doi = {10.1142/S0129167X18500076}, url = {https://doi.org/10.1142/S0129167X18500076}, author = {Jacopo Vittorio Scalise} } @article {SalmoiraghiScardigliTelibRozza2018, title = {Free-form deformation, mesh morphing and reduced-order methods: enablers for efficient aerodynamic shape optimisation}, journal = {International Journal of Computational Fluid Dynamics}, volume = {32}, number = {4-5}, year = {2018}, pages = {233-247}, publisher = {Taylor \& Francis}, abstract = {In this work, we provide an integrated pipeline for the model-order reduction of turbulent flows around parametrised geometries in aerodynamics. In particular, free-form deformation is applied for geometry parametrisation, whereas two different reduced-order models based on proper orthogonal decomposition (POD) are employed in order to speed-up the full-order simulations: the first method exploits POD with interpolation, while the second one is based on domain decomposition. For the sampling of the parameter space, we adopt a Greedy strategy coupled with Constrained Centroidal Voronoi Tessellations, in order to guarantee a good compromise between space exploration and exploitation. The proposed framework is tested on an industrially relevant application, i.e. the front-bumper morphing of the DrivAer car model, using the finite-volume method for the full-order resolution of the Reynolds-Averaged Navier{\textendash}Stokes equations.

}, doi = {10.1080/10618562.2018.1514115}, author = {Filippo Salmoiraghi and Scardigli, Angela and Telib, Haysam and Gianluigi Rozza} } @article {kozhasov2018fully, title = {On fully real eigenconfigurations of tensors}, journal = {SIAM Journal on Applied Algebra and Geometry}, volume = {2}, number = {2}, year = {2018}, pages = {339{\textendash}347}, publisher = {SIAM}, abstract = {We construct generic real symmetric tensors with only real eigenvectors or, equivalently, real homogeneous polynomials with the maximum possible finite number of critical points on the sphere.

}, doi = {10.1137/17M1145902}, url = {https://epubs.siam.org/doi/pdf/10.1137/17M1145902}, author = {Khazhgali Kozhasov} } @article {2018, title = {On Geometric Quantum Confinement in Grushin-Like Manifolds}, number = {SISSA;36/2018/MATE}, year = {2018}, note = {16 pages}, abstract = {We study the problem of so-called geometric quantum confinement in a class of two-dimensional incomplete Riemannian manifold with metric of Grushin type. We employ a constant-fibre direct integral scheme, in combination with Weyl{\textquoteright}s analysis in each fibre, thus fully characterising the regimes of presence and absence of essential self-adjointness of the associated Laplace-Beltrami operator.}, url = {http://preprints.sissa.it/handle/1963/35322}, author = {Matteo Gallone and Alessandro Michelangeli and Eugenio Pozzoli} } @article {Antonelli2018, title = {Global, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials}, journal = {Zeitschrift f{\"u}r angewandte Mathematik und Physik}, volume = {69}, number = {2}, year = {2018}, month = {Mar}, pages = {46}, abstract = {We prove the existence of weak solutions in the space of energy for a class of nonlinear Schr{\"o}dinger equations in the presence of a external, rough, time-dependent magnetic potential. Under our assumptions, it is not possible to study the problem by means of usual arguments like resolvent techniques or Fourier integral operators, for example. We use a parabolic regularisation, and we solve the approximating Cauchy problem. This is achieved by obtaining suitable smoothing estimates for the dissipative evolution. The total mass and energy bounds allow to extend the solution globally in time. We then infer sufficient compactness properties in order to produce a global-in-time finite energy weak solution to our original problem.

}, issn = {1420-9039}, doi = {10.1007/s00033-018-0938-5}, url = {https://doi.org/10.1007/s00033-018-0938-5}, author = {Paolo Antonelli and Alessandro Michelangeli and Raffaele Scandone} } @article {agostiniani2018heterogeneous, title = {Heterogeneous elastic plates with in-plane modulation of the target curvature and applications to thin gel sheets}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, year = {2018}, publisher = {EDP Sciences}, doi = {https://doi.org/10.1051/cocv/2018046}, author = {Virginia Agostiniani and Alessandro Lucantonio and Danka Lu{\v c}i{\'c}} } @article {2018, title = {Hydrogenoid Spectra with Central Perturbations}, number = {SISSA;34/2018/MATE}, year = {2018}, note = {Mathematics Subject Classification (2010) 34L10 . 34L15 . 34L16 . 47B15 . 47B25 . 47N20 . 81Q10 . 81Q80}, abstract = {Through the Krein-Vi{\v s}ik-Birman extension scheme, unlike the previous classical analysis based on von Neumann{\textquoteright}s theory, we reproduce the construction and classification of all self-adjoint realisations of two intimately related models: the three-dimensional hydrogenoid-like Hamiltonians with singular perturbation supported at the centre (the nucleus), and the Sch{\"o}rdinger operators on the halfline with Coulomb potentials centred at the origin. These two problems are technically equivalent, albeit sometimes treated by their own in the the literature. Based on such scheme, we then recover the formula to determine the eigenvalues of each self-adjoint extension, which are corrections to the non-relativistic hydrogenoid energy levels.We discuss in which respect the Krein-Vi{\v s}ik-Birman scheme is somehow more natural in yielding the typical boundary condition of self-adjointness at the centre of the perturbation and in identifying the eigenvalues of each extension.}, url = {http://preprints.sissa.it/handle/1963/35321}, author = {Matteo Gallone and Alessandro Michelangeli} } @article {20.500.11767_86219, title = {Iterative map-making with two-level preconditioning for polarized cosmic microwave background data sets. A worked example for ground-based experiments}, journal = {ASTRONOMY \& ASTROPHYSICS}, volume = {618}, year = {2018}, pages = {1{\textendash}14}, doi = {10.1051/0004-6361/201832710}, url = {https://arxiv.org/abs/1801.08937}, author = {Puglisi, Giuseppe and Poletti, Davide and Fabbian, Giulio and Baccigalupi, Carlo and Luca Heltai and Stompor, Radek} } @article {2018, title = {On Krylov solutions to infinite-dimensional inverse linear problems}, number = {SISSA;49/2018/MATE}, year = {2018}, institution = {SISSA}, abstract = {We discuss, in the context of inverse linear problems in Hilbert space, the notion of the associated infinite-dimensional Krylov subspace and we produce necessary and sufficient conditions for the Krylov-solvability of the considered inverse problem. The presentation is based on theoretical results together with a series of model examples, and it is corroborated by specific numerical experiments.}, url = {http://preprints.sissa.it/handle/1963/35327}, author = {Noe Caruso and Alessandro Michelangeli and Paolo Novati} } @article {2018, title = {Local moduli of semisimple Frobenius coalescent structures}, number = {arXiv;1712.08575}, year = {2018}, institution = {SISSA}, abstract = {There is a conjectural relation, formulated by the second author, between the enumerative geometry of a wide class of smooth projective varieties and their derived category of coherent sheaves. In particular, there is an increasing interest for an explicit description of certain local invariants, called monodromy data, of semisimple quantum cohomologies in terms of characteristic classes of exceptional collections in the derived categories. Being intentioned to address this problem, which, to our opinion, is still not well understood, we have realized that some issues in the theory of Frobenius manifolds need to be preliminarily clarified, and that an extension of the theory itself is necessary, in view of the fact that quantum cohomologies of certain classes of homogeneous spaces may show a coalescence phenomenon.

}, url = {http://preprints.sissa.it/handle/1963/35304}, author = {Giordano Cotti and Boris Dubrovin and Davide Guzzetti} } @article {Max_arXiv, title = {A Localized Reduced-Order Modeling Approach for PDEs with Bifurcating Solutions}, journal = {ArXiv e-prints}, year = {2018}, keywords = {Mathematics - Numerical Analysis}, author = {Martin W. Hess and A. Alla and Annalisa Quaini and Gianluigi Rozza and M. Gunzburger} } @article {1806.03437, title = {Long time existence for fully nonlinear NLS with small Cauchy data on the circle}, year = {2018}, author = {Feola Roberto and Felice Iandoli} } @article {Dell{\textquoteright}Antonio2018, title = {Lp-Boundedness of Wave Operators for the Three-Dimensional Multi-Centre Point Interaction}, journal = {Annales Henri Poincar{\'e}}, volume = {19}, number = {1}, year = {2018}, month = {Jan}, pages = {283{\textendash}322}, abstract = {We prove that, for arbitrary centres and strengths, the wave operators for three-dimensional Schr{\"o}dinger operators with multi-centre local point interactions are bounded in Lp(R3)for 1\<p\<3 and unbounded otherwise.

}, issn = {1424-0661}, doi = {10.1007/s00023-017-0628-4}, url = {https://doi.org/10.1007/s00023-017-0628-4}, author = {Gianfausto Dell{\textquoteright}Antonio and Alessandro Michelangeli and Raffaele Scandone and Kenji Yajima} } @article {2018, title = {A minimization approach to the wave equation on time-dependent domains}, number = {SISSA;21/2018/MATE}, year = {2018}, institution = {SISSA}, abstract = {We prove the existence of weak solutions to the homogeneous wave equation on a suitable class of time-dependent domains. Using the approach suggested by De Giorgi and developed by Serra and Tilli, such solutions are approximated by minimizers of suitable functionals in space-time.}, url = {http://preprints.sissa.it/handle/1963/35318}, author = {Gianni Dal Maso and Lucia De Luca} } @article {BELLETTINI20181, title = {Minimizing movements for mean curvature flow of droplets with prescribed contact angle}, journal = {Journal de Math{\'e}matiques Pures et Appliqu{\'e}es}, volume = {117}, year = {2018}, pages = {1 - 58}, abstract = {We study the mean curvature motion of a droplet flowing by mean curvature on a horizontal hyperplane with a possibly nonconstant prescribed contact angle. Using the solutions constructed as a limit of an approximation algorithm of Almgren{\textendash}Taylor{\textendash}Wang and Luckhaus{\textendash}Sturzenhecker, we show the existence of a weak evolution, and its compatibility with a distributional solution. We also prove various comparison results. R{\'e}sum{\'e} Nous {\'e}tudions le mouvement par courbure moyenne d{\textquoteright}une goutte qui glisse par courbure moyenne sur un hyperplan horizontal avec un angle de contact prescrit {\'e}ventuellement non constant. En utilisant les solutions construites comme limites d{\textquoteright}un algorithme d{\textquoteright}approximation d{\^u} {\`a} Almgren, Taylor et Wang et Luckhaus et Sturzenhecker, nous montrons l{\textquoteright}existence d{\textquoteright}une {\'e}volution faible, et sa compatibilit{\'e} avec une solution au sens des distributions. Nous d{\'e}montrons {\'e}galement plusieurs r{\'e}sultats de comparaison.

}, keywords = {Capillary functional, Mean curvature flow with prescribed contact angle, Minimizing movements, Sets of finite perimeter}, issn = {0021-7824}, doi = {https://doi.org/10.1016/j.matpur.2018.06.003}, url = {http://www.sciencedirect.com/science/article/pii/S0021782418300825}, author = {Giovanni Bellettini and Matteo Novaga and Shokhrukh Kholmatov} } @article {doi:10.1137/17M1159294, title = {Minimizing Movements for Mean Curvature Flow of Partitions}, journal = {SIAM Journal on Mathematical Analysis}, volume = {50}, number = {4}, year = {2018}, pages = {4117-4148}, abstract = {We prove the existence of a weak global in time mean curvature flow of a bounded partition of space using the method of minimizing movements. The result is extended to the case when suitable driving forces are present. We also prove some consistency results for a minimizing movement solution with smooth and viscosity solutions when the evolution starts from a partition made by a union of bounded sets at a positive distance. In addition, the motion starting from the union of convex sets at a positive distance agrees with the classical mean curvature flow and is stable with respect to the Hausdorff convergence of the initial partitions.

}, doi = {10.1137/17M1159294}, url = {https://doi.org/10.1137/17M1159294}, author = {Giovanni Bellettini and Shokhrukh Kholmatov} } @conference {tezzele2018model, title = {Model Order Reduction by means of Active Subspaces and Dynamic Mode Decomposition for Parametric Hull Shape Design Hydrodynamics}, booktitle = {Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship \& Maritime Research}, year = {2018}, publisher = {IOS Press}, organization = {IOS Press}, address = {Trieste, Italy}, abstract = {We present the results of the application of a parameter space reduction methodology based on active subspaces (AS) to the hull hydrodynamic design problem. Several parametric deformations of an initial hull shape are considered to assess the influence of the shape parameters on the hull wave resistance. Such problem is relevant at the preliminary stages of the ship design, when several flow simulations are carried out by the engineers to establish a certain sensibility with respect to the parameters, which might result in a high number of time consuming hydrodynamic simulations. The main idea of this work is to employ the AS to identify possible lower dimensional structures in the parameter space. The complete pipeline involves the use of free form deformation to parametrize and deform the hull shape, the full order solver based on unsteady potential flow theory with fully nonlinear free surface treatment directly interfaced with CAD, the use of dynamic mode decomposition to reconstruct the final steady state given only few snapshots of the simulation, and the reduction of the parameter space by AS, and shared subspace. Response surface method is used to minimize the total drag.}, doi = {10.3233/978-1-61499-870-9-569}, url = {http://ebooks.iospress.nl/publication/49270}, author = {Marco Tezzele and Nicola Demo and Mahmoud Gadalla and Andrea Mola and Gianluigi Rozza} } @article {doi:10.1137/17M1150591, title = {Model Reduction for Parametrized Optimal Control Problems in Environmental Marine Sciences and Engineering}, journal = {SIAM Journal on Scientific Computing}, volume = {40}, number = {4}, year = {2018}, pages = {B1055-B1079}, doi = {10.1137/17M1150591}, url = {https://doi.org/10.1137/17M1150591}, author = {Maria Strazzullo and Francesco Ballarin and Mosetti, R. and Gianluigi Rozza} } @article {riccobelli2018morpho, title = {Morpho-elastic model of the tortuous tumour vessels}, journal = {Int. J. Non-Linear Mech.}, volume = {107}, year = {2018}, pages = {1{\textendash}9}, publisher = {Elsevier BV}, author = {Davide Riccobelli and Pasquale Ciarletta} } @article {BeCaRu, title = {Noncommutative Painlev{\'e} Equations and Systems of Calogero Type}, journal = {Comm. Math. Phys}, year = {2018}, author = {Marco Bertola and Mattia Cafasso and V. Rubtsov} } @article {2018, title = {Non-linear Gross-Pitaevskii dynamics of a 2D binary condensate: a numerical analysis}, number = {SISSA;35/2018/MATE}, year = {2018}, abstract = {We present a numerical study of the two-dimensional Gross-Pitaevskii systems in a wide range of relevant regimes of population ratios and intra-species and inter-species interactions. Our numerical method is based on a Fourier collocation scheme in space combined with a fourth order integrating factor scheme in time.}, url = {http://preprints.sissa.it/handle/1963/35323}, author = {Alessandro Michelangeli and Giuseppe Pitton} } @article {1803.05374, title = {On the notion of parallel transport on RCD spaces}, year = {2018}, author = {Nicola Gigli and Enrico Pasqualetto} } @article {Stabile2018, title = {A novel reduced order model for vortex induced vibrations of long flexible cylinders}, volume = {156}, year = {2018}, month = {may}, pages = {191{\textendash}207}, publisher = {Elsevier {BV}}, doi = {10.1016/j.oceaneng.2018.02.064}, url = {https://doi.org/10.1016/j.oceaneng.2018.02.064}, author = {Giovanni Stabile and Hermann G. Matthies and Claudio Borri} } @article {doi:10.1098/rspa.2017.0458, title = {Numerical study of the Kadomtsev-Petviashvili equation and dispersive shock waves}, journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}, volume = {474}, number = {2210}, year = {2018}, pages = {20170458}, abstract = {A detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev{\textendash}Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For the description of dispersive shock waves, Whitham modulation equations for KP are obtained. It is shown that the modulation equations near the soliton line are hyperbolic for the KPII equation while they are elliptic for the KPI equation leading to a focusing effect and the formation of lumps. Such a behaviour is similar to the appearance of breathers for the focusing nonlinear Schr{\"o}dinger equation in the semiclassical limit.

}, doi = {10.1098/rspa.2017.0458}, url = {https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2017.0458}, author = {Tamara Grava and Christian Klein and Giuseppe Pitton} } @article {20.500.11767_81737, title = {NURBS-SEM: A hybrid spectral element method on NURBS maps for the solution of elliptic PDEs on surfaces}, journal = {COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING}, volume = {338}, year = {2018}, pages = {440{\textendash}462}, doi = {10.1016/j.cma.2018.04.039}, url = {https://arxiv.org/abs/1804.08271}, author = {Giuseppe Pitton and Luca Heltai} } @article {2018, title = {Observables in the equivariant A-model}, number = {arXiv:1807.08659}, year = {2018}, url = {https://arxiv.org/abs/1807.08659}, author = {Bonechi, F. and Cattaneo, A.S. and Riccardo Iraso and Maxim Zabzine} } @article {bertola2018painleve, title = {Painlev{\'e} IV Critical Asymptotics for Orthogonal Polynomials in the Complex Plane}, journal = {Symmetry, Integrability and Geometry. Methods and Applications}, volume = {14}, year = {2018}, publisher = {National Academy of Sciences of Ukraine}, abstract = {We study the asymptotic behaviour of orthogonal polynomials in the complex plane that are associated to a certain normal matrix model. The model depends on a parameter and the asymptotic distribution of the eigenvalues undergoes a transition for a special value of the parameter, where it develops a corner-type singularity. In the double scaling limit near the transition we determine the asymptotic behaviour of the orthogonal polynomials in terms of a solution of the Painlev{\textasciiacute}e IV equation. We determine the Fredholm determinant associated to such solution and we compute it numerically on the real line, showing also that the corresponding Painlev{\textasciiacute}e transcendent is pole-free on a semiaxis.

}, doi = {10.3842/SIGMA.2018.091}, author = {Marco Bertola and Jos{\'e} Gustavo Elias Rebelo and Tamara Grava} } @article {2018, title = {Peristaltic Waves as Optimal Gaits in Metameric Bio-Inspired Robots}, journal = {Frontiers in Robotics and AI}, volume = {5}, year = {2018}, month = {09/2018}, abstract = {*Peristalsis*, i.e., a motion pattern arising from the propagation of muscle contraction and expansion waves along the body, is a common locomotion strategy for limbless animals. Mimicking peristalsis in bio-inspired robots has attracted considerable attention in the literature. It has recently been observed that maximal velocity in a metameric earthworm-like robot is achieved by actuating the segments using a {\textquotedblleft}phase coordination{\textquotedblright} principle. This paper shows that, in fact, peristalsis (which requires not only phase coordination, but also that all segments oscillate at same frequency and amplitude) emerges from optimization principles. More precisely, basing our analysis on the assumption of small deformations, we show that peristaltic waves provide the optimal actuation solution in the ideal case of a periodic infinite system, and that this is approximately true, modulo edge effects, for the real, finite length system. Therefore, this paper confirms the effectiveness of mimicking peristalsis in bio-inspired robots, at least in the small-deformation regime. Further research will be required to test the effectiveness of this strategy if large deformations are allowed.

We study the periodic boundary value problem associated with the second order nonlinear equation u{\textquoteright}{\textquoteright}+(λa+(t)-μa-(t))g(u)=0, where g(u) has superlinear growth at zero and sublinear growth at infinity. For λ,μ positive and large, we prove the existence of 3^m-1 positive T-periodic solutions when the weight function a(t) has m positive humps separated by m negative ones (in a T-periodicity interval). As a byproduct of our approach we also provide abundance of positive subharmonic solutions and symbolic dynamics. The proof is based on coincidence degree theory for locally compact operators on open unbounded sets and also applies to Neumann and Dirichlet boundary conditions. Finally, we deal with radially symmetric positive solutions for the Neumann and the Dirichlet problems associated with elliptic PDEs.

}, url = {http://urania.sissa.it/xmlui/handle/1963/35264}, author = {Alberto Boscaggin and Guglielmo Feltrin and Fabio Zanolin} } @article {doi:10.1142/S0219199717500213, title = {Positive subharmonic solutions to nonlinear ODEs with indefinite weight}, journal = {Communications in Contemporary Mathematics}, volume = {20}, number = {01}, year = {2018}, pages = {1750021}, abstract = {We prove that the superlinear indefinite equation u" + a(t)up = 0, where p \> 1 and a(t) is a T-periodic sign-changing function satisfying the (sharp) mean value condition ∫0Ta(t)dt \< 0, has positive subharmonic solutions of order k for any large integer k, thus providing a further contribution to a problem raised by Butler in its pioneering paper [Rapid oscillation, nonextendability, and the existence of periodic solutions to second order nonlinear ordinary differential equations, J. Differential Equations 22 (1976) 467{\textendash}477]. The proof, which applies to a larger class of indefinite equations, combines coincidence degree theory (yielding a positive harmonic solution) with the Poincar{\'e}{\textendash}Birkhoff fixed point theorem (giving subharmonic solutions oscillating around it).

}, doi = {10.1142/S0219199717500213}, url = {https://doi.org/10.1142/S0219199717500213}, author = {Alberto Boscaggin and Guglielmo Feltrin} } @article {20.500.11767_81735, title = {Predicting and Optimizing Microswimmer Performance from the Hydrodynamics of Its Components: The Relevance of Interactions}, journal = {SOFT ROBOTICS}, volume = {5}, year = {2018}, pages = {410{\textendash}424}, doi = {10.1089/soro.2017.0099}, url = {https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6094362/}, author = {Nicola Giuliani and Luca Heltai and Antonio DeSimone} } @article {demo2018pydmd, title = {PyDMD: Python Dynamic Mode Decomposition}, journal = {The Journal of Open Source Software}, volume = {3}, number = {22}, year = {2018}, pages = {530}, doi = {10.21105/joss.00530}, url = {https://joss.theoj.org/papers/734e4326edd5062c6e8ee98d03df9e1d}, author = {Nicola Demo and Marco Tezzele and Gianluigi Rozza} } @article {Lazzaroni2018, title = {On the Quasistatic Limit of Dynamic Evolutions for a Peeling Test in Dimension One}, journal = {Journal of Nonlinear Science}, volume = {28}, number = {1}, year = {2018}, month = {Feb}, pages = {269{\textendash}304}, abstract = {The aim of this paper is to study the quasistatic limit of a one-dimensional model of dynamic debonding. We start from a dynamic problem that strongly couples the wave equation in a time-dependent domain with Griffith{\textquoteright}s criterion for the evolution of the domain. Passing to the limit as inertia tends to zero, we find that the limit evolution satisfies a stability condition; however, the activation rule in Griffith{\textquoteright}s (quasistatic) criterion does not hold in general, thus the limit evolution is not rate-independent.

}, issn = {1432-1467}, doi = {10.1007/s00332-017-9407-0}, url = {https://doi.org/10.1007/s00332-017-9407-0}, author = {Giuliano Lazzaroni and Lorenzo Nardini} } @article {2018, title = {On real resonances for the three-dimensional, multi-centre point interaction}, number = {SISSA;40/2018/MATE}, year = {2018}, author = {Alessandro Michelangeli and Raffaele Scandone} } @article {Gigli2018, title = {Recognizing the flat torus among RCD*(0,N) spaces via the study of the first cohomology group}, journal = {Calculus of Variations and Partial Differential Equations}, volume = {57}, number = {4}, year = {2018}, month = {Jun}, pages = {104}, abstract = {We prove that if the dimension of the first cohomology group of a $\mathsf{RCD}^\star (0,N)$ space is $N$, then the space is a flat torus. This generalizes a classical result due to Bochner to the non-smooth setting and also provides a first example where the study of the cohomology groups in such synthetic framework leads to geometric consequences.

}, issn = {1432-0835}, doi = {10.1007/s00526-018-1377-z}, url = {https://doi.org/10.1007/s00526-018-1377-z}, author = {Nicola Gigli and Chiara Rigoni} } @booklet {1807.07790, title = {A Reduced Basis approach for PDEs on parametrized geometries based on the Shifted Boundary Finite Element Method and application to fluid dynamics}, year = {2018}, author = {Efthymios N. Karatzas and Giovanni Stabile and Leo Nouveau and Guglielmo Scovazzi and Gianluigi Rozza} } @booklet {1807.07753, title = {A Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries}, year = {2018}, author = {Efthymios N. Karatzas and Giovanni Stabile and N. Atallah and Guglielmo Scovazzi and Gianluigi Rozza} } @article {1806.06604, title = {Reducibility for a class of weakly dispersive linear operators arising from the Degasperis Procesi equation}, year = {2018}, author = {Roberto Feola and Filippo Giuliani and Michela Procesi} } @article {doi:10.1142/S0219891618500200, title = {Regularity estimates for scalar conservation laws in one space dimension}, journal = {Journal of Hyperbolic Differential Equations}, volume = {15}, number = {04}, year = {2018}, pages = {623-691}, abstract = {We deal with the regularizing effect that, in scalar conservation laws in one space dimension, the nonlinearity of the flux function f has on the entropy solution. More precisely, if the set w : f"(w)/=0 is dense, the regularity of the solution can be expressed in terms of BVΦ spaces, where Φ depends on the nonlinearity of f. If moreover the set w : f"(w) = 0 is finite, under the additional polynomial degeneracy condition at the inflection points, we prove that f'o u(t) ∈BV loc(ℝ) for every t \> 0 and that this can be improved to SBVloc(ℝ) regularity except an at most countable set of singular times. Finally, we present some examples that show the sharpness of these results and counterexamples to related questions, namely regularity in the kinetic formulation and a property of the fractional BV spaces.

}, doi = {10.1142/S0219891618500200}, url = {https://doi.org/10.1142/S0219891618500200}, author = {Elio Marconi} } @article {gigli2018second, title = {Second order differentiation formula on RCD(K, N) spaces}, journal = {Rendiconti Lincei-Matematica e Applicazioni}, volume = {29}, number = {2}, year = {2018}, pages = {377{\textendash}386}, author = {Nicola Gigli and Luca Tamanini} } @article {1802.02463, title = {Second order differentiation formula on RCD*(K,N) spaces}, year = {2018}, author = {Nicola Gigli and Luca Tamanini} } @conference {demo2018shape, title = {Shape Optimization by means of Proper Orthogonal Decomposition and Dynamic Mode Decomposition}, booktitle = {Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship \& Maritime Research}, year = {2018}, publisher = {IOS Press}, organization = {IOS Press}, chapter = {212}, address = {Trieste, Italy}, abstract = {Shape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling, applied to a naval hull design problem. The advantage introduced by this method is that the solution for a specific parameter can be expressed as the combination of few numerical solutions computed at properly chosen parametric points. The reduced model is built using the proper orthogonal decomposition with interpolation (PODI) method. We use the free form deformation (FFD) for an automated perturbation of the shape, and the finite volume method to simulate the multiphase incompressible flow around the deformed hulls. Further computational reduction is done by the dynamic mode decomposition (DMD) technique: from few high dimensional snapshots, the system evolution is reconstructed and the final state of the simulation is faithfully approximated. Finally the global optimization algorithm iterates over the reduced space: the approximated drag and lift coefficients are projected to the hull surface, hence the resistance is evaluated for the new hulls until the convergence to the optimal shape is achieved. We will present the results obtained applying the described procedure to a typical Fincantieri cruise ship.}, doi = {10.3233/978-1-61499-870-9-212}, url = {http://ebooks.iospress.nl/publication/49229}, author = {Nicola Demo and Marco Tezzele and Gianluca Gustin and Gianpiero Lavini and Gianluigi Rozza} } @article {riccobelli2017shape, title = {Shape transitions in a soft incompressible sphere with residual stresses}, journal = {Math. Mech. Solids}, volume = {23}, number = {12}, year = {2018}, pages = {1507{\textendash}1524}, publisher = {SAGE Publications Sage UK: London, England}, author = {Davide Riccobelli and Pasquale Ciarletta} } @article {doi:10.1080/14029251.2018.1503423, title = {Singular Hartree equation in fractional perturbed Sobolev spaces}, journal = {Journal of Nonlinear Mathematical Physics}, volume = {25}, number = {4}, year = {2018}, pages = {558-588}, publisher = {Taylor \& Francis}, abstract = {We establish the local and global theory for the Cauchy problem of the singular Hartree equation in three dimensions, that is, the modification of the non-linear Schr{\"o}dinger equation with Hartree non-linearity, where the linear part is now given by the Hamiltonian of point interaction. The latter is a singular, self-adjoint perturbation of the free Laplacian, modelling a contact interaction at a fixed point. The resulting non-linear equation is the typical effective equation for the dynamics of condensed Bose gases with fixed point-like impurities. We control the local solution theory in the perturbed Sobolev spaces of fractional order between the mass space and the operator domain. We then control the global solution theory both in the mass and in the energy space.

}, doi = {10.1080/14029251.2018.1503423}, url = {https://doi.org/10.1080/14029251.2018.1503423}, author = {Alessandro Michelangeli and Alessandro Olgiati and Raffaele Scandone} } @article {1809.03586, title = {On some rigorous aspects of fragmented condensation}, year = {2018}, url = {https://arxiv.org/abs/1809.03586}, author = {Daniele Dimonte and Marco Falconi and Alessandro Olgiati} } @article {doi:10.1063/1.5026311, title = {Spectral triples on the Jiang-Su algebra}, journal = {Journal of Mathematical Physics}, volume = {59}, number = {5}, year = {2018}, pages = {053507}, doi = {10.1063/1.5026311}, url = {https://doi.org/10.1063/1.5026311}, author = {Jacopo Bassi and Ludwik Dabrowski} } @article {2018, title = {Stochastic homogenisation of free-discontinuity problems}, number = {SISSA;05/2018/MATE}, year = {2018}, abstract = {In this paper we study the stochastic homogenisation of free-discontinuity functionals. Assuming stationarity for the random volume and surface integrands, we prove the existence of a homogenised random free-discontinuity functional, which is deterministic in the ergodic case. Moreover, by establishing a connection between the deterministic convergence of the functionals at any fixed realisation and the pointwise Subadditive Ergodic Theorem by Akcoglou and Krengel, we characterise the limit volume and surface integrands in terms of asymptotic cell formulas.}, url = {http://preprints.sissa.it/handle/1963/35309}, author = {Filippo Cagnetti and Gianni Dal Maso and Lucia Scardia and Caterina Ida Zeppieri} } @article {doi:10.1098/rsta.2017.0424, title = {Symplectic invariants for parabolic orbits and cusp singularities of integrable systems}, journal = {Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences}, volume = {376}, number = {2131}, year = {2018}, pages = {20170424}, abstract = {We discuss normal forms and symplectic invariants of parabolic orbits and cuspidal tori in integrable Hamiltonian systems with two degrees of freedom. Such singularities appear in many integrable systems in geometry and mathematical physics and can be considered as the simplest example of degenerate singularities. We also suggest some new techniques which apparently can be used for studying symplectic invariants of degenerate singularities of more general type. This article is part of the theme issue {\textquoteleft}Finite dimensional integrable systems: new trends and methods{\textquoteright}.

}, doi = {10.1098/rsta.2017.0424}, url = {https://royalsocietypublishing.org/doi/abs/10.1098/rsta.2017.0424}, author = {Alexey Bolsinov and Lorenzo Guglielmi and Elena Kudryavtseva} } @article {2018, title = {Transmission conditions obtained by homogenisation}, number = {SISSA;11/2018/MATE}, year = {2018}, abstract = {We study the asymptotic behaviour of solutions to variational problems in perforated domains with Neumann boundary conditions. We consider perforations that in the limit concentrate on a smooth manifold. We characterise the limits of the solutions and show that they solve a variational problem with a transmission condition across the manifold. This is expressed through a measure on the manifold, vanishing on sets of capacity zero. Then, we prove that every such measure can be obtained by homogenising suitable perforations. Eventually, we provide an asymptotic formula for this measure by using some auxiliary minimum problems.}, url = {http://preprints.sissa.it/handle/1963/35310}, author = {Gianni Dal Maso and Giovanni Franzina and Davide Zucco} } @article {2018, title = {Truncation and convergence issues for bounded linear inverse problems in Hilbert space}, number = {SISSA;50/2018/MATE}, year = {2018}, institution = {SISSA}, abstract = {We present a general discussion of the main features and issues that (bounded) inverse linear problems in Hilbert space exhibit when the dimension of the space is infinite. This includes the set-up of a consistent notation for inverse problems that are genuinely infinite-dimensional, the analysis of the finite-dimensional truncations, a discussion of the mechanisms why the error or the residual generically fail to vanish in norm, and the identification of practically plausible sufficient conditions for such indicators to be small in some weaker sense. The presentation is based on theoretical results together with a series of model examples and numerical tests.}, url = {http://preprints.sissa.it/handle/1963/35326}, author = {Noe Caruso and Alessandro Michelangeli and Paolo Novati} } @conference {10.1007/978-3-319-91545-6_15, title = {On Uniqueness of Weak Solutions to Transport Equation with Non-smooth Velocity Field}, booktitle = {Theory, Numerics and Applications of Hyperbolic Problems I}, year = {2018}, pages = {191{\textendash}203}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, address = {Cham}, isbn = {978-3-319-91545-6}, doi = {10.1007/978-3-319-91545-6_15}, url = {https://link.springer.com/chapter/10.1007/978-3-319-91545-6_15}, author = {Paolo Bonicatto}, editor = {Klingenberg, Christian and Westdickenberg, Michael} } @article {2018, title = {Weak formulation of elastodynamics in domains with growing cracks}, number = {SISSA;51/2018/MATE}, year = {2018}, institution = {SISSA}, abstract = {In this paper we formulate and study the system of elastodynamics on domains with arbitrary growing cracks. This includes homogeneous Neumann conditions on the crack sets and mixed general Dirichlet-Neumann conditions on the boundary. The only assumptions on the crack sets are to be (n - 1)-rectifiable with finite surface measure, and increasing in the sense of set inclusions. In particular they might be dense, hence the weak formulation must fall outside the usual context of Sobolev spaces and Korn{\textquoteright}s inequality. We prove existence of a solution both for the damped and undamped systems, while in the damped case we are also able to prove uniqueness and an energy balance.}, url = {http://preprints.sissa.it/handle/1963/35328}, author = {Emanuele Tasso} } @article {giulianiEtAl2018, title = {π-BEM : A flexible parallel implementation for adaptive , geometry aware , and high order boundary element methods}, journal = {Advances in Engineering Software}, volume = {121}, year = {2018}, pages = {39{\textendash}58}, author = {Nicola Giuliani and Andrea Mola and Luca Heltai} } @article {2017, title = {On the 1D wave equation in time-dependent domains and the problem of debond initiation}, number = {SISSA;56/2017/MATE}, year = {2017}, institution = {SISSA}, abstract = {Motivated by a debonding model for a thin film peeled from a substrate, we analyse the one-dimensional wave equation, in a time-dependent domain which is degenerate at the initial time. In the first part of the paper we prove existence for the wave equation when the evolution of the domain is given; in the second part of the paper, the evolution of the domain is unknown and is governed by an energy criterion coupled with the wave equation. Our existence result for such coupled problem is a contribution to the study of crack initiation in dynamic fracture.

}, url = {http://preprints.sissa.it/handle/1963/35302}, author = {Giuliano Lazzaroni and Lorenzo Nardini} } @article {2017, title = {Advances in Reduced order modelling for CFD: vortex shedding around a circular cylinder using a POD-Galerkin method}, journal = {Communication in Applied Industrial Mathematics}, year = {2017}, type = {reviewed}, abstract = {Vortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. In this work a Reduced Order Model (ROM) of the incompressible flow around a circular cylinder, built performing a Galerkin projection of the governing equations onto a lower dimensional space is presented. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pressure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) for this purpose the projection of the Governing equations (momentum equation and Poisson equation for pressure) is performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework are presented. The accuracy of the reduced order model is assessed against full order results.

}, keywords = {finite volume, CFD, Reduced order methods}, url = {https://arxiv.org/abs/1701.03424}, author = {Giovanni Stabile and Saddam Hijazi and Stefano Lorenzi and Andrea Mola and Gianluigi Rozza} } @article {2017, title = {Almost global existence of solutions for capillarity-gravity water waves equations with periodic spatial boundary conditions}, number = {arXiv;1702.04674}, year = {2017}, abstract = {The goal of this monograph is to prove that any solution of the Cauchy problem for the capillarity-gravity water waves equations, in one space dimension, with periodic, even in space, initial data of small size ϵ, is almost globally defined in time on Sobolev spaces, i.e. it exists on a time interval of length of magnitude ϵ-N for any N, as soon as the initial data are smooth enough, and the gravity-capillarity parameters are taken outside an exceptional subset of zero measure. In contrast to the many results known for these equations on the real line, with decaying Cauchy data, one cannot make use of dispersive properties of the linear flow. Instead, our method is based on a normal forms procedure, in order to eliminate those contributions to the Sobolev energy that are of lower degree of homogeneity in the solution. Since the water waves equations are a quasi-linear system, usual normal forms approaches would face the well known problem of losses of derivatives in the unbounded transformations. In this monograph, to overcome such a difficulty, after a paralinearization of the capillarity-gravity water waves equations, necessary to obtain energy estimates, and thus local existence of the solutions, we first perform several paradifferential reductions of the equations to obtain a diagonal system with constant coefficients symbols, up to smoothing remainders. Then we may start with a normal form procedure where the small divisors are compensated by the previous paradifferential regularization.The reversible structure of the water waves equations, and the fact that we look for solutions even in x, guarantees a key cancellation which prevents the growth of the Sobolev norms of the solutions.}, url = {http://preprints.sissa.it/handle/1963/35285}, author = {Massimiliano Berti and Jean-Marc Delort} } @article {doi:10.1142/S2010326317400044, title = {Analytic geometry of semisimple coalescent Frobenius structures}, journal = {Random Matrices: Theory and Applications}, volume = {06}, number = {04}, year = {2017}, pages = {1740004}, abstract = {We present some results of a joint paper with Dubrovin (see references), as exposed at the Workshop {\textquotedblleft}Asymptotic and Computational Aspects of Complex Differential Equations{\textquotedblright} at the CRM in Pisa, in February 2017. The analytical description of semisimple Frobenius manifolds is extended at semisimple coalescence points, namely points with some coalescing canonical coordinates although the corresponding Frobenius algebra is semisimple. After summarizing and revisiting the theory of the monodromy local invariants of semisimple Frobenius manifolds, as introduced by Dubrovin, it is shown how the definition of monodromy data can be extended also at semisimple coalescence points. Furthermore, a local Isomonodromy theorem at semisimple coalescence points is presented. Some examples of computation are taken from the quantum cohomologies of complex Grassmannians.

}, doi = {10.1142/S2010326317400044}, url = {https://doi.org/10.1142/S2010326317400044}, author = {Giordano Cotti and Davide Guzzetti} } @article {feltrin2017, title = {An application of coincidence degree theory to cyclic feedback type systems associated with nonlinear differential operators}, journal = {Topol. Methods Nonlinear Anal.}, volume = {50}, number = {2}, year = {2017}, pages = {683{\textendash}726}, publisher = {Nicolaus Copernicus University, Juliusz P. Schauder Centre for Nonlinear Studies}, doi = {10.12775/TMNA.2017.038}, url = {https://doi.org/10.12775/TMNA.2017.038}, author = {Guglielmo Feltrin and Fabio Zanolin} } @article {2017, title = {On the Application of Reduced Basis Methods to Bifurcation Problems in Incompressible Fluid Dynamics}, journal = {Journal of Scientific Computing}, year = {2017}, abstract = {In this paper we apply a reduced basis framework for the computation of flow bifurcation (and stability) problems in fluid dynamics. The proposed method aims at reducing the complexity and the computational time required for the construction of bifurcation and stability diagrams. The method is quite general since it can in principle be specialized to a wide class of nonlinear problems, but in this work we focus on an application in incompressible fluid dynamics at low Reynolds numbers. The validation of the reduced order model with the full order computation for a benchmark cavity flow problem is promising.

}, doi = {10.1007/s10915-017-0419-6}, author = {Giuseppe Pitton and Gianluigi Rozza} } @article {FONDA20171064, title = {An avoiding cones condition for the Poincar{\'e}{\textendash}Birkhoff Theorem}, journal = {Journal of Differential Equations}, volume = {262}, number = {2}, year = {2017}, pages = {1064 - 1084}, abstract = {We provide a geometric assumption which unifies and generalizes the conditions proposed in [11], [12], so to obtain a higher dimensional version of the Poincar{\'e}{\textendash}Birkhoff fixed point Theorem for Poincar{\'e} maps of Hamiltonian systems.

}, keywords = {Avoiding cones condition, Hamiltonian systems, Periodic solutions, Poincar{\'e}{\textendash}Birkhoff theorem}, issn = {0022-0396}, doi = {https://doi.org/10.1016/j.jde.2016.10.002}, url = {http://www.sciencedirect.com/science/article/pii/S0022039616303278}, author = {Alessandro Fonda and Paolo Gidoni} } @inbook {2017, title = {Certified Reduced Basis Method for Affinely Parametric Isogeometric Analysis NURBS Approximation}, booktitle = {Spectral and High Order Methods for Partial Differential Equations }, volume = { 119}, number = {LNCSE}, year = {2017}, publisher = {Springer}, organization = {Springer}, edition = {Bittencourt, Dumont, Hesthaven. (Eds).}, address = {Heildeberg}, abstract = {In this work we apply reduced basis methods for parametric PDEs to an isogeometric formulation based on

NURBS. The motivation for this work is an integrated and complete work pipeline from CAD to parametrization

of domain geometry, then from full order to certified reduced basis solution. IsoGeometric Analysis

\ (IGA) is a growing research theme in scientic computing and computational mechanics, as well as reduced

basis methods for parametric PDEs. Their combination enhances the solution of some class of problems,

especially the ones characterized by parametrized geometries we introduced in this work. For a general

overview on Reduced Basis (RB) methods we recall [7, 15] and on IGA [3]. This work wants to demonstrate

that it is also possible for some class of problems to deal with ane geometrical parametrization combined

with a NURBS IGA formulation. This is what this work brings as original ingredients with respect to other

works dealing with reduced order methods and IGA (set in a non-affine formulation, and using a POD [2]\

sampling without certication: see for example for potential\ flows [12] and for Stokes\ flows [17]). In this work

we show a certication of accuracy and a complete integration between IGA formulation and parametric

certified greedy RB formulation. Section 2 recalls the abstract setting for parametrized PDEs, Section 3

recalls IGA setting, Section 4 deals with RB formulation, and Section 5 illustrates two numerical examples in heat transfer with different parametrization.

}, isbn = {978-3-319-65869-8}, author = {Denis Devaud and Gianluigi Rozza} } @article {2017, title = {On a certified smagorinsky reduced basis turbulence model}, journal = {SIAM Journal on Numerical Analysis}, volume = {55}, year = {2017}, pages = {3047-3067}, doi = {10.1137/17M1118233}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85039928218\&doi=10.1137\%2f17M1118233\&partnerID=40\&md5=221d9cd2bcc74121fcef93efd9d3d76c}, author = {Rebollo, T.C. and E.D. {\'A}vila and Marmol, M.G. and Francesco Ballarin and Gianluigi Rozza} } @article {RIZZI20175306, title = {Clifford Tori and the singularly perturbed Cahn{\textendash}Hilliard equation}, journal = {Journal of Differential Equations}, volume = {262}, number = {10}, year = {2017}, pages = {5306 - 5362}, abstract = {In this paper we construct entire solutions uε to the Cahn{\textendash}Hilliard equation -ε2Δ(-ε2Δu+W'(u))+W"(u)(-ε2Δu+W'(u))=ε4λε(1-uε), under the volume constraint ∫R3(1-uε)2dx=82π2cε, with cε{\textrightarrow}1 as ε{\textrightarrow}0, whose nodal set approaches the Clifford Torus, that is the Torus with radii of ratio 1/2 embedded in R3, as ε{\textrightarrow}0. It is crucial that the Clifford Torus is a Willmore hypersurface and it is non-degenerate, up to conformal transformations. The proof is based on the Lyapunov{\textendash}Schmidt reduction and on careful geometric expansions of the Laplacian.

}, keywords = {Cahn{\textendash}Hilliard equation, Clifford Torus, Lyapunov{\textendash}Schmidt reduction, Willmore surface}, issn = {0022-0396}, doi = {https://doi.org/10.1016/j.jde.2017.01.026}, url = {http://www.sciencedirect.com/science/article/pii/S0022039617300530}, author = {Matteo Rizzi} } @article {2017, title = {Complex Friedrichs systems and applications}, number = {SISSA;03/2017/MATE}, year = {2017}, abstract = {We provide a suitable extension of the theory of abstract Friedrichs systems from real Hilbert spaces to the complex Hilbert space setting, which allows for applications to partial differential equations with complex coeffcients. We also provide examples where the involved Hilbert space is not the space of square integrable functions, as it was the case in previous works, but rather its closed subspace or the space Hs(Rd;Cr), for real s. This setting appears to be suitable for particular systems of partial differential equations, such as the Dirac system, the Dirac-Klein-Gordon system, the Dirac-Maxwell system, and the time-harmonic Maxwell system, which are all addressed in the paper. Moreover, for the time-harmonic Maxwell system we also applied a suitable version of the two-field theory with partial coercivity assumption which is developed in the paper.}, url = {http://urania.sissa.it/xmlui/handle/1963/35270}, author = {Nenad Antoni{\'c} and Kre{\v s}imir Burazin and Ivana Crnjac and Marko Erceg} } @article {2017, title = {Computational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: Applications to Coanda effect in cardiology}, journal = {Journal of Computational Physics}, volume = {344}, year = {2017}, month = {09/2017}, pages = {557}, chapter = {534}, abstract = {We focus on reducing the computational costs associated with the hydrodynamic stability of solutions of the incompressible Navier{\textendash}Stokes equations for a Newtonian and viscous fluid in contraction{\textendash}expansion channels. In particular, we are interested in studying steady bifurcations, occurring when non-unique stable solutions appear as physical and/or geometric control parameters are varied. The formulation of the stability problem requires solving an eigenvalue problem for a partial differential operator. An alternative to this approach is the direct simulation of the flow to characterize the asymptotic behavior of the solution. Both approaches can be extremely expensive in terms of computational time. We propose to apply Reduced Order Modeling (ROM) techniques to reduce the demanding computational costs associated with the detection of a type of steady bifurcations in fluid dynamics. The application that motivated the present study is the onset of asymmetries (i.e., symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the regurgitant mitral valve orifice shape.

We present a novel quasi-Newton continuation procedure that efficiently solves the system of nonlinear equations arising from the discretization of a phase field model for wetting phenomena. We perform a comparative numerical analysis that shows the improved speed of convergence gained with respect to other numerical schemes. Moreover, we discuss the conditions that, on a theoretical level, guarantee the convergence of this method. At each iterative step, a suitable continuation procedure develops and passes to the nonlinear solver an accurate initial guess. Discretization performs through cell-centered finite differences. The resulting system of equations is solved on a composite grid that uses dynamic mesh refinement and multi-grid techniques. The final code achieves three-dimensional, realistic computer experiments comparable to those produced in laboratory settings. This code offers not only new insights into the phenomenology of super-hydrophobicity, but also serves as a reliable predictive tool for the study of hydrophobic surfaces.

}, keywords = {Multigrid, Phase field, Quasi-Newton, Super-hydrophobicity}, issn = {0021-9991}, doi = {https://doi.org/10.1016/j.jcp.2017.04.068}, url = {http://www.sciencedirect.com/science/article/pii/S002199911730356X}, author = {Livio Fedeli} } @article {2017, title = {On contact interactions realised as Friedrichs systems}, number = {SISSA;48/2017/MATE}, year = {2017}, abstract = {We realise the Hamiltonians of contact interactions in quantum mechanics within the framework of abstract Friedrichs systems. In particular, we show that the construction of the self-adjoint (or even only closed) operators of contact interaction supported at a fixed point can be associated with the construction of the bijective realisations of a suitable pair of abstract Friedrich operators. In this respect, the Hamiltonians of contact interaction provide novel examples of abstract Friedrich systems.}, url = {http://preprints.sissa.it/handle/1963/35298}, author = {Marko Erceg and Alessandro Michelangeli} } @article {BARILARI2017118, title = {Curvature terms in small time heat kernel expansion for a model class of hypoelliptic H{\"o}rmander operators}, journal = {Nonlinear Analysis}, volume = {164}, year = {2017}, pages = {118 - 134}, abstract = {We consider the heat equation associated with a class of second order hypoelliptic H{\"o}rmander operators with constant second order term and linear drift. We completely describe the small time heat kernel expansions on the diagonal giving a geometric characterization of the coefficients in terms of the divergence of the drift field and the curvature-like invariants of the optimal control problem associated with the diffusion operator.

}, keywords = {Curvature, Hypoelliptic heat equation, Small time asymptotics}, issn = {0362-546X}, doi = {https://doi.org/10.1016/j.na.2017.09.002}, url = {http://www.sciencedirect.com/science/article/pii/S0362546X17302298}, author = {Davide Barilari and Elisa Paoli} } @article {Dassi2017, title = {Curvature-adapted remeshing of {CAD} surfaces}, journal = {Engineering with Computers}, volume = {34}, number = {3}, year = {2017}, month = {dec}, pages = {565{\textendash}576}, publisher = {Springer Nature}, doi = {10.1007/s00366-017-0558-2}, url = {https://doi.org/10.1007/s00366-017-0558-2}, author = {Franco Dassi and Andrea Mola and Hang Si} } @article {20.500.11767_47950, title = {The deal.II Library, Version 8.5}, journal = {JOURNAL OF NUMERICAL MATHEMATICS}, volume = {25}, year = {2017}, pages = {137{\textendash}145}, doi = {10.1515/jnma-2017-0058}, url = {https://www.dealii.org/deal85-preprint.pdf}, author = {Arndt, Daniel and W. Bangerth and Denis Davydov and Timo Heister and Luca Heltai and Martin Kronbichler and Matthias Maier and Pelteret, Jean-Paul and B. Turcksin and David Wells} } @article {2017, title = {Derivation of a rod theory from lattice systems with interactions beyond nearest neighbours}, number = {SISSA;58/2016/MATE}, year = {2017}, abstract = {We study continuum limits of discrete models for (possibly heterogeneous) nanowires. The lattice energy includes at least nearest and next-to-nearest neighbour interactions: the latter have the role of penalising changes of orientation. In the heterogeneous case, we obtain an estimate on the minimal energy spent to match different equilibria. This gives insight into the nucleation of dislocations in epitaxially grown heterostructured nanowires.}, url = {http://urania.sissa.it/xmlui/handle/1963/35269}, author = {Roberto Alicandro and Giuliano Lazzaroni and Mariapia Palombaro} } @article {2017, title = {Discrete spectra for critical Dirac-Coulomb Hamiltonians}, number = {SISSA;44/2017/MATE}, year = {2017}, abstract = {The one-particle Dirac Hamiltonian with Coulomb interaction is known to be realised, in a regime of large (critical) couplings, by an infinite multiplicity of distinct self-adjoint operators, including a distinguished physically most natural one. For the latter, Sommerfeld{\textquoteright}s celebrated fine structure formula provides the well-known expression for the eigenvalues in the gap of the continuum spectrum. Exploiting our recent general classification of all other self-adjoint realisations, we generalise Sommerfeld{\textquoteright}s formula so as to determine the discrete spectrum of all other self-adjoint versions of the Dirac-Coulomb Hamiltonian. Such discrete spectra display naturally a fibred structure, whose bundle covers the whole gap of the continuum spectrum.}, url = {http://preprints.sissa.it/handle/1963/35300}, author = {Matteo Gallone and Alessandro Michelangeli} } @inbook {Iandoli2017, title = {Dispersive Estimates for Schr{\"o}dinger Operators with Point Interactions in ℝ3}, booktitle = {Advances in Quantum Mechanics: Contemporary Trends and Open Problems}, year = {2017}, pages = {187{\textendash}199}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, address = {Cham}, abstract = {The study of dispersive properties of Schr{\"o}dinger operators with point interactions is a fundamental tool for understanding the behavior of many body quantum systems interacting with very short range potential, whose dynamics can be approximated by non linear Schr{\"o}dinger equations with singular interactions. In this work we proved that, in the case of one point interaction in $\mathbb{R}^3$, the perturbed Laplacian satisfies the same $L^p$-$L^q$ estimates of the free Laplacian in the smaller regime $q \in [2,3)$. These estimates are implied by a recent result concerning the Lpboundedness of the wave operators for the perturbed Laplacian. Our approach, however, is more direct and relatively simple, and could potentially be useful to prove optimal weighted estimates also in the regime $q \geq 3$.

}, isbn = {978-3-319-58904-6}, doi = {10.1007/978-3-319-58904-6_11}, url = {https://doi.org/10.1007/978-3-319-58904-6_11}, author = {Felice Iandoli and Raffaele Scandone}, editor = {Alessandro Michelangeli and Gianfausto Dell{\textquoteright}Antonio} } @article {2017, title = {On the effect of interactions beyond nearest neighbours on non-convex lattice systems}, number = {SISSA;57/2016/MATE}, year = {2017}, abstract = {We analyse the rigidity of non-convex discrete energies where at least nearest and next-to-nearest neighbour interactions are taken into account. Our purpose is to show that interactions beyond nearest neighbours have the role of penalising changes of orientation and, to some extent, they may replace the positive-determinant constraint that is usually required when only nearest neighbours are accounted for. In a discrete to continuum setting, we prove a compactness result for a family of surface-scaled energies and we give bounds on its possible Gamma-limit in terms of interfacial energies that penalise changes of orientation.}, url = {http://urania.sissa.it/xmlui/handle/1963/35268}, author = {Roberto Alicandro and Giuliano Lazzaroni and Mariapia Palombaro} } @inbook {Olgiati2017, title = {Effective Non-linear Dynamics of Binary Condensates and Open Problems}, booktitle = {Advances in Quantum Mechanics: Contemporary Trends and Open Problems}, year = {2017}, pages = {239{\textendash}256}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, address = {Cham}, abstract = {We report on a recent result concerning the effective dynamics for a mixture of Bose-Einstein condensates, a class of systems much studied in physics and receiving a large amount of attention in the recent literature in mathematical physics; for such models, the effective dynamics is described by a coupled system of non-linear Sch{\"o}dinger equations. After reviewing and commenting our proof in the mean-field regime from a previous paper, we collect the main details needed to obtain the rigorous derivation of the effective dynamics in the Gross-Pitaevskii scaling limit.

}, isbn = {978-3-319-58904-6}, doi = {10.1007/978-3-319-58904-6_14}, url = {https://doi.org/10.1007/978-3-319-58904-6_14}, author = {Alessandro Olgiati}, editor = {Alessandro Michelangeli and Gianfausto Dell{\textquoteright}Antonio} } @article {1708.01518, title = {Elliptic diffeomorphisms of symplectic 4-manifolds}, year = {2017}, url = {https://arxiv.org/pdf/1708.01518.pdf}, author = {Vsevolod Shevchishin and Gleb Smirnov} } @article {almi2017energy, title = {Energy release rate and quasi-static evolution via vanishing viscosity in a fracture model depending on the crack opening}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, volume = {23}, number = {3}, year = {2017}, month = {05/2017}, pages = {791{\textendash}826}, publisher = {EDP Sciences}, abstract = {In the setting of planar linearized elasticity, we study a fracture model depending on the crack opening. Assuming that the crack path is known a priori and sufficiently smooth, we prove that the energy release rate is well defined. Then, we consider the problem of quasi-static evolution for our model. Thanks to a vanishing viscosity approach, we show the existence of such an evolution satisfying a weak Griffith{\textquoteright}s criterion.

}, doi = {10.1051/cocv/2016014}, url = {https://www.esaim-cocv.org/component/article?access=doi\&doi=10.1051/cocv/2016014}, author = {Stefano Almi} } @article {2017, title = {Friedrichs systems in a Hilbert space framework: solvability and multiplicity}, number = {SISSA;16/2017/MATE}, year = {2017}, abstract = {The Friedrichs (1958) theory of positive symmetric systems of first order partial differential equations encompasses many standard equations of mathematical physics, irrespective of their type. This theory was recast in an abstract Hilbert space setting by Ern, Guermond and Caplain (2007), and by Antoni{\'c} and Burazin (2010). In this work we make a further step, presenting a purely operator-theoretic description of abstract Friedrichs systems, and proving that any pair of abstract Friedrichs operators admits bijective extensions with a signed boundary map. Moreover, we provide suffcient and necessary conditions for existence of infinitely many such pairs of spaces, and by the universal operator extension theory (Grubb, 1968) we get a complete identification of all such pairs, which we illustrate on two concrete one-dimensional examples.}, url = {http://preprints.sissa.it/handle/1963/35280}, author = {Nenad Antoni{\'c} and Marko Erceg and Alessandro Michelangeli} } @article {2017, title = {Gamma-Convergence of Free-discontinuity problems}, number = {SISSA;18/2017/MATE}, year = {2017}, institution = {SISSA}, abstract = {We study the Gamma-convergence of sequences of free-discontinuity functionals depending on vector-valued functions u which can be discontinuous across hypersurfaces whose shape and location are not known a priori. The main novelty of our result is that we work under very general assumptions on the integrands which, in particular, are not required to be periodic in the space variable. Further, we consider the case of surface integrands which are not bounded from below by the amplitude of the jump of u. We obtain three main results: compactness with respect to Gamma-convergence, representation of the Gamma-limit in an integral form and identification of its integrands, and homogenisation formulas without periodicity assumptions. In particular, the classical case of periodic homogenisation follows as a by-product of our analysis. Moreover, our result covers also the case of stochastic homogenisation, as we will show in a forthcoming paper.}, url = {http://preprints.sissa.it/handle/1963/35276}, author = {Filippo Cagnetti and Gianni Dal Maso and Lucia Scardia and Caterina Ida Zeppieri} } @article {BERSHTEIN201740, title = {Gauge theories on compact toric surfaces, conformal field theories and equivariant Donaldson invariants}, journal = {Journal of Geometry and Physics}, volume = {118}, year = {2017}, note = {Interactions between Geometry and Physics. A Special Issue in Honor of Ugo Bruzzo{\textquoteright}s 60th Birthday}, pages = {40 - 50}, abstract = {We show that equivariant Donaldson polynomials of compact toric surfaces can be calculated as residues of suitable combinations of Virasoro conformal blocks, by building on AGT correspondence between $\mathcal{N}=2$\ supersymmetric gauge theories and two-dimensional conformal field theory. Talk presented by A.T. at the conference Interactions between Geometry and Physics {\textemdash} in honor of Ugo Bruzzo{\textquoteright}s 60th birthday 17{\textendash}22 August 2015, Guaruj{\'a}, S{\~a}o Paulo, Brazil, mostly based on Bawane et al. (0000) and Bershtein et al. (0000).

}, keywords = {AGT, Donaldson invariants, Equivariant localization, Exact partition function, Supersymmetry, Virasoro conformal blocks}, issn = {0393-0440}, doi = {https://doi.org/10.1016/j.geomphys.2017.01.012}, url = {http://www.sciencedirect.com/science/article/pii/S0393044017300165}, author = {Mikhail Bershtein and Giulio Bonelli and Massimiliano Ronzani and Alessandro Tanzini} } @article { refId0, title = {On the genesis of directional friction through bristle-like mediating elements}, journal = {ESAIM: COCV}, volume = {23}, number = {3}, year = {2017}, pages = {1023-1046}, abstract = {We propose an explanation of the genesis of directional dry friction, as emergent property of the oscillations produced in a bristle-like mediating element by the interaction with microscale fluctuations on the surface. Mathematically, we extend a convergence result by Mielke, for Prandtl{\textendash}Tomlinson-like systems, considering also non-homothetic scalings of a wiggly potential. This allows us to apply the result to some simple mechanical models, that exemplify the interaction of a bristle with a surface having small fluctuations. We find that the resulting friction is the product of two factors: a geometric one, depending on the bristle angle and on the fluctuation profile, and a energetic one, proportional to the normal force exchanged between the bristle-like element and the surface. Finally, we apply our result to discuss the with the nap/against the nap asymmetry.

}, doi = {10.1051/cocv/2017030}, url = {https://doi.org/10.1051/cocv/2017030}, author = {Paolo Gidoni and Antonio DeSimone} } @article {Crismale2017, title = {Globally stable quasistatic evolution for strain gradient plasticity coupled with damage}, journal = {Annali di Matematica Pura ed Applicata (1923 -)}, volume = {196}, number = {2}, year = {2017}, month = {Apr}, pages = {641{\textendash}685}, abstract = {We consider evolutions for a material model which couples scalar damage with strain gradient plasticity, in small strain assumptions. For strain gradient plasticity, we follow the Gurtin{\textendash}Anand formulation (J Mech Phys Solids 53:1624{\textendash}1649, 2005). The aim of the present model is to account for different phenomena: On the one hand, the elastic stiffness reduces and the plastic yield surface shrinks due to material{\textquoteright}s degradation, on the other hand the dislocation density affects the damage growth. The main result of this paper is the existence of a globally stable quasistatic evolution (in the so-called energetic formulation). Furthermore, we study the limit model as the strain gradient terms tend to zero. Under stronger regularity assumptions, we show that the evolutions converge to the ones for the coupled elastoplastic damage model studied in Crismale (ESAIM Control Optim Calc Var 22:883-912, 2016).

}, issn = {1618-1891}, doi = {10.1007/s10231-016-0590-7}, url = {https://doi.org/10.1007/s10231-016-0590-7}, author = {Vito Crismale} } @article {doi:10.1080/14029251.2017.1346348, title = {Gross-Pitaevskii non-linear dynamics for pseudo-spinor condensates}, journal = {Journal of Nonlinear Mathematical Physics}, volume = {24}, number = {3}, year = {2017}, pages = {426-464}, publisher = {Taylor \& Francis}, abstract = {We derive the equations for the non-linear effective dynamics of a so called pseudo-spinor Bose-Einstein condensate, which emerges from the linear many-body Schr{\"o}dinger equation at the leading order in the number of particles. The considered system is a three-dimensional diluted gas of identical bosons with spin, possibly confined in space, and coupled with an external time-dependent magnetic field; particles also interact among themselves through a short-scale repulsive interaction. The limit of infinitely many particles is monitored in the physically relevant Gross-Pitaevskii scaling. In our main theorem, if at time zero the system is in a phase of complete condensation (at the level of the reduced one-body marginal) and with energy per particle fixed by the Gross-Pitaevskii functional, then such conditions persist also at later times, with the one-body orbital of the condensate evolving according to a system of non-linear cubic Schr{\"o}dinger equations coupled among themselves through linear (Rabi) terms. The proof relies on an adaptation to the spinor setting of Pickl{\textquoteright}s projection counting method developed for the scalar case. Quantitative rates of convergence are available, but not made explicit because evidently non-optimal. In order to substantiate the formalism and the assumptions made in the main theorem, in an introductory section we review the mathematical formalisation of modern typical experiments with pseudo-spinor condensates.

}, doi = {10.1080/14029251.2017.1346348}, url = {https://doi.org/10.1080/14029251.2017.1346348}, author = {Alessandro Michelangeli and Alessandro Olgiati} } @article {Agrachev2017, title = {Homotopically invisible singular curves}, journal = {Calculus of Variations and Partial Differential Equations}, volume = {56}, number = {4}, year = {2017}, month = {Jul}, pages = {105}, issn = {1432-0835}, doi = {10.1007/s00526-017-1203-z}, url = {https://doi.org/10.1007/s00526-017-1203-z}, author = {Andrei A. Agrachev and Francesco Boarotto and Antonio Lerario} } @article {boarotto2017homotopy, title = {Homotopy properties of horizontal path spaces and a theorem of Serre in subriemannian geometry}, journal = {Communications in Analysis and Geometry}, volume = {25}, number = {2}, year = {2017}, pages = {269{\textendash}301}, publisher = {International Press of Boston}, doi = {10.4310/CAG.2017.v25.n2.a1}, author = {Francesco Boarotto and Antonio Lerario} } @article {2017arXiv170707595A, title = {The injectivity radius of Lie manifolds}, journal = {ArXiv e-prints}, year = {2017}, abstract = {We prove in a direct, geometric way that for any compatible Riemannian metric on a Lie manifold the injectivity radius is positive

}, keywords = {(58J40), 53C21, Mathematics - Differential Geometry}, url = {https://arxiv.org/pdf/1707.07595.pdf}, author = {Paolo Antonini and G. De Philippis and Nicola Gigli} } @article {luzzatto_2017, title = {Integrability of dominated decompositions on three-dimensional manifolds}, journal = {Ergodic Theory and Dynamical Systems}, volume = {37}, number = {2}, year = {2017}, pages = {606{\textendash}620}, publisher = {Cambridge University Press}, abstract = {

We investigate the integrability of two-dimensional invariant distributions (tangent sub-bundles) which arise naturally in the context of dynamical systems on 3-manifolds. In particular, we prove unique integrability of dynamically dominated and volume-dominated Lipschitz continuous invariant decompositions as well as distributions with some other regularity conditions.

Inspired by the work of Molino, we show that the integrability obstruction for transitive Lie algebroids can be made to vanish by adding extra dimensions. In particular, we prove that the Weinstein groupoid of a non-integrable transitive and abelian Lie algebroid, is the quotient of a finite dimensional Lie groupoid. Two constructions as such are given: First, explaining the counterexample to integrability given by Almeida and Molino, we see that it can be generalized to the construction of an "Almeida-Molino" integrable lift when the base manifold is simply connected. On the other hand, we notice that the classical de Rham isomorphism provides a universal integrable algebroid. Using it we construct a "de Rham" integrable lift for any given transitive Abelian Lie algebroid.

}, keywords = {14F40, 58H05, Mathematics - Differential Geometry}, url = {https://arxiv.org/pdf/1707.04855.pdf}, author = {Androulidakis, I. and Paolo Antonini} } @article {Bertola:2016nr, title = {The Kontsevich matrix integral: convergence to the Painlev{\'e} hierarchy and Stokes{\textquoteright} phenomenon}, journal = {Comm. Math. Phys}, volume = {DOI 10.1007/s00220-017-2856-3}, year = {2017}, url = {http://arxiv.org/abs/1603.06420}, author = {Marco Bertola and Mattia Cafasso} } @article {2017, title = {Krein-Visik-Birman self-adjoint extension theory revisited}, number = {SISSA;25/2017/MATE}, year = {2017}, abstract = {The core results of the so-called KreIn-Visik-Birman theory of self-adjoint extensions of semi-bounded symmetric operators are reproduced, both in their original and in a more modern formulation, within a comprehensive discussion that includes missing details, elucidative steps, and intermediate results of independent interest.}, url = {http://preprints.sissa.it/handle/1963/35286}, author = {Matteo Gallone and Alessandro Michelangeli and Andrea Ottolini} } @article {2017, title = {A Lagrangian approach for scalar multi-d conservation laws}, number = {SISSA;36/2017/MATE}, year = {2017}, url = {http://preprints.sissa.it/handle/1963/35290}, author = {Stefano Bianchini and Paolo Bonicatto and Elio Marconi} } @article {bianchini2017lagrangian, title = {Lagrangian representations for linear and nonlinear transport}, journal = {Contemporary Mathematics. Fundamental Directions}, volume = {63}, number = {3}, year = {2017}, pages = {418{\textendash}436}, publisher = {Peoples{\textquoteright} Friendship University of Russia}, abstract = {In this note we present a unifying approach for two classes of first order partial differential equations: we introduce the notion of Lagrangian representation in the settings of continuity equation and scalar conservation laws. This yields, on the one hand, the uniqueness of weak solutions to transport equation driven by a two dimensional BV nearly incompressible vector field. On the other hand, it is proved that the entropy dissipation measure for scalar conservation laws in one space dimension is concentrated on countably many Lipschitz curves.

}, doi = {10.22363/2413-3639-2017-63-3-418-436}, url = {http://www.mathnet.ru/php/archive.phtml?wshow=paper\&jrnid=cmfd\&paperid=327\&option_lang=eng}, author = {Stefano Bianchini and Paolo Bonicatto and Elio Marconi} } @article { refId0, title = {Limit of viscous dynamic processes in delamination as the viscosity and inertia vanish}, journal = {ESAIM: COCV}, volume = {23}, number = {2}, year = {2017}, pages = {593-625}, abstract = {We introduce a model of dynamic evolution of a delaminated visco-elastic body with viscous adhesive. We prove the existence of solutions of the corresponding system of PDEs and then study the behavior of such solutions when the data of the problem vary slowly. We prove that a rescaled version of the dynamic evolutions converge to a {\textquotedblleft}local{\textquotedblright} quasistatic evolution, which is an evolution satisfying an energy inequality and a momentum balance at all times. In the one-dimensional case we give a more detailed description of the limit evolution and we show that it behaves in a very similar way to the limit of the solutions of the dynamic model in [T. Roubicek, SIAM J. Math. Anal. 45 (2013) 101{\textendash}126], where no viscosity in the adhesive is taken into account.

}, doi = {10.1051/cocv/2016006}, url = {https://doi.org/10.1051/cocv/2016006}, author = {Riccardo Scala} } @article {2017, title = {Linear hyperbolic systems in domains with growing cracks}, number = {SISSA;05/2017/MATE}, year = {2017}, abstract = {We consider the hyperbolic system $\ddot u-{\rm div}\,(\mathbb A\nabla u)=f$ in the time varying cracked domain $\Omega\setminus\Gamma_t$, where the set $\Omega\subset\mathbb R^d$ is open, bounded, and with Lipschitz boundary, the cracks $\Gamma_t$, $t\in[0,T]$, are closed subsets of $\overline\Omega$, increasing with respect to inclusion, and $u(t):\Omega\setminus\Gamma_t\to\mathbb R^d$ for every $t\in[0,T]$. We assume the existence of suitable regular changes of variables, which reduce our problem to the transformed system $\ddot v-{\rm div}\,(\mathbb B\nabla v)+\mathbf a\nabla v -2\nabla\dot vb=g$ on the fixed domain $\Omega\setminus\Gamma_0$. Under these assumptions, we obtain existence and uniqueness of weak solutions for these two problems. Moreover, we show an energy equality for the functions $v$, which allows us to prove a continuous dependence result for both systems.}, url = {http://urania.sissa.it/xmlui/handle/1963/35271}, author = {Maicol Caponi} } @article {2017, title = {Linearisation of multiwell energies}, number = {SISSA;31/2017/MATE}, year = {2017}, abstract = {Linear elasticity can be rigorously derived from finite elasticity under the assumption of small loadings in terms of Gamma-convergence. This was first done in the case of one-well energies with super-quadratic growth and later generalised to different settings, in particular to the case of multi-well energies where the distance between the wells is very small (comparable to the size of the load). In this paper we study the case when the distance between the wells is independent of the size of the load. In this context linear elasticity can be derived by adding to the multi-well energy a singular higher order term which penalises jumps from one well to another. The size of the singular term has to satisfy certain scaling assumptions whose optimality is shown in most of the cases. Finally, the derivation of linear elasticty from a two-well discrete model is provided, showing that the role of the singular perturbation term is played in this setting by interactions beyond nearest neighbours.}, url = {http://preprints.sissa.it/handle/1963/35288}, author = {Roberto Alicandro and Gianni Dal Maso and Giuliano Lazzaroni and Mariapia Palombaro} } @article {dal2017lower, title = {Lower semicontinuity of a class of integral functionals on the space of functions of bounded deformation}, journal = {Advances in Calculus of Variations}, volume = {10}, number = {2}, year = {2017}, pages = {183{\textendash}207}, publisher = {De Gruyter}, abstract = {We study the lower semicontinuity of some free discontinuity functionals with linear growth defined on the space of functions with bounded deformation. The volume term is convex and depends only on the Euclidean norm of the symmetrized gradient. We introduce a suitable class of surface terms, which make the functional lower semicontinuous with respect to $L^1$ convergence.

}, doi = {10.1515/acv-2015-0036}, author = {Gianni Dal Maso and Gianluca Orlando and Rodica Toader} } @article {2015, title = {A lower semicontinuity result for a free discontinuity functional with a boundary term}, journal = {Journal de Math{\'e}matiques Pures et Appliqu{\'e}es}, volume = {108}, year = {2017}, pages = {952-990}, chapter = {952}, abstract = {We study the lower semicontinuity in $GSBV^{p}(\Omega;\mathbb{R}^{m})$ of a free discontinuity functional $\mathcal{F}(u)$ that can be written as the sum of a crack term, depending only on the jump set $S_{u}$, and of a boundary term, depending on the trace of $u$ on $\partial\Omega$. We give sufficient conditions on the integrands for the lower semicontinuity of $\mathcal{F}$. Moreover, we prove a relaxation result, which shows that, if these conditions are not satisfied, the lower semicontinuous envelope of $\mathcal{F}$ can be represented by the sum of two integrals on $S_{u}$ and $\partial\Omega$, respectively.

}, doi = {10.1016/j.matpur.2017.05.018}, url = {http://hdl.handle.net/20.500.11767/15979}, author = {Stefano Almi and Gianni Dal Maso and Rodica Toader} } @article {MR3665212, title = {The Malgrange form and Fredholm determinants}, journal = {SIGMA Symmetry Integrability Geom. Methods Appl.}, volume = {13}, year = {2017}, pages = {Paper No. 046, 12}, issn = {1815-0659}, doi = {10.3842/SIGMA.2017.046}, url = {http://dx.doi.org/10.3842/SIGMA.2017.046}, author = {Marco Bertola} } @article {MR3663616, title = {Maximal amplitudes of finite-gap solutions for the focusing Nonlinear Schr{\"o}dinger Equation}, journal = {Comm. Math. Phys.}, volume = {354}, number = {2}, year = {2017}, pages = {525{\textendash}547}, issn = {0010-3616}, doi = {10.1007/s00220-017-2895-9}, url = {http://dx.doi.org/10.1007/s00220-017-2895-9}, author = {Marco Bertola and Alexander Tovbis} } @article {Michelangeli2017, title = {Mean-field quantum dynamics for a mixture of Bose{\textendash}Einstein condensates}, journal = {Analysis and Mathematical Physics}, volume = {7}, number = {4}, year = {2017}, month = {Dec}, pages = {377{\textendash}416}, abstract = {We study the effective time evolution of a large quantum system consisting of a mixture of different species of identical bosons in interaction. If the system is initially prepared so as to exhibit condensation in each component, we prove that condensation persists at later times and we show quantitatively that the many-body Schr{\"o}dinger dynamics is effectively described by a system of coupled cubic non-linear Schr{\"o}dinger equations, one for each component.

}, issn = {1664-235X}, doi = {10.1007/s13324-016-0147-3}, url = {https://doi.org/10.1007/s13324-016-0147-3}, author = {Alessandro Michelangeli and Alessandro Olgiati} } @article {1534-0392_2017_4_1427, title = {Minimizers of anisotropic perimeters with cylindrical norms}, journal = {Communications on Pure \& Applied Analysis}, volume = {16}, number = {1534-0392_2017_4_142}, year = {2017}, pages = {1427}, abstract = {We study various regularity properties of minimizers of the Φ{\textendash}perimeter, where Φ is a norm. Under suitable assumptions on Φ and on the dimension of the ambient space, we prove that the boundary of a cartesian minimizer is locally a Lipschitz graph out of a closed singular set of small Hausdorff dimension. Moreover, we show the following anisotropic Bernstein-type result: any entire cartesian minimizer is the subgraph of a monotone function depending only on one variable.

}, keywords = {anisotropic Bernstein problem;, minimal cones, Non parametric minimal surfaces, Sets of finite perimeter}, issn = {1534-0392}, doi = {10.3934/cpaa.2017068}, url = {http://aimsciences.org//article/id/47054f15-00c7-40b7-9da1-4c0b1d0a103d}, author = {Giovanni Bellettini and Matteo Novaga and Shokhrukh Kholmatov} } @inbook {ChinestaHuertaRozzaWillcox2017, title = {Model Reduction Methods}, booktitle = {Encyclopedia of Computational Mechanics Second Edition}, year = {2017}, pages = {1-36}, publisher = {John Wiley \& Sons}, organization = {John Wiley \& Sons}, chapter = {Model Reduction Methods}, abstract = {This chapter presents an overview of model order reduction {\textendash} a new paradigm in the field of simulation-based engineering sciences, and one that can tackle the challenges and leverage the opportunities of modern ICT technologies. Despite the impressive progress attained by simulation capabilities and techniques, a number of challenging problems remain intractable. These problems are of different nature, but are common to many branches of science and engineering. Among them are those related to high-dimensional problems, problems involving very different time scales, models defined in degenerate domains with at least one of the characteristic dimensions much smaller than the others, model requiring real-time simulation, and parametric models. All these problems represent a challenge for standard mesh-based discretization techniques; yet the ability to solve these problems efficiently would open unexplored routes for real-time simulation, inverse analysis, uncertainty quantification and propagation, real-time optimization, and simulation-based control {\textendash} critical needs in many branches of science and engineering. Model order reduction offers new simulation alternatives by circumventing, or at least alleviating, otherwise intractable computational challenges. In the present chapter, we revisit three of these model reduction techniques: proper orthogonal decomposition, proper generalized decomposition, and reduced basis methodologies.} preprint = {http://preprints.sissa.it/xmlui/bitstream/handle/1963/35194/ECM_MOR.pdf?sequence=1\&isAllowed=y

}, doi = {10.1002/9781119176817.ecm2110}, author = {Francisco Chinesta and Antonio Huerta and Gianluigi Rozza and Karen Willcox} } @article {2017, title = {Moduli of semistable sheaves as quiver moduli}, number = {arXiv:1709.05555}, year = {2017}, abstract = {In the 1980s Dr{\'e}zet and Le Potier realized moduli spaces of Gieseker-semistable sheaves on\ P2\ as what are now called quiver moduli spaces. We discuss how this construction can be understood using t-structures and exceptional collections on derived categories, and how it can be extended to a similar result\ on\ P1{\texttimes}P1.

}, url = {https://arxiv.org/abs/1709.05555}, author = {Andrea Maiorana} } @article {1534-0392_2017_3_1083, title = {Multiple positive solutions of a sturm-liouville boundary value problem with conflicting nonlinearities}, journal = {Communications on Pure \& Applied Analysis}, volume = {16}, number = {1534-0392_2017_3_108}, year = {2017}, pages = {1083}, abstract = {We study the second order nonlinear differential equation

\begindocument $ u{\textquoteright}{\textquoteright} + \sum\limits_i = 1^m α_ia_i(x)g_i(u) - \sum\limits_j = 1^m + 1 β_jb_j(x)k_j(u) = 0,\rm $ \enddocument

where $\alpha_i, \beta_j\>0$, $a_i(x), b_j(x)$ are non-negative Lebesgue integrable functions defined in $\mathopen[0, L\mathclose]$, and the nonlinearities $g_i(s), k_j(s)$ are continuous, positive and satisfy suitable growth conditions, as to cover the classical superlinear equation $u"+a(x)u.p = 0$, with $p\>1$.When the positive parameters $\beta_j$ are sufficiently large, we prove the existence of at least $2.m-1$positive solutions for the Sturm-Liouville boundary value problems associated with the equation.The proof is based on the Leray-Schauder topological degree for locally compact operators on open and possibly unbounded sets.Finally, we deal with radially symmetric positive solutions for the Dirichlet problems associated with elliptic PDEs.

}, keywords = {Leray-Schauder topological degree;, positive solutions, Sturm-Liouville boundary conditions, Superlinear indefinite problems}, issn = {1534-0392}, doi = {10.3934/cpaa.2017052}, url = {http://aimsciences.org//article/id/1163b042-0c64-4597-b25c-3494b268e5a1}, author = {Guglielmo Feltrin} } @article {FELTRIN20174255, title = {Multiplicity of positive periodic solutions in the superlinear indefinite case via coincidence degree}, journal = {Journal of Differential Equations}, volume = {262}, number = {8}, year = {2017}, pages = {4255 - 4291}, abstract = {We study the periodic boundary value problem associated with the second order nonlinear differential equationu"+cu'+(a+(t)-μa-(t))g(u)=0, where g(u) has superlinear growth at zero and at infinity, a(t) is a periodic sign-changing weight, c∈R and μ\>0 is a real parameter. Our model includes (for c=0) the so-called nonlinear Hill{\textquoteright}s equation. We prove the existence of 2m-1 positive solutions when a(t) has m positive humps separated by m negative ones (in a periodicity interval) and μ is sufficiently large, thus giving a complete solution to a problem raised by G.J. Butler in 1976. The proof is based on Mawhin{\textquoteright}s coincidence degree defined in open (possibly unbounded) sets and applies also to Neumann boundary conditions. Our method also provides a topological approach to detect subharmonic solutions.

}, keywords = {Coincidence degree, Multiplicity results, Neumann boundary value problems, Positive periodic solutions, subharmonic solutions, Superlinear indefinite problems}, issn = {0022-0396}, doi = {https://doi.org/10.1016/j.jde.2017.01.009}, url = {http://www.sciencedirect.com/science/article/pii/S0022039617300219}, author = {Guglielmo Feltrin and Fabio Zanolin} } @article {20.500.11767_11953, title = {A natural framework for isogeometric fluid-structure interaction based on BEM-shell coupling}, journal = {COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING}, volume = {316}, year = {2017}, pages = {522{\textendash}546}, doi = {10.1016/j.cma.2016.08.008}, url = {http://cdsads.u-strasbg.fr/abs/2017CMAME.316..522H}, author = {Luca Heltai and Kiendl, J. and Antonio DeSimone and Alessandro Reali} } @article {12163, title = {A note on a fixed point theorem on topological cylinders}, journal = {Ann. Mat. Pura Appl.}, number = {Annali di Matematica Pura ed Applicata;}, year = {2017}, note = {AMS Subject Classification: 47H10, 37C25, 47H11, 54H25.}, publisher = {Springer Verlag}, abstract = {We present a fixed point theorem on topological cylinders in normed linear spaces for maps satisfying a property of stretching a space along paths. This result is a generalization of a similar theorem obtained by D. Papini and F. Zanolin. In view of the main result, we discuss the existence of fixed points for maps defined on different types of domains and we propose alternative proofs for classical fixed point theorems, as Brouwer, Schauder and Krasnosel{\textquoteright}skii ones.

}, doi = {10.1007/s10231-016-0623-2}, url = {http://urania.sissa.it/xmlui/handle/1963/35263}, author = {Guglielmo Feltrin} } @article {Nardini2017, title = {A Note on the Convergence of Singularly Perturbed Second Order Potential-Type Equations}, journal = {Journal of Dynamics and Differential Equations}, volume = {29}, number = {2}, year = {2017}, month = {Jun}, pages = {783{\textendash}797}, issn = {1572-9222}, doi = {10.1007/s10884-015-9461-y}, url = {https://doi.org/10.1007/s10884-015-9461-y}, author = {Lorenzo Nardini} } @article {2017, title = {Numerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts}, journal = {Biomechanics and Modeling in Mechanobiology}, volume = {16}, year = {2017}, pages = {1373-1399}, doi = {10.1007/s10237-017-0893-7}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85015065851\&doi=10.1007\%2fs10237-017-0893-7\&partnerID=40\&md5=c388f20bd5de14187bad9ed7d9affbd0}, author = {Francesco Ballarin and Elena Faggiano and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza and Sonia Ippolito and Roberto Scrofani} } @article {Stabile2017, title = {POD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder}, journal = {Communications in Applied and Industrial Mathematics}, volume = {8}, number = {1}, year = {2017}, month = {dec}, pages = {210{\textendash}236}, publisher = {Walter de Gruyter {GmbH}}, doi = {10.1515/caim-2017-0011}, url = {https://doi.org/10.1515/caim-2017-0011}, author = {Giovanni Stabile and Saddam Hijazi and Andrea Mola and Stefano Lorenzi and Gianluigi Rozza} } @article {GIULIANI20175052, title = {Quasi-periodic solutions for quasi-linear generalized KdV equations}, journal = {Journal of Differential Equations}, volume = {262}, number = {10}, year = {2017}, pages = {5052 - 5132}, abstract = {We prove the existence of Cantor families of small amplitude, linearly stable, quasi-periodic solutions of quasi-linear autonomous Hamiltonian generalized KdV equations. We consider the most general quasi-linear quadratic nonlinearity. The proof is based on an iterative Nash{\textendash}Moser algorithm. To initialize this scheme, we need to perform a bifurcation analysis taking into account the strongly perturbative effects of the nonlinearity near the origin. In particular, we implement a weak version of the Birkhoff normal form method. The inversion of the linearized operators at each step of the iteration is achieved by pseudo-differential techniques, linear Birkhoff normal form algorithms and a linear KAM reducibility scheme.

}, keywords = {KAM for PDE{\textquoteright}s, KdV, Nash{\textendash}Moser theory, Quasi-linear PDE{\textquoteright}s, Quasi-periodic solutions}, issn = {0022-0396}, doi = {https://doi.org/10.1016/j.jde.2017.01.021}, url = {http://www.sciencedirect.com/science/article/pii/S0022039617300487}, author = {Filippo Giuliani} } @article {Crismale2017, title = {Quasistatic crack growth based on viscous approximation: a model with branching and kinking}, journal = {Nonlinear Differential Equations and Applications NoDEA}, volume = {24}, number = {1}, year = {2017}, month = {Jan}, pages = {7}, abstract = {Employing the technique of vanishing viscosity and time rescaling, we show the existence of quasistatic evolutions of cracks in brittle materials in the setting of antiplane shear. The crack path is not prescribed a priori and is chosen in an admissible class of piecewise regular sets that allows for branching and kinking.

}, issn = {1420-9004}, doi = {10.1007/s00030-016-0426-6}, url = {https://doi.org/10.1007/s00030-016-0426-6}, author = {Vito Crismale and Giuliano Lazzaroni} } @article {1711.08253, title = {Random spectrahedra}, year = {2017}, author = {Paul Breiding and Khazhgali Kozhasov and Antonio Lerario} } @article {riccobelli2017rayleigh, title = {Rayleigh{\textendash}Taylor instability in soft elastic layers}, journal = {Phil. Trans. R. Soc. A}, volume = {375}, number = {2093}, year = {2017}, publisher = {The Royal Society}, author = {Davide Riccobelli and Pasquale Ciarletta} } @article {Narain2017, title = {Real topological string amplitudes}, journal = {Journal of High Energy Physics}, volume = {2017}, number = {3}, year = {2017}, month = {Mar}, pages = {80}, abstract = {We discuss the physical superstring correlation functions in type I theory (or equivalently type II with orientifold) that compute real topological string amplitudes. We consider the correlator corresponding to holomorphic derivative of the real topological amplitude $\mathcal{G_\chi}$, at fixed worldsheet Euler characteristic $\chi$. This corresponds in the low-energy effective action to $\mathcal{N}=2$ Weyl multiplet, appropriately reduced to the orientifold invariant part, and raised to the power $g{\textquoteright}= -\chi+ 1$. We show that the physical string correlator gives precisely the holomorphic derivative of topological amplitude. Finally, we apply this method to the standard closed oriented case as well, and prove a similar statement for the topological amplitude $\mathcal{F}_g$.

}, issn = {1029-8479}, doi = {10.1007/JHEP03(2017)080}, url = {https://doi.org/10.1007/JHEP03(2017)080}, author = {Narain, K. S. and Nicol{\`o} Piazzalunga and Alessandro Tanzini} } @article {2017, title = {Reduced Basis Methods for Uncertainty Quantification}, journal = {SIAM/ASA Journal on Uncertainty Quantification}, volume = {5}, year = {2017}, month = {08/2017}, pages = {869}, type = {reviewed}, chapter = {813}, abstract = {In this work we review a reduced basis method for the solution of uncertainty quantification problems. Based on the basic setting of an elliptic partial differential equation with random input, we introduce the key ingredients of the reduced basis method, including proper orthogonal decomposition and greedy algorithms for the construction of the reduced basis functions, a priori and a posteriori error estimates for the reduced basis approximations, as well as its computational advantages and weaknesses in comparison with a stochastic collocation method [I. Babu{\v s}ka, F. Nobile, and R. Tempone,\ *SIAM Rev.*, 52 (2010), pp. 317--355]. We demonstrate its computational efficiency and accuracy for a benchmark problem with parameters ranging from a few to a few hundred dimensions. Generalizations to more complex models and applications to uncertainty quantification problems in risk prediction, evaluation of statistical moments, Bayesian inversion, and optimal control under uncertainty are also presented to illustrate how to use the reduced basis method in practice. Further challenges, advancements, and research opportunities are outlined.

Read More:\ http://epubs.siam.org/doi/abs/10.1137/151004550

POD{\textendash}Galerkin reduced-order models (ROMs) for fluid-structure interaction problems (incompressible fluid and thin structure) are proposed in this paper. Both the high-fidelity and reduced-order methods are based on a Chorin-Temam operator-splitting approach. Two different reduced-order methods are proposed, which differ on velocity continuity condition, imposed weakly or strongly, respectively. The resulting ROMs are tested and compared on a representative haemodynamics test case characterized by wave propagation, in order to assess the capabilities of the proposed strategies.

}, doi = {10.1007/978-3-319-58786-8_10}, author = {Francesco Ballarin and Gianluigi Rozza and Yvon Maday}, editor = {Peter Benner and Mario Ohlberger and Anthony Patera and Gianluigi Rozza and Karsten Urban} } @article {2017, title = {Regularity estimates for scalar conservation laws in one space dimension}, number = {SISSA;37/2017/MATE}, year = {2017}, abstract = {In this paper we deal with the regularizing effect that, in a scalar conservation laws in one space dimension, the nonlinearity of the flux function {\textflorin} has on the entropy solution. More precisely, if the set ⟨w : {\textflorin} " (w) /= 0⟩ is dense, the regularity of the solution can be expressed in terms of BV Ф spaces, where Ф depends on the nonlinearity of {\textflorin}. If moreover the set ⟨w : {\textflorin} " (w) = 0⟩ is finite, under the additional polynomial degeneracy condition at the inflection points, we prove that {\textflorin}{\textquoteright} 0 u(t) ∈ BVloc (R) for every t > 0 and that this can be improved to SBVloc (R) regularity except an at most countable set of singular times. Finally we present some examples that shows the sharpness of these results and counterexamples to related questions, namely regularity in the kinetic formulation and a property of the fractional BV spaces.}, url = {http://preprints.sissa.it/handle/1963/35291}, author = {Elio Marconi} } @inbook {Olgiati2017, title = {Remarks on the Derivation of Gross-Pitaevskii Equation with Magnetic Laplacian}, booktitle = {Advances in Quantum Mechanics: Contemporary Trends and Open Problems}, year = {2017}, pages = {257{\textendash}266}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, address = {Cham}, abstract = {The effective dynamics for a Bose-Einstein condensate in the regime of high dilution and subject to an external magnetic field is governed by a magnetic Gross-Pitaevskii equation. We elucidate the steps needed to adapt to the magnetic case the proof of the derivation of the Gross-Pitaevskii equation within the {\textquoteleft}{\textquoteleft}projection counting{\textquoteright}{\textquoteright} scheme.

}, isbn = {978-3-319-58904-6}, doi = {10.1007/978-3-319-58904-6_15}, url = {https://doi.org/10.1007/978-3-319-58904-6_15}, author = {Alessandro Olgiati}, editor = {Alessandro Michelangeli and Gianfausto Dell{\textquoteright}Antonio} } @article {1701.03932, title = {Second order differentiation formula on compact RCD*(K,N) spaces}, year = {2017}, author = {Nicola Gigli and Luca Tamanini} } @article {2017, title = {Self-Adjoint Extensions of Dirac Operator with Coulomb Potential}, number = {SISSA;09/2017/MATE}, year = {2017}, institution = {SISSA}, abstract = {In this note we give a concise review of the present state-of-art for the problem of self-adjoint realisations for the Dirac operator with a Coulomb-like singular scalar potential V(x) = {\O}(x)I4. We try to follow the historical and conceptual path that leads to the present understanding of the problem and to highlight the techniques employed and the main ideas. In the final part we outline a few major open questions that concern the topical problem of the multiplicity of self-adjoint realisations of the model, and which are worth addressing in the future.}, url = {http://urania.sissa.it/xmlui/handle/1963/35273}, author = {Matteo Gallone} } @article {2017, title = {Self-adjoint realisations of the Dirac-Coulomb Hamiltonian for heavy nuclei}, number = {SISSA;26/2017/MATE}, year = {2017}, abstract = {We derive a classification of the self-adjoint extensions of the three-dimensional Dirac-Coulomb operator in the critical regime of the Coulomb coupling. Our approach is solely based upon the KreIn-Vi{\v s}ik- Birman extension scheme, or also on Grubb{\textquoteright}s universal classification theory, as opposite to previous works within the standard von Neu- mann framework. This let the boundary condition of self-adjointness emerge, neatly and intrinsically, as a multiplicative constraint between regular and singular part of the functions in the domain of the exten- sion, the multiplicative constant giving also immediate information on the invertibility property and on the resolvent and spectral gap of the extension.}, url = {http://preprints.sissa.it/handle/1963/35287}, author = {Matteo Gallone and Alessandro Michelangeli} } @article {2017, title = {Semistable Higgs Bundles on Calabi-Yau Manifolds}, number = {SISSA;40/2017/MATE;}, year = {2017}, abstract = {We provide a partial classification of semistable Higgs bundles over a simply connected Calabi-Yau manifold. Applications to a conjecture about a special class of semistable Higgs bundles are given. In particular, the conjecture is proved for K3 and Enriques surfaces, and some related classes of surfaces.}, url = {http://preprints.sissa.it/handle/1963/35295}, author = {Ugo Bruzzo and Valeriano Lanza and Alessio Lo Giudice} } @article {Paoli2017, title = {Small Time Asymptotics on the Diagonal for H{\"o}rmander{\textquoteright}s Type Hypoelliptic Operators}, journal = {Journal of Dynamical and Control Systems}, volume = {23}, number = {1}, year = {2017}, month = {Jan}, pages = {111{\textendash}143}, abstract = {We compute the small time asymptotics of the fundamental solution of H{\"o}rmander{\textquoteright}s type hypoelliptic operators with drift, on the diagonal at a point x0. We show that the order of the asymptotics depends on the controllability of an associated control problem and of its approximating system. If the control problem of the approximating system is controllable at x0, then so is also the original control problem, and in this case we show that the fundamental solution blows up as t-N/2\$\backslashphantom {\backslashdot {i}\backslash!}t^{-\backslashmathcal {N}/2}\$, where N\$\backslashphantom {\backslashdot {i}\backslash!}\backslashmathcal {N}\$is a number determined by the Lie algebra at x0 of the fields, that define the hypoelliptic operator.

}, issn = {1573-8698}, doi = {10.1007/s10883-016-9321-z}, url = {https://doi.org/10.1007/s10883-016-9321-z}, author = {Elisa Paoli} } @article {ambrosi2017solid, title = {Solid tumors are poroelastic solids with a chemo-mechanical feedback on growth}, journal = {J. Elast.}, volume = {129}, number = {1-2}, year = {2017}, pages = {107{\textendash}124}, publisher = {Springer Netherlands}, author = {D. Ambrosi and Pezzuto, S. and Davide Riccobelli and Stylianopoulos, T. and Pasquale Ciarletta} } @inbook {HessRozza2017, title = {A Spectral Element Reduced Basis Method in Parametric CFD}, booktitle = {Numerical Mathematics and Advanced Applications - ENUMATH 2017}, volume = {126}, year = {2017}, publisher = {Springer}, organization = {Springer}, chapter = {A Spectral Element Reduced Basis Method in Parametric CFD}, abstract = {We consider the Navier-Stokes equations in a channel with varying Reynolds numbers. The model is discretized with high-order spectral element ansatz functions, resulting in 14 259 degrees of freedom. The steady-state snapshot solu- tions define a reduced order space, which allows to accurately evaluate the steady- state solutions for varying Reynolds number with a reduced order model within a fixed-point iteration. In particular, we compare different aspects of implementing the reduced order model with respect to the use of a spectral element discretization. It is shown, how a multilevel static condensation in the pressure and velocity boundary degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios.

}, author = {Martin W. Hess and Gianluigi Rozza} } @conference {ENUMATH17_me, title = {A Spectral Element Reduced Basis Method in Parametric {CFD}}, booktitle = {Numerical Mathematics and Advanced Applications - ENUMATH 2017, Springer, in press}, year = {2017}, author = {Martin W. Hess and Gianluigi Rozza} } @article {2017, title = {Spectral Properties of the 2+1 Fermionic Trimer with Contact Interactions}, number = {SISSA;61/2017/MATE}, year = {2017}, note = {Partially supported by the 2014-2017 MIUR-FIR grant \Cond-Math: Condensed Matter and Mathematical Physics" code RBFR13WAET (S.B., A.M., A.O.), by the DAAD International Trainership Programme (S.B.), and by a 2017 visiting research fellowship at the International Center for Mathematical Research CIRM, Trento (A.M.).}, publisher = {SISSA}, abstract = {We qualify the main features of the spectrum of the Hamiltonian of point interaction for a three-dimensional quantum system consisting of three point-like particles, two identical fermions, plus a third particle of different species, with two-body interaction of zero range. For arbitrary magnitude of the interaction, and arbitrary value of the mass parameter (the ratio between the mass of the third particle and that of each fermion) above the stability threshold, we identify the essential spectrum, localise and prove the finiteness of the discrete spectrum, qualify the angular symmetry of the eigenfunctions, and prove the monotonicity of the eigenvalues with respect to the mass parameter. We also demonstrate the existence of bound states in a physically relevant regime of masses.}, url = {http://preprints.sissa.it/handle/1963/35303}, author = {Simon Becker and Alessandro Michelangeli and Andrea Ottolini} } @article {Gidoni2017, title = {Stasis domains and slip surfaces in the locomotion of a bio-inspired two-segment crawler}, journal = {Meccanica}, volume = {52}, number = {3}, year = {2017}, month = {Feb}, pages = {587{\textendash}601}, abstract = {We formulate and solve the locomotion problem for a bio-inspired crawler consisting of two active elastic segments (i.e., capable of changing their rest lengths), resting on three supports providing directional frictional interactions. The problem consists in finding the motion produced by a given, slow actuation history. By focusing on the tensions in the elastic segments, we show that the evolution laws for the system are entirely analogous to the flow rules of elasto-plasticity. In particular, sliding of the supports and hence motion cannot occur when the tensions are in the interior of certain convex regions (stasis domains), while support sliding (and hence motion) can only take place when the tensions are on the boundary of such regions (slip surfaces). We solve the locomotion problem explicitly in a few interesting examples. In particular, we show that, for a suitable range of the friction parameters, specific choices of the actuation strategy can lead to net displacements also in the direction of higher friction.

}, issn = {1572-9648}, doi = {10.1007/s11012-016-0408-0}, url = {https://doi.org/10.1007/s11012-016-0408-0}, author = {Paolo Gidoni and Antonio DeSimone} } @article {Bertola:2015tg, title = {Symplectic geometry of the moduli space of projective structures in homological coordinates}, journal = {Inventiones Mathematicae}, year = {2017}, month = {06}, pages = {1{\textendash}56}, url = {https://arxiv.org/abs/1506.07918}, author = {Marco Bertola and Dmitry Korotkin and Chaya Norton} } @article {2017, title = {Time quasi-periodic gravity water waves in finite depth}, number = {arXiv;1708.01517}, year = {2017}, abstract = {We prove the existence and the linear stability of Cantor families of small amplitude time quasi-periodic standing water wave solutions - namely periodic and even in the space variable x - of a bi-dimensional ocean with finite depth under the action of pure gravity. Such a result holds for all the values of the depth parameter in a Borel set of asymptotically full measure. This is a small divisor problem. The main difficulties are the quasi-linear nature of the gravity water waves equations and the fact that the linear frequencies grow just in a sublinear way at infinity. We overcome these problems by first reducing the linearized operators obtained at each approximate quasi-periodic solution along the Nash-Moser iteration to constant coefficients up to smoothing operators, using pseudo-differential changes of variables that are quasi-periodic in time. Then we apply a KAM reducibility scheme which requires very weak Melnikov non-resonance conditions (losing derivatives both in time and space), which we are able to verify for most values of the depth parameter using degenerate KAM theory arguments.}, url = {http://preprints.sissa.it/handle/1963/35296}, author = {P Baldi and Massimiliano Berti and Emanuele Haus and Riccardo Montalto} } @article {2017, title = {A uniqueness result for the decomposition of vector fields in Rd}, number = {SISSA;15/2017/MATE}, year = {2017}, institution = {SISSA}, abstract = {Given a vector field $\rho (1,\b) \in L^1_\loc(\R^+\times \R^{d},\R^{d+1})$ such that $\dive_{t,x} (\rho (1,\b))$ is a measure, we consider the problem of uniqueness of the representation $\eta$ of $\rho (1,\b) \mathcal L^{d+1}$ as a superposition of characteristics $\gamma : (t^-_\gamma,t^+_\gamma) \to \R^d$, $\dot \gamma (t)= \b(t,\gamma(t))$. We give conditions in terms of a local structure of the representation $\eta$ on suitable sets in order to prove that there is a partition of $\R^{d+1}$ into disjoint trajectories $\wp_\a$, $\a \in \A$, such that the PDE \begin{equation*} \dive_{t,x} \big( u \rho (1,\b) \big) \in \mathcal M(\R^{d+1}), \qquad u \in L^\infty(\R^+\times \R^{d}), \end{equation*} can be disintegrated into a family of ODEs along $\wp_\a$ with measure r.h.s.. The decomposition $\wp_\a$ is essentially unique. We finally show that $\b \in L^1_t(\BV_x)_\loc$ satisfies this local structural assumption and this yields, in particular, the renormalization property for nearly incompressible $\BV$ vector fields.

}, url = {http://preprints.sissa.it/handle/1963/35274}, author = {Stefano Bianchini and Paolo Bonicatto} } @article {MR3686488, title = {Universality of the matrix Airy and Bessel functions at spectral edges of unitary ensembles}, journal = {Random Matrices Theory Appl.}, volume = {6}, number = {3}, year = {2017}, pages = {1750010, 22}, issn = {2010-3263}, doi = {10.1142/S2010326317500101}, url = {http://dx.doi.org/10.1142/S2010326317500101}, author = {Marco Bertola and Mattia Cafasso} } @article {PhysRevLett.119.033901, title = {Universality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schr{\"o}dinger Equation}, journal = {Phys. Rev. Lett.}, volume = {119}, year = {2017}, month = {Jul}, pages = {033901}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.119.033901}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.119.033901}, author = {Tikan, Alexey and Billet, Cyril and Gennady El and Alexander Tovbis and Marco Bertola and Sylvestre, Thibaut and Gustave, Francois and Randoux, Stephane and Genty, Go{\"e}ry and Suret, Pierre and Dudley, John M.} } @article {MolaHeltaiDeSimone2017, title = {Wet and Dry Transom Stern Treatment for Unsteady and Nonlinear Potential Flow Model for Naval Hydrodynamics Simulations}, journal = {Journal of Ship Research}, volume = {61}, number = {1}, year = {2017}, pages = {1{\textendash}14}, abstract = {We present a model for the fast evaluation of the total drag of ship hulls operating in both wet and dry transom stern conditions, in calm or wavy water, based on the combination of an unsteady semi-Lagrangian potential flow formulation with fully nonlinear free-surface treatment, experimental correlations, and simplified viscous drag modeling. The implementation is entirely based on open source libraries. The spatial discretization is solved using a streamline upwind Petrov-Galerkin stabilization of an iso-parametric, collocation based, boundary element method, implemented using the open source library deal.II. The resulting nonlinear differential-algebraic system is integrated in time using implicit backward differentiation formulas, implemented in the open source library SUNDIALS. The Open CASCADE library is used to interface the model directly with computer-aided design data structures. The model accounts automatically for hulls with a transom stern, both in wet and dry regimes, by using a specific treatment of the free-surface nodes on the stern edge that automatically detects when the hull advances at low speeds. In this case, the transom stern is partially immersed, and a pressure patch is applied on the water surface detaching from the transom stern, to recover the gravity effect of the recirculating water on the underlying irrotational flow domain. The parameters of the model used to impose the pressure patch are approximated from experimental relations found in the literature. The test cases considered are those of the U.S. Navy Combatant DTMB-5415 and the National Physical Laboratory hull. Comparisons with experimental data on quasi-steady test cases for both water elevation and total hull drag are presented and discussed. The quality of the results obtained on quasi-steady simulations suggests that this model can represent a promising alternative to current unsteady solvers for simulations with Froude numbers below 0.35.

}, doi = {https://doi.org/10.5957/JOSR.61.1.160016}, author = {Andrea Mola and Luca Heltai and Antonio DeSimone} } @conference {2016, title = {Advances in geometrical parametrization and reduced order models and methods for computational fluid dynamics problems in applied sciences and engineering: overview and perspectives}, booktitle = {Proceedings of the ECCOMAS Congress 2016, VII European Conference on Computational Methods in Applied Sciences and Engineering,}, year = {2016}, month = {06/2016}, publisher = {ECCOMAS}, organization = {ECCOMAS}, address = {Crete, Greece}, abstract = {Several problems in applied sciences and engineering require reduction techniques in order to allow computational tools to be employed in the daily practice, especially in iterative procedures such as optimization or sensitivity analysis. Reduced order methods need to face increasingly complex problems in computational mechanics, especially into a multiphysics setting. Several issues should be faced: stability of the approximation, efficient treatment of nonlinearities, uniqueness or possible bifurcations of the state solutions, proper coupling between fields, as well as offline-online computing, computational savings and certification of errors as measure of accuracy. Moreover, efficient geometrical parametrization techniques should be devised to efficiently face shape optimization problems, as well as shape reconstruction and shape assimilation problems. A related aspect deals with the management of parametrized interfaces in multiphysics problems, such as fluid-structure interaction problems, and also a domain decomposition based approach for complex parametrized networks. We present some illustrative industrial and biomedical problems as examples of recent advances on methodological developments.

}, author = {Filippo Salmoiraghi and Francesco Ballarin and Giovanni Corsi and Andrea Mola and Marco Tezzele and Gianluigi Rozza}, editor = {Papadrakakis, M. and Papadopoulos, V. and Stefanou, G. and Plevris, V.} } @article {2013, title = {On the area of the graph of a piecewise smooth map from the plane to the plane with a curve discontinuity}, journal = {ESAIM: COCV}, volume = {22}, number = {arXiv:1310.2443;}, year = {2016}, pages = {29-63}, abstract = {In this paper we provide an estimate from above for the value of the relaxed area functional for a map defined on a bounded domain of the plane with values in the plane and discontinuous on a regular simple curve with two endpoints. We show that, under suitable assumptions, the relaxed area does not exceed the area of the regular part of the map, with the addition of a singular term measuring the area of a disk type solution of the Plateau{\textquoteright}s problem spanning the two traces of the map on the jump. The result is valid also when the area minimizing surface has self intersections. A key element in our argument is to show the existence of what we call a semicartesian parametrization of this surface, namely a conformal parametrization defined on a suitable parameter space, which is the identity in the first component. To prove our result, various tools of parametric minimal surface theory are used, as well as some result from Morse theory.

}, keywords = {Area functional}, doi = {10.1051/cocv/2014065}, url = {https://www.esaim-cocv.org/articles/cocv/abs/2016/01/cocv140065/cocv140065.html}, author = {Giovanni Bellettini and Lucia Tealdi and Maurizio Paolini} } @article {MR3589917, title = {On asymptotic regimes of orthogonal polynomials with complex varying quartic exponential weight}, journal = {SIGMA Symmetry Integrability Geom. Methods Appl.}, volume = {12}, year = {2016}, pages = {Paper No. 118, 50 pages}, issn = {1815-0659}, doi = {10.3842/SIGMA.2016.118}, url = {http://dx.doi.org/10.3842/SIGMA.2016.118}, author = {Marco Bertola and Alexander Tovbis} } @article {1607.05188, title = {Behaviour of the reference measure on RCD spaces under charts}, year = {2016}, author = {Nicola Gigli and Enrico Pasqualetto} } @article {1608.06868, title = {Coalescence Phenomenon of Quantum Cohomology of Grassmannians and the Distribution of Prime Numbers}, year = {2016}, author = {Giordano Cotti} } @article {Bonechi2016, title = {Comparing Poisson Sigma Model with A-model}, journal = {Journal of High Energy Physics}, volume = {2016}, number = {10}, year = {2016}, month = {Oct}, pages = {133}, abstract = {We discuss the A-model as a gauge fixing of the Poisson Sigma Model with target a symplectic structure. We complete the discussion in [4], where a gauge fixing defined by a compatible complex structure was introduced, by showing how to recover the A-model hierarchy of observables in terms of the AKSZ observables. Moreover, we discuss the off-shell supersymmetry of the A-model as a residual BV symmetry of the gauge fixed PSM action.

}, issn = {1029-8479}, doi = {10.1007/JHEP10(2016)133}, url = {https://doi.org/10.1007/JHEP10(2016)133}, author = {Bonechi, F. and Cattaneo, A.S. and Riccardo Iraso} } @article {1937-1632_2016_1_73, title = {On the concentration of entropy for scalar conservation laws}, journal = {Discrete \& Continuous Dynamical Systems - S}, volume = {9}, number = {1937-1632_2016_1_7}, year = {2016}, pages = {73}, abstract = {We prove that the entropy for an $L^$\infty$$-solution to a scalar conservation laws with continuous initial data is concentrated on a countably $1$-rectifiable set. To prove this result we introduce the notion of Lagrangian representation of the solution and give regularity estimates on the solution.

}, keywords = {concentration, Conservation laws, entropy solutions, Lagrangian representation, shocks}, issn = {1937-1632}, doi = {10.3934/dcdss.2016.9.73}, url = {http://aimsciences.org//article/id/ce4eb91e-9553-4e8d-8c4c-868f07a315ae}, author = {Stefano Bianchini and Elio Marconi} } @article {2016, title = {Confinement of dislocations inside a crystal with a prescribed external strain}, year = {2016}, note = {Preprint SISSA 20/2016/MATE}, abstract = {We study screw dislocations in an isotropic crystal undergoing antiplane shear. In the framework of linear elasticity, by fixing a suitable boundary condition for the strain (prescribed non-vanishing boundary integral), we manage to confine the dislocations inside the material. More precisely, in the presence of an external strain with circulation equal to n times the lattice spacing, it is energetically convenient to have n distinct dislocations lying inside the crystal. The novelty of introducing a Dirichlet boundary condition for the tangential strain is crucial to the confinement: it is well known that, if Neumann boundary conditions are imposed, the dislocations tend to migrate to the boundary. The results are achieved using PDE techniques and Ƭ-convergence theory, in the framework of the so-called core radius approach.}, url = {http://urania.sissa.it/xmlui/handle/1963/35247}, author = {Ilaria Lucardesi and Marco Morandotti and Riccardo Scala and Davide Zucco} } @article {Boarotto2016, title = {Conformal Equivalence of 3D Contact Structures on Lie Groups}, journal = {Journal of Dynamical and Control Systems}, volume = {22}, number = {2}, year = {2016}, month = {Apr}, pages = {251{\textendash}283}, abstract = {In this paper, a conformal classification of three dimensional left-invariant sub-Riemannian contact structures is carried out; in particular, we will prove the following dichotomy: either a structure is locally conformal to the Heisenberg group $mathbbH^3$ or its conformal classification coincides with the metric one. If a structure is locally conformally flat, then its conformal group is locally isomorphic to $SU(2,1)$.

}, issn = {1573-8698}, doi = {10.1007/s10883-015-9273-8}, url = {https://doi.org/10.1007/s10883-015-9273-8}, author = {Francesco Boarotto} } @article {Fiorenza2016, title = {Construction of Real-Valued Localized Composite Wannier Functions for Insulators}, journal = {Annales Henri Poincar{\'e}}, volume = {17}, number = {1}, year = {2016}, month = {Jan}, pages = {63{\textendash}97}, abstract = {We consider a real periodic Schr{\"o}dinger operator and a physically relevant family of $m \geq 1$ Bloch bands, separated by a gap from the rest of the spectrum, and we investigate the localization properties of the corresponding composite Wannier functions. To this aim, we show that in dimension $d\leq 3$, there exists a global frame consisting of smooth quasi-Bloch functions which are both periodic and time-reversal symmetric. Aiming to applications in computational physics, we provide a constructive algorithm to obtain such a Bloch frame. The construction yields the existence of a basis of composite Wannier functions which are real-valued and almost-exponentially localized. The proof of the main result exploits only the fundamental symmetries of the projector on the relevant bands, allowing applications, beyond the model specified above, to a broad range of gapped periodic quantum systems with a time-reversal symmetry of bosonic type.

}, issn = {1424-0661}, doi = {10.1007/s00023-015-0400-6}, url = {https://doi.org/10.1007/s00023-015-0400-6}, author = {Domenico Fiorenza and Domenico Monaco and Gianluca Panati} } @article {MR3505204, title = {Correlation functions of the KdV hierarchy and applications to intersection numbers over $\overline\CalM_g,n$}, journal = {Phys. D}, volume = {327}, year = {2016}, pages = {30{\textendash}57}, issn = {0167-2789}, doi = {10.1016/j.physd.2016.04.008}, url = {http://dx.doi.org/10.1016/j.physd.2016.04.008}, author = {Marco Bertola and Boris Dubrovin and Di Yang} } @article {BertolaCorrection, title = {CORRIGENDUM: The dependence on the monodromy data of the isomonodromic tau function}, year = {2016}, month = {01}, url = {http://arxiv.org/abs/1601.04790}, author = {Marco Bertola} } @article {rizzi2016critical, title = {Critical points of a perturbed Otha-Kawasaki functional}, journal = {arXiv preprint arXiv:1601.07093}, year = {2016}, author = {Matteo Rizzi} } @article {scala2016currents, title = {Currents and dislocations at the continuum scale}, journal = {Methods and Applications of Analysis}, volume = {23}, number = {1}, year = {2016}, pages = {1{\textendash}34}, publisher = {International Press of Boston}, abstract = {A striking geometric property of elastic bodies with dislocations is that the deformation tensor cannot be written as the gradient of a one-to-one immersion, its curl being nonzero and equal to the density of the dislocations, a measure concentrated in the dislocation lines. In this work, we discuss the mathematical properties of such constrained deformations and study a variational problem in finite-strain elasticity, where Cartesian maps allow us to consider deformations in $L^p$ with $1\leq p\<2$, as required for dislocation-induced strain singularities. Firstly, we address the problem of mathematical modeling of dislocations. It is a key purpose of the paper to build a framework where dislocations are described in terms of integral 1-currents and to extract from this theoretical setting a series of notions having a mechanical meaning in the theory of dislocations. In particular, the paper aims at classifying integral 1-currents, with modeling purposes. In the second part of the paper, two variational problems are solved for two classes of dislocations, at the mesoscopic and at the continuum scale. By continuum it is here meant that a countable family of dislocations is considered, allowing for branching and cluster formation, with possible complex geometric patterns. Therefore, modeling assumptions of the defect part of the energy must also be provided, and discussed.

}, doi = {10.4310/MAA.2016.v23.n1.a1}, author = {Riccardo Scala and Nicolas Van Goethem} } @article {20.500.11767_14497, title = {The deal.II Library, Version 8.3}, journal = {ARCHIVE OF NUMERICAL SOFTWARE}, volume = {4}, year = {2016}, pages = {1{\textendash}11}, doi = {10.11588/ans.2016.100.23122}, url = {http://nbn-resolving.de/urn:nbn:de:bsz:16-ans-231226}, author = {W. Bangerth and Timo Heister and Luca Heltai and G. Kanschat and Martin Kronbichler and Matthias Maier and B. Turcksin} } @article {20.500.11767_14498, title = {The deal.II library, Version 8.4}, journal = {JOURNAL OF NUMERICAL MATHEMATICS}, volume = {24}, year = {2016}, pages = {135{\textendash}141}, doi = {10.1515/jnma-2016-1045}, url = {https://www.math.clemson.edu/ heister/preprints/deal84-preprint.pdf}, author = {W. Bangerth and Denis Davydov and Timo Heister and Luca Heltai and G. Kanschat and Martin Kronbichler and Matthias Maier and B. Turcksin and David Wells} } @article {1611.09645, title = {Equivalence of two different notions of tangent bundle on rectifiable metric measure spaces}, year = {2016}, author = {Nicola Gigli and Enrico Pasqualetto} } @article {20.500.11767_11949, title = {Error Estimates of B-spline based finite-element method for the wind-driven ocean circulation}, journal = {JOURNAL OF SCIENTIFIC COMPUTING}, volume = {69}, year = {2016}, pages = {430{\textendash}459}, doi = {10.1007/s10915-016-0201-1}, author = {Rotundo, N. and Kim, T. -Y. and Jiang, W. and Luca Heltai and Fried, E.} } @article {2016, title = {Eulerian, Lagrangian and Broad continuous solutions to a balance law with non convex flux II}, number = {SISSA;32/2016/MATE}, year = {2016}, url = {http://urania.sissa.it/xmlui/handle/1963/35197}, author = {Giovanni Alberti and Stefano Bianchini and Laura Caravenna} } @article {2016, title = {Eulerian, Lagrangian and Broad continuous solutions to a balance law with non-convex flux I}, journal = {Journal of Differential Equations, vol. 261, issue 8 (2016): 4298-4337}, number = {Journal of Differential Equations;261}, year = {2016}, publisher = {Elsevier}, doi = {10.1016/j.jde.2016.06.026}, url = {http://urania.sissa.it/xmlui/handle/1963/35207}, author = {Giovanni Alberti and Stefano Bianchini and Laura Caravenna} } @article {Bershtein2016, title = {Exact results for N=2 supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants}, journal = {Journal of High Energy Physics}, volume = {2016}, number = {7}, year = {2016}, month = {Jul}, pages = {23}, abstract = {We provide a contour integral formula for the exact partition function of $\mathcal{N}=2$ supersymmetric $U(N)$ gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the contour integral for $U(2)\; \mathcal{N}=2^\star$ theory on $\mathbb{P}^2$ for all instanton numbers. In the zero mass case, corresponding to the $\mathcal{N}=4$ supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of mock-modular forms. In the decoupling limit of infinite mass we find that the generating function of local and surface observables computes equivariant Donaldson invariants, thus proving in this case a longstanding conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new.

}, issn = {1029-8479}, doi = {10.1007/JHEP07(2016)023}, url = {https://doi.org/10.1007/JHEP07(2016)023}, author = {Mikhail Bershtein and Giulio Bonelli and Massimiliano Ronzani and Alessandro Tanzini} } @article {BATTAGLIA20163750, title = {Existence and non-existence results for the SU(3) singular Toda system on compact surfaces}, journal = {Journal of Functional Analysis}, volume = {270}, number = {10}, year = {2016}, pages = {3750 - 3807}, abstract = {We consider the SU(3) singular Toda system on a compact surface (Σ,g)-Δu1=2ρ1(h1eu1∫Σh1eu1dVg-1)-ρ2(h2eu2∫Σh2eu2dVg-1)-4π∑m=1Mα1m(δpm-1)-Δu2=2ρ2(h2eu2∫Σh2eu2dVg-1)-ρ1(h1eu1∫Σh1eu1dVg-1)-4π∑m=1Mα2m(δpm-1), where hi are smooth positive functions on Σ, ρi∈R+, pm∈Σ and αim\>-1. We give both existence and non-existence results under some conditions on the parameters ρi and αim. Existence results are obtained using variational methods, which involve a geometric inequality of new type; non-existence results are obtained using blow-up analysis and localized Poho{\v z}aev-type identities."

}, keywords = {Liouville-type equations, Min{\textendash}max solutions, Non-existence results, Toda system}, issn = {0022-1236}, doi = {https://doi.org/10.1016/j.jfa.2015.12.011}, url = {http://www.sciencedirect.com/science/article/pii/S0022123615004942}, author = {Luca Battaglia and Andrea Malchiodi} } @article {DALMASO20164897, title = {Existence and uniqueness of dynamic evolutions for a peeling test in dimension one}, journal = {Journal of Differential Equations}, volume = {261}, number = {9}, year = {2016}, pages = {4897 - 4923}, abstract = {In this paper we present a one-dimensional model of a dynamic peeling test for a thin film, where the wave equation is coupled with a Griffith criterion for the propagation of the debonding front. Our main results provide existence and uniqueness for the solution to this coupled problem under different assumptions on the data.

}, keywords = {Dynamic debonding, Dynamic energy release rate, Dynamic fracture, Griffith{\textquoteright}s criterion, Maximum dissipation principle, Wave equation in time-dependent domains}, issn = {0022-0396}, doi = {https://doi.org/10.1016/j.jde.2016.07.012}, url = {http://www.sciencedirect.com/science/article/pii/S0022039616301772}, author = {Gianni Dal Maso and Giuliano Lazzaroni and Lorenzo Nardini} } @article {2016, title = {A fast virtual surgery platform for many scenarios haemodynamics of patient-specific coronary artery bypass grafts}, year = {2016}, institution = {Submitted}, abstract = {A fast computational framework is devised to the study of several configurations of patient-specific coronary artery bypass grafts. This is especially useful to perform a sensitivity analysis of the haemodynamics for different flow conditions occurring in native coronary arteries and bypass grafts, the investigation of the progression of the coronary artery disease and the choice of the most appropriate surgical procedure. A complete pipeline, from the acquisition of patientspecific medical images to fast parametrized computational simulations, is proposed. Complex surgical configurations employed in the clinical practice, such as Y-grafts and sequential grafts, are studied. A virtual surgery platform based on model reduction of unsteady Navier Stokes equations for blood dynamics is proposed to carry out sensitivity analyses in a very rapid and reliable way. A specialized geometrical parametrization is employed to compare the effect of stenosis and anastomosis variation on the outcome of the surgery in several relevant cases.}, url = {http://urania.sissa.it/xmlui/handle/1963/35240}, author = {Francesco Ballarin and Elena Faggiano and Andrea Manzoni and Gianluigi Rozza and Alfio Quarteroni and Sonia Ippolito and Roberto Scrofani and Carlo Antona} } @article {DalMaso2016, title = {Fracture models for elasto-plastic materials as limits of gradient damage models coupled with plasticity: the antiplane case}, journal = {Calculus of Variations and Partial Differential Equations}, volume = {55}, number = {3}, year = {2016}, month = {Apr}, pages = {45}, abstract = {We study the asymptotic behavior of a variational model for damaged elasto-plastic materials in the case of antiplane shear. The energy functionals we consider depend on a small parameter $\varepsilon$, which forces damage concentration on regions of codimension one. We determine the $\Gamma$-limit as $\varepsilon$ tends to zero and show that it contains an energy term involving the crack opening.

}, issn = {1432-0835}, doi = {10.1007/s00526-016-0981-z}, url = {https://doi.org/10.1007/s00526-016-0981-z}, author = {Gianni Dal Maso and Gianluca Orlando and Rodica Toader} } @mastersthesis {2016, title = {Frames symplectic sheaves on surfaces and their ADHM data}, year = {2016}, school = {SISSA}, abstract = {This dissertation is centered on the moduli space of what we call framed symplectic sheaves on a surface, compactifying the corresponding moduli space of framed principal SP-bundles. It contains the construction of the moduli space, which is carried out for every smooth projective surface X with a big and nef framing divisor, and a study of its deformation theory. We also develop an in-depth analysis of the examples X = P2 and X = Blp (P2 ), showing that the corresponding moduli spaces enjoy an ADHM-type description. In the former case, we prove irreducibility of the space and exhibit a relation with the space of framed ideal instantons on S4 in type C.}, keywords = {moduli spaces}, author = {Jacopo Vittorio Scalise} } @article {doi:10.1142/S0129167X16500610, title = {A Frobenius theorem for corank-1 continuous distributions in dimensions two and three}, journal = {International Journal of Mathematics}, volume = {27}, number = {08}, year = {2016}, pages = {1650061}, abstract = {We formulate a notion of (uniform) asymptotic involutivity and show that it implies (unique) integrability of corank-1 continuous distributions in dimensions three or less. This generalizes and extends a classical Frobenius theorem, which says that an involutive C1 distribution is uniquely integrable.

}, doi = {10.1142/S0129167X16500610}, url = {https://doi.org/10.1142/S0129167X16500610}, author = {Stefano Luzzatto and Sina T{\"u}reli and Khadim Mbacke War} } @article {Fonda2016, title = {Generalizing the Poincar{\'e}{\textendash}Miranda theorem: the avoiding cones condition}, journal = {Annali di Matematica Pura ed Applicata (1923 -)}, volume = {195}, number = {4}, year = {2016}, month = {Aug}, pages = {1347{\textendash}1371}, abstract = {After proposing a variant of the Poincar{\'e}{\textendash}Bohl theorem, we extend the Poincar{\'e}{\textendash}Miranda theorem in several directions, by introducing an avoiding cones condition. We are thus able to deal with functions defined on various types of convex domains, and situations where the topological degree may be different from \$\$\backslashpm \$\${\textpm}1. An illustrative application is provided for the study of functionals having degenerate multi-saddle points.

}, issn = {1618-1891}, doi = {10.1007/s10231-015-0519-6}, url = {https://doi.org/10.1007/s10231-015-0519-6}, author = {Alessandro Fonda and Paolo Gidoni} } @article {crismale2016globally, title = {Globally stable quasistatic evolution for a coupled elastoplastic{\textendash}damage model}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, volume = {22}, number = {3}, year = {2016}, pages = {883{\textendash}912}, publisher = {EDP Sciences}, abstract = {We show the existence of globally stable quasistatic evolutions for a rate-independent material model with elastoplasticity and incomplete damage, in small strain assumptions. The main feature of our model is that the scalar internal variable which describes the damage affects both the elastic tensor and the plastic yield surface. It is also possible to require that the history of plastic strain up to the current state influences the future evolution of damage.

}, doi = {10.1051/cocv/2015037}, url = {https://www.esaim-cocv.org/articles/cocv/abs/2016/03/cocv150037/cocv150037.html}, author = {Vito Crismale} } @article {arici2016gysin, title = {The Gysin sequence for quantum lens spaces}, journal = {Journal of Noncommutative Geometry}, volume = {9}, number = {4}, year = {2016}, pages = {1077{\textendash}1111}, abstract = {We define quantum lens spaces as {\textquoteleft}direct sums of line bundles{\textquoteright} and exhibit them as {\textquoteleft}total spaces{\textquoteright} of certain principal bundles over quantum projective spaces. For each of these quantum lens spaces we construct an analogue of the classical Gysin sequence in K-theory. We use the sequence to compute the K-theory of the quantum lens spaces, in particular to give explicit geometric representatives of their K-theory classes. These representatives are interpreted as {\textquoteleft}line bundles{\textquoteright} over quantum lens spaces and generically define {\textquoteleft}torsion classes{\textquoteright}. We work out explicit examples of these classes.

}, doi = {10.4171/JNCG/216}, author = {Francesca Arici and Simon Brain and Giovanni Landi} } @article {BertoBothBalogh, title = {Hankel determinant approach to generalized Vorob{\textquoteright}ev-Yablonski polynomials and their roots}, journal = {Constr. Approx.}, volume = {44}, number = {3}, year = {2016}, pages = {417{\textendash}453}, issn = {0176-4276}, doi = {10.1007/s00365-016-9328-4}, url = {http://dx.doi.org/10.1007/s00365-016-9328-4}, author = {Ferenc Balogh and Marco Bertola and Thomas Bothner} } @mastersthesis {2016, title = {Instanton counting on compact manifolds}, year = {2016}, school = {SISSA}, abstract = {In this thesis we analyze supersymmetric gauge theories on compact manifolds and their relation with representation theory of infinite Lie algebras associated to conformal field theories, and with the computation of geometric invariants and superconformal indices. The thesis contains the work done by the candidate during the doctorate programme at SISSA under the supervision of A. Tanzini and G. Bonelli. {\textbullet} in Chapter 2, we consider N = 2 supersymmetric gauge theories on four manifolds admitting an isometry. Generalized Killing spinor equations are derived from the consistency of supersymmetry algebrae and solved in the case of four manifolds admitting a U(1) isometry. This is used to explicitly compute the supersymmetric path integral on S2 {\texttimes} S2 via equivariant localization. The building blocks of the resulting partition function are shown to contain the three point functions and the conformal blocks of Liouville Gravity. {\textbullet} in Chapter 3, we provide a contour integral formula for the exact partition function of N = 2 supersymmetric U(N) gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the contour integral for U(2) N = 2* theory on P2 for all instanton numbers. In the zero mass case, corresponding to the N = 4 supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of mock-modular forms. In the decoupling limit of infinite mass we find that the generating function of local and surface observables computes equivariant Donaldson invariants, thus proving in this case a long-standing conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new. {\textbullet} in Chapter 4, we explore N = (1, 0) superconformal six-dimensional theories arising from M5 branes probing a transverse Ak singularity. Upon circle compactification to five dimensions, we describe this system with a dual pq-web of five-branes and propose the spectrum of basic five-dimensional in- stanton operators driving global symmetry enhancement. For a single M5 brane, we find that the exact partition function of the 5d quiver gauge theory matches the 6d (1, 0) index, which we compute by letter counting. We finally show which relations among vertex correlators of qW algebrae are implied by the S-duality of the pq-web.}, keywords = {Supersymmetry}, url = {http://urania.sissa.it/xmlui/handle/1963/35219}, author = {Massimiliano Ronzani} } @article {doi:10.1080/14689367.2015.1057480, title = {Integrability of C1 invariant splittings}, journal = {Dynamical Systems}, volume = {31}, number = {1}, year = {2016}, pages = {79-88}, publisher = {Taylor \& Francis}, abstract = {We derive some new conditions for integrability of dynamically defined C1 invariant splittings, formulated in terms of the singular values of the iterates of the derivative of the diffeomorphism which defines the splitting.

}, doi = {10.1080/14689367.2015.1057480}, url = {https://doi.org/10.1080/14689367.2015.1057480}, author = {Stefano Luzzatto and Sina T{\"u}reli and Khadim Mbacke War} } @mastersthesis {2016, title = {Integrability of continuous bundles and applications to dynamical systems}, year = {2016}, school = {SISSA}, abstract = {In this dissertation we study the problem of integrability of bundles with low regularities.}, author = {Khadim Mbacke War} } @article {2016, title = {Isogeometric analysis-based reduced order modelling for incompressible linear viscous flows in parametrized shapes}, number = {AMOS Advanced Modelling and Simulation in Engineering Sciences}, year = {2016}, institution = {Springer, AMOS Advanced Modelling and Simulation in Engineering Sciences}, abstract = {In this work we provide a combination of isogeometric analysis with reduced order modelling techniques, based on proper orthogonal decomposition, to guarantee computational reduction for the numerical model, and with free-form deformation, for versatile geometrical parametrization. We apply it to computational fluid dynamics problems considering a Stokes flow model. The proposed reduced order model combines efficient shape deformation and accurate and stable velocity and pressure approximation for incompressible viscous flows, computed with a reduced order method. Efficient offine-online computational decomposition is guaranteed in view of repetitive calculations for parametric design and optimization problems. Numerical test cases show the efficiency and accuracy of the proposed reduced order model.}, url = {http://urania.sissa.it/xmlui/handle/1963/35199}, author = {Filippo Salmoiraghi and Francesco Ballarin and Luca Heltai and Gianluigi Rozza} } @article {2016, title = {Large KAM tori for perturbations of the dNLS equation}, number = {arXiv;1603.09252}, year = {2016}, abstract = {We prove that small, semi-linear Hamiltonian perturbations of the defocusing nonlinear Schr\"odinger (dNLS) equation on the circle have an abundance of invariant tori of any size and (finite) dimension which support quasi-periodic solutions. When compared with previous results the novelty consists in considering perturbations which do not satisfy any symmetry condition (they may depend on x in an arbitrary way) and need not be analytic. The main difficulty is posed by pairs of almost resonant dNLS frequencies. The proof is based on the integrability of the dNLS equation, in particular the fact that the nonlinear part of the Birkhoff coordinates is one smoothing. We implement a Newton-Nash-Moser iteration scheme to construct the invariant tori. The key point is the reduction of linearized operators, coming up in the iteration scheme, to 2{\texttimes}2 block diagonal ones with constant coefficients together with sharp asymptotic estimates of their eigenvalues.}, url = {http://preprints.sissa.it/handle/1963/35284}, author = {Massimiliano Berti and Thomas Kappeler and Riccardo Montalto} } @article {20.500.11767_11950, title = {LinearOperator {\textendash} a generic, high-level expression syntax for linear algebra}, journal = {COMPUTERS \& MATHEMATICS WITH APPLICATIONS}, volume = {72}, year = {2016}, pages = {1{\textendash}24}, doi = {10.1016/j.camwa.2016.04.024}, author = {Matthias Maier and Mauro Bardelloni and Luca Heltai} } @article {2016, title = {A model for the quasistatic growth of cracks with fractional dimension}, number = {SISSA;10/2016/MATE}, year = {2016}, abstract = {We study a variational model for the quasistatic growth of cracks with fractional dimension in brittle materials. We give a minimal set of properties of the collection of admissible cracks which ensure the existence of a quasistatic evolution. Both the antiplane and the planar cases are treated.}, url = {http://urania.sissa.it/xmlui/handle/1963/35175}, author = {Gianni Dal Maso and Marco Morandotti} } @inbook {2016, title = {Model Order Reduction: a survey}, booktitle = {Wiley Encyclopedia of Computational Mechanics, 2016}, year = {2016}, publisher = {Wiley}, organization = {Wiley}, url = {http://urania.sissa.it/xmlui/handle/1963/35194}, author = {Francisco Chinesta and Antonio Huerta and Gianluigi Rozza and Karen Willcox} } @article {Battaglia2016, title = {Moser{\textendash}Trudinger inequalities for singular Liouville systems}, journal = {Mathematische Zeitschrift}, volume = {282}, number = {3}, year = {2016}, month = {Apr}, pages = {1169{\textendash}1190}, abstract = {In this paper we prove a Moser{\textendash}Trudinger inequality for the Euler{\textendash}Lagrange functional of general singular Liouville systems on a compact surface. We characterize the values of the parameters which yield coercivity for the functional, hence the existence of energy-minimizing solutions for the system, and we give necessary conditions for boundedness from below. We also provide a sharp inequality under assuming the coefficients of the system to be non-positive outside the diagonal. The proofs use a concentration-compactness alternative, Poho{\v z}aev-type identities and blow-up analysis.

}, issn = {1432-1823}, doi = {10.1007/s00209-015-1584-7}, url = {https://doi.org/10.1007/s00209-015-1584-7}, author = {Luca Battaglia} } @article {Cicconofri2016, title = {Motion planning and motility maps for flagellar microswimmers}, journal = {The European Physical Journal E}, volume = {39}, number = {7}, year = {2016}, month = {Jul}, pages = {72}, abstract = {We study two microswimmers consisting of a spherical rigid head and a passive elastic tail. In the first one the tail is clamped to the head, and the system oscillates under the action of an external torque. In the second one, head and tail are connected by a joint allowing the angle between them to vary periodically, as a result of an oscillating internal torque. Previous studies on these models were restricted to sinusoidal actuations, showing that the swimmers can propel while moving on average along a straight line, in the direction given by the symmetry axis around which beating takes place. We extend these results to motions produced by generic (non-sinusoidal) periodic actuations within the regime of small compliance of the tail. We find that modulation in the velocity of actuation can provide a mechanism to select different directions of motion. With velocity-modulated inputs, the externally actuated swimmer can translate laterally with respect to the symmetry axis of beating, while the internally actuated one is able to move along curved trajectories. The governing equations are analysed with an asymptotic perturbation scheme, providing explicit formulas, whose results are expressed through motility maps. Asymptotic approximations are further validated by numerical simulations.

}, issn = {1292-895X}, doi = {10.1140/epje/i2016-16072-y}, url = {https://doi.org/10.1140/epje/i2016-16072-y}, author = {Giancarlo Cicconofri and Antonio DeSimone} } @article {11966, title = {A multi-physics reduced order model for the analysis of Lead Fast Reactor single channel}, journal = {Annals of Nuclear Energy, 87, 2 (2016): pp. 198-208}, volume = {87}, number = {Annals of Nuclear Energy;87}, year = {2016}, pages = {208}, publisher = {Elsevier}, chapter = {198}, abstract = {In this work, a Reduced Basis method, with basis functions sampled by a Proper Orthogonal Decomposition technique, has been employed to develop a reduced order model of a multi-physics parametrized Lead-cooled Fast Reactor single-channel. Being the first time that a reduced order model is developed in this context, the work focused on a methodological approach and the coupling between the neutronics and the heat transfer, where the thermal feedbacks on neutronics are explicitly taken into account, in time-invariant settings. In order to address the potential of such approach, two different kinds of varying parameters have been considered, namely one related to a geometric quantity (i.e., the inner radius of the fuel pellet) and one related to a physical quantity (i.e., the inlet lead velocity). The capabilities of the presented reduced order model (ROM) have been tested and compared with a high-fidelity finite element model (upon which the ROM has been constructed) on different aspects. In particular, the comparison focused on the system reactivity prediction (with and without thermal feedbacks on neutronics), the neutron flux and temperature field reconstruction, and on the computational time. The outcomes provided by the reduced order model are in good agreement with the high-fidelity finite element ones, and a computational speed-up of at least three orders of magnitude is achieved as well.}, doi = {doi:10.1016/j.anucene.2015.09.002}, url = {http://urania.sissa.it/xmlui/handle/1963/35191}, author = {Alberto Sartori and Antonio Cammi and Lelio Luzzi and Gianluigi Rozza} } @article {2016, title = {Multiplicity of self-adjoint realisations of the (2+1)-fermionic model of Ter-Martirosyan--Skornyakov type}, number = {SISSA;65/2016/MATE}, year = {2016}, abstract = {We reconstruct the whole family of self-adjoint Hamiltonians of Ter-Martirosyan- Skornyakov type for a system of two identical fermions coupled with a third particle of different nature through an interaction of zero range. We proceed through an operator-theoretic approach based on the self-adjoint extension theory of Krein, Vi{\v s}iik, and Birman. We identify the explicit {\textquoteleft}Krein-Vi{\v s}ik-Birman extension param- eter{\textquoteright} as an operator on the {\textquoteleft}space of charges{\textquoteright} for this model (the {\textquoteleft}Krein space{\textquoteright}) and we come to formulate a sharp conjecture on the dimensionality of its kernel. Based on our conjecture, for which we also discuss an amount of evidence, we explain the emergence of a multiplicity of extensions in a suitable regime of masses and we re- produce for the first time the previous partial constructions obtained by means of an alternative quadratic form approach.}, url = {http://urania.sissa.it/xmlui/handle/1963/35267}, author = {Alessandro Michelangeli and Andrea Ottolini} } @article {jevnikar_2016, title = {New existence results for the mean field equation on compact surfaces via degree theory}, journal = {Rend. Sem. Mat. Univ. Padova}, volume = {136}, year = {2016}, pages = {11{\textendash}17}, doi = {10.4171/RSMUP/136-2}, author = {Aleks Jevnikar} } @article {2016, title = {Non-linear Schr{\"o}dinger system for the dynamics of a binary condensate: theory and 2D numerics}, number = {SISSA;63/2016/MATE}, year = {2016}, abstract = {We present a comprehensive discussion of the mathematical framework for binary Bose-Einstein condensates and for the rigorous derivation of their effective dynamics, governed by a system of coupled non-linear Gross-Pitaevskii equations. We also develop in the 2D case a systematic numerical study of the Gross-Pitaevskii systems in a wide range of relevant regimes of population ratios and intra-species and inter-species interactions. Our numerical method is based on a Fourier collocation scheme in space combined with a fourth order integrating factor scheme in time.}, url = {http://urania.sissa.it/xmlui/handle/1963/35266}, author = {Alessandro Michelangeli and Giuseppe Pitton} } @article {jevnikar2016note, title = {A note on a multiplicity result for the mean field equation on compact surfaces}, journal = {Advanced Nonlinear Studies}, volume = {16}, year = {2016}, pages = {221{\textendash}229}, publisher = {De Gruyter}, doi = {10.1515/ans-2015-5009}, author = {Aleks Jevnikar} } @article {2016, title = {Pairs of positive periodic solutions of nonlinear ODEs with indefinite weight: a topological degree approach for the super-sublinear case}, journal = {Proc. Roy. Soc. Edinburgh Sect. A 146 (2016), 449{\textendash}474.}, number = {Proceedings of the Royal Society of Edinburgh. Section A. Mathematics;volume 146; issue 3; pages 449-474;}, year = {2016}, note = {AMS Subject Classification: Primary 34B18; 34C25; Secondary 34B15; 47H11;}, publisher = {Cambridge University Press}, abstract = {We study the periodic and Neumann boundary value problems associated with the second order nonlinear differential equation u{\textquoteright}{\textquoteright}+cu{\textquoteright}+λa(t)g(u)=0, where g:[0,+$\infty$[{\textrightarrow}[0,+$\infty$[ is a sublinear function at infinity having superlinear growth at zero. We prove the existence of two positive solutions when ∫a(t)dt 0 is sufficiently large. Our approach is based on Mawhin{\textquoteright}s coincidence degree theory and index computations.

}, doi = {10.1017/S0308210515000621}, url = {http://urania.sissa.it/xmlui/handle/1963/35262}, author = {Alberto Boscaggin and Guglielmo Feltrin and Fabio Zanolin} } @article {fonda2016periodic, title = {Periodic perturbations of Hamiltonian systems}, journal = {Advances in Nonlinear Analysis}, volume = {5}, number = {4}, year = {2016}, pages = {367{\textendash}382}, publisher = {De Gruyter}, abstract = {We prove existence and multiplicity results for periodic solutions of Hamiltonian systems, by the use of a higher dimensional version of the Poincar{\'e}{\textendash}Birkhoff fixed point theorem. The first part of the paper deals with periodic perturbations of a completely integrable system, while in the second part we focus on some suitable global conditions, so to deal with weakly coupled systems.

}, doi = {10.1515/anona-2015-0122}, author = {Alessandro Fonda and Maurizio Garrione and Paolo Gidoni} } @inbook {Arici2016, title = {Pimsner Algebras and Circle Bundles}, booktitle = {Noncommutative Analysis, Operator Theory and Applications}, year = {2016}, pages = {1{\textendash}25}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, address = {Cham}, abstract = {We report on the connections between noncommutative principal circle bundles, Pimsner algebras and strongly graded algebras. We illustrate several results with examples of quantum weighted projective and lens spaces and θ-deformations.

}, isbn = {978-3-319-29116-1}, doi = {10.1007/978-3-319-29116-1_1}, url = {https://doi.org/10.1007/978-3-319-29116-1_1}, author = {Francesca Arici and Francesco D{\textquoteright}Andrea and Giovanni Landi}, editor = {Alpay, Daniel and Cipriani, Fabio and Colombo, Fabrizio and Guido, Daniele and Sabadini, Irene and Sauvageot, Jean-Luc} } @article {arici2016pimsner, title = {Pimsner algebras and Gysin sequences from principal circle actions}, journal = {Journal of Noncommutative Geometry}, volume = {10}, year = {2016}, pages = {29{\textendash}64}, issn = {1661-6952}, doi = {10.4171/jncg/228}, url = {http://hdl.handle.net/2066/162951}, author = {Francesca Arici and Jens Kaad and Giovanni Landi} } @article {2016, title = {POD-Galerkin Method for Finite Volume Approximation of Navier-Stokes and RANS Equations}, year = {2016}, publisher = {Computer Methods in Applied Mechanics and Engineering, Elsevier}, abstract = {Numerical simulation of fluid flows requires important computational efforts but it is essential in engineering applications. Reduced Order Model (ROM) can be employed whenever fast simulations are required, or in general, whenever a trade-off between computational cost and solution accuracy is a preeminent issue as in process optimization and control. In this work, the efforts have been put to develop a ROM for Computational Fluid Dynamics (CFD) application based on Finite Volume approximation, starting from the results available in turbulent Reynold-Averaged Navier Stokes simulations in order to enlarge the application field of Proper Orthogonal Decomposition {\textendash} Reduced Order Model (POD {\textendash} ROM) technique to more industrial fields. The approach is tested in the classic benchmark of the numerical simulation of the 2D lid-driven cavity. In particular, two simulations at Re = 103 and Re = 105 have been considered in order to assess both a laminar and turbulent case. Some quantities have been compared with the Full Order Model in order to assess the performance of the proposed ROM procedure i.e., the kinetic energy of the system and the reconstructed quantities of interest (velocity, pressure and turbulent viscosity). In addition, for the laminar case, the comparison between the ROM steady-state solution and the data available in literature has been presented. The results have turned out to be very satisfactory both for the accuracy and the computational times. As a major outcome, the approach turns out not to be affected by the energy blow up issue characterizing the results obtained by classic turbulent POD-Galerkin methods.}, author = {Stefano Lorenzi and Antonio Cammi and Lelio Luzzi and Gianluigi Rozza} } @article {11943, title = {POD{\textendash}Galerkin monolithic reduced order models for parametrized fluid-structure interaction problems}, journal = {International Journal Numerical Methods for Fluids}, year = {2016}, publisher = {Wiley}, abstract = {In this paper we propose a monolithic approach for reduced order modelling of parametrized fluid-structure interaction problems based on a proper orthogonal decomposition (POD){\textendash}Galerkin method. Parameters of the problem are related to constitutive properties of the fluid or structural problem, or to geometrical parameters related to the domain configuration at the initial time. We provide a detailed description of the parametrized formulation of the multiphysics problem in its components, together with some insights on how to obtain an offline-online efficient computational procedure through the approximation of parametrized nonlinear tensors. Then, we present the monolithic POD{\textendash}Galerkin method for the online computation of the global structural displacement, fluid velocity and pressure of the coupled problem. Finally, we show some numerical results to highlight the capabilities of the proposed reduced order method and its computational performances}, doi = {10.1002/fld.4252}, author = {Francesco Ballarin and Gianluigi Rozza} } @article {2016, title = {On point interactions realised as Ter-Martirosyan-Skornyakov Hamiltonians}, number = {SISSA;11/2016/MATE}, year = {2016}, abstract = {For quantum systems of zero-range interaction we discuss the mathematical scheme within which modelling the two-body interaction by means of the physically relevant ultra-violet asymptotics known as the {\textquoteleft}{\textquoteleft}Ter-Martirosyan--Skornyakov condition{\textquoteright}{\textquoteright} gives rise to a self-adjoint realisation of the corresponding Hamiltonian. This is done within the self-adjoint extension scheme of Krein, Visik, and Birman. We show that the Ter-Martirosyan--Skornyakov asymptotics is a condition of self-adjointness only when is imposed in suitable functional spaces, and not just as a point-wise asymptotics, and we discuss the consequences of this fact on a model of two identical fermions and a third particle of different nature.}, url = {http://urania.sissa.it/xmlui/handle/1963/35195}, author = {Alessandro Michelangeli and Andrea Ottolini} } @mastersthesis {2016, title = {Positive solutions to indefinite problems: a topological approach}, year = {2016}, note = {The research work described in this Ph.D. thesis has produced 10 papers.}, school = {SISSA}, abstract = {The present Ph.D. thesis is devoted to the study of positive solutions to indefinite problems. In particular, we deal with the second order nonlinear differential equation u{\textquoteright}{\textquoteright} + a(t) g(u) = 0, where g : [0,+$\infty$[{\textrightarrow}[0,+$\infty$[ is a continuous nonlinearity and a : [0,T]{\textrightarrow}R is a Lebesgue integrable sign-changing weight. We analyze the Dirichlet, Neumann and periodic boundary value problems on [0,T] associated with the equation and we provide existence, nonexistence and multiplicity results for positive solutions. In the first part of the manuscript, we investigate nonlinearities g(u) with a superlinear growth at zero and at infinity (including the classical superlinear case g(u)=u^p, with p>1). In particular, we prove that there exist 2^m-1 positive solutions when a(t) has m positive humps separated by negative ones and the negative part of a(t) is sufficiently large. Then, for the Dirichlet problem, we solve a conjecture by G{\'o}mez-Re{\~n}asco and L{\'o}pez-G{\'o}mez (JDE, 2000) and, for the periodic problem, we give a complete answer to a question raised by Butler (JDE, 1976). In the second part, we study the super-sublinear case (i.e. g(u) is superlinear at zero and sublinear at infinity). If a(t) has m positive humps separated by negative ones, we obtain the existence of 3^m-1 positive solutions of the boundary value problems associated with the parameter-dependent equation u{\textquoteright}{\textquoteright} + λ a(t) g(u) = 0, when both λ>0 and the negative part of a(t) are sufficiently large. We propose a new approach based on topological degree theory for locally compact operators on open possibly unbounded sets, which applies for Dirichlet, Neumann and periodic boundary conditions. As a byproduct of our method, we obtain infinitely many subharmonic solutions and globally defined positive solutions with complex behavior, and we deal with chaotic dynamics. Moreover, we study positive radially symmetric solutions to the Dirichlet and Neumann problems associated with elliptic PDEs on annular domains. Furthermore, this innovative technique has the potential and the generality needed to deal with indefinite problems with more general differential operators. Indeed, our approach apply also for the non-Hamiltonian equation u{\textquoteright}{\textquoteright} + cu{\textquoteright} + a(t) g(u) = 0. Meanwhile, more general operators in the one-dimensional case and problems involving PDEs will be subjects of future investigations.}, keywords = {positive solutions}, author = {Guglielmo Feltrin} } @article {Modena2016, title = {A quadratic interaction estimate for conservation laws: motivations, techniques and open problems}, journal = {Bulletin of the Brazilian Mathematical Society, New Series}, volume = {47}, number = {2}, year = {2016}, month = {Jun}, pages = {589{\textendash}604}, abstract = {In a series of joint works with S. Bianchini [3, 4, 5], we proved a quadratic interaction estimate for general systems of conservation laws. Aim of this paper is to present the results obtained in the three cited articles [3, 4, 5], discussing how they are related with the general theory of hyperbolic conservation laws. To this purpose, first we explain why this quadratic estimate is interesting, then we give a brief overview of the techniques we used to prove it and finally we present some related open problems.

}, issn = {1678-7714}, doi = {10.1007/s00574-016-0171-9}, url = {https://doi.org/10.1007/s00574-016-0171-9}, author = {Stefano Modena} } @article {modena2016quadratic, title = {Quadratic interaction estimate for hyperbolic conservation laws, an overview}, journal = {Contemporary Mathematics. Fundamental Directions}, volume = {59}, year = {2016}, pages = {148{\textendash}172}, publisher = {Peoples{\textquoteright} Friendship University of Russia}, author = {Stefano Modena} } @mastersthesis {2016, title = {Qualitative properties and construction of solutions to some semilinear elliptic PDEs}, year = {2016}, school = {SISSA}, abstract = {This thesis is devoted to the study of elliptic equations. On the one hand, we study some qualitative properties, such as symmetry of solutions, on the other hand we explicitly construct some solutions vanishing near some fixed manifold. The main techniques are the moving planes method, in order to investigate the qualitative properties and the Lyapunov-Schmidt reduction.}, keywords = {moving planes method, maximum principle, Lyapunov-Schmidt reduction, Willmore surfaces, Otha-Kawasaki functional}, author = {Matteo Rizzi} } @article {2016, title = {Quasi-static hydraulic crack growth driven by Darcy{\textquoteright}s law}, number = {SISSA;29/2016/MATE}, year = {2016}, abstract = {In the framework of rate independent processes, we present a variational model of quasi-static crack growth in hydraulic fracture. We first introduce the energy functional and study the equilibrium conditions of an unbounded linearly elastic body subject to a remote strain ε ∈ R and with a sufficiently regular crack Γ filled by a volume V of incompressible fluid. In particular, we are able to find the pressure p of the fluid inside the crack as a function of Γ, V , and ε. Then, we study the problem of quasi-static evolution for our model, imposing that the fluid volume V and the fluid pressure p are related by Darcy{\textquoteright}s law. We show the existence of such an evolution, and we prove that it satisfies a weak notion of the so-called Griffith{\textquoteright}s criterion.

}, url = {http://urania.sissa.it/xmlui/handle/1963/35198}, author = {Stefano Almi} } @article {11967, title = {A Reduced Basis Approach for Modeling the Movement of Nuclear Reactor Control Rods}, journal = {NERS-14-1062; ASME J of Nuclear Rad Sci, 2, 2 (2016) 021019}, volume = {2}, number = {Journal of Nuclear Engineering and Radiation Science;2}, year = {2016}, note = {8 pages}, month = {02/2016}, pages = {8}, publisher = {ASME}, abstract = {This work presents a reduced order model (ROM) aimed at simulating nuclear reactor control rods movement and featuring fast-running prediction of reactivity and neutron flux distribution as well. In particular, the reduced basis (RB) method (built upon a high-fidelity finite element (FE) approximation) has been employed. The neutronics has been modeled according to a parametrized stationary version of the multigroup neutron diffusion equation, which can be formulated as a generalized eigenvalue problem. Within the RB framework, the centroidal Voronoi tessellation is employed as a sampling technique due to the possibility of a hierarchical parameter space exploration, without relying on a {\textquotedblleft}classical{\textquotedblright} a posteriori error estimation, and saving an important amount of computational time in the offline phase. Here, the proposed ROM is capable of correctly predicting, with respect to the high-fidelity FE approximation, both the reactivity and neutron flux shape. In this way, a computational speedup of at least three orders of magnitude is achieved. If a higher precision is required, the number of employed basis functions (BFs) must be increased.}, doi = {10.1115/1.4031945}, url = {http://urania.sissa.it/xmlui/handle/1963/35192}, author = {Alberto Sartori and Antonio Cammi and Lelio Luzzi and Gianluigi Rozza} } @article {2015, title = {Reduced basis approaches in time-dependent noncoercive settings for modelling the movement of nuclear reactor control rods}, journal = {Communications in Computational Physics}, year = {2016}, month = {2016}, publisher = {SISSA}, abstract = {In this work, two approaches, based on the certified Reduced Basis method, have been developed for simulating the movement of nuclear reactor control rods, in time-dependent non-coercive settings featuring a 3D geometrical framework. In particular, in a first approach, a piece-wise affine transformation based on subdomains division has been implemented for modelling the movement of one control rod. In the second approach, a {\textquotedblleft}staircase{\textquotedblright} strategy has been adopted for simulating the movement of all the three rods featured by the nuclear reactor chosen as case study. The neutron kinetics has been modelled according to the so-called multi-group neutron diffusion, which, in the present case, is a set of ten coupled parametrized parabolic equations (two energy groups for the neutron flux, and eight for the precursors). Both the reduced order models, developed according to the two approaches, provided a very good accuracy compared with high-fidelity results, assumed as {\textquotedblleft}truth{\textquotedblright} solutions. At the same time, the computational speed-up in the Online phase, with respect to the fine {\textquotedblleft}truth{\textquotedblright} finite element discretization, achievable by both the proposed approaches is at least of three orders of magnitude, allowing a real-time simulation of the rod movement and control.

}, url = {http://urania.sissa.it/xmlui/handle/1963/34963}, author = {Alberto Sartori and Antonio Cammi and Lelio Luzzi and Gianluigi Rozza} } @article {2015, title = {Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries}, journal = {Computers and Mathematics with Applications }, volume = {71}, year = {2016}, month = {01/2016}, pages = {430}, publisher = {Elsevier}, chapter = {408}, abstract = {The aim of this work is to solve parametrized partial differential equations in computational domains represented by networks of repetitive geometries by combining reduced basis and domain decomposition techniques. The main idea behind this approach is to compute once, locally and for few reference shapes, some representative finite element solutions for different values of the parameters and with a set of different suitable boundary conditions on the boundaries: these functions will represent the basis of a reduced space where the global solution is sought for. The continuity of the latter is assured by a classical domain decomposition approach. Test results on Poisson problem show the flexibility of the proposed method in which accuracy and computational time may be tuned by varying the number of reduced basis functions employed, or the set of boundary conditions used for defining locally the basis functions. The proposed approach simplifies the pre-computation of the reduced basis space by splitting the global problem into smaller local subproblems. Thanks to this feature, it allows dealing with arbitrarily complex network and features more flexibility than a classical global reduced basis approximation where the topology of the geometry is fixed.}, author = {Laura Iapichino and Alfio Quarteroni and Gianluigi Rozza} } @article {gottsche2016refined, title = {Refined node polynomials via long edge graphs}, journal = {Communications in Number Theory and Physics}, volume = {10}, number = {2}, year = {2016}, pages = {193{\textendash}234}, publisher = {International Press of Boston}, abstract = {The generating functions of the Severi degrees for sufficiently ample line bundles on algebraic surfaces are multiplicative in the topological invariants of the surface and the line bundle. Recently new proofs of this fact were given for toric surfaces by Block, Colley, Kennedy and Liu, Osserman, using tropical geometry and in particular the combinatorial tool of long-edged graphs. In the first part of this paper these results are for $\mathbb{P}^2$ and rational ruled surfaces generalised to refined Severi degrees. In the second part of the paper we give a number of mostly conjectural generalisations of this result to singular surfaces, and curves with prescribed multiple points. The formulas involve modular forms and theta functions.

}, doi = {10.4310/CNTP.2016.v10.n2.a2}, url = {http://dx.doi.org/10.4310/CNTP.2016.v10.n2.a2}, author = {Lothar G{\"o}ttsche and Benjamin Kipkirui Kikwai} } @article {doi:10.1137/15M1007380, title = {Renormalization for Autonomous Nearly Incompressible BV Vector Fields in Two Dimensions}, journal = {SIAM Journal on Mathematical Analysis}, volume = {48}, number = {1}, year = {2016}, pages = {1-33}, abstract = {Given a bounded autonomous vector field $b \colon \mathbb{R}^d \to \mathbb{R}^d$, we study the uniqueness of bounded solutions to the initial value problem for the related transport equation \begin{equation*} \partial_t u + b \cdot \nabla u= 0. \end{equation*} We are interested in the case where $b$ is of class BV and it is nearly incompressible. Assuming that the ambient space has dimension $d=2$, we prove uniqueness of weak solutions to the transport equation. The starting point of the present work is the result which has been obtained in [7] (where the steady case is treated). Our proof is based on splitting the equation onto a suitable partition of the plane: this technique was introduced in [3], using the results on the structure of level sets of Lipschitz maps obtained in [1]. Furthermore, in order to construct the partition, we use Ambrosio{\textquoteright}s superposition principle [4].

}, doi = {10.1137/15M1007380}, url = {https://doi.org/10.1137/15M1007380}, author = {Stefano Bianchini and Paolo Bonicatto and N.A. Gusev} } @article {MR3592329, title = {Rogue waves in multiphase solutions of the focusing nonlinear Schr{\"o}dinger equation}, journal = {Proc. A.}, volume = {472}, number = {2194}, year = {2016}, pages = {20160340, 12}, issn = {1364-5021}, doi = {10.1098/rspa.2016.0340}, url = {http://dx.doi.org/10.1098/rspa.2016.0340}, author = {Marco Bertola and Gennady El and Alexander Tovbis} } @article {2016, title = {Second-order structured deformations}, year = {2016}, institution = {SISSA}, author = {Ana Cristina Barroso and Jose Matias and Marco Morandotti and David R. Owen} } @conference {mola2016ship, title = {Ship Sinkage and Trim Predictions Based on a CAD Interfaced Fully Nonlinear Potential Model}, booktitle = {The 26th International Ocean and Polar Engineering Conference}, volume = {3}, year = {2016}, pages = {511{\textendash}518}, publisher = {International Society of Offshore and Polar Engineers}, organization = {International Society of Offshore and Polar Engineers}, author = {Andrea Mola and Luca Heltai and Antonio DeSimone and Massimiliano Berti} } @article {BertoDiDub, title = {Simple Lie Algebras and Topological ODEs}, journal = {Int. Math. Res. Not.}, volume = {2016}, number = {rnw285}, year = {2016}, author = {Marco Bertola and Boris Dubrovin and Di Yang} } @article {BKT-sobolev, title = {On Sobolev instability of the interior problem of tomography}, journal = {Journal of Mathematical Analysis and Applications}, year = {2016}, author = {Marco Bertola and Alexander Katsevich and Alexander Tovbis} } @mastersthesis {2016, title = {Some results on quasistatic evolution problems for unidirectional processes}, year = {2016}, school = {SISSA}, author = {Vito Crismale} } @mastersthesis {2016, title = {Some results on the mathematical analysis of crack problems with forces applied on the fracture lips}, year = {2016}, school = {SISSA}, abstract = {This thesis is devoted to the study of some models of fracture growth in elastic materials, characterized by the presence of forces acting on the crack lips. Working in the general framework of rate-independent processes, we first discuss a variational formulation of the problem of quasi-static crack evolution in hydraulic fracture. Then, we investigate the crack growth process in a cohesive fracture model, showing the existence of an evolution satisfying a weak Griffith{\textquoteright}s criterion. Finally, in the last chapter of this work we investigate, in the static case, the interaction between the energy spent in order to create a new fracture and the energy spent by the applied surface forces. This leads us to study the lower semicontinuity properties of a free discontinuity functional F(u) that can be written as the sum of a crack term, depending on the jump set of u, and of a boundary term, depending on the trace of u.}, keywords = {Fracture mechanics}, author = {Stefano Almi} } @article {doi:10.1080/03605302.2015.1095766, title = {Spectral analysis and the Aharonov-Bohm effect on certain almost-Riemannian manifolds}, journal = {Communications in Partial Differential Equations}, volume = {41}, number = {1}, year = {2016}, pages = {32-50}, publisher = {Taylor \& Francis}, abstract = {We study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. This operator contains first order diverging terms caused by the divergence of the volume. We get explicit descriptions of the spectrum and the eigenfunctions. In particular in both cases we get a Weyl{\textquoteright}s law with leading term Elog E. We then study the drastic effect of Aharonov-Bohm magnetic potentials on the spectral properties. Other generalized Riemannian structures including conic and anti-conic type manifolds are also studied. In this case, the Aharonov-Bohm magnetic potential may affect the self-adjointness of the Laplace-Beltrami operator.

}, doi = {10.1080/03605302.2015.1095766}, url = {https://doi.org/10.1080/03605302.2015.1095766}, author = {Ugo Boscain and Dario Prandi and M. Seri} } @article {2016, title = {On the structure of $L^\infty$-entropy solutions to scalar conservation laws in one-space dimension}, year = {2016}, institution = {SISSA}, abstract = {We prove that if $u$ is the entropy solution to a scalar conservation law in one space dimension, then the entropy dissipation is a measure concentrated on countably many Lipschitz curves. This result is a consequence of a detailed analysis of the structure of the characteristics. In particular the characteristic curves are segments outside a countably 1-rectifiable set and the left and right traces of the solution exist in a $C^0$-sense up to the degeneracy due to the segments where $f{\textquoteright}{\textquoteright}=0$. We prove also that the initial data is taken in a suitably strong sense and we give some counterexamples which show that these results are sharp.

}, url = {http://urania.sissa.it/xmlui/handle/1963/35209}, author = {Stefano Bianchini and Elio Marconi} } @article {Benvenuti2016, title = {Symmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index}, journal = {Journal of High Energy Physics}, volume = {2016}, number = {9}, year = {2016}, month = {Sep}, pages = {53}, abstract = {We explore $\mathcal{N}=(1,0)$ superconformal six-dimensional theories arising from M5 branes probing a transverse $A_k$ singularity. Upon circle compactification to 5 dimensions, we describe this system with a dual pq-web of five-branes and propose the spectrum of basic five-dimensional instanton operators driving global symmetry enhancement. For a single M5 brane, we find that the exact partition function of the 5d quiver gauge theory matches the 6d (1, 0) index, which we compute by letter counting. We finally show that S-duality of the pq-web implies new relations among vertex correlators of $q\mathcal{W}$ algebrae.

}, issn = {1029-8479}, doi = {10.1007/JHEP09(2016)053}, url = {https://doi.org/10.1007/JHEP09(2016)053}, author = {Benvenuti, Sergio and Giulio Bonelli and Massimiliano Ronzani and Alessandro Tanzini} } @article {farina2016symmetry, title = {Symmetry properties of some solutions to some semilinear elliptic equations}, journal = {Annali della Scuola Normale Superiore di Pisa. Classe di scienze}, volume = {16}, number = {4}, year = {2016}, pages = {1209{\textendash}1234}, publisher = {Classe di Scienze}, author = {Farina, Alberto and Andrea Malchiodi and Matteo Rizzi} } @article {2016, title = {On the third critical speed for rotating Bose-Einstein condensates}, journal = {Correggi, M., Dimonte, D., 2016. On the third critical speed for rotating Bose-Einstein condensates. J. Math. Phys. 57, 71901}, number = {Journal of Mathematical Physics;57}, year = {2016}, publisher = {AIP Publisher}, abstract = {We study a two-dimensional rotating Bose-Einstein condensate confined by an anharmonic trap in the framework of the Gross-Pitaevskii theory. We consider a rapid rotation regime close to the transition to a giant vortex state. It was proven in Correggi et al. [J. Math. Phys. 53, 095203 (2012)] that such a transition occurs when the angular velocity is of order ε-4, with ε-2 denoting the coefficient of the nonlinear term in the Gross-Pitaevskii functional and ε << 1 (Thomas-Fermi regime). In this paper, we identify a finite value Ωc such that if Ω = Ω0/ε4 with Ω0 > Ωc, the condensate is in the giant vortex phase. Under the same condition, we prove a refined energy asymptotics and an estimate of the winding number of any Gross-Pitaevskii minimizer.}, doi = {10.1063/1.4954805}, url = {http://urania.sissa.it/xmlui/handle/1963/35246}, author = {Daniele Dimonte and Michele Correggi} } @article {PhysRevD.93.066001, title = {Towards a gauge theory interpretation of the real topological string}, journal = {Phys. Rev. D}, volume = {93}, year = {2016}, month = {Mar}, pages = {066001}, publisher = {American Physical Society}, abstract = {We consider the real topological string on certain noncompact toric Calabi-Yau three-folds $\mathbb{X}$, in its physical realization describing an orientifold of type IIA on $\mathbb{X}$\ with an O4-plane and a single D4-brane stuck on top. The orientifold can be regarded as a new kind of surface operator on the gauge theory with 8 supercharges arising from the singular geometry. We use the M-theory lift of this system to compute the real Gopakumar-Vafa invariants (describing wrapped M2-brane Bogomol{\textquoteright}nyi-Prasad-Sommerfield (BPS) states) for diverse geometries. We show that the real topological string amplitudes pick up certain signs across flop transitions, in a well-defined pattern consistent with continuity of the real BPS invariants. We further give some preliminary proposals of an intrinsically gauge theoretical description of the effect of the surface operator in the gauge theory partition function.

}, doi = {10.1103/PhysRevD.93.066001}, url = {https://link.aps.org/doi/10.1103/PhysRevD.93.066001}, author = {Hayashi, Hirotaka and Nicol{\`o} Piazzalunga and Uranga, Angel M.} } @article {Fiorenza2016, title = {t-Structures are Normal Torsion Theories}, journal = {Applied Categorical Structures}, volume = {24}, number = {2}, year = {2016}, month = {Apr}, pages = {181{\textendash}208}, abstract = {We characterize $t$-structures in stable $\infty$-categories as suitable quasicategorical factorization systems. More precisely we show that a $t$-structure $\mathcal{t}$ on a stable $\infty$-category $\mathbb{C}$ is equivalent to a normal torsion theory $\mathbf{F}$ on $\mathbb{C}$, i.e. to a factorization system $\mathbf{F} = (\mathcal{\epsilon}, \mathcal{M})$ where both classes satisfy the 3-for-2 cancellation property, and a certain compatibility with pullbacks/pushouts.

}, issn = {1572-9095}, doi = {10.1007/s10485-015-9393-z}, url = {https://doi.org/10.1007/s10485-015-9393-z}, author = {Domenico Fiorenza and Fosco Loregian} } @mastersthesis {2016, title = {t-structures on stable (infinity,1)-categories}, year = {2016}, school = {SISSA}, abstract = {The present work re-enacts the classical theory of t-structures reducing the classical definition coming from Algebraic Geometry to a rather primitive categorical gadget: suitable reflective factorization systems (defined in the work of Rosick{\'y}, Tholen, and Cassidy-H{\'e}bert-Kelly), which we call "normal torsion theories" following. A relation between these two objects has previously been noticed by other authors, on the level of the triangulated homotopy categories of stable (infinity,1)-categories. The main achievement of the present thesis is to observe and prove that this relation exists genuinely when the definition is lifted to the higher-dimensional world where the notion of triangulated category comes from.}, keywords = {category theory, higher category theory, factorization system, torsion theory, homological algebra, higher algebra}, url = {http://urania.sissa.it/xmlui/handle/1963/35202}, author = {Fosco Loregian} } @mastersthesis {2016, title = {Two explorations in Dynamical Systems and Mechanics}, year = {2016}, school = {SISSA}, abstract = {This thesis contains the work done by Paolo Gidoni during the doctorate programme in Matematical Analysis at SISSA, under the supervision of A. Fonda and A. DeSimone. The thesis is composed of two parts: "Avoiding cones conditions and higher dimensional twist" and "Directional friction in bio-inspired locomotion".}, keywords = {Poincar{\'e}-Birkhoff Theorem}, author = {Paolo Gidoni} } @article {Crismale2016, title = {Viscous approximation of quasistatic evolutions for a coupled elastoplastic-damage model}, journal = {Calculus of Variations and Partial Differential Equations}, volume = {55}, number = {1}, year = {2016}, month = {Jan}, pages = {17}, abstract = {Employing the technique of vanishing viscosity and time rescaling, we show the existence of quasistatic evolutions for elastoplastic materials with incomplete damage affecting both the elastic tensor and the plastic yield surface, in a softening framework and in small strain assumptions.

}, issn = {1432-0835}, doi = {10.1007/s00526-015-0947-6}, url = {https://doi.org/10.1007/s00526-015-0947-6}, author = {Vito Crismale and Giuliano Lazzaroni} } @article {agrachev2016volume, title = {Volume geodesic distortion and Ricci curvature for Hamiltonian dynamics}, journal = {arXiv preprint arXiv:1602.08745}, year = {2016}, author = {Andrei A. Agrachev and Davide Barilari and Elisa Paoli} } @article {1078-0947_2016_3_1465, title = {Young towers for product systems}, journal = {Discrete \& Continuous Dynamical Systems - A}, volume = {36}, number = {1078-0947_2016_3_146}, year = {2016}, pages = {1465}, abstract = {We show that the direct product of maps with Young towers admits a Young tower whose return times decay at a rate which is bounded above by the slowest of the rates of decay of the return times of the component maps. An application of this result, together with other results in the literature, yields various statistical properties for the direct product of various classes of systems, including Lorenz-like maps, multimodal maps, piecewise $C^2$ interval maps with critical points and singularities, H{\'e}non maps and partially hyperbolic systems.

}, issn = {1078-0947}, doi = {10.3934/dcds.2016.36.1465}, url = {http://aimsciences.org//article/id/18d4526e-470d-467e-967a-a0345ad4c642}, author = {Stefano Luzzatto and Marks Ruziboev} } @article {Fiorenza2016, title = {Z2 Invariants of Topological Insulators as Geometric Obstructions}, journal = {Communications in Mathematical Physics}, volume = {343}, number = {3}, year = {2016}, month = {May}, pages = {1115{\textendash}1157}, abstract = {We consider a gapped periodic quantum system with time-reversal symmetry of fermionic (or odd) type, i.e. the time-reversal operator squares to $-\mathbb{1}$. We investigate the existence of periodic and time-reversal invariant Bloch frames in dimensions 2 and 3. In 2d, the obstruction to the existence of such a frame is shown to be encoded in a $\mathbb{Z}_2$-valued topological invariant, which can be computed by a simple algorithm. We prove that the latter agrees with the Fu-Kane index. In 3d, instead, four $\mathbb{Z}_2$ invariants emerge from the construction, again related to the Fu-Kane-Mele indices. When no topological obstruction is present, we provide a constructive algorithm yielding explicitly a periodic and time-reversal invariant Bloch frame. The result is formulated in an abstract setting, so that it applies both to discrete models and to continuous ones.

}, issn = {1432-0916}, doi = {10.1007/s00220-015-2552-0}, url = {https://doi.org/10.1007/s00220-015-2552-0}, author = {Domenico Fiorenza and Domenico Monaco and Gianluca Panati} } @article {2015, title = {Anisotropic mean curvature on facets and relations with capillarity}, number = {Geometric Flows;1}, year = {2015}, publisher = {de Gruyter}, abstract = {We discuss the relations between the anisotropic calibrability of a facet F of a solid crystal E, and the capillary problem on a capillary tube with base F. When F is parallel to a facet of the Wulff shape, calibrability is equivalent to show the existence of an anisotropic subunitary vector field in $F, with suitable normal trace on the boundary of the facet, and with constant divergence equal to the anisotropic mean curvature of F. When the Wulff shape is a cylynder, assuming E convex at F, and F (strictly) calibrable, such a vector field is obtained by solving the capillary problem on F in absence of gravity and with zero contact angle. We show some examples of facets for which it is possible, even without the strict calibrability assumption, to build one of these vector fields. The construction provides, at least for convex facets of class C^{1,1}, the solution of the total variation flow starting at 1_F.

}, doi = {10.1515/geofl-2015-0005}, url = {http://urania.sissa.it/xmlui/handle/1963/34481}, author = {Stefano Amato and Lucia Tealdi and Giovanni Bellettini} } @article {MR3346719, title = {Asymptotics of orthogonal polynomials with complex varying quartic weight: global structure, critical point behavior and the first Painlev{\'e} equation}, journal = {Constr. Approx.}, volume = {41}, number = {3}, year = {2015}, pages = {529{\textendash}587}, issn = {0176-4276}, doi = {10.1007/s00365-015-9288-0}, url = {http://dx.doi.org/10.1007/s00365-015-9288-0}, author = {Marco Bertola and Alexander Tovbis} } @article {2015, title = {Benchmarking the Immersed Finite Element Method for Fluid-Structure Interaction Problems}, journal = {Computers and Mathematics with Applications 69 (2015) 1167{\textendash}1188}, number = {;69}, year = {2015}, abstract = {We present an implementation of a fully variational formulation of an immersed methods for fluid-structure interaction problems based on the finite element method. While typical implementation of immersed methods are characterized by the use of approximate Dirac delta distributions, fully variational formulations of the method do not require the use of said distributions. In our implementation the immersed solid is general in the sense that it is not required to have the same mass density and the same viscous response as the surrounding fluid. We assume that the immersed solid can be either viscoelastic of differential type or hyperelastic. Here we focus on the validation of the method via various benchmarks for fluid-structure interaction numerical schemes. This is the first time that the interaction of purely elastic compressible solids and an incompressible fluid is approached via an immersed method allowing a direct comparison with established benchmarks.}, doi = {10.1016/j.camwa.2015.03.012}, author = {Roy Saswati and Luca Heltai and Francesco Costanzo} } @article {2015, title = {A bridging mechanism in the homogenisation of brittle composites with soft inclusions}, number = {SISSA;02/2015/MATE}, year = {2015}, institution = {SISSA}, abstract = {We provide a homogenisation result for the energy-functional associated with a purely brittle composite whose microstructure is characterised by soft periodic inclusions embedded in a stiffer matrix. We show that the two constituents as above can be suitably arranged on a microscopic scale ε to obtain, in the limit as ε tends to zero, a homogeneous macroscopic energy-functional explicitly depending on the opening of the crack.}, url = {http://urania.sissa.it/xmlui/handle/1963/7492}, author = {Marco Barchiesi and Giuliano Lazzaroni and Caterina Ida Zeppieri} } @book {2015, title = {Certified Reduced Basis Methods for Parametrized Partial Differential Equations}, series = {Springer Briefs in Mathematics}, year = {2015}, pages = {135}, publisher = {Springer}, organization = {Springer}, edition = {1}, address = {Switzerland}, abstract = {This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.

}, keywords = {a posteriori error bounds, empirical interpolation, parametrized partial differential equations, reduced basis methods, greedy algorithms}, isbn = {978-3-319-22469-5}, issn = {2191-8201}, author = {Jan S Hesthaven and Gianluigi Rozza and Benjamin Stamm} } @article {2015, title = {A class of Hamiltonians for a three-particle fermionic system at unitarity}, year = {2015}, note = {This SISSA preprint is composed of 29 pages and is recorded in PDF format}, abstract = {We consider a quantum mechanical three-particle system made of two identical fermions of mass one and a different particle of mass $m$, where each fermion interacts via a zero-range force with the different particle. In particular we study the unitary regime, i.e., the case of infinite two-body scattering length. The Hamiltonians describing the system are, by definition, self-adjoint extensions of the free Hamiltonian restricted on smooth functions vanishing at the two-body coincidence planes, i.e., where the positions of two interacting particles coincide. It is known that for $m$ larger than a critical value $m^* \simeq (13.607)^{-1}$ a self-adjoint and lower bounded Hamiltonian $H_0$ can be constructed, whose domain is characterized in terms of the standard point-interaction boundary condition at each coincidence plane. Here we prove that for $m\in(m^*,m^{**})$, where $m^{**}\simeq (8.62)^{-1}$, there is a further family of self-adjoint and lower bounded Hamiltonians $H_{0,\beta}$, $\beta \in \mathbb{R}$, describing the system. Using a quadratic form method, we give a rigorous construction of such Hamiltonians and we show that the elements of their domains satisfy a further boundary condition, characterizing the singular behavior when the positions of all the three particles coincide.}, url = {http://urania.sissa.it/xmlui/handle/1963/34469}, author = {Michele Correggi and Gianfausto Dell{\textquoteright}Antonio and Domenico Finco and Alessandro Michelangeli and Alessandro Teta} } @article {doi:10.1002/mma.3450, title = {A compatible-incompatible decomposition of symmetric tensors in Lp with application to elasticity}, journal = {Mathematical Methods in the Applied Sciences}, volume = {38}, number = {18}, year = {2015}, pages = {5217-5230}, abstract = {In this paper, we prove the Saint-Venant compatibility conditions in $L^p$ for $p\in(1,$\infty$)$, in a simply connected domain of any space dimension. As a consequence, alternative, simple, and direct proofs of some classical Korn inequalities in Lp are provided. We also use the Helmholtz decomposition in $L^p$ to show that every symmetric tensor in a smooth domain can be decomposed in a compatible part, which is the symmetric part of a displacement gradient, and in an incompatible part, which is the incompatibility of a certain divergence-free tensor. Moreover, under a suitable Dirichlet boundary condition, this Beltrami-type decomposition is proved to be unique. This decomposition result has several applications, one of which being in dislocation models, where the incompatibility part is related to the dislocation density and where $1 \< p \< 2$. This justifies the need to generalize and prove these rather classical results in the Hilbertian case ($p = 2$), to the full range $p\in(1,$\infty$)$. Copyright {\textcopyright} 2015\ John Wiley \& Sons, Ltd.

}, keywords = {35J58, 35Q74, compatibility conditions, elasticity, Korn inequality, strain decomposition, subclass74B05}, doi = {10.1002/mma.3450}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/mma.3450}, author = {Maggiani, Giovanni Battista and Riccardo Scala and Nicolas Van Goethem} } @article {doi:10.1137/130950793, title = {Complexity of Control-Affine Motion Planning}, journal = {SIAM Journal on Control and Optimization}, volume = {53}, number = {2}, year = {2015}, pages = {816-844}, abstract = {In this paper we study the complexity of the motion planning problem for control-affine systems. Such complexities are already defined and rather well understood in the particular case of nonholonomic (or sub-Riemannian) systems. Our aim is to generalize these notions and results to systems with a drift. Accordingly, we present various definitions of complexity, as functions of the curve that is approximated, and of the precision of the approximation. Due to the lack of time-rescaling invariance of these systems, we consider geometric and parametrized curves separately. Then, we give some asymptotic estimates for these quantities. As a byproduct, we are able to treat the long time local controllability problem, giving quantitative estimates on the cost of stabilizing the system near a nonequilibrium point of the drift.

}, doi = {10.1137/130950793}, url = {https://doi.org/10.1137/130950793}, author = {Jean, F. and Dario Prandi} } @article {2014, title = {Constrained BV functions on double coverings for Plateau{\textquoteright}s type problems}, journal = {Adv. Calc. Var.}, year = {2015}, abstract = {We link Brakke{\textquoteright}s "soap films" covering construction with the theory of finite perimeter sets, in order to study Plateau{\textquoteright}s problem without fixing a priori the topology of the solution. The minimization is set up in the class of $BV$ functions defined on a double covering space of the complement of an $(n - 2)$-dimensional smooth compact manifold $S$ without boundary. The main novelty of our approach stands in the presence of a suitable constraint on the fibers, which couples together the covering sheets. The model allows to avoid all issues concerning the presence of the boundary $S$. The constraint is lifted in a natural way to Sobolev spaces, allowing also an approach based on $Γ$-convergence theory.

}, author = {Stefano Amato and Giovanni Bellettini and Maurizio Paolini} } @article {modena2015convergence, title = {Convergence rate of the Glimm scheme}, journal = {Bulletin of the Institute of Mathematics of Academia Sinica (New Series)}, year = {2015}, author = {Stefano Modena and Stefano Bianchini} } @article {2015, title = {Convex combinations of low eigenvalues, Fraenkel asymmetries and attainable sets}, year = {2015}, institution = {SISSA}, abstract = {We consider the problem of minimizing convex combinations of the first two eigenvalues of the Dirichlet-Laplacian among open set of $R^N$ of fixed measure. We show that, by purely elementary arguments, based on the minimality condition, it is possible to obtain informations on the geometry of the minimizers of convex combinations: we study, in particular, when these minimizers are no longer convex, and the optimality of balls. As an application of our results we study the boundary of the attainable set for the Dirichlet spectrum. Our techniques involve symmetry results {\`a} la Serrin, explicit constants in quantitative inequalities, as well as a purely geometrical problem: the minimization of the Fraenkel 2-asymmetry among convex sets of fixed measure.}, url = {http://urania.sissa.it/xmlui/handle/1963/35140}, author = {Dario Mazzoleni and Davide Zucco} } @article {2015, title = {Deal2lkit: a Toolkit Library for High Performance Programming in deal.II}, year = {2015}, publisher = {SISSA}, abstract = {We present version 1.0.0 of the deal2lkit (deal.II ToolKit) library. deal2lkit is a collection of modules and classes for the general purpose finite element library deal.II. Its principal aim is to provide a high level interface, controlled via parameter files, for those steps that are common in all finite element programs: mesh generation, selection of the finite element type, application of boundary conditions and many others. Each module can be used as a building block independently on the others, and can be integrated in existing finite element codes based on deal.II, drastically reducing the size of programs, rendering their use automatically parametrised, and reducing the overall time-to-market of finite element programming. Moreover, deal2lkit features interfaces with the SUNDIALS (SUite of Nonlinear and DIfferential/ALgebraic equation Solvers) and ASSIMP (Open Asset Import Library) libraries. Some examples are provided which show the aim and scopes of deal2lkit. The deal2lkit library is released under the GNU Lesser General Public License (LGPL) and can be retrieved from the deal2lkit repository https://github.com/mathLab/deal2lkit.}, url = {http://urania.sissa.it/xmlui/handle/1963/35006}, author = {Alberto Sartori and Nicola Giuliani and Mauro Bardelloni and Luca Heltai} } @article {2015, title = {The deal.II Library, Version 8.2}, journal = {Archive of Numerical Software, vol. 3, n. 100, (2015), pages : 1-8}, year = {2015}, abstract = {This paper provides an overview of the new features of the finite element library deal.II version 8.2}, doi = {10.11588/ans.2015.100.18031}, url = {http://urania.sissa.it/xmlui/handle/1963/34464}, author = {W. Bangerth and Timo Heister and Luca Heltai and G. Kanschat and Martin Kronbichler and Matthias Maier and B. Turcksin and T. D. Young} } @article {doi:10.1080/14689367.2015.1046816, title = {Decay of correlations for invertible maps with non-H{\"o}lder observables}, journal = {Dynamical Systems}, volume = {30}, number = {3}, year = {2015}, pages = {341-352}, publisher = {Taylor \& Francis}, abstract = {An invertible dynamical system with some hyperbolic structure is considered. Upper estimates for the correlations of continuous observables are given in terms of modulus of continuity. The result is applied to certain H{\'e}non maps and Solenoid maps with intermittency.

}, doi = {10.1080/14689367.2015.1046816}, url = {https://doi.org/10.1080/14689367.2015.1046816}, author = {Marks Ruziboev} } @article {MR3369874, title = {A degeneration of two-phase solutions of the focusing nonlinear Schr{\"o}dinger equation via Riemann-Hilbert problems}, journal = {J. Math. Phys.}, volume = {56}, number = {6}, year = {2015}, pages = {061507, 17}, issn = {0022-2488}, doi = {10.1063/1.4922362}, url = {http://dx.doi.org/10.1063/1.4922362}, author = {Marco Bertola and Giavedoni, Pietro} } @article {2015, title = {Dispersive deformations of the Hamiltonian structure of Euler{\textquoteright}s equations}, year = {2015}, abstract = {Euler{\textquoteright}s equations for a two-dimensional system can be written in Hamiltonian form, where the Poisson bracket is the Lie-Poisson bracket associated to the Lie algebra of divergence free vector fields. We show how to derive the Poisson brackets of 2d hydrodynamics of ideal fluids as a reduction from the one associated to the full algebra of vector fields. Motivated by some recent results about the deformations of Lie-Poisson brackets of vector fields, we study the dispersive deformations of the Poisson brackets of Euler{\textquoteright}s equation and show that, up to the second order, they are trivial.}, author = {Matteo Casati} } @article {2015, title = {Dynamics of screw dislocations: a generalised minimising-movements scheme approach}, number = {SISSA;38/2015/MATE}, year = {2015}, institution = {SISSA}, abstract = {The gradient flow structure of the model introduced in [CG99] for the dynamics of screw dislocations is investigated by means of a generalised minimising-movements scheme approach. The assumption of a finite number of available glide directions, together with the "maximal dissipation criterion" that governs the equations of motion, results into solving a differential inclusion rather than an ODE. This paper addresses how the model in [CG99] is connected to a time-discrete evolution scheme which explicitly confines dislocations to move each time step along a single glide direction. It is proved that the time-continuous model in [CG99] is the limit of these time-discrete minimising-movement schemes when the time step converges to 0. The study presented here is a first step towards a generalization of the setting in [AGS08, Chap. 2 and 3] that allows for dissipations which cannot be described by a metric.}, url = {http://urania.sissa.it/xmlui/handle/1963/34495}, author = {Giovanni A. Bonaschi and Patrick Van Meurs and Marco Morandotti} } @article {BATTAGLIA201549, title = {Existence and multiplicity result for the singular Toda system}, journal = {Journal of Mathematical Analysis and Applications}, volume = {424}, number = {1}, year = {2015}, pages = {49 - 85}, abstract = {We consider the Toda system on a compact surface (Σ,g)-Δu1=2ρ1(h1eu1∫Σh1eu1dVg-1)-ρ2(h2eu2∫Σh2eu2dVg-1)-4π∑j=1Jα1j(δpj-1),-Δu2=2ρ2(h2eu2∫Σh2eu2dVg-1)-ρ1(h1eu1∫Σh1eu1dVg-1)-4π∑j=1Jα2j(δpj-1), where hi are smooth positive functions, ρi are positive real parameters, pj are given points on Σ and αij are numbers greater than -1. We give existence and multiplicity results, using variational and Morse-theoretical methods. It is the first existence result when some of the αij{\textquoteright}s are allowed to be negative."

}, keywords = {Existence result, Liouville-type equations, Multiplicity result, PDEs on compact surfaces, Toda system}, issn = {0022-247X}, doi = {https://doi.org/10.1016/j.jmaa.2014.10.081}, url = {http://www.sciencedirect.com/science/article/pii/S0022247X14010191}, author = {Luca Battaglia} } @article {2015, title = {Existence for constrained dynamic Griffith fracture with a weak maximal dissipation condition}, year = {2015}, abstract = {There are very few existence results for fracture evolution, outside of globally minimizing quasi-static evolutions. Dynamic evolutions are particularly problematic, due to the difficulty of showing energy balance, as well as of showing that solutions obey a maximal dissipation condition, or some similar condition that prevents stationary cracks from always being solutions. Here we introduce a new weak maximal dissipation condition and show that it is compatible with cracks constrained to grow smoothly on a smooth curve. In particular, we show existence of dynamic fracture evolutions satisfying this maximal dissipation condition, subject to the above smoothness constraints, and exhibit explicit examples to show that this maximal dissipation principle can indeed rule out stationary cracks as solutions.}, url = {http://urania.sissa.it/xmlui/handle/1963/35045}, author = {Gianni Dal Maso and Cristopher J. Larsen and Rodica Toader} } @article {2015, title = {Existence of positive solutions in the superlinear case via coincidence degree: the Neumann and the periodic boundary value problems}, journal = {Adv. Differential Equations 20 (2015), 937{\textendash}982.}, number = {Advances in Differential Equations;volume 20; issue 9/10; pages 937-982;}, year = {2015}, note = {AMS Subject Classification: 34B18, 34B15, 34C25, 47H11.}, publisher = {Khayyam Publishing}, abstract = {We prove the existence of positive periodic solutions for the second order nonlinear equation u{\textquoteright}{\textquoteright} + a(x) g(u) = 0, where g(u) has superlinear growth at zero and at infinity. The weight function a(x) is allowed to change its sign. Necessary and sufficient conditions for the existence of nontrivial solutions are obtained. The proof is based on Mawhin{\textquoteright}s coincidence degree and applies also to Neumann boundary conditions. Applications are given to the search of positive solutions for a nonlinear PDE in annular domains and for a periodic problem associated to a non-Hamiltonian equation.

}, url = {http://projecteuclid.org/euclid.ade/1435064518}, author = {Guglielmo Feltrin and Fabio Zanolin} } @article {0133-0189_2015_special_436, title = {Existence of positive solutions of a superlinear boundary value problem with indefinite weight}, journal = {Conference Publications}, volume = {2015}, number = {0133-0189_2015_special_43}, year = {2015}, pages = {436}, abstract = {We deal with the existence of positive solutions for a two-point boundary value problem associated with the nonlinear second order equation $u{\textquoteright}{\textquoteright}+a(x)g(u)=0$. The weight $a(x)$ is allowed to change sign. We assume that the function $g\colon\mathopen[0,+$\infty$\mathclose[\to\mathbb{R}$ is continuous, $g(0)=0$ and satisfies suitable growth conditions, including the superlinear case $g(s)=s^p$, with $p\>1$. In particular we suppose that $g(s)/s$ is large near infinity, but we do not require that $g(s)$ is non-negative in a neighborhood of zero. Using a topological approach based on the Leray-Schauder degree we obtain a result of existence of at least a positive solution that improves previous existence theorems.

}, keywords = {boundary value problem, indefinite weight, Positive solution; existence result., superlinear equation}, issn = {0133-0189}, doi = {10.3934/proc.2015.0436}, url = {http://aimsciences.org//article/id/b3c1c765-e8f5-416e-8130-05cc48478026}, author = {Guglielmo Feltrin} } @conference {calore2015experience, title = {Experience on vectorizing lattice Boltzmann kernels for multi-and many-core architectures}, booktitle = {International Conference on Parallel Processing and Applied Mathematics}, year = {2015}, pages = {53{\textendash}62}, publisher = {Springer}, organization = {Springer}, author = {Calore, Enrico and Nicola Demo and Schifano, Sebastiano Fabio and Tripiccione, Raffaele} } @article {2015, title = {Explicit formulas for relaxed disarrangement densities arising from structured deformations}, number = {SISSA;37/2015/MATE}, year = {2015}, institution = {SISSA}, abstract = {Structured deformations provide a multiscale geometry that captures the contributions at the macrolevel of both smooth geometrical changes and non-smooth geometrical changes (disarrangements) at submacroscopic levels. For each (first-order) structured deformation (g,G) of a continuous body, the tensor field G is known to be a measure of deformations without disarrangements, and M:=∇g-G is known to be a measure of deformations due to disarrangements. The tensor fields G and M together deliver not only standard notions of plastic deformation, but M and its curl deliver the Burgers vector field associated with closed curves in the body and the dislocation density field used in describing geometrical changes in bodies with defects. Recently, Owen and Paroni [13] evaluated explicitly some relaxed energy densities arising in Choksi and Fonseca{\textquoteright}s energetics of structured deformations [4] and thereby showed: (1) (trM)+ , the positive part of trM, is a volume density of disarrangements due to submacroscopic separations, (2) (trM)-, the negative part of trM, is a volume density of disarrangements due to submacroscopic switches and interpenetrations, and (3) trM, the absolute value of trM, is a volume density of all three of these non-tangential disarrangements: separations, switches, and interpenetrations. The main contribution of the present research is to show that a different approach to the energetics of structured deformations, that due to Ba\'{i}a, Matias, and Santos [1], confirms the roles of (trM)+, (trM)-, and trM established by Owen and Paroni. In doing so, we give an alternative, shorter proof of Owen and Paroni{\textquoteright}s results, and we establish additional explicit formulas for other measures of disarrangements.}, url = {http://urania.sissa.it/xmlui/handle/1963/34492}, author = {Ana Cristina Barroso and Jose Matias and Marco Morandotti and David R. Owen} } @article {2015, title = {Extended affine Weyl groups of BCD type, Frobenius manifolds and their Landau-Ginzburg superpotentials}, year = {2015}, institution = {SISSA}, abstract = {For the root systems of type Bl, Cl and Dl, we generalize the result of [7] by showing the existence of Frobenius manifold structures on the orbit spaces of the extended affine Weyl groups that correspond to any vertex of the Dynkin diagram instead of a particular choice made in [7]. It also depends on certain additional data. We also construct LG superpotentials for these Frobenius manifold structures.}, url = {http://preprints.sissa.it/handle/1963/35316}, author = {Boris Dubrovin and Ian A.B. Strachan and Youjin Zhang and Dafeng Zuo} } @article {2015, title = {Fast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization}, year = {2015}, abstract = {In this work a reduced-order computational framework for the study of haemodynamics in three-dimensional patient-specific configurations of coronary artery bypass grafts dealing with a wide range of scenarios is proposed. We combine several efficient algorithms to face at the same time both the geometrical complexity involved in the description of the vascular network and the huge computational cost entailed by time dependent patient-specific flow simulations. Medical imaging procedures allow to reconstruct patient-specific configurations from clinical data. A centerlines-based parametrization is proposed to efficiently handle geometrical variations. POD{\textendash}Galerkin reduced-order models are employed to cut down large computational costs. This computational framework allows to characterize blood flows for different physical and geometrical variations relevant in the clinical practice, such as stenosis factors and anastomosis variations, in a rapid and reliable way. Several numerical results are discussed, highlighting the computational performance of the proposed framework, as well as its capability to perform sensitivity analysis studies, so far out of reach.}, url = {http://urania.sissa.it/xmlui/handle/1963/34623}, author = {Francesco Ballarin and Elena Faggiano and Sonia Ippolito and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza and Roberto Scrofani} } @article {2015, title = {FEM SUPG stabilisation of mixed isoparametric BEMs: application to linearised free surface flows}, journal = {Engineering Analysis with Boundary Elements 59 (2015), pp. 8-22}, year = {2015}, abstract = {In finite element formulations, transport dominated problems are often stabilised through the Streamline-Upwind-Petrov{\textendash}Galerkin (SUPG) method. Its application is straightforward when the problem at hand is solved using Galerkin methods. Applications of boundary integral formulations often resort to collocation techniques which are computationally more tractable. In this framework, the Galerkin method and the stabilisation may still be used to successfully apply boundary conditions and resolve instabilities that are frequently observed in transport dominated problems. We apply this technique to an adaptive collocation boundary element method for the solution of stationary potential flows, where we solve a mixed Poisson problem in boundary integral form, with the addition of linearised free surface boundary conditions. We use a mixed boundary element formulation to allow for different finite dimensional spaces describing the flow potential and its normal derivative, and we validate our method simulating the flow around both a submerged body and a surface piercing body. The coupling of mixed surface finite elements and strongly consistent stabilisation techniques with boundary elements opens up the possibility to use non conformal unstructured grids with local refinement, without introducing the inconsistencies of other stabilisation techniques based on up-winding and finite difference schemes.

}, doi = {10.1016/j.enganabound.2015.04.006}, url = {http://urania.sissa.it/xmlui/handle/1963/34466}, author = {Nicola Giuliani and Andrea Mola and Luca Heltai and L. Formaggia} } @article {BATTAGLIA2015937, title = {A general existence result for the Toda system on compact surfaces}, journal = {Advances in Mathematics}, volume = {285}, year = {2015}, pages = {937 - 979}, abstract = {In this paper we consider the following Toda system of equations on a compact surface:-Δu1=2ρ1(h1eu1∫Σh1eu1dVg-1)-ρ2(h2eu2∫Σh2eu2dVg-1)-Δu1=-4π∑j=1mα1,j(δpj-1),-Δu2=2ρ2(h2eu2∫Σh2eu2dVg-1)-ρ1(h1eu1∫Σh1eu1dVg-1)-Δu2=-4π∑j=1mα2,j(δpj-1), which is motivated by the study of models in non-abelian Chern{\textendash}Simons theory. Here h1,h2 are smooth positive functions, ρ1,ρ2 two positive parameters, pi points of the surface and α1,i,α2,j non-negative numbers. We prove a general existence result using variational methods. The same analysis applies to the following mean field equation-Δu=ρ1(heu∫ΣheudVg-1)-ρ2(he-u∫Σhe-udVg-1), which arises in fluid dynamics."

}, keywords = {Geometric PDEs, Min{\textendash}max schemes, Variational methods}, issn = {0001-8708}, doi = {https://doi.org/10.1016/j.aim.2015.07.036}, url = {http://www.sciencedirect.com/science/article/pii/S0001870815003072}, author = {Luca Battaglia and Aleks Jevnikar and Andrea Malchiodi and David Ruiz} } @article {agrachev2015geodesics, title = {Geodesics and horizontal-path spaces in Carnot groups}, journal = {Geometry \& Topology}, volume = {19}, number = {3}, year = {2015}, pages = {1569{\textendash}1630}, publisher = {Mathematical Sciences Publishers}, abstract = {We study properties of the space of horizontal paths joining the origin with a vertical point on a generic two-step Carnot group. The energy is a Morse-Bott functional on paths and its critical points (sub-Riemannian geodesics) appear in families (compact critical manifolds) with controlled topology. We study the asymptotic of the number of critical manifolds as the energy grows. The topology of the horizontal-path space is also investigated, and we find asymptotic results for the total Betti number of the sublevels of the energy as it goes to infinity. We interpret these results as local invariants of the sub-Riemannian structure.

}, doi = {10.2140/gt.2015.19.1569}, author = {Andrei A. Agrachev and Alessandro Gentile and Antonio Lerario} } @mastersthesis {2015, title = {Geometric phases in graphene and topological insulators}, year = {2015}, school = {SISSA}, abstract = {This thesis collects three of the publications that the candidate produced during his Ph.D. studies. They all focus on geometric phases in solid state physics. We first study topological phases of 2-dimensional periodic quantum systems, in absence of a spectral gap, like e.g. (multilayer) graphene. A topological invariant n_v in Z, baptized eigenspace vorticity, is attached to any intersection of the energy bands, and characterizes the local topology of the eigenprojectors around that intersection. With the help of explicit models, each associated to a value of n_v in Z, we are able to extract the decay at infinity of the single-band Wannier function w in mono- and bilayer graphene, obtaining |w(x)| <= const |x|^{-2} as |x| tends to infinity. Next, we investigate gapped periodic quantum systems, in presence of time-reversal symmetry. When the time-reversal operator Theta is of bosonic type, i.e. it satisfies Theta^2 = 1, we provide an explicit algorithm to construct a frame of smooth, periodic and time-reversal symmetric (quasi-)Bloch functions, or equivalently a frame of almost-exponentially localized, real-valued (composite) Wannier functions, in dimension d <= 3. In the case instead of a fermionic time-reversal operator, satisfying Theta^2 = -1, we show that the existence of such a Bloch frame is in general topologically obstructed in dimension d=2 and d=3. This obstruction is encoded in Z_2-valued topological invariants, which agree with the ones proposed in the solid state literature by Fu, Kane and Mele.}, keywords = {Geometric phases, graphene, topological insulators, Wannier functions, Bloch frames}, author = {Domenico Monaco} } @mastersthesis {2015, title = {Gibbs-Markov-Young Structures and Decay of Correlations}, year = {2015}, school = {SISSA}, abstract = {In this work we study mixing properties of discrete dynamical systems and related to them geometric structure. In the first chapter we show that the direct product of maps with Young towers admits a Young tower whose return times decay at a rate which is bounded above by the slowest of the rates of decay of the return times of the component maps. An application of this result, together with other results in the literature, yields various statistical properties for the direct product of various classes of systems, including Lorenz-like maps, multimodal maps, piecewise $C^2$ interval maps with critical points and singularities, H\'enon maps and partially hyperbolic systems. The second chapter is dedicated to the problem of decay of correlations for continuous observables. First we show that if the underlying system admits Young tower then the rate of decay of correlations for continuous observables can be estimated in terms of modulus of continuity and the decay rate of tail of Young tower. In the rest of the second chapter we study the relations between the rates of decay of correlations for smooth observables and continuous observables. We show that if the rates of decay of correlations is known for $C^r,$ observables ($r\ge 1$) then it is possible to obtain decay of correlations for continuous observables in terms of modulus of continuity.}, keywords = {Decay of Correlations, GMY-towers}, author = {Marks Ruziboev} } @article {2015, title = {Gli abachi: antichi strumenti precursori delle moderne macchine da calcolo}, year = {2015}, url = {http://hdl.handle.net/10077/10884}, author = {Giuliano Klun} } @article {2015, title = {Global well-posedness of the magnetic Hartree equation with non-Strichartz external fields}, number = {SISSA;07/2015/MATE}, year = {2015}, institution = {SISSA}, abstract = {We study the magnetic Hartree equation with external fields to which magnetic Strichartz estimates are not necessarily applicable. We characterise the appropriate notion of energy space and in such a space we prove the global well-posedness of the associated initial value problem by means of energy methods only.}, url = {http://urania.sissa.it/xmlui/handle/1963/34440}, author = {Alessandro Michelangeli} } @article {2015, title = {Hilbert schemes of points of OP1(-n) as quiver varieties}, year = {2015}, publisher = {arXiv:1504.02987 [math.AG]}, abstract = {Relying on a representation of framed torsion-free sheaves on Hirzebruch surfaces in terms of monads, we construct ADHM data for the Hilbert scheme of points of the total space of the line bundle $\mathcal O(-n)$ on $\mathbb P^1$. This ADHM description is then used to realize these Hilbert schemes as quiver varieties.}, url = {http://urania.sissa.it/xmlui/handle/1963/34487}, author = {Ugo Bruzzo} } @article {2015, title = {Homogenization problems in the Calculus of Variations: an overview}, number = {SISSA;13/2015/MATE}, year = {2015}, note = {DEDICATED TO PROF. ORLANDO LOPES}, institution = {SISSA}, abstract = {In this note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundamental theoretical tools, both classical and modern. We conclude by mentioning some open problems.}, url = {http://urania.sissa.it/xmlui/handle/1963/34455}, author = {Jose Matias and Marco Morandotti} } @mastersthesis {2015, title = {Integrability of Continuous Tangent Sub-bundles}, year = {2015}, school = {SISSA}, abstract = {In this thesis, the main aim is to study the integrability properties of continuous tangent sub-bundles, especially those that arise in the study of dynamical systems. After the introduction and examples part we start by studying integrability of such sub-bundles under different regularity and dynamical assumptions. Then we formulate a continuous version of the classical Frobenius theorem and state some applications to such bundles, to ODE and PDE. Finally we close of by stating some ongoing work related to interactions between integrability, sub-Riemannian geometry and contact geometry.}, keywords = {Dynamical Systems, Global Analysis, Frobenius Theorem, Integrability}, url = {http://urania.sissa.it/xmlui/handle/1963/34630}, author = {Sina T{\"u}reli} } @mastersthesis {2015, title = {Interaction functionals, Glimm approximations and Lagrangian structure of BV solutions for Hyperbolic Systems of Conservations Laws}, year = {2015}, school = {SISSA}, abstract = {This thesis is a contribution to the mathematical theory of Hyperbolic Conservation Laws. Three are the main results which we collect in this work. The first and the second result (denoted in the thesis by Theorem A and Theorem B respectively) deal with the following problem. The most comprehensive result about existence, uniqueness and stability of the solution to the Cauchy problem \begin{equation}\tag{$\mathcal C$} \label{E:abstract} \begin{cases} u_t + F(u)_x = 0, \\u(0, x) = \bar u(x), \end{cases} \end{equation} where $F: \R^N \to \R^N$ is strictly hyperbolic, $u = u(t,x) \in \R^N$, $t \geq 0$, $x \in \R$, $\TV(\bar u) \ll 1$, can be found in [Bianchini, Bressan 2005], where the well-posedness of \eqref{E:abstract} is proved by means of vanishing viscosity approximations. After the paper [Bianchini, Bressan 2005], however, it seemed worthwhile to develop a \emph{purely hyperbolic} theory (based, as in the genuinely nonlinear case, on Glimm or wavefront tracking approximations, and not on vanishing viscosity parabolic approximations) to prove existence, uniqueness and stability results. The reason of this interest can be mainly found in the fact that hyperbolic approximate solutions are much easier to study and to visualize than parabolic ones. Theorems A and B in this thesis are a contribution to this line of research. In particular, Theorem A proves an estimate on the change of the speed of the wavefronts present in a Glimm approximate solution when two of them interact; Theorem B proves the convergence of the Glimm approximate solutions to the weak admissible solution of \eqref{E:abstract} and provides also an estimate on the rate of convergence. Both theorems are proved in the most general setting when no assumption on $F$ is made except the strict hyperbolicity. The third result of the thesis, denoted by Theorem C, deals with the Lagrangian structure of the solution to \eqref{E:abstract}. The notion of Lagrangian flow is a well-established concept in the theory of the transport equation and in the study of some particular system of conservation laws, like the Euler equation. However, as far as we know, the general system of conservations laws \eqref{E:abstract} has never been studied from a Lagrangian point of view. This is exactly the subject of Theorem C, where a Lagrangian representation for the solution to the system \eqref{E:abstract} is explicitly constructed. The main reasons which led us to look for a Lagrangian representation of the solution of \eqref{E:abstract} are two: on one side, this Lagrangian representation provides the continuous counterpart in the exact solution of \eqref{E:abstract} to the well established theory of wavefront approximations; on the other side, it can lead to a deeper understanding of the behavior of the solutions in the general setting, when the characteristic field are not genuinely nonlinear or linearly degenerate.}, keywords = {Hyperbolic conservation laws}, url = {http://urania.sissa.it/xmlui/handle/1963/34542}, author = {Stefano Modena} } @article {DESIMONE2015254, title = {Liquid crystal elastomer strips as soft crawlers}, journal = {Journal of the Mechanics and Physics of Solids}, volume = {84}, year = {2015}, pages = {254 - 272}, abstract = {In this paper, we speculate on a possible application of Liquid Crystal Elastomers to the field of soft robotics. In particular, we study a concept for limbless locomotion that is amenable to miniaturisation. For this purpose, we formulate and solve the evolution equations for a strip of nematic elastomer, subject to directional frictional interactions with a flat solid substrate, and cyclically actuated by a spatially uniform, time-periodic stimulus (e.g., temperature change). The presence of frictional forces that are sensitive to the direction of sliding transforms reciprocal, {\textquoteleft}breathing-like{\textquoteright} deformations into directed forward motion. We derive formulas quantifying this motion in the case of distributed friction, by solving a differential inclusion for the displacement field. The simpler case of concentrated frictional interactions at the two ends of the strip is also solved, in order to provide a benchmark to compare the continuously distributed case with a finite-dimensional benchmark. We also provide explicit formulas for the axial force along the crawler body.

}, keywords = {Crawling motility, Directional surfaces, Frictional interactions, Liquid crystal elastomers, Soft biomimetic robots}, issn = {0022-5096}, doi = {https://doi.org/10.1016/j.jmps.2015.07.017}, url = {http://www.sciencedirect.com/science/article/pii/S0022509615300430}, author = {Antonio DeSimone and Paolo Gidoni and Giovanni Noselli} } @mastersthesis {2015, title = {Mathematical Models of Locomotion: Legged Crawling, Snake-like Motility, and Flagellar Swimming}, year = {2015}, school = {SISSA}, keywords = {Motility}, author = {Giancarlo Cicconofri} } @article {MR3305428, title = {Meromorphic differentials with imaginary periods on degenerating hyperelliptic curves}, journal = {Anal. Math. Phys.}, volume = {5}, number = {1}, year = {2015}, pages = {1{\textendash}22}, issn = {1664-2368}, doi = {10.1007/s13324-014-0088-7}, url = {http://dx.doi.org/10.1007/s13324-014-0088-7}, author = {Marco Bertola and Alexander Tovbis} } @article {BennerOhlbergerPateraRozzaSorensenUrban2015, title = {Model order reduction of parameterized systems ({MoRePaS}): Preface to the special issue of advances in computational mathematics}, journal = {Advances in Computational Mathematics}, volume = {41}, number = {5}, year = {2015}, pages = {955{\textendash}960}, doi = {10.1007/s10444-015-9443-y}, author = {Peter Benner and Mario Ohlberger and Anthony Patera and Gianluigi Rozza and Sorensen, D.C. and Karsten Urban} } @article {CICCONOFRI2015233, title = {Motility of a model bristle-bot: A theoretical analysis}, journal = {International Journal of Non-Linear Mechanics}, volume = {76}, year = {2015}, pages = {233 - 239}, abstract = {Bristle-bots are legged robots that can be easily made out of a toothbrush head and a small vibrating engine. Despite their simple appearance, the mechanism enabling them to propel themselves by exploiting friction with the substrate is far from trivial. Numerical experiments on a model bristle-bot have been able to reproduce such a mechanism revealing, in addition, the ability to switch direction of motion by varying the vibration frequency. This paper provides a detailed account of these phenomena through a fully analytical treatment of the model. The equations of motion are solved through an expansion in terms of a properly chosen small parameter. The convergence of the expansion is rigorously proven. In addition, the analysis delivers formulas for the average velocity of the robot and for the frequency at which the direction switch takes place. A quantitative description of the mechanism for the friction modulation underlying the motility of the bristle-bot is also provided.

}, keywords = {Bristle-robots, Crawling motility, Frictional interactions}, issn = {0020-7462}, doi = {https://doi.org/10.1016/j.ijnonlinmec.2014.12.010}, url = {http://www.sciencedirect.com/science/article/pii/S0020746215000025}, author = {Giancarlo Cicconofri and Antonio DeSimone} } @mastersthesis {2015, title = {Multidimensional Poisson Vertex Algebras and Poisson cohomology of Hamiltonian operators of hydrodynamic type}, year = {2015}, note = {161 pages}, school = {SISSA}, abstract = {The Poisson brackets of hydrodynamic type, also called Dubrovin-Novikov brackets, constitute the Hamiltonian structure of a broad class of evolutionary PDEs, that are ubiquitous in the theory of Integrable Systems, ranging from Hopf equation to the principal hierarchy of a Frobenius manifold. They can be regarded as an analogue of the classical Poisson brackets, defined on an infinite dimensional space of maps Σ {\textrightarrow} M between two manifolds. Our main problem is the study of Poisson-Lichnerowicz cohomology of such space when dim Σ > 1. We introduce the notion of multidimensional Poisson Vertex Algebras, generalizing and adapting the theory by A. Barakat, A. De Sole, and V. Kac [Poisson Vertex Algebras in the theory of Hamiltonian equations, 2009]; within this framework we explicitly compute the first nontrivial cohomology groups for an arbitrary Poisson bracket of hydrodynamic type, in the case dim Σ = dim M = 2. For the case of the so-called scalar brackets, namely the ones for which dim M = 1, we give a complete description on their Poisson{\textendash}Lichnerowicz cohomology. From this computations it follows, already in the particular case dim Σ = 2, that the cohomology is infinite dimensional.}, keywords = {Poisson Vertex Algebras, Poisson brackets, Hamiltonian operators, Integrable Systems}, author = {Matteo Casati} } @article {2015, title = {Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations}, journal = {Numerische Mathematik, (2015), 36 p. Article in Press}, number = {Numerische Mathematik;}, year = {2015}, publisher = {Springer}, abstract = {In this paper we develop and analyze a multilevel weighted reduced basis method for solving stochastic optimal control problems constrained by Stokes equations. We prove the analytic regularity of the optimal solution in the probability space under certain assumptions on the random input data. The finite element method and the stochastic collocation method are employed for the numerical approximation of the problem in the deterministic space and the probability space, respectively, resulting in many large-scale optimality systems to solve. In order to reduce the unaffordable computational effort, we propose a reduced basis method using a multilevel greedy algorithm in combination with isotropic and anisotropic sparse-grid techniques. A weighted a posteriori error bound highlights the contribution stemming from each method. Numerical tests on stochastic dimensions ranging from 10 to 100 demonstrate that our method is very efficient, especially for solving high-dimensional and large-scale optimization problems.}, doi = {10.1007/s00211-015-0743-4}, url = {http://urania.sissa.it/xmlui/handle/1963/34491}, author = {Gianluigi Rozza and Peng Chen and Alfio Quarteroni} } @article {2015, title = {Multiple positive solutions for a superlinear problem: a topological approach}, journal = {J. Differential Equations 259 (2015), 925{\textendash}963.}, number = {Journal of Differential Equations;volume 259; issue 3; pages 925-963;}, year = {2015}, note = {Work presented at the "Special Session 21" of the "10th AIMS Conference on Dynamical Systems, Differential Equations and Applications" (Madrid, July 7-11, 2014).}, publisher = {Elsevier}, abstract = {We study the multiplicity of positive solutions for a two-point boundary value problem associated to the nonlinear second order equation u{\textquoteright}{\textquoteright}+f(x,u)=0. We allow x ↦ f(x,s) to change its sign in order to cover the case of scalar equations with indefinite weight. Roughly speaking, our main assumptions require that f(x,s)/s is below λ_1 as s{\textrightarrow}0^+ and above λ_1 as s{\textrightarrow}+$\infty$. In particular, we can deal with the situation in which f(x,s) has a superlinear growth at zero and at infinity. We propose a new approach based on the topological degree which provides the multiplicity of solutions. Applications are given for u{\textquoteright}{\textquoteright} + a(x) g(u) = 0, where we prove the existence of 2^n-1 positive solutions when a(x) has n positive humps and a^-(x) is sufficiently large.

}, doi = {10.1016/j.jde.2015.02.032}, url = {http://urania.sissa.it/xmlui/handle/1963/35147}, author = {Guglielmo Feltrin and Fabio Zanolin} } @article {Bawane2015, title = {N=2 supersymmetric gauge theories on S^2xS^2 and Liouville Gravity}, journal = {Journal of High Energy Physics}, volume = {2015}, number = {7}, year = {2015}, month = {Jul}, pages = {54}, abstract = {We consider $\mathcal{N}=2$ supersymmetric gauge theories on four manifolds admitting an isometry. Generalized Killing spinor equations are derived from the consistency of supersymmetry algebrae and solved in the case of four manifolds admitting a $U(1)$ isometry. This is used to explicitly compute the supersymmetric path integral on $S^2 \times S^2$ via equivariant localization. The building blocks of the resulting partition function are shown to contain the three point functions and the conformal blocks of Liouville Gravity.

}, issn = {1029-8479}, doi = {10.1007/JHEP07(2015)054}, url = {https://doi.org/10.1007/JHEP07(2015)054}, author = {Aditya Bawane and Giulio Bonelli and Massimiliano Ronzani and Alessandro Tanzini} } @mastersthesis {2015, title = {Normal matrix models and orthogonal polynomials for a class of potentials with discrete rotational symmetries}, year = {2015}, school = {SISSA}, abstract = {In this thesis we are going to study normal random matrix models which generalize naturally the polynomially perturbed Ginibre ensamble, focusing in particular on their eigenvalue distribution and on the asymptotics of the associated orthogonal polynomials. \\ The main result we are going to present are the following: \begin{itemize} \item we describe the explicit derivation of the equilibrium measure for a class of potentials with discrete rotational symmetries, namely of the form \[V(z)=|z|^{2n}-t(z^{d}+\bar{z}^{d})\qquad n,d\in\mathbb{N},\ \ d\leq2n\ \ t>0 .\] \item We obtain the strong asymptotics for the orthogonal polynomials associated to the weight \[ e^{-NV(z)},\quad V(z)=|z|^{2s}-t(z^s+\bar{z}^{s}) \qquad z \in \mathbb{C},\;s\in \mathbb{N},\quad t>0,\] and we will show how the density of their zeroes is related to the eigenvalue distribution of the corresponding matrix model; \item We show how the conformal maps used to describe the support of the equilibrium measure for polynomial perturbation of the potential $V(z)=|z|^{2n}$ lead to a natural generalization of the concept of polynomial curves introduced in by Elbau. \end{itemize}}, keywords = {Mathematical Physics}, author = {Dario Merzi} } @article {2015, title = {A note on compactness properties of the singular Toda system}, journal = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. }, volume = {26}, number = {Rendiconti Lincei. Mathematics and Applications;vol. 26, Issue 3}, year = {2015}, pages = {299-307}, abstract = {In this note, we consider blow-up for solutions of the SU(3) Toda system on compact surfaces. In particular, we give a complete proof of a compactness result stated by Jost, Lin and Wang and we extend it to the case of singular systems. This is a necessary tool to find solutions through variational methods.

}, doi = {10.4171/RLM/708}, author = {Luca Battaglia and Gabriele Mancini} } @article {2015, title = {Onofri-Type Inequalities for Singular Liouville Equations}, year = {2015}, publisher = {Springer US}, abstract = {We study the blow-up behavior of minimizing sequences for the singular Moser{\textendash}Trudinger functional on compact surfaces. Assuming non-existence of minimum points, we give an estimate for the infimum value of the functional. This result can be applied to give sharp Onofri-type inequalities on the sphere in the presence of at most two singularities.

}, doi = {10.1007/s12220-015-9589-3}, author = {Gabriele Mancini} } @article {MR3342766, title = {The partition function of the extended $r$-reduced Kadomtsev-Petviashvili hierarchy}, journal = {J. Phys. A}, volume = {48}, number = {19}, year = {2015}, pages = {195205, 20}, issn = {1751-8113}, doi = {10.1088/1751-8113/48/19/195205}, url = {http://dx.doi.org/10.1088/1751-8113/48/19/195205}, author = {Marco Bertola and Di Yang} } @article {FONDA201573, title = {A permanence theorem for local dynamical systems}, journal = {Nonlinear Analysis: Theory, Methods \& Applications}, volume = {121}, year = {2015}, note = {Nonlinear Partial Differential Equations, in honor of Enzo Mitidieri for his 60th birthday}, pages = {73 - 81}, abstract = {We provide a necessary and sufficient condition for permanence related to a local dynamical system on a suitable topological space. We then present an illustrative application to a Lotka{\textendash}Volterra predator{\textendash}prey model with intraspecific competition.

}, keywords = {Lotka{\textendash}Volterra, permanence, Predator{\textendash}prey, Uniform persistence}, issn = {0362-546X}, doi = {https://doi.org/10.1016/j.na.2014.10.011}, url = {http://www.sciencedirect.com/science/article/pii/S0362546X14003332}, author = {Alessandro Fonda and Paolo Gidoni} } @article {2015, title = {The phototransduction machinery in the rod outer segment has a strong efficacy gradient}, number = {Proceedings of the National Academy of Sciences of the United States of America;Volume 112, issue 20; pp. E2715-E2724}, year = {2015}, note = {Open Access article}, publisher = {National Academy of Sciences}, doi = {10.1073/pnas.1423162112}, url = {http://urania.sissa.it/xmlui/handle/1963/35157}, author = {Monica Mazzolini and Giuseppe Facchetti and L. Andolfi and R. Proietti Zaccaria and S. Tuccio and J. Treud and Claudio Altafini and Enzo M. Di Fabrizio and Marco Lazzarino and G. Rapp and Vincent Torre} } @article {2015, title = {Poisson cohomology of scalar multidimensional Dubrovin-Novikov brackets}, year = {2015}, abstract = {We compute the Poisson cohomology of a scalar Poisson bracket of Dubrovin-Novikov type with D independent variables. We find that the second and third cohomology groups are generically non-vanishing in D>1. Hence, in contrast with the D=1 case, the deformation theory in the multivariable case is non-trivial.}, author = {Guido Carlet and Matteo Casati and Sergey Shadrin} } @mastersthesis {2015, title = {Principal circle bundles, Pimsner algebras and Gysin sequences}, year = {2015}, school = {SISSA}, abstract = {Principal circle bundles and Gysin sequences play a crucial role in mathematical physics, in particular in Chern-Simons theories and T-duality. This works focuses on the noncommutative topology of principal circle bundles: we investigate the connections between noncommutative principal circle bundles, Pimsner algebras and strongly graded algebras. At the C*-algebraic level, we start from a self-Morita equivalence bimodule E for a C*-algebra B which we think of as a non commutative line bundle over the {\textquoteleft}base space{\textquoteright} algebra B. The corresponding Pimsner algebra O_E, is then the total space algebra of an associated circle bundle. A natural six term exact sequence, an analogue of the Gysin sequence for circle bundles, relates the KK-theories of O_E and of the base space B. We illustrate several results with the examples of quantum weighted projective and lens spaces.}, author = {Francesca Arici} } @article {bianchini2015quadratic, title = {Quadratic Interaction Functional for General Systems of Conservation Laws}, journal = {Communications in Mathematical Physics}, volume = {338}, year = {2015}, pages = {1075{\textendash}1152}, abstract = {For the Glimm scheme approximation to the solution of the system of conservation laws in one space dimension with initial data u 0 with small total variation, we prove a quadratic (w.r.t. Tot. Var. ( u 0)) interaction estimate, which has been used in the literature for stability and convergence results. No assumptions on the structure of the flux f are made (apart from smoothness), and this estimate is the natural extension of the Glimm type interaction estimate for genuinely nonlinear systems. More precisely, we obtain the following results: a new analysis of the interaction estimates of simple waves;

}, doi = {10.1007/s00220-015-2372-2}, author = {Stefano Bianchini and Stefano Modena} } @article {2015, title = {Reduced basis approximation and a-posteriori error estimation for the coupled Stokes-Darcy system}, journal = {Advances in Computational Mathematics}, volume = {special issue for MoRePaS 2012}, year = {2015}, abstract = {The coupling of a free flow with a flow through porous media has many potential applications in several fields related with computational science and engineering, such as blood flows, environmental problems or food technologies. We present a reduced basis method for such coupled problems. The reduced basis method is a model order reduction method applied in the context of parametrized systems. Our approach is based on a heterogeneous domain decomposition formulation, namely the Stokes-Darcy problem. Thanks to an offline/online-decomposition, computational times can be drastically reduced. At the same time the induced error can be bounded by fast evaluable a-posteriori error bounds. In the offline-phase the proposed algorithms make use of the decomposed problem structure. Rigorous a-posteriori error bounds are developed, indicating the accuracy of certain lifting operators used in the offline-phase as well as the accuracy of the reduced coupled system. Also, a strategy separately bounding pressure and velocity errors is extended. Numerical experiments dealing with groundwater flow scenarios demonstrate the efficiency of the approach as well as the limitations regarding a-posteriori error estimation.

}, keywords = {Domain decomposition, Error estimation, Non-coercive problem, Porous medium equation, Reduced basis method, Stokes flow}, issn = {1019-7168}, doi = { 10.1007/s10444-014-9396-6}, author = {Immanuel Martini and Gianluigi Rozza and Bernard Haasdonk} } @article {PacciariniRozza2015, title = {Reduced basis approximation of parametrized advection-diffusion PDEs with high P{\'e}clet number}, journal = {Lecture Notes in Computational Science and Engineering}, volume = {103}, year = {2015}, pages = {419{\textendash}426}, abstract = {In this work we show some results about the reduced basis approximation of advection dominated parametrized problems, i.e. advection-diffusion problems with high P{\'e}clet number. These problems are of great importance in several engineering applications and it is well known that their numerical approximation can be affected by instability phenomena. In this work we compare two possible stabilization strategies in the framework of the reduced basis method, by showing numerical results obtained for a steady advection-diffusion problem.

}, doi = {10.1007/978-3-319-10705-9__41}, author = {Pacciarini, P. and Gianluigi Rozza} } @article {NegriManzoniRozza2015, title = {Reduced basis approximation of parametrized optimal flow control problems for the Stokes equations}, journal = {Computers and Mathematics with Applications}, volume = {69}, number = {4}, year = {2015}, pages = {319{\textendash}336}, abstract = {This paper extends the reduced basis method for the solution of parametrized optimal control problems presented in Negri et al. (2013) to the case of noncoercive (elliptic) equations, such as the Stokes equations. We discuss both the theoretical properties-with particular emphasis on the stability of the resulting double nested saddle-point problems and on aggregated error estimates-and the computational aspects of the method. Then, we apply it to solve a benchmark vorticity minimization problem for a parametrized bluff body immersed in a two or a three-dimensional flow through boundary control, demonstrating the effectivity of the methodology.

}, doi = {10.1016/j.camwa.2014.12.010}, author = {Federico Negri and Andrea Manzoni and Gianluigi Rozza} } @article {2015, title = {Reduced Basis Isogeometric Methods (RB-IGA) for the real-time simulation of potential flows about parametrized NACA airfoils}, journal = {Comput Methods Appl Mech Eng. 2015;284:1147{\textendash}1180}, number = {;284}, year = {2015}, abstract = {We present a Reduced Basis (RB) method based on Isogeometric Analysis (IGA) for the rapid and reliable evaluation of PDE systems characterized by complex geometrical features. At the current state of the art, this is the first case of coupling between RB and IGA methods. The construction of the RB method relies on an Isogeometric Boundary Element Method (IGA-BEM) as the high-fidelity technique, allowing a direct interface with Computer Aided Design (CAD) tools. A suitable Empirical Interpolation Method (EIM) ensures an efficient offline/online decomposition between the construction and the evaluation of the RB method. We consider the real-time simulation of potential flows past airfoils, parametrized with respect to the angle of attack and the NACA number identifying their shape, and we provide a validation of our methodology with respect to experimental data and reference numerical codes, showing in both cases a very good agreement.We present a Reduced Basis (RB) method based on Isogeometric Analysis (IGA) for the rapid and reliable evaluation of PDE systems characterized by complex geometrical features. At the current state of the art, this is the first case of coupling between RB and IGA methods. The construction of the RB method relies on an Isogeometric Boundary Element Method (IGA-BEM) as the high-fidelity technique, allowing a direct interface with Computer Aided Design (CAD) tools. A suitable Empirical Interpolation Method (EIM) ensures an efficient offline/online decomposition between the construction and the evaluation of the RB method. We consider the real-time simulation of potential flows past airfoils, parametrized with respect to the angle of attack and the NACA number identifying their shape, and we provide a validation of our methodology with respect to experimental data and reference numerical codes, showing in both cases a very good agreement.}, doi = {10.1016/j.cma.2014.11.037}, author = {Andrea Manzoni and Filippo Salmoiraghi and Luca Heltai} } @mastersthesis {2015, title = {The relaxed area of maps from the plane to the plane with a line discontinuity, and the role of semicartesian surfaces.}, year = {2015}, school = {SISSA}, abstract = {In this thesis we study the relaxation of the area functional w.r.t. the L^1 topology of a map from a bounded planar domain with values in the plane and jumping on a segment. We estimate from above the singular contribution of this functional due to the presence of the jump in terms of the infimum of the area among a suitable family of surfaces that we call semicartesian surfaces. In our analysis, we also introduce a different notion of area, namely the relaxation of the area w.r.t. a convergence stronger than the L^1 convergence, whose singular contribution is completely characterized in terms of suitable semicartesian area minimizing problems. We propose also some examples of maps for which the two notions of relaxation are different: these examples underline the highly non-local behaviour of the L^1-relaxation, and justify the introduction of the other functional. Some result about the existence of a semicartesian area-minimizing surface is also provided.}, keywords = {Area functional}, author = {Lucia Tealdi} } @article {2015, title = {Results on the minimization of the Dirichlet functional among semicartesian parametrizations}, year = {2015}, note = {The article is compsed of 18 pages and is recorded in PDF format}, abstract = {We start to investigate the existence of conformal minimizers for the Dirichlet functional in the setting of the so-called semicartesian parametrizations, adapting to this context some techniques used in solving the classical Plateau{\textquoteright}s problem. The final goal is to find area minimizing semicartesian parametrizations spanning a Jordan curve obtained as union of two graphs; this problem appeared in the study of the relaxed area functional for maps from the plane to the plane jumping on a line.

}, url = {http://urania.sissa.it/xmlui/handle/1963/34488}, author = {Lucia Tealdi and Giovanni Bellettini and Maurizio Paolini} } @article {2015, title = {Rigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires}, number = {SISSA;04/2015/MATE}, year = {2015}, institution = {SISSA}, abstract = {In the context of nanowire heterostructures we perform a discrete to continuum limit of the corresponding free energy by means of Γ-convergence techniques. Nearest neighbours are identified by employing the notions of Voronoi diagrams and Delaunay triangulations. The scaling of the nanowire is done in such a way that we perform not only a continuum limit but a dimension reduction simultaneously. The main part of the proof is a discrete geometric rigidity result that we announced in an earlier work and show here in detail for a variety of three-dimensional lattices. We perform the passage from discrete to continuum twice: once for a system that compensates a lattice mismatch between two parts of the heterogeneous nanowire without defects and once for a system that creates dislocations. It turns out that we can verify the experimentally observed fact that the nanowires show dislocations when the radius of the specimen is large}, url = {http://urania.sissa.it/xmlui/handle/1963/7494}, author = {Giuliano Lazzaroni and Mariapia Palombaro and Anja Schlomerkemper} } @article {2015, title = {Sch{\"o}dinger operators on half-line with shrinking potentials at the origin}, number = {SISSA;06/2015/MATE}, year = {2015}, institution = {SISSA}, abstract = {We discuss the general model of a Schr{\"o}dinger quantum particle constrained on a straight half-line with given self-adjoint boundary condition at the origin and an interaction potential supported around the origin. We study the limit when the range of the potential scales to zero and its magnitude blows up. We show that in the limit the dynamics is generated by a self-adjoint negative Laplacian on the half-line, with a possible preservation or modification of the boundary condition at the origin, depending on the magnitude of the scaling and of the strength of the potential.}, url = {http://urania.sissa.it/xmlui/handle/1963/34439}, author = {Gianfausto Dell{\textquoteright}Antonio and Alessandro Michelangeli} } @article {2015, title = {Semicartesian surfaces and the relaxed area of maps from the plane to the plane with a line discontinuity}, year = {2015}, note = {The preprint is compsed of 37 pages and is recorded in PDF format}, abstract = {We address the problem of estimating the area of the graph of a map u, defined on a bounded planar domain O and taking values in the plane, jumping on a segment J, either compactly contained in O or having both the end points on the boundary of O. We define the relaxation of the area functional w.r.t. a sort of uniform convergence, and we characterize it in terms of the infimum of the area among those surfaces in the space spanning the graphs of the traces of u on the two side of J and having what we have called a semicartesian structure. We exhibit examples showing that the relaxed area functional w.r.t the L^1 convergence may depend also on the values of u far from J, and on the relative position of J w.r.t. the boundary of O; these examples confirm the non-local behaviour of the L^1 relaxed area functional, and justify the interest in studying the relaxation w.r.t. a stronger convergence. We prove also that the L^1 relaxed area functional in non-subadditive for a rather class of maps.

}, url = {http://urania.sissa.it/xmlui/handle/1963/34483}, author = {Lucia Tealdi and Giovanni Bellettini and Maurizio Paolini} } @mastersthesis {2015, title = {Sharp Inequalities and Blow-up Analysis for Singular Moser-Trudinger Embeddings.}, year = {2015}, school = {SISSA}, abstract = {We investigate existence of solutions for a singular Liouville equation on S^2 and prove sharp Onofri-type inequalities for a Moser-Trudinger functional in the presence of singular potentials. As a consequence we obtain existence of extremal functions for the Moser-Trudinger embedding on compact surfaces with conical singularities. Finally we study the blow-up behavior for sequences of solutions Liouville-type systems and prove a compactness condition which plays an important role in the variational analysis of Toda systems.}, keywords = {Moser-Trudinger}, author = {Gabriele Mancini} } @article {2015, title = {Singular Liouville Equations on S^2: Sharp Inequalities and Existence Results}, year = {2015}, abstract = {We prove a sharp Onofri-type inequality and non-existence of extremals for a Moser-Tudinger functional on S^2 in the presence of potentials having positive order singularities. We also investigate the existence of critical points and give some sufficient conditions under symmetry or nondegeneracy assumptions.

}, url = {http://urania.sissa.it/xmlui/handle/1963/34489}, author = {Gabriele Mancini} } @mastersthesis {2015, title = {Some results on anisotropic mean curvature and other phase-transition problems}, year = {2015}, school = {SISSA}, abstract = {The present thesis is divided into three parts. In the first part, we analyze a suitable regularization {\textemdash} which we call nonlinear multidomain model {\textemdash} of the motion of a hypersurface under smooth anisotropic mean curvature flow. The second part of the thesis deals with crystalline mean curvature of facets of a solid set of R^3 . Finally, in the third part we study a phase-transition model for Plateau{\textquoteright}s type problems based on the theory of coverings and of BV functions.}, keywords = {Anisotropic mean curvature}, author = {Stefano Amato} } @article {2015, title = {Stability of closed gaps for the alternating Kronig-Penney Hamiltonian}, number = {SISSA;16/2015/MATE}, year = {2015}, institution = {SISSA}, abstract = {We consider the Kronig-Penney model for a quantum crystal with equispaced periodic delta-interactions of alternating strength. For this model all spectral gaps at the centre of the Brillouin zone are known to vanish, although so far this noticeable property has only been proved through a very delicate analysis of the discriminant of the corresponding ODE and the associated monodromy matrix. We provide a new, alternative proof by showing that this model can be approximated, in the norm resolvent sense, by a model of regular periodic interactions with finite range for which all gaps at the centre of the Brillouin zone are still vanishing. In particular this shows that the vanishing gap property is stable in the sense that it is present also for the "physical" approximants and is not only a feature of the idealised model of zero-range interactions.}, url = {http://urania.sissa.it/xmlui/handle/1963/34460}, author = {Alessandro Michelangeli and Domenico Monaco} } @article {2015, title = {Stability of the (2+2)-fermionic system with zero-range interaction}, number = {SISSA;29/2015/MATE}, year = {2015}, note = {This SISSA preprint has 17 pages and recorded in PDF format}, abstract = {We introduce a 3D model, and we study its stability, consisting of two distinct pairs of identical fermions coupled with a two-body interaction between fermions of different species, whose effective range is essentially zero (a so called (2+2)-fermionic system with zero-range interaction). The interaction is modelled by implementing the the celebrated (and ubiquitous, in the literature of this field) Bethe-Peierls contact condition with given two-body scattering length within the Krein-Visik-Birman theory of extensions of semi-bounded symmetric operators, in order to make the Hamiltonian a well-defined (self-adjoint) physical observable. After deriving the expression for the associated energy quadratic form, we show analytically and numerically that the energy of the model is bounded below, thus describing a stable system.}, url = {http://urania.sissa.it/xmlui/handle/1963/34474}, author = {Alessandro Michelangeli and Paul Pfeiffer} } @article {2013, title = {Stable regular critical points of the Mumford-Shah functional are local minimizers}, journal = {Annales de l{\textquoteright}Institut Henri Poincare (C) Non Linear Analysis}, volume = {32}, number = {SISSA preprint;SISSA 33/2013/MATE}, year = {2015}, pages = {533-570}, publisher = {SISSA}, chapter = {533}, abstract = {In this paper it is shown that any regular critical point of the Mumford{\textendash}Shah functional, with positive definite second variation, is an isolated local minimizer with respect to competitors which are sufficiently close in the $L^1$

-topology. A global\ minimality\ result in small tubular neighborhoods of the\ discontinuity\ set is also established.

We examine the problem of snake-like locomotion by studying a system consisting of a planar inextensible elastic rod with adjustable spontaneous curvature, which provides an internal actuation mechanism that mimics muscular action in a snake. Using a Cosserat model, we derive the equations of motion in two special cases: one in which the rod can only move along a prescribed curve, and one in which the rod is constrained to slide longitudinally without slipping laterally, but the path is not fixed a priori (free-path case). The second setting is inspired by undulatory locomotion of snakes on flat surfaces. The presence of constraints leads in both cases to non-standard boundary conditions that allow us to close and solve the equations of motion. The kinematics and dynamics of the system can be recovered from a one-dimensional equation, without any restrictive assumption on the followed trajectory or the actuation. We derive explicit formulae highlighting the role of spontaneous curvature in providing the driving force (and the steering, in the free-path case) needed for locomotion. We also provide analytical solutions for a special class of serpentine motions, which enable us to discuss the connection between observed trajectories, internal actuation and forces exchanged with the environment.

}, doi = {10.1098/rspa.2015.0054}, url = {https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2015.0054}, author = {Giancarlo Cicconofri and Antonio DeSimone} } @article {2015, title = {Supremizer stabilization of POD-Galerkin approximation of parametrized Navier-Stokes equations}, number = {International Journal for Numerical Methods in Engineering;Volume 102, issue 5; pp.1136-1161;}, year = {2015}, publisher = {Wiley}, abstract = {In this work, we present a stable proper orthogonal decomposition{\textendash}Galerkin approximation for parametrized steady incompressible Navier{\textendash}Stokes equations with low Reynolds number.}, doi = {10.1002/nme.4772}, url = {http://urania.sissa.it/xmlui/handle/1963/34701}, author = {Francesco Ballarin and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza} } @article {2015, title = {Symmetry and localization in periodic crystals: triviality of Bloch bundles with a fermionic time-reversal symmetry}, journal = {Acta Applicandae Mathematicae, vol. 137, Issue 1, 2015, pages: 185-203}, year = {2015}, note = {The article is composed of 23 pages and recorded in PDF format}, publisher = {Springer}, abstract = {We describe some applications of group- and bundle-theoretic methods in solid state physics, showing how symmetries lead to a proof of the localization of electrons in gapped crystalline solids, as e.g. insulators and semiconductors. We shortly review the Bloch-Floquet decomposition of periodic operators, and the related concepts of Bloch frames and composite Wannier functions. We show that the latter are almost-exponentially localized if and only if there exists a smooth periodic Bloch frame, and that the obstruction to the latter condition is the triviality of a Hermitian vector bundle, called the Bloch bundle. The r{\^o}le of additional Z_2-symmetries, as time-reversal and space-reflection symmetry, is discussed, showing how time-reversal symmetry implies the triviality of the Bloch bundle, both in the bosonic and in the fermionic case. Moreover, the same Z_2-symmetry allows to define a finer notion of isomorphism and, consequently, to define new topological invariants, which agree with the indices introduced by Fu, Kane and Mele in the context of topological insulators.

}, doi = {10.1007/s10440-014-9995-8}, url = {http://urania.sissa.it/xmlui/handle/1963/34468}, author = {Domenico Monaco and Gianluca Panati} } @article {2015, title = {Three-sphere low-Reynolds-number swimmer with a passive elastic arm}, number = {European Physical Journal E; Volume 38; Issue 5; Article number 42}, year = {2015}, publisher = {Springer}, abstract = {One of the simplest model swimmers at low Reynolds number is the three-sphere swimmer by Najafi and Golestanian. It consists of three spheres connected by two rods which change their lengths periodically in non-reciprocal fashion. Here we investigate a variant of this model in which one rod is periodically actuated while the other is replaced by an elastic spring. We show that the competition between the elastic restoring force and the hydrodynamic drag produces a delay in the response of the passive elastic arm with respect to the active one. This leads to non-reciprocal shape changes and self-propulsion. After formulating the equations of motion, we study their solutions qualitatively and numerically. The leading-order term of the solution is computed analytically. We then address questions of optimization with respect to both actuation frequency and swimmer{\textquoteright}s geometry. Our results can provide valuable conceptual guidance in the engineering of robotic microswimmers.}, doi = {10.1140/epje/i2015-15042-3}, url = {http://urania.sissa.it/xmlui/handle/1963/34530}, author = {Alessandro Montino and Antonio DeSimone} } @article {jevnikar2015topological, title = {A topological join construction and the Toda system on compact surfaces of arbitrary genus}, journal = {Analysis \& PDE}, volume = {8}, number = {8}, year = {2015}, pages = {1963{\textendash}2027}, publisher = {Mathematical Sciences Publishers}, doi = {10.2140/apde.2015.8.1963}, author = {Aleks Jevnikar and Kallel, Sadok and Andrea Malchiodi} } @article {2015, title = {Translation and adaptation of Birman{\textquoteright}s paper "On the theory of self-adjoint extensions of positive definite operators" (1956)}, number = {SISSA;08/2015/MATE}, year = {2015}, institution = {SISSA}, abstract = {This is an accurate translation from Russian and adaptation to the modern mathematical jargon of a classical paper by M. Sh. Birman published in 1956, which is still today central in the theory of self-adjoint extensions of semi-bounded operators, and for which yet no English version was available so far.}, url = {http://urania.sissa.it/xmlui/handle/1963/34443}, author = {Mikhail Khotyakov and Alessandro Michelangeli} } @article {Bertola-Bothner-MeijerG, title = {Universality Conjecture and Results for a Model of Several Coupled Positive-Definite Matrices}, journal = {Commun. Math. Phys.}, volume = {337}, number = {3}, year = {2015}, month = {08}, pages = {1077{\textendash}1141}, doi = {10.1007/s00220-015-2327-7}, url = {http://link.springer.com/article/10.1007/s00220-015-2327-7}, author = {Marco Bertola and Thomas Bothner} } @mastersthesis {2015, title = {Variational aspects of Liouville equations and systems}, year = {2015}, note = {The PHD thesis is composed of 112 pages and is recorded in PDF format}, school = {SISSA}, keywords = {Toda system}, author = {Aleks Jevnikar} } @mastersthesis {2015, title = {Variational aspects of singular Liouville systems}, year = {2015}, school = {SISSA}, abstract = {I studied singular Liouville systems on compact surfaces from a variational point of view. I gave sufficient and necessary conditions for the existence of globally minimizing solutions, then I found min-max solutions for some particular systems. Finally, I also gave some non-existence results.}, keywords = {Variational methods, Liouville systems, Moser-Trudinger inequalities, min-max methods}, author = {Luca Battaglia} } @mastersthesis {2015, title = {Volume variation and heat kernel for affine control problems}, year = {2015}, school = {SISSA}, abstract = {In this thesis we study two main problems. The first one is the small-time heat kernel expansion on the diagonal for second order hypoelliptic opeartors. We consider operators that can depend on a drift field and that satisfy only the weak H{\"o}rmander condition. In a first work we use perturbation techniques to determine the exact order of decay of the heat kernel, that depends on the Lie algebra generated by the fields involved in the hypoelliptic operator. We generalize in particular some results already obtained in the sub-Riemannian setting. In a second work we consider a model class of hypoelliptic operators and we characterize geometrically all the coefficients in the on-the diagonal asymptotics at the equilibrium points of the drift field. The class of operators that we consider contains the linear hypoelliptic operators with constant second order part on the Euclidean space. We describe the coefficients in terms only of the divergence of the drift field and of curvature-like invariants, related to the minimal cost of geodesics of the associated optimal control problem. In the second part of the thesis we consider the variation of a smooth volume along a geodesic. The structure of the manifold is induced by a quadratic Hamiltonian and the geodesic in described as the projection of the Hamiltonian flow. We find an expansion similar to the classical Riemannian one. It depends on the curvature operator associated to the Hamiltonian, on the symbol of the geodesic and on a new metric-measure invariant determined by the symbol of the geodesic and by the given volume.}, keywords = {Heat kernel asymptotics}, author = {Elisa Paoli} } @article {2015, title = {The wave equation on domains with cracks growing on a prescribed path: existence, uniqueness, and continuous dependence on the data}, number = {SISSA;47/2015/MATE}, year = {2015}, abstract = {Given a bounded open set $\Omega \subset \mathbb R^d$ with Lipschitz boundary and an increasing family $\Gamma_t$, $t\in [0,T]$, of closed subsets of $\Omega$, we analyze the scalar wave equation $\ddot{u} - div (A \nabla u) = f$ in the time varying cracked domains $\Omega\setminus\Gamma_t$. Here we assume that the sets $\Gamma_t$ are contained into a prescribed $(d-1)$-manifold of class $C^2$. Our approach relies on a change of variables: recasting the problem on the reference configuration $\Omega\setminus \Gamma_0$, we are led to consider a hyperbolic problem of the form $\ddot{v} - div (B\nabla v) + a \cdot \nabla v - 2 b \cdot \nabla \dot{v} = g$ in $\Omega \setminus \Gamma_0$. Under suitable assumptions on the regularity of the change of variables that transforms $\Omega\setminus \Gamma_t$ into $\Omega\setminus \Gamma_0$, we prove existence and uniqueness of weak solutions for both formulations. Moreover, we provide an energy equality, which gives, as a by-product, the continuous dependence of the solutions with respect to the cracks.}, url = {http://urania.sissa.it/xmlui/handle/1963/34629}, author = {Gianni Dal Maso and Ilaria Lucardesi} } @article {2014, title = {An Abstract Nash{\textendash}Moser Theorem and Quasi-Periodic Solutions for NLW and NLS on Compact Lie Groups and Homogeneous Manifolds}, number = {Communications in mathematical physics;volume 334; issue 3; pages 1413-1454;}, year = {2014}, publisher = {Springer}, abstract = {We prove an abstract implicit function theorem with parameters for smooth operators defined on scales of sequence spaces, modeled for the search of quasi-periodic solutions of PDEs. The tame estimates required for the inverse linearised operators at each step of the iterative scheme are deduced via a multiscale inductive argument. The Cantor-like set of parameters where the solution exists is defined in a non inductive way. This formulation completely decouples the iterative scheme from the measure theoretical analysis of the parameters where the small divisors non-resonance conditions are verified. As an application, we deduce the existence of quasi-periodic solutions for forced NLW and NLS equations on any compact Lie group or manifold which is homogeneous with respect to a compact Lie group, extending previous results valid only for tori. A basic tool of harmonic analysis is the highest weight theory for the irreducible representations of compact Lie groups.}, doi = {10.1007/s00220-014-2128-4}, url = {http://urania.sissa.it/xmlui/handle/1963/34651}, author = {Massimiliano Berti and Livia Corsi and Michela Procesi} } @article {2014, title = {Achieving unanimous opinions in signed social networks}, number = {2014 European Control Conference;article number 6862161; pages 184-189;}, year = {2014}, publisher = {Institute of Electrical and Electronics Engineers Inc.}, abstract = {Being able to predict the outcome of an opinion forming process is an important problem in social network theory. However, even for linear dynamics, this becomes a difficult task as soon as non-cooperative interactions are taken into account. Such interactions are naturally modeled as negative weights on the adjacency matrix of the social network. In this paper we show how the Perron-Frobenius theorem can be used for this task also beyond its standard formulation for cooperative systems. In particular we show how it is possible to associate the achievement of unanimous opinions with the existence of invariant cones properly contained in the positive orthant. These cases correspond to signed adjacency matrices having the eventual positivity property, i.e., such that in sufficiently high powers all negative entries have disappeared. More generally, we show how for social networks the achievement of a, possibily non-unanimous, opinion can be associated to the existence of an invariant cone fully contained in one of the orthants of n.}, doi = {10.1109/ECC.2014.6862161}, url = {http://urania.sissa.it/xmlui/handle/1963/34935}, author = {Claudio Altafini and Gabriele Lini} } @article {2014, title = {Adler-Gelfand-Dickey approach to classical W-algebras within the theory of Poisson vertex algebras}, number = {arXiv:1401.2082}, year = {2014}, note = {45 pages}, publisher = {SISSA}, abstract = {We put the Adler-Gelfand-Dickey approach to classical W-algebras in the framework of Poisson vertex algebras. We show how to recover the bi-Poisson structure of the KP hierarchy, together with its generalizations and reduction to the N-th KdV hierarchy, using the formal distribution calculus and the lambda-bracket formalism. We apply the Lenard-Magri scheme to prove integrability of the corresponding hierarchies. We also give a simple proof of a theorem of Kupershmidt and Wilson in this framework. Based on this approach, we generalize all these results to the matrix case. In particular, we find (non-local) bi-Poisson structures of the matrix KP and the matrix N-th KdV hierarchies, and we prove integrability of the N-th matrix KdV hierarchy.}, url = {http://hdl.handle.net/1963/7242}, author = {Alberto De Sole and Victor G. Kac and Daniele Valeri} } @article {2014, title = {Approximate Hermitian{\textendash}Yang{\textendash}Mills structures on semistable principal Higgs bundles}, number = {Annals of global analysis and geometry;volume 47; issue 1; pp 1-11}, year = {2014}, publisher = {Springer}, abstract = {We generalize the Hitchin-Kobayashi correspondence between semistability and the existence of approximate Hermitian-Yang-Mills structures to the case of principal Higgs bundles. We prove that a principal Higgs bundle on a compact Kaehler manifold, with structure group a connected linear algebraic reductive group, is semistable if and only if it admits an approximate Hermitian-Yang-Mills structure.}, doi = {10.1007/s10455-014-9433-1}, url = {http://urania.sissa.it/xmlui/handle/1963/34645}, author = {Ugo Bruzzo and Beatriz Grana-Otero} } @article {2014, title = {Approximate Hitchin-Kobayashi correspondence for Higgs G-bundles}, number = {International Journal of Geometric Methods in Modern Physics;volume 11; issue 7; article number 1460015;}, year = {2014}, publisher = {World Scientific Publishing}, abstract = {We announce a result about the extension of the Hitchin-Kobayashi correspondence to principal Higgs bundles. A principal Higgs bundle on a compact K{\"a}hler manifold, with structure group a connected linear algebraic reductive group, is semistable if and only if it admits an approximate Hermitian-Yang-Mills structure.}, doi = {10.1142/S0219887814600159}, url = {http://urania.sissa.it/xmlui/handle/1963/35095}, author = {Ugo Bruzzo and Beatriz Gra{\~n}a Otero} } @article {2014, title = {Buckling dynamics of a solvent-stimulated stretched elastomeric sheet}, number = {Soft Matter;volume 10; issue 16; pages 2800-2804;}, year = {2014}, publisher = {Royal Society of Chemistry}, abstract = {When stretched uniaxially, a thin elastic sheet may exhibit buckling. The occurrence of buckling depends on the geometrical properties of the sheet and the magnitude of the applied strain. Here we show that an elastomeric sheet initially stable under uniaxial stretching can destabilize when exposed to a solvent that swells the elastomer. We demonstrate experimentally and computationally that the features of the buckling pattern depend on the magnitude of stretching, and this observation offers a new way for controlling the shape of a swollen homogeneous thin sheet.}, doi = {10.1039/c3sm52941j}, url = {http://urania.sissa.it/xmlui/handle/1963/34967}, author = {Alessandro Lucantonio and Matthieu Roch{\'e} and Paola Nardinocchi and Howard A. Stone} } @article {MR3162486, title = {Cauchy-Laguerre two-matrix model and the Meijer-G random point field}, journal = {Comm. Math. Phys.}, volume = {326}, number = {1}, year = {2014}, pages = {111{\textendash}144}, issn = {0010-3616}, doi = {10.1007/s00220-013-1833-8}, url = {http://dx.doi.org/10.1007/s00220-013-1833-8}, author = {Marco Bertola and Gekhtman, M. and Szmigielski, J.} } @article {2013, title = {Classical W-algebras and generalized Drinfeld-Sokolov hierarchies for minimal and short nilpotents}, journal = {Communications in Mathematical Physics 331, nr. 2 (2014) 623-676}, number = {arXiv:1306.1684;}, year = {2014}, note = {46 pages}, publisher = {SISSA}, abstract = {We derive explicit formulas for lambda-brackets of the affine classical W-algebras attached to the minimal and short nilpotent elements of any simple Lie algebra g. This is used to compute explicitly the first non-trivial PDE of the corresponding intgerable generalized Drinfeld-Sokolov hierarchies. It turns out that a reduction of the equation corresponding to a short nilpotent is Svinolupov{\textquoteright}s equation attached to a simple Jordan algebra, while a reduction of the equation corresponding to a minimal nilpotent is an integrable Hamiltonian equation on 2h-3 functions, where h is the dual Coxeter number of g. In the case when g is sl_2 both these equations coincide with the KdV equation. In the case when g is not of type C_n, we associate to the minimal nilpotent element of g yet another generalized Drinfeld-Sokolov hierarchy.}, doi = {10.1007/s00220-014-2049-2}, url = {http://hdl.handle.net/1963/6979}, author = {Alberto De Sole and Victor G. Kac and Daniele Valeri} } @article {2014, title = {Comparison between reduced basis and stochastic collocation methods for elliptic problems}, number = {Journal of scientific computing;volume 59; issue 1; pages 187-216;}, year = {2014}, publisher = {Springer}, abstract = {The stochastic collocation method (Babu{\v s}ka et al. in SIAM J Numer Anal 45(3):1005-1034, 2007; Nobile et al. in SIAM J Numer Anal 46(5):2411-2442, 2008a; SIAM J Numer Anal 46(5):2309-2345, 2008b; Xiu and Hesthaven in SIAM J Sci Comput 27(3):1118-1139, 2005) has recently been applied to stochastic problems that can be transformed into parametric systems. Meanwhile, the reduced basis method (Maday et al. in Comptes Rendus Mathematique 335(3):289-294, 2002; Patera and Rozza in Reduced basis approximation and a posteriori error estimation for parametrized partial differential equations Version 1.0. Copyright MIT, http://augustine.mit.edu, 2007; Rozza et al. in Arch Comput Methods Eng 15(3):229-275, 2008), primarily developed for solving parametric systems, has been recently used to deal with stochastic problems (Boyaval et al. in Comput Methods Appl Mech Eng 198(41-44):3187-3206, 2009; Arch Comput Methods Eng 17:435-454, 2010). In this work, we aim at comparing the performance of the two methods when applied to the solution of linear stochastic elliptic problems. Two important comparison criteria are considered: (1), convergence results of the approximation error; (2), computational costs for both offline construction and online evaluation. Numerical experiments are performed for problems from low dimensions O (1) to moderate dimensions O (10) and to high dimensions O (100). The main result stemming from our comparison is that the reduced basis method converges better in theory and faster in practice than the stochastic collocation method for smooth problems, and is more suitable for large scale and high dimensional stochastic problems when considering computational costs.}, doi = {10.1007/s10915-013-9764-2}, url = {http://urania.sissa.it/xmlui/handle/1963/34727}, author = {Peng Chen and Alfio Quarteroni and Gianluigi Rozza} } @article {2014, title = {Comparison of a Modal Method and a Proper Orthogonal Decomposition approach for multi-group time-dependent reactor spatial kinetics}, journal = {Annals of Nuclear Energy}, volume = {71}, number = {Annals of Nuclear Energy;volume 71; pages 217-229;}, year = {2014}, month = {09/2014}, pages = {229}, publisher = {Elsevier}, chapter = {217}, abstract = {In this paper, two modelling approaches based on a Modal Method (MM) and on the Proper Orthogonal Decomposition (POD) technique, for developing a control-oriented model of nuclear reactor spatial kinetics, are presented and compared. Both these methods allow developing neutronics description by means of a set of ordinary differential equations. The comparison of the outcomes provided by the two approaches focuses on the capability of evaluating the reactivity and the neutron flux shape in different reactor configurations, with reference to a TRIGA Mark II reactor. The results given by the POD-based approach are higher-fidelity with respect to the reference solution than those computed according to the MM-based approach, in particular when the perturbation concerns a reduced region of the core. If the perturbation is homogeneous throughout the core, the two approaches allow obtaining comparable accuracy results on the quantities of interest. As far as the computational burden is concerned, the POD approach ensures a better efficiency rather than direct Modal Method, thanks to the ability of performing a longer computation in the preprocessing that leads to a faster evaluation during the on-line phase.

}, doi = {10.1016/j.anucene.2014.03.043}, url = {http://urania.sissa.it/xmlui/handle/1963/35039}, author = {Alberto Sartori and Davide Baroli and Antonio Cammi and Davide Chiesa and Lelio Luzzi and Roberto R. Ponciroli and Ezio Previtali and Marco E. Ricotti and Gianluigi Rozza and Monica Sisti} } @article {2014, title = {Conformal invariants from nodal sets. I. negative eigenvalues and curvature prescription}, number = {International Mathematics Research Notices;volume 2014; issue 9; pages 2356-2400;}, year = {2014}, publisher = {Oxford University Press}, abstract = {In this paper, we study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators; more specifically, the Graham, Jenne, Mason, and Sparling (GJMS) operators, which include the Yamabe and Paneitz operators. We give several applications to curvature prescription problems. We establish a version in conformal geometry of Courant{\textquoteright}s Nodal Domain Theorem. We also show that on any manifold of dimension n>=3, there exist many metrics for which our invariants are nontrivial. We prove that the Yamabe operator can have an arbitrarily large number of negative eigenvalues on any manifold of dimension n>=3. We obtain similar results for some higher order GJMS operators on some Einstein and Heisenberg manifolds. We describe the invariants arising from the Yamabe and Paneitz operators associated to left-invariant metrics on Heisenberg manifolds. Finally, in Appendix, the second named author and Andrea Malchiodi study the Q-curvature prescription problems for noncritical Q-curvatures.}, doi = {10.1093/imrn/rns295}, url = {http://urania.sissa.it/xmlui/handle/1963/35128}, author = {Rod R. Gover and Yaiza Canzani and Dmitry Jakobson and Rapha{\"e}l Ponge and Andrea Malchiodi} } @article {2013, title = {On conjugate times of LQ optimal control problems}, number = {Journal of Dynamical and Control Systems}, year = {2014}, note = {14 pages, 1 figure}, publisher = {Springer}, abstract = {Motivated by the study of linear quadratic optimal control problems, we consider a dynamical system with a constant, quadratic Hamiltonian, and we characterize the number of conjugate times in terms of the spectrum of the Hamiltonian vector field $\vec{H}$. We prove the following dichotomy: the number of conjugate times is identically zero or grows to infinity. The latter case occurs if and only if $\vec{H}$ has at least one Jordan block of odd dimension corresponding to a purely imaginary eigenvalue. As a byproduct, we obtain bounds from below on the number of conjugate times contained in an interval in terms of the spectrum of $\vec{H}$.}, keywords = {Optimal control, Lagrange Grassmannian, Conjugate point}, doi = {10.1007/s10883-014-9251-6}, url = {http://hdl.handle.net/1963/7227}, author = {Andrei A. Agrachev and Luca Rizzi and Pavel Silveira} } @article {2014, title = {A correction and an extension of Stampacchia{\textquoteright}s work on the geometric BVP}, number = {Advanced Nonlinear Studies;volume 14; issue 4; pages 813-837;}, year = {2014}, publisher = {Advanced Nonlinear Studies}, abstract = {G. Stampacchia introduced the geometric boundary value problem for ODEs in his doctoral thesis and published four papers related to it. Here we point out that the proof of his last theorem on the subject is incorrect and we provide a substitute for it as well as a generalizations of some of his earlier results.}, url = {http://urania.sissa.it/xmlui/handle/1963/35023}, author = {Giovanni Vidossich} } @article {GIDONI201465, title = {Crawling on directional surfaces}, journal = {International Journal of Non-Linear Mechanics}, volume = {61}, year = {2014}, pages = {65 - 73}, abstract = {In this paper we study crawling locomotion based on directional frictional interactions, namely, frictional forces that are sensitive to the sign of the sliding velocity. Surface interactions of this type are common in biology, where they arise from the presence of inclined hairs or scales at the crawler/substrate interface, leading to low resistance when sliding {\textquoteleft}along the grain{\textquoteright}, and high resistance when sliding {\textquoteleft}against the grain{\textquoteright}. This asymmetry can be exploited for locomotion, in a way analogous to what is done in cross-country skiing (classic style, diagonal stride). We focus on a model system, namely, a continuous one-dimensional crawler and provide a detailed study of the motion resulting from several strategies of shape change. In particular, we provide explicit formulae for the displacements attainable with reciprocal extensions and contractions (breathing), or through the propagation of extension or contraction waves. We believe that our results will prove particularly helpful for the study of biological crawling motility and for the design of bio-mimetic crawling robots.

}, keywords = {Bio-mimetic micro-robots, Cell migration, Crawling motility, Directional surfaces, Self-propulsion}, issn = {0020-7462}, doi = {https://doi.org/10.1016/j.ijnonlinmec.2014.01.012}, url = {http://www.sciencedirect.com/science/article/pii/S0020746214000213}, author = {Paolo Gidoni and Giovanni Noselli and Antonio DeSimone} } @article {2012, title = {Critical points of the Moser-Trudinger functional on a disk}, number = {Journal of the European Mathematical Society}, year = {2014}, note = {16 pages}, publisher = {European Mathematical Society}, abstract = {On the 2-dimensional unit disk $B_1$ we study the Moser-Trudinger functional $$E(u)=\int_{B_1}(e^{u^2}-1)dx, u\in H^1_0(B_1)$$ and its restrictions to $M_\Lambda:=\{u \in H^1_0(B_1):\|u\|^2_{H^1_0}=\Lambda\}$ for $\Lambda>0$. We prove that if a sequence $u_k$ of positive critical points of $E|_{M_{\Lambda_k}}$ (for some $\Lambda_k>0$) blows up as $k\to\infty$, then $\Lambda_k\to 4\pi$, and $u_k\to 0$ weakly in $H^1_0(B_1)$ and strongly in $C^1_{\loc}(\bar B_1\setminus\{0\})$. Using this we also prove that when $\Lambda$ is large enough, then $E|_{M_\Lambda}$ has no positive critical point, complementing previous existence results by Carleson-Chang, M. Struwe and Lamm-Robert-Struwe.}, doi = {10.4171/JEMS/450}, url = {http://hdl.handle.net/1963/6560}, author = {Andrea Malchiodi and Luca Martinazzi} } @mastersthesis {2014, title = {The curvature of optimal control problems with applications to sub-Riemannian geometry}, year = {2014}, note = {The PhD thesis is composed of 211 pages and is recorded in PDF format}, school = {SISSA}, abstract = {Optimal control theory is an extension of the calculus of variations, and deals with the optimal behaviour of a system under a very general class of constraints. This field has been pioneered by the group of mathematicians led by Lev Pontryagin in the second half of the 50s and nowadays has countless applications to the real worlds (robotics, trains, aerospace, models for human behaviour, human vision, image reconstruction, quantum control, motion of self-propulsed micro-organism). In this thesis we introduce a novel definition of curvature for an optimal control problem. In particular it works for any sub-Riemannian and sub-Finsler structure. Related problems, such as comparison theorems for sub-Riemannian manifolds, LQ optimal control problem and Popp{\textquoteright}s volume and are also investigated.}, keywords = {Sub-Riemannian geometry}, url = {http://hdl.handle.net/1963/7321}, author = {Luca Rizzi} } @article {2014, title = {Curvature-adapted remeshing of CAD surfaces}, journal = {Procedia Engineering}, volume = {82}, number = {Procedia Engineering;volume 82; issue C; pages 253-265;}, year = {2014}, note = {This is an open access article under the CC BY-NC-ND license}, pages = {253{\textendash}265}, publisher = {Elsevier}, abstract = {A common representation of surfaces with complicated topology and geometry is through composite parametric surfaces as is the case for most CAD modelers. A challenging problem is how to generate a mesh of such a surface that well approximates the geometry of the surface, preserves its topology and important geometric features, and contains nicely shaped elements. In this work, we present an optimization-based surface remeshing method that is able to satisfy many of these requirements simultaneously. This method is inspired by the recent work of L{\'e}vy and Bonneel (Proc. 21th International Meshing Roundtable, October 2012), which embeds a smooth surface into a high-dimensional space and remesh it uniformly in that embedding space. Our method works directly in the 3d spaces and uses an embedding space in R6 to evaluate mesh size and mesh quality. It generates a curvatureadapted anisotropic surface mesh that well represents the geometry of the surface with a low number of elements. We illustrate our approach through various examples.

}, doi = {10.1016/j.proeng.2014.10.388}, url = {https://doi.org/10.1016/j.proeng.2014.10.388}, author = {Franco Dassi and Andrea Mola and Hang Si} } @article {BertolaCafasso5, title = {Darboux Transformations and Random Point Processes}, journal = {IMRN}, volume = {rnu122}, year = {2014}, pages = {56}, author = {Marco Bertola and Mattia Cafasso} } @article {2014, title = {The decomposition of optimal transportation problems with convex cost}, number = {SISSA;45/2014/MATE}, year = {2014}, institution = {SISSA}, url = {http://hdl.handle.net/1963/7433}, author = {Stefano Bianchini and Mauro Bardelloni} } @mastersthesis {2014, title = {The decomposition of optimal transportation problems with convex cost}, year = {2014}, school = {SISSA}, keywords = {Optimal Transportation}, url = {http://urania.sissa.it/xmlui/handle/1963/7475}, author = {Mauro Bardelloni} } @article {2014, title = {A density result for GSBD and its application to the approximation of brittle fracture energies}, number = {Calculus of variations and partial differential equations;volume 51; issue 1-2; pages 315-342;}, year = {2014}, publisher = {Springer}, abstract = {We present an approximation result for functions u: Ω {\textrightarrow} ℝ^n belonging to the space GSBD(Ω) ∩ L2(Ω, ℝn) with e(u) square integrable and Hn-1(Ju) finite. The approximating functions uk are piecewise continuous functions such that uk {\textrightarrow} u in (Formula Presented). As an application, we provide the extension to the vector-valued case of the Γ-convergence result in GSBV(Ω) proved by Ambrosio and Tortorelli (Commun Pure Appl Math 43:999-1036, 1990; Boll. Un. Mat. Ital. B (7) 6:105-123, 1992).

}, doi = {10.1007/s00526-013-0676-7}, url = {http://urania.sissa.it/xmlui/handle/1963/34647}, author = {Flaviana Iurlano} } @article {2014, title = {Dirac operators on noncommutative principal circle bundles}, number = {International Journal of Geometric Methods in Modern Physics;volume 11; issue 1; article number 1450012;}, year = {2014}, publisher = {World Scientific Publishing}, abstract = {We study spectral triples over noncommutative principal U(1)-bundles of arbitrary dimension and a compatibility condition between the connection and the Dirac operator on the total space and on the base space of the bundle. Examples of low-dimensional noncommutative tori are analyzed in more detail and all connections found that are compatible with an admissible Dirac operator. Conversely, a family of new Dirac operators on the noncommutative tori, which arise from the base-space Dirac operator and a suitable connection is exhibited. These examples are extended to the theta-deformed principal U(1)-bundle S 3 θ {\textrightarrow} S2.}, doi = {10.1142/S0219887814500121}, url = {http://urania.sissa.it/xmlui/handle/1963/35125}, author = {Andrzej Sitarz and Alessandro Zucca and Ludwik Dabrowski} } @article {2013, title = {Dirac reduction for Poisson vertex algebras}, journal = {Communications in Mathematical Physics 331, nr. 3 (2014) 1155-1190}, number = {arXiv:1306.6589;}, year = {2014}, note = {31 pages}, publisher = {SISSA}, abstract = {We construct an analogue of Dirac{\textquoteright}s reduction for an arbitrary local or non-local Poisson bracket in the general setup of non-local Poisson vertex algebras. This leads to Dirac{\textquoteright}s reduction of an arbitrary non-local Poisson structure. We apply this construction to an example of a generalized Drinfeld-Sokolov hierarchy.}, doi = {10.1007/s00220-014-2103-0}, url = {http://hdl.handle.net/1963/6980}, author = {Alberto De Sole and Victor G. Kac and Daniele Valeri} } @article {2014, title = {Discrete one-dimensional crawlers on viscous substrates: achievable net displacements and their energy cost}, number = {Mechanics Research Communications}, year = {2014}, publisher = {Elsevier}, abstract = {We study model one-dimensional crawlers, namely, model mechanical systems that can achieve self-propulsion by controlled shape changes of their body (extension or contraction of portions of the body), thanks to frictional interactions with a rigid substrate. We evaluate the achievable net displacement and the related energetic cost for self-propulsion by discrete crawlers (i.e., whose body is made of a discrete number of contractile or extensile segments) moving on substrates with either a Newtonian (linear) or a Bingham-type (stick-slip) rheology. Our analysis is aimed at constructing the basic building blocks towards an integrative, multi-scale description of crawling cell motility.}, keywords = {Cell migration}, doi = {10.1016/j.mechrescom.2013.10.023}, url = {http://urania.sissa.it/xmlui/handle/1963/34449}, author = {Giovanni Noselli and Amabile Tatone and Antonio DeSimone} } @article {scala2014dislocations, title = {Dislocations at the continuum scale: functional setting and variational properties}, year = {2014}, url = {http://cvgmt.sns.it/paper/2294/}, author = {Riccardo Scala and Nicolas Van Goethem} } @article {2014, title = {Donagi{\textendash}Markman cubic for the generalised Hitchin system}, year = {2014}, abstract = {Donagi and Markman (1993) have shown that the infinitesimal period map for an algebraic completely integrable Hamiltonian system (ACIHS) is encoded in a section of the third symmetric power of the cotangent bundle to the base of the system. For the ordinary Hitchin system the cubic is given by a formula of Balduzzi and Pantev. We show that the Balduzzi{\textendash}Pantev formula holds on maximal rank symplectic leaves of the G-generalised Hitchin system.}, keywords = {Generalized Hitchin system, Donagi-Markman cubic, algebraically completely integrable systems, moduli space of Higgs G-bundles}, url = {http://hdl.handle.net/1963/7253}, author = {Ugo Bruzzo and Peter Dalakov} } @article {2014, title = {Dynamics on a graph as the limit of the dynamics on a "fat graph"}, number = {SISSA;69/2014/MATE}, year = {2014}, institution = {SISSA}, abstract = {We discuss how the vertex boundary conditions for the dynamics of a quantum particle constrained on a graph emerge in the limit of the dynamics of a particle in a tubular region around the graph (\fat graph") when the transversal section of this region shrinks to zero. We give evidence of the fact that if the limit dynamics exists and is induced by the Laplacian on the graph with certain self-adjoint boundary conditions, such conditions are determined by the possible presence of a zero energy resonance on the fat graph. Pictorially, one may say that in the shrinking limit the resonance acts as a bridge connecting the boundary values at the vertex along the different rays.}, url = {http://urania.sissa.it/xmlui/handle/1963/7485}, author = {Gianfausto Dell{\textquoteright}Antonio and Alessandro Michelangeli} } @article {2014, title = {Editorial}, number = {Rendiconti del circolo matematico di Palermo;volume 63; issue 3; pages 317-318;}, year = {2014}, publisher = {Springer}, doi = {10.1007/s12215-014-0172-8}, url = {http://urania.sissa.it/xmlui/handle/1963/34712}, author = {Ciro Ciliberto and Gianni Dal Maso and Pasquale Vetro} } @article {2014, title = {An effective model for nematic liquid crystal composites with ferromagnetic inclusions}, number = {SIAM Journal on Applied Mathematics;volume 74; issue 2; pages 237-262;}, year = {2014}, publisher = {Society for Industrial and Applied Mathematics Publications}, abstract = {Molecules of a nematic liquid crystal respond to an applied magnetic field by reorienting themselves in the direction of the field. Since the dielectric anisotropy of a nematic is small, it takes relatively large fields to elicit a significant liquid crystal response. The interaction may be enhanced in colloidal suspensions of ferromagnetic particles in a liquid crystalline matrix- ferronematics-as proposed by Brochard and de Gennes in 1970. The ability of these particles to align with the field and simultaneously cause reorientation of the nematic molecules greatly increases the magnetic response of the mixture. Essentially the particles provide an easy axis of magnetization that interacts with the liquid crystal via surface anchoring. We derive an expression for the effective energy of ferronematic in the dilute limit, that is, when the number of particles tends to infinity while their total volume fraction tends to zero. The total energy of the mixture is assumed to be the sum of the bulk elastic liquid crystal contribution, the anchoring energy of the liquid crystal on the surfaces of the particles, and the magnetic energy of interaction between the particles and the applied magnetic field. The homogenized limiting ferronematic energy is obtained rigorously using a variational approach. It generalizes formal expressions previously reported in the physical literature.}, doi = {10.1137/130910348}, url = {http://urania.sissa.it/xmlui/handle/1963/34940}, author = {Maria Carme Calderer and Antonio DeSimone and Dmitry Golovaty and Alexander Panchenko} } @article {2014, title = {An efficient computational framework for reduced basis approximation and a posteriori error estimation of parametrized Navier-Stokes flows}, year = {2014}, abstract = {We present the current Reduced Basis framework for the efficient numerical approximation of parametrized steady Navier-Stokes equations. We have extended the existing setting developed in the last decade (see e.g. [Deparis, Veroy \& Patera, Quarteroni \& Rozza] to more general affine and nonaffine parametrizations (such as volume-based techniques), to a simultaneous velocity-pressure error estimates and to a fully decoupled Offline/Online procedure in order to speedup the solution of the reduced-order problem. This is particularly suitable for real-time and many-query contexts, which are both part of our final goal. Furthermore, we present an efficient numerical implementation for treating nonlinear advection terms in a convenient way. A residual-based a posteriori error estimation with respect to a truth, full-order Finite Element approximation is provided for joint pressure/velocity errors, according to the Brezzi-Rappaz-Raviart stability theory. To do this, we take advantage of an extension of the Successive Constraint Method for the estimation of stability factors and of a suitable fixed-point algorithm for the approximation of Sobolev embedding constants. Finally, we present some numerical test cases, in order to show both the approximation properties and the computational efficiency of the derived framework.}, keywords = {Reduced Basis Method, parametrized Navier-Stokes equations, steady incompressible fluids, a posteriori error estimation, approximation stability}, author = {Andrea Manzoni} } @article {FortiRozza2014, title = {Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid{\textendash}structure interaction coupling problems}, journal = {International Journal of Computational Fluid Dynamics}, volume = {28}, number = {3-4}, year = {2014}, pages = {158{\textendash}169}, abstract = {We present some recent advances and improvements in shape parametrisation techniques of interfaces for reduced-order modelling with special attention to fluid{\textendash}structure interaction problems and the management of structural deformations, namely, to represent them into a low-dimensional space (by control points). This allows to reduce the computational effort, and to significantly simplify the (geometrical) deformation procedure, leading to more efficient and fast reduced-order modelling applications in this kind of problems. We propose an efficient methodology to select the geometrical control points for the radial basis functions based on a modal greedy algorithm to improve the computational efficiency in view of more complex fluid{\textendash}structure applications in several fields. The examples provided deal with aeronautics and wind engineering.}, doi = {10.1080/10618562.2014.932352}, author = {Forti, D. and Gianluigi Rozza} } @article {2014, title = {Existence and uniqueness of the gradient flow of the Entropy in the space of probability measures}, number = {Rendiconti dell{\textquoteright}Istituto di Matematica dell{\textquoteright}Universita di Trieste;Volume 46; issue 1; pp. 43-70;}, year = {2014}, note = {This paper resumes the main part of the Bachelor thesis of the second author, discussed in 2013 at the University of Trieste.}, publisher = {EUT Edizioni Universita di Trieste}, abstract = {After a brief introduction on gradient flows in metric spaces and on geodesically convex functionals, we give an account of the proof (following the outline of [3, 7]) of the existence and uniqueness of the gradient flow of the Entropy in the space of Borel probability measures over a compact geodesic metric space with Ricci curvature bounded from below.}, url = {http://urania.sissa.it/xmlui/handle/1963/34693}, author = {Stefano Bianchini and Alexander Dabrowski} } @article {MONDINO2014707, title = {Existence of immersed spheres minimizing curvature functionals in non-compact 3-manifolds}, journal = {Annales de l{\textquoteright}Institut Henri Poincare (C) Non Linear Analysis}, volume = {31}, number = {4}, year = {2014}, pages = {707 - 724}, abstract = {We study curvature functionals for immersed 2-spheres in non-compact, three-dimensional Riemannian manifold $(M,h)$ without boundary. First, under the assumption that $(M,h)$ is the euclidean 3-space endowed with a semi-perturbed metric with perturbation small in $C^1$ norm and of compact support, we prove that if there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})\>0$ then there exists a smooth embedding $ f:\mathbb{S}^2\ \hookrightarrow\ M$ minimizing the Willmore functional $\frac{1}{4}\int |H|^2$, where $H$ is the mean curvature. Second, assuming that $(M,h)$ is of bounded geometry (i.e. bounded sectional curvature and strictly positive injectivity radius) and asymptotically euclidean or hyperbolic we prove that if there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})\>6$ then there exists a smooth immersion $f:\mathbb{S}^2\hookrightarrow\ M$ minimizing the functional $\int (\frac{1}{2}|A|^2+1)$, where $A$ is the second fundamental form. Finally, adding the bound $K^M \leq 2$ to the last assumptions, we obtain a smooth minimizer $f:\mathbb{S}^2\ \hookrightarrow\ M$ for the functional $\int \frac{1}{4}(|H|^2+1)$. The assumptions of the last two theorems are satisfied in a large class of 3-manifolds arising as spacelike timeslices solutions of the Einstein vacuum equation in case of null or negative cosmological constant.

}, keywords = {Direct methods in the calculus of variations, General Relativity, Geometric measure theory, second fundamental form, Willmore functional}, issn = {0294-1449}, doi = {https://doi.org/10.1016/j.anihpc.2013.07.002}, url = {http://www.sciencedirect.com/science/article/pii/S0294144913000851}, author = {Andrea Mondino and Johannes Schygulla} } @article {Kuwert2014, title = {Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds}, journal = {Mathematische Annalen}, volume = {359}, number = {1}, year = {2014}, month = {Jun}, pages = {379{\textendash}425}, abstract = {We study curvature functionals for immersed 2-spheres in a compact, three-dimensional Riemannian manifold $M$. Under the assumption that the sectional curvature $K^M$ is strictly positive, we prove the existence of a smooth immersion $f:{\mathbb{S}}^2 \rightarrow M$ minimizing the $L^2$ integral of the second fundamental form. Assuming instead that $K^M \leq 2 $ and that there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})\>6$, we obtain a smooth minimizer $f:{\mathbb{S}}^2 \rightarrow M$ for the functional $\int \frac{1}{4}|H|^2+1$, where $H$ is the mean curvature.

}, issn = {1432-1807}, doi = {10.1007/s00208-013-1005-3}, url = {https://doi.org/10.1007/s00208-013-1005-3}, author = {Kuwert, Ernst and Andrea Mondino and Johannes Schygulla} } @article {Mondino2014, title = {Existence of integral m-varifolds minimizing $\int |A|^p $ and $\int |H|^p$ , p>m, in Riemannian manifolds}, journal = {Calculus of Variations and Partial Differential Equations}, volume = {49}, number = {1}, year = {2014}, month = {Jan}, pages = {431{\textendash}470}, abstract = {We prove existence of integral rectifiable $m$-dimensional varifolds minimizing functionals of the type $\int |H|^p$ and $\int |A|^p$ in a given Riemannian $n$-dimensional manifold $(N,g)$, $2 \leq m\<n$ and $p\>m$ under suitable assumptions on $N$ (in the end of the paper we give many examples of such ambient manifolds). To this aim we introduce the following new tools: some monotonicity formulas for varifolds in ${\mathbb{R }^S}$ involving $\int\ |H|^p$to\ avoid degeneracy of the minimizer, and a sort of isoperimetric inequality to bound the mass in terms of the mentioned functionals.

}, issn = {1432-0835}, doi = {10.1007/s00526-012-0588-y}, url = {https://doi.org/10.1007/s00526-012-0588-y}, author = {Andrea Mondino} } @article {2014, title = {Finite dimensional Kadomtsev-Petviashvili τ-functions. I. Finite Grassmannians}, number = {Journal of Mathematical Physics;volume 55; issue 8; article number 1.4890818;}, year = {2014}, publisher = {American Institute of Physics Inc.}, abstract = {We study τ-functions of the Kadomtsev-Petviashvili hierarchy in terms of abelian group actions on finite dimensional Grassmannians, viewed as subquotients of the Hilbert space Grassmannians of Sato, Segal, and Wilson. A determinantal formula of Gekhtman and Kasman involving exponentials of finite dimensional matrices is shown to follow naturally from such reductions. All reduced flows of exponential type generated by matrices with arbitrary nondegenerate Jordan forms are derived, both in the Grassmannian setting and within the fermionic operator formalism. A slightly more general determinantal formula involving resolvents of the matrices generating the flow, valid on the big cell of the Grassmannian, is also derived. An explicit expression is deduced for the Pl{\"u}cker coordinates appearing as coefficients in the Schur function expansion of the τ-function.}, doi = {10.1063/1.4890818}, url = {http://urania.sissa.it/xmlui/handle/1963/34952}, author = {Ferenc Balogh and Tiago Fonseca and John P. Harnad} } @proceedings {2014, title = {A fully nonlinear potential model for ship hydrodynamics directly interfaced with CAD data structures}, year = {2014}, publisher = {SISSA}, abstract = {We present a model for ship hydrodynamics simulations currently under development at SISSA. The model employs potential flow theory and fully nonlinear free surface boundary conditions. The spatial discretization of the equations is performed by means of a collocation BEM. This gives rise to a Differential Algbraic Equations (DAE) system, solved using an implicit BDF scheme to time advance the solution. The model has been implemented into a C++ software able to automatically generate the computational grids from the CAD geometry of the hull. Numerical results on Kriso KCS and KVLCC2 hulls are presented and discussed.}, keywords = {ship hydrodynamics}, author = {Andrea Mola and Luca Heltai and Antonio DeSimone} } @inbook {2014, title = {Fundamentals of Reduced Basis Method for problems governed by parametrized PDEs and applications}, booktitle = {Separated representations and PGD-based model reduction : fundamentals and applications}, series = { CISM International Centre for Mechanical Sciences}, volume = {554}, year = {2014}, publisher = {Springer}, organization = {Springer}, chapter = {4}, address = {Wien}, abstract = {In this chapter we consider Reduced Basis (RB) approximations of parametrized Partial Differential Equations (PDEs). The the idea behind RB is to decouple the generation and projection stages (Offline/Online computational procedures) of the approximation process in order to solve parametrized PDEs in a fast, inexpensive and reliable way. The RB method, especially applied to 3D problems, allows great computational savings with respect to the classical Galerkin Finite Element (FE) Method. The standard FE method is typically ill suited to (i) iterative contexts like optimization, sensitivity analysis and many-queries in general, and (ii) real time evaluation. We consider for simplicity coercive PDEs. We discuss all the steps to set up a RB approximation, either from an analytical and a numerical point of view. Then we present an application of the RB method to a steady thermal conductivity problem in heat transfer with emphasis on geometrical and physical parameters.

}, keywords = {reduced basis method, linear elasticity, heat transfer, error bounds, parametrized PDEs}, doi = {10.1007/978-3-7091-1794-1_4}, author = {Gianluigi Rozza} } @mastersthesis {2014, title = {Geometry and analysis of control-affine systems: motion planning, heat and Schr{\"o}dinger evolution}, year = {2014}, school = {SISSA}, abstract = {This thesis is dedicated to two problems arising from geometric control theory, regarding control-affine systems $\dot q= f_0(q)+\sum_{j=1}^m u_j f_j(q)$, where $f_0$ is called the drift. In the first part we extend the concept of complexity of non-admissible trajectories, well understood for sub-Riemannian systems, to this more general case, and find asymptotic estimates. In order to do this, we also prove a result in the same spirit as the Ball-Box theorem for sub-Riemannian systems, in the context of control-affine systems equipped with the L1 cost. Then, in the second part of the thesis, we consider a family of 2-dimensional driftless control systems. For these, we study how the set where the control vector fields become collinear affects the diffusion dynamics. More precisely, we study whether solutions to the heat and Schr{\"o}dinger equations associated with this Laplace-Beltrami operator are able to cross this singularity, and how its the presence affects the spectral properties of the operator, in particular under a magnetic Aharonov{\textendash}Bohm-type perturbation.}, keywords = {control theory}, url = {http://urania.sissa.it/xmlui/handle/1963/7474}, author = {Dario Prandi} } @article {2014, title = {Global Structure of Admissible BV Solutions to Piecewise Genuinely Nonlinear, Strictly Hyperbolic Conservation Laws in One Space Dimension}, number = {Communications in Partial Differential Equations;Volume 39; issue 2; pp. 244-273;}, year = {2014}, publisher = {Taylor \& Francis}, abstract = {The paper describes the qualitative structure of an admissible BV solution to a strictly hyperbolic system of conservation laws whose characteristic families are piecewise genuinely nonlinear. More precisely, we prove that there are a countable set of points Θ and a countable family of Lipschitz curves T{script} such that outside T{script} ∪ Θ the solution is continuous, and for all points in T{script}{set minus}Θ the solution has left and right limit. This extends the corresponding structural result in [7] for genuinely nonlinear systems. An application of this result is the stability of the wave structure of solution w.r.t. -convergence. The proof is based on the introduction of subdiscontinuities of a shock, whose behavior is qualitatively analogous to the discontinuities of the solution to genuinely nonlinear systems.

}, doi = {10.1080/03605302.2013.775153}, url = {http://urania.sissa.it/xmlui/handle/1963/34694}, author = {Stefano Bianchini and Lei Yu} } @article {prandi_2014, title = {H{\"o}lder equivalence of the value function for control-affine systems}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, volume = {20}, number = {4}, year = {2014}, pages = {1224{\textendash}1248}, publisher = {EDP Sciences}, doi = {10.1051/cocv/2014014}, author = {Dario Prandi} } @mastersthesis {2014, title = {Holomorphically symplectic varieties with Prym Lagrangian fibrations}, year = {2014}, school = {SISSA}, abstract = {The thesis presents a construction of singular holomorphically symplectic varieties as Lagrangian fibrations. They are relative compactified Prym varieties associated to curves on symplectic surfaces with an antisymplectic involution. They are identified with the fixed locus of a symplectic involution on singular moduli spaces of sheaves of dimension 1. An explicit example, giving a singular irreducible symplectic 6-fold without symplectic resolutions, is described for a K3 surface which is the double cover of a cubic surface. In the case of abelian surfaces, a variation of this construction is studied to get irreducible symplectic varieties: relative compactified 0-Prym varieties. A partial classification result is obtained for involutions without fixed points: either the 0-Prym variety is birational to an irreducible symplectic variety of K3[n]-type, or it does not admit symplectic resolutions.}, keywords = {Holomorphically symplectic varieties}, url = {http://urania.sissa.it/xmlui/handle/1963/7434}, author = {Tommaso Matteini} } @article {2014, title = {Homogenization of functional with linear growth in the context of A-quasiconvexity}, number = {SISSA;49/2014/MATE}, year = {2014}, institution = {SISSA}, abstract = {This work deals with the homogenization of functionals with linear growth in the context of A-quasiconvexity. A representation theorem is proved, where the new integrand function is obtained by solving a cell problem where the coupling between homogenization and the A-free condition plays a crucial role. This result extends some previous work to the linear case, thus allowing for concentration effects.}, url = {http://urania.sissa.it/xmlui/handle/1963/7436}, author = {Jose Matias and Marco Morandotti and Pedro M. Santos} } @article {2014, title = {Homology computation for a class of contact structures on T3}, number = {Calculus of variations and partial differential equations;volume 50; issue 3; pages 599-614;}, year = {2014}, publisher = {Springer}, abstract = {We consider a family of tight contact forms on the three-dimensional torus and we compute the relative Contact Homology by using the variational theory of critical points at infinity. We will also show local stability.}, doi = {10.1007/s00526-013-0648-y}, url = {http://urania.sissa.it/xmlui/handle/1963/34649}, author = {Ali Maalaoui and Vittorio Martino} } @article {JaggliIapichinoRozza2014, title = {An improvement on geometrical parameterizations by transfinite maps}, journal = {Comptes Rendus Mathematique}, volume = {352}, number = {3}, year = {2014}, pages = {263{\textendash}268}, abstract = {We present a method to generate a non-affine transfinite map from a given reference domain to a family of deformed domains. The map is a generalization of the Gordon-Hall transfinite interpolation approach. It is defined globally over the reference domain. Once we have computed some functions over the reference domain, the map can be generated by knowing the parametric expressions of the boundaries of the deformed domain. Being able to define a suitable map from a reference domain to a desired deformation is useful for the management of parameterized geometries.}, doi = {10.1016/j.crma.2013.12.017}, author = {J{\"a}ggli, C. and Laura Iapichino and Gianluigi Rozza} } @article {2014, title = {Infinite-dimensional Frobenius manifolds underlying the Toda lattice hierarchy}, number = {Advances in Mathematics;volume 255; pages 487-524;}, year = {2014}, publisher = {Elsevier}, abstract = {Following the approach of Carlet et al. (2011) [9], we construct a class of infinite-dimensional Frobenius manifolds underlying the Toda lattice hierarchy, which are defined on the space of pairs of meromorphic functions with possibly higher-order poles at the origin and at infinity. We also show a connection between these infinite-dimensional Frobenius manifolds and the finite-dimensional Frobenius manifolds on the orbit space of extended affine Weyl groups of type A defined by Dubrovin and Zhang.}, doi = {10.1016/j.aim.2014.01.013}, url = {http://urania.sissa.it/xmlui/handle/1963/35026}, author = {Chaozhong Wu and Dafeng Zuo} } @article {2014, title = {Integrability of Dirac reduced bi-Hamiltonian equations}, number = {arXiv:1401.6006;}, year = {2014}, note = {15 pages}, institution = {SISSA}, abstract = {First, we give a brief review of the theory of the Lenard-Magri scheme for a non-local bi-Poisson structure and of the theory of Dirac reduction. These theories are used in the remainder of the paper to prove integrability of three hierarchies of bi-Hamiltonian PDE{\textquoteright}s, obtained by Dirac reduction from some generalized Drinfeld-Sokolov hierarchies.}, url = {http://hdl.handle.net/1963/7247}, author = {Alberto De Sole and Victor G. Kac and Daniele Valeri} } @article {2014, title = {An irreducible symplectic orbifold of dimension 6 with a Lagrangian Prym fibration}, number = {arXiv:1403.5523;}, year = {2014}, abstract = {A new example of an irreducible symplectic variety of dimension 6, with only finite quotient singularities, is described as a relative compactified Prymian of a family of genus 4 curves with involution. It is associated to a K3 surface which is a double cover of a cubic surface. It has a natural Lagrangian fibration in abelian 3-folds with polarization type (1,1,2). It does not admit any symplectic resolution.}, keywords = {Irreducible symplectic variety, Lagrangian fibration, Prym variety, automorphism of symplectic varieties}, author = {Tommaso Matteini} } @article {2013, title = {On an isomonodromy deformation equation without the Painlev{\'e} property}, number = {Russian Journal of Mathematical Physics}, year = {2014}, note = {34 pages, 8 figures, references added}, publisher = {Maik Nauka-Interperiodica Publishing}, abstract = {We show that the fourth order nonlinear ODE which controls the pole dynamics in the general solution of equation $P_I^2$ compatible with the KdV equation exhibits two remarkable properties: 1) it governs the isomonodromy deformations of a $2\times2$ matrix linear ODE with polynomial coefficients, and 2) it does not possesses the Painlev\'e property. We also study the properties of the Riemann--Hilbert problem associated to this ODE and find its large $t$ asymptotic solution for the physically interesting initial data.}, doi = {10.1134/S1061920814010026}, url = {http://hdl.handle.net/1963/6466}, author = {Boris Dubrovin and Andrey Kapaev} } @article {Baldi20141, title = {KAM for quasi-linear and fully nonlinear forced perturbations of Airy equation}, journal = {Mathematische Annalen}, year = {2014}, note = {cited By (since 1996)0; Article in Press}, pages = {1-66}, abstract = {We prove the existence of small amplitude quasi-periodic solutions for quasi-linear and fully nonlinear forced perturbations of the linear Airy equation. For Hamiltonian or reversible nonlinearities we also prove their linear stability. The key analysis concerns the reducibility of the linearized operator at an approximate solution, which provides a sharp asymptotic expansion of its eigenvalues. For quasi-linear perturbations this cannot be directly obtained by a KAM iteration. Hence we first perform a regularization procedure, which conjugates the linearized operator to an operator with constant coefficients plus a bounded remainder. These transformations are obtained by changes of variables induced by diffeomorphisms of the torus and pseudo-differential operators. At this point we implement a Nash-Moser iteration (with second order Melnikov non-resonance conditions) which completes the reduction to constant coefficients. {\textcopyright} 2014 Springer-Verlag Berlin Heidelberg.}, issn = {00255831}, doi = {10.1007/s00208-013-1001-7}, author = {P Baldi and Massimiliano Berti and Riccardo Montalto} } @mastersthesis {2014, title = {KAM for quasi-linear and fully nonlinear perturbations of Airy and KdV equations}, year = {2014}, school = {SISSA}, url = {http://urania.sissa.it/xmlui/handle/1963/7476}, author = {Riccardo Montalto} } @article {2014, title = {KAM for quasi-linear KdV}, journal = {C. R. Math. Acad. Sci. Paris}, volume = {352}, number = {Comptes Rendus Mathematique;volume 352; issue 7-8; pages 603-607;}, year = {2014}, pages = {603-607}, publisher = {Elsevier}, abstract = {We prove the existence and stability of Cantor families of quasi-periodic, small-amplitude solutions of quasi-linear autonomous Hamiltonian perturbations of KdV.

}, doi = {10.1016/j.crma.2014.04.012}, url = {http://urania.sissa.it/xmlui/handle/1963/35067}, author = {P Baldi and Massimiliano Berti and Riccardo Montalto} } @article {2014, title = {KAM for Reversible Derivative Wave Equations}, journal = {Arch. Ration. Mech. Anal.}, volume = {212}, number = {Archive for rational mechanics and analysis;volume 212; issue 3; pages 905-955;}, year = {2014}, pages = {905-955}, publisher = {Springer}, abstract = {We prove the existence of Cantor families of small amplitude, analytic, linearly stable quasi-periodic solutions of reversible derivative wave equations.

}, doi = {10.1007/s00205-014-0726-0}, url = {http://urania.sissa.it/xmlui/handle/1963/34646}, author = {Massimiliano Berti and Luca Biasco and Michela Procesi} } @article {2014, title = {Laplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length}, number = {Nonlinear Differential Equations and Applications}, year = {2014}, publisher = {SISSA}, abstract = {We consider the weak solution of the Laplace equation in a planar domain with a straight crack, prescribing a homogeneous Neumann condition on the crack and a nonhomogeneous Dirichlet condition on the rest of the boundary. For every k we express the k-th derivative of the energy with respect to the crack length in terms of a finite number of coefficients of the asymptotic expansion of the solution near the crack tip and of a finite number of other parameters, which only depend on the shape of the domain.

}, keywords = {cracked domains, energy release rate, higher order derivatives, asymptotic expansion of solutions}, doi = {10.1007/s00030-014-0291-0}, url = {http://hdl.handle.net/1963/7271}, author = {Gianni Dal Maso and Gianluca Orlando and Rodica Toader} } @inbook {2014, title = {Lecture notes on gradient flows and optimal transport}, number = {London Mathematical Society Lecture Note Series;volume 413; pages 100-144;}, year = {2014}, note = {Book title: Optimal transportation}, publisher = {Cambridge University Press}, organization = {Cambridge University Press}, abstract = {We present a short overview on the strongest variational formulation for gradient flows of geodesically λ-convex functionals in metric spaces, with applications to diffusion equations in Wasserstein spaces of probability measures. These notes are based on a series of lectures given by the second author for the Summer School "Optimal transportation: Theory and applications" in Grenoble during the week of June 22-26, 2009.}, doi = {10.1017/CBO9781107297296}, url = {http://urania.sissa.it/xmlui/handle/1963/35093}, author = {Sara Daneri and Giuseppe Savar{\`e}} } @article {2014, title = {Legendre duality on hypersurfaces in K{\"a}hler manifolds}, number = {Advances in Geometry;volume 14; issue 2; pages 277-286;}, year = {2014}, publisher = {Walter de Gruyter and Co.}, abstract = {We give a sufficient condition on real strictly Levi-convex hypersurfaces M, embedded in four-dimensional K{\"a}hler manifolds V , such that Legendre duality can be performed. We consider the contact form onM whose kernel is the restriction of the holomorphic tangent space of V and show that if there exists a Legendrian Killing vector field v, then the dual form β(̇) := d(v, ̇) is a contact form on M with the same orientation than theta.}, doi = {10.1515/advgeom-2014-0016}, url = {http://urania.sissa.it/xmlui/handle/1963/34777}, author = {Vittorio Martino} } @article {davoli_2014, title = {Linearized plastic plate models as Γ-limits of 3D finite elastoplasticity}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, volume = {20}, number = {3}, year = {2014}, pages = {725{\textendash}747}, publisher = {EDP Sciences}, abstract = {The subject of this paper is the rigorous derivation of reduced models for a thin plate by means of $\Gamma$-convergence, in the framework of finite plasticity. Denoting by $\epsilon$ the thickness of the plate, we analyse the case where the scaling factor of the elasto-plastic energy per unit volume is of order $\epsilon^{2 \alpha -2}$, with $\alpha \geq 3$. According to the value of $\alpha$, partially or fully linearized models are deduced, which correspond, in the absence of plastic deformation, to the Von K{\'a}rm{\'a}n plate theory and the linearized plate theory.

}, doi = {10.1051/cocv/2013081}, author = {Elisa Davoli} } @article {2014, title = {Lipschitz continuous viscosity solutions for a class of fully nonlinear equations on lie groups}, number = {Journal of geometric analysis;volume 24; issue 1; pages 169-189;}, year = {2014}, publisher = {Springer}, abstract = {In this paper, we prove existence and uniqueness of Lipschitz continuous viscosity solutions for Dirichlet problems involving a class a fully non-linear operators on Lie groups. In particular, we consider the elementary symmetric functions of the eigenvalues of the Hessian built with left-invariant vector fields.}, doi = {10.1007/s12220-012-9332-2}, url = {http://urania.sissa.it/xmlui/handle/1963/34699}, author = {Vittorio Martino and Annamaria Montanari} } @article {2013, title = {Local and global minimality results for a nonlocal isoperimetric problem on R^N}, journal = { SIAM Journal on Mathematical Analysis}, volume = {46}, number = {Siam journal on mathematical analysis}, year = {2014}, pages = {2310-2349}, publisher = {SIAM Publications}, abstract = {We consider a nonlocal isoperimetric problem defined in the whole space R^N, whose nonlocal part is given by a Riesz potential with exponent $\alpha\in(0, N-1)$. We show that critical configurations with positive second variation are local minimizers and satisfy a quantitative inequality with respect to the L^1-norm. This criterion provides the existence of a (explicitly determined) critical threshold determining the interval of volumes for which the ball is a local minimizer, and allows to address several global minimality issues.

}, keywords = {Nonlocal isoperimetric problem}, doi = {10.1137/130929898}, url = {http://hdl.handle.net/1963/6984}, author = {Marco Bonacini and Riccardo Cristoferi} } @article {11062, title = {Local behavior of fractional p-minimizers}, number = {SISSA preprint;10/2014/MATE}, year = {2014}, publisher = {SISSA}, abstract = {We extend the De Giorgi-Nash Moser theory to nonlocal, possibly degerate integro-differential operators

}, keywords = {fractional Sobolev spaces}, author = {Agnese Di Castro and Tuomo Kuusi and Giampiero Palatucci} } @article {2014, title = {On the Lp-differentiability of certain classes of functions}, number = {Revista Matematica Iberoamericana;Volume 30; issue 1; pp. 349-367;}, year = {2014}, publisher = {European Mathematical Society}, abstract = {We prove the Lp-differentiability at almost every point for convolution products on ℝd of the form K*μ, where μ is bounded measure and K is a homogeneous kernel of degree 1-d. From this result we derive the Lp-differentiability for vector fields on R d whose curl and divergence are measures, and also for vector fields with bounded deformation.}, doi = {10.4171/rmi/782}, url = {http://urania.sissa.it/xmlui/handle/1963/34695}, author = {Giovanni Alberti and Stefano Bianchini and Gianluca Crippa} } @article {2014, title = {Maximal generalized solution of eikonal equation}, number = {Journal of differential equations;volume 257; issue 1; pages 231-263;}, year = {2014}, publisher = {Elsevier}, abstract = {We study the Dirichlet problem for the eikonal equation: 1/2 |∇u(x)|^2-a(x)=0 in Ω u(x)=(x) on Ω, without continuity assumptions on the map a(.). We find a class of maps a(.) contained in the space L$\infty$(Ω) for which the problem admits a (maximal) generalized solution, providing a generalization of the notion of viscosity solution.}, doi = {10.1016/j.jde.2014.04.001}, url = {http://urania.sissa.it/xmlui/handle/1963/34642}, author = {Sandro Zagatti} } @article {2014, title = {Minimal Liouville gravity correlation numbers from Douglas string equation}, number = {Journal of high energy physics;volume 2014; issue 1; article number 156;}, year = {2014}, publisher = {Springer}, abstract = {We continue the study of $(q,p)$ Minimal Liouville Gravity with the help of Douglas string equation. We generalize the results of \cite{Moore:1991ir}, \cite{Belavin:2008kv}, where Lee-Yang series $(2,2s+1)$ was studied, to $(3,3s+p_0)$ Minimal Liouville Gravity, where $p_0=1,2$. We demonstrate that there exist such coordinates $\tau_{m,n}$ on the space of the perturbed Minimal Liouville Gravity theories, in which the partition function of the theory is determined by the Douglas string equation. The coordinates $\tau_{m,n}$ are related in a non-linear fashion to the natural coupling constants $\lambda_{m,n}$ of the perturbations of Minimal Lioville Gravity by the physical operators $O_{m,n}$. We find this relation from the requirement that the correlation numbers in Minimal Liouville Gravity must satisfy the conformal and fusion selection rules. After fixing this relation we compute three- and four-point correlation numbers when they are not zero. The results are in agreement with the direct calculations in Minimal Liouville Gravity available in the literature \cite{Goulian:1990qr}, \cite{Zamolodchikov:2005sj}, \cite{Belavin:2006ex}.}, doi = {10.1007/JHEP01(2014)156}, url = {http://urania.sissa.it/xmlui/handle/1963/34588}, author = {Alexander Belavin and Boris Dubrovin and Baur Mukhametzhanov} } @article {2013, title = {A model for crack growth with branching and kinking}, journal = {Asymptotic Analysis}, volume = {89}, year = {2014}, pages = {63-110}, publisher = {SISSA}, type = {Research Article}, chapter = {63}, abstract = {We study an evolution model for fractured elastic materials in the 2-dimensional case, for which the crack path is not assumed to be known a priori. We introduce some general assumptions on the structure of the fracture sets suitable to remove the restrictions on the regularity of the crack sets and to allow for kinking and branching to develop. In addition we define the front of the fracture and its velocity. By means of a time-discretization approach, we prove the existence of a continuous-time evolution that satisfies an energy inequality and a stability criterion. The energy balance also takes into account the energy dissipated at the front of the fracture. The stability criterion is stated in the framework of Griffith{\textquoteright}s theory, in terms of the energy release rate, when the crack grows at least at one point of its front.

}, keywords = {quasistatic crack evolution, branching, kinking, Griffith\\\'s criterion}, doi = {10.3233/ASY-141233}, url = {https://content.iospress.com/articles/asymptotic-analysis/asy1233}, author = {Simone Racca} } @article {2014, title = {Model Order Reduction in Fluid Dynamics: Challenges and Perspectives}, number = {Modeling simulation and applications;volume 9; pages 235-273;}, year = {2014}, publisher = {Springer}, abstract = {This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities - which are mainly related either to nonlinear convection terms and/or some geometric variability - that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration. We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of inf-sup stability, certification through error estimation, computational issues and-in the unsteady case - long-time stability of the reduced model. Moreover, we provide an extensive list of literature references.}, doi = {10.1007/978-3-319-02090-7_9}, author = {Toni Lassila and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza} } @article {2014, title = {A modular spectral triple for κ-Minkowski space}, number = {Journal of Geometry and Physics;volume 76; pages 136-157;}, year = {2014}, publisher = {Elsevier}, abstract = {We present a spectral triple for κ-Minkowski space in two dimensions. Starting from an algebra naturally associated to this space, a Hilbert space is built using a weight which is invariant under the κ-Poincar{\'e} algebra. The weight satisfies a KMS condition and its associated modular operator plays an important role in the construction. This forces us to introduce two ingredients which have a modular flavour: the first is a twisted commutator, used to obtain a boundedness condition for the Dirac operator, and the second is a weight replacing the usual operator trace, used to measure the growth of the resolvent of the Dirac operator. We show that, under some assumptions related to the symmetries and the classical limit, there is a unique Dirac operator and automorphism such that the twisted commutator is bounded. Then, using the weight mentioned above, we compute the spectral dimension associated to the spectral triple and find that is equal to the classical dimension. Finally we briefly discuss the introduction of a real structure.}, doi = {10.1016/j.geomphys.2013.10.023}, url = {http://urania.sissa.it/xmlui/handle/1963/34895}, author = {Marco Matassa} } @article {battaglia2013moser, title = {A Moser-Trudinger inequality for the singular Toda system}, journal = {Bull. Inst. Math. Acad. Sin.}, volume = {9}, number = {1}, year = {2014}, pages = {1{\textendash}23}, author = {Luca Battaglia and Andrea Malchiodi} } @article {Piazzalunga2014, title = {M-theory interpretation of the real topological string}, journal = {Journal of High Energy Physics}, volume = {2014}, number = {8}, year = {2014}, month = {Aug}, pages = {54}, abstract = {We describe the type IIA physical realization of the unoriented topological string introduced by Walcher, describe its M-theory lift, and show that it allows to compute the open and unoriented topological amplitude in terms of one-loop diagram of BPS M2-brane states. This confirms and allows to generalize the conjectured BPS integer expansion of the topological amplitude. The M-theory lift of the orientifold is freely acting on the M-theory circle, so that integer multiplicities are a weighted version of the (equivariant subsector of the) original closed oriented Gopakumar-Vafa invariants. The M-theory lift also provides new perspective on the topological tadpole cancellation conditions. We finally comment on the M-theory version of other unoriented topological strings, and clarify certain misidentifications in earlier discussions in the literature.

}, issn = {1029-8479}, doi = {10.1007/JHEP08(2014)054}, url = {https://doi.org/10.1007/JHEP08(2014)054}, author = {Nicol{\`o} Piazzalunga and Uranga, Angel M.} } @article {2014, title = {N = 2 Quiver Gauge Theories on A-type ALE Spaces}, number = {Letters in mathematical physics;volume 105; issue 3; pages 401-445;}, year = {2014}, publisher = {Springer}, abstract = {We survey and compare recent approaches to the computation of the partition functions and correlators of chiral BPS observables in N = 2 gauge theories on ALE spaces based on quiver varieties and the minimal resolution Xk of the Ak-1 toric singularity C2/Zk, in light of their recently conjectured duality with two-dimensional coset conformal field theories. We review and elucidate the rigorous constructions of gauge theories for a particular family of ALE spaces, using their relation to the cohomology of moduli spaces of framed torsion-free sheaves on a suitable orbifold compactification of Xk. We extend these computations to generic N = 2 superconformal quiver gauge theories, obtaining in these instances new constraints on fractional instanton charges, a rigorous proof of the Nekrasov master formula, and new quantizations of Hitchin systems based on the underlying Seiberg{\textendash}Witten geometry.}, doi = {10.1007/s11005-014-0734-x}, url = {http://urania.sissa.it/xmlui/handle/1963/34719}, author = {Ugo Bruzzo and Francesco Sala and Richard J. Szabo} } @article {2012, title = {New results on Gamma-limits of integral functionals}, number = {Annales de l{\textquoteright}Institut Henri Poincare. Analyse Non Lineaire}, year = {2014}, publisher = {Elsevier}, keywords = {Gamma-convergence}, doi = {10.1016/j.anihpc.2013.02.005}, url = {http://hdl.handle.net/1963/5880}, author = {Nadia Ansini and Gianni Dal Maso and Caterina Ida Zeppieri} } @mastersthesis {2014, title = {Non-commutative integration for spectral triples associated to quantum groups}, year = {2014}, school = {SISSA}, abstract = {This thesis is dedicated to the study of non-commutative integration, in the sense of spectral triples, for some non-commutative spaces associated to quantum groups.}, keywords = {Non-commutative geometry}, author = {Marco Matassa} } @article {2012, title = {Nonsingular Isogeometric Boundary Element Method for Stokes Flows in 3D}, number = {Computer Methods in Applied Mechanics and Engineering}, year = {2014}, publisher = {Elsevier}, abstract = {Isogeometric analysis (IGA) is emerging as a technology bridging Computer Aided Geometric Design (CAGD), most commonly based on Non-Uniform Rational B-Splines (NURBS) surfaces, and engineering analysis. In finite element and boundary element isogeometric methods (FE-IGA and IGA-BEM), the NURBS basis functions that de- scribe the geometry define also the approximation spaces. In the FE-IGA approach, the surfaces generated by the CAGD tools need to be extended to volumetric descriptions, a major open problem in 3D. This additional passage can be avoided in principle when the partial differential equations to be solved admit a formulation in terms of bound- ary integral equations, leading to Boundary Element Isogeometric Analysis (IGA-BEM). The main advantages of such an approach are given by the dimensionality reduction of the problem (from volumetric-based to surface-based), by the fact that the interface with CAGD tools is direct, and by the possibility to treat exterior problems, where the computational domain is infinite. By contrast, these methods produce system matrices which are full, and require the integration of singular kernels. In this paper we address the second point and propose a nonsingular formulation of IGA-BEM for 3D Stokes flows, whose convergence is carefully tested numerically. Standard Gaussian quadrature rules suffice to integrate the boundary integral equations, and carefully chosen known exact solutions of the interior Stokes problem are used to correct the resulting matrices, extending the work by Klaseboer et al. [27] to IGA-BEM.}, keywords = {Isogeometric Analysis}, doi = {10.1016/j.cma.2013.09.017}, url = {http://hdl.handle.net/1963/6326}, author = {Luca Heltai and Marino Arroyo and Antonio DeSimone} } @article {2014, title = {Pfaffian representations of cubic surfaces}, number = {Geometriae dedicata;volume 168; issue 1; pages 69-86;}, year = {2014}, publisher = {Springer}, abstract = {Let K be a field of characteristic zero. We describe an algorithm which requires a homogeneous polynomial F of degree three in K[x0,x1,x2,x3] and a zero a of F in P3 K and ensures a linear Pfaffian representation of V(F) with entries in K[x0,x1,x2,x3], under mild assumptions on F and a. We use this result to give an explicit construction of (and to prove the existence of) a linear Pfaffian representation of V (F), with entries in K'[x0,x1,x2,x3], being K' an algebraic extension of K of degree at most six. An explicit example of such a construction is given.

}, doi = {10.1007/s10711-012-9818-x}, url = {http://urania.sissa.it/xmlui/handle/1963/34688}, author = {Fabio Tanturri} } @conference {mola2014ship, title = {Potential Model for Ship Hydrodynamics Simulations Directly Interfaced with CAD Data Structures}, booktitle = {The 24th International Ocean and Polar Engineering Conference}, volume = {4}, year = {2014}, pages = {815{\textendash}822}, publisher = {International Society of Offshore and Polar Engineers}, organization = {International Society of Offshore and Polar Engineers}, author = {Andrea Mola and Luca Heltai and Antonio DeSimone and Massimiliano Berti} } @article {2014, title = {Pseudo-automorphisms of positive entropy on the blowups of products of projective spaces}, number = {Mathematische annalen;volume 359; issue 1-2; pages 189-209;}, year = {2014}, publisher = {Springer}, abstract = {We use a concise method to construct pseudo-automorphisms fn of the first dynamical degree d1(fn) > 1 on the blowups of the projective n-space for all n >= 2 and more generally on the blowups of products of projective spaces. These fn, for n=3 have positive entropy, and for n>= 4 seem to be the first examples of pseudo-automorphisms with d1(fn) > 1 (and of non-product type) on rational varieties of higher dimensions.}, doi = {10.1007/s00208-013-0992-4}, url = {http://urania.sissa.it/xmlui/handle/1963/34714}, author = {Fabio Perroni and Deqi Zhang} } @article {2014, title = {On a quadratic functional for scalar conservation laws}, journal = {Journal of Hyperbolic Differential Equations}, volume = {11}, number = {Journal of Hyperbolic Differential Equations;Volume 11; issue 2; pp. 355-435;}, year = {2014}, pages = {355-435}, publisher = {World Scientific Publishing}, abstract = {We prove a quadratic interaction estimate for approximate solutions to scalar conservation laws obtained by the wavefront tracking approximation or the Glimm scheme. This quadratic estimate has been used in the literature to prove the convergence rate of the Glimm scheme.

}, doi = {10.1142/S0219891614500118}, url = {http://arxiv.org/abs/1311.2929}, author = {Stefano Bianchini and Stefano Modena} } @article {bianchini2013quadratic, title = {Quadratic interaction functional for systems of conservation laws: a case study}, journal = {Bulletin of the Institute of Mathematics of Academia Sinica (New Series)}, volume = {9}, year = {2014}, pages = {487-546}, url = {https://w3.math.sinica.edu.tw/bulletin_ns/20143/2014308.pdf}, author = {Stefano Bianchini and Stefano Modena} } @article {2014, title = {Quantum dimension and quantum projective spaces}, number = {Symmetry, Integrability and Geometry: Methods and Applications (SIGMA);volume 10; 13p;}, year = {2014}, publisher = {Institute of Mathematics}, abstract = {We show that the family of spectral triples for quantum projective spaces introduced by D{\textquoteright}Andrea and Dbrowski, which have spectral dimension equal to zero, can be reconsidered as modular spectral triples by taking into account the action of the element K2por its inverse. The spectral dimension computed in this sense coincides with the dimension of the classical projective spaces. The connection with the well known notion of quantum dimension of quantum group theory is pointed out.}, doi = {10.3842/SIGMA.2014.097}, url = {http://urania.sissa.it/xmlui/handle/1963/34764}, author = {Marco Matassa} } @article {2014, title = {Quantum gauge symmetries in noncommutative geometry}, number = {Journal of Noncommutative Geometry;volume 8; issue 2; pages 433-471;}, year = {2014}, publisher = {European Mathematical Society Publishing House}, abstract = {We discuss generalizations of the notion of i) the group of unitary elements of a (real or complex) finite-dimensional C*-algebra, ii) gauge transformations and iii) (real) automorphisms in the framework of compact quantum group theory and spectral triples. The quantum analogue of these groups are defined as universal (initial) objects in some natural categories. After proving the existence of the universal objects, we discuss several examples that are of interest to physics, as they appear in the noncommutative geometry approach to particle physics: in particular, the C*-algebras M n(R), Mn(C) and Mn(H), describing the finite noncommutative space of the Einstein-Yang-Mills systems, and the algebras A F = C H M3 (C) and Aev = H H M4(C), that appear in Chamseddine-Connes derivation of the Standard Model of particle physics coupled to gravity. As a byproduct, we identify a "free" version of the symplectic group Sp.n/ (quaternionic unitary group).}, doi = {10.4171/JNCG/161}, url = {http://urania.sissa.it/xmlui/handle/1963/34897}, author = {Jyotishman Bhowmick and Francesco D{\textquoteright}Andrea and Biswarup Krishna Das and Ludwik Dabrowski} } @article {2014, title = {Quasi-static crack growth in hydraulic fracture}, journal = {Nonlinear Analysis}, volume = {109}, number = {Nonlinear Analysis, Theory, Methods and Applications;109}, year = {2014}, pages = {301-318}, publisher = {Elsevier}, type = {Journal article}, chapter = {301}, abstract = {We present a variational model for the quasi-static crack growth in hydraulic fracture in the framework of the energy formulation of rate-independent processes. The cracks are assumed to lie on a prescribed plane and to satisfy a very weak regularity assumption.

}, doi = {10.1016/j.na.2014.07.009}, url = {http://hdl.handle.net/20.500.11767/17350}, author = {Stefano Almi and Gianni Dal Maso and Rodica Toader} } @article {Maso2014, title = {Quasistatic Evolution in Perfect Plasticity as Limit of Dynamic Processes}, journal = {Journal of Dynamics and Differential Equations}, volume = {26}, number = {4}, year = {2014}, month = {Dec}, pages = {915{\textendash}954}, abstract = {We introduce a model of dynamic visco-elasto-plastic evolution in the linearly elastic regime and prove an existence and uniqueness result. Then we study the limit of (a rescaled version of) the solutions when the data vary slowly. We prove that they converge, up to a subsequence, to a quasistatic evolution in perfect plasticity.

}, issn = {1572-9222}, doi = {10.1007/s10884-014-9409-7}, url = {https://doi.org/10.1007/s10884-014-9409-7}, author = {Gianni Dal Maso and Riccardo Scala} } @article {doi:10.1142/S021820251450016X, title = {Quasistatic evolution models for thin plates arising as low energy Γ-limits of finite plasticity}, journal = {Mathematical Models and Methods in Applied Sciences}, volume = {24}, number = {10}, year = {2014}, pages = {2085-2153}, abstract = {In this paper we deduce by $\Gamma$-convergence some partially and fully linearized quasistatic evolution models for thin plates, in the framework of finite plasticity. Denoting by $\epsilon$ the thickness of the plate, we study the case where the scaling factor of the elasto-plastic energy is of order $\epsilon^{2 \alpha -2}$, with $\alpha\geq 3$. These scalings of the energy lead, in the absence of plastic dissipation, to the Von K{\'a}rm{\'a}n and linearized Von K{\'a}rm{\'a}n functionals for thin plates. We show that solutions to the three-dimensional quasistatic evolution problems converge, as the thickness of the plate tends to zero, to a quasistatic evolution associated to a suitable reduced model depending on $\alpha$.

}, doi = {10.1142/S021820251450016X}, url = {https://doi.org/10.1142/S021820251450016X}, author = {Elisa Davoli} } @article {2014, title = {Rate-independent damage in thermo-viscoelastic materials with inertia}, number = {SISSA;52/2014/MATE}, year = {2014}, institution = {SISSA}, abstract = {We present a model for rate-independent, unidirectional, partial damage in visco-elastic materials with inertia and thermal effects. The damage process is modeled by means of an internal variable, governed by a rate-independent flow rule. The heat equation and the momentum balance for the displacements are coupled in a highly nonlinear way. Our assumptions on the corresponding energy functional also comprise the case of the Ambrosio-Tortorelli phase-field model (without passage to the brittle limit). We discuss a suitable weak formulation and prove an existence theorem obtained with the aid of a (partially) decoupled time-discrete scheme and variational convergence methods. We also carry out the asymptotic analysis for vanishing viscosity and inertia and obtain a fully rate-independent limit model for displacements and damage, which is Independent of temperature.}, url = {http://urania.sissa.it/xmlui/handle/1963/7444}, author = {Giuliano Lazzaroni and Riccarda Rossi and Marita Thomas and Rodica Toader} } @mastersthesis {2014, title = {Rational curves and instantons on the Fano threefold Y_5}, year = {2014}, school = {arXiv preprint}, abstract = {This thesis is an investigation of the moduli spaces of instanton bundles on the Fano threefold Y_5 (a linear section of Gr(2,5)). It contains new proofs of classical facts about lines, conics and cubics on Y_5, and about linear sections of Y_5. The main original results are a Grauert-M{\"u}lich theorem for the splitting type of instantons on conics, a bound to the splitting type of instantons on lines and an SL_2-equivariant description of the moduli space in charge 2 and 3. Using these results we prove the existence of a unique SL_2-equivariant instanton of minimal charge and we show that for all instantons of charge 2 the divisor of jumping lines is smooth. In charge 3, we provide examples of instantons with reducible divisor of jumping lines. Finally, we construct a natural compactification for the moduli space of instantons of charge 3, together with a small resolution of singularities for it.}, keywords = {Moduli space of vector bundles}, url = {http://urania.sissa.it/xmlui/handle/1963/7482}, author = {Giangiacomo Sanna} } @conference {IapichinoQuarteroniRozzaVolkwein2014, title = {Reduced basis method for the Stokes equations in decomposable domains using greedy optimization}, booktitle = {ECMI 2014 proceedings}, year = {2014}, pages = {1{\textendash}7}, author = {Laura Iapichino and Alfio Quarteroni and Gianluigi Rozza and Volkwein, Stefan} } @book {2014, title = {Reduced Order Methods for Modeling and Computational Reduction}, series = {MS\&A}, volume = {9}, year = {2014}, pages = {334}, publisher = {Springer}, organization = {Springer}, edition = {1}, address = {Milano}, abstract = {This monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics.

Several topics are covered, including: design, optimization, and control theory in real-time with applications in engineering; data assimilation, geometry registration, and parameter estimation with special attention to real-time computing in biomedical engineering and computational physics; real-time visualization of physics-based simulations in computer science; the treatment of high-dimensional problems in state space, physical space, or parameter space; the interactions between different model reduction and dimensionality reduction approaches; the development of general error estimation frameworks which take into account both model and discretization effects.

This book is primarily addressed to computational scientists interested in computational reduction techniques for large scale differential problems.

\

}, keywords = {reduced order methods, MOR, ROM, POD, RB, greedy, CFD, Numerical Analysis}, issn = {978-3-319-02089-1}, doi = {10.1007/978-3-319-02090-7}, author = {Alfio Quarteroni and Gianluigi Rozza} } @proceedings {2014, title = {A reduced order model for multi-group time-dependent parametrized reactor spatial kinetics}, number = {International Conference on Nuclear Engineering, Proceedings, ICONE;volume 5;}, year = {2014}, note = {2014 22nd International Conference on Nuclear Engineering, ICONE 2014; Prague; Czech Republic; 7 July 2014 through 11 July 2014; Code 109131;}, month = {07/2014}, pages = {V005T17A048-V005T17A048}, publisher = {American Society of Mechanical Engineers (ASME)}, edition = {American Society Mechanical Engineering}, address = {Prague, Czech Republic}, abstract = {In this work, a Reduced Order Model (ROM) for multigroup time-dependent parametrized reactor spatial kinetics is presented. The Reduced Basis method (built upon a high-fidelity "truth" finite element approximation) has been applied to model the neutronics behavior of a parametrized system composed by a control rod surrounded by fissile material. The neutron kinetics has been described by means of a parametrized multi-group diffusion equation where the height of the control rod (i.e., how much the rod is inserted) plays the role of the varying parameter. In order to model a continuous movement of the rod, a piecewise affine transformation based on subdomain division has been implemented. The proposed ROM is capable to efficiently reproduce the neutron flux distribution allowing to take into account the spatial effects induced by the movement of the control rod with a computational speed-up of 30000 times, with respect to the "truth" model.

}, isbn = {978-079184595-0}, doi = {10.1115/ICONE22-30707}, url = {http://urania.sissa.it/xmlui/handle/1963/35123}, author = {Alberto Sartori and Davide Baroli and Antonio Cammi and Lelio Luzzi and Gianluigi Rozza} } @inbook {2013, title = {Reduction on characteristics for continuous of a scalar balance law}, booktitle = {AIMS Series on Applied Mathematics, vol. 8 (2014): 399 - 406}, number = {AIMS Series on Applied Mathematics}, year = {2014}, publisher = {SISSA}, organization = {SISSA}, keywords = {Method of characteristics}, url = {http://hdl.handle.net/1963/6562}, author = {Giovanni Alberti and Stefano Bianchini and Laura Caravenna} } @article {2014, title = {A Review of the Sixth Painlev{\'e} Equation}, number = {Constructive approximation;volume 41; issue 3; pages 495-527;}, year = {2014}, publisher = {Springer}, abstract = {For the Painlev{\'e} VI transcendents, we provide a unitary description of the critical behaviours, the connection formulae, their complete tabulation, and the asymptotic distribution of poles close to a critical point.}, doi = {10.1007/s00365-014-9250-6}, url = {http://urania.sissa.it/xmlui/handle/1963/34658}, author = {Davide Guzzetti} } @article {2014, title = {A robotic crawler exploiting directional frictional interactions: experiments, numerics, and derivation of a reduced model}, journal = {Proceedings of the Royal Society A 470, 20140333 (2014)}, year = {2014}, publisher = {Royal Society Publishing}, abstract = {We present experimental and numerical results for a model crawler which is able to extract net positional changes from reciprocal shape changes, i.e. {\textquoteleft}breathing-like{\textquoteright} deformations, thanks to directional, frictional interactions with a textured solid substrate, mediated by flexible inclined feet. We also present a simple reduced model that captures the essential features of the kinematics and energetics of the gait, and compare its predictions with the results from experiments and from numerical simulations.}, doi = {10.1098/rspa.2014.0333}, author = {Giovanni Noselli and Antonio DeSimone} } @article {2014, title = {SBV Regularity of Systems of Conservation Laws and Hamilton{\textendash}Jacobi Equations}, number = {Journal of Mathematical Sciences;Volume 201; issue 6; pp. 733-745;}, year = {2014}, publisher = {Springer}, abstract = {We review the SBV regularity for solutions to hyperbolic systems of conservation laws and Hamilton-Jacobi equations. We give an overview of the techniques involved in the proof, and a collection of related problems concludes the paper.}, doi = {10.1007/s10958-014-2022-9}, url = {http://urania.sissa.it/xmlui/handle/1963/34691}, author = {Stefano Bianchini} } @article {2014, title = {Second Order Asymptotic Development for the Anisotropic Cahn-Hilliard Functional}, year = {2014}, note = {This article is composed if 33 pages and recorded in PDF format}, publisher = {SISSA}, abstract = {The asymptotic behavior of an anisotropic Cahn-Hilliard functional with prescribed mass and Dirichlet boundary condition is studied when the parameter $\varepsilon$ that determines the width of the transition layers tends to zero. The double-well potential is assumed to be even and equal to $|s-1|^\beta$ near $s=1$, with $1<\beta<2$. The first order term in the asymptotic development by $\Gamma$-convergence is well-known, and is related to a suitable anisotropic perimeter of the interface. Here it is shown that, under these assumptions, the second order term is zero, which gives an estimate on the rate of convergence of the minimum values.}, keywords = {Gamma-convergence, Cahn-Hilliard functional, phase transitions}, url = {http://hdl.handle.net/1963/7390}, author = {Gianni Dal Maso and Irene Fonseca and Giovanni Leoni} } @article {2014, title = {Semiclassical limit of focusing NLS for a family of square barrier initial data}, number = {Communications on Pure and Applied Mathematics;volume 67; issue 2; pages 246-320;}, year = {2014}, publisher = {Wiley Periodicals}, abstract = {The small dispersion limit of the focusing nonlinear Schr{\"o}dinger equation (NLS) exhibits a rich structure of sharply separated regions exhibiting disparate rapid oscillations at microscopic scales. The non-self-adjoint scattering problem and ill-posed limiting Whitham equations associated to focusing NLS make rigorous asymptotic results difficult. Previous studies have focused on special classes of analytic initial data for which the limiting elliptic Whitham equations are wellposed. In this paper we consider another exactly solvable family of initial data,the family of square barriers,ψ 0(x) = qχ[-L,L] for real amplitudes q. Using Riemann-Hilbert techniques, we obtain rigorous pointwise asymptotics for the semiclassical limit of focusing NLS globally in space and up to an O(1) maximal time. In particular, we show that the discontinuities in our initial data regularize by the immediate generation of genus-one oscillations emitted into the support of the initial data. To the best of our knowledge, this is the first case in which the genus structure of the semiclassical asymptotics for focusing NLS have been calculated for nonanalytic initial data.}, doi = {10.1002/cpa.21494}, url = {http://urania.sissa.it/xmlui/handle/1963/35066}, author = {Robert Jenkins and Kenneth McLaughlin} } @article {2014, title = {Shape control of active surfaces inspired by the movement of euglenids}, number = {Journal of the Mechanics and Physics of Solids;volume 62; issue 1; pages 99-112;}, year = {2014}, publisher = {Elsevier}, abstract = {We examine a novel mechanism for active surface morphing inspired by the cell body deformations of euglenids. Actuation is accomplished through in-plane simple shear along prescribed slip lines decorating the surface. Under general non-uniform actuation, such local deformation produces Gaussian curvature, and therefore leads to shape changes. Geometrically, a deformation that realizes the prescribed local shear is an isometric embedding. We explore the possibilities and limitations of this bio-inspired shape morphing mechanism, by first characterizing isometric embeddings under axisymmetry, understanding the limits of embeddability, and studying in detail the accessibility of surfaces of zero and constant curvature. Modeling mechanically the active surface as a non-Euclidean plate (NEP), we further examine the mechanism beyond the geometric singularities arising from embeddability, where mechanics and buckling play a decisive role. We also propose a non-axisymmetric actuation strategy to accomplish large amplitude bending and twisting motions of elongated cylindrical surfaces. Besides helping understand how euglenids delicately control their shape, our results may provide the background to engineer soft machines.}, doi = {10.1016/j.jmps.2013.09.017}, url = {http://urania.sissa.it/xmlui/handle/1963/35118}, author = {Marino Arroyo and Antonio DeSimone} } @article {2014, title = {Shape Optimization by Free-Form Deformation: Existence Results and Numerical Solution for Stokes Flows}, number = {Journal of scientific computing;volume 60; issue 3; pages 537-563;}, year = {2014}, publisher = {Springer}, abstract = {Shape optimization problems governed by PDEs result from many applications in computational fluid dynamics. These problems usually entail very large computational costs and require also a suitable approach for representing and deforming efficiently the shape of the underlying geometry, as well as for computing the shape gradient of the cost functional to be minimized. Several approaches based on the displacement of a set of control points have been developed in the last decades, such as the so-called free-form deformations. In this paper we present a new theoretical result which allows to recast free-form deformations into the general class of perturbation of identity maps, and to guarantee the compactness of the set of admissible shapes. Moreover, we address both a general optimization framework based on the continuous shape gradient and a numerical procedure for solving efficiently three-dimensional optimal design problems. This framework is applied to the optimal design of immersed bodies in Stokes flows, for which we consider the numerical solution of a benchmark case study from literature.}, doi = {10.1007/s10915-013-9807-8}, url = {http://urania.sissa.it/xmlui/handle/1963/34698}, author = {Francesco Ballarin and Andrea Manzoni and Gianluigi Rozza and Sandro Salsa} } @article {berto-Tovbis-Katsevich-CPAM, title = {Singular Value Decomposition of a Finite Hilbert Transform Defined on Several Intervals and the Interior Problem of Tomography: The Riemann-Hilbert Problem Approach}, journal = {Comm. Pure Appl. Math.}, year = {2014}, author = {Marco Bertola and Alexander Katsevich and Alexander Tovbis} } @article {2014, title = {Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics}, number = {Journal of high energy physics;volume 2014; issue 7; article number 141;}, year = {2014}, publisher = {Springer}, abstract = {We show that the exact partition function of U(N) six-dimensional gauge theory with eight supercharges on C^2 x S^2 provides the quantization of the integrable system of hydrodynamic type known as gl(N) periodic Intermediate Long Wave (ILW). We characterize this system as the hydrodynamic limit of elliptic Calogero-Moser integrable system. We compute the Bethe equations from the effective gauged linear sigma model on S^2 with target space the ADHM instanton moduli space, whose mirror computes the Yang-Yang function of gl(N) ILW. The quantum Hamiltonians are given by the local chiral ring observables of the six-dimensional gauge theory. As particular cases, these provide the gl(N) Benjamin-Ono and Korteweg-de Vries quantum Hamiltonians. In the four dimensional limit, we identify the local chiral ring observables with the conserved charges of Heisenberg plus W_N algebrae, thus providing a gauge theoretical proof of AGT correspondence.}, doi = {10.1007/JHEP07(2014)141}, url = {http://urania.sissa.it/xmlui/handle/1963/34546}, author = {Giulio Bonelli and Antonio Sciarappa and Alessandro Tanzini and Petr Vasko} } @article {DANERI2014567, title = {Smooth approximation of bi-Lipschitz orientation-preserving homeomorphisms}, journal = {Annales de l{\textquoteright}Institut Henri Poincare (C) Non Linear Analysis}, volume = {31}, number = {3}, year = {2014}, pages = {567 - 589}, abstract = {We show that a planar bi-Lipschitz orientation-preserving homeomorphism can be approximated in the W1,p norm, together with its inverse, with an orientation-preserving homeomorphism which is piecewise affine or smooth.

}, issn = {0294-1449}, doi = {https://doi.org/10.1016/j.anihpc.2013.04.007}, url = {http://www.sciencedirect.com/science/article/pii/S0294144913000711}, author = {Sara Daneri and Aldo Pratelli} } @article {2014, title = {Some remarks on a model for rate-independent damage in thermo-visco-elastodynamics}, number = {SISSA;53/2014/MATE}, year = {2014}, institution = {SISSA}, abstract = {This note deals with the analysis of a model for partial damage, where the rateindependent, unidirectional flow rule for the damage variable is coupled with the rate-dependent heat equation, and with the momentum balance featuring inertia and viscosity according to Kelvin-Voigt rheology. The results presented here combine the approach from Roubicek [1] with the methods from Lazzaroni/Rossi/Thomas/Toader [2] and extend the analysis to the setting of inhomogeneous time-dependent Dirichlet data.}, url = {http://urania.sissa.it/xmlui/handle/1963/7463}, author = {Giuliano Lazzaroni and Riccarda Rossi and Marita Thomas and Rodica Toader} } @article {2014, title = {Some remarks on the seismic behaviour of embedded cantilevered retaining walls}, number = {Geotechnique;volume 64; issue 1; pages 40-50;}, year = {2014}, publisher = {Thomas Telford}, abstract = {This paper is a numerical investigation of the physical phenomena that control the dynamic behaviour of embedded cantilevered retaining walls. Recent experimental observations obtained from centrifuge tests have shown that embedded cantilevered retaining walls experience permanent displacements even before the acceleration reaches its critical value, corresponding to full mobilisation of the soil strength. The motivation for this work stems from the need to incorporate these observations in simplified design procedures. A parametric study was carried out on a pair of embedded cantilevered walls in dry sand, subjected to real earthquakes scaled at different values of the maximum acceleration. The results of these analyses indicate that, for the geotechnical design of the wall, the equivalent acceleration to be used in pseudo-static calculations can be related to the maximum displacement that the structure can sustain, and can be larger than the maximum acceleration expected at the site. For the structural design of the wall, it is suggested that the maximum bending moments of the wall can be computed using a realistic distribution of contact stress and a conservative value of the pseudo-static acceleration, taking into account two-dimensional amplification effects near the walls.}, doi = {10.1680/geot.13.P.031}, url = {http://urania.sissa.it/xmlui/handle/1963/35073}, author = {Riccardo Conti and F. Burali D{\textquoteright}Arezzo and Giulia M.B. Viggiani} } @article {2014, title = {Spontaneous division and motility in active nematic droplets}, number = {Physical review letters;volume 112; issue 14; article number 147802;}, year = {2014}, publisher = {American Physical Society}, abstract = {We investigate the mechanics of an active droplet endowed with internal nematic order and surrounded by an isotropic Newtonian fluid. Using numerical simulations we demonstrate that, due to the interplay between the active stresses and the defective geometry of the nematic director, this system exhibits two of the fundamental functions of living cells: spontaneous division and motility, by means of self-generated hydrodynamic flows. These behaviors can be selectively activated by controlling a single physical parameter, namely, an active variant of the capillary number.}, doi = {10.1103/PhysRevLett.112.147802}, url = {http://urania.sissa.it/xmlui/handle/1963/34902}, author = {Luca Giomi and Antonio DeSimone} } @article {2013, title = {Stability of equilibrium configurations for elastic films in two and three dimensions}, journal = {Advances in Calculus of Variations}, volume = {8}, number = {SISSA preprint;SISSA 38/2013/MATE}, year = {2014}, month = {01/2014}, pages = {117-153}, publisher = {SISSA}, chapter = {117}, abstract = {We establish a local minimality sufficiency criterion, based on the strict positivity of the second variation, in the context of a variational model for the epitaxial growth of elastic films. Our result holds also in the three-dimensional case and for a general class of nonlinear elastic energies. Applications to the study of the local minimality of flat morphologies are also shown.

}, keywords = {Epitaxially strained elastic films}, issn = {Online: 1864-8266; Print: 1864-8258}, doi = { https://doi.org/10.1515/acv-2013-0018}, url = {https://www.degruyter.com/view/j/acv.2015.8.issue-2/acv-2013-0018/acv-2013-0018.xml}, author = {Marco Bonacini} } @article {PacciariniRozza2014, title = {Stabilized reduced basis method for parametrized advection-diffusion PDEs}, journal = {Computer Methods in Applied Mechanics and Engineering}, volume = {274}, year = {2014}, pages = {1{\textendash}18}, abstract = {In this work, we propose viable and efficient strategies for the stabilization of the reduced basis approximation of an advection dominated problem. In particular, we investigate the combination of a classic stabilization method (SUPG) with the Offline-Online structure of the RB method. We explain why the stabilization is needed in both stages and we identify, analytically and numerically, which are the drawbacks of a stabilization performed only during the construction of the reduced basis (i.e. only in the Offline stage). We carry out numerical tests to assess the performances of the {\textquoteleft}{\textquoteleft}double{\textquoteright}{\textquoteright} stabilization both in steady and unsteady problems, also related to heat transfer phenomena.

}, doi = {10.1016/j.cma.2014.02.005}, author = {Pacciarini, P. and Gianluigi Rozza} } @conference {PacciariniRozza2014a, title = {Stabilized reduced basis method for parametrized scalar advection-diffusion problems at higher P{\'e}clet number: Roles of the boundary layers and inner fronts}, booktitle = {11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014}, year = {2014}, pages = {5614{\textendash}5624}, abstract = {Advection-dominated problems, which arise in many engineering situations, often require a fast and reliable approximation of the solution given some parameters as inputs. In this work we want to investigate the coupling of the reduced basis method - which guarantees rapidity and reliability - with some classical stabilization techiques to deal with the advection-dominated condition. We provide a numerical extension of the results presented in [1], focusing in particular on problems with curved boundary layers and inner fronts whose direction depends on the parameter.

}, url = {https://infoscience.epfl.ch/record/203327/files/ECCOMAS_PP_GR.pdf}, author = {Pacciarini, P. and Gianluigi Rozza} } @article {2014, title = {Steady nearly incompressible vector elds in 2D: chain rule and renormalization}, year = {2014}, institution = {SISSA}, author = {Stefano Bianchini and N.A. Gusev} } @article {2014, title = {The stringy instanton partition function}, number = {Journal of high energy physics;volume 2014; issue 1; article number 038;}, year = {2014}, publisher = {Springer}, abstract = {We perform an exact computation of the gauged linear sigma model associated to a D1-D5 brane system on a resolved A_1 singularity. This is accomplished via supersymmetric localization on the blown-up two-sphere. We show that in the blow-down limit C^2/Z_2 the partition function reduces to the Nekrasov partition function evaluating the equivariant volume of the instanton moduli space. For finite radius we obtain a tower of world-sheet instanton corrections, that we identify with the equivariant Gromov-Witten invariants of the ADHM moduli space. We show that these corrections can be encoded in a deformation of the Seiberg-Witten prepotential. From the mathematical viewpoint, the D1-D5 system under study displays a twofold nature: the D1-branes viewpoint captures the equivariant quantum cohomology of the ADHM instanton moduli space in the Givental formalism, and the D5-branes viewpoint is related to higher rank equivariant Donaldson-Thomas invariants of P^1 x C^2.}, doi = {10.1007/JHEP01(2014)038}, url = {http://urania.sissa.it/xmlui/handle/1963/34589}, author = {Giulio Bonelli and Antonio Sciarappa and Alessandro Tanzini and Petr Vasko} } @article {2014, title = {Structure of classical (finite and affine) W-algebras}, number = {arXiv:1404.0715;}, year = {2014}, note = {40 pages}, institution = {SISSA}, abstract = {First, we derive an explicit formula for the Poisson bracket of the classical finite W-algebra W^{fin}(g,f), the algebra of polynomial functions on the Slodowy slice associated to a simple Lie algebra g and its nilpotent element f. On the other hand, we produce an explicit set of generators and we derive an explicit formula for the Poisson vertex algebra structure of the classical affine W-algebra W(g,f). As an immediate consequence, we obtain a Poisson algebra isomorphism between W^{fin}(g,f) and the Zhu algebra of W(g,f). We also study the generalized Miura map for classical W-algebras.}, url = {http://hdl.handle.net/1963/7314}, author = {Alberto De Sole and Victor G. Kac and Daniele Valeri} } @article {2014, title = {Structure of entropy solutions to general scalar conservation laws in one space dimension}, journal = {Journal of Mathematical Analysis and Applications}, volume = {428}, number = {SISSA;11/2014/MATE}, year = {2014}, month = {08/2015}, pages = {356-386}, publisher = {SISSA}, chapter = {356}, doi = {https://doi.org/10.1016/j.jmaa.2015.03.006}, url = {https://www.sciencedirect.com/science/article/pii/S0022247X15002218}, author = {Stefano Bianchini and Lei Yu} } @article {2014, title = {Swelling dynamics of a thin elastomeric sheet under uniaxial pre-stretch}, number = {Journal of Applied Physics;volume 115; issue 8; article number 083505;}, year = {2014}, publisher = {American Institute of Physics}, abstract = {It has been demonstrated experimentally that pre-stretch affects the swelling of an elastomeric membrane when it is exposed to a solvent. We study theoretically the one-dimensional swelling of a pre-stretched thin elastomeric sheet, bonded to an impermeable rigid substrate, to quantify the influence of pre-stretch. We show that the solvent uptake increases when pre-stretch increases, both at equilibrium and during the swelling transient, where it exhibits two different scaling regimes. The coupling between the solvent uptake and pre-stretch may be practically exploited to design soft actuators where the swelling-induced deformations can be controlled by varying the pre-stretch.}, doi = {10.1063/1.4866576}, url = {http://urania.sissa.it/xmlui/handle/1963/35113}, author = {Alessandro Lucantonio and Paola Nardinocchi and Howard A. Stone} } @article {2014, title = {Swelling-induced and controlled curving in layered gel beams}, number = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences;volume 470; issue 2171;}, year = {2014}, publisher = {Royal Society of London}, abstract = {We describe swelling-driven curving in originally straight and non-homogeneous beams. We present and verify a structural model of swollen beams, based on a new point of view adopted to describe swelling-induced deformation processes in bilayered gel beams, that is based on the split of the swelling-induced deformation of the beam at equilibrium into two components, both depending on the elastic properties of the gel. The method allows us to: (i) determine beam stretching and curving, once assigned the characteristics of the solvent bath and of the non-homogeneous beam, and (ii) estimate the characteristics of non-homogeneous flat gel beams in such a way as to obtain, under free-swelling conditions, three-dimensional shapes. The study was pursued by means of analytical, semi-analytical and numerical tools; excellent agreement of the outcomes of the different techniques was found, thus confirming the strength of the method.}, doi = {10.1098/rspa.2014.0467}, url = {http://urania.sissa.it/xmlui/handle/1963/34987}, author = {Alessandro Lucantonio and Paola Nardinocchi and Matteo Pezzulla} } @article {2014, title = {Topological Invariants of Eigenvalue Intersections and Decrease of Wannier Functions in Graphene}, journal = {J. Stat. Phys 155 (2014) 1027-1071}, year = {2014}, publisher = {Journal of Statistical Physics}, abstract = {We investigate the asymptotic decrease of the Wannier functions for the valence and conduction band of graphene, both in the monolayer and the multilayer case. Since the decrease of the Wannier functions is characterised by the structure of the Bloch eigenspaces around the Dirac points, we introduce a geometric invariant of the family of eigenspaces, baptised eigenspace vorticity. We compare it with the pseudospin winding number. For every value n∈Z of the eigenspace vorticity, we exhibit a canonical model for the local topology of the eigenspaces. With the help of these canonical models, we show that the single band Wannier function w satisfies |w(x)|<=const |x|^{-2} as |x|{\textrightarrow}$\infty$, both in monolayer and bilayer graphene.

}, keywords = {Wannier functions, Bloch bundles, conical intersections, eigenspace vorticity, pseudospin winding number, graphene}, doi = {10.1007/s10955-014-0918-x}, author = {Domenico Monaco and Gianluca Panati} } @article {2014, title = {The topology of a subspace of the Legendrian curves on a closed contact 3-manifold}, number = {Advanced Nonlinear Studies;volume 14; issue 2; pages 393-426;}, year = {2014}, publisher = {Advanced Nonlinear Studies}, abstract = {In this paper we study a subspace of the space of Legendrian loops and we show that the injection of this space into the full loop space is an S 1-equivariant homotopy equivalence. This space can be also seen as the space of zero Maslov index Legendrian loops and it shows up as a suitable space of variations in contact form geometry.}, url = {http://urania.sissa.it/xmlui/handle/1963/35016}, author = {Ali Maalaoui and Vittorio Martino} } @article {2014, title = {A uniqueness result for the continuity equation in two dimensions: dedicated to constantine dafermos on the occasion of his 70th birthday}, number = {Journal of the European Mathematical Society;Volume 16; issue 2; pp. 201-234;}, year = {2014}, publisher = {European Mathematical Society; Springer Verlag}, abstract = {We characterize the autonomous, divergence-free vector fields b on the plane such that the Cauchy problem for the continuity equation ∂tu +div(bu) = 0 admits a unique bounded solution (in the weak sense) for every bounded initial datum; the characterization is given in terms of a property of Sard type for the potential f associated to b. As a corollary we obtain uniqueness under the assumption that the curl of b is a measure. This result can be extended to certain nonautonomous vector fields b with bounded divergence.}, doi = {10.4171/JEMS/431}, url = {http://urania.sissa.it/xmlui/handle/1963/34692}, author = {Giovanni Alberti and Stefano Bianchini and Gianluca Crippa} } @mastersthesis {2014, title = {A variational approach to statics and dynamics of elasto-plastic systems}, year = {2014}, school = {SISSA}, abstract = {We prove some existence results for dynamic evolutions in elasto-plasticity and delamination. We study the limit as the data vary very slowly and prove convergence results to quasistatic evolutions. We model dislocations by mean of currents, we introduce the space of deformations in the presence of dislocations and study the graphs of these maps. We prove existence results for minimum problems. We study the properties of minimizers.}, keywords = {delamination}, url = {http://urania.sissa.it/xmlui/handle/1963/7471}, author = {Riccardo Scala} } @article {10829, title = {A variational model for the quasi-static growth of fractional dimensional brittle fractures}, number = {Interfaces and Free Boundaries}, year = {2014}, publisher = {European Mathematical Society}, abstract = {We propose a variational model for the irreversible quasi-static evolution of brittle fractures having fractional Hausdorff dimension in the setting of two-dimensional antiplane and plane elasticity. The evolution along such irregular crack paths can be obtained as $\Gamma$-limit of evolutions along one-dimensional cracks when the fracture toughness tends to zero.

}, keywords = {Variational models}, doi = {10.4171/IFB/328}, url = {http://hdl.handle.net/1963/6983}, author = {Simone Racca and Rodica Toader} } @article {2014, title = {Vortex Partition Functions, Wall Crossing and Equivariant Gromov{\textendash}Witten Invariants}, number = {Communications in mathematical physics;volume 333; issue 2; pages 717-760;}, year = {2014}, publisher = {Springer}, abstract = {In this paper we identify the problem of equivariant vortex counting in a (2,2) supersymmetric two dimensional quiver gauged linear sigma model with that of computing the equivariant Gromov{\textendash}Witten invariants of the GIT quotient target space determined by the quiver. We provide new contour integral formulae for the I and J-functions encoding the equivariant quantum cohomology of the target space. Its chamber structure is shown to be encoded in the analytical properties of the integrand. This is explained both via general arguments and by checking several key cases. We show how several results in equivariant Gromov{\textendash}Witten theory follow just by deforming the integration contour. In particular, we apply our formalism to compute Gromov{\textendash}Witten invariants of the C3/Zn orbifold, of the Uhlembeck (partial) compactification of the moduli space of instantons on C2, and of An and Dn singularities both in the orbifold and resolved phases. Moreover, we analyse dualities of quantum cohomology rings of holomorphic vector bundles over Grassmannians, which are relevant to BPS Wilson loop algebrae.}, doi = {10.1007/s00220-014-2193-8}, url = {http://urania.sissa.it/xmlui/handle/1963/34652}, author = {Giulio Bonelli and Antonio Sciarappa and Alessandro Tanzini and Petr Vasko} } @article {2014, title = {A weighted empirical interpolation method: A priori convergence analysis and applications}, number = {ESAIM: Mathematical Modelling and Numerical Analysis;volume 48; issue 4; pages 943-953}, year = {2014}, publisher = {EDP Sciences}, abstract = {We extend the classical empirical interpolation method [M. Barrault, Y. Maday, N.C. Nguyen and A.T. Patera, An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations. Compt. Rend. Math. Anal. Num. 339 (2004) 667-672] to a weighted empirical interpolation method in order to approximate nonlinear parametric functions with weighted parameters, e.g. random variables obeying various probability distributions. A priori convergence analysis is provided for the proposed method and the error bound by Kolmogorov N-width is improved from the recent work [Y. Maday, N.C. Nguyen, A.T. Patera and G.S.H. Pau, A general, multipurpose interpolation procedure: the magic points. Commun. Pure Appl. Anal. 8 (2009) 383-404]. We apply our method to geometric Brownian motion, exponential Karhunen-Lo{\`e}ve expansion and reduced basis approximation of non-affine stochastic elliptic equations. We demonstrate its improved accuracy and efficiency over the empirical interpolation method, as well as sparse grid stochastic collocation method.}, doi = {10.1051/m2an/2013128}, url = {http://urania.sissa.it/xmlui/handle/1963/35021}, author = {Peng Chen and Alfio Quarteroni and Gianluigi Rozza} } @article {2014, title = {Weighted quantile correlation test for the logistic family}, number = {Acta Scientiarum Mathematicarum;volume 80; issue 1-2; pages 307-326;}, year = {2014}, publisher = {University of Szeged}, abstract = {We summarize the results of investigating the asymptotic behavior of the weighted quantile correlation tests for the location-scale family associated to the logistic distribution. Explicit representations of the limiting distribution are given in terms of integrals of weighted Brownian bridges or alternatively as infinite series of independent Gaussian random variables. The power of this test and the test for the location logistic family against some alternatives are demonstrated by numerical simulations.}, doi = {10.14232/actasm-013-809-8}, url = {http://urania.sissa.it/xmlui/handle/1963/35025}, author = {Ferenc Balogh and {\'E}va Krauczi} } @article {2014, title = {Where best to place a Dirichlet condition in an anisotropic membrane?}, number = {SISSA;61/2014/MATE}, year = {2014}, institution = {SISSA}, abstract = {We study a shape optimization problem for the first eigenvalue of an elliptic operator in divergence form, with non constant coefficients, over a fixed domain $\Omega$. Dirichlet conditions are imposed along $\partial\Omega$ and, in addition, along a set $\Sigma$ of prescribed length ($1$-dimensional Hausdorff measure). We look for the best shape and position for the supplementary Dirichlet region $\Sigma$ in order to maximize the first eigenvalue. We characterize the limit distribution of the optimal sets, as their prescribed length tends to infinity, via $\Gamma$-convergence.}, url = {http://urania.sissa.it/xmlui/handle/1963/7481}, author = {Paolo Tilli and Davide Zucco} } @article {Berto-Bothner-YV, title = {Zeros of Large Degree Vorob{\textquoteright}ev-Yablonski Polynomials via a Hankel Determinant Identity}, journal = {International Mathematics Research Notices}, volume = {rnu239}, year = {2014}, author = {Marco Bertola and Thomas Bothner} } @article {2013, title = {Ambrosio-Tortorelli approximation of cohesive fracture models in linearized elasticity}, year = {2013}, institution = {SISSA}, abstract = {We provide an approximation result in the sense of $\Gamma$-convergence for cohesive fracture energies of the form \[ \int_\Omega \mathscr{Q}_1(e(u))\,dx+a\,\mathcal{H}^{n-1}(J_u)+b\,\int_{J_u}\mathscr{Q}_0^{1/2}([u]\odot\nu_u)\,d\mathcal{H}^{n-1}, \] where $\Omega\subset{\mathbb R}^n$ is a bounded open set with Lipschitz boundary, $\mathscr{Q}_0$ and $\mathscr{Q}_1$ are coercive quadratic forms on ${\mathbb M}^{n\times n}_{sym}$, $a,\,b$ are positive constants, and $u$ runs in the space of fields $SBD^2(\Omega)$ , i.e., it{\textquoteright}s a special field with bounded deformation such that its symmetric gradient $e(u)$ is square integrable, and its jump set $J_u$ has finite $(n-1)$-Hausdorff measure in ${\mathbb R}^n$. The approximation is performed by means of Ambrosio-Tortorelli type elliptic regularizations, the prototype example being \[ \int_\Omega\Big(v|e(u)|^2+\frac{(1-v)^2}{\varepsilon}+{\gamma\,\varepsilon}|\nabla v|^2\Big)\,dx, \] where $(u,v)\in H^1(\Omega,{\mathbb R}^n){\times} H^1(\Omega)$, $\varepsilon\leq v\leq 1$ and $\gamma\>0$.

}, keywords = {Functions of bounded deformation}, url = {http://hdl.handle.net/1963/6615}, author = {Matteo Focardi and Flaviana Iurlano} } @article {2013, title = {Analytical validation of a continuum model for epitaxial growth with elasticity on vicinal surfaces}, number = {Archive for Rational Mechanics and Analysis}, year = {2013}, publisher = {Springer}, abstract = {In this paper it is shown existence of weak solutions of a variational inequality derived from the continuum model introduced by Xiang [7, formula (3.62)] (see also the work of Xiang and E [8] and Xu and Xiang [9]) to describe the self-organization of terraces and steps driven by misfit elasticity between a film and a substrate in heteroepitaxial growth. This model is obtained as a continuum limit of discrete theories of Duport, Politi, and Villain [3] and Tersoff, Phang, Zhang, and Lagally[6].}, keywords = {singular nonlinear parabolic equations, Hilbert transform, thin films}, doi = {10.1007/s00205-014-0730-4}, url = {http://hdl.handle.net/1963/7245}, author = {Gianni Dal Maso and Irene Fonseca and Giovanni Leoni} } @mastersthesis {2013, title = {An Approximation Result for Generalised Functions of Bounded Deformation and Applications to Damage Problems}, year = {2013}, school = {SISSA}, keywords = {Functions of bounded deformation}, author = {Flaviana Iurlano} } @article {2013, title = {Asymptotics of the first Laplace eigenvalue with Dirichlet regions of prescribed length}, number = {SIAM Journal on Mathematical Analysis;volume 45; issue 6; pp. 3266-3282}, year = {2013}, publisher = {Society for Industrial and Applied Mathematics}, abstract = {We consider the problem of maximizing the first eigenvalue of the $p$-Laplacian (possibly with nonconstant coefficients) over a fixed domain $\Omega$, with Dirichlet conditions along $\partial\Omega$ and along a supplementary set $\Sigma$, which is the unknown of the optimization problem. The set $\Sigma$, which plays the role of a supplementary stiffening rib for a membrane $\Omega$, is a compact connected set (e.g., a curve or a connected system of curves) that can be placed anywhere in $\overline{\Omega}$ and is subject to the constraint of an upper bound $L$ to its total length (one-dimensional Hausdorff measure). This upper bound prevents $\Sigma$ from spreading throughout $\Omega$ and makes the problem well-posed. We investigate the behavior of optimal sets $\Sigma_L$ as $L\to\infty$ via $\Gamma$-convergence, and we explicitly construct certain asymptotically optimal configurations. We also study the behavior as $p\to\infty$ with $L$ fixed, finding connections with maximum-distance problems related to the principal frequency of the $\infty$-Laplacian.}, doi = {10.1137/130916825}, url = {http://urania.sissa.it/xmlui/handle/1963/35141}, author = {Paolo Tilli and Davide Zucco} } @article {2013, title = {Attainment results for nematic elastomers}, year = {2013}, institution = {SISSA}, abstract = {We consider a class of non-quasiconvex frame indifferent energy densities which includes Ogden-type energy densities for nematic elastomers. For the corresponding geometrically linear problem we provide an explicit minimizer of the energy functional satisfying a nontrivial boundary condition. Other attainment results, both for the nonlinear and the linearized model, are obtained by using the theory of convex integration introduced by Mueller and Sverak in the context of crystalline solids.}, url = {http://hdl.handle.net/1963/7174}, author = {Virginia Agostiniani and Gianni Dal Maso and Antonio DeSimone} } @mastersthesis {2013, title = {Biregular and Birational Geometry of Algebraic Varieties}, year = {2013}, school = {SISSA}, abstract = {Every area of mathematics is characterized by a guiding problem. In algebraic geometry such problem is the classification of algebraic varieties. In its strongest form it means to classify varieties up to biregular morphisms. However, birationally equivalent varieties share many interesting properties. Therefore for any birational equivalence class it is natural to work out a variety, which is the simplest in a suitable sense, and then study these varieties. This is the aim of birational geometry. In the first part of this thesis we deal with the biregular geometry of moduli spaces of curves, and in particular with their biregular automorphisms. However, in doing this we will consider some aspects of their birational geometry. The second part is devoted to the birational geometry of varieties of sums of powers and to some related problems which will lead us to computational geometry and geometric complexity theory.}, keywords = {Moduli spaces of curves, automorphisms, Hassett{\textquoteright}s moduli spaces, varieties of sums of powers}, author = {Alex Massarenti} } @article {2012, title = {Classical W-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras}, journal = {Communications in Mathematical Physics 323, nr. 2 (2013) 663-711}, number = {arXiv:1207.6286;}, year = {2013}, note = {43 pages. Second version with minor editing and corrections}, publisher = {Springer}, abstract = {We provide a description of the Drinfeld-Sokolov Hamiltonian reduction for the construction of classical W-algebras within the framework of Poisson vertex algebras. In this context, the gauge group action on the phase space is translated in terms of (the exponential of) a Lie conformal algebra action on the space of functions. Following the ideas of Drinfeld and Sokolov, we then establish under certain sufficient conditions the applicability of the Lenard-Magri scheme of integrability and the existence of the corresponding integrable hierarchy of bi-Hamiltonian equations.}, doi = {10.1007/s00220-013-1785-z}, url = {http://hdl.handle.net/1963/6978}, author = {Alberto De Sole and Victor G. Kac and Daniele Valeri} } @article {2013, title = {A combination between the reduced basis method and the ANOVA expansion: On the computation of sensitivity indices}, journal = {Comptes Rendus Mathematique. Volume 351, Issue 15-16, August 2013, Pages 593-598}, year = {2013}, publisher = {Elsevier}, abstract = {We consider a method to efficiently evaluate in a real-time context an output based on the numerical solution of a partial differential equation depending on a large number of parameters. We state a result allowing to improve the computational performance of a three-step RB-ANOVA-RB method. This is a combination of the reduced basis (RB) method and the analysis of variations (ANOVA) expansion, aiming at compressing the parameter space without affecting the accuracy of the output. The idea of this method is to compute a first (coarse) RB approximation of the output of interest involving all the parameter components, but with a large tolerance on the a posteriori error estimate; then, we evaluate the ANOVA expansion of the output and freeze the least important parameter components; finally, considering a restricted model involving just the retained parameter components, we compute a second (fine) RB approximation with a smaller tolerance on the a posteriori error estimate. The fine RB approximation entails lower computational costs than the coarse one, because of the reduction of parameter dimensionality. Our result provides a criterion to avoid the computation of those terms in the ANOVA expansion that are related to the interaction between parameters in the bilinear form, thus making the RB-ANOVA-RB procedure computationally more feasible.

}, keywords = {Partial differential equations}, doi = {10.1016/j.crma.2013.07.023}, url = {http://hdl.handle.net/1963/7389}, author = {Denis Devaud and Andrea Manzoni and Gianluigi Rozza} } @article {2013, title = {Common dynamical features of sensory adaptation in photoreceptors and olfactory sensory neurons.}, journal = {Nature. Scientific Reports 3, Article number: 1251, Published : 13 February 2013}, year = {2013}, publisher = {SISSA}, abstract = {Sensory systems adapt, i.e., they adjust their sensitivity to external stimuli according to the ambient level. In this paper we show that single cell electrophysiological responses of vertebrate olfactory receptors and of photoreceptors to different input protocols exhibit several common features related to adaptation, and that these features can be used to investigate the dynamical structure of the feedback regulation responsible for the adaptation. In particular, we point out that two different forms of adaptation can be observed, in response to steps and to pairs of pulses. These two forms of adaptation appear to be in a dynamical trade-off: the more adaptation to a step is close to perfect, the slower is the recovery in adaptation to pulse pairs and viceversa. Neither of the two forms is explained by the dynamical models currently used to describe adaptation, such as the integral feedback model.

}, doi = {10.1038/srep01251}, author = {Giovanna De Palo and Giuseppe Facchetti and Monica Mazzolini and Anna Menini and Vincent Torre and Claudio Altafini} } @article {DIPIERRO201330, title = {Concentration of solutions for a singularly perturbed mixed problem in non-smooth domains}, journal = {Journal of Differential Equations}, volume = {254}, number = {1}, year = {2013}, pages = {30 - 66}, abstract = {We consider a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^n$ whose boundary has an $(n-2)$-dimensional singularity. Assuming $1\<p\<\frac{n+2}{n-2}$, we prove that, under suitable geometric conditions on the boundary of the domain, there exist solutions which approach the intersection of the Neumann and the Dirichlet parts as the singular perturbation parameter tends to zero.

}, keywords = {Finite-dimensional reductions, Local inversion, Singularly perturbed elliptic problems}, issn = {0022-0396}, doi = {https://doi.org/10.1016/j.jde.2012.08.017}, url = {http://www.sciencedirect.com/science/article/pii/S0022039612003312}, author = {Serena Dipierro} } @article {Mondino2013, title = {The Conformal Willmore Functional: A Perturbative Approach}, journal = {Journal of Geometric Analysis}, volume = {23}, number = {2}, year = {2013}, month = {Apr}, pages = {764{\textendash}811}, abstract = {The conformal Willmore functional (which is conformal invariant in general Riemannian manifolds $(M,g)$ is studied with a perturbative method: the Lyapunov{\textendash}Schmidt reduction. Existence of critical points is shown in ambient manifolds $(\mathbb{R}^3,g_\epsilon)$ {\textendash} where $g_\epsilon$ is a metric close and asymptotic to the Euclidean one. With the same technique a non-existence result is proved in general Riemannian manifolds $(M,g)$ of dimension three.

}, issn = {1559-002X}, doi = {10.1007/s12220-011-9263-3}, url = {https://doi.org/10.1007/s12220-011-9263-3}, author = {Andrea Mondino} } @article {2013, title = {Connected Sum Construction for σk-Yamabe Metrics}, journal = {Journal of Geometric Analysis 23, nr.2 (2013), pages 812-854}, number = {arXiv:0910.5353;}, year = {2013}, note = {This article has not yet been published.}, publisher = {Springer}, abstract = {In this paper we produce families of Riemannian metrics with positive constant $\sigma_k$-curvature equal to $2^{-k} {n \choose k}$ by performing the connected sum of two given compact {\em non degenerate} $n$--dimensional solutions $(M_1,g_1)$ and $(M_2,g_2)$ of the (positive) $\sigma_k$-Yamabe problem, provided $2 \leq 2k < n$. The problem is equivalent to solve a second order fully nonlinear elliptic equation.}, doi = {10.1007/s12220-011-9265-1}, url = {http://hdl.handle.net/1963/6441}, author = {Giovanni Catino and Lorenzo Mazzieri} } @article {2013, title = {Crawlers in viscous environments: linear vs nonlinear rheology}, journal = {International Journal of Non-Linear Mechanics 56, 142-147 (2013)}, year = {2013}, publisher = {Elsevier}, abstract = {We study model self-propelled crawlers which derive their propulsive capabilities from the tangential resistance to motion offered by the environment. Two types of relationships between tangential forces and slip velocities are considered: a linear, Newtonian one and a nonlinear one of Bingham-type. Different behaviors result from the two different rheologies. These differences and their implications in terms of motility performance are discussed. Our aim is to develop new tools and insight for future studies of cell motility by crawling.}, doi = {10.1016/j.ijnonlinmec.2013.02.007}, author = {Antonio DeSimone and Federica Guarnieri and Giovanni Noselli and Amabile Tatone} } @article {10978, title = {On critical behaviour in systems of Hamiltonian partial differential equations}, year = {2013}, institution = {SISSA}, abstract = {We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by particular solutions to the Painlev\'e-I (P$_I$) equation or its fourth order analogue P$_I^2$. As concrete examples we discuss nonlinear Schr\"odinger equations in the semiclassical limit. A numerical study of these cases provides strong evidence in support of the conjecture.

}, author = {Boris Dubrovin and Tamara Grava and Christian Klein and Antonio Moro} } @article {2013, title = {The curvature: a variational approach}, number = {arXiv:1306.5318;}, year = {2013}, note = {88 pages, 10 figures, (v2) minor typos corrected, (v3) added sections on Finsler manifolds, slow growth distributions, Heisenberg group}, institution = {SISSA}, abstract = {The curvature discussed in this paper is a rather far going generalization of the Riemannian sectional curvature. We define it for a wide class of optimal control problems: a unified framework including geometric structures such as Riemannian, sub-Riemannian, Finsler and sub-Finsler structures; a special attention is paid to the sub-Riemannian (or Carnot-Caratheodory) metric spaces. Our construction of the curvature is direct and naive, and it is similar to the original approach of Riemann. Surprisingly, it works in a very general setting and, in particular, for all sub-Riemannian spaces.}, keywords = {Crurvature, subriemannian metric, optimal control problem}, url = {http://hdl.handle.net/1963/7226}, author = {Andrei A. Agrachev and Davide Barilari and Luca Rizzi} } @article {2013, title = {Curved noncommutative torus and Gauss--Bonnet}, journal = {Journal of Mathematical Physics. Volume 54, Issue 1, 22 January 2013, Article number 013518}, number = {arXiv:1204.0420v1;}, year = {2013}, note = {The article is composed of 13 pages and is recorded in PDF format}, publisher = {American Institute of Physics}, abstract = {We study perturbations of the flat geometry of the noncommutative two-dimensional torus T^2_\theta (with irrational \theta). They are described by spectral triples (A_\theta, \H, D), with the Dirac operator D, which is a differential operator with coefficients in the commutant of the (smooth) algebra A_\theta of T_\theta. We show, up to the second order in perturbation, that the zeta-function at 0 vanishes and so the Gauss-Bonnet theorem holds. We also calculate first two terms of the perturbative expansion of the corresponding local scalar curvature.}, keywords = {Geometry}, doi = {10.1063/1.4776202}, url = {http://hdl.handle.net/1963/7376}, author = {Ludwik Dabrowski and Andrzej Sitarz} } @article {2013, title = {The deal.II Library, Version 8.1}, number = {arXiv:1312.2266;}, year = {2013}, note = {5 pages}, institution = {SISSA}, abstract = {This paper provides an overview of the new features of the finite element library deal.II version 8.0.}, url = {http://hdl.handle.net/1963/7236}, author = {W. Bangerth and Timo Heister and Luca Heltai and G. Kanschat and Martin Kronbichler and Matthias Maier and B. Turcksin and T. D. Young} } @article {2013, title = {Defect annihilation and proliferation in active nematics}, number = {arXiv:1303.4720;}, year = {2013}, note = {5 pages, 4 figures}, institution = {SISSA}, abstract = {Liquid crystals inevitably possess topological defect excitations generated\r\nthrough boundary conditions, applied fields or in quenches to the ordered\r\nphase. In equilibrium pairs of defects coarsen and annihilate as the uniform\r\nground state is approached. Here we show that defects in active liquid crystals\r\nexhibit profoundly different behavior, depending on the degree of activity and\r\nits contractile or extensile character. While contractile systems enhance the\r\nannihilation dynamics of passive systems, extensile systems act to drive\r\ndefects apart so that they swarm around in the manner of topologically\r\nwell-characterized self-propelled particles. We develop a simple analytical\r\nmodel for the defect dynamics which reproduces the key features of both the\r\nnumerical solutions and recent experiments on microtuble-kinesin assemblies.}, url = {http://hdl.handle.net/1963/6566}, author = {Luca Giomi and Mark J. Bowick and Xu Ma and M. Cristina Marchetti} } @article {2013, title = {On deformations of multidimensional Poisson brackets of hydrodynamic type}, number = {arXiv:1312.1878;}, year = {2013}, institution = {SISSA}, abstract = {The theory of Poisson Vertex Algebras (PVAs) is a good framework to treat Hamiltonian partial differential equations. A PVA consist of a pair $(\mathcal{A},\{\cdot_{\lambda}\cdot\})$ of a differential algebra $\mathcal{A}$ and a bilinear operation called the $\lambda$-bracket. We extend the definition to the class of algebras $\mathcal{A}$ endowed with $d\geq 1$ commuting derivations. We call this structure a multidimensional PVA: it is a suitable setting to the study of deformations of the Poisson bracket of hydrodynamic type associated to the Euler{\textquoteright}s equation of motion of $d$-dimensional incompressible fluids. We prove that for $d=2$ all the first order deformations of such class of Poisson brackets are trivial.}, keywords = {Hamiltonian operator}, url = {http://hdl.handle.net/1963/7235}, author = {Matteo Casati} } @mastersthesis {2013, title = {On the desingularization of Kahler orbifolds with constant scalar curvature}, year = {2013}, school = {SISSA}, author = {Riccardo Lena} } @article {2013, title = {Dirac operator on spinors and diffeomorphisms}, journal = {Classical and Quantum Gravity. Volume 30, Issue 1, 7 January 2013, Article number 015006}, number = {arXiv:1209.2021v1;}, year = {2013}, note = {This article is composed of 13 pages and is recorded in PDF format}, publisher = {IOP Publishing}, abstract = {The issue of general covariance of spinors and related objects is reconsidered. Given an oriented manifold $M$, to each spin structure $\sigma$ and Riemannian metric $g$ there is associated a space $S_{\sigma, g}$ of spinor fields on $M$ and a Hilbert space $\HH_{\sigma, g}= L^2(S_{\sigma, g},\vol{M}{g})$ of $L^2$-spinors of $S_{\sigma, g}$. The group $\diff{M}$ of orientation-preserving diffeomorphisms of $M$ acts both on $g$ (by pullback) and on $[\sigma]$ (by a suitably defined pullback $f^*\sigma$). Any $f\in \diff{M}$ lifts in exactly two ways to a unitary operator $U$ from $\HH_{\sigma, g} $ to $\HH_{f^*\sigma,f^*g}$. The canonically defined Dirac operator is shown to be equivariant with respect to the action of $U$, so in particular its spectrum is invariant under the diffeomorphisms.}, keywords = {gravity}, doi = {10.1088/0264-9381/30/1/015006}, url = {http://hdl.handle.net/1963/7377}, author = {Ludwik Dabrowski and Giacomo Dossena} } @article {2013, title = {Dislocation dynamics in crystals: a macroscopic theory in a fractional Laplace setting}, number = {SISSA preprint;43/2013/MATE}, year = {2013}, institution = {SISSA}, abstract = {We consider an evolution equation arising in the Peierls-Nabarro model for crystal dislocation. We study the evolution of such dislocation function and show that, at a macroscopic scale, the dislocations have the tendency to concentrate at single points of the crystal, where the size of the slip coincides with the natural periodicity of the medium. These dislocation points evolve according to the external stress and an interior repulsive potential.}, keywords = {nonlocal Allen-Cahn equation}, url = {http://hdl.handle.net/1963/7124}, author = {Serena Dipierro and Giampiero Palatucci and Enrico Valdinoci} } @article {2013, title = {Early phase of plasticity-related gene regulation and SRF dependent transcription in the hippocampus}, journal = {PloS one. Volume 8, Issue 7, July 2013 : e68078}, number = {PMID:23935853;}, year = {2013}, note = {The article is composed of 15 pages}, publisher = {Public Library of Science}, abstract = {Hippocampal organotypic cultures are a highly reliable in vitro model for studying neuroplasticity: in this paper, we analyze the early phase of the transcriptional response induced by a 20 {\textmu}M gabazine treatment (GabT), a GABA-Ar antagonist, by using Affymetrix oligonucleotide microarray, RT-PCR based time-course and chromatin-immuno-precipitation. The transcriptome profiling revealed that the pool of genes up-regulated by GabT, besides being strongly related to the regulation of growth and synaptic transmission, is also endowed with neuro-protective and pro-survival properties. By using RT-PCR, we quantified a time-course of the transient expression for 33 of the highest up-regulated genes, with an average sampling rate of 10 minutes and covering the time interval [10:90] minutes. The cluster analysis of the time-course disclosed the existence of three different dynamical patterns, one of which proved, in a statistical analysis based on results from previous works, to be significantly related with SRF-dependent regulation (p-value<0.05). The chromatin immunoprecipitation (chip) assay confirmed the rich presence of working CArG boxes in the genes belonging to the latter dynamical pattern and therefore validated the statistical analysis. Furthermore, an in silico analysis of the promoters revealed the presence of additional conserved CArG boxes upstream of the genes Nr4a1 and Rgs2. The chip assay confirmed a significant SRF signal in the Nr4a1 CArG box but not in the Rgs2 CArG box.}, doi = {10.1371/journal.pone.0068078}, url = {http://hdl.handle.net/1963/7287}, author = {Giovanni Iacono and Claudio Altafini and Vincent Torre} } @article {2013, title = {Epitaxially strained elastic films: the case of anisotropic surface energies}, journal = {ESAIM Control. Optim. Calc. Var. 19 (2013) 167-189}, number = {SISSA;31/2011/M}, year = {2013}, publisher = {EDP Sciences}, abstract = {In the context of a variational model for the epitaxial growth of strained elastic films, we study the effects of the presence of anisotropic surface energies in the determination of equilibrium configurations. We show that the threshold effect that describes the stability of flat morphologies in the isotropic case remains valid for weak anisotropies, but is no longer present in the case of highly anisotropic surface energies, where we show that the flat configuration is always a local minimizer of the total energy. The main tool used to obtain these results is a minimality criterion based on the positivity of the second variation.

}, doi = {10.1051/cocv/2012003}, url = {http://hdl.handle.net/1963/4268}, author = {Marco Bonacini} } @article {2013, title = {Equilibrium measures for a class of potentials with discrete rotational symmetries}, number = {arXiv:1312.1483;}, year = {2013}, note = {23 pages, 3 figures}, institution = {SISSA}, abstract = {In this note the logarithmic energy problem with external potential $|z|^{2n}+tz^d+\bar{t}\bar{z}^d$ is considered in the complex plane, where $n$ and $d$ are positive integers satisfying $d\leq 2n$. Exploiting the discrete rotational invariance of the potential, a simple symmetry reduction procedure is used to calculate the equilibrium measure for all admissible values of $n,d$ and $t$. It is shown that, for fixed $n$ and $d$, there is a critical value $|t|=t_{cr}$ such that the support of the equilibrium measure is simply connected for $|t|This paper deals with the following class of nonlocal Schr\"odinger equations $$ \displaystyle (-\Delta)^s u + u = |u|^{p-1}u \ \ \text{in} \ \mathbb{R}^N, \quad \text{for} \ s\in (0,1). $$ We prove existence and symmetry results for the solutions $u$ in the fractional Sobolev space $H^s(\mathbb{R}^N)$. Our results are in clear accordance with those for the classical local counterpart, that is when $s=1$.

}, author = {Serena Dipierro and Giampiero Palatucci and Enrico Valdinoci} } @article {jevnikar_2013, title = {An existence result for the mean-field equation on compact surfaces in a doubly supercritical regime}, journal = {Proceedings of the Royal Society of Edinburgh: Section A Mathematics}, volume = {143}, number = {5}, year = {2013}, pages = {1021{\textendash}1045}, publisher = {Royal Society of Edinburgh Scotland Foundation}, doi = {10.1017/S030821051200042X}, author = {Aleks Jevnikar} } @article {2013, title = {Expanded degenerations and pairs}, journal = {Communications in Algebra. Volume 41, Issue 6, May 2013, Pages 2346-2386}, number = {arXiv:1110.2976v1;}, year = {2013}, note = {This article is composed of 41 pages and is recorded in PDF format}, publisher = {Taylor and Francis}, abstract = {Since Jun Li{\textquoteright}s original definition, several other definitions of expanded pairs and expanded degenerations have appeared in the literature. We explain how these definitions are related and introduce several new variants and perspectives. Among these are the twisted expansions used by Abramovich and Fantechi as a basis for orbifold techniques in degeneation formulas.}, keywords = {Expanded pairs}, doi = {10.1080/00927872.2012.658589}, url = {http://hdl.handle.net/1963/7383}, author = {Dan Abramovich and Charles Cadman and Barbara Fantechi and Jonathan Wise} } @article {2013, title = {Fields of bounded deformation for mesoscopic dislocations}, year = {2013}, publisher = {SISSA}, abstract = {In this paper we discuss the consequences of the distributional approach to dislocations in terms of the mathematical properties\\r\\nof the auxiliary model fields such as displacement and displacement gradient which are obtained directly from \\r\\nthe main model field here considered as the linear strain. We show that these fields cannot be introduced rigourously without \\r\\nthe introduction of gauge fields, or equivalently, without cuts in the Riemann foliation associated to the dislocated crystal.\\r\\nIn a second step we show that the space of bounded deformations follows from the distributional approach in a natural way and \\r\\ndiscuss the reasons why it is adequate to model dislocations. The case of dislocation clusters is also addressed, as it represents an important issue in industrial crystal growth while from a mathematical point of view, peculiar phenomena might appear at the set of accumulation points. \\r\\nThe elastic-plastic decomposition of the strain within this approach is also given a precise meaning.}, url = {http://hdl.handle.net/1963/6378}, author = {Nicolas Van Goethem} } @article {2013, title = {Fracture models as Gamma-limits of damage models}, journal = {Communications on Pure and Applied Analysis 12 (2013) 1657-1686}, number = {SISSA;25/2011/M}, year = {2013}, publisher = {American Institute of Mathematical Sciences}, abstract = {We analyze the asymptotic behavior of a variational model for damaged elastic materials. This model depends on two small parameters, which govern the width of the damaged regions and the minimum elasticity constant attained in the damaged regions. When these parameters tend to zero, we find that the corresponding functionals Gamma-converge to a functional related to fracture mechanics. The corresponding problem is brittle or cohesive, depending on the asymptotic ratio of the two parameters.

}, doi = {10.3934/cpaa.2013.12.1657}, url = {http://hdl.handle.net/1963/4225}, author = {Gianni Dal Maso and Flaviana Iurlano} } @article {2013, title = {Framed sheaves on projective stacks}, year = {2013}, abstract = {Given a normal projective irreducible stack $\mathscr X$ over an algebraically closed field of characteristic zero we consider {\em framed sheaves} on $\mathscr X$, i.e., pairs $(\mathcal E,\phi_{\mathcal E})$, where $\mathcal E$ is a coherent sheaf on $\mathscr X$ and $\phi_{\mathcal E}$ is a morphism from $\mathcal E$ to a fixed coherent sheaf $\mathcal F$. After introducing a suitable notion of (semi)stability, we construct a projective scheme, which is a moduli space for semistable framed sheaves with fixed Hilbert polynomial, and an open subset of it, which is a fine moduli space for stable framed sheaves. If $\mathscr X$ is a projective irreducible orbifold of dimension two and $\mathcal F$ a locally free sheaf on a smooth divisor $\mathscr D\subset \mathscr X$ satisfying certain conditions, we consider {\em $(\mathscr{D}, \mathcal{F})$-framed sheaves}, i.e., framed sheaves $(\mathcal E,\phi_{\mathcal E})$ with $\mathcal E$ a torsion-free sheaf which is locally free in a neighborhood of $\mathscr D$, and ${\phi_{\mathcal{E}}}_{\vert \mathscr{D}}$ an isomorphism. These pairs are $\mu$-stable for a suitable choice of a parameter entering the (semi)stability condition, and of the polarization of $\mathscr X$. This implies the existence of a fine moduli space parameterizing isomorphism classes of $(\mathscr{D}, \mathcal{F})$-framed sheaves on $\mathscr{X}$ with fixed Hilbert polynomial, which is a quasi-projective scheme. In an appendix we develop the example of stacky Hirzebruch surfaces. This is the first paper of a project aimed to provide an algebro-geometric approach to the study of gauge theories on a wide class of 4-dimensional Riemannian manifolds by means of framed sheaves on {\textquoteleft}{\textquoteleft}stacky" compactifications of them. In particular, in a subsequent paper \cite{art:bruzzopedrinisalaszabo2013} these results are used to study gauge theories on ALE spaces of type $A_k$.}, url = {http://urania.sissa.it/xmlui/handle/1963/7438}, author = {Ugo Bruzzo and Francesco Sala} } @article {KoshakjiQuarteroniRozza2013, title = {Free Form Deformation Techniques Applied to 3D Shape Optimization Problems}, journal = {Communications in Applied and Industrial Mathematics}, year = {2013}, abstract = {The purpose of this work is to analyse and study an efficient parametrization technique for a 3D shape optimization problem. After a brief review of the techniques and approaches already available in literature, we recall the Free Form Deformation parametrization, a technique which proved to be efficient and at the same time versatile, allowing to manage complex shapes even with few parameters. We tested and studied the FFD technique by establishing a path, from the geometry definition, to the method implementation, and finally to the simulation and to the optimization of the shape. In particular, we have studied a bulb and a rudder of a race sailing boat as model applications, where we have tested a complete procedure from Computer-Aided-Design to build the geometrical model to discretization and mesh generation.}, doi = {10.1685/journal.caim.452}, author = {Anwar Koshakji and Alfio Quarteroni and Gianluigi Rozza} } @article {BertolaCafasso4, title = {The gap probabilities of the tacnode, Pearcey and Airy point processes, their mutual relationship and evaluation}, journal = {Random Matrices: Theory and Applications}, volume = {02}, number = {02}, year = {2013}, pages = {1350003}, doi = {10.1142/S2010326313500032}, url = {http://www.worldscientific.com/doi/abs/10.1142/S2010326313500032}, author = {Marco Bertola and Mattia Cafasso} } @article {fonda2013, title = {Generalized Sturm-Liouville boundary conditions for first order differential systems in the plane}, journal = {Topol. Methods Nonlinear Anal.}, volume = {42}, number = {2}, year = {2013}, pages = {293{\textendash}325}, publisher = {Nicolaus Copernicus University, Juliusz P. Schauder Centre for Nonlinear Studies}, abstract = {We study asymptotically positively homogeneous first order systems in the plane, with boundary conditions which are positively homogeneous, as well. Defining a generalized concept of Fu{\v c}{\'\i}k spectrum which extends the usual one for the scalar second order equation, we prove existence and multiplicity of solutions. In this way, on one hand we extend to the plane some known results for scalar second order equations (with Dirichlet, Neumann or Sturm-Liouville boundary conditions), while, on the other hand, we investigate some other kinds of boundary value problems, where the boundary points are chosen on a polygonal line, or in a cone. Our proofs rely on the shooting method.

}, url = {https://projecteuclid.org:443/euclid.tmna/1461248981}, author = {Alessandro Fonda and Maurizio Garrione} } @article {2013, title = {Genus stabilization for moduli of curves with symmetries}, number = {arXiv:1301.4409;}, year = {2013}, note = {21 pages, 2 figures}, publisher = {SISSA}, abstract = {In a previous paper, arXiv:1206.5498, we introduced a new homological\r\ninvariant $\\e$ for the faithful action of a finite group G on an algebraic\r\ncurve.\r\n We show here that the moduli space of curves admitting a faithful action of a\r\nfinite group G with a fixed homological invariant $\\e$, if the genus g\' of the\r\nquotient curve is sufficiently large, is irreducible (and non empty iff the\r\nclass satisfies the condition which we define as \'admissibility\'). In the\r\nunramified case, a similar result had been proven by Dunfield and Thurston\r\nusing the classical invariant in the second homology group of G, H_2(G, \\ZZ).\r\n We achieve our result showing that the stable classes are in bijection with\r\nthe set of admissible classes $\\e$.}, keywords = {group actions, mapping class group, Moduli space of curves, Teichm{\"u}ller space}, url = {http://hdl.handle.net/1963/6509}, author = {Fabrizio Catanese and Michael L{\"o}nne and Fabio Perroni} } @article {2012, title = {An improved geometric inequality via vanishing moments, with applications to singular Liouville equations}, journal = {Communications in Mathematical Physics 322, nr.2 (2013): 415-452}, number = {arXiv:1206.0225;}, year = {2013}, publisher = {SISSA}, doi = {10.1007/s00220-013-1731-0}, url = {http://hdl.handle.net/1963/6561}, author = {Mauro Bardelloni and Andrea Malchiodi} } @article {BertolaKatsevichTovbis1, title = {Inversion formulae for the $\romancosh$-weighted Hilbert transform}, journal = {Proc. Amer. Math. Soc.}, volume = {141}, number = {8}, year = {2013}, pages = {2703{\textendash}2718}, issn = {0002-9939}, doi = {10.1090/S0002-9939-2013-11642-4}, url = {http://dx.doi.org/10.1090/S0002-9939-2013-11642-4}, author = {Marco Bertola and Katsevich, A. and Alexander Tovbis} } @article {Berti2013301, title = {KAM theory for the Hamiltonian derivative wave equation}, journal = {Annales Scientifiques de l{\textquoteright}Ecole Normale Superieure}, volume = {46}, number = {2}, year = {2013}, note = {cited By (since 1996)4}, pages = {301-373}, abstract = {We prove an infinite dimensional KAM theorem which implies the existence of Can- tor families of small-amplitude, reducible, elliptic, analytic, invariant tori of Hamiltonian derivative wave equations. {\textcopyright} 2013 Soci{\'e}t{\'e} Math{\'e}matique de France.

}, issn = {00129593}, author = {Massimiliano Berti and Luca Biasco and Michela Procesi} } @article {Boscain2013, title = {Lipschitz Classification of Almost-Riemannian Distances on Compact Oriented Surfaces}, journal = {Journal of Geometric Analysis}, volume = {23}, number = {1}, year = {2013}, month = {Jan}, pages = {438{\textendash}455}, abstract = {Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We consider the Carnot{\textendash}Carath{\'e}odory distance canonically associated with an almost-Riemannian structure and study the problem of Lipschitz equivalence between two such distances on the same compact oriented surface. We analyze the generic case, allowing in particular for the presence of tangency points, i.e., points where two generators of the distribution and their Lie bracket are linearly dependent. The main result of the paper provides a characterization of the Lipschitz equivalence class of an almost-Riemannian distance in terms of a labeled graph associated with it.

}, issn = {1559-002X}, doi = {10.1007/s12220-011-9262-4}, url = {https://doi.org/10.1007/s12220-011-9262-4}, author = {Ugo Boscain and Gr{\'e}goire Charlot and Roberta Ghezzi and Mario Sigalotti} } @article {cacace_chambolle_desimone_fedeli_2013, title = {Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis}, volume = {47}, number = {3}, year = {2013}, pages = {837{\textendash}858}, publisher = {EDP Sciences}, doi = {10.1051/m2an/2012048}, author = {Cacace, S. and Antonin Chambolle and Antonio DeSimone and Livio Fedeli} } @article {2013, title = {Minimal partitions and image classification using a gradient-free perimeter approximation}, year = {2013}, institution = {SISSA}, abstract = {In this paper a new mathematically-founded method for the optimal partitioning of domains, with applications to the classification of greyscale and color images, is proposed. Since optimal partition problems are in general ill-posed, some regularization strategy is required. Here we regularize by a non-standard approximation of the total interface length, which does not involve the gradient of approximate characteristic functions, in contrast to the classical Modica-Mortola approximation. Instead, it involves a system of uncoupled linear partial differential equations and nevertheless shows $\Gamma$-convergence properties in appropriate function spaces. This approach leads to an alternating algorithm that ensures a decrease of the objective function at each iteration, and which always provides a partition, even during the iterations. The efficiency of this algorithm is illustrated by various numerical examples. Among them we consider binary and multilabel minimal partition problems including supervised or automatic image classification, inpainting, texture pattern identification and deblurring.}, keywords = {Image classification, deblurring, optimal partitions, perimeter approximation}, url = {http://hdl.handle.net/1963/6976}, author = {Samuel Amstutz and Nicolas Van Goethem and Antonio Andr{\'e} Novotny} } @mastersthesis {2013, title = {Minimality and stability results for a class of free-discontinuity and nonlocal isoperimetric problems}, year = {2013}, school = {SISSA}, keywords = {free-discontinuity problems}, author = {Marco Bonacini} } @article {2013, title = {Monads for framed sheaves on Hirzebruch surfaces}, number = {SISSA preprint;05/2014/mate}, year = {2013}, abstract = {We define monads for framed torsion-free sheaves on Hirzebruch surfaces and use them to construct moduli spaces for these objects. These moduli spaces are smooth algebraic varieties, and we show that they are fine by constructing a universal monad.}, keywords = {Monads, framed sheaves, Hirzebruch surfaces}, author = {Claudio Bartocci and Ugo Bruzzo and Claudio L.S. Rava} } @article {Bianchini2013, title = {The Monge Problem for Distance Cost in Geodesic Spaces}, journal = {Communications in Mathematical Physics}, volume = {318}, number = {3}, year = {2013}, month = {Mar}, pages = {615{\textendash}673}, abstract = {We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish space and dLis a geodesic Borel distance which makes (X, dL) a non branching geodesic space. We show that under the assumption that geodesics are d-continuous and locally compact, we can reduce the transport problem to 1-dimensional transport problems along geodesics. We introduce two assumptions on the transport problem π which imply that the conditional probabilities of the first marginal on each geodesic are continuous or absolutely continuous w.r.t. the 1-dimensional Hausdorff distance induced by dL. It is known that this regularity is sufficient for the construction of a transport map. We study also the dynamics of transport along the geodesic, the stability of our conditions and show that in this setting dL-cyclical monotonicity is not sufficient for optimality.

}, issn = {1432-0916}, doi = {10.1007/s00220-013-1663-8}, url = {https://doi.org/10.1007/s00220-013-1663-8}, author = {Stefano Bianchini and Fabio Cavalletti} } @article {2013, title = {Multiplicity result for a nonhomogeneous Yamabe type equation involving the Kohn Laplacian}, journal = {Journal of Mathematical Analysis and Applications. Volume 399, Issue 1, 1 March 2013, Pages 333-339}, year = {2013}, note = {The article is composed of 13 pages and is recorded in PDF format}, publisher = {Elsevier}, keywords = {CR-Yamabe}, doi = {10.1016/j.jmaa.2012.10.014}, url = {http://hdl.handle.net/1963/7374}, author = {Ali Maalaoui and Vittorio Martino} } @article {2013, title = {N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae}, number = {arXiv:1208.0790;}, year = {2013}, note = {33 pages, 1 figure; v2: discussions on U(1) gauge theory and\r\n Frenkel-Kac construction have been added in section 5.1, and typos corrected;\r\n v3: published version; v4: typos corrected}, institution = {SISSA}, abstract = {We compute the Nekrasov partition function of gauge theories on the\r\n(resolved) toric singularities C^2/\\Gamma in terms of blow-up formulae. We\r\ndiscuss the expansion of the partition function in the \\epsilon_1,\\epsilon_2\r\n\\to 0 limit along with its modular properties and how to derive them from the\r\nM-theory perspective. On the two-dimensional conformal field theory side, our\r\nresults can be interpreted in terms of representations of the direct sum of\r\nHeisenberg plus W_N-algebrae with suitable central charges, which can be\r\ncomputed from the fan of the resolved toric variety.We provide a check of this\r\ncorrespondence by computing the central charge of the two-dimensional theory\r\nfrom the anomaly polynomial of M5-brane theory. Upon using the AGT\r\ncorrespondence our results provide a candidate for the conformal blocks and\r\nthree-point functions of a class of the two-dimensional CFTs which includes\r\nparafermionic theories.}, url = {http://hdl.handle.net/1963/6577}, author = {Giulio Bonelli and Kazunobu Maruyoshi and Alessandro Tanzini and Futoshi Yagi} } @article {modena2013, title = {A New Quadratic Potential for Scalar Conservation Laws}, journal = {Oberwolfach Reports}, volume = {29}, year = {2013}, author = {Stefano Bianchini and Stefano Modena} } @article {11011, title = {Nonabelian Lie algebroid extensions}, number = {SISSA preprint;06/2014/mate}, year = {2013}, abstract = {We classify nonabelian extensions of Lie algebroids in the holomorphic or algebraic category, and introduce and study a spectral sequence that one can attach to any such extension and generalizes the Hochschild-Serre spectral sequence associated to an ideal in a Lie algebra. We compute the differentials of the spectral sequence up to $d_2$

}, keywords = {Lie algebroids, nonabelian extensions, spectral sequences}, author = {Ugo Bruzzo and Igor Mencattini and Pietro Tortella and Vladimir Rubtsov} } @article {2013, title = {Noncommutative circle bundles and new Dirac operators}, journal = {Communications in Mathematical Physics. Volume 318, Issue 1, 2013, Pages 111-130}, number = {arXiv:1012.3055v2;}, year = {2013}, note = {This article is composed of 25 pages and is recorded in PDF format}, publisher = {Springer}, abstract = {We study spectral triples over noncommutative principal U(1) bundles. Basing on the classical situation and the abstract algebraic approach, we propose an operatorial definition for a connection and compatibility between the connection and the Dirac operator on the total space and on the base space of the bundle. We analyze in details the example of the noncommutative three-torus viewed as a U(1) bundle over the noncommutative two-torus and find all connections compatible with an admissible Dirac operator. Conversely, we find a family of new Dirac operators on the noncommutative tori, which arise from the base-space Dirac operator and a suitable connection.}, keywords = {Quantum principal bundles}, doi = {10.1007/s00220-012-1550-8}, url = {http://hdl.handle.net/1963/7384}, author = {Ludwik Dabrowski and Andrzej Sitarz} } @article {2013, title = {The nonlinear multidomain model: a new formal asymptotic analysis.}, journal = {Geometry Partial Differential Equations {\textendash} proceedings, CRM Series (15), 2013.}, number = {SISSA preprint;SISSA 54/2013/MATE}, year = {2013}, abstract = {We study the asymptotic analysis of a singularly perturbed weakly parabolic system of m- equations of anisotropic reaction-diffusion type. Our main result formally shows that solutions to the system approximate a geometric motion of a hypersurface by anisotropic mean curvature. The anisotropy, supposed to be uniformly convex, is explicit and turns out to be the dual of the star-shaped combination of the m original anisotropies.

}, keywords = {bidomain model, anisotropic mean curvature, star-shaped combination}, isbn = {8876424724}, author = {Stefano Amato and Giovanni Bellettini and Maurizio Paolini} } @article {2013, title = {A note on KAM theory for quasi-linear and fully nonlinear forced KdV}, journal = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 24 (2013), no. 3: 437{\textendash}450}, year = {2013}, publisher = {European Mathematical Society}, abstract = {We present the recent results in [3] concerning quasi-periodic solutions for quasi-linear and fully nonlinear forced perturbations of KdV equations. For Hamiltonian or reversible nonlinearities the solutions are linearly stable. The proofs are based on a combination of di erent ideas and techniques: (i) a Nash-Moser iterative scheme in Sobolev scales. (ii) A regularization procedure, which conjugates the linearized operator to a di erential operator with constant coe cients plus a bounded remainder. These transformations are obtained by changes of variables induced by di eomorphisms of the torus and pseudo-di erential operators. (iii) A reducibility KAM scheme, which completes the reduction to constant coe cients of the linearized operator, providing a sharp asymptotic expansion of the perturbed eigenvalues.}, keywords = {KAM for PDEs}, doi = {10.4171/RLM/660}, author = {P Baldi and Massimiliano Berti and Riccardo Montalto} } @article {1305.1133, title = {A note on non-homogeneous hyperbolic operators with low-regularity coefficients}, year = {2013}, abstract = {In this paper we obtain an energy estimate for a complete strictly hyperbolic operator with second order coefficients satisfying a log-Zygmund-continuity condition with respect to $t$, uniformly with respect to $x$, and a log-Lipschitz-continuity condition with respect to $x$, uniformly with respect to $t$.

}, author = {Ferruccio Colombini and Francesco Fanelli} } @article {2013, title = {One-dimensional swimmers in viscous fluids: dynamics, controllability, and existence of optimal controls}, number = {arXiv:1302.0901;}, year = {2013}, publisher = {SISSA}, abstract = {In this paper we study a mathematical model of one-dimensional swimmers performing a planar motion while fully immersed in a viscous fluid. The swimmers are assumed to be of small size, and all inertial effects are neglected. Hydrodynamic interactions are treated in a simplified way, using the local drag approximation of resistive force theory. We prove existence and uniqueness of the solution of the equations of motion driven by shape changes of the swimmer. Moreover, we prove a controllability result showing that given any pair of initial and final states, there exists a history of shape changes such that the resulting motion takes the swimmer from the initial to the final state. We give a constructive proof, based on the composition of elementary maneuvers (straightening and its inverse, rotation, translation), each of which represents the solution of an interesting motion planning problem. Finally, we prove the existence of solutions for the optimal control problem of finding, among the histories of shape changes taking the swimmer from an initial to a final state, the one of minimal energetic cost.

}, url = {http://hdl.handle.net/1963/6467}, author = {Gianni Dal Maso and Antonio DeSimone and Marco Morandotti} } @article {boscaggin2013pairs, title = {Pairs of nodal solutions for a class of nonlinear problems with one-sided growth conditions}, journal = {Advanced Nonlinear Studies}, volume = {13}, number = {1}, year = {2013}, pages = {13{\textendash}53}, publisher = {Advanced Nonlinear Studies, Inc.}, doi = {10.1515/ans-2013-0103}, author = {Alberto Boscaggin and Fabio Zanolin} } @article {fonda2013periodic, title = {Periodic bouncing solutions for nonlinear impact oscillators}, journal = {Advanced Nonlinear Studies}, volume = {13}, number = {1}, year = {2013}, pages = {179{\textendash}189}, publisher = {Advanced Nonlinear Studies, Inc.}, doi = {10.1515/ans-2013-0110}, author = {Alessandro Fonda and Andrea Sfecci} } @article {Boscaggin2013, title = {Planar Hamiltonian systems at resonance: the Ahmad{\textendash}Lazer{\textendash}Paul condition}, journal = {Nonlinear Differential Equations and Applications NoDEA}, volume = {20}, number = {3}, year = {2013}, month = {Jun}, pages = {825{\textendash}843}, abstract = {We consider the planar Hamiltonian system\$\$Ju^{\backslashprime} = \backslashnabla F(u) + \backslashnabla_u R(t,u), \backslashquad t \backslashin [0,T], \backslash,u \backslashin \backslashmathbb{R}^2,\$\$with F(u) positive and positively 2-homogeneous and \$\${\backslashnabla_{u}R(t, u)}\$\$sublinear in u. By means of an Ahmad-Lazer-Paul type condition, we prove the existence of a T-periodic solution when the system is at resonance. The proof exploits a symplectic change of coordinates which transforms the problem into a perturbation of a linear one. The relationship with the Landesman{\textendash}Lazer condition is analyzed, as well.

}, issn = {1420-9004}, doi = {10.1007/s00030-012-0181-2}, url = {https://doi.org/10.1007/s00030-012-0181-2}, author = {Alberto Boscaggin and Maurizio Garrione} } @article {2013, title = {Quadratic cohomology}, year = {2013}, note = {24 pages}, publisher = {SISSA}, abstract = {We study homological invariants of smooth families of real quadratic forms as\r\na step towards a \"Lagrange multipliers rule in the large\" that intends to\r\ndescribe topology of smooth vector functions in terms of scalar Lagrange\r\nfunctions.}, author = {Andrei A. Agrachev} } @article {Berti2013229, title = {Quasi-periodic solutions with Sobolev regularity of NLS on Td with a multiplicative potential}, journal = {Journal of the European Mathematical Society}, volume = {15}, number = {1}, year = {2013}, note = {cited By (since 1996)5}, pages = {229-286}, abstract = {We prove the existence of quasi-periodic solutions for Schr{\"o}dinger equations with a multiplicative potential on Td , d >= 1, finitely differentiable nonlinearities, and tangential frequencies constrained along a pre-assigned direction. The solutions have only Sobolev regularity both in time and space. If the nonlinearity and the potential are C$\infty$ then the solutions are C$\infty$. The proofs are based on an improved Nash-Moser iterative scheme, which assumes the weakest tame estimates for the inverse linearized operators ("Green functions") along scales of Sobolev spaces. The key off-diagonal decay estimates of the Green functions are proved via a new multiscale inductive analysis. The main novelty concerns the measure and "complexity" estimates. {\textcopyright} European Mathematical Society 2013.}, issn = {14359855}, doi = {10.4171/JEMS/361}, author = {Massimiliano Berti and Philippe Bolle} } @article {DAVOLI2013615, title = {A quasistatic evolution model for perfectly plastic plates derived by Γ-convergence}, journal = {Annales de l{\textquoteright}Institut Henri Poincare (C) Non Linear Analysis}, volume = {30}, number = {4}, year = {2013}, pages = {615 - 660}, abstract = {The subject of this paper is the rigorous derivation of a quasistatic evolution model for a linearly elastic{\textendash}perfectly plastic thin plate. As the thickness of the plate tends to zero, we prove via Γ-convergence techniques that solutions to the three-dimensional quasistatic evolution problem of Prandtl{\textendash}Reuss elastoplasticity converge to a quasistatic evolution of a suitable reduced model. In this limiting model the admissible displacements are of Kirchhoff{\textendash}Love type and the stretching and bending components of the stress are coupled through a plastic flow rule. Some equivalent formulations of the limiting problem in rate form are derived, together with some two-dimensional characterizations for suitable choices of the data.

}, keywords = {-convergence, Perfect plasticity, Prandtl{\textendash}Reuss plasticity, Quasistatic evolution, Rate-independent processes, Thin plates}, issn = {0294-1449}, doi = {https://doi.org/10.1016/j.anihpc.2012.11.001}, url = {http://www.sciencedirect.com/science/article/pii/S0294144912001035}, author = {Elisa Davoli and Maria Giovanna Mora} } @article {2013, title = {Reduced basis approximation and a posteriori error estimation for Stokes flows in parametrized geometries: roles of the inf-sup stability constants}, journal = {Numerische Mathematik, 2013}, number = {SISSA Preprint;43/2012/M}, year = {2013}, publisher = {Springer}, abstract = {In this paper we review and we extend the reduced basis approximation and a posteriori error estimation for steady Stokes flows in a ffinely parametrized geometries, focusing on the role played by the Brezzi\\\'s and Babu ska\\\'s stability constants. The crucial ingredients of the methodology are a Galerkin projection onto a low-dimensional space of basis functions properly selected, an a ne parametric dependence enabling to perform competitive Off ine-Online splitting in the computational\\r\\nprocedure and a rigorous a posteriori error estimation on eld variables.\\r\\nThe combination of these three factors yields substantial computational savings which are at the basis of an e fficient model order reduction, ideally suited for real-time simulation and many-query contexts (e.g. optimization, control or parameter identi cation). In particular, in this work we focus on i) the stability of the reduced basis approximation based on the Brezzi\\\'s saddle point theory and the introduction of a supremizer operator on the pressure terms, ii) a rigorous a posteriori error estimation procedure for velocity and pressure elds based on the Babu ska\\\'s inf-sup constant (including residuals calculations), iii) the computation of a lower bound of the stability constant, and iv) di erent options for the reduced basis spaces construction. We present some illustrative results for both\\r\\ninterior and external steady Stokes flows in parametrized geometries representing two parametrized classical Poiseuille and Couette \\r\\nflows, a channel contraction and a simple flow control problem around a curved obstacle.}, keywords = {parametrized Stokes equations}, url = {http://hdl.handle.net/1963/6339}, author = {Gianluigi Rozza and Phuong Huynh and Andrea Manzoni} } @inbook {2015, title = {Reduced Basis Approximation for the Structural-Acoustic Design based on Energy Finite Element Analysis (RB-EFEA)}, booktitle = {CEMRACS 2013 - Modelling and simulation of complex systems: stochastic and deterministic approaches}, volume = {48}, number = {ESAIM Proceedings}, year = {2013}, pages = {98-115}, doi = { http://dx.doi.org/10.1051/proc/201448004}, author = {Denis Devaud and Gianluigi Rozza} } @article {NegriRozzaManzoniQuarteroni2013, title = {Reduced basis method for parametrized elliptic optimal control problems}, journal = {SIAM Journal on Scientific Computing}, volume = {35}, number = {5}, year = {2013}, pages = {A2316{\textendash}A2340}, abstract = {We propose a suitable model reduction paradigm-the certified reduced basis method (RB)-for the rapid and reliable solution of parametrized optimal control problems governed by partial differential equations. In particular, we develop the methodology for parametrized quadratic optimization problems with elliptic equations as a constraint and infinite-dimensional control variable. First, we recast the optimal control problem in the framework of saddle-point problems in order to take advantage of the already developed RB theory for Stokes-type problems. Then, the usual ingredients of the RB methodology are called into play: a Galerkin projection onto a low-dimensional space of basis functions properly selected by an adaptive procedure; an affine parametric dependence enabling one to perform competitive offline-online splitting in the computational procedure; and an efficient and rigorous a posteriori error estimate on the state, control, and adjoint variables as well as on the cost functional. Finally, we address some numerical tests that confirm our theoretical results and show the efficiency of the proposed technique.}, doi = {10.1137/120894737}, author = {Federico Negri and Gianluigi Rozza and Andrea Manzoni and Alfio Quarteroni} } @article {2013, title = {A Reduced Computational and Geometrical Framework for Inverse Problems in Haemodynamics}, number = {SISSA preprint;15/2013/MATE}, year = {2013}, institution = {SISSA}, author = {Toni Lassila and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza} } @article {2013, title = {A reduced-order strategy for solving inverse Bayesian identification problems in physiological flows}, number = {SISSA preprint;14/2013/MATE}, year = {2013}, institution = {SISSA}, author = {Toni Lassila and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza} } @article {2013, title = {Reduction Strategies for Shape Dependent Inverse Problems in Haemodynamics}, number = {SISSA preprint;13/2013/MATE}, year = {2013}, institution = {SISSA}, author = {Toni Lassila and Andrea Manzoni and Gianluigi Rozza} } @article {11613, title = {Remarks on the Moser{\textendash}Trudinger inequality}, journal = {Advances in Nonlinear Analysis}, volume = {2}, number = {Advances in nonlinear analysis;volume 2; issue 4}, year = {2013}, note = {The article is composed of 32 pages inad recorded in PDF format}, pages = {389-425}, publisher = {Advances in Nonlinear Analysis}, abstract = {We extend the Moser-Trudinger inequality to any Euclidean domain satisfying Poincar{\'e}{\textquoteright}s inequality. We find out that the same equivalence does not hold in general for conformal metrics on the unit ball, showing counterexamples. We also study the existence of extremals for the Moser-Trudinger inequalities for unbounded domains, proving it for the infinite planar strip.

}, doi = {10.1515/anona-2013-0014}, url = {http://edoc.unibas.ch/43974/}, author = {Gabriele Mancini and Luca Battaglia} } @article {1305.5271, title = {Self-adjoint extensions and stochastic completeness of the Laplace-Beltrami operator on conic and anticonic surfaces}, year = {2013}, doi = {10.1016/j.jde.2015.10.011}, author = {Ugo Boscain and Dario Prandi} } @mastersthesis {2013, title = {Semistability and Decorated Bundles}, year = {2013}, school = {SISSA}, abstract = {This thesis is devoted to the study of semistability condition of type t=(a,b,c,N) decorated bundles and sheaves in order to better understand and simplify it. We approach the problem in two different ways: on one side we {\textquotedblleft}enclose{\textquotedblright} the above semistability condition between a stronger semistability condition (\epsilon-semistability) and a weaker one (k-semistability), on the other side we try, and succeed for the case of a = 2, to bound the length of weighted filtrations on which one checks the semistability condition.}, keywords = {Decorated sheaves, semistability, moduli space, Mehta-Ramanathan, maximal destabilizing subsheaf}, url = {http://hdl.handle.net/1963/7130}, author = {Andrea Pustetto} } @article {2013, title = {Softly Constrained Films}, number = {arXiv:1304.1077;}, year = {2013}, note = {Review article, 21 pages, 16 figures, submitted to Soft Matter}, publisher = {SISSA}, abstract = {The shape of materials is often subject to a number of geometric constraints\r\nthat limit the size of the system or fix the structure of its boundary. In soft\r\nand biological materials, however, these constraints are not always hard, but\r\nare due to other physical mechanisms that affect the overall force balance. A\r\ncapillary film spanning a flexible piece of wire or a cell anchored to a\r\ncompliant substrate by mean of adhesive contacts are examples of these softly\r\nconstrained systems in the macroscopic and microscopic world. In this article I\r\nreview some of the important mathematical and physical developments that\r\ncontributed to our understanding of shape formation in softly constrained films\r\nand their recent application to the mechanics of adherent cells.}, url = {http://hdl.handle.net/1963/6563}, author = {Luca Giomi} } @mastersthesis {2013, title = {Some models of crack growth in brittle materials}, year = {2013}, school = {SISSA}, keywords = {Quasi-static crack evolution}, author = {Simone Racca} } @article {2013, title = {Some open problems}, number = {arXiv:1304.2590;}, year = {2013}, publisher = {SISSA}, abstract = {We discuss some challenging open problems in the geometric control theory and sub-Riemannian geometry.}, keywords = {Geometry}, url = {http://hdl.handle.net/1963/7070}, author = {Andrei A. Agrachev} } @article {2001, title = {Some remarks on the viscous approximation of crack growth}, journal = {Discrete Contin. Dyn. Syst. Ser. S}, volume = {6}, number = {SISSA;24/2011/M}, year = {2013}, publisher = {SISSA}, chapter = {131-146}, abstract = {We describe an existence result for quasistatic evolutions of cracks in antiplane elasticity obtained in [16] by a vanishing viscosity approach, with free (but regular enough) crack path. We underline in particular the motivations for the choice of the class of admissible cracks and of the dissipation potential. Moreover, we extend the result to a model with applied forces depending on time.

}, keywords = {Variational models}, url = {http://hdl.handle.net/1963/4206}, author = {Giuliano Lazzaroni and Rodica Toader} } @mastersthesis {2013, title = {Some topics on Higgs bundles over projective varieties and their moduli spaces}, year = {2013}, school = {SISSA}, abstract = {In this thesis we study vector bundles on projective varieties and their moduli spaces. In Chapters 2, 3 and 4 we recall some basic notions as Higgs bundles, decorated bundles and generalized parabolic sheaves and introduce the problem we want to study. In chapter 5, we study Higgs bundles on nodal curves. After moving the problem on the normalization of the curve, starting from a Higgs bundle we obtain a generalized parabolic Higgs bundle. Using decorated bundles we are able to construct a projective moduli space which parametrizes equivalence classes of Higgs bundles on a nodal curve X. This chapter is an extract of a joint work with Andrea Pustetto Later on Chapter 6 is devoted to the study of holomorphic pairs (or twisted Higgs bundles) on elliptic curve. Holomorphic pairs were introduced by Nitsure and they are a natural generalization of the concept of Higgs bundles. In this Chapter we extend a result of E. Franco, O. Garc\'ia-Prada And P.E. Newstead valid for Higgs bundles to holomorphic pairs. Finally the last Chapter describes a joint work with Professor Ugo Bruzzo. We study Higgs bundles over varieties with nef tangent bundle. In particular generalizing a result of Nitsure we prove that if a Higgs bundle $(E,\phi)$ over the variety X with nef tangent remains semisatble when pulled-back to any smooth curve then it discrimiant vanishes.}, keywords = {Algebraic Geometry, Moduli spaces, Vector bundles}, author = {Alessio Lo Giudice} } @article {MR3117621, title = {Spectra of random Hermitian matrices with a small-rank external source: the supercritical and subcritical regimes}, journal = {J. Stat. Phys.}, volume = {153}, number = {4}, year = {2013}, pages = {654{\textendash}697}, issn = {0022-4715}, doi = {10.1007/s10955-013-0845-2}, url = {http://dx.doi.org/10.1007/s10955-013-0845-2}, author = {Marco Bertola and Buckingham, R. and Lee, S. Y. and Pierce, V.} } @article {2013, title = {The splitting theorem in non-smooth context}, year = {2013}, abstract = {We prove that an infinitesimally Hilbertian $CD(0,N)$ space containing a line splits as the product of $R$ and an infinitesimally Hilbertian $CD(0,N -1)$ space. By {\textquoteleft}infinitesimally Hilbertian{\textquoteright} we mean that the Sobolev space $W^{1,2}(X,d,m)$, which in general is a Banach space, is an Hilbert space. When coupled with a curvature-dimension bound, this condition is known to be stable with respect to measured Gromov-Hausdorff convergence.}, url = {http://preprints.sissa.it/handle/1963/35306}, author = {Nicola Gigli} } @article {2013, title = {Stabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control}, journal = {IEEE Transactions on Automatic Control. Volume 58, Issue 1, 2013, Article number6228517, Pages 74-85}, year = {2013}, abstract = {In this paper, we investigate parametrization-free solutions of the problem of quantum pure state preparation and subspace stabilization by means of Hamiltonian control, continuous measurement, and quantum feedback, in the presence of a Markovian environment. In particular, we show that whenever suitable dissipative effects are induced either by the unmonitored environment, or by non-Hermitian measurements, there is no need for feedback, as open-loop time-invariant control is sufficient to achieve stabilization of the target set in probability. Constructive necessary and sufficient conditions on the form of the control Hamiltonian can be provided in this case. When time-invariant control is not sufficient, state stabilization can be attained by the addition of filtering-based feedback control}, doi = {10.1109/TAC.2012.2206713}, url = {http://hdl.handle.net/1963/6503}, author = {Claudio Altafini and Francesco Ticozzi and K. Nishio} } @article {2012, title = {A stable and adaptive semi-Lagrangian potential model for unsteady and nonlinear ship-wave interactions}, journal = {Engineering Analysis with Boundary Elements, 37(1):128 {\textendash} 143, 2013.}, number = {SISSA;06/2012/M}, year = {2013}, publisher = {SISSA}, abstract = {We present an innovative numerical discretization of the equations of inviscid potential flow for the simulation of three dimensional unsteady and nonlinear water waves generated by a ship hull advancing in water. The equations of motion are written in a semi-Lagrangian framework, and the resulting integro-diff erential equations are discretized in space via an adaptive iso-parametric collocation Boundary Element Method, and in time via adaptive implicit Backward Di erentiation Formulas (BDF) with variable step and variable order. When the velocity of the advancing ship hull is non-negligible, the semi-Lagrangian formulation (also known as Arbitrary Lagrangian Eulerian formulation, or ALE) of the free surface equations contains dominant transport terms which are stabilized with a Streamwise Upwind Petrov-Galerkin (SUPG) method. The SUPG stabilization allows automatic and robust adaptation of the spatial discretization with unstructured quadrilateral grids. Preliminary results are presented where we compare our numerical model with experimental results on the case of a Wigley hull advancing in calm water with fi xed sink and trim.

}, keywords = {Unsteady ship-wave interaction}, url = {http://hdl.handle.net/1963/5669}, author = {Andrea Mola and Luca Heltai and Antonio DeSimone} } @article {doi:10.1080/00036811.2011.628173, title = {Stable determination of a body immersed in a fluid: the nonlinear stationary case}, journal = {Applicable Analysis}, volume = {92}, number = {3}, year = {2013}, pages = {460-481}, publisher = {Taylor \& Francis}, abstract = {We consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the stationary Navier{\textendash}Stokes equations, from a single measurement of force and velocity on a portion of the boundary. We obtain an estimate of stability of log{\textendash}log type.

}, doi = {10.1080/00036811.2011.628173}, url = {https://doi.org/10.1080/00036811.2011.628173}, author = {Andrea Ballerini} } @article {ChenQuarteroniRozza2013, title = {Stochastic optimal robin boundary control problems of advection-dominated elliptic equations}, journal = {SIAM Journal on Numerical Analysis}, volume = {51}, number = {5}, year = {2013}, pages = {2700{\textendash}2722}, abstract = {In this work we deal with a stochastic optimal Robin boundary control problem constrained by an advection-diffusion-reaction elliptic equation with advection-dominated term. We assume that the uncertainty comes from the advection field and consider a stochastic Robin boundary condition as control function. A stochastic saddle point system is formulated and proved to be equivalent to the first order optimality system for the optimal control problem, based on which we provide the existence and uniqueness of the optimal solution as well as some results on stochastic regularity with respect to the random variables. Stabilized finite element approximations in physical space and collocation approximations in stochastic space are applied to discretize the optimality system. A global error estimate in the product of physical space and stochastic space for the numerical approximation is derived. Illustrative numerical experiments are provided.}, doi = {10.1137/120884158}, author = {Peng Chen and Alfio Quarteroni and Gianluigi Rozza} } @article {MR3088819, title = {Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two-matrix model}, journal = {J. Math. Phys.}, volume = {54}, number = {4}, year = {2013}, pages = {043517, 25}, issn = {0022-2488}, author = {Marco Bertola and Gekhtman, M. and Szmigielski, J.} } @mastersthesis {2013, title = {The structure and regularity of admissible BV solutions to hyperbolic conservation laws in one space dimension}, year = {2013}, school = {SISSA}, abstract = {This thesis is devoted to the study of the qualitative properties of admissible BV solutions to the strictly hyperbolic conservation laws in one space dimension by using wave-front tracking approximation. This thesis consists of two parts: {\textbullet} SBV-like regularity of vanishing viscosity BV solutions to strict hyperbolic systems of conservation laws. {\textbullet} Global structure of admissible BV solutions to strict hyperbolic conservation laws.}, author = {Lei Yu} } @article {1078-0947_2013_1_89, title = {Subharmonic solutions for nonlinear second order equations in presence of lower and upper solutions}, journal = {Discrete \& Continuous Dynamical Systems - A}, volume = {33}, number = {1078-0947_2013_1_8}, year = {2013}, pages = {89}, abstract = {We study the problem of existence and multiplicity of subharmonic solutions for a second order nonlinear ODE in presence of lower and upper solutions. We show how such additional information can be used to obtain more precise multiplicity results. Applications are given to pendulum type equations and to Ambrosetti-Prodi results for parameter dependent equations.

}, keywords = {lower and upper solutions, parameter dependent equations, Periodic solutions, Poincar{\'e}-Birkhoff twist theorem, subharmonic solutions}, issn = {1078-0947}, doi = {10.3934/dcds.2013.33.89}, url = {http://aimsciences.org//article/id/3638a93e-4f3e-4146-a927-3e8a64e6863f}, author = {Alberto Boscaggin and Fabio Zanolin} } @article {2013, title = {On Sudakov{\textquoteright}s type decomposition of transference plans with norm costs}, number = {SISSA;51/2013/MATE}, year = {2013}, institution = {SISSA}, url = {http://hdl.handle.net/1963/7206}, author = {Stefano Bianchini and Sara Daneri} } @article {2013, title = {Symplectic instanton bundles on P3 and {\textquoteright}t Hooft instantons}, year = {2013}, note = {This preprint has been published with the title "Moduli of symplectic instanton vector bundles of higher rank on projective space P-3 " in CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, Volume: 10, issue 4, Augst 2012, pages 1232-1245.}, institution = {arXiv:1312.5554 [math.AG]}, abstract = {We introduce the notion of tame symplectic instantons by excluding a kind of pathological monads and show that the locus $I^*_{n,r}$ of tame symplectic instantons is irreducible and has the expected dimension, equal to $4n(r+1)-r(2r+1)$. The proof is inherently based on a relation between the spaces $I^*_{n,r}$ and the moduli spaces of {\textquoteright}t Hooft instantons.}, url = {http://urania.sissa.it/xmlui/handle/1963/34486}, author = {Ugo Bruzzo and Dimitri Markushevich and Alexander Tikhomirov} } @mastersthesis {2013, title = {Topology of moduli spaces of framed sheaves}, year = {2013}, school = {SISSA}, keywords = {Moduli spaces, framed sheaves, instantons}, url = {http://hdl.handle.net/1963/7152}, author = {Gharchia Abdellaoui} } @article {10979, title = {On the tritronqu{\'e}e solutions of P$_I^2$}, year = {2013}, institution = {SISSA}, abstract = {For equation P$_I^2$, the second member in the P$_I$ hierarchy, we prove existence of various degenerate solutions depending on the complex parameter $t$ and evaluate the asymptotics in the complex $x$ plane for $|x|\to\infty$ and $t=o(x^{2/3})$. Using this result, we identify the most degenerate solutions $u^{(m)}(x,t)$, $\hat u^{(m)}(x,t)$, $m=0,\dots,6$, called {\em tritronqu\'ee}, describe the quasi-linear Stokes phenomenon and find the large $n$ asymptotics of the coefficients in a formal expansion of these solutions. We supplement our findings by a numerical study of the tritronqu\'ee solutions.

}, author = {Tamara Grava and Andrey Kapaev and Christian Klein} } @article {BertolaTovbisNLS2, title = {Universality for the focusing nonlinear Schr{\"o}dinger equation at the gradient catastrophe point: rational breathers and poles of the \it Tritronqu{\'e}e solution to Painlev{\'e} I}, journal = {Comm. Pure Appl. Math.}, volume = {66}, number = {5}, year = {2013}, pages = {678{\textendash}752}, issn = {0010-3640}, doi = {10.1002/cpa.21445}, url = {http://dx.doi.org/10.1002/cpa.21445}, author = {Marco Bertola and Alexander Tovbis} } @article {2013, title = {A variational Analysis of the Toda System on Compact Surfaces}, journal = {Communications on Pure and Applied Mathematics, Volume 66, Issue 3, March 2013, Pages 332-371}, number = {arXiv:1105.3701;}, year = {2013}, note = {pre-peer version, to appear in Comm. Pure Applied Math}, publisher = {Wiley}, abstract = {In this paper we consider the Toda system of equations on a compact surface. We will give existence results by using variational methods in a non coercive case. A key tool in our analysis is a new Moser-Trudinger type inequality under suitable conditions on the center of mass and the scale of concentration of the two components u_1, u_2.}, doi = {10.1002/cpa.21433}, url = {http://hdl.handle.net/1963/6558}, author = {Andrea Malchiodi and David Ruiz} } @article {ChenQuarteroniRozza2013a, title = {A weighted reduced basis method for elliptic partial differential equations with random input data}, journal = {SIAM Journal on Numerical Analysis}, volume = {51}, number = {6}, year = {2013}, pages = {3163{\textendash}3185}, abstract = {In this work we propose and analyze a weighted reduced basis method to solve elliptic partial differential equations (PDEs) with random input data. The PDEs are first transformed into a weighted parametric elliptic problem depending on a finite number of parameters. Distinctive importance of the solution at different values of the parameters is taken into account by assigning different weights to the samples in the greedy sampling procedure. A priori convergence analysis is carried out by constructive approximation of the exact solution with respect to the weighted parameters. Numerical examples are provided for the assessment of the advantages of the proposed method over the reduced basis method and the stochastic collocation method in both univariate and multivariate stochastic problems.}, doi = {10.1137/130905253}, author = {Peng Chen and Alfio Quarteroni and Gianluigi Rozza} } @article {2012, title = {On 2-step, corank 2 nilpotent sub-Riemannian metrics}, journal = {SIAM J. Control Optim., 50 (2012) 559{\textendash}582}, number = {arXiv:1105.5766;}, year = {2012}, publisher = {Society for Industrial and Applied Mathematics}, abstract = {In this paper we study the nilpotent 2-step, corank 2 sub-Riemannian metrics\\r\\nthat are nilpotent approximations of general sub-Riemannian metrics. We exhibit optimal syntheses for these problems. It turns out that in general the cut time is not equal to the first conjugate time but has a simple explicit expression. As a byproduct of this study we get some smoothness properties of the spherical Hausdorff measure in the case of a generic 6 dimensional, 2-step corank 2 sub-Riemannian metric.}, doi = {10.1137/110835700}, url = {http://hdl.handle.net/1963/6065}, author = {Davide Barilari and Ugo Boscain and Jean-Paul Gauthier} } @article {2012, title = {Asymptotics of the s-perimeter as s {\textrightarrow}0 }, journal = {Discrete Contin. Dyn. Syst. 33, nr.7 (2012): 2777-2790}, number = {arXiv:1204.0750v2;}, year = {2012}, publisher = {American Institute of Mathematical Sciences}, abstract = {We deal with the asymptotic behavior of the $s$-perimeter of a set $E$ inside a domain $\Omega$ as $s\searrow0$. We prove necessary and sufficient conditions for the existence of such limit, by also providing an explicit formulation in terms of the Lebesgue measure of $E$ and $\Omega$. Moreover, we construct examples of sets for which the limit does not exist.

}, doi = {10.3934/dcds.2013.33.2777}, author = {Serena Dipierro and Alessio Figalli and Giampiero Palatucci and Enrico Valdinoci} } @article {2012, title = {On the behaviour of flexible retaining walls under seismic actions}, journal = {Geotechnique, Volume 62, Issue 12, December 2012, Pages 1081-1094}, year = {2012}, publisher = {ICE Publishing}, abstract = {This paper describes an experimental investigation of the behaviour of embedded retaining walls under seismic actions. Nine centrifuge tests were carried out on reduced-scale models of pairs of retaining walls in dry sand, either cantilevered or with one level of props near the top. The experimental data indicate that, for maximum accelerations that are smaller than the critical limit equilibrium value, the retaining walls experience significant permanent displacements under increasing structural loads, whereas for larger accelerations the walls rotate under constant internal forces. The critical acceleration at which the walls start to rotate increases with increasing maximum acceleration. No significant displacements are measured if the current earthquake is less severe than earthquakes previously experienced by the wall. The increase of critical acceleration is explained in terms of redistribution of earth pressures and progressive mobilisation of the passive strength in front of the wall. The experimental data for cantilevered retaining walls indicate that the permanent displacements of the wall can be reasonably predicted adopting a Newmark-type calculation with a critical acceleration that is a fraction of the limit equilibrium value.}, keywords = {Centrifuge modelling}, doi = {10.1680/geot.11.P.029}, url = {http://hdl.handle.net/1963/6933}, author = {Riccardo Conti and G.S.P. Madabhushi and Giulia M.B. Viggiani} } @article {2012, title = {Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty}, journal = {Mathematical Modelling and Numerical Analysis, in press, 2012-13}, number = {SISSA;42/2012/M}, year = {2012}, publisher = {Cambridge University Press}, abstract = {We review the optimal design of an arterial bypass graft following either a (i) boundary optimal control approach, or a (ii) shape optimization formulation. The main focus is quantifying and treating the uncertainty in the residual flow when the hosting artery is not completely occluded,\\r\\nfor which the worst-case in terms of recirculation e ffects is inferred to correspond to a strong ori fice flow through near-complete occlusion. A worst-case optimal control approach is applied to the steady\\r\\nNavier-Stokes equations in 2D to identify an anastomosis angle and a cu ed shape that are robust with respect to a possible range of residual \\r\\nflows. We also consider a reduced order modelling framework\\r\\nbased on reduced basis methods in order to make the robust design problem computationally feasible. The results obtained in 2D are compared with simulations in a 3D geometry but without model\\r\\nreduction or the robust framework.}, keywords = {shape optimization}, url = {http://hdl.handle.net/1963/6337}, author = {Toni Lassila and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza} } @article {2012, title = {On a class of vector fields with discontinuity of divide-by-zero type and its applications}, journal = {Journal of dynamical and control systems }, volume = {18}, number = {arXiv:1007.0912;}, year = {2012}, pages = {135-158}, publisher = {Springer}, abstract = {We study phase portraits and singular points of vector fields of a special type, that is, vector fields whose components are fractions with a common denominator vanishing on a smooth regular hypersurface in the phase space. We assume also some additional conditions, which are fulfilled, for instance, if the vector field is divergence-free. This problem is motivated by a large number of applications. In this paper, we consider three of them in the framework of differential geometry: singularities of geodesic flows in various singular metrics on surfaces.

}, doi = {10.1007/s10883-012-9137-4}, author = {Roberta Ghezzi and Alexey O. Remizov} } @article {2012, title = {Classical double, R-operators, and negative flows of integrable hierarchies}, journal = {Theoretical and Mathematical Physics. Volume 172, Issue 1, July 2012, Pages 911-931}, year = {2012}, publisher = {SISSA}, abstract = {Using the classical double G of a Lie algebra g equipped with the classical R-operator, we define two sets of functions commuting with respect to the initial Lie{\textendash}Poisson bracket on g and its extensions. We consider examples of Lie algebras g with the {\textquotedblleft}Adler{\textendash}Kostant{\textendash}Symes{\textquotedblright} R-operators and the two corresponding sets of mutually commuting functions in detail. Using the constructed commutative Hamiltonian flows on different extensions of g, we obtain zero-curvature equations with g-valued U{\textendash}V pairs. The so-called negative flows of soliton hierarchies are among such equations. We illustrate the proposed approach with examples of two-dimensional Abelian and non-Abelian Toda field equations.}, doi = {10.1007/s11232-012-0086-6}, url = {http://hdl.handle.net/1963/6468}, author = {Boris Dubrovin and Taras V. Skrypnyk} } @article {2012, title = {A Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group.}, journal = {Journal fur die Reine und Angewandte Mathematik, Issue 671, October 2012, Pages 131-198}, year = {2012}, publisher = {SISSA}, abstract = {In this paper, we study the structure of the singular set for a C 1 smooth surface in the 3-dimensional Heisenberg group ℍ 1. We discover a Codazzi-like equation for the p-area element along the characteristic curves on the surface. Information obtained from this ordinary differential equation helps us to analyze the local configuration of the singular set and the characteristic curves. In particular, we can estimate the size and obtain the regularity of the singular set. We understand the global structure of the singular set through a Hopf-type index theorem. We also justify the Codazzi-like equation by proving a fundamental theorem for local surfaces in ℍ 1}, doi = {10.1515/CRELLE.2011.159}, url = {http://hdl.handle.net/1963/6556}, author = {Andrea Malchiodi and Paul Yang and Jih-Hsin Cheng and JennFang Hwang} } @inbook {9897, title = {Computing optimal strokes for low reynolds number swimmers}, booktitle = {Natural locomotion in fluids and on surfaces : swimming, flying, and sliding / editors Stephen Childress, Anette Hosoi, William W. Schultz, and Z. Jane Wang, editors,}, number = {The IMA volumes in mathematics and its applications;155}, year = {2012}, publisher = {Springer}, organization = {Springer}, abstract = {We discuss connections between low-Reynolds-number swimming and geometric control theory, and present a general algorithm for the numerical computation of energetically optimal strokes. As an illustration of our approach, we show computed motility maps and optimal strokes for two model swimmers.

}, keywords = {Numerical analysis.}, isbn = {9781461439967}, doi = {10.1007/978-1-4614-3997-4_13}, url = {http://hdl.handle.net/1963/6445}, author = {Antonio DeSimone and Luca Heltai and Fran{\c c}ois Alouges and Lefebvre-Lepot Aline} } @article {bonheure2012concentration, title = {Concentration on circles for nonlinear Schr{\"o}dinger{\textendash}Poisson systems with unbounded potentials vanishing at infinity}, journal = {Communications in Contemporary Mathematics}, volume = {14}, number = {02}, year = {2012}, pages = {1250009}, publisher = {World Scientific}, abstract = {The present paper is devoted to weighted nonlinear Schr{\"o}dinger{\textendash}Poisson systems with potentials possibly unbounded and vanishing at infinity. Using a purely variational approach, we prove the existence of solutions concentrating on a circle.

}, doi = {10.1142/S0219199712500095}, url = {https://doi.org/10.1142/S0219199712500095}, author = {Bonheure, Denis and Di Cosmo, Jonathan and Mercuri, Carlo} } @article {doi:10.1080/03605302.2012.698343, title = {Conservation of Geometric Structures for Non-Homogeneous Inviscid Incompressible Fluids}, journal = {Communications in Partial Differential Equations}, volume = {37}, number = {9}, year = {2012}, pages = {1553-1595}, publisher = {Taylor \& Francis}, abstract = {In this article we get a result on propagation of geometric properties for solutions of the non-homogeneous incompressible Euler system in any dimension N >= 2. In particular, we investigate conservation of striated and conormal regularity, which generalize the 2-D structure of vortex patches. The results we get are only local in time, even for N = 2; however, we provide an explicit lower bound for the lifespan of the solution. In the case of physical dimension N = 2 or 3, we investigate also propagation of H{\"o}lder regularity in the interior of a bounded domain.

}, doi = {10.1080/03605302.2012.698343}, url = {https://doi.org/10.1080/03605302.2012.698343}, author = {Francesco Fanelli} } @article {2012, title = {Convergence of equilibria of thin elastic plates under physical growth conditions for the energy density}, number = {arXiv:0901.4041;}, year = {2012}, note = {21 pages}, publisher = {Elsevier}, abstract = {The asymptotic behaviour of the equilibrium configurations of a thin elastic plate is studied, as the thickness $h$ of the plate goes to zero. More precisely, it is shown that critical points of the nonlinear elastic functional $\mathcal E^h$, whose energies (per unit thickness) are bounded by $Ch^4$, converge to critical points of the $\Gamma$-limit of $h^{-4}\mathcal E^h$. This is proved under the physical assumption that the energy density $W(F)$ blows up as $\det F\to0$.

}, doi = {10.1016/j.jde.2011.09.009}, url = {http://hdl.handle.net/1963/3466}, author = {Maria Giovanna Mora and Lucia Scardia} } @article {2012, title = {Convex pencils of real quadratic forms}, journal = {Discrete and Computational Geometry, Volume 48, Issue 4, December 2012, Pages 1025-1047}, number = {arXiv:1106.4678v3;}, year = {2012}, note = {Updated version to be published in DCG ; was published in : Discrete and Computational Geometry, Volume 48, Issue 4, December 2012, Pages 1025-1047}, publisher = {Springer}, abstract = {We study the topology of the set X of the solutions of a system of two quadratic inequalities in the real projective space RP^n (e.g. X is the intersection of two real quadrics). We give explicit formulae for its Betti numbers and for those of its double cover in the sphere S^n; we also give similar formulae for level sets of homogeneous quadratic maps to the plane. We discuss some applications of these results, especially in classical convexity theory. We prove the sharp bound b(X)\leq 2n for the total Betti number of X; we show that for odd n this bound is attained only by a singular X. In the nondegenerate case we also prove the bound on each specific Betti number b_k(X)\leq 2(k+2).}, doi = {10.1007/s00454-012-9460-2}, url = {http://hdl.handle.net/1963/7099}, author = {Antonio Lerario} } @article {2012, title = {Crawling motility through the analysis of model locomotors: two case studies}, journal = {The European Physical Journal E, Volume 35, Issue 9, September 2012, Article number85}, number = {PMID:22972227;}, year = {2012}, publisher = {Springer}, abstract = {We study model locomotors on a substrate, which derive their propulsive capabilities from the tangential (viscous or frictional) resistance offered by the substrate. Our aim is to develop new tools and insight for future studies of cellular motility by crawling and of collective bacterial motion. The purely viscous case (worm) is relevant for cellular motility by crawling of individual cells. We re-examine some recent results on snail locomotion in order to assess the role of finely regulated adhesion mechanisms in crawling motility. Our main conclusion is that such regulation, although well documented in several biological systems, is not indispensable to accomplish locomotion driven by internal deformations, provided that the crawler may execute sufficiently large body deformations. Thus, there is no snail theorem. Namely, the crawling analog of the scallop theorem of low Reynolds number hydrodynamics does not hold for snail-like crawlers. The frictional case is obtained by assuming that the viscous coefficient governing tangential resistance forces, which act parallel and in the direction opposite to the velocity of the point to which they are applied, depends on the normal force acting at that point. We combine these surface interactions with inertial effects in order to investigate the mechanisms governing the motility of a bristle-robot. This model locomotor is easily manufactured and has been proposed as an effective tool to replicate and study collective bacterial motility.}, doi = {10.1140/epje/i2012-12085-x}, url = {http://hdl.handle.net/1963/7017}, author = {Antonio DeSimone and Amabile Tatone} } @article {2012, title = {On the critical behavior in nonlinear evolutionary PDEs with small viscocity}, journal = {Russian Journal of Mathematical Physics. Volume 19, Issue 4, December 2012, Pages 449-460}, year = {2012}, publisher = {SISSA}, abstract = {We address the problem of general dissipative regularization of the quasilinear transport equation. We argue that the local behavior of solutions to the regularized equation near the point of gradient catastrophe for the transport equation is described by the logarithmic derivative of the Pearcey function, a statement generalizing the result of A.M.Il\\\'in \\\\cite{ilin}. We provide some analytic arguments supporting such conjecture and test it numerically.}, doi = {10.1134/S106192081204005X}, url = {http://hdl.handle.net/1963/6465}, author = {Boris Dubrovin and Maria Elaeva} } @article {2012, title = {Decompositions of large-scale biological systems based on dynamical properties}, journal = {Bioinformatics (Oxford, England). 2012 Jan; 28(1):76-83}, number = {PMID:22072388;}, year = {2012}, publisher = {Oxford University Press}, abstract = {MOTIVATION: Given a large-scale biological network represented as an influence graph, in this article we investigate possible decompositions of the network aimed at highlighting specific dynamical properties.\\r\\nRESULTS: The first decomposition we study consists in finding a maximal directed acyclic subgraph of the network, which dynamically corresponds to searching for a maximal open-loop subsystem of the given system. Another dynamical property investigated is strong monotonicity. We propose two methods to deal with this property, both aimed at decomposing the system into strongly monotone subsystems, but with different structural characteristics: one method tends to produce a single large strongly monotone component, while the other typically generates a set of smaller disjoint strongly monotone subsystems.\\r\\nAVAILABILITY: Original heuristics for the methods investigated are described in the article.}, doi = {10.1093/bioinformatics/btr620}, url = {http://hdl.handle.net/1963/5226}, author = {Nicola Soranzo and Fahimeh Ramezani and Giovanni Iacono and Claudio Altafini} } @article {2012, title = {Deformed Lorentz symmetry and relative locality in a curved/expanding spacetime}, journal = {Phys. Rev. D 86 (2012) 124035}, number = {arXiv:1206.5315;}, year = {2012}, note = {12 pages, 5 figures}, publisher = {American Physical Society}, abstract = {The interest of part of the quantum-gravity community in the possibility of\r\nPlanck-scale-deformed Lorentz symmetry is also fueled by the opportunities for testing the relevant scenarios with analyses, from a signal-propagation perspective, of observations of bursts of particles from cosmological distances. In this respect the fact that so far the implications of deformed Lorentz symmetry have been investigated only for flat (Minkowskian) spacetimes represents a very significant limitation, since for propagation over cosmological distances the curvature/expansion of spacetime is evidently tangible. We here provide a significant step toward filling this gap by exhibiting an explicit example of Planck-scale-deformed relativistic symmetries of a spacetime with constant rate of expansion (deSitterian). Technically we obtain the first ever example of a relativistic theory of worldlines of particles with 3 nontrivial relativistic invariants: a large speed scale (\"speed-of-light scale\"), a large distance scale (inverse of the \"expansion-rate scale\"), and a large momentum scale (\"Planck scale\"). We address some of the challenges that had obstructed success for previous attempts by exploiting the recent understanding of the connection between deformed Lorentz symmetry and relativity of spacetime locality. We also offer a preliminary analysis of the differences between the scenario we here propose and the most studied scenario for broken (rather than deformed) Lorentz symmetry in expanding spacetimes.}, keywords = {Doubly special relativity}, doi = {10.1103/PhysRevD.86.124035}, author = {Giovanni Amelino-Camelia and Antonino Marciano and Marco Matassa and Giacomo Rosati} } @article {2012, title = {Detection of transcriptional triggers in the dynamics of microbial growth: application to the respiratory-versatile bacterium Shewanella oneidensis}, journal = {Nucleic Acids Research, Volume 40, Issue 15, August 2012, Pages 7132-7149}, year = {2012}, publisher = {SISSA}, abstract = {The capacity of microorganisms to respond to variable external conditions requires a coordination of environment-sensing mechanisms and decisionmaking regulatory circuits. Here, we seek to understand the interplay between these two processes by combining high-throughput measurement of time-dependent mRNA profiles with a novel computational approach that searches for key genetic triggers of transcriptional changes. Our approach helped us understand the regulatory strategies of a respiratorily versatile bacterium with promising bioenergy and bioremediation applications, Shewanella oneidensis, in minimal and rich media. By comparing expression profiles across these two conditions, we unveiled components of the transcriptional program that depend mainly on the growth phase. Conversely, by integrating our time-dependent data with a previously available large compendium of static perturbation responses, we identified transcriptional changes that cannot be explained solely by internal network dynamics, but are rather triggered by specific genes acting as key mediators of an environment-dependent response. These transcriptional triggers include known and novel regulators that respond to carbon, nitrogen and oxygen limitation. Our analysis suggests a sequence of physiological responses, including a coupling between nitrogen depletion and glycogen storage, partially recapitulated through dynamic flux balance analysis, and experimentally confirmed by metabolite measurements. Our approach is broadly applicable to other systems}, doi = {10.1093/nar/gks467}, url = {http://hdl.handle.net/1963/6506}, author = {Q Beg and Mattia Zampieri and N Klitgord and S Collins and M Serres and Daniel Segr{\`e} and Claudio Altafini} } @article {2012, title = {A dynamical feedback model for adaptation in the olfactory transduction pathway}, journal = {Biophysical Journal. Volume 102, Issue 12, 20 June 2012, Pages 2677-2686}, number = {PMID:22735517;}, year = {2012}, publisher = {Biophysical Society, Elsevier}, abstract = {Olfactory transduction exhibits two distinct types of adaptation, which we denote multipulse and step adaptation. In terms of measured transduction current, multipulse adaptation appears as a decrease in the amplitude of the second of two consecutive responses when the olfactory neuron is stimulated with two brief pulses. Step adaptation occurs in response to a sustained steplike stimulation and is characterized by a return to a steady-state current amplitude close to the prestimulus value, after a transient peak. In this article, we formulate a dynamical model of the olfactory transduction pathway, which includes the kinetics of the CNG channels, the concentration of Ca ions flowing through them, and the Ca-complexes responsible for the regulation. Based on this model, a common dynamical explanation for the two types of adaptation is suggested. We show that both forms of adaptation can be well described using different time constants for the kinetics of Ca ions (faster) and the kinetics of the feedback mechanisms (slower). The model is validated on experimental data collected in voltage-clamp conditions using different techniques and animal species.}, doi = {10.1016/j.bpj.2012.04.040}, url = {http://hdl.handle.net/1963/7019}, author = {Giovanna De Palo and Anna Boccaccio and Andrew Miri and Anna Menini and Claudio Altafini} } @article {2012, title = {Dynamics of opinion forming in structurally balanced social networks}, journal = {PloS one. 2012 ; 7(6):e38135}, number = {PMID:22761667;}, year = {2012}, publisher = {PLoS}, abstract = {A structurally balanced social network is a social community that splits into two antagonistic factions (typical example being a two-party political system). The process of opinion forming on such a community is most often highly predictable, with polarized opinions reflecting the bipartition of the network. The aim of this paper is to suggest a class of dynamical systems, called monotone systems, as natural models for the dynamics of opinion forming on structurally balanced social networks. The high predictability of the outcome of a decision process is explained in terms of the order-preserving character of the solutions of this class of dynamical systems. If we represent a social network as a signed graph in which individuals are the nodes and the signs of the edges represent friendly or hostile relationships, then the property of structural balance corresponds to the social community being splittable into two antagonistic factions, each containing only friends.}, doi = {10.1371/journal.pone.0038135}, url = {http://hdl.handle.net/1963/6051}, author = {Claudio Altafini} } @article {2012, title = {Exploring the low-energy landscape of large-scale signed social networks}, journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. Volume 86, Issue 3, 26 September 2012, Article number036116}, year = {2012}, publisher = {SISSA}, abstract = {Analogously to a spin glass, a large-scale signed social network is characterized by the presence of disorder, expressed in this context (and in the social network literature) by the concept of structural balance. If, as we have recently shown, the signed social networks currently available have a limited amount of true disorder (or frustration), it is also interesting to investigate how this frustration is organized, by exploring the landscape of near-optimal structural balance. What we obtain in this paper is that while one of the networks analyzed shows a unique valley of minima, and a funneled landscape that gradually and smoothly worsens as we move away from the optimum, another network shows instead several distinct valleys of optimal or near-optimal structural balance, separated by energy barriers determined by internally balanced subcommunities of users, a phenomenon similar to the replica-symmetry breaking of spin glasses. Multiple, essentially isoenergetic, arrangements of these communities are possible. Passing from one valley to another requires one to destroy the internal arrangement of these balanced subcommunities and then to reform it again. It is essentially this process of breaking the internal balance of the subcommunities which gives rise to the energy barriers.}, doi = {10.1103/PhysRevE.86.036116}, url = {http://hdl.handle.net/1963/6504}, author = {Giuseppe Facchetti and Giovanni Iacono and Claudio Altafini} } @article {2012, title = {A formula for Popp\'s volume in sub-Riemannian geometry}, journal = {Analysis and Geometry in Metric Spaces, vol. 1 (2012), pages : 42-57}, number = {arXiv:1211.2325;}, year = {2012}, note = {16 pages, minor revisions}, publisher = {SISSA}, abstract = {For an equiregular sub-Riemannian manifold M, Popp\'s volume is a smooth\r\nvolume which is canonically associated with the sub-Riemannian structure, and\r\nit is a natural generalization of the Riemannian one. In this paper we prove a\r\ngeneral formula for Popp\'s volume, written in terms of a frame adapted to the\r\nsub-Riemannian distribution. As a first application of this result, we prove an\r\nexplicit formula for the canonical sub-Laplacian, namely the one associated\r\nwith Popp\'s volume. Finally, we discuss sub-Riemannian isometries, and we prove\r\nthat they preserve Popp\'s volume. We also show that, under some hypotheses on\r\nthe action of the isometry group of M, Popp\'s volume is essentially the unique\r\nvolume with such a property.}, keywords = {subriemannian, volume, Popp, control}, doi = {10.2478/agms-2012-0004}, url = {http://hdl.handle.net/1963/6501}, author = {Luca Rizzi and Davide Barilari} } @article {BertolaCafasso3, title = {Fredholm determinants and pole-free solutions to the noncommutative Painlev{\'e} II equation}, journal = {Comm. Math. Phys.}, volume = {309}, number = {3}, year = {2012}, pages = {793{\textendash}833}, issn = {0010-3616}, doi = {10.1007/s00220-011-1383-x}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00220-011-1383-x}, author = {Marco Bertola and Mattia Cafasso} } @article {2012, title = {Frobenius manifold for the dispersionless Kadomtsev-Petviashvili equation}, journal = {Communications in Mathematical Physics 311 (2012) 557-594}, number = {arXiv:1008.2128;}, year = {2012}, publisher = {Springer}, abstract = {We consider a Frobenius structure associated with the dispersionless\\r\\nKadomtsev-Petviashvili equation. This is done, essentially, by applying a\\r\\ncontinuous analogue of the finite dimensional theory in the space of Schwartz\\r\\nfunctions on the line. The potential of the Frobenius manifold is found to be a\\r\\nlogarithmic potential with quadratic external field. Following the construction\\r\\nof the principal hierarchy, we construct a set of infinitely many commuting\\r\\nflows, which extends the classical dKP hierarchy.}, doi = {10.1007/s00220-012-1470-7}, url = {http://hdl.handle.net/1963/6040}, author = {Andrea Raimondo} } @article {2012, title = {A Fully Coupled Immersed Finite Element Method for Fluid Structure Interaction via the Deal.II Library}, number = {arXiv:1209.2811;}, year = {2012}, note = {28 pages, 9 figures}, institution = {SISSA}, abstract = {We present the implementation of a solution scheme for fluid-structure\\r\\ninteraction problems via the finite element software library deal.II. The\\r\\nsolution scheme is an immersed finite element method in which two independent discretizations are used for the fluid and immersed deformable body. In this type of formulation the support of the equations of motion of the fluid is extended to cover the union of the solid and fluid domains. The equations of motion over the extended solution domain govern the flow of a fluid under the action of a body force field. This body force field informs the fluid of the presence of the immersed solid. The velocity field of the immersed solid is the restriction over the immersed domain of the velocity field in the extended equations of motion. The focus of this paper is to show how the determination of the motion of the immersed domain is carried out in practice. We show that our implementation is general, that is, it is not dependent on a specific choice of the finite element spaces over the immersed solid and the extended fluid domains. We present some preliminary results concerning the accuracy of the proposed method.}, keywords = {Finite Element Method, Immersed Boundary Method, Immersed Finite Element Method}, url = {http://hdl.handle.net/1963/6255}, author = {Luca Heltai and Saswati Roy and Francesco Costanzo} } @article {2012, title = {Gamma-convergence and H-convergence of linear elliptic operators}, journal = {Journal de Math{\'e}matiques Pures et Appliqu{\'e}es, Available online 12 September 2012}, number = {SISSA;04/2012/M}, year = {2012}, publisher = {Elsevier}, keywords = {Linear elliptic operators}, doi = {10.1016/j.matpur.2012.09.004}, url = {http://hdl.handle.net/1963/5878}, author = {Nadia Ansini and Gianni Dal Maso and Caterina Ida Zeppieri} } @article {2012, title = {Gauge Theories on ALE Space and Super Liouville Correlation Functions}, journal = {Lett. Math. Phys. 101 (2012) 103-124}, number = {arXiv:1107.4609v1;}, year = {2012}, note = {21 pages}, publisher = {SISSA}, abstract = {We present a relation between N=2 quiver gauge theories on the ALE space O_{P^1}(-2) and correlators of N=1 super Liouville conformal field theory, providing checks in the case of punctured spheres and tori. We derive a blow-up formula for the full Nekrasov partition function and show that, up to a U(1) factor, the N=2^* instanton partition function is given by the product of the character of \\\\hat{SU}(2)_2 times the super Virasoro conformal block on the torus with one puncture.}, doi = {10.1007/s11005-012-0553-x}, url = {http://hdl.handle.net/1963/4305}, author = {Giulio Bonelli and Kazunobu Maruyoshi and Alessandro Tanzini} } @article {FONDA20121369, title = {A general method for the existence of periodic solutions of differential systems in the plane}, journal = {Journal of Differential Equations}, volume = {252}, number = {2}, year = {2012}, pages = {1369 - 1391}, abstract = {We propose a general method to prove the existence of periodic solutions for planar systems of ordinary differential equations, which can be used in many different circumstances. Applications are given to some nonresonant cases, even for systems with superlinear growth in some direction, or with a singularity. Systems {\textquotedblleft}at resonance{\textquotedblright} are also considered, provided a Landesman{\textendash}Lazer type of condition is assumed.

}, keywords = {Nonlinear dynamics, Periodic solutions}, issn = {0022-0396}, doi = {https://doi.org/10.1016/j.jde.2011.08.005}, url = {http://www.sciencedirect.com/science/article/pii/S0022039611003196}, author = {Alessandro Fonda and Andrea Sfecci} } @inbook {2012, title = {Generalized reduced basis methods and n-width estimates for the approximation of the solution manifold of parametric PDEs}, booktitle = {Springer, Indam Series, Vol. 4, 2012}, number = {SISSA Preprint;44/2012/M}, year = {2012}, publisher = {Springer}, organization = {Springer}, abstract = {The set of solutions of a parameter-dependent linear partial di fferential equation with smooth coe fficients typically forms a compact manifold in a Hilbert space. In this paper we review the generalized reduced basis method as a fast computational tool for the uniform approximation of the solution manifold. We focus on operators showing an affi ne parametric dependence, expressed as a linear combination of parameter-independent operators through some smooth, parameter-dependent scalar functions. In the case that the parameter-dependent operator has a dominant term in its affi ne expansion, one can prove the existence of exponentially convergent uniform approximation spaces for the entire solution manifold. These spaces can be constructed without any assumptions on the parametric regularity of the manifold \\r\\nonly spatial regularity of the solutions is required. The exponential convergence rate is then inherited by the generalized reduced basis method. We provide a numerical example related to parametrized elliptic\\r\\nequations con rming the predicted convergence rates.}, keywords = {solution manifold}, url = {http://hdl.handle.net/1963/6340}, author = {Toni Lassila and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza} } @article {2012, title = {On the genus two free energies for semisimple Frobenius manifolds}, journal = {Russian Journal of Mathematical Physics. Volume 19, Issue 3, September 2012, Pages 273-298}, number = {arXiv:1205.5990;}, year = {2012}, note = {36 pages, 3 figures}, publisher = {SISSA}, abstract = {We represent the genus two free energy of an arbitrary semisimple Frobenius\\r\\nmanifold as a sum of contributions associated with dual graphs of certain\\r\\nstable algebraic curves of genus two plus the so-called \\\"genus two G-function\\\".\\r\\nConjecturally the genus two G-function vanishes for a series of important\\r\\nexamples of Frobenius manifolds associated with simple singularities as well as\\r\\nfor ${\\\\bf P}^1$-orbifolds with positive Euler characteristics. We explain the\\r\\nreasons for such Conjecture and prove it in certain particular cases.}, doi = {10.1134/S1061920812030028}, url = {http://hdl.handle.net/1963/6464}, author = {Boris Dubrovin and Si-Qi Liu and Youjin Zhang} } @article {2012, title = {On the Hausdorff volume in sub-Riemannian geometry}, journal = {Calculus of Variations and Partial Differential Equations. Volume 43, Issue 3-4, March 2012, Pages 355-388}, number = {arXiv:1005.0540;}, year = {2012}, publisher = {SISSA}, abstract = {For a regular sub-Riemannian manifold we study the Radon-Nikodym derivative\r\nof the spherical Hausdorff measure with respect to a smooth volume. We prove\r\nthat this is the volume of the unit ball in the nilpotent approximation and it\r\nis always a continuous function. We then prove that up to dimension 4 it is\r\nsmooth, while starting from dimension 5, in corank 1 case, it is C^3 (and C^4\r\non every smooth curve) but in general not C^5. These results answer to a\r\nquestion addressed by Montgomery about the relation between two intrinsic\r\nvolumes that can be defined in a sub-Riemannian manifold, namely the Popp and\r\nthe Hausdorff volume. If the nilpotent approximation depends on the point (that\r\nmay happen starting from dimension 5), then they are not proportional, in\r\ngeneral.}, doi = {10.1007/s00526-011-0414-y}, url = {http://hdl.handle.net/1963/6454}, author = {Andrei A. Agrachev and Davide Barilari and Ugo Boscain} } @article {2012, title = {Hybridization in nanostructured DNA monolayers probed by AFM: theory versus experiment}, journal = {Nanoscale. 2012 Mar; 4(5):1734-41}, number = {PMID:22301788;}, year = {2012}, publisher = {Royal Society of Chemistry}, abstract = {Nanografted monolayers (NAMs) of DNA show novel physico-chemical properties that make them ideally suited for advanced biosensing applications. In comparison with alternative solid-phase techniques for diagnostic DNA detection, NAMs have the advantage of combining a small size with a high homogeneity of the DNA surface coverage. These two properties favour the extreme miniaturization and ultrasensitivity in high-throughput biosensing devices. The systematic use of NAMs for quantitative DNA (and protein) detection has so far suffered from the lack of a control on key fabrication parameters, such as the ss- or ds-DNA surface coverage. Here we report on a combined experimental-computational study that allows us to estimate the surface density of the grafted DNA by analyzing the sample mechanical response, that is the DNA patch height vs. applied tip load curves. It is shown that the same analysis scheme can be used to detect the occurrence of hybridization with complementary strands in solution and estimate its efficiency. Thanks to these quantitative relationships it is possible to use a single AFM-based setup to: (i) fabricate a DNA NAM, (ii) control the DNA surface coverage, and (iii) characterize its level of hybridization helping the design of NAMs with pre-determined fabrication parameters.}, doi = {10.1039/c2nr11662f}, author = {Alessandro Bosco and Fouzia Bano and Pietro Parisse and Loredana Casalis and Antonio DeSimone and Cristian Micheletti} } @article {2012, title = {Introduction to Riemannian and sub-Riemannian geometry}, number = {SISSA;09/2012/M}, year = {2012}, institution = {SISSA}, url = {http://hdl.handle.net/1963/5877}, author = {Andrei A. Agrachev and Davide Barilari and Ugo Boscain} } @article {2012, title = {The KdV hierarchy: universality and a Painleve transcendent}, journal = {International Mathematics Research Notices, vol. 22 (2012) , page 5063-5099}, number = {arXiv:1101.2602;}, year = {2012}, note = {This article was published in "International Mathematics Research Notices, vol. 22 (2012) , page 5063-5099}, publisher = {Oxford University Press}, abstract = {We study the Cauchy problem for the Korteweg-de Vries (KdV) hierarchy in the small dispersion limit where $\e\to 0$. For negative analytic initial data with a single negative hump, we prove that for small times, the solution is approximated by the solution to the hyperbolic transport equation which corresponds to $\e=0$. Near the time of gradient catastrophe for the transport equation, we show that the solution to the KdV hierarchy is approximated by a particular Painlev\'e transcendent. This supports Dubrovins universality conjecture concerning the critical behavior of Hamiltonian perturbations of hyperbolic equations. We use the Riemann-Hilbert approach to prove our results.}, keywords = {Small-Dispersion limit}, url = {http://hdl.handle.net/1963/6921}, author = {Tom Claeys and Tamara Grava} } @article {2012, title = {Linear elasticity obtained from finite elasticity by Gamma-convergence under weak coerciveness conditions}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire}, volume = {29}, number = {SISSA;30/2011/M}, year = {2012}, pages = {715-735}, publisher = {Gauthier-Villars;Elsevier}, abstract = {The energy functional of linear elasticity is obtained as G-limit of suitable rescalings of the energies of finite elasticity...

}, keywords = {Nonlinear elasticity}, doi = {10.1016/j.anihpc.2012.04.001}, url = {http://hdl.handle.net/1963/4267}, author = {Virginia Agostiniani and Gianni Dal Maso and Antonio DeSimone} } @article {2012, title = {On localization in holomorphic equivariant cohomology}, journal = {Central European Journal of Mathematics, Volume 10, Issue 4, August 2012, Pages 1442-1454}, number = {arXiv:0910.2019;}, year = {2012}, publisher = {Springer}, abstract = {We prove a localization formula for a "holomorphic equivariant cohomology" attached to the Atiyah algebroid of an equivariant holomorphic vector bundle. This generalizes Feng-Ma, Carrell-Liebermann, Baum-Bott and K. Liu{\textquoteright}s localization formulas.}, keywords = {Lie algebroids}, doi = {10.2478/s11533-012-0054-2}, url = {http://hdl.handle.net/1963/6584}, author = {Ugo Bruzzo and Vladimir Rubtsov} } @article {Bertola:P2poles, title = {On the location of poles for the Ablowitz-Segur family of solutions to the second Painlev{\'e} equation}, journal = {Nonlinearity}, volume = {25}, number = {4}, year = {2012}, pages = {1179{\textendash}1185}, issn = {0951-7715}, doi = {10.1088/0951-7715/25/4/1179}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1088/0951-7715/25/4/1179}, author = {Marco Bertola} } @proceedings {2012, title = {Mathematical and numerical modeling of liquid crystal elastomer phase transition and deformation}, year = {2012}, publisher = {Cambridge University Press}, abstract = {Liquid crystal (in particular, nematic) elastomers consist of cross-linked flexible polymer chains with embedded stiff rod molecules that allow them to behave as a rubber and a liquid crystal. Nematic elastomers are characterized by a phase transition from isotropic to nematic past a temperature threshold. They behave as rubber at high temperature and show nematic behavior below the temperature threshold. Such transition is reversible. While in the nematic phase, the rod molecules are aligned along the direction of the "nematic director". This molecular rearrangement induces a stretch in the polymer chains and hence macroscopic spontaneous deformations. The coupling between nematic order parameter and deformation gives rise to interesting phenomena with a potential for new interesting applications. In the biological field, the ability to considerably change their length makes them very promising as artificial muscles actuators. Their tunable optical properties make them suitable, for example, as lenses for new imaging systems. We present a mathematical model able to describe the behavior of nematic elastomers and numerical simulations reproducing such peculiar behavior. We use a geometrically linear version of the Warner and Terentjev model [1] and consider cooling experiments and stretching experiments in the direction perpendicular to the one of the director at cross-linking.}, keywords = {Artificial muscle}, isbn = {9781605113807}, doi = {10.1557/opl.2012.249}, url = {http://hdl.handle.net/1963/7020}, author = {Mariarita De Luca and Antonio DeSimone} } @article {2012, title = {Modeling and control of quantum systems: An introduction}, journal = {IEEE Transactions on Automatic Control. Volume 57, Issue 8, 2012, Article number6189035, Pages 1898-1917}, year = {2012}, publisher = {Institute of Electrical and Electronics Engineers}, abstract = {The scope of this work is to provide a self-contained introduction to a selection of basic theoretical aspects in the modeling and control of quantum mechanical systems, as well as a brief survey on the main approaches to control synthesis. While part of the existing theory, especially in the open-loop setting, stems directly from classical control theory (most notably geometric control and optimal control), a number of tools specifically tailored for quantum systems have been developed since the 1980s, in order to take into account their distinctive features: the probabilistic nature of atomic-scale physical systems, the effect of dissipation and the irreversible character of the measurements have all proved to be critical in feedback-design problems. The relevant dynamical models for both closed and open quantum systems are presented, along with the main results on their controllability and stability. A brief review of several currently available control design methods is meant to provide the interested reader with a roadmap for further studies}, doi = {10.1109/TAC.2012.2195830}, url = {http://hdl.handle.net/1963/6505}, author = {Claudio Altafini and Francesco Ticozzi} } @article {2011, title = {Moduli of symplectic instanton vector bundles of higher rank on projective space $\\mathbb{P}^3$}, journal = {Central European Journal of Mathematics 10, nr. 4 (2012) 1232}, number = {arXiv:1109.2292v1;}, year = {2012}, note = {14 pages}, publisher = {SISSA}, abstract = {Symplectic instanton vector bundles on the projective space $\\mathbb{P}^3$ constitute a natural generalization of mathematical instantons of rank 2. We study the moduli space $I_{n,r}$ of rank-$2r$ symplectic instanton vector bundles on $\\mathbb{P}^3$ with $r\\ge2$ and second Chern class $n\\ge r,\\ n\\equiv r({\\rm mod}2)$. We give an explicit construction of an irreducible component $I^*_{n,r}$ of this space for each such value of $n$ and show that $I^*_{n,r}$ has the expected dimension $4n(r+1)-r(2r+1)$.}, doi = {10.2478/s11533-012-0062-2}, url = {http://hdl.handle.net/1963/4656}, author = {Ugo Bruzzo and Dimitri Markushevich and Alexander Tikhomirov} } @article {2012, title = {Moduli spaces of noncommutative instantons: gauging away noncommutative parameters}, journal = {Quarterly Journal of Mathematics (2012) 63 (1): 41-86}, number = {SISSA;62/2009/FM}, year = {2012}, publisher = {Oxford University Press}, abstract = {Using the theory of noncommutative geometry in a braided monoidal category, we improve upon a previous construction of noncommutative families of instantons of arbitrary charge on the deformed sphere S^4_\\\\theta. We formulate a notion of noncommutative parameter spaces for families of instantons and we explore what it means for such families to be gauge equivalent, as well as showing how to remove gauge parameters using a noncommutative quotient construction. Although the parameter spaces are a priori noncommutative, we show that one may always recover a classical parameter space by making an appropriate choice of gauge transformation.}, doi = {10.1093/qmath/haq036}, url = {http://hdl.handle.net/1963/3777}, author = {Simon Brain and Giovanni Landi} } @article {Cavalletti2012, title = {The Monge problem in Wiener space}, journal = {Calculus of Variations and Partial Differential Equations}, volume = {45}, number = {1}, year = {2012}, month = {Sep}, pages = {101{\textendash}124}, abstract = {We address the Monge problem in the abstract Wiener space and we give an existence result provided both marginal measures are absolutely continuous with respect to the infinite dimensional Gaussian measure γ.

}, issn = {1432-0835}, doi = {10.1007/s00526-011-0452-5}, url = {https://doi.org/10.1007/s00526-011-0452-5}, author = {Fabio Cavalletti} } @article {2012, title = {Nonlinear thin-walled beams with a rectangular cross-section-Part I}, journal = {Math. Models Methods Appl. Sci. 22, 1150016 (2012)}, number = {SISSA;79/2010/M}, year = {2012}, publisher = {World Scientific}, abstract = {Our aim is to rigorously derive a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section, starting from three-dimensional nonlinear elasticity. The different limit models are distinguished by the different scaling of the elastic energy and of the ratio between the sides of the cross-section. In this paper we report the first part of our results.}, doi = {10.1142/S0218202511500163}, url = {http://hdl.handle.net/1963/4104}, author = {Lorenzo Freddi and Maria Giovanna Mora and Roberto Paroni} } @article {SFECCI20126191, title = {A nonresonance condition for radial solutions of a nonlinear Neumann elliptic problem}, journal = {Nonlinear Analysis: Theory, Methods \& Applications}, volume = {75}, number = {16}, year = {2012}, pages = {6191 - 6202}, abstract = {We prove an existence result for radial solutions of a Neumann elliptic problem whose nonlinearity asymptotically lies between the first two eigenvalues. To this aim, we introduce an alternative nonresonance condition with respect to the second eigenvalue which, in the scalar case, generalizes the classical one, in the spirit of Fonda et al. (1991) [2]. Our approach also applies for nonlinearities which do not necessarily satisfy a subcritical growth assumption.

}, keywords = {Neumann problem, Nonresonance, Radial solutions, Time-map}, issn = {0362-546X}, doi = {https://doi.org/10.1016/j.na.2012.06.023}, url = {http://www.sciencedirect.com/science/article/pii/S0362546X12002659}, author = {Andrea Sfecci} } @article {2012, title = {Non-uniqueness results for critical metrics of regularized determinants in four dimensions}, journal = {Communications in Mathematical Physics, Volume 315, Issue 1, September 2012, Pages 1-37}, number = {arXiv:1105.3762;}, year = {2012}, note = {35 pages, title changed, added determinant of half-torsion, references added. Comm. Math. Phys., to appear}, publisher = {Springer}, abstract = {The regularized determinant of the Paneitz operator arises in quantum gravity (see Connes 1994, IV.4.$\gamma$). An explicit formula for the relative determinant of two conformally related metrics was computed by Branson in Branson (1996). A similar formula holds for Cheeger{\textquoteright}s half-torsion, which plays a role in self-dual field theory (see Juhl, 2009), and is defined in terms of regularized determinants of the Hodge laplacian on $p$-forms ($p < n/2$). In this article we show that the corresponding actions are unbounded (above and below) on any conformal four-manifold. We also show that the conformal class of the round sphere admits a second solution which is not given by the pull-back of the round metric by a conformal map, thus violating uniqueness up to gauge equivalence. These results differ from the properties of the determinant of the conformal Laplacian established in Chang and Yang (1995), Branson, Chang, and Yang (1992), and Gursky (1997). We also study entire solutions of the Euler-Lagrange equation of $\log \det P$ and the half-torsion $\tau_h$ on $\mathbb{R}^4 \setminus {0}$, and show the existence of two families of periodic solutions. One of these families includes Delaunay-type solutions.}, doi = {10.1007/s00220-012-1535-7}, url = {http://hdl.handle.net/1963/6559}, author = {Matthew Gursky and Andrea Malchiodi} } @article {2012, title = {Numerical modelling of installation effects for diaphragm walls in sand}, journal = {Acta Geotechnica, Volume 7, Issue 3, September 2012, Pages 219-237}, year = {2012}, publisher = {Springer}, abstract = {The scopes of this work are to study the mechanisms of load transfer and the deformations of the ground during slurry trenching and concreting in dry sand and to evaluate their effects on service structural loads, wall deflections and ground displacements behind the wall caused by subsequent excavation. A series of three-dimensional finite element analyses was carried out modelling the installation of diaphragm walls consisting of panels of different length. The soil was modelled as either linearly elastic-perfectly plastic or incrementally non-linear (hypoplastic) with elastic strain range. Plane strain analyses of diaphragm walls of identical cross section were also carried out in which wall installation was either modelled or the wall was wished in place (WIP). The analyses predict ground movements consistent with the experimental observations both in magnitude and trend. The results also show that the maximum horizontal wall deflections and structural loads reduce with increasing panel aspect ratio towards a minimum which is about twice the value computed for WIP analyses. Panel aspect ratios should be larger than about three to take advantage of the three-dimensional effects. The pattern and magnitude of surface vertical displacements obtained from linearly elastic-perfectly plastic analyses, no matter whether three- or two-dimensional, are unrealistic.}, keywords = {Constitutive relations}, doi = {10.1007/s11440-011-0157-0}, url = {http://hdl.handle.net/1963/6934}, author = {Riccardo Conti and Luca de Sanctis and Giulia M.B. Viggiani} } @article {2012, title = {Numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions}, journal = {Physica D 241, nr. 23-24 (2012): 2246-2264}, number = {arXiv:1202.0962;}, year = {2012}, publisher = {Elsevier}, abstract = {We study numerically the small dispersion limit for the Korteweg-de Vries (KdV) equation $u_t+6uu_x+\epsilon^{2}u_{xxx}=0$ for $\epsilon\ll1$ and give a quantitative comparison of the numerical solution with various asymptotic formulae for small $\epsilon$ in the whole $(x,t)$-plane. The matching of the asymptotic solutions is studied numerically.}, keywords = {Korteweg-de Vries equation}, doi = {10.1016/j.physd.2012.04.001}, author = {Tamara Grava and Christian Klein} } @article {2012, title = {Ogden-type energies for nematic elastomers}, journal = {International Journal of Non-Linear mechanics }, volume = {47}, year = {2012}, pages = {402-412}, publisher = {Elsevier}, abstract = {Ogden-type extensions of the free-energy densities currently used to model the mechanical behavior of nematic elastomers are proposed and analyzed. Based on a multiplicative decomposition of the deformation gradient into an elastic and a spontaneous or remanent part, they provide a suitable framework to study the stiffening response at high imposed stretches. Geometrically linear versions of the models (Taylor expansions at order two) are provided and discussed. These small strain theories provide a clear illustration of the geometric structure of the underlying energy landscape (the energy grows quadratically with the distance from a non-convex set of spontaneous strains or energy wells). The comparison between small strain and finite deformation theories may also be useful in the opposite direction, inspiring finite deformation generalizations of small strain theories currently used in the mechanics of active and phase-transforming materials. The energy well structure makes the free-energy densities non-convex. Explicit quasi-convex envelopes are provided, and applied to compute the stiffening response of a specimen tested in plane strain extension experiments (pure shear).

}, keywords = {Nonlinear elasticity}, doi = {10.1016/j.ijnonlinmec.2011.10.001}, author = {Virginia Agostiniani and Antonio DeSimone} } @article {boscaggin2012one, title = {One-signed harmonic solutions and sign-changing subharmonic solutions to scalar second order differential equations}, journal = {Advanced Nonlinear Studies}, volume = {12}, number = {3}, year = {2012}, pages = {445{\textendash}463}, publisher = {Advanced Nonlinear Studies, Inc.}, doi = {10.1515/ans-2012-0302}, author = {Alberto Boscaggin} } @article {doi:10.1137/100801433, title = {Optimal Transport with Branching Distance Costs and the Obstacle Problem}, journal = {SIAM Journal on Mathematical Analysis}, volume = {44}, number = {1}, year = {2012}, pages = {454-482}, doi = {10.1137/100801433}, url = {https://doi.org/10.1137/100801433}, author = {Fabio Cavalletti} } @article {BOSCAGGIN20122900, title = {Pairs of positive periodic solutions of second order nonlinear equations with indefinite weight}, journal = {Journal of Differential Equations}, volume = {252}, number = {3}, year = {2012}, pages = {2900 - 2921}, abstract = {We study the problem of the existence and multiplicity of positive periodic solutions to the scalar ODEu"+λa(t)g(u)=0,λ\>0, where g(x) is a positive function on R+, superlinear at zero and sublinear at infinity, and a(t) is a T-periodic and sign indefinite weight with negative mean value. We first show the nonexistence of solutions for some classes of nonlinearities g(x) when λ is small. Then, using critical point theory, we prove the existence of at least two positive T-periodic solutions for λ large. Some examples are also provided.

}, keywords = {Critical points, Necessary conditions, Pairs of positive solutions, Periodic solutions}, issn = {0022-0396}, doi = {https://doi.org/10.1016/j.jde.2011.09.011}, url = {http://www.sciencedirect.com/science/article/pii/S0022039611003895}, author = {Alberto Boscaggin and Fabio Zanolin} } @article {fonda2012, title = {Periodic solutions of a system of coupled oscillators with one-sided superlinear retraction forces}, journal = {Differential Integral Equations}, volume = {25}, number = {11/12}, year = {2012}, month = {11}, pages = {993{\textendash}1010}, publisher = {Khayyam Publishing, Inc.}, url = {https://projecteuclid.org:443/euclid.die/1356012248}, author = {Alessandro Fonda and Andrea Sfecci} } @article {boscaggin2012periodic, title = {Periodic solutions to superlinear planar Hamiltonian systems}, journal = {Portugaliae Mathematica}, volume = {69}, number = {2}, year = {2012}, pages = {127{\textendash}141}, publisher = {European Mathematical Society Publishing House}, abstract = {We prove the existence of infinitely many periodic (harmonic and subharmonic) solutions to planar Hamiltonian systems satisfying a suitable superlinearity condition at infinity. The proof relies on the Poincare-Birkhoff fixed point theorem.

}, author = {Alberto Boscaggin} } @article {2012, title = {Poles Distribution of PVI Transcendents close to a Critical Point (summer 2011)}, journal = {Physica D: Nonlinear Phenomena, Volume 241, Issue 23-24, 1 December 2012, Pages 2188-2203}, number = {arXiv:1104.5066;}, year = {2012}, publisher = {Elsevier}, abstract = {The distribution of the poles of Painlev{\'e} VI transcendents associated to semi-simple Frobenius manifolds is determined close to a critical point. It is shown that the poles accumulate at the critical point,asymptotically along two rays. As an example, the Frobenius manifold given by the quantum cohomology of CP2 is considered. The general PVI is also considered.}, keywords = {Painleve{\textquoteright} equations}, doi = {doi:10.1016/j.physd.2012.02.015}, url = {http://hdl.handle.net/1963/6526}, author = {Davide Guzzetti} } @article {BOSCAGGIN20122922, title = {Positive periodic solutions of second order nonlinear equations with indefinite weight: Multiplicity results and complex dynamics}, journal = {Journal of Differential Equations}, volume = {252}, number = {3}, year = {2012}, pages = {2922 - 2950}, abstract = {We prove the existence of a pair of positive T-periodic solutions as well as the existence of positive subharmonic solutions of any order and the presence of chaotic-like dynamics for the scalar second order ODEu"+aλ,μ(t)g(u)=0, where g(x) is a positive function on R+, superlinear at zero and sublinear at infinity, and aλ,μ(t) is a T-periodic and sign indefinite weight of the form λa+(t)-μa-(t), with λ,μ\>0 and large.

}, keywords = {Complex dynamics, Poincar{\'e} map, Positive periodic solutions, Subharmonics}, issn = {0022-0396}, doi = {https://doi.org/10.1016/j.jde.2011.09.010}, url = {http://www.sciencedirect.com/science/article/pii/S0022039611003883}, author = {Alberto Boscaggin and Fabio Zanolin} } @article {2012, title = {Predicting and characterizing selective multiple drug treatments for metabolic diseases and cancer.}, journal = {BMC Systems Biology. 29 August 2012, Page 115}, year = {2012}, publisher = {BioMed Central}, abstract = {Background: In the field of drug discovery, assessing the potential of multidrug therapies is a difficult task because of the combinatorial complexity (both theoretical and experimental) and because of the requirements on the selectivity of the therapy. To cope with this problem, we have developed a novel method for the systematic in silico investigation of synergistic effects of currently available drugs on genome-scale metabolic networks. The algorithm finds the optimal combination of drugs which guarantees the inhibition of an objective function, while minimizing the side effect on the overall network. Results: Two different applications are considered: finding drug synergisms for human metabolic diseases (like diabetes, obesity and hypertension) and finding antitumoral drug combinations with minimal side effect on the normal human metabolism.The results we obtain are consistent with some of the available therapeutic indications and predict some new multiple drug treatments.A cluster analysis on all possible interactions among the currently available drugs indicates a limited variety on the metabolic targets for the approved drugs. Conclusion: The in silico prediction of drug synergism can represent an important tool for the repurposing of drug in a realistic perspective which considers also the selectivty of the therapy. Moreover, for a more profitable exploitation of drug-drug interactions, also drugs which show a too low efficacy but which have a non-common mechanism of action, can be reconsider as potential ingredients of new multicompound therapeutic indications.Needless to say the clues provided by a computational study like ours need in any case to be thoroughly evaluated experimentally.}, doi = {doi:10.1186/1752-0509-6-115}, url = {http://hdl.handle.net/1963/6515}, author = {Giuseppe Facchetti and Claudio Altafini and Mattia Zampieri} } @article {2012, title = {Quasistatic evolution for Cam-Clay plasticity: properties of the viscosity solution}, journal = {Calculus of variations and partial differential equations 44 (2012) 495-541}, number = {SISSA;46/2010/M}, year = {2012}, publisher = {Springer}, abstract = {Cam-Clay plasticity is a well established model for the description of the mechanics of fine grained soils. As solutions can develop discontinuities in time, a weak notion of solution, in terms of a rescaled time s , has been proposed in [8] to give a meaning to this discontinuous evolution. In this paper we first prove that this rescaled evolution satisfies the flow-rule for the rate of plastic strain, in a suitable measure-theoretical sense. In the second part of the paper we consider the behavior of the evolution in terms of the original time variable t . We prove that the unrescaled solution satisfies an energy-dissipation balance and an evolution law for the internal variable, which can be expressed in terms of integrals depending only on the original time. Both these integral identities contain terms concentrated on the jump times, whose size can only be determined by looking at the rescaled formulation.

}, doi = {10.1007/s00526-011-0443-6}, url = {http://hdl.handle.net/1963/3900}, author = {Gianni Dal Maso and Antonio DeSimone and Francesco Solombrino} } @article {2011, title = {Quasistatic evolution in non-associative plasticity - the cap models}, journal = {SIAM Journal on Mathematical Analysis 44, nr. 1 (2012) 245-292}, number = {SISSA;05/2011/M}, year = {2012}, publisher = {SIAM}, abstract = {Non-associative elasto-plasticity is the working model of plasticity for soil and rocks mechanics. Yet, it is usually viewed as non-variational. In this work, we prove a contrario the existence of a variational evolution for such a model under a natural capping assumption on the hydrostatic stresses and a less natural mollification of the stress admissibility constraint. The obtained elasto-plastic evolution is expressed for times that are conveniently rescaled.}, keywords = {Elasto-plasticity}, doi = {10.1137/110823511}, url = {http://hdl.handle.net/1963/4139}, author = {Jean-Francois Babadjian and Gilles A. Francfort and Maria Giovanna Mora} } @proceedings {2012, title = {Reduction strategies for PDE-constrained oprimization problems in Haemodynamics}, number = {SISSA;41/2012/M}, year = {2012}, abstract = {Solving optimal control problems for many different scenarios obtained by varying a set of parameters in the state system is a computationally extensive task. In this paper we present a new reduced framework for the formulation, the analysis and the numerical solution of parametrized PDE-constrained optimization problems. This framework is based on a suitable saddle-point formulation of the optimal control problem and exploits the reduced basis method for the rapid and reliable solution of parametrized PDEs, leading to a relevant computational reduction with respect to traditional discretization techniques such as the finite element method. This allows a very efficient evaluation of state solutions and cost functionals, leading to an effective solution of repeated optimal control problems, even on domains of variable shape, for which a further (geometrical) reduction is pursued, relying on flexible shape parametrization techniques. This setting is applied to the solution of two problems arising from haemodynamics, dealing with both data reconstruction and data assimilation over domains of variable shape,\\r\\nwhich can be recast in a common PDE-constrained optimization formulation.}, keywords = {inverse problems}, url = {http://hdl.handle.net/1963/6338}, author = {Gianluigi Rozza and Andrea Manzoni and Federico Negri} } @article {garrione2012, title = {Resonance at the first eigenvalue for first-order systems in the plane: vanishing Hamiltonians and the Landesman-Lazer condition}, journal = {Differential Integral Equations}, volume = {25}, number = {5/6}, year = {2012}, month = {05}, pages = {505{\textendash}526}, publisher = {Khayyam Publishing, Inc.}, url = {https://projecteuclid.org:443/euclid.die/1356012676}, author = {Maurizio Garrione} } @article {2012, title = {Reverse engineering the euglenoid movement}, journal = {Proceedings of the National Academy of Sciences of the United States of America. Volume 109, Issue 44, 30 October 2012, Pages 17874-17879}, year = {2012}, abstract = {Euglenids exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large-amplitude highly concerted deformations of the entire body (euglenoid movement or metaboly). A plastic cell envelope called pellicle mediates these deformations. Unlike ciliary or flagellar motility, the biophysics of this mode is not well understood, including its efficiency and molecular machinery. We quantitatively examine video recordings of four euglenids executing such motions with statistical learning methods. This analysis reveals strokes of high uniformity in shape and pace. We then interpret the observations in the light of a theory for the pellicle kinematics, providing a precise understanding of the link between local actuation by pellicle shear and shape control. We systematically understand common observations, such as the helical conformations of the pellicle, and identify previously unnoticed features of metaboly. While two of our euglenids execute their stroke at constant body volume, the other two exhibit deviations of about 20\% from their average volume, challenging current models of low Reynolds number locomotion. We find that the active pellicle shear deformations causing shape changes can reach 340\%, and estimate the velocity of the molecular motors. Moreover, we find that metaboly accomplishes locomotion at hydrodynamic efficiencies comparable to those of ciliates and flagellates. Our results suggest new quantitative experiments, provide insight into the evolutionary history of euglenids, and suggest that the pellicle may serve as a model for engineered active surfaces with applications in microfluidics.}, keywords = {microswimmers}, doi = {10.1073/pnas.1213977109}, url = {http://hdl.handle.net/1963/6444}, author = {Marino Arroyo and Luca Heltai and Daniel Mill{\'a}n and Antonio DeSimone} } @article {2012, title = {A Review on The Sixth Painlev{\'e} Equation}, number = {arXiv:1210.0311;}, year = {2012}, note = {31 pages, 10 figures}, publisher = {SISSA}, abstract = {For the Painlev\\\'e 6 transcendents, we provide a unitary description of the\r\ncritical behaviours, the connection formulae, their complete tabulation, and\r\nthe asymptotic distribution of the poles close to a critical point.

}, keywords = {Painlev{\'e} equation}, url = {http://hdl.handle.net/1963/6525}, author = {Davide Guzzetti} } @article {BertolaCafasso2, title = {Riemann{\textendash}Hilbert approach to multi-time processes: The Airy and the Pearcey cases}, journal = {Physica D: Nonlinear Phenomena}, volume = {241}, number = {23-24}, year = {2012}, note = {Integrable Systems in Pure and Applied Mathematics}, pages = {2237 - 2245}, keywords = {Integrable kernels}, issn = {0167-2789}, doi = {10.1016/j.physd.2012.01.003}, url = {http://www.sciencedirect.com/science/article/pii/S0167278912000115}, author = {Marco Bertola and Mattia Cafasso} } @article {2012, title = {On robust Lie-algebraic stability conditions for switched linear systems}, journal = {Systems and Control Letters. Volume 61, Issue 2, February 2012, Pages 347-353}, year = {2012}, abstract = {This paper presents new sufficient conditions for exponential stability of switched linear systems under arbitrary switching, which involve the commutators (Lie brackets) among the given matrices generating the switched system. The main novelty feature of these stability criteria is that, unlike their earlier counterparts, they are robust with respect to small perturbations of the system parameters.}, doi = {10.1016/j.sysconle.2011.11.016}, url = {http://hdl.handle.net/1963/6455}, author = {Andrei A. Agrachev and Yurij Baryshnikov and Daniel Liberzon} } @article {2012, title = {SBV regularity for genuinely nonlinear, strictly hyperbolic systems of conservation laws in one space dimension}, journal = {Communications in Mathematical Physics 313 (2012) 1-33}, number = {SISSA;71/2010/M}, year = {2012}, publisher = {Springer}, doi = {10.1007/s00220-012-1480-5}, url = {http://hdl.handle.net/1963/4091}, author = {Stefano Bianchini and Laura Caravenna} } @article {2011, title = {SBV regularity for Hamilton-Jacobi equations with Hamiltonian depending on (t,x)}, journal = {Siam Journal on Mathematical Analysis}, volume = {44}, number = {SISSA;13/2011/M}, year = {2012}, pages = {2179-2203}, publisher = {SISSA}, doi = {10.1137/110827272}, url = {http://hdl.handle.net/20.500.11767/14066}, author = {Stefano Bianchini and Daniela Tonon} } @article {2012, title = {SBV regularity of genuinely nonlinear hyperbolic systems of conservation laws in one space dimension}, journal = {Acta Mathematica Scientia, Volume 32, Issue 1, January 2012, Pages 380-388}, year = {2012}, publisher = {Elsevier}, abstract = {The problem of the presence of Cantor part in the derivative of a solution to a hyperbolic system of conservation laws is considered. An overview of the techniques involved in the proof is given, and a collection of related problems concludes the paper. Key words hyperbolic systems; conservation laws; SBV; regularity}, keywords = {Hyperbolic systems}, doi = {10.1016/S0252-9602(12)60024-1}, url = {http://hdl.handle.net/1963/6535}, author = {Stefano Bianchini} } @article {bianchini2012sbv, title = {SBV-like regularity for general hyperbolic systems of conservation laws in one space dimension}, journal = {Rend. Istit. Mat. Univ. Trieste}, volume = {44}, year = {2012}, pages = {439{\textendash}472}, author = {Stefano Bianchini and Lei Yu} } @article {2012, title = {SBV-like regularity for Hamilton-Jacobi equations with a convex Hamiltonian}, journal = {Journal of Mathematical Analysis and Applications}, volume = {391}, number = {SISSA;45/2011/M}, year = {2012}, pages = {190-208}, publisher = {SISSA}, doi = {10.1016/j.jmaa.2012.02.017}, url = {http://hdl.handle.net/20.500.11767/13909}, author = {Stefano Bianchini and Daniela Tonon} } @article {1078-0947_2012_4_1125, title = {Second order approximations of quasistatic evolution problems in finite dimension}, journal = {Discrete \& Continuous Dynamical Systems - A}, volume = {32}, number = {1078-0947_2012_4_112}, year = {2012}, pages = {1125}, abstract = {In this paper, we study the limit, as ε goes to zero, of a particular solution of the equation $\epsilon^2A\ddot u^ε(t)+εB\dot u^ε(t)+\nabla_xf(t,u^ε(t))=0$, where $f(t,x)$ is a potential satisfying suitable coerciveness conditions. The limit $u(t)$ of $u^ε(t)$ is piece-wise continuous and verifies $\nabla_xf(t,u(t))=0$. Moreover, certain jump conditions characterize the behaviour of $u(t)$ at the discontinuity times. The same limit behaviour is obtained by considering a different approximation scheme based on time discretization and on the solutions of suitable autonomous systems.

}, keywords = {discrete approximations, perturbation methods, saddle-node bifurcation, Singular perturbations, vanishing viscosity}, issn = {1078-0947}, doi = {10.3934/dcds.2012.32.1125}, url = {http://aimsciences.org//article/id/560b82d9-f289-498a-a619-a4b132aaf9f8}, author = {Virginia Agostiniani} } @article {doi:10.1080/17513758.2011.611260, title = {Self-propelled micro-swimmers in a Brinkman fluid}, journal = {Journal of Biological Dynamics}, volume = {6}, number = {sup1}, year = {2012}, note = {PMID: 22873677}, pages = {88-103}, publisher = {Taylor \& Francis}, abstract = {We prove an existence, uniqueness, and regularity result for the motion of a self-propelled micro-swimmer in a particulate viscous medium, modelled as a Brinkman fluid. A suitable functional setting is introduced to solve the Brinkman system for the velocity field and the pressure of the fluid by variational techniques. The equations of motion are written by imposing a self-propulsion constraint, thus allowing the viscous forces and torques to be the only ones acting on the swimmer. From an infinite-dimensional control on the shape of the swimmer, a system of six ordinary differential equations for the spatial position and the orientation of the swimmer is obtained. This is dealt with standard techniques for ordinary differential equations, once the coefficients are proved to be measurable and bounded. The main result turns out to extend an analogous result previously obtained for the Stokes system.

}, doi = {10.1080/17513758.2011.611260}, url = {https://doi.org/10.1080/17513758.2011.611260}, author = {Marco Morandotti} } @article {10671, title = {Simulation-based uncertainty quantification of human arterial network hemodynamics}, journal = {International Journal Numerical Methods Biomedical Engineering}, number = {SISSA preprint;}, year = {2012}, publisher = {Wiley}, abstract = {This work aims at identifying and quantifying uncertainties from various sources in human cardiovascular\r\nsystem based on stochastic simulation of a one dimensional arterial network. A general analysis of\r\ndifferent uncertainties and probability characterization with log-normal distribution of these uncertainties\r\nis introduced. Deriving from a deterministic one dimensional fluid structure interaction model, we establish\r\nthe stochastic model as a coupled hyperbolic system incorporated with parametric uncertainties to describe\r\nthe blood flow and pressure wave propagation in the arterial network. By applying a stochastic collocation\r\nmethod with sparse grid technique, we study systemically the statistics and sensitivity of the solution with\r\nrespect to many different uncertainties in a relatively complete arterial network with potential physiological\r\nand pathological implications for the first time.}, keywords = {uncertainty quantification, mathematical modelling of the cardiovascular system, fluid-structure interaction}, author = {Peng Chen and Alfio Quarteroni and Gianluigi Rozza} } @article {Berti20122579, title = {Sobolev quasi-periodic solutions of multidimensional wave equations with a multiplicative potential}, journal = {Nonlinearity}, volume = {25}, number = {9}, year = {2012}, note = {cited By (since 1996)3}, pages = {2579-2613}, abstract = {We prove the existence of quasi-periodic solutions for wave equations with a multiplicative potential on T d , d >= 1, and finitely differentiable nonlinearities, quasi-periodically forced in time. The only external parameter is the length of the frequency vector. The solutions have Sobolev regularity both in time and space. The proof is based on a Nash-Moser iterative scheme as in [5]. The key tame estimates for the inverse linearized operators are obtained by a multiscale inductive argument, which is more difficult than for NLS due to the dispersion relation of the wave equation. We prove the {\textquoteright}separation properties{\textquoteright} of the small divisors assuming weaker non-resonance conditions than in [11]. {\textcopyright} 2012 IOP Publishing Ltd.}, issn = {09517715}, doi = {10.1088/0951-7715/25/9/2579}, author = {Massimiliano Berti and Philippe Bolle} } @article {2012, title = {Solving the Sixth Painlev{\'e} Equation: Towards the Classification of all the Critical Behaviors and the Connection Formulae}, journal = {Int Math Res Notices (2012) 2012 (6): 1352-1413}, number = {arXiv:1010.1895;}, year = {2012}, note = {53 pages, 2 figures}, publisher = {Oxford University Press}, abstract = {The critical behavior of a three real parameter class of solutions of the\\r\\nsixth Painlev\\\\\\\'e equation is computed, and parametrized in terms of monodromy\\r\\ndata of the associated $2\\\\times 2$ matrix linear Fuchsian system of ODE. The\\r\\nclass may contain solutions with poles accumulating at the critical point. The\\r\\nstudy of this class closes a gap in the description of the transcendents in one\\r\\nto one correspondence with the monodromy data. These transcendents are reviewed in the paper. Some formulas that relate the monodromy data to the critical behaviors of the four real (two complex) parameter class of solutions are\\r\\nmissing in the literature, so they are computed here. A computational procedure to write the full expansion of the four and three real parameter class of solutions is proposed.}, doi = {10.1093/imrn/rnr071}, url = {http://hdl.handle.net/1963/6093}, author = {Davide Guzzetti} } @article {tonon2012some, title = {Some applications of the SBV Regularity Theorem for entropy solutions of 1D scalar conservation laws to ConvectionTheory and sticky particles}, journal = {Riv. Mat. Univ. Parma}, volume = {3}, number = {1}, year = {2012}, pages = {163{\textendash}175}, abstract = {We show how it is possible to apply the SBV Regularity Theorem for entropy solutions of one-dimensional scalar conservation laws, proved by Ambrosio and De Lellis, to Convection Theory and sticky particles. In the multi-dimensional case we present a counterexample which prevent us from using the same approach.

}, url = {https://hal.archives-ouvertes.fr/hal-00918409}, author = {Daniela Tonon} } @mastersthesis {2012, title = {Some aspects of spinors {\textendash} classical and noncommutative}, year = {2012}, school = {SISSA}, url = {http://hdl.handle.net/1963/6317}, author = {Giacomo Dossena} } @article {2012, title = {Some remarks on quantum mechanics}, journal = {International Journal of Geometric Methods in Modern Physics, Volume 9, Issue 2, March 2012, Article number1260018}, year = {2012}, publisher = {World Scientific Publishing}, abstract = {We discuss the similarities and differences between the formalism of Hamiltonian Classical Mechanics and of Quantum Mechanics and exemplify the differences through an analysis of tracks in a cloud chamber.}, keywords = {Quantum mechanics}, doi = {10.1142/S0219887812600183}, url = {http://hdl.handle.net/1963/7018}, author = {Gianfausto Dell{\textquoteright}Antonio} } @article {MR2880030, title = {Spectra of random Hermitian matrices with a small-rank external source: the critical and near-critical regimes}, journal = {J. Stat. Phys.}, volume = {146}, number = {3}, year = {2012}, pages = {475{\textendash}518}, issn = {0022-4715}, doi = {10.1007/s10955-011-0409-2}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1007/s10955-011-0409-2}, author = {Marco Bertola and Buckingham, R. and Lee, S. Y. and Pierce, V.} } @article {2012, title = {Stability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions}, journal = {Rev. Math. Phys. 24 (2012), 1250017}, number = {arXiv:1201.5740;}, year = {2012}, publisher = {World Scientific}, abstract = {We study the stability problem for a non-relativistic quantum system in\\r\\ndimension three composed by $ N \\\\geq 2 $ identical fermions, with unit mass,\\r\\ninteracting with a different particle, with mass $ m $, via a zero-range\\r\\ninteraction of strength $ \\\\alpha \\\\in \\\\R $. We construct the corresponding\\r\\nrenormalised quadratic (or energy) form $ \\\\form $ and the so-called\\r\\nSkornyakov-Ter-Martirosyan symmetric extension $ H_{\\\\alpha} $, which is the\\r\\nnatural candidate as Hamiltonian of the system. We find a value of the mass $\\r\\nm^*(N) $ such that for $ m > m^*(N)$ the form $ \\\\form $ is closed and bounded from below. As a consequence, $ \\\\form $ defines a unique self-adjoint and bounded from below extension of $ H_{\\\\alpha}$ and therefore the system is stable. On the other hand, we also show that the form $ \\\\form $ is unbounded from below for $ m < m^*(2)$. In analogy with the well-known bosonic case, this suggests that the system is unstable for $ m < m^*(2)$ and the so-called Thomas effect occurs.}, doi = {10.1142/S0129055X12500171}, url = {http://hdl.handle.net/1963/6069}, author = {Michele Correggi and Gianfausto Dell{\textquoteright}Antonio and Domenico Finco and Alessandro Michelangeli and Alessandro Teta} } @conference {Mola2012, title = {A stable semi-lagrangian potential method for the simulation of ship interaction with unsteady and nonlinear waves}, booktitle = {17th Int. Conf. Ships Shipp. Res.}, year = {2012}, author = {Andrea Mola and Luca Heltai and Antonio DeSimone} } @article {2012, title = {Sub-Riemannian structures on 3D Lie groups}, journal = {Journal of Dynamical and Control Systems. Volume 18, Issue 1, January 2012, Pages 21-44}, number = {arXiv:1007.4970;}, year = {2012}, publisher = {SISSA}, abstract = {We give a complete classification of left-invariant sub-Riemannian structures on three dimensional Lie groups in terms of the basic differential invariants. As a corollary we explicitly find a sub-Riemannian isometry between the nonisomorphic Lie groups $SL(2)$ and $A^+(\mathbb{R})\times S^1$, where $A^+(\mathbb{R})$ denotes the group of orientation preserving affine maps on the real line.

}, doi = {10.1007/s10883-012-9133-8}, url = {http://hdl.handle.net/1963/6453}, author = {Andrei A. Agrachev and Davide Barilari} } @article {2012, title = {Systems of Quadratic Inequalities}, journal = {Proceedings of the London Mathematical Society, Volume 105, Issue 3, September 2012, Pages 622-660}, number = {arXiv:1012.5731;}, year = {2012}, publisher = {SISSA}, abstract = {We present a spectral sequence which efficiently computes Betti numbers of a closed semi-algebraic subset of RP^n defined by a system of quadratic inequalities and the image of the homology homomorphism induced by the inclusion of this subset in RP^n. We do not restrict ourselves to the term E_2 of the spectral sequence and give a simple explicit formula for the differential d_2.}, doi = {DOI: 10.1112/plms/pds010}, url = {http://hdl.handle.net/1963/7072}, author = {Andrei A. Agrachev and Antonio Lerario} } @article {2012, title = {Tabulation of Painlev{\'e} 6 transcendents}, journal = {Nonlinearity, Volume 25, Issue 12, December 2012, Pages 3235-3276}, number = {arXiv:1108.3401;}, year = {2012}, note = {30 pages, 1 figure; this article was published in "Nonlinearity" in 2012}, publisher = {IOP Publishing}, abstract = {The critical and asymptotic behaviors of solutions of the sixth Painlev{\textquoteright}e equation PVI, obtained in the framework of the monodromy preserving deformation method, and their explicit parametrization in terms of monodromy data, are tabulated.}, doi = {10.1088/0951-7715/25/12/3235}, url = {http://hdl.handle.net/1963/6520}, author = {Davide Guzzetti} } @article {2012, title = {Thermodynamic phase transitions and shock singularities}, journal = {Proc. R. Soc. A 8 March 2012 vol. 468 no. 2139 701-719}, number = {arXiv:1107.0394;}, year = {2012}, publisher = {The Royal Society}, abstract = {We show that under rather general assumptions on the form of the entropy\\r\\nfunction, the energy balance equation for a system in thermodynamic equilibrium is equivalent to a set of nonlinear equations of hydrodynamic type. This set of equations is integrable via the method of the characteristics and it provides the equation of state for the gas. The shock wave catastrophe set identifies the phase transition. A family of explicitly solvable models of\\r\\nnon-hydrodynamic type such as the classical plasma and the ideal Bose gas are\\r\\nalso discussed.}, doi = {10.1098/rspa.2011.0459}, url = {http://hdl.handle.net/1963/6090}, author = {Giuseppe De Nittis and Antonio Moro} } @article {2012, title = {Topological sensitivity analysis for high order elliptic operators}, number = {SISSA;36/2012/M}, year = {2012}, institution = {SISSA}, abstract = {The topological derivative is defined as the first term of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of a singular domain perturbation. It has applications in many different fields such as shape and topology optimization, inverse problems, image processing and mechanical modeling including synthesis and/or optimal design of microstructures, fracture mechanics sensitivity analysis and damage evolution modeling. The topological derivative has been fully developed for a wide range of second order differential operators. In this paper we deal with the topological asymptotic expansion of a class of shape functionals associated with elliptic differential operators of order 2m, m>=1. The general structure of the polarization tensor is derived and the concept of degenerate polarization tensor is introduced. We provide full mathematical justifications for the derived formulas, including precise estimates of remainders.}, keywords = {Topological derivative, Elliptic operators, Polarization tensor}, url = {http://hdl.handle.net/1963/6343}, author = {Samuel Amstutz and Antonio Andr{\'e} Novotny and Nicolas Van Goethem} } @article {2012, title = {Variational implementation of immersed finite element methods}, journal = {Computer Methods in Applied Mechanics and Engineering. Volume 229-232, 1 July 2012, Pages 110-127}, number = {arXiv:1110.2063;}, year = {2012}, note = {42 pages, 5 figures, Revision 1}, publisher = {Elsevier}, abstract = {Dirac-delta distributions are often crucial components of the solid-fluid coupling operators in immersed solution methods for fluid-structure interaction (FSI) problems. This is certainly so for methods like the Immersed Boundary Method (IBM) or the Immersed Finite Element Method (IFEM), where Dirac-delta distributions are approximated via smooth functions. By contrast, a truly variational formulation of immersed methods does not require the use of Dirac-delta distributions, either formally or practically. This has been shown in the Finite Element Immersed Boundary Method (FEIBM), where the variational structure of the problem is exploited to avoid Dirac-delta distributions at both the continuous and the discrete level. In this paper, we generalize the FEIBM to the case where an incompressible Newtonian fluid interacts with a general hyperelastic solid. Specifically, we allow (i) the mass density to be different in the solid and the fluid, (ii) the solid to be either viscoelastic of differential type or purely elastic, and (iii) the solid to be and either compressible or incompressible. At the continuous level, our variational formulation combines the natural stability estimates of the fluid and elasticity problems. In immersed methods, such stability estimates do not transfer to the discrete level automatically due to the non- matching nature of the finite dimensional spaces involved in the discretization. After presenting our general mathematical framework for the solution of FSI problems, we focus in detail on the construction of natural interpolation operators between the fluid and the solid discrete spaces, which guarantee semi-discrete stability estimates and strong consistency of our spatial discretization.

}, keywords = {Turbulent flow}, doi = {10.1016/j.cma.2012.04.001}, url = {http://hdl.handle.net/1963/6462}, author = {Luca Heltai and Francesco Costanzo} } @article {2012, title = {Vertices, vortices \& interacting surface operators}, journal = {JHEP 06(2012)178}, number = {SISSA;03/2011/FM-EP}, year = {2012}, note = {22 pages, 4 figures}, publisher = {SISSA}, abstract = {We show that the vortex moduli space in non-abelian supersymmetric N=(2,2) gauge theories on the two dimensional plane with adjoint and anti-fundamental matter can be described as an holomorphic submanifold of the instanton moduli space in four dimensions. The vortex partition functions for these theories are computed via equivariant localization. We show that these coincide with the field theory limit of the topological vertex on the strip with boundary conditions corresponding to column diagrams. Moreover, we resum the field theory limit of the vertex partition functions in terms of generalized hypergeometric functions formulating their AGT dual description as interacting surface operators of simple type. Analogously we resum the topological open string amplitudes in terms of q-deformed generalized hypergeometric functions proving that they satisfy appropriate finite difference equations.}, doi = {10.1007/JHEP06(2012)178}, url = {http://hdl.handle.net/1963/4134}, author = {Giulio Bonelli and Alessandro Tanzini and Zhao Jian} } @article {2012, title = {A Viscosity-driven crack evolution}, journal = {Advances in Calculus of Variations 5 (2012) 433-483}, number = {SISSA;63/2011/M}, year = {2012}, publisher = {SISSA}, abstract = {We present a model of crack growth in brittle materials which couples dissipative effects on the crack tip and viscous effects. We consider the 2 -dimensional antiplane case with pre-assigned crack path, and firstly prove an existence result for a rate-dependent evolution problem by means of time-discretization. The next goal is to describe the rate-independent evolution as limit of the rate-dependent ones when the dissipative and viscous effects vanish. The rate-independent evolution satisfies a Griffith{\textquoteright}s criterion for the crack growth, but, in general, it does not fulfil a global minimality condition; its fracture set may exhibit jump discontinuities with respect to time. Under suitable regularity assumptions, the quasi-static crack growth is described by solving a finite-dimensional problem.

}, doi = {10.1515/acv-2011-0012}, url = {http://hdl.handle.net/1963/5130}, author = {Simone Racca} } @article {2012, title = {Weighted barycentric sets and singular Liouville equations on compact surfaces}, journal = {Journal of Functional Analysis 262 (2012) 409-450}, number = {arXiv:1105.2363;}, year = {2012}, publisher = {Elsevier}, abstract = {Given a closed two dimensional manifold, we prove a general existence result\\r\\nfor a class of elliptic PDEs with exponential nonlinearities and negative Dirac\\r\\ndeltas on the right-hand side, extending a theory recently obtained for the\\r\\nregular case. This is done by global methods: since the associated Euler\\r\\nfunctional is in general unbounded from below, we need to define a new model\\r\\nspace, generalizing the so-called space of formal barycenters and\\r\\ncharacterizing (up to homotopy equivalence) its very low sublevels. As a\\r\\nresult, the analytic problem is reduced to a topological one concerning the\\r\\ncontractibility of this model space. To this aim, we prove a new functional\\r\\ninequality in the spirit of [16] and then we employ a min-max scheme based on a cone-style construction, jointly with the blow-up analysis given in [5] (after\\r\\n[6] and [8]). This study is motivated by abelian Chern- Simons theory in\\r\\nself-dual regime, or from the problem of prescribing the Gaussian curvature in\\r\\npresence of conical singularities (hence generalizing a problem raised by\\r\\nKazdan and Warner in [26]).}, doi = {10.1016/j.jfa.2011.09.012}, url = {http://hdl.handle.net/1963/5218}, author = {Alessandro Carlotto and Andrea Malchiodi} } @article {2012, title = {Wild quiver gauge theories}, journal = {JHEP 02(2012)031}, number = {arXiv:1112.1691v1;}, year = {2012}, note = {34 pages}, publisher = {SISSA}, abstract = {We study $N=2$ supersymmetric $SU(2)$ gauge theories coupled to non-Lagrangian superconformal field theories induced by compactifying the six dimensional $A_1 (2,0)$ theory on Riemann surfaces with irregular punctures. These are naturally associated to Hitchin systems with wild ramification whose spectral curves provide the relevant Seiberg-Witten geometries. We propose that the prepotential of these gauge theories on the Omega-background can be obtained from the corresponding irregular conformal blocks on the Riemann surfaces via a generalization of the coherent state construction to the case of higher order singularities.

}, doi = {10.1007/JHEP02(2012)031}, url = {http://hdl.handle.net/1963/5184}, author = {Giulio Bonelli and Kazunobu Maruyoshi and Alessandro Tanzini} } @article {2011, title = {Adaptation as a genome-wide autoregulatory principle in the stress response of yeast.}, journal = {IET systems biology. 2011 Jul; 5(4):269-79}, number = {PMID:21823758;}, year = {2011}, publisher = {The Institution of Engineering and Technology}, abstract = {The gene expression response of yeast to various types of stresses/perturbations shows a common functional and dynamical pattern for the vast majority of genes, characterised by a quick transient peak (affecting primarily short genes) followed by a return to the pre-stimulus level. Kinetically, this process of adaptation following the transient excursion can be modelled using a genome-wide autoregulatory mechanism by means of which yeast aims at maintaining a preferential concentration in its mRNA levels. The resulting feedback system explains well the different time constants observable in the transient response, while being in agreement with all the known experimental dynamical features. For example, it suggests that a very rapid transient can be induced also by a slowly varying concentration of the gene products.}, doi = {10.1049/iet-syb.2009.0050}, url = {http://hdl.handle.net/1963/5106}, author = {F Eduati and B Di Camillo and G Toffolo and Claudio Altafini and Giovanna De Palo and Mattia Zampieri} } @article {2011, title = {An asymptotic reduction of a Painlev{\'e} VI equation to a Painlev{\'e} III}, journal = {J.Phys.A: Math.Theor. 44 (2011) 215203}, number = {arXiv:1101.4705;}, year = {2011}, publisher = {IOP Publishing}, abstract = {When the independent variable is close to a critical point, it is shown that\\r\\nPVI can be asymptotically reduced to PIII. In this way, it is possible to\\r\\ncompute the leading term of the critical behaviors of PVI transcendents\\r\\nstarting from the behaviors of PIII transcendents.}, doi = {10.1088/1751-8113/44/21/215203}, url = {http://hdl.handle.net/1963/5124}, author = {Davide Guzzetti} } @article {2011, title = {Axial symmetry of some steady state solutions to nonlinear Schr{\"o}dinger equations}, journal = {Proc. Amer. Math. Soc. 139 (2011), 1023-1032}, number = {SISSA;75/2010/M}, year = {2011}, publisher = {American Mathematical Society}, abstract = {In this note, we show the axial symmetry of steady state solutions of nonlinear Schrodinger equations when the exponent of the nonlinearity is between the critical Sobolev exponent of n dimensional space and n - 1 dimensional space.}, keywords = {Nonlinear Schr{\"o}dinger equation}, doi = {10.1090/S0002-9939-2010-10638-X}, url = {http://hdl.handle.net/1963/4100}, author = {Changfeng Gui and Andrea Malchiodi and Haoyuan Xu and Paul Yang} } @article {2011, title = {Bishop and Laplacian Comparison Theorems on Three Dimensional Contact Subriemannian Manifolds with Symmetry}, year = {2011}, note = {25 pages}, publisher = {SISSA}, abstract = {We prove a Bishop volume comparison theorem and a Laplacian comparison\r\ntheorem for three dimensional contact subriemannian manifolds with symmetry.}, url = {http://hdl.handle.net/1963/6508}, author = {Andrei A. Agrachev and Paul Lee} } @article {Bertola:Boutroux, title = {Boutroux curves with external field: equilibrium measures without a variational problem}, journal = {Anal. Math. Phys.}, volume = {1}, number = {2-3}, year = {2011}, pages = {167{\textendash}211}, issn = {1664-2368}, doi = {10.1007/s13324-011-0012-3}, url = {http://dx.doi.org/10.1007/s13324-011-0012-3}, author = {Marco Bertola} } @article {Berti2011741, title = {Branching of Cantor Manifolds of Elliptic Tori and Applications to PDEs}, journal = {Communications in Mathematical Physics}, volume = {305}, number = {3}, year = {2011}, note = {cited By (since 1996)8}, pages = {741-796}, abstract = {We consider infinite dimensional Hamiltonian systems. We prove the existence of "Cantor manifolds" of elliptic tori-of any finite higher dimension-accumulating on a given elliptic KAM torus. Then, close to an elliptic equilibrium, we show the existence of Cantor manifolds of elliptic tori which are "branching" points of other Cantor manifolds of higher dimensional tori. We also answer to a conjecture of Bourgain, proving the existence of invariant elliptic tori with tangential frequency along a pre-assigned direction. The proofs are based on an improved KAM theorem. Its main advantages are an explicit characterization of the Cantor set of parameters and weaker smallness conditions on the perturbation. We apply these results to the nonlinear wave equation. {\textcopyright} 2011 Springer-Verlag.}, issn = {00103616}, doi = {10.1007/s00220-011-1264-3}, author = {Massimiliano Berti and Luca Biasco} } @article {2011, title = {A class of existence results for the singular Liouville equation}, journal = {Comptes Rendus Mathematique 349 (2011) 161-166}, year = {2011}, publisher = {Elsevier}, abstract = {We consider a class of elliptic PDEs on closed surfaces with exponential nonlinearities and Dirac deltas on the right-hand side. The study arises from abelian Chern{\textendash}Simons theory in self-dual regime, or from the problem of prescribing the Gaussian curvature in presence of conical singularities. A general existence result is proved using global variational methods: the analytic problem is reduced to a topological problem concerning the contractibility of a model space, the so-called space of formal barycenters, characterizing the very low sublevels of a suitable functional.}, doi = {10.1016/j.crma.2010.12.016}, url = {http://hdl.handle.net/1963/5793}, author = {Alessandro Carlotto and Andrea Malchiodi} } @article {ruiz2011, title = {Cluster solutions for the Schr{\"o}dinger-Poisson-Slater problem around a local minimum of the potential}, journal = {Rev. Mat. Iberoamericana}, volume = {27}, number = {1}, year = {2011}, month = {01}, pages = {253{\textendash}271}, publisher = {Real Sociedad Matem{\'a}tica Espa{\~n}ola}, url = {https://projecteuclid.org:443/euclid.rmi/1296828834}, author = {David Ruiz and Giusi Vaira} } @article {2011, title = {Compactness by maximality}, year = {2011}, abstract = {We derive a compactness property in the Sobolev space $W^{1,1}(\O)$ in order to study the Dirichlet problem for the eikonal equation \begin{displaymath} \begin{cases} \ha |\n u(x)|^2 - a(x) = 0 \& \ \textrm{in} \ \O\cr u(x)=\varphi(x) \& \ \textrm{on} \ \partial \O, \end{cases} \end{displaymath} without continuity assumptions on the map $a$.}, url = {http://preprints.sissa.it/handle/1963/35317}, author = {Sandro Zagatti} } @article {2011, title = {Computing global structural balance in large-scale signed social networks.}, journal = {Proceedings of the National Academy of Sciences of the United States of America. Volume 108, Issue 52, 27 December 2011, Pages 20953-20958}, number = {PMID:22167802;}, year = {2011}, note = {Free fulltext article in Pubmed Central}, publisher = {National Academy of Sciences}, abstract = {Structural balance theory affirms that signed social networks (i.e., graphs whose signed edges represent friendly/hostile interactions among individuals) tend to be organized so as to avoid conflictual situations, corresponding to cycles of negative parity. Using an algorithm for ground-state calculation in large-scale Ising spin glasses, in this paper we compute the global level of balance of very large online social networks and verify that currently available networks are indeed extremely balanced. This property is explainable in terms of the high degree of skewness of the sign distributions on the nodes of the graph. In particular, individuals linked by a large majority of negative edges create mostly \\\"apparent disorder,\\\" rather than true \\\"frustration.\\\"}, keywords = {Combinatorial optimization}, doi = {10.1073/pnas.1109521108}, url = {http://hdl.handle.net/1963/6426}, author = {Giuseppe Facchetti and Giovanni Iacono and Claudio Altafini} } @article {AIHPC_2011__28_1_107_0, title = {Concentration of solutions for a singularly perturbed Neumann problem in non-smooth domains}, journal = {Annales de l{\textquoteright}I.H.P. Analyse non lin{\'e}aire}, volume = {28}, number = {1}, year = {2011}, pages = {107-126}, publisher = {Elsevier}, doi = {10.1016/j.anihpc.2010.11.003}, url = {http://www.numdam.org/item/AIHPC_2011__28_1_107_0}, author = {Serena Dipierro} } @article {10654, title = {Cones of divisors of blow-ups of projective spaces}, journal = {Le Matematiche (Catania), volume 66, Issue no.2, (2011), pages : 153-187}, year = {2011}, publisher = {Universit{\`a} degli Studi di Catania. Dipartimento di matematica}, abstract = {We investigate Mori dream spaces obtained by blowing-up the n-dimensional complex projective space at n+1, n+2 or n+3 points in very general position. Using toric techniques we study the movable cone of the blow-up of Pn at n+1 points, its decomposition into nef chambers and the action of theWeyl group on the set of chambers. Moreover, using different methods, we explicitly write down the equations of the movable cone also for Pn blown-up at n+2 points.}, keywords = {Mori dream space}, doi = {10.4418/2011.66.2.13}, url = {http://hdl.handle.net/1963/6613}, author = {Alessio Lo Giudice and Salvatore Cacciola and M. Donten-Bury and O. Dumitrescu and J. Park} } @article {2011, title = {Covered by lines and Conic connected varieties}, journal = {Le Matematiche 66 (2011) 137-151}, number = {arXiv:1105.5918;}, year = {2011}, publisher = {Universita\\\' di Catania, Dipartimento di Matematica e Informatica}, abstract = {We study some properties of an embedded variety covered by lines and give a\\r\\nnumerical criterion ensuring the existence of a singular conic through two of\\r\\nits general points. We show that our criterion is sharp. Conic-connected,\\r\\ncovered by lines, QEL, LQEL, prime Fano, defective, and dual defective\\r\\nvarieties are closely related. We study some relations between the above\\r\\nmentioned classes of objects using celebrated results by Ein and Zak.}, doi = {10.4418/2011.66.2.12}, url = {http://hdl.handle.net/1963/5788}, author = {Simone Marchesi and Alex Massarenti and Saeed Tafazolian} } @article {2011, title = {Crack growth with non-interpenetration : a simplified proof for the pure Neumann problem}, journal = {Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1219-1231}, number = {SISSA;70/2009/M}, year = {2011}, publisher = {American Institute of Mathematical Sciences}, abstract = {We present a recent existence result concerning the quasi-static evolution of cracks in hyperelastic brittle materials, in the frame-work of finite elasticity with non-interpenetration. In particular, here we consider the problem where no Dirichlet conditions are imposed, the boundary is traction-free, and the body is subject only to time-dependent volume forces. This allows us to present the main ideas of the proof in a simpler way, avoiding some of the technicalities needed in the general case, studied in.}, doi = {10.3934/dcds.2011.31.1219}, url = {http://hdl.handle.net/1963/3801}, author = {Gianni Dal Maso and Giuliano Lazzaroni} } @article {2011, title = {Crepant resolutions of weighted projective spaces and quantum deformations}, journal = {This article will be published in 2011 in the \"Nagoya Mathematical Journal\" Volume 201, March 2011, Pages 1-22, under the title \"Computing certain Gromov-Witten invariants of the crepant resolution of P{double-strock}(1, 3, 4, 4)}, number = {arXiv:math/0610617;}, year = {2011}, note = {Exposition improved, new title, typos corrected. The section\r\n concerning the model for the orbifold Chow ring has been removed (appears now\r\n in our new preprint 0709.4559)}, publisher = {SISSA}, abstract = {We compare the Chen-Ruan cohomology ring of the weighted projective spaces\r\n$\\IP(1,3,4,4)$ and $\\IP(1,...,1,n)$ with the cohomology ring of their crepant\r\nresolutions. In both cases, we prove that the Chen-Ruan cohomology ring is\r\nisomorphic to the quantum corrected cohomology ring of the crepant resolution\r\nafter suitable evaluation of the quantum parameters. For this, we prove a\r\nformula for the Gromov-Witten invariants of the resolution of a transversal\r\n${\\rm A}_3$ singularity.}, url = {http://hdl.handle.net/1963/6514}, author = {Samuel Boissiere and Etienne Mann and Fabio Perroni} } @article {2011, title = {Critical points of the Moser-Trudinger functional}, number = {SISSA;46/2011/M}, year = {2011}, institution = {SISSA}, keywords = {Moser-Trudinger inequality}, url = {http://hdl.handle.net/1963/4592}, author = {Francesca De Marchis and Andrea Malchiodi and Luca Martinazzi} } @article {2011, title = {Cytoskeletal actin networks in motile cells are critically self-organized systems synchronized by mechanical interactions}, journal = {PNAS 108 (2011) 13978}, year = {2011}, publisher = {National Academy of Sciences}, doi = {10.1073/pnas.1100549108}, url = {http://hdl.handle.net/1963/4358}, author = {Luca Cardamone and Alessandro Laio and Rajesh Shahapure and Antonio DeSimone} } @article {2011, title = {D-branes, surface operators, and ADHM quiver representations}, number = {SISSA;01/2011/FM}, year = {2011}, note = {45 pages, v2: minor corrections}, institution = {SISSA}, abstract = {A supersymmetric quantum mechanical model is constructed for BPS states bound to surface operators in five dimensional SU(r) gauge theories using D-brane engineering. This model represents the effective action of a certain D2-brane configuration, and is naturally obtained by dimensional reduction of a quiver $(0,2)$ gauged linear sigma model. In a special stability chamber, the resulting moduli space of quiver representations is shown to be smooth and isomorphic to a moduli space of framed quotients on the projective plane. A precise conjecture relating a K-theoretic partition function of this moduli space to refined open string invariants of toric lagrangian branes is formulated for conifold and local P^1 x P^1 geometries.}, url = {http://hdl.handle.net/1963/4133}, author = {Ugo Bruzzo and Duiliu-Emanuel Diaconescu and M. Yardim and G. Pan and Yi Zhang and Chuang Wu-yen} } @article {2011, title = {A Decomposition Theorem for BV functions}, journal = {Communications on Pure and Applied Analysis}, volume = {10}, number = {SISSA;20/2009/M}, year = {2011}, pages = {1549-1566}, publisher = {American Institute of Mathematical Sciences}, doi = {10.3934/cpaa.2011.10.1549}, url = {http://hdl.handle.net/20.500.11767/14599}, author = {Stefano Bianchini and Daniela Tonon} } @article {Bambusi20113379, title = {Degenerate KAM theory for partial differential equations}, journal = {Journal of Differential Equations}, volume = {250}, number = {8}, year = {2011}, note = {cited By (since 1996)3}, pages = {3379-3397}, abstract = {This paper deals with degenerate KAM theory for lower dimensional elliptic tori of infinite dimensional Hamiltonian systems, depending on one parameter only. We assume that the linear frequencies are analytic functions of the parameter, satisfy a weak non-degeneracy condition of R{\"u}ssmann type and an asymptotic behavior. An application to nonlinear wave equations is given. {\textcopyright} 2010 Elsevier Inc.}, issn = {00220396}, doi = {10.1016/j.jde.2010.11.002}, author = {Dario Bambusi and Massimiliano Berti and Elena Magistrelli} } @mastersthesis {2011, title = {Dimensional Reduction and Approximation of Measures and Weakly Differentiable Homeomorphisms}, year = {2011}, school = {SISSA}, abstract = {This thesis is devoted to the study of two different problems: the properties of the disintegration of the Lebesgue measure on the faces of a convex function and the existence of smooth approximations of bi-Lipschitz orientation-preserving homeomorphisms in the plane.}, url = {http://hdl.handle.net/1963/5348}, author = {Sara Daneri} } @article {FONDA20111052, title = {Double resonance with Landesman{\textendash}Lazer conditions for planar systems of ordinary differential equations}, journal = {Journal of Differential Equations}, volume = {250}, number = {2}, year = {2011}, pages = {1052 - 1082}, abstract = {We prove the existence of periodic solutions for first order planar systems at resonance. The nonlinearity is indeed allowed to interact with two positively homogeneous Hamiltonians, both at resonance, and some kind of Landesman{\textendash}Lazer conditions are assumed at both sides. We are thus able to obtain, as particular cases, the existence results proposed in the pioneering papers by Lazer and Leach (1969) [27], and by Frederickson and Lazer (1969) [18]. Our theorem also applies in the case of asymptotically piecewise linear systems, and in particular generalizes Fabry{\textquoteright}s results in Fabry (1995) [10], for scalar equations with double resonance with respect to the Dancer{\textendash}Fu{\v c}ik spectrum.

}, keywords = {Double resonance, Landesman{\textendash}Lazer conditions, Nonlinear planar systems}, issn = {0022-0396}, doi = {https://doi.org/10.1016/j.jde.2010.08.006}, url = {http://www.sciencedirect.com/science/article/pii/S0022039610002901}, author = {Alessandro Fonda and Maurizio Garrione} } @article {bonheure2011embedding, title = {Embedding theorems and existence results for nonlinear Schr{\"o}dinger{\textendash}Poisson systems with unbounded and vanishing potentials}, journal = {Journal of Differential Equations}, volume = {251}, number = {4-5}, year = {2011}, pages = {1056{\textendash}1085}, publisher = {Elsevier}, abstract = {Motivated by existence results for positive solutions of non-autonomous nonlinear Schr{\"o}dinger{\textendash}Poisson systems with potentials possibly unbounded or vanishing at infinity, we prove embedding theorems for weighted Sobolev spaces. We both consider a general framework and spaces of radially symmetric functions when assuming radial symmetry of the potentials.

}, doi = {10.1016/j.jde.2011.04.010}, url = {https://doi.org/10.1016/j.jde.2011.04.010}, author = {Bonheure, Denis and Mercuri, Carlo} } @article {2011, title = {Energy release rate and stress intensity factor in antiplane elasticity}, journal = {Journal de Mathematiques Pures et Appliquees 95 (2011) 565-584}, number = {SISSA;67/2009/M}, year = {2011}, publisher = {Elsevier}, abstract = {In the setting of antiplane linearized elasticity, we show the existence of the stress intensity factor and its relation with the energy release rate when the crack path is a C1,1 curve. Finally, we show that the energy release rate is continuous with respect to the Hausdorff convergence in a class of admissible cracks.}, doi = {10.1016/j.matpur.2011.01.001}, url = {http://hdl.handle.net/1963/3780}, author = {Giuliano Lazzaroni and Rodica Toader} } @article {2011, title = {Ennio De Giorgi and Γ-convergence}, journal = {Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1017-1021}, year = {2011}, publisher = {American Institute of Mathematical Sciences}, abstract = {Γ-convergence was introduced by Ennio De Giorgi in a series of papers published between 1975 and 1983. In the same years he developed many applications of this tool to a great variety of asymptotic problems in the calculus of variations and in the theory of partial differential equations.}, doi = {10.3934/dcds.2011.31.1017}, url = {http://hdl.handle.net/1963/5308}, author = {Gianni Dal Maso} } @article {2011, title = {An Estimate on the Flow Generated by Monotone Operators}, journal = {Communications in Partial Differential Equations 36 (2011) 777-796}, number = {SISSA;29/2009/M}, year = {2011}, publisher = {Taylor \& Francis}, doi = {10.1080/03605302.2010.534224}, url = {http://hdl.handle.net/1963/3646}, author = {Stefano Bianchini and Matteo Gloyer} } @article {2011, title = {An Existence and Uniqueness Result for the Motion of Self-Propelled Microswimmers}, journal = {SIAM J. Math. Anal.}, volume = { 43}, number = {SISSA;44/2010/M}, year = {2011}, pages = {1345-1368}, publisher = {Society for Industrial and Applied Mathematics}, abstract = {We present an analytical framework to study the motion of micro-swimmers in a viscous fluid. Our main result is that, under very mild regularity assumptions, the change of shape determines uniquely the motion of the swimmer. We assume that the Reynolds number is very small, so that the velocity field of the surrounding, infinite fluid is governed by the Stokes system and all inertial effects can be neglected. Moreover, we enforce the self propulsion constraint (no external forces and torques). Therefore, Newton\\\'s equations of motion reduce to the vanishing of the viscous drag force and torque acting on the body. By exploiting an integral representation of viscous force and torque, the equations of motion can be reduced to a system of six ordinary differential equations. Variational techniques are used to prove the boundedness and measurability of its coefficients, so that classical results on ordinary differential equations can be invoked to prove existence and uniqueness of the solution.

}, doi = {10.1137/10080083X}, url = {http://hdl.handle.net/1963/3894}, author = {Gianni Dal Maso and Antonio DeSimone and Marco Morandotti} } @article {2011, title = {Existence for wave equations on domains with arbitrary growing cracks}, journal = {Rend. Lincei Mat. Appl. 22 (2011) 387-408}, number = {SISSA;32/2011/M}, year = {2011}, publisher = {European Mathematical Society}, abstract = {In this paper we formulate and study scalar wave equations on domains with arbitrary growing cracks. This includes a zero Neumann condition on the crack sets, and the only assumptions on these sets are that they have bounded surface measure and are growing in the sense of set inclusion. In particular, they may be dense, so the weak formulations must fall outside of the usual weak formulations using Sobolev spaces. We study both damped and undamped equations, showing existence and, for the damped equation, uniqueness and energy conservation.}, keywords = {Wave equation}, doi = {10.4171/RLM/606}, url = {http://hdl.handle.net/1963/4284}, author = {Gianni Dal Maso and Cristopher J. Larsen} } @article {10226, title = {Fracture and plastic models as Gamma-limits of damage models under different regimes}, journal = {Advances in Calculus of Variations., to appear.}, number = {SISSA;59/2011/M}, year = {2011}, publisher = {Walter de Gruyter}, abstract = {We consider a variational model for damaged elastic materials. This model depends on three small parameters, which are related to the cost of the damage, to the width of the damaged regions, and to the minimum elasticity constant attained in the damaged regions. As these parameters tend to zero, our models Gamma-converge to a model for brittle fracture, for fracture with a cohesive zone, or for perfect plasticity, depending on the asymptotic ratios of the three parameters.

}, doi = {10.1515/acv-2011-0011}, url = {http://hdl.handle.net/1963/5069}, author = {Flaviana Iurlano} } @article {2011, title = {Gamma-convergence of energies for nematic elastomers in the small strain limit}, journal = {Continuum. Mech. Therm.}, volume = { 23}, number = {SISSA;07/2011/M}, year = {2011}, publisher = {Springer}, chapter = {257}, abstract = {We study two variational models recently proposed in the literature to describe the mechanical behaviour of nematic elastomers either in the fully nonlinear regime or in the framework of a geometrically linear theory. We show that, in the small strain limit, the energy functional of the first one I\\\"-converges to the relaxation of the second one, a functional for which an explicit representation formula is available.

}, keywords = {Liquid crystals}, doi = {10.1007/s00161-011-0180-2}, url = {http://hdl.handle.net/1963/4141}, author = {Virginia Agostiniani and Antonio DeSimone} } @article {9991, title = {Generalised functions of bounded deformation}, journal = {J. Eur. Math. Soc. (JEMS), to appear}, year = {2011}, publisher = {SISSA}, abstract = {We introduce the space GBD of generalized functions of bounded deformation and study the structure properties of these functions: the rectifiability and the slicing properties of their jump sets, and the existence of their approximate symmetric gradients. We conclude by proving a compactness results for GBD, which leads to a compactness result for the space GSBD of generalized special functions of bounded deformation. The latter is connected to the existence of solutions to a weak formulation of some variational problems arising in fracture mechanics in the framework of linearized elasticity.

}, keywords = {free discontinuity problems, special functions of bounded deformation, jump set, rec- tifiability, slicing, approximate differentiability}, url = {http://hdl.handle.net/1963/6374}, author = {Gianni Dal Maso} } @article {2011, title = {Generalized matrix models and AGT correspondence at all genera}, journal = {JHEP, Volume 2011, Issue 7, 2011, Article number055}, number = {arXiv:1011.5417;}, year = {2011}, note = {This version is published in : Journal of High Energy Physics, Volume 2011, Issue 7, 2011, Article number055}, publisher = {SISSA}, abstract = {We study generalized matrix models corresponding to n-point Virasoro\r\nconformal blocks on Riemann surfaces with arbitrary genus g. Upon AGT\r\ncorrespondence, these describe four dimensional N=2 SU(2)^{n+3g-3} gauge\r\ntheories with generalized quiver diagrams. We obtain the generalized matrix\r\nmodels from the perturbative evaluation of the Liouville correlation functions\r\nand verify the consistency of the description with respect to degenerations of\r\nthe Riemann surface. Moreover, we derive the Seiberg-Witten curve for the N=2\r\ngauge theory as the spectral curve of the generalized matrix model, thus\r\nproviding a check of AGT correspondence at all genera.}, doi = {10.1007/JHEP07(2011)055}, url = {http://hdl.handle.net/1963/6568}, author = {Giulio Bonelli and Kazunobu Maruyoshi and Alessandro Tanzini and Futoshi Yagib} } @article {2011, title = {Generalized Ricci Curvature Bounds for Three Dimensional Contact Subriemannian manifolds}, number = {arXiv:0903.2550;}, year = {2011}, note = {This is a revised extended version that contains new results.}, publisher = {SISSA}, url = {http://hdl.handle.net/1963/6507}, author = {Andrei A. Agrachev and Paul Lee} } @article {2011, title = {The geometry of Maximum Principle}, journal = {Proceedings of the Steklov Institute of mathematics. vol. 273 (2011), page: 5-27 ; ISSN: 0081-5438}, number = {Proceedings of the Steklov Institute of mathematics;v.273}, year = {2011}, abstract = {An invariant formulation of the maximum principle in optimal control is presented, and some second-order invariants are discussed.}, url = {http://hdl.handle.net/1963/6456}, author = {Andrei A. Agrachev and Revaz Gamkrelidze} } @article {2011, title = {Holomorphic Cartan geometry on manifolds with numerically effective tangent bundle}, journal = {Differential Geometry and its Applications 29 (2011) 147-153}, number = {SISSA;05/2010/FM}, year = {2011}, publisher = {Elsevier}, doi = {10.1016/j.difgeo.2011.02.001}, url = {http://hdl.handle.net/1963/3830}, author = {Indranil Biswas and Ugo Bruzzo} } @mastersthesis {2011, title = {Homology invariants of quadratic maps}, year = {2011}, school = {SISSA}, abstract = {Given a real projective algebraic set X we could hope that the equations describing it can give some information on its topology, e.g. on the number of its connected components. Unfortunately in the general case this hope is too vague and there is no direct way to extract such information from the algebraic description of X: Even the problem to decide whether X is empty or not is far from an easy visualization and requires some complicated algebraic machinery. A fi rst step observation is that as long as we are interested only in the topology of X, we can replace, using some Veronese embedding, the original ambient space with a much bigger RPn and assume that X is cut by quadratic equations. The price for this is the increase of the number of equations de ning our set; the advantage is that quadratic polynomials are easier to handle and our hope becomes more concrete...}, url = {http://hdl.handle.net/1963/6245}, author = {Antonio Lerario} } @article {2011, title = {Infinite-dimensional Frobenius manifolds for 2 + 1 integrable systems}, journal = {Matematische Annalen 349 (2011) 75-115}, number = {SISSA;12/2009/FM}, year = {2011}, publisher = {Springer}, abstract = {We introduce a structure of an infinite-dimensional Frobenius manifold on a subspace in the space of pairs of functions analytic inside/outside the unit circle with simple poles at 0/infinity respectively. The dispersionless 2D Toda equations are embedded into a bigger integrable hierarchy associated with this Frobenius manifold.}, doi = {10.1007/s00208-010-0509-3}, url = {http://hdl.handle.net/1963/3584}, author = {Guido Carlet and Boris Dubrovin and Luca Philippe Mertens} } @article {DAVENIA20115705, title = {Infinitely many positive solutions for a Schr{\"o}dinger{\textendash}Poisson system}, journal = {Nonlinear Analysis: Theory, Methods \& Applications}, volume = {74}, number = {16}, year = {2011}, pages = {5705 - 5721}, abstract = {We are interested in the existence of infinitely many positive solutions of the Schr{\"o}dinger{\textendash}Poisson system -Δu+u+V(|x|)ϕu=|u|p-1u,x∈R3,-Δϕ=V(|x|)u2,x∈R3, where V(|x|) is a positive bounded function, 1\<p\<5 and V(r

}, keywords = {Non-autonomous Schr{\"o}dinger{\textendash}Poisson system, Perturbation method}, issn = {0362-546X}, doi = {https://doi.org/10.1016/j.na.2011.05.057}, url = {http://www.sciencedirect.com/science/article/pii/S0362546X11003518}, author = {Pietro d{\textquoteright}Avenia and Alessio Pomponio and Giusi Vaira} } @article {2011, title = {Instantons on ALE spaces and Super Liouville Conformal Field Theories}, number = {arXiv:1106.2505v1;}, year = {2011}, note = {10 pages}, institution = {SISSA}, abstract = {We provide evidence that the conformal blocks of N=1 super Liouville\\r\\nconformal field theory are described in terms of the SU(2) Nekrasov partition\\r\\nfunction on the ALE space O_{P^1}(-2).}, url = {http://hdl.handle.net/1963/4262}, author = {Giulio Bonelli and Kazunobu Maruyoshi and Alessandro Tanzini} } @article {2011, title = {An Integro-Extremization Approach for Non Coercive and Evolution Hamilton-Jacobi Equations}, journal = {Journal of Convex Analysis 18 (2011) 1141-1170}, year = {2011}, publisher = {Heldermann Verlag}, abstract = {We devote the \\\\textit{integro-extremization} method to the study of the Dirichlet problem for homogeneous Hamilton-Jacobi equations \\\\begin{displaymath} \\\\begin{cases} F(Du)=0 \& \\\\quad \\\\textrm{in} \\\\quad\\\\O\\\\cr u(x)=\\\\varphi(x) \& \\\\quad \\\\textrm{for} \\\\quad x\\\\in \\\\partial \\\\O, \\\\end{cases} \\\\end{displaymath} with a particular interest for non coercive hamiltonians $F$, and to the Cauchy-Dirichlet problem for the corresponding homogeneous time-dependent equations \\\\begin{displaymath} \\\\begin{cases} \\\\frac{\\\\partial u}{\\\\partial t}+ F(\\\\nabla u)=0 \& \\\\quad \\\\textrm{in} \\\\quad ]0,T[\\\\times \\\\O\\\\cr u(0,x)=\\\\eta(x) \& \\\\quad \\\\textrm{for} \\\\quad x\\\\in\\\\O \\\\cr u(t,x)=\\\\psi(x) \& \\\\quad \\\\textrm{for} \\\\quad (t,x)\\\\in[0,T]\\\\times \\\\partial \\\\O. \\\\end{cases} \\\\end{displaymath} We prove existence and some qualitative results for viscosity and almost everywhere solutions, under suitably convexity conditions on the hamiltonian $F$, on the domain $\\\\O$ and on the boundary datum, without any growth assumptions on $F$.}, url = {http://hdl.handle.net/1963/5538}, author = {Sandro Zagatti} } @article {2011, title = {Invariant manifolds for a singular ordinary differential equation}, journal = {Journal of Differential Equations 250 (2011) 1788-1827}, number = {SISSA;04/2008/M}, year = {2011}, publisher = {Elsevier}, doi = {10.1016/j.jde.2010.11.010}, url = {http://hdl.handle.net/1963/2554}, author = {Stefano Bianchini and Laura Spinolo} } @mastersthesis {2011, title = {Invariants, volumes and heat kernels in sub-Riemannian geometry}, year = {2011}, school = {SISSA}, abstract = {Sub-Riemannian geometry can be seen as a generalization of Riemannian geometry under non-holonomic constraints. From the theoretical point of view, sub-Riemannian geometry is the geometry underlying the theory of hypoelliptic operators (see [32, 57, 70, 92] and references therein) and many problems of geometric measure theory (see for instance [18, 79]). In applications it appears in the study of many mechanical problems (robotics, cars with trailers, etc.) and recently in modern elds of research such as mathematical models of human behaviour, quantum control or motion of self-propulsed micro-organism (see for instance [15, 29, 34])\\r\\nVery recently, it appeared in the eld of cognitive neuroscience to model the\\r\\nfunctional architecture of the area V1 of the primary visual cortex, as proposed by Petitot in [87, 86], and then by Citti and Sarti in [51]. In this context, the sub-Riemannian heat equation has been used as basis to new applications in image reconstruction (see [35]).}, keywords = {Sub-Riemannian geometry}, url = {http://hdl.handle.net/1963/6124}, author = {Davide Barilari} } @article {2011, title = {Large Time Existence for Thin Vibrating Plates}, journal = {Communication in Partial Differential Equations 36 (2011) 2062-2102}, number = {SISSA;59/2009/M}, year = {2011}, publisher = {Taylor \& Francis}, abstract = {We construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence of strong solutions for large\\r\\ntimes under appropriate scaling of the initial values such that the limit system as h --> 0 is either the nonlinear von Karman plate equation or the linear fourth order Germain-Lagrange equation. In the case of the\\r\\nlinear Germain-Lagrange equation we even obtain a convergence rate of the three-dimensional solution to the solution of the two-dimensional linear plate equation.}, doi = {10.1080/03605302.2011.618209}, url = {http://hdl.handle.net/1963/3755}, author = {Helmut Abels and Maria Giovanna Mora and Stefan M{\"u}ller} } @article {2011, title = {Linearly degenerate Hamiltonian PDEs and a new class of solutions to the WDVV associativity equations}, journal = {Functional Analysis and Its Applications. Volume 45, Issue 4, December 2011, Pages 278-290}, year = {2011}, publisher = {Springer}, abstract = {We define a new class of solutions to the WDVV associativity equations. This class is determined by the property that one of the commuting PDEs associated with such a WDVV solution is linearly degenerate. We reduce the problem of classifying such solutions of the WDVV equations to the particular case of the so-called algebraic Riccati equation and, in this way, arrive at a complete classification of irreducible solutions.}, keywords = {Frobenius manifold}, doi = {10.1007/s10688-011-0030-9}, url = {http://hdl.handle.net/1963/6430}, author = {Boris Dubrovin and M.V. Pavlov and Sergei A. Zykov} } @article {2011, title = {The Liouville side of the vortex}, journal = {JHEP 09(2011)096}, number = {arXiv:1107.2787v1;}, year = {2011}, note = {25pages,11figures}, publisher = {SISSA}, abstract = {We analyze conformal blocks with multiple (semi-)degenerate field insertions in Liouville/Toda conformal field theories an show that their vector space is fully reproduced by the four-dimensional limit of open topological string amplitudes on the strip with generic boundary conditions associated to a suitable quiver gauge theory. As a byproduct we identify the non-abelian vortex partition function with a specific fusion channel of degenerate conformal blocks.}, doi = {10.1007/JHEP09(2011)096}, url = {http://hdl.handle.net/1963/4304}, author = {Giulio Bonelli and Alessandro Tanzini and Jian Zhao} } @article {2011, title = {The matching property of infinitesimal isometries on elliptic surfaces and elasticity on thin shells}, journal = {Archive for Rational Mechanics and Analysis 200 (2011) 1023-1050}, number = {SISSA;75/2008/M}, year = {2011}, publisher = {Springer}, abstract = {Using the notion of Γ-convergence, we discuss the limiting behavior of the three-dimensional nonlinear elastic energy for thin elliptic shells, as their thickness h converges to zero, under the assumption that the elastic energy of deformations scales like h β with 2 < β < 4. We establish that, for the given scaling regime, the limiting theory reduces to linear pure bending. Two major ingredients of the proofs are the density of smooth infinitesimal isometries in the space of W 2,2 first order infinitesimal isometries, and a result on matching smooth infinitesimal isometries with exact isometric immersions on smooth elliptic surfaces.}, doi = {10.1007/s00205-010-0387-6}, url = {http://hdl.handle.net/1963/3392}, author = {Marta Lewicka and Maria Giovanna Mora and Mohammad Reza Pakzad} } @article {Fedeli2011, title = {Metastable equilibria of capillary drops on solid surfaces: a phase field approach}, journal = {Continuum Mechanics and Thermodynamics}, volume = {23}, number = {5}, year = {2011}, month = {Sep}, pages = {453{\textendash}471}, abstract = {We discuss a phase field model for the numerical simulation of metastable equilibria of capillary drops resting on rough solid surfaces and for the description of contact angle hysteresis phenomena in wetting. The model is able to reproduce observed transitions of drops on micropillars from Cassie{\textendash}Baxter to Wenzel states. When supplemented with a dissipation potential which describes energy losses due to frictional forces resisting the motion of the contact line, the model can describe metastable states such as drops in equilibrium on vertical glass plates. The reliability of the model is assessed by a detailed comparison of its predictions with experimental data on the maximal size of water drops that can stick on vertical glass plates which have undergone different surface treatments.

}, issn = {1432-0959}, doi = {10.1007/s00161-011-0189-6}, url = {https://doi.org/10.1007/s00161-011-0189-6}, author = {Livio Fedeli and Turco, Alessandro and Antonio DeSimone} } @article { ISI:000296627000002, title = {A MODEL FOR CRACK PROPAGATION BASED ON VISCOUS APPROXIMATION}, journal = {{MATHEMATICAL MODELS \& METHODS IN APPLIED SCIENCES}}, volume = {{21}}, number = {{10}}, year = {2011}, month = {{OCT}}, pages = {{2019-2047}}, publisher = {{WORLD SCIENTIFIC PUBL CO PTE LTD}}, type = {{Article}}, address = {{5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE}}, abstract = {{In the setting of antiplane linearized elasticity, we show the existence of quasistatic evolutions of cracks in brittle materials by using a vanishing viscosity approach, thus taking into account local minimization. The main feature of our model is that the path followed by the crack need not be prescribed a priori: indeed, it is found as the limit (in the sense of Hausdorff convergence) of curves obtained by an incremental procedure. The result is based on a continuity property for the energy release rate in a suitable class of admissible cracks.}

}, keywords = {Brittle fracture, Crack propagation, energy derivative, energy release rate, free-discontinuity problems, Griffith{\textquoteright}s criterion, local minimizers, stress intensity factor}, vanishing viscosity, {Variational models}, issn = {{0218-2025}}, doi = {{10.1142/S0218202511005647}}, author = {Giuliano Lazzaroni and Rodica Toader} } @article {2011, title = {Moduli of framed sheaves on projective surfaces}, journal = {Doc. Math. 16 (2011) 399-410}, number = {arXiv:0906.1436;}, year = {2011}, publisher = {Documenta Mathematica}, abstract = {We show that there exists a fine moduli space for torsion-free sheaves on a\\r\\nprojective surface, which have a \\\"good framing\\\" on a big and nef divisor. This\\r\\nmoduli space is a quasi-projective scheme. This is accomplished by showing that such framed sheaves may be considered as stable pairs in the sense of\\r\\nHuybrechts and Lehn. We characterize the obstruction to the smoothness of the moduli space, and discuss some examples on rational surfaces.}, url = {http://hdl.handle.net/1963/5126}, author = {Ugo Bruzzo and Dimitri Markushevich} } @conference {10.1007/978-1-4419-9554-4_10, title = {The Monge Problem in Geodesic Spaces}, booktitle = {Nonlinear Conservation Laws and Applications}, year = {2011}, pages = {217{\textendash}233}, publisher = {Springer US}, organization = {Springer US}, address = {Boston, MA}, abstract = {We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish non branching geodesic space. We show that we can reduce the transport problem to 1-dimensional transport problems along geodesics. We introduce an assumption on the transport problem π which implies that the conditional probabilities of the first marginal on each geodesic are continuous. It is known that this regularity is sufficient for the construction of an optimal transport map.

}, isbn = {978-1-4419-9554-4}, author = {Stefano Bianchini and Fabio Cavalletti}, editor = {Alberto Bressan and Chen, Gui-Qiang G. and Marta Lewicka and Wang, Dehua} } @article {Mola2011, title = {Multi-physics modelling and sensitivity analysis of olympic rowing boat dynamics}, journal = {Sports Engineering}, volume = {14}, number = {2-4}, year = {2011}, month = {nov}, pages = {85{\textendash}94}, publisher = {Springer Nature}, doi = {10.1007/s12283-011-0075-2}, url = {https://doi.org/10.1007/s12283-011-0075-2}, author = {Andrea Mola and Mehdi Ghommem and Muhammad R. Hajj} } @article {de2011multiplicity, title = {Multiplicity of solutions for a mean field equation on compact surfaces}, journal = {Boll. Unione Mat. Ital.(9)}, volume = {4}, year = {2011}, pages = {245{\textendash}257}, abstract = {We consider a scalar field equation on compact surfaces which has variational structure. When the surface is a torus and a physical parameter ρ belongs to $(8\pi, 4\pi^2 )$ we show under some extra assumptions that, as conjectured in [9], the functional admits at least three saddle points other than a local minimum.

}, author = {Francesca De Marchis} } @article {2011, title = {New improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces}, journal = {Geometric and Functional Analysis 21 (2011) 1196-1217}, number = {SISSA;74/2010/M}, year = {2011}, publisher = {Springer}, abstract = {We consider a singular Liouville equation on a compact surface, arising from the study of Chern-Simons vortices in a self dual regime. Using new improved versions of the Moser-Trudinger inequalities (whose main feature is to be scaling invariant) and a variational scheme, we prove new existence results.}, doi = {10.1007/s00039-011-0134-7}, url = {http://hdl.handle.net/1963/4099}, author = {Andrea Malchiodi and David Ruiz} } @article {fonda2011nonlinear, title = {Nonlinear resonance: a comparison between Landesman-Lazer and Ahmad-Lazer-Paul conditions}, journal = {Advanced Nonlinear Studies}, volume = {11}, number = {2}, year = {2011}, pages = {391{\textendash}404}, publisher = {Advanced Nonlinear Studies, Inc.}, abstract = {We show that the Ahmad-Lazer-Paul condition for resonant problems is more general than the Landesman-Lazer one, discussing some relations with other existence conditions, as well. As a consequence, such a relation holds, for example, when considering resonant boundary value problems associated with linear elliptic operators, the p-Laplacian and, in the scalar case, with an asymmetric oscillator.

}, doi = {10.1515/ans-2011-0209}, author = {Alessandro Fonda and Maurizio Garrione} } @article {2011, title = {Nonlinear thin-walled beams with a rectangular cross-section - Part II}, number = {SISSA;14/2011/M}, year = {2011}, institution = {SISSA}, abstract = {In this paper we report the second part of our results concerning the rigorous derivation of a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section..}, keywords = {Thin-walled cross-section beams}, url = {http://hdl.handle.net/1963/4169}, author = {Lorenzo Freddi and Maria Giovanna Mora and Roberto Paroni} } @article {2011, title = {Nonlinear wave and Schr{\"o}dinger equations on compact Lie groups and homogeneous spaces}, journal = {Duke Mathematical Journal}, volume = {159}, year = {2011}, month = {2011}, chapter = {479}, abstract = {We develop linear and nonlinear harmonic analysis on compact Lie groups and homogeneous spaces relevant for the theory of evolutionary Hamiltonian PDEs. A basic tool is the theory of the highest weight for irreducible representations of compact Lie groups. This theory provides an accurate description of the eigenvalues of the Laplace-Beltrami operator as well as the multiplication rules of its eigenfunctions. As an application, we prove the existence of Cantor families of small amplitude time-periodic solutions for wave and Schr{\textasciidieresis}odinger equations with differentiable nonlinearities. We apply an abstract Nash-Moser implicit function theorem to overcome the small divisors problem produced by the degenerate eigenvalues of the Laplace operator. We provide a new algebraic framework to prove the key tame estimates for the inverse linearized operators on Banach scales of Sobolev functions.}, issn = {0012-7094}, doi = {10.1215/00127094-1433403}, author = {Massimiliano Berti and Michela Procesi} } @article {BOSCAGGIN2011259, title = {A note on a superlinear indefinite Neumann problem with multiple positive solutions}, journal = {Journal of Mathematical Analysis and Applications}, volume = {377}, number = {1}, year = {2011}, pages = {259 - 268}, abstract = {We prove the existence of three positive solutions for the Neumann problem associated to u"+a(t)uγ+1=0, assuming that a(t) has two positive humps and ∫0Ta-(t)dt is large enough. Actually, the result holds true for a more general class of superlinear nonlinearities.

}, keywords = {Indefinite weight, Nonlinear boundary value problems, positive solutions, Shooting method}, issn = {0022-247X}, doi = {https://doi.org/10.1016/j.jmaa.2010.10.042}, url = {http://www.sciencedirect.com/science/article/pii/S0022247X10008796}, author = {Alberto Boscaggin} } @article {2011, title = {On the number of eigenvalues of a model operator related to a system of three particles on lattices}, journal = {J. Phys. A 44 (2011) 315302}, year = {2011}, publisher = {IOP Publishing}, doi = {10.1088/1751-8113/44/31/315302}, url = {http://hdl.handle.net/1963/5496}, author = {Gianfausto Dell{\textquoteright}Antonio and Zahriddin I. Muminov and Y.M. Shermatova} } @article {2011, title = {Numerical Strategies for Stroke Optimization of Axisymmetric Microswimmers}, journal = {Mathematical Models and Methods in Applied Sciences 21 (2011) 361-387}, number = {SISSA;33/2009/M}, year = {2011}, publisher = {World Scientific}, abstract = {We propose a computational method to solve optimal swimming problems, based on the boundary integral formulation of the hydrodynamic interaction between swimmer and surrounding fluid and direct constrained minimization of the energy consumed by the swimmer. We apply our method to axisymmetric model examples. We consider a classical model swimmer (the three-sphere swimmer of Golestanian et al.) as well as a novel axisymmetric swimmer inspired by the observation of biological micro-organisms.}, keywords = {Optimal swimming}, doi = {10.1142/S0218202511005088}, url = {http://hdl.handle.net/1963/3657}, author = {Fran{\c c}ois Alouges and Antonio DeSimone and Luca Heltai} } @article {2011, title = {Numerical Study of breakup in generalized Korteweg-de Vries and Kawahara equations}, journal = {SIAM J. Appl. Math. 71 (2011) 983-1008}, number = {arXiv:1101.0268;}, year = {2011}, publisher = {SIAM}, abstract = {This article is concerned with a conjecture in [B. Dubrovin, Comm. Math. Phys., 267 (2006), pp. 117{\textendash}139] on the formation of dispersive shocks in a class of Hamiltonian dispersive regularizations of the quasi-linear transport equation. The regularizations are characterized by two arbitrary functions of one variable, where the condition of integrability implies that one of these functions must not vanish. It is shown numerically for a large class of equations that the local behavior of their solution near the point of gradient catastrophe for the transport equation is described by a special solution of a Painlev{\'e}-type equation. This local description holds also for solutions to equations where blowup can occur in finite time. Furthermore, it is shown that a solution of the dispersive equations away from the point of gradient catastrophe is approximated by a solution of the transport equation with the same initial data, modulo terms of order $\\\\epsilon^2$, where $\\\\epsilon^2$ is the small dispersion parameter. Corrections up to order $\\\\epsilon^4$ are obtained and tested numerically.}, doi = {10.1137/100819783}, url = {http://hdl.handle.net/1963/4951}, author = {Boris Dubrovin and Tamara Grava and Christian Klein} } @article {2011, title = {Osservazioni sui teoremi di inversione globale}, journal = {Rendiconti Lincei - Matematica e Applicazioni 22 (2011) 3-15}, number = {SISSA;64/2010/M}, year = {2011}, publisher = {European Mathematical Society}, abstract = {Some global inversion theorems with applications to semilinear elliptic equation are discussed.}, doi = {10.4171/RLM/584}, url = {http://hdl.handle.net/1963/4068}, author = {Antonio Ambrosetti} } @article {1110.6124, title = {A planar bi-Lipschitz extension Theorem}, year = {2011}, url = {http://arxiv.org/abs/1110.6124}, author = {Sara Daneri and Aldo Pratelli} } @article {2011, title = {Planar loops with prescribed curvature: existence, multiplicity and uniqueness results}, journal = {Proceedings of the American Mathematical Society 139 (2011) 4445-4459}, number = {SISSA;08/2010/M}, year = {2011}, publisher = {American Mathematical Society}, keywords = {Plane curves}, doi = {10.1090/S0002-9939-2011-10915-8}, url = {http://hdl.handle.net/1963/3842}, author = {Roberta Musina} } @article {2011, title = {Poincar{\'e} covariance and κ-Minkowski spacetime}, journal = {Physics Letters A 375 (2011) 3496-3498}, number = {SISSA;43/2010/FM}, year = {2011}, publisher = {Elsevier}, abstract = {A fully Poincar{\'e} covariant model is constructed out of the k-Minkowski spacetime. Covariance is implemented by a unitary representation of the Poincar{\'e} group, and thus complies with the original Wigner approach to quantum symmetries. This provides yet another example (besides the DFR model), where Poincar{\'e} covariance is realised {\'a} la Wigner in the presence of two characteristic dimensionful parameters: the light speed and the Planck length. In other words, a Doubly Special Relativity (DSR) framework may well be realised without deforming the meaning of \\\"Poincar{\'e} covariance\\\".}, doi = {10.1016/j.physleta.2011.08.011}, url = {http://hdl.handle.net/1963/3893}, author = {Ludwik Dabrowski and Gherardo Piacitelli} } @article {2011, title = {Poincar{\'e} polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces}, journal = {Communications in Mathematical Physics 304 (2011) 395-409}, volume = {304}, number = {SISSA;56/2009/FM}, year = {2011}, month = {06/2011}, pages = {395-409}, publisher = {Springer}, abstract = {We perform a study of the moduli space of framed torsion-free sheaves on Hirzebruch surfaces by using localization techniques. We discuss some general properties of this moduli space by studying it in the framework of Huybrechts-Lehn theory of framed modules. We classify the fixed points under a toric action on the moduli space, and use this to compute the Poincare polynomial of the latter. This will imply that the moduli spaces we are considering are irreducible. We also consider fractional first Chern classes, which means that we are extending our computation to a stacky deformation of a Hirzebruch surface. From the physical viewpoint, our results provide the partition function of N=4 Vafa-Witten theory on total spaces of line bundles on P1, which is relevant in black hole entropy counting problems according to a conjecture due to Ooguri, Strominger and Vafa.

}, doi = {10.1007/s00220-011-1231-z}, url = {http://hdl.handle.net/1963/3738}, author = {Ugo Bruzzo and Rubik Poghossian and Alessandro Tanzini} } @article {2011, title = {Product of real spectral triples}, journal = {International Journal of Geometric Methods in Modern Physics 8 (2011) 1833-1848}, number = {arXiv:1011.4456;}, year = {2011}, note = {Based on the talk given at the conference \\\"Noncommutative Geometry and Quantum Physics, Vietri sul Mare, Aug 31 - Sept 5, 2009\\\"}, publisher = {World Scientific}, abstract = {We construct the product of real spectral triples of arbitrary finite dimension (and arbitrary parity) taking into account the fact that in the even case there are two possible real structures, in the odd case there are two inequivalent representations of the gamma matrices (Clifford algebra), and in the even-even case there are two natural candidates for the Dirac operator of the product triple.}, doi = {10.1142/S021988781100597X}, url = {http://hdl.handle.net/1963/5510}, author = {Ludwik Dabrowski and Giacomo Dossena} } @article {2011, title = {A proof of Sudakov theorem with strictly convex norms}, journal = {Mathematische Zeitschrift 268 (2011) 371-407}, number = {SISSA;64/2008/M}, year = {2011}, publisher = {Springer}, abstract = {We establish a solution to the Monge problem in Rn, with an asymmetric, strictly convex norm cost function, when the initial measure is absolutely continuous. We focus on the strategy, based on disintegration of measures, initially proposed by Sudakov. As known, there is a gap to fill. The missing step is completed when the unit ball is strictly convex, but not necessarily differentiable nor uniformly convex. The key disintegration is achieved following a similar proof for a variational problem.}, doi = {10.1007/s00209-010-0677-6}, url = {http://hdl.handle.net/1963/2967}, author = {Laura Caravenna} } @article {2011, title = {Q-factorial Laurent rings}, number = {arXiv:1108.4116v1;}, year = {2011}, note = {5 pages}, institution = {SISSA}, abstract = {Dolgachev proved that, for any field k, the ring naturally associated to a\\r\\ngeneric Laurent polynomial in d variables, $d \\\\geq 4$, is factorial. We prove a\\r\\nsufficient condition for the ring associated to a very general complex Laurent\\r\\npolynomial in d=3 variables to be Q-factorial.}, url = {http://hdl.handle.net/1963/4183}, author = {Ugo Bruzzo and Antonella Grassi} } @article {2011, title = {Quantum Geometry on Quantum Spacetime: Distance, Area and Volume Operators}, journal = {Commun. Math. Phys. 308 (2011) 567-589}, number = {arXiv:1005.2130;}, year = {2011}, publisher = {Springer}, abstract = {We develop the first steps towards an analysis of geometry on the quantum\\r\\nspacetime proposed in Doplicher et al. (Commun Math Phys 172:187{\textendash}220, 1995). The homogeneous elements of the universal differential algebra are naturally identified with operators living in tensor powers of Quantum Spacetime; this allows us to compute their spectra. In particular, we consider operators that can be interpreted as distances, areas, 3- and 4-volumes. The Minkowski distance operator between two independent events is shown to have pure Lebesgue spectrum with infinite multiplicity. The Euclidean distance operator is shown to have spectrum bounded below by a constant of the order of the Planck length. The corresponding statement is proved also for both the space-space and space-time area operators, as well as for the Euclidean length of the vector representing the 3-volume operators. However, the space 3-volume operator (the time component of that vector) is shown to have spectrum equal to the whole complex plane. All these operators are normal, while the distance operators are also selfadjoint. The Lorentz invariant spacetime volume operator, representing the 4- volume spanned by five\\r\\nindependent events, is shown to be normal. Its spectrum is pure point with a\\r\\nfinite distance (of the order of the fourth power of the Planck length) away\\r\\nfrom the origin. The mathematical formalism apt to these problems is developed and its relation to a general formulation of Gauge Theories on Quantum Spaces is outlined. As a byproduct, a Hodge Duality between the absolute differential and the Hochschild boundary is pointed out.}, doi = {10.1007/s00220-011-1358-y}, url = {http://hdl.handle.net/1963/5203}, author = {Dorothea Bahns and Sergio Doplicher and Klaus Fredenhagen and Gherardo Piacitelli} } @article {2011, title = {Quantum Hitchin Systems via beta-deformed Matrix Models}, number = {arXiv:1104.4016v2;}, year = {2011}, note = {29 pages; v2. refs. added and typos corrected}, institution = {SISSA}, abstract = {We study the quantization of Hitchin systems in terms of beta-deformations of generalized matrix models related to conformal blocks of Liouville theory on punctured Riemann surfaces. We show that in a suitable limit, corresponding to the Nekrasov-Shatashvili one, the loop equations of the matrix model reproduce the Hamiltonians of the quantum Hitchin system on the sphere and the torus with marked points. The eigenvalues of these Hamiltonians are shown to be the epsilon1-deformation of the chiral observables of the corresponding N=2 four ndimensional gauge theory. Moreover, we find the exact wave-functions in terms of the matrix model representation of the conformal blocks with degenerate field insertions.

}, url = {http://hdl.handle.net/1963/4181}, author = {Giulio Bonelli and Kazunobu Maruyoshi and Alessandro Tanzini} } @article {2011, title = {Quantum Isometries of the finite noncommutative geometry of the Standard Model}, journal = {Commun. Math. Phys. 307:101-131, 2011}, number = {arXiv:1009.2850;}, year = {2011}, publisher = {Springer}, abstract = {We compute the quantum isometry group of the finite noncommutative geometry F describing the internal degrees of freedom in the Standard Model of particle physics. We show that this provides genuine quantum symmetries of the spectral triple corresponding to M x F where M is a compact spin manifold. We also prove that the bosonic and fermionic part of the spectral action are preserved by these symmetries.}, doi = {10.1007/s00220-011-1301-2}, url = {http://hdl.handle.net/1963/4906}, author = {Jyotishman Bhowmick and Francesco D{\textquoteright}Andrea and Ludwik Dabrowski} } @article {2011, title = {Quasiconvex envelopes of energies for nematic elastomers in the small strain regime and applications}, journal = {Journal of the Mechanics and Physics of Solids 59 (2011) 787-803}, number = {SISSA;62/2010/M}, year = {2011}, abstract = {We provide some explicit formulas for the quasiconvex envelope of energy densities for nematic elastomers in the small strain regime and plane strain conditions. We then demonstrate their use as a powerful tool for the interpretation of mechanical experiments.}, url = {http://hdl.handle.net/1963/4065}, author = {Pierluigi Cesana and Antonio DeSimone} } @article {2011, title = {Quasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a Young measures approach}, journal = {ESAIM: COCV 17 (2011) 1-27}, number = {SISSA;56/2007/M}, year = {2011}, publisher = {Cambridge University Press / EDP Sciences}, abstract = {A new approach to irreversible quasistatic fracture growth is given, by means of Young measures. The study concerns a cohesive zone model with prescribed crack path, when the material gives different responses to loading and unloading phases. In the particular situation of constant unloading response, the result contained in [6] is recovered. In this case, the convergence of the discrete time approximations is improved.}, doi = {10.1051/cocv/2009037}, url = {http://hdl.handle.net/1963/2355}, author = {Filippo Cagnetti and Rodica Toader} } @article { ISI:000286300100012, title = {Quasistatic crack growth in finite elasticity with Lipschitz data}, journal = {{ANNALI DI MATEMATICA PURA ED APPLICATA}}, volume = {{190}}, number = {{1}}, year = {2011}, month = {{JAN}}, pages = {{165-194}}, publisher = {{SPRINGER HEIDELBERG}}, type = {{Article}}, address = {{TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY}}, abstract = {{We extend the recent existence result of Dal Maso and Lazzaroni (Ann Inst H Poincare Anal Non Lineaire 27:257-290, 2010) for quasistatic evolutions of cracks in finite elasticity, allowing for boundary conditions and external forces with discontinuous first derivatives.}

}, keywords = {Brittle fracture, Crack propagation, Energy minimization, Finite elasticity, free-discontinuity problems, Griffith{\textquoteright}s criterion, Non-interpenetration}, Polyconvexity, Quasistatic evolution, Rate-independent processes, {Variational models}, issn = {{0373-3114}}, doi = {{10.1007/s10231-010-0145-2}}, author = {Giuliano Lazzaroni} } @article {2011, title = {Quasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling}, journal = {Calculus of Variations and Partial Differential Equations 40 (2011) 125-181}, number = {SISSA;36/2009/M}, year = {2011}, publisher = {Springer}, abstract = {Cam-Clay nonassociative plasticity exhibits both hardening and softening behaviour, depending on the loading. For many initial data the classical formulation of the quasistatic evolution problem has no smooth solution. We propose here a notion of generalized solution, based on a viscoplastic approximation. To study the limit of the viscoplastic evolutions we rescale time, in such a way that the plastic strain is uniformly Lipschitz with respect to the rescaled time. The limit of these rescaled solutions, as the viscosity parameter tends to zero, is characterized through an energy-dissipation balance, that can be written in a natural way using the rescaled time. As shown in [4] and [6], the proposed solution may be discontinuous with respect to the original time. Our formulation allows to compute the amount of viscous dissipation occurring instantaneously at each discontinuity time.

}, keywords = {Cam-Clay plasticity}, doi = {10.1007/s00526-010-0336-0}, url = {http://hdl.handle.net/1963/3670}, author = {Gianni Dal Maso and Antonio DeSimone and Francesco Solombrino} } @article {2011, title = {Quasistatic evolution of sessile drops and contact angle hysteresis}, journal = {Arch. Rational Mech. Anal. 202 (2011) 295-348}, year = {2011}, publisher = {Springer}, abstract = {We consider the classical model of capillarity coupled with a rate-independent dissipation mechanism due to frictional forces acting on the contact line, and prove the existence of quasistatic evolutions with prescribed initial configuration. We also discuss in detail some explicit solutions to show that the model does account for contact angle hysteresis, and to compare its predictions with experimental observations.}, doi = {10.1007/s00205-011-0427-x}, url = {http://hdl.handle.net/1963/4912}, author = {Giovanni Alberti and Antonio DeSimone} } @article {garrione2011resonance, title = {Resonance and Landesman-Lazer conditions for first order systems in R^2}, journal = {Le Matematiche}, volume = {66}, number = {1}, year = {2011}, pages = {153{\textendash}160}, abstract = {The first part of the paper surveys the concept of resonance for $T$-periodic nonlinear problems. In the second part, some new results about existence conditions for nonlinear planar systems are presented. In particular, the Landesman-Lazer conditions are generalized to systems in $\mathbbR^2$ where the nonlinearity interacts with two resonant Hamiltonians. Such results apply to second order equations, generalizing previous theorems by Fabry [4] (for the undamped case), and Frederickson-Lazer [9] (for the case with friction). The results have been obtained with A. Fonda, and have been published in [8].

}, author = {Maurizio Garrione} } @article {BOSCAGGIN20114166, title = {Resonance and rotation numbers for planar Hamiltonian systems: Multiplicity results via the Poincar{\'e}{\textendash}Birkhoff theorem}, journal = {Nonlinear Analysis: Theory, Methods \& Applications}, volume = {74}, number = {12}, year = {2011}, pages = {4166 - 4185}, abstract = {In the general setting of a planar first order system (0.1)u'=G(t,u),u∈R2, with G:[0,T]{\texttimes}R2{\textrightarrow}R2, we study the relationships between some classical nonresonance conditions (including the Landesman{\textendash}Lazer one) {\textemdash} at infinity and, in the unforced case, i.e. G(t,0)=0, at zero {\textemdash} and the rotation numbers of {\textquotedblleft}large{\textquotedblright} and {\textquotedblleft}small{\textquotedblright} solutions of (0.1), respectively. Such estimates are then used to establish, via the Poincar{\'e}{\textendash}Birkhoff fixed point theorem, new multiplicity results for T-periodic solutions of unforced planar Hamiltonian systems Ju'=∇uH(t,u) and unforced undamped scalar second order equations x"+g(t,x)=0. In particular, by means of the Landesman{\textendash}Lazer condition, we obtain sharp conclusions when the system is resonant at infinity.

}, keywords = {Multiple periodic solutions, Poincar{\'e}{\textendash}Birkhoff theorem, Resonance, Rotation number}, issn = {0362-546X}, doi = {https://doi.org/10.1016/j.na.2011.03.051}, url = {http://www.sciencedirect.com/science/article/pii/S0362546X11001817}, author = {Alberto Boscaggin and Maurizio Garrione} } @article {2011, title = {SBV regularity for Hamilton-Jacobi equations in R^n}, journal = {Arch. Rational Mech. Anal. 200 (2011) 1003-1021}, number = {arXiv:1002.4087;}, year = {2011}, publisher = {Springer}, abstract = {In this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$ \partial_t u + H(D_{x} u)=0 \qquad \textrm{in}\quad \Omega\subset \mathbb{R}\times \mathbb{R}^{n} . $$ In particular, under the assumption that the Hamiltonian $H\in C^2(\mathbb{R}^n)$ is uniformly convex, we prove that $D_{x}u$ and $\partial_t u$ belong to the class $SBV_{loc}(\Omega)$.

}, doi = {10.1007/s00205-010-0381-z}, url = {http://hdl.handle.net/1963/4911}, author = {Stefano Bianchini and Camillo De Lellis and Roger Robyr} } @article {2011, title = {Semistable and numerically effective principal (Higgs) bundles}, journal = {Advances in Mathematics 226 (2011) 3655-3676}, number = {SISSA;27/2009/FM}, year = {2011}, publisher = {Elsevier}, abstract = {We study Miyaoka-type semistability criteria for principal Higgs G-bundles E on complex projective manifolds of any dimension. We prove that E has the property of being semistable after pullback to any projective curve if and only if certain line bundles, obtained from some characters of the parabolic subgroups of G, are numerically effective. One also proves that these conditions are met for semistable principal Higgs bundles whose adjoint bundle has vanishing second Chern class.\\r\\n\\r\\nIn a second part of the paper, we introduce notions of numerical effectiveness and numerical flatness for principal (Higgs) bundles, discussing their main properties. For (non-Higgs) principal bundles, we show that a numerically flat principal bundle admits a reduction to a Levi factor which has a flat Hermitian{\textendash}Yang{\textendash}Mills connection, and, as a consequence, that the cohomology ring of a numerically flat principal bundle with coefficients in R is trivial. To our knowledge this notion of numerical effectiveness is new even in the case of (non-Higgs) principal bundles.}, doi = {10.1016/j.aim.2010.10.026}, url = {http://hdl.handle.net/1963/3638}, author = {Ugo Bruzzo and Beatriz Grana-Otero} } @article {2011, title = {Singular perturbation models in phase transitions for second order materials}, journal = {Indiana Univ. Math. J. 60 (2011) 367-409}, number = {SISSA;20/2010/M}, year = {2011}, publisher = {Indiana University}, abstract = {A variational model proposed in the physics literature to describe the onset of pattern formation in two-component bilayer membranes and amphiphilic monolayers leads to the analysis of a Ginzburg-Landau type energy with a negative term depending on the first derivative of the phase function. Scaling arguments motivate the study of the family of second order singular perturbed energies Fe having a negative term depending on the first derivative of the phase function. Here, the asymptotic behavior of {Fe} is studied using G-convergence techniques. In particular, compactness results and an integral representation of the limit energy are obtained.}, doi = {10.1512/iumj.2011.60.4346}, url = {http://hdl.handle.net/1963/3858}, author = {Milena Chermisi and Gianni Dal Maso and Irene Fonseca and Giovanni Leoni} } @inbook {2011, title = {Solving PVI by Isomonodromy Deformations}, booktitle = {Painlevé equations and related topics : proceedings of the international conference, Saint Petersburg, Russia, June 17-23, 2011 / Aleksandr Dmitrievich Briuno; Alexander B Batkhin. - Berlin : De Gruyter, [2012]. - p. 101-105}, number = {arXiv:1106.2636;}, year = {2011}, note = {12 pages, 1 figurethis paper has been}, publisher = {SISSA}, organization = {SISSA}, abstract = {The critical and asymptotic behaviors of solutions of the sixth Painlev\\\'e\r\nequation, an their parametrization in terms of monodromy data, are\r\nsynthetically reviewed. The explicit formulas are given. This paper has been\r\nwithdrawn by the author himself, because some improvements are necessary.\r\nThis is a proceedings of the international conference \"Painlevé Equations and Related Topics\" which was taking place at the Euler International Mathematical Institute, a branch of the Saint Petersburg Department of the SteklovInstitute of Mathematicsof theRussian Academy of Sciences, in Saint Petersburg on June 17 to 23, 2011.}, keywords = {Painlevé Equations}, isbn = {9783110275582}, url = {http://hdl.handle.net/1963/6522}, author = {Davide Guzzetti} } @article {2011, title = {On the Space of Symmetric Operators with Multiple Ground States}, journal = {Functional Analysis and its Applications, Volume 45, Issue 4, December 2011, Pages 241-251}, number = {arXiv:1107.3010;}, year = {2011}, publisher = {SISSA}, abstract = {We study homological structure of the filtrations of the spaces of self-adjoint operators by the multiplicity of the ground state. We consider only operators acting in a finite dimensional complex or real Hilbert space but infinite dimensional generalizations are easily guessed.}, keywords = {Multiple eigenvalue}, doi = {DOI: 10.1007/s10688-011-0026-5}, url = {http://hdl.handle.net/1963/7069}, author = {Andrei A. Agrachev} } @article {2011, title = {The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry}, journal = {Journal of Dynamical and Control Systems }, volume = {17 }, number = {arXiv:1009.2612;}, year = {2011}, pages = {141-161}, publisher = {Springer}, abstract = {We study the tangential case in 2-dimensional almost-Riemannian geometry. We\\r\\nanalyse the connection with the Martinet case in sub-Riemannian geometry. We\\r\\ncompute estimations of the exponential map which allow us to describe the\\r\\nconjugate locus and the cut locus at a tangency point. We prove that this last\\r\\none generically accumulates at the tangency point as an asymmetric cusp whose branches are separated by the singular set.

}, doi = {10.1007/s10883-011-9113-4}, url = {http://hdl.handle.net/1963/4914}, author = {Bernard Bonnard and Gr{\'e}goire Charlot and Roberta Ghezzi and Gabriel Janin} } @article {2011, title = {Structure of level sets and Sard-type properties of Lipschitz maps}, number = {SISSA;51/2011/M}, year = {2011}, institution = {SISSA}, url = {http://hdl.handle.net/1963/4657}, author = {Giovanni Alberti and Stefano Bianchini and Gianluca Crippa} } @article {boscaggin2011subharmonic, title = {Subharmonic solutions of planar Hamiltonian systems: a rotation number approach}, journal = {Advanced Nonlinear Studies}, volume = {11}, number = {1}, year = {2011}, pages = {77{\textendash}103}, publisher = {Advanced Nonlinear Studies, Inc.}, doi = {10.1515/ans-2011-0104}, author = {Alberto Boscaggin} } @article {boscaggin2011subharmonic, title = {Subharmonic solutions of planar Hamiltonian systems via the Poincar{\'e}́-Birkhoff theorem}, journal = {Le Matematiche}, volume = {66}, number = {1}, year = {2011}, pages = {115{\textendash}122}, abstract = {We revisit some recent results obtained in [1] about the existence of subharmonic solutions for a class of (nonautonomous) planar Hamiltonian systems, and we compare them with the existing literature. New applications to undamped second order equations are discussed, as well.

}, author = {Alberto Boscaggin} } @article {2011, title = {Supercritical conformal metrics on surfaces with conical singularities}, journal = {Int Math Res Notices (2011) 2011 (24): 5625-5643}, number = {SISSA;56/2010/M}, year = {2011}, publisher = {Oxford University Press}, abstract = {We study the problem of prescribing the Gaussian curvature on surfaces with conical singularities in supercritical regimes. Using a Morse-theoretical approach we prove a general existence theorem on surfaces with positive genus, with a generic multiplicity result.

}, doi = {10.1093/imrn/rnq285}, url = {http://hdl.handle.net/1963/4095}, author = {Mauro Bardelloni and Francesca De Marchis and Andrea Malchiodi} } @article {2011, title = {A system-level approach for deciphering the transcriptional response to prion infection}, journal = {Bioinformatics (Oxford, England). 2011 Dec; 27(24):3407-14}, number = {PMID:22016408;}, year = {2011}, publisher = {Oxford University Press}, abstract = {MOTIVATION: Deciphering the response of a complex biological system to an insulting event, at the gene expression level, requires adopting theoretical models that are more sophisticated than a one-to-one comparison (i.e. t-test). Here, we investigate the ability of a novel reverse engineering approach (System Response Inference) to unveil non-obvious transcriptional signatures of the system response induced by prion infection.\\r\\nRESULTS: To this end, we analyze previously published gene expression data, from which we extrapolate a putative full-scale model of transcriptional gene-gene dependencies in the mouse central nervous system. Then, we use this nominal model to interpret the gene expression changes caused by prion replication, aiming at selecting the genes primarily influenced by this perturbation. Our method sheds light on the mode of action of prions by identifying key transcripts that are the most likely to be responsible for the overall transcriptional rearrangement from a nominal regulatory network. As a first result of our inference, we have been able to predict known targets of prions (i.e. PrP(C)) and to unveil the potential role of previously unsuspected genes.\\r\\nCONTACT: altafini@sissa.it\\r\\nSUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.}, doi = {10.1093/bioinformatics/btr580}, url = {http://hdl.handle.net/1963/5745}, author = {Mattia Zampieri and Giuseppe Legname and Daniel Segr{\`e} and Claudio Altafini} } @article {1106.6245, title = {Thin-walled beams with a cross-section of arbitrary geometry: derivation of linear theories starting from 3D nonlinear elasticity}, year = {2011}, abstract = {The subject of this paper is the rigorous derivation of lower dimensional models for a nonlinearly elastic thin-walled beam whose cross-section is given by a thin tubular neighbourhood of a smooth curve. Denoting by h and δ_h, respectively, the diameter and the thickness of the cross-section, we analyse the case where the scaling factor of the elastic energy is of order ε_h^2, with ε_h/δ_h^2 \rightarrow l \in [0, +\infty). Different linearized models are deduced according to the relative order of magnitude of δ_h with respect to h.

}, author = {Elisa Davoli} } @article {2011, title = {The time-dependent von K{\'a}rm{\'a}n plate equation as a limit of 3d nonlinear elasticity}, journal = {Calculus of Variations and Partial Differential Equations 41 (2011) 241-259}, number = {SISSA;74/2009/M}, year = {2011}, publisher = {Springer}, abstract = {The asymptotic behaviour of the solutions of three-dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness $h$ of the plate tends to zero. Under appropriate scalings of the applied force and of the initial values in terms of $h$, it is shown that three-dimensional solutions of the nonlinear elastodynamic equation converge to solutions of the time-dependent von K\\\\\\\'arm\\\\\\\'an plate equation.}, doi = {10.1007/s00526-010-0360-0}, url = {http://hdl.handle.net/1963/3835}, author = {Helmut Abels and Maria Giovanna Mora and Stefan M{\"u}ller} } @article {BertolaCafasso1, title = {The Transition between the Gap Probabilities from the Pearcey to the Airy Process{\textendash}a Riemann-Hilbert Approach}, journal = {International Mathematics Research Notices}, volume = {doi: 10.1093/imrn/rnr066}, year = {2011}, pages = {1-50}, author = {Marco Bertola and Mattia Cafasso} } @article {SELVITELLA20111731, title = {Uniqueness and nondegeneracy of the ground state for a quasilinear Schr{\"o}dinger equation with a small parameter}, journal = {Nonlinear Analysis: Theory, Methods \& Applications}, volume = {74}, number = {5}, year = {2011}, pages = {1731 - 1737}, abstract = {We study least energy solutions of a quasilinear Schr{\"o}dinger equation with a small parameter. We prove that the ground state is nondegenerate and unique up to translations and phase shifts using bifurcation theory.

}, keywords = {Bifurcation theory, Nonlinear Schr{\"o}dinger equations, Stationary solutions}, issn = {0362-546X}, doi = {https://doi.org/10.1016/j.na.2010.10.045}, url = {http://www.sciencedirect.com/science/article/pii/S0362546X10007613}, author = {Alessandro Selvitella} } @article {2011, title = {A uniqueness result for the continuity equation in two dimensions}, number = {SISSA;52/2011/M}, year = {2011}, institution = {SISSA}, url = {http://hdl.handle.net/1963/4663}, author = {Giovanni Alberti and Stefano Bianchini and Gianluca Crippa} } @article {DANCHIN2011253, title = {The well-posedness issue for the density-dependent Euler equations in endpoint Besov spaces}, journal = {Journal de Math{\'e}matiques Pures et Appliqu{\'e}es}, volume = {96}, number = {3}, year = {2011}, pages = {253 - 278}, abstract = {This work is the continuation of the recent paper (Danchin, 2010) [9] devoted to the density-dependent incompressible Euler equations. Here we concentrate on the well-posedness issue in Besov spaces of type B$\infty$,rs embedded in the set of Lipschitz continuous functions, a functional framework which contains the particular case of H{\"o}lder spaces C1,α and of the endpoint Besov space B$\infty$,11. For such data and under the non-vacuum assumption, we establish the local well-posedness and a continuation criterion in the spirit of that of Beale, Kato and Majda (1984) [2]. In the last part of the paper, we give lower bounds for the lifespan of a solution. In dimension two, we point out that the lifespan tends to infinity when the initial density tends to be a constant. This is, to our knowledge, the first result of this kind for the density-dependent incompressible Euler equations. R{\'e}sum{\'e} Ce travail compl{\`e}te l'article r{\'e}cent (Danchin, 2010) [9] consacr{\'e} au syst{\`e}me d'Euler incompressible {\`a} densit{\'e} variable. Lorsque l'{\'e}tat initial ne comporte pas de vide, on montre ici que le syst{\`e}me est bien pos{\'e} dans tous les espaces de Besov B$\infty$,rs inclus dans l'ensemble des fonctions lipschitziennes. Ce cadre fonctionnel contient en particulier les espaces de H{\"o}lder C1,α et l'espace de Besov limite B$\infty$,11. On {\'e}tablit {\'e}galement un crit{\`e}re de prolongement dans l'esprit de celui de Beale, Kato et Majda (1984) [2] pour le cas homog{\`e}ne. Dans la derni{\`e}re partie de l'article, on donne des minorations pour le temps de vie des solutions du syst{\`e}me. En dimension deux, on montre que ce temps de vie tend vers l'infini lorsque la densit{\'e} tend {\`a} {\^e}tre homog{\`e}ne. {\`A} notre connaissance, il s'agit du premier r{\'e}sultat de ce type pour le syst{\`e}me d'Euler incompressible {\`a} densit{\'e} variable.

}, keywords = {Blow-up criterion, Critical regularity, Incompressible Euler equations, Lifespan, Nonhomogeneous inviscid fluids}, issn = {0021-7824}, doi = {https://doi.org/10.1016/j.matpur.2011.04.005}, url = {http://www.sciencedirect.com/science/article/pii/S0021782411000511}, author = {Rapha{\"e}l Danchin and Francesco Fanelli} } @article {Berti2010377, title = {An abstract Nash-Moser theorem with parameters and applications to PDEs}, journal = {Annales de l{\textquoteright}Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis}, volume = {27}, number = {1}, year = {2010}, note = {cited By (since 1996)9}, pages = {377-399}, abstract = {We prove an abstract Nash-Moser implicit function theorem with parameters which covers the applications to the existence of finite dimensional, differentiable, invariant tori of Hamiltonian PDEs with merely differentiable nonlinearities. The main new feature of the abstract iterative scheme is that the linearized operators, in a neighborhood of the expected solution, are invertible, and satisfy the "tame" estimates, only for proper subsets of the parameters. As an application we show the existence of periodic solutions of nonlinear wave equations on Riemannian Zoll manifolds. A point of interest is that, in presence of possibly very large "clusters of small divisors", due to resonance phenomena, it is more natural to expect solutions with only Sobolev regularity. {\textcopyright} 2009 Elsevier Masson SAS. All rights reserved.}, keywords = {Abstracting, Aircraft engines, Finite dimensional, Hamiltonian PDEs, Implicit function theorem, Invariant tori, Iterative schemes, Linearized operators, Mathematical operators, Moser theorem, Non-Linearity, Nonlinear equations, Nonlinear wave equation, Periodic solution, Point of interest, Resonance phenomena, Small divisors, Sobolev, Wave equations}, issn = {02941449}, doi = {10.1016/j.anihpc.2009.11.010}, author = {Massimiliano Berti and Philippe Bolle and Michela Procesi} } @mastersthesis {2010, title = {Almost-Riemannian Geometry from a Control Theoretical Viewpoint}, year = {2010}, school = {SISSA}, url = {http://hdl.handle.net/1963/4705}, author = {Roberta Ghezzi} } @proceedings {2010, title = {Aspects of Quantum Field Theory on Quantum Spacetime}, number = {arXiv:1103.3405v1;}, year = {2010}, note = {25 pages, active hyperlinks. Corfu Summer Institute on Elementary\\r\\n Particles and Physics - Workshop on Non Commutative Field Theory and Gravity,\\r\\n September 8-12, 2010, Corfu Greece}, publisher = {SISSA}, abstract = {We provide a minimal, self-contained introduction to the covariant DFR flat\\r\\nquantum spacetime, and to some partial results for the corresponding quantum field theory. Explicit equations are given in the Dirac notation.}, url = {http://hdl.handle.net/1963/4171}, author = {Gherardo Piacitelli} } @article {2010, title = {Canonical k-Minkowski Spacetime}, number = {SISSA;26/2010/FM}, year = {2010}, abstract = {A complete classification of the regular representations of the relations [T,X_j] = (i/k)X_j, j=1,...,d, is given. The quantisation of RxR^d canonically (in the sense of Weyl) associated with the universal representation of the above relations is intrinsically \\\"radial\\\", this meaning that it only involves the time variable and the distance from the origin; angle variables remain classical. The time axis through the origin is a spectral singularity of the model: in the large scale limit it is topologically disjoint from the rest. The symbolic calculus is developed; in particular there is a trace functional on symbols. For suitable choices of states localised very close to the origin, the uncertainties of all spacetime coordinates can be made simultaneously small at wish. On the contrary, uncertainty relations become important at \\\"large\\\" distances: Planck scale effects should be visible at LHC energies, if processes are spread in a region of size 1mm (order of peak nominal beam size) around the origin of spacetime.}, url = {http://hdl.handle.net/1963/3863}, author = {Gherardo Piacitelli and Ludwik Dabrowski} } @article {Bertola:CBOPs, title = {Cauchy biorthogonal polynomials}, journal = {J. Approx. Theory}, volume = {162}, number = {4}, year = {2010}, pages = {832{\textendash}867}, issn = {0021-9045}, doi = {10.1016/j.jat.2009.09.008}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1016/j.jat.2009.09.008}, author = {Marco Bertola and Gekhtman, M. and Szmigielski, J.} } @article {2010, title = {Chern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality}, journal = {J. Geom. Phys. 60 (2010) 417-429}, number = {SISSA;56/2008/FM}, year = {2010}, abstract = {We consider aspects of Chern-Simons theory on L(p,q) lens spaces and its relation with matrix models and topological string theory on Calabi-Yau threefolds, searching for possible new large N dualities via geometric transition for non-SU(2) cyclic quotients of the conifold. To this aim we find, on one hand, some novel matrix integral representations of the SU(N) CS partition function in a generic flat background for the whole L(p,q) family and provide a solution for its large N dynamics; on the other, we perform in full detail the construction of a family of would-be dual closed string backgrounds via conifold geometric transition from T^*L(p,q). We can then explicitly prove that Gopakumar-Vafa duality in a fixed vacuum fails in the case q>1, and briefly discuss how it could be restored in a non-perturbative setting.}, doi = {10.1016/j.geomphys.2009.11.006}, url = {http://hdl.handle.net/1963/2938}, author = {Andrea Brini and Luca Griguolo and Domenico Seminara and Alessandro Tanzini} } @article {2010, title = {Cohomology of Skew-holomorphic lie algebroids}, number = {SISSA;15/2010/FM}, year = {2010}, abstract = {We introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.}, url = {http://hdl.handle.net/1963/3853}, author = {Ugo Bruzzo and Vladimir Rubtsov} } @article {2010, title = {Concentration of solutions for some singularly perturbed mixed problems. Part I: existence results}, journal = {Arch. Ration. Mech. Anal. 196 (2010) 907-950}, number = {SISSA;02/2009/M}, year = {2010}, abstract = {In this paper we study the asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions. We prove that, under suitable geometric conditions on the boundary of the domain, there exist solutions which approach the intersection of the Neumann and the Dirichlet parts as the singular perturbation parameter tends to zero.}, doi = {10.1007/s00205-009-0259-0}, url = {http://hdl.handle.net/1963/3406}, author = {Jesus Garcia Azorero and Andrea Malchiodi and Luigi Montoro and Ireneo Peral} } @article {2010, title = {Concentration of solutions for some singularly perturbed mixed problems: Asymptotics of minimal energy solutions}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 37-56}, number = {SISSA;03/2009/M}, year = {2010}, abstract = {In this paper we carry on the study of asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions, started in the first paper. Here we are mainly interested in the analysis of the location and shape of least energy solutions when the singular perturbation parameter tends to zero. We show that in many cases they coincide with the new solutions produced in.}, doi = {10.1016/j.anihpc.2009.06.005}, url = {http://hdl.handle.net/1963/3409}, author = {Jesus Garcia Azorero and Andrea Malchiodi and Luigi Montoro and Ireneo Peral} } @article {2010, title = {Continuity of optimal control costs and its application to weak KAM theory}, journal = {Calculus of Variations and Partial Differential Equations. Volume 39, Issue 1, 2010, Pages 213-232}, number = {arXiv:0909.3826;}, year = {2010}, note = {23 pages, 1 figures}, publisher = {SISSA}, abstract = {We prove continuity of certain cost functions arising from optimal control of\\r\\naffine control systems. We give sharp sufficient conditions for this\\r\\ncontinuity. As an application, we prove a version of weak KAM theorem and\\r\\nconsider the Aubry-Mather problems corresponding to these systems.}, doi = {10.1007/s00526-010-0308-4}, url = {http://hdl.handle.net/1963/6459}, author = {Andrei A. Agrachev and Paul Lee} } @article {2010, title = {Convergence of equilibria of thin elastic rods under physical growth conditions for the energy density}, number = {SISSA;67/2010/M}, year = {2010}, abstract = {The subject of this paper is the study of the asymptotic behaviour of the equilibrium configurations of a nonlinearly elastic thin rod, as the diameter of the cross-section tends to zero. Convergence results are established assuming physical growth conditions for the elastic energy density and suitable scalings of the applied loads, that correspond at the limit to different rod models: the constrained linear theory, the analogous of von K{\'a}rm{\'a}n plate theory for rods, and the linear theory.}, url = {http://hdl.handle.net/1963/4086}, author = {Elisa Davoli and Maria Giovanna Mora} } @article {BertolaIsoTau, title = {The dependence on the monodromy data of the isomonodromic tau function}, journal = {Comm. Math. Phys.}, volume = {294}, number = {2}, year = {2010}, pages = {539{\textendash}579}, issn = {0010-3616}, doi = {10.1007/s00220-009-0961-7}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00220-009-0961-7}, author = {Marco Bertola} } @article {2010, title = {Dirac Operators on Quantum Projective Spaces}, journal = {Comm. Math. Phys. 295 (2010) 731-790}, number = {SISSA;17/2009/FM}, year = {2010}, note = {Quantum Algebra}, abstract = {We construct a family of self-adjoint operators D_N which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space CP_q(l), for any l>1 and 0We consider the disintegration of the Lebesgue measure on the graph of a convex function f:\\\\Rn-\> \\\\R w.r.t. the partition into its faces, which are convex sets and therefore have a well defined linear dimension, and we prove that each conditional measure is equivalent to the k-dimensional Hausdorff measure of the k-dimensional face on which it is concentrated. The remarkable fact is that a priori the directions of the faces are just Borel and no Lipschitz regularity is known. Notwithstanding that, we also prove that a Green-Gauss formula for these directions holds on special sets.}, doi = {10.1016/j.jfa.2010.01.024}, url = {http://hdl.handle.net/1963/3622}, author = {Laura Caravenna and Sara Daneri} } @article {2010, title = {Dynamics control by a time-varying feedback}, journal = {Journal of Dynamical and Control Systems. Volume 16, Issue 2, April 2010, Pages :149-162}, year = {2010}, publisher = {SISSA}, abstract = {We consider a smooth bracket generating control-affine system in R^d and show that any orientation preserving diffeomorphism of R^d can be approximated, in the very strong sense, by a diffeomorphism included in the flow generated by a time-varying feedback control which is polynomial with respect to the state variables and trigonometric-polynomial with respect to the time variable.}, keywords = {Discrete-time dynamics}, doi = {10.1007/s10883-010-9087-7}, url = {http://hdl.handle.net/1963/6461}, author = {Andrei A. Agrachev and Marco Caponigro} } @article {2010, title = {Effective Schroedinger dynamics on $ ε$-thin Dirichlet waveguides via Quantum Graphs I: star-shaped graphs}, journal = {J. Phys. A 43 (2010) 474014}, number = {arXiv.org;1004.4750v2}, year = {2010}, publisher = {IOP Publishing}, abstract = {We describe the boundary conditions at the vertex that one must choose to obtain a dynamical system that best describes the low-energy part of the evolution of a quantum system confined to a very small neighbourhood of a star-shaped metric graph.}, doi = {10.1088/1751-8113/43/47/474014}, url = {http://hdl.handle.net/1963/4106}, author = {Gianfausto Dell{\textquoteright}Antonio and Emanuele Costa} } @article {2010, title = {Estimates on path functionals over Wasserstein Spaces}, journal = {SIAM J. Math. Anal. 42 (2010) 1179-1217}, number = {SISSA;11/2009/M}, year = {2010}, abstract = {In this paper we consider the class a functionals (introduced in [Brancolini, Buttazzo, and Santambrogio, J. Eur. Math. Soc. (JEMS), 8 (2006), pp. 415-434] $\\\\mathcal{G}_{r,p}$ defined on Lipschitz curves $\\\\gamma$ valued in the $p$-Wasserstein space. The problem considered is the following: given a measure $\\\\mu$, give conditions in order to assure the existence of a curve $\\\\gamma$ such that $\\\\gamma(0)=\\\\mu$, $\\\\gamma(1)=\\\\delta_{x_0}$, and $\\\\mathcal{G}_{r,p}(\\\\gamma)<+\\\\infty$. To this end, new estimates on $\\\\mathcal{G}_{r,p}(\\\\mu)$ are given, and a notion of dimension of a measure (called path dimension) is introduced: the path dimension specifies the values of the parameters $(r,p)$ for which the answer to the previous reachability problem is positive. Finally, we compare the path dimension with other known dimensions.}, doi = {10.1137/100782693}, url = {http://hdl.handle.net/1963/3583}, author = {Stefano Bianchini and Alessio Brancolini} } @article {2010, title = {On the Euler-Lagrange equation for a variational problem : the general case II}, journal = {Math. Z. 265 (2010) 889-923}, number = {SISSA;75/2007/M}, year = {2010}, doi = {10.1007/s00209-009-0547-2}, url = {http://hdl.handle.net/1963/2551}, author = {Stefano Bianchini and Matteo Gloyer} } @article {2010, title = {Exact reconstruction of damaged color images using a total variation model}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 1291-1331}, year = {2010}, publisher = {Elsevier}, abstract = {In this paper the reconstruction of damaged piecewice constant color images is studied using a RGB total variation based model for colorization/inpainting. In particular, it is shown that when color is known in a uniformly distributed region, then reconstruction is possible with maximal fidelity.}, doi = {10.1016/j.anihpc.2010.06.004}, url = {http://hdl.handle.net/1963/4039}, author = {Irene Fonseca and Giovanni Leoni and Francesco Maggi and Massimiliano Morini} } @article {2010, title = {Existence of planar curves minimizing length and curvature}, journal = {Proc. Steklov Inst. Math. 270 (2010) 43-56}, number = {arXiv.org;0906.5290v2}, year = {2010}, publisher = {Springer}, abstract = {In this paper we consider the problem of reconstructing a curve that is partially hidden or corrupted by minimizing the functional $\\\\int \\\\sqrt{1+K_\\\\gamma^2} ds$, depending both on length and curvature $K$. We fix starting and ending points as well as initial and final directions.\\nFor this functional we discuss the problem of existence of minimizers on various functional spaces. We find non-existence of minimizers in cases in which initial and final directions are considered with orientation. In this case, minimizing sequences of trajectories can converge to curves with angles.\\nWe instead prove existence of minimizers for the \\\"time-reparameterized\\\" functional $$\\\\int \\\\| \\\\dot\\\\gamma(t) \\\\|\\\\sqrt{1+K_\\\\ga^2} dt$$ for all boundary conditions if initial and final directions are considered regardless to orientation. In this case, minimizers can present cusps (at most two) but not angles.}, doi = {10.1134/S0081543810030041}, url = {http://hdl.handle.net/1963/4107}, author = {Ugo Boscain and Gr{\'e}goire Charlot and Francesco Rossi} } @article {2010, title = {Feedback schemes for radiation damping suppression in NMR: a control-theoretical perspective}, journal = {Systems and Control Letters, 59 (12):782-786, 2010}, year = {2010}, publisher = {Elsevier}, abstract = {In NMR spectroscopy, the collective measurement is weakly invasive and its back-action is called radiation damping. The aim of this paper is to provide a control-theoretical analysis of the problem of suppressing this radiation damping. It is shown that the two feedback schemes commonly used in the NMR practice correspond one to a high gain oputput feedback for the simple case of maintaining the spin 1/2 in its inverted state, and the second to a 2-degree of freedom control design with a prefeedback that exactly cancels the radiation damping field. A general high gain feedback stabilization design not requiring the knowledge of the radiation damping time constant is also investigated.}, doi = {10.1016/j.sysconle.2010.09.004}, url = {http://hdl.handle.net/1963/4384}, author = {Claudio Altafini and Paola Cappellaro and David Cory} } @article {Bertola:wj, title = {First colonization of a hard-edge in random matrix theory}, journal = {Constr. Approx.}, volume = {31}, number = {2}, year = {2010}, pages = {231{\textendash}257}, issn = {0176-4276}, doi = {10.1007/s00365-009-9052-4}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00365-009-9052-4}, author = {Marco Bertola and Lee, S. Y.} } @article {2010, title = {Gauge theory: from physics to geometry}, journal = {Rend. Istit. Mat. Univ. Trieste 42 (2010) 103-128}, number = {SISSA;80/2010/FM}, year = {2010}, publisher = {Istituto di matematica. Universita\\\' di Trieste}, abstract = {Maxwell theory may be regarded as a prototype of gauge theory and generalized to nonabelian gauge theory. We briey sketch the history of the gauge theories, from Maxwell to Yang-Mills theory, and the identification of gauge fields with connections on fibre bundles. We introduce the notion of instanton and consider the moduli spaces of such objects. Finally, we discuss some modern techniques for studying the topology of these moduli spaces.}, url = {http://hdl.handle.net/1963/4105}, author = {Ugo Bruzzo} } @article {2010, title = {Gene expression analysis of the emergence of epileptiform activity after focal injection of kainic acid into mouse hippocampus.}, journal = {The European journal of neuroscience. 2010 Oct; 32(8):1364-79}, number = {PMID:20950280;}, year = {2010}, publisher = {Wiley}, abstract = {We report gene profiling data on genomic processes underlying the progression towards recurrent seizures after injection of kainic acid (KA) into the mouse hippocampus. Focal injection enabled us to separate the effects of proepileptic stimuli initiated by KA injection. Both the injected and contralateral hippocampus participated in the status epilepticus. However, neuronal death induced by KA treatment was restricted to the injected hippocampus, although there was some contralateral axonal degeneration. We profiled gene expression changes in dorsal and ventral regions of both the injected and contralateral hippocampus. Changes were detected in the expression of 1526 transcripts in samples from three time-points: (i) during the KA-induced status epilepticus, (ii) at 2 weeks, before recurrent seizures emerged, and (iii) at 6 months after seizures emerged. Grouping genes with similar spatio-temporal changes revealed an early transcriptional response, strong immune, cell death and growth responses at 2 weeks and an activation of immune and extracellular matrix genes persisting at 6 months. Immunostaining for proteins coded by genes identified from array studies provided evidence for gliogenesis and suggested that the proteoglycan biglycan is synthesized by astrocytes and contributes to a glial scar. Gene changes at 6 months after KA injection were largely restricted to tissue from the injection site. This suggests that either recurrent seizures might depend on maintained processes including immune responses and changes in extracellular matrix proteins near the injection site or alternatively might result from processes, such as growth, distant from the injection site and terminated while seizures are maintained.

}, doi = {10.1111/j.1460-9568.2010.07403.x}, url = {http://hdl.handle.net/1963/4480}, author = {Dario Motti and Caroline Le Duigou and Nicole Chemaly and Lucia Wittner and Dejan Lazarevic and Helena Krmac and Troels Torben Marstrand and Eivind Valen and Remo Sanges and Elia Stupka and Albin Sandelin and Enrico Cherubini and Stefano Gustincich and Richard Miles} } @article {DEMARCHIS20102165, title = {Generic multiplicity for a scalar field equation on compact surfaces}, journal = {Journal of Functional Analysis}, volume = {259}, number = {8}, year = {2010}, pages = {2165 - 2192}, abstract = {We prove generic multiplicity of solutions for a scalar field equation on compact surfaces via Morse inequalities. In particular our result improves significantly the multiplicity estimate which can be deduced from the degree-counting formula in Chen and Lin (2003) [12]. Related results are derived for the prescribed Q-curvature equation.

}, keywords = {Generic multiplicity, Geometric PDE{\textquoteright}s, Morse inequalities, Scalar field equations}, issn = {0022-1236}, doi = {https://doi.org/10.1016/j.jfa.2010.07.003}, url = {http://www.sciencedirect.com/science/article/pii/S0022123610002697}, author = {Francesca De Marchis} } @article {2010, title = {On the geometric origin of the bi-Hamiltonian structure of the Calogero-Moser system}, journal = {Int. Math. Res. Not. (2010) 2010:279-296}, number = {arXiv.org;0902.0953v2}, year = {2010}, publisher = {Oxford University Press}, abstract = {We show that the bi-Hamiltonian structure of the rational n-particle (attractive) Calogero-Moser system can be obtained by means of a double projection from a very simple Poisson pair on the cotangent bundle of gl(n,R). The relation with the Lax formalism is also discussed.}, doi = {10.1093/imrn/rnp130}, url = {http://hdl.handle.net/1963/3800}, author = {Claudio Bartocci and Gregorio Falqui and Igor Mencattini and Giovanni Ortenzi and Marco Pedroni} } @article {2010, title = {The geometry emerging from the symmetries of a quantum system}, number = {SISSA;72/2009/FM}, year = {2010}, abstract = {We investigate the relation between the symmetries of a quantum system and its topological quantum numbers, in a general C*-algebraic framework. We prove that, under suitable assumptions on the symmetry algebra, there exists a generalization of the Bloch-Floquet transform which induces a direct-integral decomposition of the algebra of observables. Such generalized transform selects uniquely the set of \\\"continuous sections\\\" in the direct integral, thus yielding a Hilbert bundle. The emerging geometric structure provides some topological invariants of the quantum system. Two running examples provide an Ariadne\\\'s thread through the paper. For the sake of completeness, we review two related theorems by von Neumann and Maurin and compare them with our result.}, url = {http://hdl.handle.net/1963/3834}, author = {Giuseppe De Nittis and Gianluca Panati} } @article {mercuri2010global, title = {A global compactness result for the p-Laplacian involving critical nonlinearities}, journal = {Discrete \& Continuous Dynamical Systems-A}, volume = {28}, number = {2}, year = {2010}, pages = {469{\textendash}493}, abstract = {We prove a representation theorem for Palais-Smale sequences involving the p-Laplacian and critical nonlinearities. Applications are given to a critical problem.\

}, doi = {10.3934/dcds.2010.28.469}, url = {http://www.aimsciences.org/journals/displayArticles.jsp?paperID=5097}, author = {Mercuri, Carlo and Willem, Michel} } @article {2010, title = {Hamiltonian PDEs: deformations, integrability, solutions}, journal = {Journal of Physics A: Mathematical and Theoretical. Volume 43, Issue 43, 29 October 2010, Article number 434002}, year = {2010}, publisher = {SISSA}, abstract = {We review recent classification results on the theory of systems of nonlinear\\r\\nHamiltonian partial differential equations with one spatial dimension, including\\r\\na perturbative approach to the integrability theory of such systems, and discuss\\r\\nuniversality conjectures describing critical behaviour of solutions to such\\r\\nsystems.}, doi = {10.1088/1751-8113/43/43/434002}, url = {http://hdl.handle.net/1963/6469}, author = {Boris Dubrovin} } @article {2010, title = {Hitchin systems, N=2 gauge theories and W-gravity}, journal = {Phys. Lett. B 691 (2010) 111-115}, number = {SISSA;60/2009/EP-FM}, year = {2010}, abstract = {We propose some arguments supporting an M-theory derivation of the duality recently discovered by Alday, Gaiotto and Tachikawa between two-dimensional conformal field theories and N=2 superconformal gauge theories in four dimensions. We find that A_{N-1} Toda field theory is the simplest two-dimensional conformal field theory quantizing the moduli of N M5-branes wrapped on a Riemann surface. This leads us to identify chiral operators of the N=2 gauge theories with W-algebra currents. As a check of this correspondence we study some relevant OPE\\\'s obtaining that Nekrasov\\\'s partition function satisfies W-geometry constraints.}, doi = {10.1016/j.physletb.2010.06.027}, url = {http://hdl.handle.net/1963/3831}, author = {Giulio Bonelli and Alessandro Tanzini} } @article {2010, title = {Homogeneous binary trees as ground states of quantum critical Hamiltonians}, journal = {Phys. Rev. A 81 (2010) 062335}, number = {arXiv.org;0912.0466v2}, year = {2010}, publisher = {American Physical Society}, abstract = {Many-body states whose wave-function admits a representation in terms of a uniform binary-tree tensor decomposition are shown to obey to power-law two-body correlations functions. Any such state can be associated with the ground state of a translational invariant Hamiltonian which, depending on the dimension of the systems sites, involve at most couplings between third-neighboring sites. A detailed analysis of their spectra shows that they admit an exponentially large ground space.

}, doi = {10.1103/PhysRevA.81.062335}, url = {http://hdl.handle.net/1963/3909}, author = {Pietro Silvi and Vittorio Giovannetti and Simone Montangero and Matteo Rizzi and J. Ignacio Cirac and Rosario Fazio} } @article {2010, title = {Homogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems}, journal = {New J. Phys. 12 (2010) 075018}, year = {2010}, publisher = {IOP Publishing}, abstract = {In this paper, we review the properties of homogeneous multiscale entanglement renormalization ansatz (MERA) to describe quantum critical systems.We discuss in more detail our results for one-dimensional (1D) systems (the Ising and Heisenberg models) and present new data for the 2D Ising model. Together with the results for the critical exponents, we provide a detailed description of the numerical algorithm and a discussion of new optimization\\nstrategies. The relation between the critical properties of the system and the tensor structure of the MERA is expressed using the formalism of quantum channels, which we review and extend.

}, doi = {10.1088/1367-2630/12/7/075018}, url = {http://hdl.handle.net/1963/4067}, author = {Matteo Rizzi and Simone Montangero and Pietro Silvi and Vittorio Giovannetti and Rosario Fazio} } @article {2010, title = {Homogenization of fiber reinforced brittle material: the intermediate case}, journal = {Adv. Calc. Var. 3 (2010) 345-370}, number = {SISSA;14/2009/M}, year = {2010}, publisher = {Walter de Gruyter}, abstract = {We derive a cohesive fracture model by homogenizing a periodic composite material whose microstructure is characterized by the presence of brittle inclusions in a reticulated unbreakable elastic structure.}, doi = {10.1515/ACV.2010.011}, url = {http://hdl.handle.net/1963/3607}, author = {Gianni Dal Maso and Caterina Ida Zeppieri} } @article {2010, title = {Invariant Lagrange submanifolds of dissipative systems}, journal = {Russian Mathematical Surveys. Volume 65, Issue 5, 2010, Pages: 977-978}, number = {arXiv:0912.2248;}, year = {2010}, publisher = {SISSA}, abstract = {We study solutions of modified Hamilton-Jacobi equations H(du/dq,q) + cu(q) =\\r\\n0, q \\\\in M, on a compact manifold M .}, doi = {10.1070/RM2010v065n05ABEH004707}, url = {http://hdl.handle.net/1963/6457}, author = {Andrei A. Agrachev} } @article {2010, title = {A kinetic mechanism inducing oscillations in simple chemical reactions networks}, journal = {Mathematical Biosciences and Engineering 7(2):301-312, 2010}, number = {SISSA;82/2007/M}, year = {2010}, publisher = {American Institute of Mathematical Sciences}, abstract = {It is known that a kinetic reaction network in which one or more secondary substrates are acting as cofactors may exhibit an oscillatory behavior. The aim of this work is to provide a description of the functional form of such a cofactor action guaranteeing the\\r\\nonset of oscillations in sufficiently simple reaction networks.}, doi = {10.3934/mbe.2010.7.301}, url = {http://hdl.handle.net/1963/2393}, author = {Julien Coatleven and Claudio Altafini} } @article {2010, title = {Lorentz Covariant k-Minkowski Spacetime}, journal = {Phys. Rev. D 81 (2010) 125024}, number = {SISSA;04/2010/FM}, year = {2010}, abstract = {In recent years, different views on the interpretation of Lorentz covariance of non commuting coordinates were discussed. Here, by a general procedure, we construct the minimal canonical central covariantisation of the k-Minkowski spacetime. We then show that, though the usual k-Minkowski spacetime is covariant under deformed (or twisted) Lorentz action, the resulting framework is equivalent to taking a non covariant restriction of the covariantised model. We conclude with some general comments on the approach of deformed covariance.}, doi = {10.1103/PhysRevD.81.125024}, url = {http://hdl.handle.net/1963/3829}, author = {Ludwik Dabrowski and Michal Godlinski and Gherardo Piacitelli} } @article {2010, title = {Monotonicity, frustration, and ordered response: an analysis of the energy landscape of perturbed large-scale biological networks}, journal = {BMC Systems Biology 2010, 4:83}, year = {2010}, publisher = {BioMed Central}, abstract = {Background. \\nFor large-scale biological networks represented as signed graphs, the index of frustration measures how far a network is from a monotone system, i.e., how incoherently the system responds to perturbations.\\nResults. \\nIn this paper we find that the frustration is systematically lower in transcriptional networks (modeled at functional level) than in signaling and metabolic networks (modeled at stoichiometric level). A possible interpretation of this result is in terms of energetic cost of an interaction: an erroneous or contradictory transcriptional action costs much more than a signaling/metabolic error, and therefore must be avoided as much as possible. Averaging over all possible perturbations, however, we also find that unlike for transcriptional networks, in the signaling/metabolic networks the probability of finding the system in its least frustrated configuration tends to be high also in correspondence of a moderate energetic regime, meaning that, in spite of the higher frustration, these networks can achieve a globally ordered response to perturbations even for moderate values of the strength of the interactions. Furthermore, an analysis of the energy landscape shows that signaling and metabolic networks lack energetic barriers around their global optima, a property also favouring global order.\\nConclusion. \\nIn conclusion, transcriptional and signaling/metabolic networks appear to have systematic differences in both the index of frustration and the transition to global order. These differences are interpretable in terms of the different functions of the various classes of networks.}, doi = {10.1186/1752-0509-4-83}, url = {http://hdl.handle.net/1963/4055}, author = {Giovanni Iacono and Claudio Altafini} } @article {2010, title = {Moore-Read Fractional Quantum Hall wavefunctions and SU(2) quiver gauge theories}, number = {SISSA;14/2010/FM}, year = {2010}, abstract = {We identify Moore-Read wavefunctions, describing non-abelian statistics in fractional quantum Hall systems, with the instanton partition of N=2 superconformal quiver gauge theories at suitable values of masses and \\\\Omega-background parameters. This is obtained by extending to rational conformal field theories the SU(2) gauge quiver/Liouville field theory duality recently found by Alday-Gaiotto-Tachikawa. A direct link between the Moore-Read Hall $n$-body wavefunctions and Z_n-equivariant Donaldson polynomials is pointed out.}, url = {http://hdl.handle.net/1963/3852}, author = {Raoul Santachiara and Alessandro Tanzini} } @mastersthesis {2010, title = {New approximation results for free discontinuity problems}, year = {2010}, type = {Master{\textquoteright}s thesis}, author = {Flaviana Iurlano} } @article {2010, title = {Nonlocal character of the reduced theory of thin films with higher order perturbations}, journal = {Adv. Calc. Var. 3 (2010) 287-319}, number = {SISSA;57/2009/M}, year = {2010}, doi = {10.1515/ACV.2010.012, /July/2010}, url = {http://hdl.handle.net/1963/3754}, author = {Gianni Dal Maso and Irene Fonseca and Giovanni Leoni} } @article {boscain2010normal, title = {A normal form for generic 2-dimensional almost-Riemannian structures at a tangency point}, journal = {arXiv preprint arXiv:1008.5036}, year = {2010}, author = {Ugo Boscain and Gr{\'e}goire Charlot and Roberta Ghezzi} } @article {2010, title = {On the number of positive solutions of some semilinear elliptic problems}, number = {SISSA;66/2010/M}, year = {2010}, url = {http://hdl.handle.net/1963/4083}, author = {Antonio Ambrosetti} } @article {2010, title = {Numerical Solution of the Small Dispersion Limit of the Camassa-Holm and Whitham Equations and Multiscale Expansions}, number = {SISSA;10/2010/FM}, year = {2010}, abstract = {The small dispersion limit of solutions to the Camassa-Holm (CH) equation is characterized by the appearance of a zone of rapid modulated oscillations. An asymptotic description of these oscillations is given, for short times, by the one-phase solution to the CH equation, where the branch points of the corresponding elliptic curve depend on the physical coordinates via the Whitham equations. We present a conjecture for the phase of the asymptotic solution. A numerical study of this limit for smooth hump-like initial data provides strong evidence for the validity of this conjecture....}, url = {http://hdl.handle.net/1963/3840}, author = {Simonetta Abenda and Tamara Grava and Christian Klein} } @article {2010, title = {On optimality of c-cyclically monotone transference plans}, journal = {Comptes Rendus Mathematique 348 (2010) 613-618}, year = {2010}, publisher = {Elsevier}, abstract = {Abstract. This note deals with the equivalence between the optimality of a transport plan for the Monge-Kantorovich problem and the condition of c-cyclical monotonicity, as an outcome of the construction in [7]. We emphasize the measurability assumption on the hidden structure of linear preorder, applied also to extremality and uniqueness problems. Resume. Dans la presente note nous decrivons brievement la construction introduite dans [7] a propos de l\\\'equivalence entre l\\\'optimalite d\\\'un plan de transport pour le probleme de Monge-Kantorovich et la condition de monotonie c-cyclique ainsi que d\\\'autres sujets que cela nous amene a aborder. Nous souhaitons mettre en evidence l\\\'hypothese de mesurabilite sur la structure sous-jacente de pre-ordre lineaire.}, doi = {10.1016/j.crma.2010.03.022}, url = {http://hdl.handle.net/1963/4023}, author = {Stefano Bianchini and Laura Caravenna} } @article {2010, title = {Optimally swimming Stokesian Robots}, number = {SISSA;54/2010/M}, year = {2010}, abstract = {We study self propelled stokesian robots composed of assemblies of balls, in dimen-\\nsions 2 and 3, and prove that they are able to control their position and orientation. This is a result of controllability, and its proof relies on applying Chow\\\'s theorem in an analytic framework, similarly to what has been done in [3] for an axisymmetric system swimming along the axis of symmetry. However, we simplify drastically\\nthe analyticity result given in [3] and apply it to a situation where more complex swimmers move either in a plane or in three-dimensional space, hence experiencing also rotations. We then focus our attention on energetically optimal strokes, which we are able to compute numerically. Some examples of computed optimal strokes are discussed in detail.}, url = {http://hdl.handle.net/1963/3929}, author = {Fran{\c c}ois Alouges and Antonio DeSimone and Luca Heltai and Aline Lefebvre and Benoit Merlet} } @article {2010, title = {Painlev{\'e} II asymptotics near the leading edge of the oscillatory zone for the Korteweg-de Vries equation in the small-dispersion limit}, journal = {Comm. Pure Appl. Math. 63 (2010) 203-232}, number = {arXiv.org;0812.4142v1}, year = {2010}, publisher = {Wiley}, abstract = {In the small dispersion limit, solutions to the Korteweg-de Vries equation develop an interval of fast oscillations after a certain time. We obtain a universal asymptotic expansion for the Korteweg-de Vries solution near the leading edge of the oscillatory zone up to second order corrections. This expansion involves the Hastings-McLeod solution of the Painlev\\\\\\\'e II equation. We prove our results using the Riemann-Hilbert approach.}, doi = {10.1002/cpa.20277}, url = {http://hdl.handle.net/1963/3799}, author = {Tom Claeys and Tamara Grava} } @conference {10.1007/978-90-481-9195-6_4, title = {A Phase Field Approach to Wetting and Contact Angle Hysteresis Phenomena}, booktitle = {IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials}, year = {2010}, pages = {51{\textendash}63}, publisher = {Springer Netherlands}, organization = {Springer Netherlands}, address = {Dordrecht}, abstract = {We discuss a phase field model for the numerical simulation of contact angle hysteresis phenomena in wetting. The performance of the model is assessed by comparing its predictions with experimental data on the critical size of drops that can stick on a vertical glass plate.

}, isbn = {978-90-481-9195-6}, author = {Antonio DeSimone and Livio Fedeli and Turco, Alessandro}, editor = {Hackl, Klaus} } @article {2010, title = {Picard group of hypersurfaces in toric varieties}, number = {SISSA;78/2010/FM}, year = {2010}, abstract = {We show that the usual sufficient criterion for a generic hypersurface in a smooth projective manifold to have the same Picard number as the ambient variety can be generalized to hypersurfaces in complete simplicial toric varieties. This sufficient condition is always satisfied by generic K3 surfaces embedded in Fano toric 3-folds.}, url = {http://hdl.handle.net/1963/4103}, author = {Ugo Bruzzo and Antonella Grassi} } @article {2010, title = {Poles of Integrale Tritronquee and Anharmonic Oscillators. Asymptotic localization from WKB analysis}, journal = {Nonlinearity. vol. 23, (2010), page 2501-2507}, number = {SISSA;11/2010/FM}, year = {2010}, abstract = {Poles of integrale tritronquee are in bijection with cubic oscillators that admit the simultaneous solutions of two quantization conditions. We show that the poles lie near the solutions of a pair of Bohr-Sommerfeld quantization conditions (the Bohr-Sommerfeld-Boutroux system): the distance between a pole and the corresponding solution of the Bohr-Sommerfeld-Boutroux system vanishes asymptotically.

}, doi = {10.1088/0951-7715/23/10/008}, url = {http://hdl.handle.net/1963/3841}, author = {Davide Masoero} } @article {cerami2010positive, title = {Positive solutions for some non-autonomous Schr{\"o}dinger{\textendash}Poisson systems}, journal = {Journal of Differential Equations}, volume = {248}, number = {3}, year = {2010}, pages = {521{\textendash}543}, publisher = {Academic Press}, author = {Giovanna Cerami and Giusi Vaira} } @article {2010, title = {Projective Reeds-Shepp car on $S^2$ with quadratic cost}, journal = {ESAIM COCV 16 (2010) 275-297}, number = {SISSA;34/2008/M}, year = {2010}, abstract = {Fix two points $x,\\\\bar{x}\\\\in S^2$ and two directions (without orientation) $\\\\eta,\\\\bar\\\\eta$ of the velocities in these points. In this paper we are interested to the problem of minimizing the cost $$ J[\\\\gamma]=\\\\int_0^T g_{\\\\gamma(t)}(\\\\dot\\\\gamma(t),\\\\dot\\\\gamma(t))+\\nK^2_{\\\\gamma(t)}g_{\\\\gamma(t)}(\\\\dot\\\\gamma(t),\\\\dot\\\\gamma(t)) ~dt$$ along all smooth curves starting from $x$ with direction $\\\\eta$ and ending in $\\\\bar{x}$ with direction $\\\\bar\\\\eta$. Here $g$ is the standard Riemannian metric on $S^2$ and $K_\\\\gamma$ is the corresponding geodesic curvature.\\nThe interest of this problem comes from mechanics and geometry of vision. It can be formulated as a sub-Riemannian problem on the lens space L(4,1).\\nWe compute the global solution for this problem: an interesting feature is that some optimal geodesics present cusps. The cut locus is a stratification with non trivial topology.}, doi = {10.1051/cocv:2008075}, url = {http://hdl.handle.net/1963/2668}, author = {Ugo Boscain and Francesco Rossi} } @article {2010, title = {Quantum Spacetime: a Disambiguation}, number = {SISSA;27/2010/FM}, year = {2010}, abstract = {We review an approach to non-commutative geometry, where models are constructed by quantisation of the coordinates. In particular we focus on the full DFR model and its irreducible components; the (arbitrary) restriction to a particular irreducible component is often referred to as the \\\"canonical quantum spacetime\\\". The aim is to distinguish and compare the approaches under various points of view, including motivations, prescriptions for quantisation, the choice of mathematical objects and concepts, approaches to dynamics and to covariance. Some incorrect statements as \\\"universality of Planck scale conflicts with Lorentz-Fitzgerald contraction and requires a modification of covariance\\\", or \\\"stability of the geometric background requires an absolute lower bound of (\\\\Delta x^\\\\mu)\\\", or \\\"violations of unitarity are due to time/space non-commutativity\\\" are put in context, and discussed.}, url = {http://hdl.handle.net/1963/3864}, author = {Gherardo Piacitelli} } @article {2010, title = {Quasistatic crack growth in elasto-plastic materials: the two-dimensional case}, journal = {Arch. Ration. Mech. Anal. 196 (2010) 867-906}, number = {SISSA;62/2008/M}, year = {2010}, abstract = {We study a variational model for the quasistatic evolution of elasto-plastic materials with cracks in the case of planar small strain associative elasto-plasticity.}, doi = {10.1007/s00205-009-0258-1}, url = {http://hdl.handle.net/1963/2964}, author = {Gianni Dal Maso and Rodica Toader} } @article {2010, title = {Quasistatic crack growth in finite elasticity with non-interpenetration}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 257-290}, number = {SISSA;80/2008/M}, year = {2010}, abstract = {We present a variational model to study the quasistatic growth of brittle cracks in hyperelastic materials, in the framework of finite elasticity, taking\\ninto account the non-interpenetration condition.

}, doi = {10.1016/j.anihpc.2009.09.006}, url = {http://hdl.handle.net/1963/3397}, author = {Gianni Dal Maso and Giuliano Lazzaroni} } @article {2010, title = {Quasistatic evolution for Cam-Clay plasticity: the spatially homogeneous case}, journal = {Netw. Heterog. Media 5 (2010) 97-132}, number = {SISSA;39/2009/M}, year = {2010}, abstract = {We study the spatially uniform case of the problem of quasistatic evolution in small strain nonassociative elastoplasticity (Cam-Clay model). Through the introdution of a viscous approximation, the problem reduces to determine the limit behavior of the solutions of a singularly perturbed system of ODE\\\'s in a finite dimensional Banach space. Depending on the sign of two explicit scalar indicators, we see that the limit dynamics presents, under quite generic assumptions, the alternation of three possible regimes: the elastic regime, when the limit equation is just the equation of linearized elasticity, the slow dynamics, when the strain evolves smoothly on the yield surface and plastic flow is produced, and the fast dynamics, which may happen only in the softening regime, where\\nviscous solutions exhibit a jump across a heteroclinic orbit of an auxiliary system.

}, keywords = {Cam-Clay plasticity}, doi = {10.3934/nhm.2010.5.97}, url = {http://hdl.handle.net/1963/3671}, author = {Gianni Dal Maso and Francesco Solombrino} } @article {1078-0947_2010_3_1189, title = {Quasistatic evolution for plasticity with softening: The spatially homogeneous case}, journal = {Discrete \& Continuous Dynamical Systems - A}, volume = {27}, number = {1078-0947_2010_3_118}, year = {2010}, pages = {1189}, abstract = {The spatially uniform case of the problem of quasistatic evolution in small strain associative elastoplasticity with softening is studied. Through the introdution of a viscous approximation, the problem reduces to determine the limit behaviour of the solutions of a singularly perturbed system of ODE{\textquoteright}s in a finite dimensional Banach space. We see that the limit dynamics presents, for a generic choice of the initial data, the alternation of three possible regimes (elastic regime, slow dynamics, fast dynamics), which is determined by the sign of two scalar indicators, whose explicit expression is given.

}, keywords = {plasticity with softening, rate independent processes}, issn = {1078-0947}, doi = {10.3934/dcds.2010.27.1189}, url = {http://aimsciences.org//article/id/4c2301d8-f553-493e-b672-b4f76a3ede2f}, author = {Francesco Solombrino} } @article {2010, title = {The reductions of the dispersionless 2D Toda hierarchy and their Hamiltonian structures}, journal = {J. Phys. A 43 (2010) 045201}, number = {arXiv.org;0910.1210v1}, year = {2010}, publisher = {IOP Publishing}, abstract = {We study finite-dimensional reductions of the dispersionless 2D Toda hierarchy showing that the consistency conditions for such reductions are given by a system of radial Loewner equations. We then construct their Hamiltonian structures, following an approach proposed by Ferapontov.}, doi = {10.1088/1751-8113/43/4/045201}, url = {http://hdl.handle.net/1963/3846}, author = {Guido Carlet and Paolo Lorenzoni and Andrea Raimondo} } @article {2010, title = {Riemann-Roch theorems and elliptic genus for virtually smooth schemes}, journal = {Geom. Topol. 14 (2010) 83-115}, number = {arXiv.org;0706.0988v1}, year = {2010}, publisher = {Mathematical Sciences Publishers}, abstract = {For a proper scheme X with a fixed 1-perfect obstruction theory, we define virtual versions of holomorphic Euler characteristic, chi y-genus, and elliptic genus; they are deformation invariant, and extend the usual definition in the smooth case. We prove virtual versions of the Grothendieck-Riemann-Roch and Hirzebruch-Riemann-Roch theorems. We show that the virtual chi y-genus is a polynomial, and use this to define a virtual topological Euler characteristic. We prove that the virtual elliptic genus satisfies a Jacobi modularity property; we state and prove a localization theorem in the toric equivariant case. We show how some of our results apply to moduli spaces of stable sheaves.}, doi = {10.2140/gt.2010.14.83}, url = {http://hdl.handle.net/1963/3888}, author = {Barbara Fantechi and Lothar G{\"o}ttsche} } @article {2010, title = {The role of membrane viscosity in the dynamics of fluid membranes}, number = {SISSA;55/2010/M}, year = {2010}, abstract = {Fluid membranes made out of lipid bilayers are the fundamental separation structure in eukaryotic cells. Many physiological processes rely on dramatic shape and topological changes (e.g. fusion, fission) of fluid membrane systems. Fluidity is key to the versatility and constant reorganization of lipid bilayers. Here, we study the role of the membrane intrinsic viscosity, arising from the friction of the lipid molecules as they rearrange to accommodate shape changes, in the dynamics of morphological changes of fluid vesicles. In particular, we analyze the competition between the membrane viscosity and the viscosity of the bulk fluid surrounding the vesicle as the dominant dissipative mechanism. We consider the relaxation dynamics of fluid vesicles put in an out-of-equilibrium state, but conclusions can be drawn regarding the kinetics or power consumption in regulated shape changes in the cell. On the basis of numerical calculations, we find that the dynamics arising from the membrane viscosity are qualitatively different from the dynamics arising from the bulk viscosity. When these two dissipation mechanisms are put in competition, we find that for small vesicles the membrane dissipation dominates, with a relaxation time that scales as the size of the vesicle to the power 2. For large vesicles, the bulk dissipation dominates, and the exponent in the relaxation time vs. size relation is 3.}, url = {http://hdl.handle.net/1963/3930}, author = {Marino Arroyo and Antonio DeSimone and Luca Heltai} } @article {selvitella2010, title = {Semiclassical evolution of two rotating solitons for the Nonlinear Schr{\"o}dinger Equation with electric potential}, journal = {Adv. Differential Equations}, volume = {15}, number = {3/4}, year = {2010}, month = {03}, pages = {315{\textendash}348}, publisher = {Khayyam Publishing, Inc.}, url = {https://projecteuclid.org:443/euclid.ade/1355854752}, author = {Alessandro Selvitella} } @article {2010, title = {On semistable principal bundles over complex projective manifolds, II}, journal = {Geom. Dedicata 146 (2010) 27-41}, number = {SISSA;85/2008/FM}, year = {2010}, abstract = {Let (X, \\\\omega) be a compact connected Kaehler manifold of complex dimension d and E_G a holomorphic principal G-bundle on X, where G is a connected reductive linear algebraic group defined over C. Let Z (G) denote the center of G. We prove that the following three statements are equivalent: (1) There is a parabolic subgroup P of G and a holomorphic reduction of the structure group of E_G to P (say, E_P) such that the bundle obtained by extending the structure group of E_P to L(P)/Z(G) (where L(P) is the Levi quotient of P) admits a flat connection; (2) The adjoint vector bundle ad(E_G) is numerically flat; (3) The principal G-bundle E_G is pseudostable, and the degree of the charateristic class c_2(ad(E_G) is zero.}, doi = {10.1007/s10711-009-9424-8}, url = {http://hdl.handle.net/1963/3404}, author = {Indranil Biswas and Ugo Bruzzo} } @article {2010, title = {Sharp nonexistence results for a linear elliptic inequality involving Hardy and Leray potentials}, number = {SISSA;31/2010/M}, year = {2010}, abstract = {In this paper we deal with nonnegative distributional supersolutions for a class of linear\\nelliptic equations involving inverse-square potentials and logarithmic weights. We prove sharp nonexistence results.}, url = {http://hdl.handle.net/1963/3869}, author = {Mouhamed Moustapha Fall and Roberta Musina} } @article {2010, title = {Shell theories arising as low energy Gamma-limit of 3d nonlinear elasticity}, journal = {Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. IX (2010) 253-295}, number = {SISSA;12/2008/M}, year = {2010}, abstract = {We discuss the limiting behavior (using the notion of gamma-limit) of the 3d nonlinear elasticity for thin shells around an arbitrary smooth 2d surface. In particular, under the assumption that the elastic energy of deformations scales like h4, h being the thickness of a shell, we derive a limiting theory which is a generalization of the von Karman theory for plates.}, doi = {10.2422/2036-2145.2010.2.02}, url = {http://hdl.handle.net/1963/2601}, author = {Marta Lewicka and Maria Giovanna Mora and Mohammad Reza Pakzad} } @article {Berti2009609, title = {Sobolev periodic solutions of nonlinear wave equations in higher spatial dimensions}, journal = {Archive for Rational Mechanics and Analysis}, volume = {195}, number = {2}, year = {2010}, note = {cited By (since 1996)6}, pages = {609-642}, abstract = {We prove the existence of Cantor families of periodic solutions for nonlinear wave equations in higher spatial dimensions with periodic boundary conditions. We study both forced and autonomous PDEs. In the latter case our theorems generalize previous results of Bourgain to more general nonlinearities of class C k and assuming weaker non-resonance conditions. Our solutions have Sobolev regularity both in time and space. The proofs are based on a differentiable Nash-Moser iteration scheme, where it is sufficient to get estimates of interpolation-type for the inverse linearized operators. Our approach works also in presence of very large "clusters of small divisors". {\textcopyright} Springer-Verlag (2009).}, issn = {00039527}, doi = {10.1007/s00205-008-0211-8}, author = {Massimiliano Berti and Philippe Bolle} } @article {2010, title = {Solitonic asymptotics for the Korteweg-de Vries equation in the small dispersion limit}, journal = {SIAM J. Math. Anal. 42 (2010) 2132-2154}, number = {SISSA;09/2010/FM}, year = {2010}, abstract = {We study the small dispersion limit for the Korteweg-de Vries (KdV) equation $u_t+6uu_x+\\\\epsilon^{2}u_{xxx}=0$ in a critical scaling regime where $x$ approaches the trailing edge of the region where the KdV solution shows oscillatory behavior. Using the Riemann-Hilbert approach, we obtain an asymptotic expansion for the KdV solution in a double scaling limit, which shows that the oscillations degenerate to sharp pulses near the trailing edge. Locally those pulses resemble soliton solutions of the KdV equation.}, doi = {10.1137/090779103}, url = {http://hdl.handle.net/1963/3839}, author = {Tamara Grava and Tom Claeys} } @article {Ballerini_2010, title = {Stable determination of an immersed body in a stationary Stokes fluid}, journal = {Inverse Problems}, volume = {26}, number = {12}, year = {2010}, month = {nov}, pages = {125015}, publisher = {IOP Publishing}, abstract = {We consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the Stokes equations, from a single measurement of force and velocity on a portion of the boundary. We obtain an estimate of the stability of log{\textendash}log type.

}, doi = {10.1088/0266-5611/26/12/125015}, url = {https://doi.org/10.1088\%2F0266-5611\%2F26\%2F12\%2F125015}, author = {Andrea Ballerini} } @article {2010, title = {Taming open/closed string duality with a Losev trick}, journal = {JHEP 06(2010)063}, number = {SISSA;17/2010/FM-EP}, year = {2010}, abstract = {A target space string field theory formulation for open and closed B-model is provided by giving a Batalin-Vilkovisky quantization of the holomorphic Chern-Simons theory with off-shell gravity background. The target space expression for the coefficients of the holomorphic anomaly equation for open strings are obtained. Furthermore, open/closed string duality is proved from a judicious integration over the open string fields. In particular, by restriction to the case of independence on continuous open moduli, the shift formulas of [7] are reproduced and shown therefore to encode the data of a closed string dual.}, doi = {10.1007/JHEP06(2010)063}, url = {http://hdl.handle.net/1963/3855}, author = {Giulio Bonelli and Andrea Prudenziati and Alessandro Tanzini} } @article {FormaggiaEtAlRowing2010, title = {A three-dimensional model for the dynamics and hydrodynamics of rowing boats}, journal = {Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology}, volume = {224}, number = {1}, year = {2010}, pages = {51-61}, abstract = {This paper proposes a new model describing the dynamics of a rowing boat for general three-dimensional motions. The complex interaction between the different components of the rowers{\textendash}-oars{\textendash}-boat system is analysed and reduced to a set of ordinary differential equations governing the rigid motion along the six degrees of freedom. To treat the unstable nature of the physical problem, a rather simple (but effective) control model is included, which mimics the main active control techniques adopted by the rowers during their action.

}, doi = {10.1243/17543371jset46}, url = {https://doi.org/10.1243/17543371jset46}, author = {L. Formaggia and Andrea Mola and N Parolini and M Pischiutta} } @article {2010, title = {A time-dependent perturbative analysis for a quantum particle in a cloud chamber}, journal = {Annales Henri Poincare 11 (2010) 539-564}, number = {arXiv.org;0907.5503v1}, year = {2010}, publisher = {Springer}, abstract = {We consider a simple model of a cloud chamber consisting of a test particle (the alpha-particle) interacting with two other particles (the atoms of the vapour) subject to attractive potentials centered in $a_1, a_2 \\\\in \\\\mathbb{R}^3$. At time zero the alpha-particle is described by an outgoing spherical wave centered in the origin and the atoms are in their ground state. We show that, under suitable assumptions on the physical parameters of the system and up to second order in perturbation theory, the probability that both atoms are ionized is negligible unless $a_2$ lies on the line joining the origin with $a_1$. The work is a fully time-dependent version of the original analysis proposed by Mott in 1929.}, doi = {10.1007/s00023-010-0037-4}, url = {http://hdl.handle.net/1963/3969}, author = {Gianfausto Dell{\textquoteright}Antonio and Rodolfo Figari and Alessandro Teta} } @article {2010, title = {Twisted Covariance as a Non Invariant Restriction of the Fully Covariant DFR Model}, journal = {Comm. Math. Phys. 295 (2010) 701-729}, number = {SISSA;16/2009/FM}, year = {2010}, abstract = {We discuss twisted covariance over the noncommutative spacetime algebra generated by the relations [q_theta^mu,q_theta^nu]=i theta^{mu nu}, where the matrix theta is treated as fixed (not a tensor), and we refrain from using the asymptotic Moyal expansion of the twists. We show that the tensor nature of theta is only hidden in the formalism: in particular if theta fulfils the DFR conditions, the twisted Lorentz covariant model of the flat quantum spacetime may be equivalently described in terms of the DFR model, if we agree to discard a huge non invariant set of localisation states; it is only this last step which, if taken as a basic assumption, severely breaks the relativity principle. We also will show that the above mentioned, relativity breaking, ad hoc rejection of localisation states is an independent, unnecessary assumption, as far as some popular approaches to quantum field theory on the quantum Minkowski spacetime are concerned. The above should raise some concerns about speculations on possible observable consequences of arbitrary choices of theta in arbitrarily selected privileged frames.}, doi = {10.1007/s00220-010-0988-9}, url = {http://hdl.handle.net/1963/3605}, author = {Gherardo Piacitelli} } @article {2010, title = {Two-dimensional almost-Riemannian structures with tangency points}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire }, volume = {27}, number = {arXiv.org;0908.2564v1}, year = {2010}, pages = {793-807}, publisher = {Elsevier}, abstract = {Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We study the relation between the topological invariants of an almost-Riemannian structure on a compact oriented surface and the rank-two vector bundle over the surface which defines the structure. We analyse the generic case including the presence of tangency points, i.e. points where two generators of the distribution and their Lie bracket are linearly dependent. The main result of the paper provides a classification of oriented almost-Riemannian structures on compact oriented surfaces in terms of the Euler number of the vector bundle corresponding to the structure. Moreover, we present a Gauss-Bonnet formula for almost-Riemannian structures with tangency points.

}, doi = {10.1016/j.anihpc.2009.11.011}, url = {http://hdl.handle.net/1963/3870}, author = {Andrei A. Agrachev and Ugo Boscain and Gr{\'e}goire Charlot and Roberta Ghezzi and Mario Sigalotti} } @article {2010, title = {Uhlenbeck-Donaldson compactification for framed sheaves on projective surfaces}, number = {SISSA;59/2010/FM}, year = {2010}, abstract = {We construct a compactification $M^{\\\\mu ss}$ of the Uhlenbeck-Donaldson type for the moduli space of slope stable framed bundles. This is a kind of a moduli space of slope semistable framed sheaves. We show that there exists a projective morphism $\\\\gamma \\\\colon M^s \\\\to M^{\\\\mu ss}$, where $M^s$ is the moduli space of S-equivalence classes of Gieseker-semistable framed sheaves. The space $M^{\\\\mu ss}$ has a natural set-theoretic stratification which allows one, via a Hitchin-Kobayashi correspondence, to compare it with the moduli spaces of framed ideal instantons.}, url = {http://hdl.handle.net/1963/4049}, author = {Ugo Bruzzo and Dimitri Markushevich and Alexander Tikhomirov} } @article {BertolaTovbis1, title = {Universality in the profile of the semiclassical limit solutions to the focusing nonlinear Schr{\"o}dinger equation at the first breaking curve}, journal = {Int. Math. Res. Not. IMRN}, number = {11}, year = {2010}, pages = {2119{\textendash}2167}, issn = {1073-7928}, doi = {10.1093/imrn/rnp196}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1093/imrn/rnp196}, author = {Marco Bertola and Alexander Tovbis} } @article {2010, title = {Well-posed infinite horizon variational problems on a compact manifold}, journal = {Proceedings of the Steklov Institute of Mathematics. Volume 268, Issue 1, 2010, Pages 17-31}, number = {arXiv:0906.4433;}, year = {2010}, publisher = {SISSA}, abstract = {We give an effective sufficient condition for a variational problem with infinite horizon on a compact Riemannian manifold M to admit a smooth optimal synthesis, i. e., a smooth dynamical system on M whose positive semi-trajectories are solutions to the problem. To realize the synthesis, we construct an invariant Lagrangian submanifold (well-projected to M) of the flow of extremals in the cotangent bundle T*M. The construction uses the curvature of the flow in the cotangent bundle and some ideas of hyperbolic dynamics}, doi = {10.1134/S0081543810010037}, url = {http://hdl.handle.net/1963/6458}, author = {Andrei A. Agrachev} } @article {2009, title = {1D periodic potentials with gaps vanishing at k=0}, journal = {Mem. Differential Equations Math. Phys. 47 (2009) 133-158}, number = {SISSA;12/2006/FM}, year = {2009}, abstract = {Appearance of energy bands and gaps in the dispersion relations of a periodic potential is a standard feature of Quantum Mechanics. We investigate the class of one-dimensional periodic potentials for which all gaps vanish at the center of the Brillouin zone. We characterise themthrough a necessary and sufficient condition. Potentials of the form we focus on arise in different fields of Physics, from supersymmetric Quantum Mechanics, to Korteweg-de Vries equation theory and classical diffusion problems. The O.D.E. counterpart to this problem is the characterisation of periodic potentials for which coexistence occurs of linearly independent solutions of the corresponding Schr{\"o}dinger equation (Hill\\\'s equation). This result is placed in the perspective of the previous related results available in the literature.}, url = {http://hdl.handle.net/1963/1818}, author = {Alessandro Michelangeli and Osvaldo Zagordi} } @inbook {2009, title = {Biological Fluid Dynamics, Non-linear Partial Differential Equations}, booktitle = {Encyclopedia of Complexity and Systems Science / Robert A. Meyers (ed.). - Springer, 2009, 548-554}, number = {SISSA;21/2008/M}, year = {2009}, url = {http://hdl.handle.net/1963/2630}, author = {Antonio DeSimone and Fran{\c c}ois Alouges and Aline Lefebvre} } @article {2009, title = {The boundary Riemann solver coming from the real vanishing viscosity approximation}, journal = {Arch. Ration. Mech. Anal. 191 (2009) 1-96}, number = {SISSA;24/2006/M}, year = {2009}, abstract = {We study the limit of the hyperbolic-parabolic approximation $$ \\\\begin{array}{lll} v_t + \\\\tilde{A} ( v, \\\\, \\\\varepsilon v_x ) v_x = \\\\varepsilon \\\\tilde{B}(v ) v_{xx} \\\\qquad v \\\\in R^N\\\\\\\\ \\\\tilde \\\\beta (v (t, \\\\, 0)) = \\\\bar g \\\\\\\\ v (0, \\\\, x) = \\\\bar v_0. \\\\\\\\ \\\\end{array} \\\\right. $$\\nThe function $\\\\tilde \\\\beta$ is defined in such a way to guarantee that the initial boundary value problem is well posed even if $\\\\tilde \\\\beta$ is not invertible.\\nThe data $\\\\bar g$ and $\\\\bar v_0$ are constant. When $\\\\tilde B$ is invertible, the previous problem takes the simpler form $$ \\\\left\\\\{ \\\\begin{array}{lll} v_t + \\\\tilde{A} \\\\big( v, \\\\, \\\\varepsilon v_x \\\\big) v_x = \\\\varepsilon \\\\tilde{B}(v ) v_{xx} \\\\qquad v \\\\in \\\\mathbb{R}^N\\\\\\\\ v (t, \\\\, 0) \\\\equiv \\\\bar v_b \\\\\\\\ v (0, \\\\, x) \\\\equiv \\\\bar{v}_0. \\\\\\\\ \\\\end{array} \\\\right. $$\\nAgain, the data $\\\\bar v_b$ and $\\\\bar v_0$ are constant. The conservative case is included in the previous formulations. It is assumed convergence of the v, smallness of the total variation and other technical hypotheses and it is provided a complete characterization of the limit. The most interesting points are the following two. First, the boundary characteristic case is considered, i.e. one eigenvalue of $\\\\tilde A$ can be 0.\\n Second, as pointed out before we take into account the possibility that $\\\\tilde B$ is not invertible. To deal with this case, we take as hypotheses conditions that were introduced by Kawashima and Shizuta relying on physically meaningful examples. We also introduce a new condition of block linear degeneracy. We prove that, if it is not satisfied, then pathological behaviours may occur.}, doi = {10.1007/s00205-008-0177-6}, url = {http://hdl.handle.net/1963/1831}, author = {Stefano Bianchini and Laura Spinolo} } @article {2009, title = {Bubbles with prescribed mean curvature: the variational approach}, number = {SISSA;35/2009/M}, year = {2009}, note = {H-systems, prescribed mean curvature equation, blowup}, url = {http://hdl.handle.net/1963/3659}, author = {Paolo Caldiroli and Roberta Musina} } @article {Bertola:CauchyMM, title = {The Cauchy two{\textendash}matrix model}, journal = {Comm. Math. Phys.}, volume = {287}, number = {3}, year = {2009}, pages = {983{\textendash}1014}, author = {Marco Bertola and M Gekhtman and J Szmigielski} } @article {2009, title = {Characterization of the time course of changes of the evoked electrical activity in a model of a chemically-induced neuronal plasticity}, journal = {BMC Research Notes (2009) 2:13}, year = {2009}, publisher = {BioMed Central}, abstract = {BACKGROUND: Neuronal plasticity is initiated by transient elevations of neuronal networks activity leading to changes of synaptic properties and providing the basis for memory and learning 1. An increase of electrical activity can be caused by electrical stimulation 2 or by pharmacological manipulations: elevation of extracellular K+ 3, blockage of inhibitory pathways 4 or by an increase of second messengers intracellular concentrations 5. Neuronal plasticity is mediated by several biochemical pathways leading to the modulation of synaptic strength, density of ionic channels and morphological changes of neuronal arborisation 6. On a time scale of a few minutes, neuronal plasticity is mediated by local protein trafficking 7 while, in order to sustain modifications beyond 2-3 h, changes of gene expression are required 8. FINDINGS: In the present manuscript we analysed the time course of changes of the evoked electrical activity during neuronal plasticity and we correlated it with a transcriptional analysis of the underlying changes of gene expression. Our investigation shows that treatment for 30 min. with the GABAA receptor antagonist gabazine (GabT) causes a potentiation of the evoked electrical activity occurring 2-4 hours after GabT and the concomitant up-regulation of 342 genes. Inhibition of the ERK1/2 pathway reduced but did not abolish the potentiation of the evoked response caused by GabT. In fact not all the genes analysed were blocked by ERK1/2 inhibitors. CONCLUSION: These results are in agreement with the notion that neuronal plasticity is mediated by several distinct pathways working in unison.}, doi = {10.1186/1756-0500-2-13}, url = {http://hdl.handle.net/1963/3706}, author = {Frederic D. Broccard and Silvia Pegoraro and Maria Elisabetta Ruaro and Claudio Altafini and Vincent Torre} } @article {BertolaAdvances, title = {Commuting difference operators, spinor bundles and the asymptotics of orthogonal polynomials with respect to varying complex weights}, journal = {Adv. Math.}, volume = {220}, number = {1}, year = {2009}, pages = {154{\textendash}218}, issn = {0001-8708}, author = {Marco Bertola and Mo, M. Y.} } @article {2009, title = {A connection between viscous profiles and singular ODEs}, journal = {Rend. Istit. Mat. Univ. Trieste 41 (2009) 35-41}, number = {SISSA;05/2008/M}, year = {2009}, url = {http://hdl.handle.net/1963/2555}, author = {Stefano Bianchini and Laura Spinolo} } @article {2009, title = {Controllability and simultaneous controllability of isospectral bilinear control systems on complex flag manifolds}, journal = {Systems Control Lett. 58 (2009) 213-216}, year = {2009}, publisher = {Elsevier}, abstract = {For isospectral bilinear control systems evolving on the so-called complex flag manifolds (i.e., on the orbits of the Hermitian matrices under unitary conjugation action) it is shown that controllability is almost always verified. Easy and generic sufficient conditions are provided. The result applies to the problem of density operator controllability of finite dimensional quantum mechanical systems. In addition, we show that systems having different drifts (corresponding for example to different Larmor frequencies) are simultaneously controllable by the same control field.}, doi = {10.1016/j.sysconle.2008.10.008}, url = {http://hdl.handle.net/1963/3523}, author = {Claudio Altafini} } @article {2009, title = {Controllability of the discrete-spectrum Schrodinger equation driven by an external field}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 26 (2009) 329-349}, number = {SISSA;01/2008/M}, year = {2009}, abstract = {We prove approximate controllability of the bilinear Schrodinger equation in the case in which the uncontrolled Hamiltonian has discrete nonresonant\\nspectrum. The results that are obtained apply both to bounded or unbounded domains and to the case in which the control potential is bounded or unbounded. The method relies on finite-dimensional techniques applied to the\\nGalerkin approximations and permits, in addition, to get some controllability properties for the density matrix. Two examples are presented: the harmonic oscillator and the 3D well of potential controlled by suitable potentials.}, doi = {10.1016/j.anihpc.2008.05.001}, url = {http://hdl.handle.net/1963/2547}, author = {Thomas Chambrion and Paolo Mason and Mario Sigalotti and Ugo Boscain} } @article {2009, title = {Controllability on the group of diffeomorphisms}, journal = {Ann. Inst. H. Poincar{\'e} Anal. Non Lin{\'e}aire 26 (2009) 2503-2509}, number = {SISSA;79/2008/M}, year = {2009}, abstract = {Given a compact manifold M, we prove that any bracket generating family of vector fields on M, which is invariant under multiplication by smooth functions, generates the connected component of identity of the group of diffeomorphisms of M.}, doi = {10.1016/j.anihpc.2009.07.003}, url = {http://hdl.handle.net/1963/3396}, author = {Andrei A. Agrachev and Marco Caponigro} } @article {2009, title = {On the convergence of viscous approximations after shock interactions}, journal = {Discrete Contin. Dyn. Syst. 23 (2009) 29-48}, year = {2009}, publisher = {American Institute of Mathematical Sciences}, abstract = {We consider a piecewise smooth solution to a scalar conservation law, with possibly interacting shocks. We show that, after the interactions have taken place, vanishing viscosity approximations can still be represented by a regular expansion on smooth regions and by a singular perturbation expansion near the shocks, in terms of powers of the viscosity coefficient.}, doi = {10.3934/dcds.2009.23.29}, url = {http://hdl.handle.net/1963/3412}, author = {Alberto Bressan and Carlotta Donadello} } @article {Bertola:Cubic, title = {Cubic string boundary value problems and Cauchy biorthogonal polynomials}, journal = {J. Phys. A}, volume = {42}, number = {45}, year = {2009}, pages = {454006, 13}, issn = {1751-8113}, doi = {10.1088/1751-8113/42/45/454006}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1088/1751-8113/42/45/454006}, author = {Marco Bertola and Gekhtman, M. and Szmigielski, J.} } @article {2009, title = {Decoupling A and B model in open string theory: topological adventures in the world of tadpoles}, journal = {JHEP 06 (2009) 046}, number = {SISSA;26/2009/FM-EP}, year = {2009}, abstract = {In this paper we analyze the problem of tadpole cancellation in open topological strings. We prove that the inclusion of unorientable worldsheet diagrams guarantees a consistent decoupling of A and B model for open superstring amplitudes at all genera. This is proven by direct microscopic computation in Super Conformal Field Theory. For the B-model we explicitly calculate one loop amplitudes in terms of analytic Ray-Singer torsions of appropriate vector bundles and obtain that the decoupling corresponds to the cancellation of D-brane and orientifold charges. Local tadpole cancellation on the worldsheet then guarantees the decoupling at all loops. The holomorphic anomaly equations for open topological strings at one loop are also obtained and compared with the results of the Quillen formula.}, doi = {10.1088/1126-6708/2009/06/046}, url = {http://hdl.handle.net/1963/3632}, author = {Giulio Bonelli and Andrea Prudenziati and Alessandro Tanzini and Yang Jie} } @article {2009, title = {Differential geometry of curves in Lagrange Grassmannians with given Young diagram}, journal = {Differential Geom. Appl. 27 (2009) 723-742}, number = {arXiv.org;0708.1100v1}, year = {2009}, publisher = {Elsevier}, abstract = {Curves in Lagrange Grassmannians appear naturally in the intrinsic study of geometric structures on manifolds. By a smooth geometric structure on a manifold we mean any submanifold of its tangent bundle, transversal to the fibers. One can consider the time-optimal problem naturally associate with a geometric structure. The Pontryagin extremals of this optimal problem are integral curves of certain Hamiltonian system in the cotangent bundle. The dynamics of the fibers of the cotangent bundle w.r.t. this system along an extremal is described by certain curve in a Lagrange Grassmannian, called Jacobi curve of the extremal. Any symplectic invariant of the Jacobi curves produces the invariant of the original geometric structure. The basic characteristic of a curve in a Lagrange Grassmannian is its Young diagram. The number of boxes in its kth column is equal to the rank of the kth derivative of the curve (which is an appropriately defined linear mapping) at a generic point. We will describe the construction of the complete system of symplectic invariants for parameterized curves in a Lagrange Grassmannian with given Young diagram. It allows to develop in a unified way local differential geometry of very wide classes of geometric structures on manifolds, including both classical geometric structures such as Riemannian and Finslerian structures and less classical ones such as sub-Riemannian and sub-Finslerian structures, defined on nonholonomic distributions.}, doi = {10.1016/j.difgeo.2009.07.002}, url = {http://hdl.handle.net/1963/3819}, author = {Igor Zelenko and Li Chengbo} } @article {2009, title = {Discrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers}, journal = {Netw. Heterog. Media 4 (2009) 667-708}, year = {2009}, publisher = {American Institute of Mathematical Sciences}, abstract = {In the framework of linear elasticity, we study the limit of a class of discrete free energies modeling strain-alignment-coupled systems by a rigorous coarse-graining procedure, as the number of molecules diverges. We focus on three paradigmatic examples: magnetostrictive solids, ferroelectric crystals and nematic elastomers, obtaining in the limit three continuum models consistent with those commonly employed in the current literature. We also derive the correspondent macroscopic energies in the presence of displacement boundary conditions and of various kinds of applied external fields.}, doi = {10.3934/nhm.2009.4.667}, url = {http://hdl.handle.net/1963/3788}, author = {Marco Cicalese and Antonio DeSimone and Caterina Ida Zeppieri} } @mastersthesis {2009, title = {The Disintegration Theorem and Applications to Optimal Mass Transportation}, year = {2009}, school = {SISSA}, url = {http://hdl.handle.net/1963/5900}, author = {Laura Caravenna} } @article {2009, title = {Equivariant cohomology and localization for Lie algebroids}, journal = {Funct. Anal. Appl. 43 (2009) 18-29}, number = {SISSA;40/2005/FM}, year = {2009}, abstract = {Let M be a manifold carrying the action of a Lie group G, and A a Lie algebroid on M equipped with a compatible infinitesimal G-action. Out of these data we construct an equivariant Lie algebroid cohomology and prove for compact G a related localization formula. As an application we prove a Bott-type formula.}, isbn = {978-981-270-377-4}, doi = {10.1007/s10688-009-0003-4}, url = {http://hdl.handle.net/1963/1724}, author = {Ugo Bruzzo and Lucio Cirio and Paolo Rossi and Vladimir Rubtsov} } @article {2009, title = {ERNEST: a toolbox for chemical reaction network theory}, journal = {Bioinformatics 25 (2009) 2853-2854}, year = {2009}, publisher = {Oxford University Press}, abstract = {Summary: ERNEST Reaction Network Equilibria Study Toolbox is a MATLAB package which, by checking various different criteria on the structure of a chemical reaction network, can exclude the multistationarity of the corresponding reaction system. The results obtained are independent of the rate constants of the reactions, and can be used for model discrimination.\\nAvailability and Implementation: The software, implemented in MATLAB, is available under the GNU GPL free software license from http://people.sissa.it/~altafini/papers/SoAl09/. It requires the MATLAB Optimization Toolbox.}, doi = {10.1093/bioinformatics/btp513}, url = {http://hdl.handle.net/1963/3826}, author = {Nicola Soranzo and Claudio Altafini} } @article {2009, title = {Exact results for topological strings on resolved Yp,q singularities}, journal = {Comm. Math. Phys. 289 (2009) 205-252}, number = {SISSA;22/2008/FM}, year = {2009}, doi = {10.1007/s00220-009-0814-4}, url = {http://hdl.handle.net/1963/2631}, author = {Andrea Brini and Alessandro Tanzini} } @article {2009, title = {Existence of extremals for the Maz\\\'ya and for the Caffarelli-Kohn-Nirenberg inequalities}, journal = {Nonlinear Anal. 70 (2009) 3002-3007}, number = {SISSA;53/2008/M}, year = {2009}, abstract = {This paper deals with some Sobolev-type inequalities with weights that were proved by Maz\\\'ya in 1980 and by Caffarelli-Kohn-Nirenberg in 1984.}, doi = {10.1016/j.na.2008.12.024}, url = {http://hdl.handle.net/1963/2739}, author = {Roberta Musina} } @article {2009, title = {An existence result for the Monge problem in R^n with norm cost}, number = {SISSA;30/2009/M}, year = {2009}, url = {http://hdl.handle.net/1963/3647}, author = {Laura Caravenna} } @article {2009, title = {On the extremality, uniqueness and optimality of transference plans}, journal = {Bull. Inst. Math. Acad. Sin. (N.S.) 4 (2009) 353-458}, number = {SISSA;46/2009/M}, year = {2009}, abstract = {We consider the following standard problems appearing in optimal mass transportation theory: when a transference plan is extremal; when a transference plan is the unique transference plan concentrated on a set A,; when a transference plan is optimal.}, url = {http://hdl.handle.net/1963/3692}, author = {Stefano Bianchini and Laura Caravenna} } @article {2009, title = {Families of Monads and Instantons from a Noncommutative ADHM Construction}, number = {SISSA;59/2008/FM}, year = {2009}, abstract = {We give a \\\\theta-deformed version of the ADHM construction of SU(2) instantons with arbitrary topological charge on the sphere S^4. Classically the instanton gauge fields are constructed from suitable monad data; we show that in the deformed case the set of monads is itself a noncommutative space. We use these monads to construct noncommutative {\textquoteleft}families\\\' of SU(2) instantons on the deformed sphere S^4_\\\\theta. We also compute the topological charge of each of the families. Finally we discuss what it means for such families to be gauge equivalent.}, url = {http://hdl.handle.net/1963/3478}, author = {Simon Brain and Giovanni Landi} } @article {Bertola:Lee, title = {First colonization of a spectral outpost in random matrix theory}, journal = {Constr. Approx.}, volume = {30}, number = {2}, year = {2009}, pages = {225{\textendash}263}, issn = {0176-4276}, doi = {10.1007/s00365-008-9026-y}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00365-008-9026-y}, author = {Marco Bertola and Lee, S. Y.} } @article {fall2009foliations, title = {Foliations of small tubes in Riemannian manifolds by capillary minimal discs}, journal = {Nonlinear Analysis: Theory, Methods \& Applications}, volume = {70}, number = {12}, year = {2009}, pages = {4422{\textendash}4440}, publisher = {Elsevier}, abstract = {Letting\ \ be an embedded curve in a Riemannian manifold\ , we prove the existence of minimal disc-type surfaces centered at\ inside the surface of revolution of\ \ around\ , having small radius, and intersecting it with constant angles. In particular we obtain that small tubular neighborhoods can be foliated by minimal discs.

}, doi = {10.1016/j.na.2008.10.024}, url = {https://doi.org/10.1016/j.na.2008.10.024}, author = {Fall, Mouhamed Moustapha and Mercuri, Carlo} } @article {2009, title = {Gauged Laplacians on quantum Hopf bundles}, journal = {Comm. Math. Phys. 287 (2009) 179-209}, number = {arXiv.org;0801.3376v2}, year = {2009}, publisher = {Springer}, abstract = {We study gauged Laplacian operators on line bundles on a quantum 2-dimensional sphere. Symmetry under the (co)-action of a quantum group allows for their complete diagonalization. These operators describe {\textquoteleft}excitations moving on the quantum sphere\\\' in the field of a magnetic monopole. The energies are not invariant under the exchange monopole/antimonopole, that is under inverting the direction of the magnetic field. There are potential applications to models of quantum Hall effect.}, doi = {10.1007/s00220-008-0672-5}, url = {http://hdl.handle.net/1963/3540}, author = {Giovanni Landi and Cesare Reina and Alessandro Zampini} } @inbook {2009, title = {Hamiltonian perturbations of hyperbolic PDEs: from classification results to the properties of solutions}, booktitle = {New Trends in Mathematical Physics : Selected contributions of the XVth International Congress on Mathematical Physics, Springer Netherlands, 2009, pp. 231-276.}, year = {2009}, publisher = {SISSA}, organization = {SISSA}, abstract = {We begin with presentation of classi cation results in the theory of Hamiltonian\\r\\nPDEs with one spatial dimension depending on a small parameter. Special\\r\\nattention is paid to the deformation theory of integrable hierarchies, including an\\r\\nimportant subclass of the so-called integrable hierarchies of the topological type\\r\\nassociated with semisimple Frobenius manifolds. Many well known equations of\\r\\nmathematical physics, such as KdV, NLS, Toda, Boussinesq etc., belong to this\\r\\nsubclass, but there are many new integrable PDEs, some of them being of interest\\r\\nfor applications. Connections with the theory of Gromov{Witten invariants\\r\\nand random matrices are outlined. We then address the problem of comparative\\r\\nstudy of singularities of solutions to the systems of first order quasilinear\\r\\nPDEs and their Hamiltonian perturbations containing higher derivatives. We\\r\\nformulate Universality Conjectures describing different types of critical behavior\\r\\nof perturbed solutions near the point of gradient catastrophe of the unperturbed\\r\\none.}, isbn = {978-90-481-2810-5}, url = {http://hdl.handle.net/1963/6470}, author = {Boris Dubrovin} } @article {2009, title = {Hardy-Sobolev-Maz\\\'ja inequalities: symmetry and breaking symmetry of extremal functions}, journal = {Commun. Contemp. Math. 11 (2009) 993-1007}, number = {SISSA;06/2008/M}, year = {2009}, doi = {10.1142/S0219199709003636}, url = {http://hdl.handle.net/1963/2569}, author = {Marita Gazzini and Roberta Musina} } @article {2009, title = {A higher order model for image restoration: the one dimensional case}, journal = {SIAM J. Math. Anal. 40 (2009) 2351-2391}, number = {SISSA;66/2008/M}, year = {2009}, abstract = {The higher order total variation-based model for image restoration proposed by Chan, Marquina, and Mulet in [6] is analyzed in one dimension. A suitable functional framework in which the minimization problem is well posed is being proposed and it is proved analytically that the\\nhigher order regularizing term prevents the occurrence of the staircase effect. The generalized version of the model considered here includes, as particular cases, some curvature dependent functionals.}, doi = {10.1137/070697823}, url = {http://hdl.handle.net/1963/3174}, author = {Gianni Dal Maso and Irene Fonseca and Giovanni Leoni and Massimiliano Morini} } @article {2009, title = {Holomorphic equivariant cohomology of Atiyah algebroids and localization}, number = {SISSA;65/2009/FM}, year = {2009}, url = {http://hdl.handle.net/1963/3774}, author = {Ugo Bruzzo and Vladimir Rubtsov} } @article {2009, title = {Homogenization of fiber reinforced brittle materials: the extremal cases}, journal = {SIAM J. Math. Anal. 41 (2009) 1874-1889}, number = {SISSA;49/2008/M}, year = {2009}, publisher = {SIAM}, abstract = {We analyze the behavior of a fragile material reinforced by a reticulated elastic unbreakable structure in the case of antiplane shear. The microscopic geometry of this material is described by means of two small parameters: the period $\\\\varepsilon$ of the grid and the ratio $\\\\delta$ between the thickness of the fibers and the period $\\\\varepsilon$. We show that the asymptotic behavior as $\\\\varepsilon\\\\to0^+$ and $\\\\delta\\\\to0^+$ depends dramatically on the relative size of these parameters. Indeed, in the two cases considered, i.e., $\\\\varepsilon\\\\ll\\\\delta$ and $\\\\varepsilon\\\\gg\\\\delta$, we obtain two different limit models: a perfectly elastic model and an elastic model with macroscopic cracks, respectively.}, url = {http://hdl.handle.net/1963/2705}, author = {Marco Barchiesi and Gianni Dal Maso} } @article {2009, title = {Initial value problem of the Whitham equations for the Camassa-Holm equation}, journal = {Physica D 238 (2009) 55-66}, number = {arXiv.org;0805.2558v1}, year = {2009}, publisher = {Elsevier}, abstract = {We study the Whitham equations for the Camassa-Holm equation. The equations are neither strictly hyperbolic nor genuinely nonlinear. We are interested in the initial value problem of the Whitham equations. When the initial values are given by a step function, the Whitham solution is self-similar. When the initial values are given by a smooth function, the Whitham solution exists within a cusp in the x-t plane. On the boundary of the cusp, the Whitham equation matches the Burgers solution, which exists outside the cusp.}, doi = {10.1016/j.physd.2008.08.016}, url = {http://hdl.handle.net/1963/3429}, author = {Tamara Grava and Virgil U. Pierce and Fei-Ran Tian} } @article {2009, title = {The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups}, journal = {J. Funct. Anal. 256 (2009) 2621-2655}, number = {SISSA;33/2008/M}, year = {2009}, abstract = {We present an invariant definition of the hypoelliptic Laplacian on sub-Riemannian structures with constant growth vector, using the Popp\\\'s volume form introduced by Montgomery. This definition generalizes the one of the Laplace-Beltrami operator in Riemannian geometry. In the case of left-invariant problems on unimodular Lie groups we prove that it coincides with the usual sum of squares.\\nWe then extend a method (first used by Hulanicki on the Heisenberg group) to compute explicitly the kernel of the hypoelliptic heat equation on any unimodular Lie group of type I. The main tool is the noncommutative Fourier transform. We then study some relevant cases: SU(2), SO(3), SL(2) (with the metrics inherited by the Killing form), and the group SE(2) of rototranslations of the plane.\\nOur study is motivated by some recent results about the cut and conjugate loci on these sub-Riemannian manifolds. The perspective is to understand how singularities of the sub-Riemannian distance reflect on the kernel of the corresponding hypoelliptic heat equation.}, doi = {10.1016/j.jfa.2009.01.006}, url = {http://hdl.handle.net/1963/2669}, author = {Andrei A. Agrachev and Ugo Boscain and Jean-Paul Gauthier and Francesco Rossi} } @article {2009, title = {Investigating the Conformational Stability of Prion Strains through a Kinetic Replication Model}, journal = {PLoS Comput Biol 2009;5(7): e1000420}, year = {2009}, publisher = {PLoS}, abstract = {Prion proteins are known to misfold into a range of different aggregated forms, showing different phenotypic and pathological states. Understanding strain specificities is an important problem in the field of prion disease. Little is known about which PrPSc structural properties and molecular mechanisms determine prion replication, disease progression and strain phenotype. The aim of this work is to investigate, through a mathematical model, how the structural stability of different aggregated forms can influence the kinetics of prion replication. The model-based results suggest that prion strains with different conformational stability undergoing in vivo replication are characterizable in primis by means of different rates of breakage. A further role seems to be played by the aggregation rate (i.e. the rate at which a prion fibril grows). The kinetic variability introduced in the model by these two parameters allows us to reproduce the different characteristic features of the various strains (e.g., fibrils\\\' mean length) and is coherent with all experimental observations concerning strain-specific behavior.}, doi = {10.1371/journal.pcbi.1000420}, url = {http://hdl.handle.net/1963/3989}, author = {Mattia Zampieri and Giuseppe Legname and Claudio Altafini} } @article {2009, title = {Jacobi Equations and Comparison Theorems for Corank 1 Sub-Riemannian structures with symmetries}, number = {SISSA;53/2009/M}, year = {2009}, abstract = {The Jacobi curve of an extremal of optimal control problem is a curve in a Lagrangian Grassmannian defined up to a symplectic transformation and containing all information about the solutions of the Jacobi equations along this extremal. In our previous works we constructed the canonical\\nbundle of moving frames and the complete system of symplectic invariants, called curvature maps, for\\nparametrized curves in Lagrange Grassmannians satisfying very general assumptions. The structural\\nequation for a canonical moving frame of the Jacobi curve of an extremal can be interpreted as the\\nnormal form for the Jacobi equation along this extremal and the curvature maps can be seen as the\\n\\\"coefficients\\\"of this normal form. In the case of a Riemannian metric there is only one curvature map and it is naturally related to the Riemannian sectional curvature. In the present paper we study the curvature maps for a sub-Riemannian structure on a corank 1 distribution having an additional transversal infinitesimal symmetry. After the factorization by the integral foliation of this symmetry, such sub-Riemannian structure can be reduced to a Riemannian manifold equipped with a closed 2-form(a magnetic field). We obtain explicit expressions for the curvature maps of the original sub-Riemannian structure in terms of the curvature tensor of this Riemannian manifold and the magnetic field. We also estimate the number of conjugate points along the sub-Riemannian extremals in terms of the bounds for the curvature tensor of this Riemannian manifold and the magnetic field in the case of an uniform magnetic field. The language developed for the calculation of the curvature maps can be applied to more general sub-Riemannian structures with symmetries, including sub-Riemmannian structures appearing naturally in Yang-Mills fields.}, url = {http://hdl.handle.net/1963/3736}, author = {Li Chengbo and Igor Zelenko} } @article {Mola2009, title = {Low-Frequency Variations of Force Coefficients on Square Cylinders with Sharp and Rounded Corners}, journal = {Journal of Structural Engineering}, volume = {135}, number = {7}, year = {2009}, month = {jul}, pages = {828{\textendash}835}, publisher = {American Society of Civil Engineers ({ASCE})}, doi = {10.1061/(asce)st.1943-541x.0000034}, url = {https://doi.org/10.1061/(asce)st.1943-541x.0000034}, author = {Andrea Mola and Giancarlo Bordonaro and Muhammad R. Hajj} } @article {BertolaLeeMo, title = {Mesoscopic colonization in a spectral band}, journal = {J. Phys. A}, volume = {42}, number = {41}, year = {2009}, pages = {415204, 17}, issn = {1751-8113}, doi = {10.1088/1751-8113/42/41/415204}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1088/1751-8113/42/41/415204}, author = {Marco Bertola and Lee, S. Y. and Mo, M. Y.} } @article {fall2009minimal, title = {Minimal disc-type surfaces embedded in a perturbed cylinder}, journal = {Differential and Integral Equations}, volume = {22}, number = {11/12}, year = {2009}, pages = {1115{\textendash}1124}, publisher = {Khayyam Publishing, Inc.}, abstract = {In the present note we deal with small perturbations of an infinite cylinder in the 3D euclidian space. We find minimal disc-type surfaces embedded in the cylinder and intersecting its boundary perpendicularly. The existence and localization of those minimal discs is a consequence of a non-degeneracy condition for the critical points of a functional related to the oscillations of the cylinder from the flat configuration.

}, url = {https://projecteuclid.org/euclid.die/1356019407}, author = {Fall, Mouhamed Moustapha and Mercuri, Carlo} } @article {Formaggia2009, title = {A model for the dynamics of rowing boats}, journal = {International Journal for Numerical Methods in Fluids}, volume = {61}, number = {2}, year = {2009}, month = {sep}, pages = {119{\textendash}143}, publisher = {Wiley}, doi = {10.1002/fld.1940}, url = {https://doi.org/10.1002/fld.1940}, author = {L. Formaggia and Edie Miglio and Andrea Mola and Antonio Montano} } @article {2009, title = {A model for the orbifold Chow ring of weighted projective spaces}, journal = {Comm. Algebra 37 (2009) 503-514}, number = {arXiv.org;0709.4559v1}, year = {2009}, publisher = {Taylor and Francis}, abstract = {We construct an isomorphism of graded Frobenius algebras between the orbifold Chow ring of weighted projective spaces and graded algebras of groups of roots of the unity.}, doi = {10.1080/00927870802248902}, url = {http://hdl.handle.net/1963/3589}, author = {Samuel Boissiere and Etienne Mann and Fabio Perroni} } @article {Bertola:MomentTau, title = {Moment determinants as isomonodromic tau functions}, journal = {Nonlinearity}, volume = {22}, number = {1}, year = {2009}, pages = {29{\textendash}50}, author = {Marco Bertola} } @article {2009, title = {mRNA stability and the unfolding of gene expression in the long-period yeast metabolic cycle}, journal = {BMC Systems Biology (2009) 3:18}, year = {2009}, publisher = {BioMed Central}, abstract = {Background: In yeast, genome-wide periodic patterns associated with energy-metabolic oscillations have been shown recently for both short (approx. 40 min) and long (approx. 300 min) periods.\\nResults: The dynamical regulation due to mRNA stability is found to be an important aspect of the genome-wide coordination of the long-period yeast metabolic cycle. It is shown that for periodic genes, arranged in classes according either to expression profile or to function, the pulses of mRNA abundance have phase and width which are directly proportional to the corresponding turnover rates.\\nConclusion: The cascade of events occurring during the yeast metabolic cycle (and their correlation with mRNA turnover) reflects to a large extent the gene expression program observable in other dynamical contexts such as the response to stresses/stimuli.}, doi = {10.1186/1752-0509-3-18}, url = {http://hdl.handle.net/1963/3630}, author = {Nicola Soranzo and Mattia Zampieri and Lorenzo Farina and Claudio Altafini} } @article {2009, title = {A nonlinear theory for shells with slowly varying thickness}, journal = {C. R. Math. 347 (2009) 211-216}, number = {SISSA;23/2008/M}, year = {2009}, abstract = {We study the Γ-limit of 3d nonlinear elasticity for shells of small, variable thickness, around an arbitrary smooth 2d surface.}, doi = {10.1016/j.crma.2008.12.017}, url = {http://hdl.handle.net/1963/2632}, author = {Marta Lewicka and Maria Giovanna Mora and Mohammad Reza Pakzad} } @article {2009, title = {A note on the paper \\\"Optimizing improved Hardy inequalities\\\" by S. Filippas and A. Tertikas}, journal = {J. Funct. Anal. 256 (2009) 2741-2745}, number = {SISSA;45/2008/M}, year = {2009}, doi = {10.1016/j.jfa.2008.08.009}, url = {http://hdl.handle.net/1963/2698}, author = {Roberta Musina} } @article {2009, title = {Optimal transportation under nonholonomic constraints}, journal = {Trans. Amer. Math. Soc. 361 (2009) 6019-6047}, number = {SISSA;68/2007/M}, year = {2009}, abstract = {We study the Monge\\\'s optimal transportation problem where the cost is given by optimal control cost. We prove the existence and uniqueness of optimal map under certain regularity conditions on the Lagrangian, absolute continuity of the measures and most importantly the absent of sharp abnormal minimizers. In particular, this result is applicable in the case of subriemannian manifolds with a 2-generating distribution and cost given by d2, where d is the subriemannian distance. Also, we discuss some properties of the optimal plan when abnormal minimizers are present. Finally, we consider some examples of displacement interpolation in the case of Grushin plane.}, doi = {10.1090/S0002-9947-09-04813-2}, url = {http://hdl.handle.net/1963/2176}, author = {Andrei A. Agrachev and Paul Lee} } @article {Bertola:IZtau, title = {The partition function of the two-matrix model as an isomonodromic τ function}, journal = {J. Math. Phys.}, volume = {50}, number = {1}, year = {2009}, pages = {013529, 17}, issn = {0022-2488}, doi = {10.1063/1.3054865}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1063/1.3054865}, author = {Marco Bertola and Marchal, O.} } @article {2009, title = {Quasistatic evolution for Cam-Clay plasticity: examples of spatially homogeneous solutions}, journal = {Math. Models Methods Appl. Sci. 19 (2009) 1643-1711}, number = {SISSA;78/2008/M}, year = {2009}, abstract = {We study a quasistatic evolution problem for Cam-Clay plasticity under a special loading program which leads to spatially homogeneous solutions. Under some initial conditions, the solutions exhibit a softening behaviour and time discontinuities.\\nThe behavior of the solutions at the jump times is studied by a viscous approximation.}, doi = {10.1142/S0218202509003942}, url = {http://hdl.handle.net/1963/3395}, author = {Gianni Dal Maso and Antonio DeSimone} } @article {solombrino2009quasistatic, title = {Quasistatic evolution problems for nonhomogeneous elastic plastic materials}, journal = {J. Convex Anal.}, volume = {16}, year = {2009}, pages = {89{\textendash}119}, abstract = {The paper studies the quasistatic evolution for elastoplastic materials when the yield surface depends on the position in the reference configuration. The main results are obtained when the yield surface is continuous with respect to the space variable. The case of piecewise constant dependence is also considered. The evolution is studied in the framework of the variational formulation for rate independent problems developed by Mielke. The results are proved by adapting the arguments introduced for a constant yield surface, using some properties of convex valued semicontinuous multifunctions. A strong formulation of the problem is also obtained, which includes a pointwise version of the plastic flow rule. Some examples are considered, which show that strain concentration may occur as a consequence of a nonconstant yield surface.

}, author = {Francesco Solombrino} } @article {BertolaBalogh, title = {Regularity of a vector potential problem and its spectral curve}, journal = {J. Approx. Theory}, volume = {161}, number = {1}, year = {2009}, pages = {353{\textendash}370}, issn = {0021-9045}, doi = {10.1016/j.jat.2008.10.010}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1016/j.jat.2008.10.010}, author = {Ferenc Balogh and Marco Bertola} } @article {2009, title = {Relaxation dynamics of fluid membranes}, journal = {Phys. Rev. E 79 (2009) 031915}, year = {2009}, publisher = {American Physical Society}, abstract = {We study the effect of membrane viscosity in the dynamics of liquid membranes-possibly with free or internal boundaries-driven by conservative forces (curvature elasticity and line tension) and dragged by the bulk dissipation of the ambient fluid and the friction occurring when the amphiphilic molecules move relative to each other. To this end, we formulate a continuum model which includes a form of the governing equations for a two-dimensional viscous fluid moving on a curved, time-evolving surface. The effect of membrane viscosity has received very limited attention in previous continuum studies of the dynamics of fluid membranes, although recent coarse-grained discrete simulations suggest its importance. By applying our model to the study of vesiculation and membrane fusion in a simplified geometry, we conclude that membrane viscosity plays a dominant role in the relaxation dynamics of fluid membranes of sizes comparable to those found in eukaryotic cells, and is not negligible in many large synthetic systems of current interest.}, doi = {10.1103/PhysRevE.79.031915}, url = {http://hdl.handle.net/1963/3618}, author = {Marino Arroyo and Antonio DeSimone} } @article {2009, title = {On a Sobolev type inequality related to the weighted p-Laplace operator}, journal = {J. Math. Anal. Appl. 352 (2009) 99-111}, number = {SISSA;18/2008/M}, year = {2009}, doi = {10.1016/j.jmaa.2008.06.021}, url = {http://hdl.handle.net/1963/2613}, author = {Marita Gazzini and Roberta Musina} } @article {doi:10.1142/S0218202509003589, title = {Solutions of the Schr{\"o}dinger{\textendash}Poisson problem concentrating on spheres, part I: necessary conditions}, journal = {Mathematical Models and Methods in Applied Sciences}, volume = {19}, number = {05}, year = {2009}, pages = {707-720}, abstract = {In this paper we study a coupled nonlinear Schr{\"o}dinger{\textendash}Poisson problem with radial functions. This system has been introduced as a model describing standing waves for the nonlinear Schr{\"o}dinger equations in the presence of the electrostatic field. We provide necessary conditions for concentration on sphere for the solutions of this kind of problem extending the results already known.

}, doi = {10.1142/S0218202509003589}, url = {https://doi.org/10.1142/S0218202509003589}, author = {Ianni, Isabella and Giusi Vaira} } @article {2009, title = {Some new entire solutions of semilinear elliptic equations on Rn}, journal = {Adv. Math. 221 (2009) 1843-1909}, year = {2009}, publisher = {Elsevier}, doi = {10.1016/j.aim.2009.03.012}, url = {http://hdl.handle.net/1963/3645}, author = {Andrea Malchiodi} } @article {2009, title = {Strain-order coupling in nematic elastomers: equilibrium configurations}, journal = {Math. Models Methods Appl. Sci. 19 (2009) 601-630}, number = {SISSA;24/2008/M}, year = {2009}, abstract = {We consider models that describe liquid crystal elastomers either in a biaxial or in a uniaxial phase and in the framework of Frank\\\'s director theory. We prove existence of static equilibrium solutions in the presence of frustrations due to electro-mechanical boundary conditions and to applied loads and fields. We find explicit solutions arising in connection with special boundary conditions and the corresponding phase diagrams, leading to significant implications on possible experimental observations.}, url = {http://hdl.handle.net/1963/2700}, author = {Pierluigi Cesana and Antonio DeSimone} } @article {2009, title = {Stratos: a code for 3D free surface flows with floating constraints}, number = {SISSA;41/2009/M}, year = {2009}, abstract = {This report presents a brief discussion of the theoretical aspects and practical implementation of STRATOS . STRATOS is a 3D code for the simulation\\nof hydrodynamic flows for incompressible fluids, in the presence of a free surface, capable of simulating the interaction between the free surface and a\\nfloating object via Lagrange multipliers......}, url = {http://hdl.handle.net/1963/3701}, author = {Antonio DeSimone and B. Bianchi and Luca Heltai} } @article {2009, title = {Tools for the Solution of PDEs Defined on Curved Manifolds with deal.II}, number = {SISSA;42/2009/M}, year = {2009}, abstract = {The deal.II finite element library was originally designed to solve partial differential equations defined on one, two or three space dimensions, mostly\\nvia the Finite Element Method. In its versions prior to version 6.2, the user could not solve problems defined on curved manifolds embedded in two or\\nthree spacial dimensions. This infrastructure is needed if one wants to solve, for example, Boundary Integral Equations.}, url = {http://hdl.handle.net/1963/3700}, author = {Antonio DeSimone and Luca Heltai and Cataldo Manigrasso} } @article {2009, title = {Topological branes, p-algebras and generalized Nahm equations}, journal = {Phys. Lett. B 672 (2009) 390-395}, number = {SISSA;47/2008/FM}, year = {2009}, abstract = {Inspired by the recent advances in multiple M2-brane theory, we consider the generalizations of Nahm equations for arbitrary p-algebras. We construct the topological p-algebra quantum mechanics associated to them and we show that this can be obtained as a truncation of the topological p-brane theory previously studied by the authors. The resulting topological p-algebra quantum mechanics is discussed in detail and the relation with the M2-M5 system is pointed out in the p=3 case, providing a geometrical argument for the emergence of the 3-algebra structure in the Bagger-Lambert-Gustavsson theory}, doi = {10.1016/j.physletb.2009.01.051}, url = {http://hdl.handle.net/1963/2702}, author = {Giulio Bonelli and Alessandro Tanzini and Maxim Zabzine} } @article {MR2525872, title = {Topological expansion for the Cauchy two-matrix model}, journal = {J. Phys. A}, volume = {42}, number = {33}, year = {2009}, pages = {335201, 28}, issn = {1751-8113}, doi = {10.1088/1751-8113/42/33/335201}, url = {http://dx.doi.org/10.1088/1751-8113/42/33/335201}, author = {Marco Bertola and Ferrer, A. Prats} } @article {2009, title = {Twisted Covariance vs Weyl Quantisation}, number = {SISSA;13/2009/FM}, year = {2009}, abstract = {In this letter we wish to clarify in which sense the tensor nature of the commutation relations [x^mu,x^nu]=i theta ^{mu nu} underlying Minkowski spacetime quantisation cannot be suppressed even in the twisted approach to Lorentz covariance. We then address the vexata quaestio \\\"why theta\\\"?}, url = {http://hdl.handle.net/1963/3451}, author = {Gherardo Piacitelli} } @article {2009, title = {On universality of critical behaviour in the focusing nonlinear Schr{\"o}dinger equation, elliptic umbilic catastrophe and the {\\\\it tritronqu{\'e}e} solution to the Painlev{\'e}-I equation}, journal = {J. Nonlinear Sci. 19 (2009) 57-94}, number = {arXiv.org;0704.0501}, year = {2009}, abstract = {We argue that the critical behaviour near the point of {\textquoteleft}{\textquoteleft}gradient catastrophe\\\" of the solution to the Cauchy problem for the focusing nonlinear Schr\\\\\\\"odinger equation $ i\\\\epsilon \\\\psi_t +\\\\frac{\\\\epsilon^2}2\\\\psi_{xx}+ |\\\\psi|^2 \\\\psi =0$ with analytic initial data of the form $\\\\psi(x,0;\\\\epsilon) =A(x) e^{\\\\frac{i}{\\\\epsilon} S(x)}$ is approximately described by a particular solution to the Painlev\\\\\\\'e-I equation.}, doi = {10.1007/s00332-008-9025-y}, url = {http://hdl.handle.net/1963/2525}, author = {Boris Dubrovin and Tamara Grava and Christian Klein} } @article {2009, title = {Universality of the break-up profile for the KdV equation in the small dispersion limit using the Riemann-Hilbert approach}, journal = {Comm. Math. Phys. 286 (2009) 979-1009}, number = {arXiv.org;0801.2326}, year = {2009}, abstract = {We obtain an asymptotic expansion for the solution of the Cauchy problem for the Korteweg-de Vries (KdV) equation in the small dispersion limit near the point of gradient catastrophe (x_c,t_c) for the solution of the dispersionless equation.\\nThe sub-leading term in this expansion is described by the smooth solution of a fourth order ODE, which is a higher order analogue to the Painleve I equation. This is in accordance with a conjecture of Dubrovin, suggesting that this is a universal phenomenon for any Hamiltonian perturbation of a hyperbolic equation. Using the Deift/Zhou steepest descent method applied on the Riemann-Hilbert problem for the KdV equation, we are able to prove the asymptotic expansion rigorously in a double scaling limit.}, doi = {10.1007/s00220-008-0680-5}, url = {http://hdl.handle.net/1963/2636}, author = {Tamara Grava and Tom Claeys} } @article {2009, title = {A variational model for quasistatic crack growth in nonlinear elasticity: some qualitative properties of the solutions}, journal = {Boll. Unione Mat. Ital. (9) 2 (2009) 371-390}, number = {SISSA;41/2008/M}, year = {2009}, url = {http://hdl.handle.net/1963/2675}, author = {Gianni Dal Maso and Alessandro Giacomini and Marcello Ponsiglione} } @article {2009, title = {On viscosity solutions of Hamilton-Jacobi equations}, journal = {Trans. Amer. Math. Soc. 361 (2009) 41-59}, year = {2009}, publisher = {American Mathematical Society}, abstract = {We consider the Dirichlet problem for Hamilton-Jacobi equations and prove existence, uniqueness and continuous dependence on boundary data of Lipschitz continuous maximal viscosity solutions.}, doi = {10.1090/S0002-9947-08-04557-1}, url = {http://hdl.handle.net/1963/3420}, author = {Sandro Zagatti} } @article {SELVITELLA20082566, title = {Asymptotic evolution for the semiclassical nonlinear Schr{\"o}dinger equation in presence of electric and magnetic fields}, journal = {Journal of Differential Equations}, volume = {245}, number = {9}, year = {2008}, pages = {2566 - 2584}, abstract = {In this paper we study the semiclassical limit for the solutions of a subcritical focusing NLS with electric and magnetic potentials. We consider in particular the Cauchy problem for initial data close to solitons and show that, when the Planck constant goes to zero, the motion shadows that of a classical particle. Several works were devoted to the case of standing waves: differently from these we show that, in the dynamic version, the Lorentz force appears crucially.

}, issn = {0022-0396}, doi = {https://doi.org/10.1016/j.jde.2008.05.012}, url = {http://www.sciencedirect.com/science/article/pii/S002203960800243X}, author = {Alessandro Selvitella} } @article {Berti2008151, title = {Cantor families of periodic solutions for completely resonant wave equations}, journal = {Frontiers of Mathematics in China}, volume = {3}, number = {2}, year = {2008}, note = {cited By (since 1996)0}, pages = {151-165}, abstract = {We present recent existence results of Cantor families of small amplitude periodic solutions for completely resonant nonlinear wave equations. The proofs rely on the Nash-Moser implicit function theory and variational methods. {\textcopyright} 2008 Higher Education Press.}, issn = {16733452}, doi = {10.1007/s11464-008-0011-3}, author = {Massimiliano Berti and Philippe Bolle} } @article {Berti20081671, title = {Cantor families of periodic solutions for wave equations via a variational principle}, journal = {Advances in Mathematics}, volume = {217}, number = {4}, year = {2008}, note = {cited By (since 1996)6}, pages = {1671-1727}, abstract = {We prove existence of small amplitude periodic solutions of completely resonant wave equations with frequencies in a Cantor set of asymptotically full measure, via a variational principle. A Lyapunov-Schmidt decomposition reduces the problem to a finite dimensional bifurcation equation-variational in nature-defined on a Cantor set of non-resonant parameters. The Cantor gaps are due to "small divisors" phenomena. To solve the bifurcation equation we develop a suitable variational method. In particular, we do not require the typical "Arnold non-degeneracy condition" of the known theory on the nonlinear terms. As a consequence our existence results hold for new generic sets of nonlinearities. {\textcopyright} 2007 Elsevier Inc. All rights reserved.}, issn = {00018708}, doi = {10.1016/j.aim.2007.11.004}, author = {Massimiliano Berti and Philippe Bolle} } @article {Berti2008247, title = {Cantor families of periodic solutions of wave equations with C k nonlinearities}, journal = {Nonlinear Differential Equations and Applications}, volume = {15}, number = {1-2}, year = {2008}, note = {cited By (since 1996)10}, pages = {247-276}, abstract = {We prove bifurcation of Cantor families of periodic solutions for wave equations with nonlinearities of class C k . It requires a modified Nash-Moser iteration scheme with interpolation estimates for the inverse of the linearized operators and for the composition operators. {\textcopyright} 2008 Birkhaueser.}, issn = {10219722}, doi = {10.1007/s00030-007-7025-5}, author = {Massimiliano Berti and Philippe Bolle} } @article {2008, title = {Concentrating solutions of some singularly perturbed elliptic equations}, journal = {Front. Math. China 3 (2008) 239-252}, year = {2008}, abstract = {We study singularly perturbed elliptic equations arising from models in physics or biology, and investigate the asymptotic behavior of some special solutions. We also discuss some connections with problems arising in differential geometry.}, doi = {10.1007/s11464-008-0015-z}, url = {http://hdl.handle.net/1963/2657}, author = {Andrea Malchiodi} } @article {ianni2008concentration, title = {On concentration of positive bound states for the Schr{\"o}dinger-Poisson problem with potentials}, journal = {Advanced nonlinear studies}, volume = {8}, number = {3}, year = {2008}, pages = {573{\textendash}595}, publisher = {Advanced Nonlinear Studies, Inc.}, abstract = {We study the existence of semiclassical states for a nonlinear Schr{\"o}dinger-Poisson system that concentrate near critical points of the external potential and of the density charge function. We use a perturbation scheme in a variational setting, extending the results in [1]. We also discuss necessary conditions for concentration.

}, doi = {10.1515/ans-2008-0305.}, author = {Ianni, Isabella and Giusi Vaira} } @article {2008, title = {Convergence of equilibria of three-dimensional thin elastic beams}, journal = {Proc. Roy. Soc. Edinburgh Sect. A 138 (2008) 873-896}, number = {SISSA;69/2006/M}, year = {2008}, abstract = {A convergence result is proved for the equilibrium configurations of a three-dimensional thin elastic beam, as the diameter $h$ of the cross-section tends to zero. More precisely, we show that stationary points of the nonlinear elastic functional $E^h$, whose energies (per unit cross-section) are bounded by $Ch^2$, converge to stationary points of the $\\\\varGamma$-limit of $E^h/h^2$. This corresponds to a nonlinear one-dimensional model for inextensible rods, describing bending and torsion effects. The proof is based on the rigidity estimate for low-energy deformations by Friesecke, James and M{\"u}ller and on a compensated compactness argument in a singular geometry. In addition, possible concentration effects of the strain are controlled by a careful truncation argument.}, doi = {10.1017/S0308210506001120}, url = {http://hdl.handle.net/1963/1896}, author = {Maria Giovanna Mora and Stefan M{\"u}ller} } @article {2008, title = {Decomposition results for functions with bounded variation}, journal = {Boll. Unione Mat. Ital. (9) 1 (2008) 497-505}, year = {2008}, publisher = {Unione Matematica Italiana}, url = {http://hdl.handle.net/1963/3535}, author = {Gianni Dal Maso and Rodica Toader} } @article {2008, title = {Discerning static and causal interactions in genome-wide reverse engineering problems}, journal = {Bioinformatics 24 (2008) 1510-1515}, year = {2008}, abstract = {Background. In the past years devicing methods for discovering gene regulatory mechanisms at a genome-wide level has become a fundamental topic in the field of system biology. The aim is to infer gene-gene interactions in a more sophisticated and reliable way through the continuously improvement of reverse engineering algorithms exploiting microarray technologies. Motivation. This work is inspired by the several studies suggesting that co-expression is mostly related to \\\"static\\\" stable binding relationships, like belonging to the same protein complex, rather than other types of interactions more of a \\\"causal\\\" and transient nature (metabolic pathway or transcription factor-binding site interaction). Discerning static relationships from causal ones on the basis of their characteristic regulatory structures and in particular identifing \\\"dense modules\\\" with protein complex, and \\\"sparse modules\\\" with causal interactions such as those between transcription factor and corresponding binding site, the performances of different network inference algorithms in artificial and real networks (derived from E.coli and S.cerevisiae) can be tested and compared. Results. Our study shows that methods that try to prune indirect interactions from the inferred gene networks may fail to retrieve genes co-participating in a protein complex. On the other hand they are more robust in the identification of transcription factor-binding sites dependences when multiple transcription factors regulate the expression of the same gene. In the end we confirm the stronger co-expression regarding genes belonging to a protein complex than transcription factor-binding site, according, also, to the effect of multiple transcription factors and a low expression variance.}, doi = {10.1093/bioinformatics/btn220}, url = {http://hdl.handle.net/1963/2757}, author = {Mattia Zampieri and Nicola Soranzo and Claudio Altafini} } @article {2008, title = {Entire solutions of autonomous equations on Rn with nontrivial asymptotics}, journal = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 19 (2008) 65-72}, year = {2008}, abstract = {We prove existence of a new type of solutions for the semilinear equation $- \\\\D u + u = u^p$ on $\\\\R^n$, with $1 < p < \\\\frac{n+2}{n-2}$. These solutions are positive, bounded, decay exponentially to zero away from three half-lines with a common origin, and at infinity are asymptotically periodic.}, url = {http://hdl.handle.net/1963/2640}, author = {Andrea Malchiodi} } @article {2008, title = {An entropy based Glimm-type functional}, journal = {J. Hyperbolic Differ. Equ. 5 (2008) 643-662}, year = {2008}, publisher = {World Scientific}, doi = {10.1142/S0219891608001635}, url = {http://hdl.handle.net/1963/4051}, author = {Laura Caravenna} } @article {2008, title = {Equivalent definitions of asymptotic 100\% B.E.C.}, journal = {Nuovo Cimento B 123 (2008) 181-192}, number = {SISSA;102/2007/MP}, year = {2008}, abstract = {In the mathematical analysis Bose-Einstein condensates, in particular in the study of the quantum dynamics, some kind of factorisation property has been recently proposed as a convenient technical assumption of condensation. After having surveyed both the standard definition of complete Bose-Einstein condensation in the limit of infinitely many particles and some forms of asymptotic factorisation, we prove that these characterisations are equivalent.}, doi = {10.1393/ncb/i2008-10521-y}, url = {http://hdl.handle.net/1963/2546}, author = {Alessandro Michelangeli} } @article {2008, title = {Eulerian calculus for the displacement convexity in the Wasserstein distance}, journal = {SIAM J. Math. Anal. 40 (2008) 1104-1122}, number = {arXiv.org;0801.2455v1}, year = {2008}, publisher = {SIAM}, abstract = {In this paper we give a new proof of the (strong) displacement convexity of a class of integral functionals defined on a compact Riemannian manifold satisfying a lower Ricci curvature bound. Our approach does not rely on existence and regularity results for optimal transport maps on Riemannian manifolds, but it is based on the Eulerian point of view recently introduced by Otto and Westdickenberg [SIAM J. Math. Anal., 37 (2005), pp. 1227-1255] and on the metric characterization of the gradient flows generated by the functionals in the Wasserstein space.}, doi = {10.1137/08071346X}, url = {http://hdl.handle.net/1963/3413}, author = {Sara Daneri and Giuseppe Savar{\`e}} } @article {2008, title = {Existence of conformal metrics with constant $Q$-curvature}, journal = {Ann. of Math. 168 (2008) 813-858}, number = {SISSA;70/2004/M}, year = {2008}, abstract = {Given a compact four dimensional manifold, we prove existence of conformal metrics with constant $Q$-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure. Since the corresponding Euler functional is in general unbounded from above and from below, we employ topological methods and minimax schemes, jointly with a compactness result by the second author.}, url = {http://hdl.handle.net/1963/2308}, author = {Zindine Djadli and Andrea Malchiodi} } @article {Formaggia2008, title = {Fluid{\textendash}structure interaction problems in free surface flows: Application to boat dynamics}, journal = {International Journal for Numerical Methods in Fluids}, volume = {56}, number = {8}, year = {2008}, pages = {965{\textendash}978}, publisher = {Wiley}, doi = {10.1002/fld.1583}, url = {https://doi.org/10.1002/fld.1583}, author = {L. Formaggia and Edie Miglio and Andrea Mola and N Parolini} } @article {2008, title = {Forced Vibrations of a Nonhomogeneous String}, journal = {SIAM J. Math. Anal. 40 (2008) 382-412}, number = {SISSA;36/2006/M}, year = {2008}, abstract = {We prove existence of vibrations of a nonhomogeneous string under a nonlinear time periodic forcing term in the case in which the forcing frequency avoids resonances with the vibration modes of the string (nonresonant case). The proof relies on a Lyapunov-Schmidt reduction and a Nash-Moser iteration scheme.}, doi = {10.1137/060665038}, url = {http://hdl.handle.net/1963/2643}, author = {P Baldi and Massimiliano Berti} } @article {2008, title = {Frobenius Manifolds and Central Invariants for the Drinfeld - Sokolov Bihamiltonian Structures}, journal = {Adv. Math. 219 (2008) 780-837}, number = {arXiv.org;0710.3115}, year = {2008}, abstract = {The Drinfeld - Sokolov construction associates a hierarchy of bihamiltonian integrable systems with every untwisted affine Lie algebra. We compute the complete set of invariants of the related bihamiltonian structures with respect to the group of Miura type transformations.}, doi = {10.1016/j.aim.2008.06.009}, url = {http://hdl.handle.net/1963/2523}, author = {Boris Dubrovin and Liu Si-Qi and Zhang Youjin} } @article {2008, title = {Fulde-Ferrell-Larkin-Ovchinnikov pairing in one-dimensional optical lattices}, journal = {Phys. Rev. B 77 (2008) 245105}, number = {arXiv.org;0712.3364v1}, year = {2008}, abstract = {Spin-polarized attractive Fermi gases in one-dimensional (1D) optical lattices are expected to be remarkably good candidates for the observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We model these systems with an attractive Hubbard model with population imbalance. By means of the density-matrix renormalization-group method we compute the pairing correlations as well as the static spin and charge structure factors in the whole range from weak to strong coupling. We demonstrate that pairing correlations exhibit quasi-long range order and oscillations at the wave number expected from FFLO theory. However, we also show by numerically computing the mixed spin-charge static structure factor that charge and spin degrees of freedom appear to be coupled already for small imbalance. We discuss the consequences of this coupling for the observation of the FFLO phase, as well as for the stabilization of the quasi-long range order into long-range order by coupling many identical 1D systems, as in quasi-1D optical lattices.

}, doi = {10.1103/PhysRevB.77.245105}, url = {http://hdl.handle.net/1963/2694}, author = {Matteo Rizzi and Marco Polini and Miguel A. Cazalilla and M.R. Bakhtiari and Mario P. Tosi and Rosario Fazio} } @article {2008, title = {A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds}, journal = {Discrete Contin. Dyn. Syst. 20 (2008) 801-822}, number = {SISSA;55/2006/M}, year = {2008}, abstract = {We consider a generalization of Riemannian geometry that naturally arises in the framework of control theory. Let $X$ and $Y$ be two smooth vector fields on a two-dimensional manifold $M$. If $X$ and $Y$ are everywhere linearly independent, then they define a classical Riemannian metric on $M$ (the metric for which they are orthonormal) and they give to $M$ the structure of metric space. If $X$ and $Y$ become linearly dependent somewhere on $M$, then the corresponding Riemannian metric has singularities, but under generic conditions the metric structure is still well defined. Metric structures that can be defined locally in this way are called almost-Riemannian structures. They are special cases of rank-varying sub-Riemannian structures, which are naturally defined in terms of submodules of the space of smooth vector fields on $M$. Almost-Riemannian structures show interesting phenomena, in particular for what concerns the relation between curvature, presence of conjugate points, and topology of the manifold. The main result of the paper is a generalization to almost-Riemannian structures of the Gauss-Bonnet formula.}, doi = {10.3934/dcds.2008.20.801}, url = {http://hdl.handle.net/1963/1869}, author = {Andrei A. Agrachev and Ugo Boscain and Mario Sigalotti} } @article {2008, title = {Globally stable quasistatic evolution in plasticity with softening}, journal = {Netw. Heterog. Media 3 (2008) 567-614}, number = {SISSA;23/2007/M}, year = {2008}, abstract = {We study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is characterized by the following properties: global stability at each time and energy balance on each\\ntime interval. An example developed in detail compares the solutions obtained by this method with the ones provided by a vanishing viscosity approximation, and shows that only the latter capture a decreasing branch in the stress-strain response.}, url = {http://hdl.handle.net/1963/1965}, author = {Gianni Dal Maso and Antonio DeSimone and Maria Giovanna Mora and Massimiliano Morini} } @article {2008, title = {Gradient bounds for minimizers of free discontinuity problems related to cohesive zone models in fracture mechanics}, journal = {Calc. Var. Partial Differential Equations 31 (2008) 137-145}, number = {SISSA;50/2005/M}, year = {2008}, abstract = {In this note we consider a free discontinuity problem for a scalar function, whose energy depends also on the size of the jump. We prove that the gradient of every smooth local minimizer never exceeds a constant, determined only by the data of the problem.}, doi = {10.1007/s00526-006-0084-3}, url = {http://hdl.handle.net/1963/1723}, author = {Gianni Dal Maso and Adriana Garroni} } @article {2008, title = {Hamiltonian partial differential equations and Frobenius manifolds}, journal = {Russian Mathematical Surveys. Volume 63, Issue 6, 2008, Pages 999-1010}, year = {2008}, publisher = {SISSA}, abstract = {In the first part of this paper the theory of Frobenius manifolds\\r\\nis applied to the problem of classification of Hamiltonian systems of partial\\r\\ndifferential equations depending on a small parameter. Also developed is\\r\\na deformation theory of integrable hierarchies including the subclass of\\r\\nintegrable hierarchies of topological type. Many well-known examples\\r\\nof integrable hierarchies, such as the Korteweg{\textendash}de Vries, non-linear\\r\\nSchr{\textasciidieresis}odinger, Toda, Boussinesq equations, and so on, belong to this\\r\\nsubclass that also contains new integrable hierarchies. Some of these new\\r\\nintegrable hierarchies may be important for applications. Properties of the\\r\\nsolutions to these equations are studied in the second part. Consideration\\r\\nis given to the comparative study of the local properties of perturbed and\\r\\nunperturbed solutions near a point of gradient catastrophe. A Universality\\r\\nConjecture is formulated describing the various types of critical behaviour\\r\\nof solutions to perturbed Hamiltonian systems near the point of gradient\\r\\ncatastrophe of the unperturbed solution.}, doi = {10.1070/RM2008v063n06ABEH004575}, url = {http://hdl.handle.net/1963/6471}, author = {Boris Dubrovin} } @article {MR2435752, title = {Harish-Chandra integrals as nilpotent integrals}, journal = {Int. Math. Res. Not. IMRN}, number = {16}, year = {2008}, pages = {Art. ID rnn062, 15}, issn = {1073-7928}, author = {Marco Bertola and Ferrer, Aleix Prats} } @article {2008, title = {Instanton counting on Hirzebruch surfaces}, number = {SISSA;55/2008/FM}, year = {2008}, abstract = {We perform a study of the moduli space of framed torsion free sheaves on Hirzebruch surfaces by using localization techniques. After discussing general properties of this moduli space, we classify its fixed points under the appropriate toric action and compute its Poincare\\\' polynomial. From the physical viewpoint, our results provide the partition function of N=4 Vafa-Witten theory on Hirzebruch surfaces, which is relevant in black hole entropy counting problems according to a conjecture due to Ooguri, Strominger and Vafa.}, url = {http://hdl.handle.net/1963/2852}, author = {Ugo Bruzzo and Rubik Poghossian and Alessandro Tanzini} } @article {2008, title = {Invariant Carnot-Caratheodory metrics on S3, SO(3), SL(2) and Lens Spaces}, journal = {SIAM J. Control Optim. 47 (2008) 1851-1878}, number = {SISSA;58/2007/M}, year = {2008}, abstract = {In this paper we study the invariant Carnot-Caratheodory metrics on SU(2) \\\' S3,\\nSO(3) and SL(2) induced by their Cartan decomposition. Beside computing explicitly geodesics and conjugate loci, we compute the cut loci (globally) and we give the expression of the Carnot-Caratheodory distance as the inverse of an elementary function. We then prove that the metric\\ngiven on SU(2) projects on the so called Lens Spaces L(p; q). Also for Lens Spaces, we compute\\nthe cut loci (globally).}, doi = {10.1137/070703727}, url = {http://hdl.handle.net/1963/2144}, author = {Ugo Boscain and Francesco Rossi} } @article {2008, title = {Invariant Manifolds for Viscous Profiles of a Class of Mixed Hyperbolic-Parabolic Systems}, number = {SISSA;83/2008/M}, year = {2008}, url = {http://hdl.handle.net/1963/3400}, author = {Stefano Bianchini and Laura Spinolo} } @article {2008, title = {The Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere}, journal = {Comm. Math. Phys. 279 (2008) 77-116}, number = {SISSA;95/2007/MP}, year = {2008}, abstract = {Equivariance under the action of Uq(so(5)) is used to compute the left regular and (chiral) spinorial representations of the algebra of the quantum Euclidean 4-sphere S^4_q. These representations are the constituents of a spectral triple on this sphere with a Dirac operator which is isospectral to the canonical one of the spin structure of the round undeformed four-sphere and which gives metric dimension four for the noncommutative geometry. Non-triviality of the geometry is proved by pairing the associated Fredholm module with an {\textquoteleft}instanton\\\' projection. A real structure which satisfies all required properties modulo a suitable ideal of {\textquoteleft}infinitesimals\\\' is also introduced.}, doi = {10.1007/s00220-008-0420-x}, url = {http://hdl.handle.net/1963/2567}, author = {Francesco D{\textquoteright}Andrea and Ludwik Dabrowski and Giovanni Landi} } @article {2008, title = {Limit Time Optimal Syntheses for a control-affine system on S{\texttwosuperior}}, journal = {SIAM J. Control Optim. 47 (2008) 111-143}, number = {SISSA;48/2006/M}, year = {2008}, abstract = {For $\\\\alpha \\\\in ]0,\\\\pi/2[$, let $(\\\\Sigma)_\\\\alpha$ be the control system $\\\\dot{x}=(F+uG)x$, where $x$ belongs to the two-dimensional unit sphere $S^2$, $u\\\\in [-1,1]$, and $F,G$ are $3\\\\times3$ skew-symmetric matrices generating rotations with perpendicular axes and of respective norms $\\\\cos(\\\\alpha)$ and $\\\\sin(\\\\alpha)$. In this paper, we study the time optimal synthesis (TOS) from the north pole $(0,0,1)^T$ associated to $(\\\\Sigma)_\\\\alpha$, as the parameter $\\\\alpha$ tends to zero; this problem is motivated by specific issues in the control of quantum systems. We first prove that the TOS is characterized by a \\\"two-snakes\\\" configuration on the whole $S^2$, except for a neighborhood $U_\\\\alpha$ of the south pole $(0,0,-1)^T$ of diameter at most ${\\\\cal O}(\\\\alpha)$. We next show that, inside $U_\\\\alpha$, the TOS depends on the relationship between $r(\\\\alpha):=\\\\pi/2\\\\alpha-[\\\\pi/2\\\\alpha]$ and $\\\\alpha$. More precisely, we characterize three main relationships by considering sequences $(\\\\alpha_k)_{k\\\\geq 0}$ satisfying (a) $r(\\\\alpha_k)=\\\\bar{r}$, (b) $r(\\\\alpha_k)=C\\\\alpha_k$, and (c) $r(\\\\alpha_k)=0$, where $\\\\bar{r}\\\\in (0,1)$ and $C>0$. In each case, we describe the TOS and provide, after a suitable rescaling, the limiting behavior, as $\\\\alpha$ tends to zero, of the corresponding TOS inside $U_\\\\alpha$.}, doi = {10.1137/060675988}, url = {http://hdl.handle.net/1963/1862}, author = {Paolo Mason and Rebecca Salmoni and Ugo Boscain and Yacine Chitour} } @article {2008, title = {On the Logarithmic Asymptotics of the Sixth Painleve\' Equation (Summer 2007)}, journal = {J.Phys.A: Math.Theor. 41,(2008), 205201-205247}, number = {arXiv:0801.1157;}, year = {2008}, note = {This paper appeared as a preprint in August 2007. It is published in Journal of Physics A: Mathematical and Theoretical, Volume 41, Issue 20, 6 May 2008, p. 205201-205247. It was on the archive in January 2008 (arXiv:0801.1157). This version does not differ from the published one except for two facts: 1)the addition of subsection 8.2, which proves that tr(M0Mx) = -2 for solutions y(x) \~{} a (ln x)n , n = 1, 2, x {\textrightarrow} 0. 2). The title of the journal article is : The logarithmic asymptotics of the sixth Painlev{\'e} equation}, publisher = {SISSA}, abstract = {We study the solutions of the sixth Painlev\'e equation with a logarithmic\r\nasymptotic behavior at a critical point. We compute the monodromy group\r\nassociated to the solutions by the method of monodromy preserving deformations\r\nand we characterize the asymptotic behavior in terms of the monodromy itself.}, doi = {10.1088/1751-8113/41/20/205201}, url = {http://hdl.handle.net/1963/6521}, author = {Davide Guzzetti} } @article {2008, title = {Minimization of non quasiconvex functionals by integro-extremization method}, journal = {Discrete Contin. Dyn. Syst. 21 (2008) 625-641}, year = {2008}, doi = {10.3934/dcds.2008.21.625}, url = {http://hdl.handle.net/1963/2761}, author = {Sandro Zagatti} } @article {2008, title = {Minimizers of non convex scalar functionals and viscosity solutions of Hamilton-Jacobi equations}, journal = {Calc. Var. Partial Differential Equations 31 (2008) 511-519}, year = {2008}, doi = {10.1007/s00526-007-0124-7}, url = {http://hdl.handle.net/1963/2760}, author = {Sandro Zagatti} } @article {2008, title = {Morse theory and a scalar field equation on compact surfaces}, journal = {Adv. Differential Equations 13 (2008) 1109-1129}, year = {2008}, publisher = {Khayyam Publishing}, url = {http://hdl.handle.net/1963/3531}, author = {Andrea Malchiodi} } @article {2008, title = {Multiple bound states for the Schroedinger-Poisson problem}, journal = {Commun. Contemp. Math. 10 (2008) 391-404}, year = {2008}, doi = {10.1142/S021919970800282X}, url = {http://hdl.handle.net/1963/2679}, author = {Antonio Ambrosetti and David Ruiz} } @article {2008, title = {Noncommutative families of instantons}, journal = {Int. Math. Res. Not. vol. 2008, Article ID rnn038}, number = {arXiv.org;0710.0721v2}, year = {2008}, publisher = {Oxford University Press}, abstract = {We construct $\\\\theta$-deformations of the classical groups SL(2,H) and Sp(2). Coacting on the basic instanton on a noncommutative four-sphere $S^4_\\\\theta$, we construct a noncommutative family of instantons of charge 1. The family is parametrized by the quantum quotient of $SL_\\\\theta(2,H)$ by $Sp_\\\\theta(2)$.}, doi = {10.1093/imrn/rnn038}, url = {http://hdl.handle.net/1963/3417}, author = {Giovanni Landi and Chiara Pagani and Cesare Reina and Walter van Suijlekom} } @article {2008, title = {The Noncommutative Geometry of the Quantum Projective Plane}, journal = {Rev. Math. Phys. 20 (2008) 979-1006}, number = {SISSA;100/2007/MP}, year = {2008}, abstract = {We study the spectral geometry of the quantum projective plane CP^2_q. In particular, we construct a Dirac operator which gives a 0^+ summable triple, equivariant under U_q(su(3)).}, doi = {10.1142/S0129055X08003493}, url = {http://hdl.handle.net/1963/2548}, author = {Francesco D{\textquoteright}Andrea and Ludwik Dabrowski and Giovanni Landi} } @article {2008, title = {A note on the differentiability of Lipschitz functions and the chain rule in Sobolev spaces}, number = {SISSA;29/2008/M}, year = {2008}, url = {http://hdl.handle.net/1963/2654}, author = {Massimiliano Morini} } @article {2008, title = {Numerical study of a multiscale expansion of the Korteweg-de Vries equation and Painlev{\'e}-II equation}, journal = {Proc. R. Soc. A 464 (2008) 733-757}, number = {arXiv.org;0708.0638v3}, year = {2008}, abstract = {The Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion of order $\\\\e^2$, $\\\\e\\\\ll 1$, is characterized by the appearance of a zone of rapid modulated oscillations. These oscillations are approximately described by the elliptic solution of KdV where the amplitude, wave-number and frequency are not constant but evolve according to the Whitham equations. Whereas the difference between the KdV and the asymptotic solution decreases as $\\\\epsilon$ in the interior of the Whitham oscillatory zone, it is known to be only of order $\\\\epsilon^{1/3}$ near the leading edge of this zone. To obtain a more accurate description near the leading edge of the oscillatory zone we present a multiscale expansion of the solution of KdV in terms of the Hastings-McLeod solution of the Painlev\\\\\\\'e-II equation. We show numerically that the resulting multiscale solution approximates the KdV solution, in the small dispersion limit, to the order $\\\\epsilon^{2/3}$.}, doi = {10.1098/rspa.2007.0249}, url = {http://hdl.handle.net/1963/2592}, author = {Tamara Grava and Christian Klein} } @article {2008, title = {Optimal Strokes for Low Reynolds Number Swimmers: An Example}, journal = {J. Nonlinear Sci. 18 (2008) 277-302}, year = {2008}, publisher = {Springer}, abstract = {Swimming, i.e., being able to advance in the absence of external forces by performing cyclic shape changes, is particularly demanding at low Reynolds numbers. This is the regime of interest for micro-organisms and micro- or nano-robots. We focus in this paper on a simple yet representative example: the three-sphere swimmer of Najafi and Golestanian (Phys. Rev. E, 69, 062901-062904, 2004). For this system, we show how to cast the problem of swimming in the language of control theory, prove global controllability (which implies that the three-sphere swimmer can indeed swim), and propose a numerical algorithm to compute optimal strokes (which turn out to be suitably defined sub-Riemannian geodesics).}, doi = {10.1007/s00332-007-9013-7}, url = {http://hdl.handle.net/1963/4006}, author = {Fran{\c c}ois Alouges and Antonio DeSimone and Aline Lefebvre} } @article {2008, title = {Origin of Co-Expression Patterns in E.coli and S.cerevisiae Emerging from Reverse Engineering Algorithms}, journal = {PLoS ONE 3 (2008) e2981}, year = {2008}, abstract = {Background: The concept of reverse engineering a gene network, i.e., of inferring a genome-wide graph of putative genegene interactions from compendia of high throughput microarray data has been extensively used in the last few years to deduce/integrate/validate various types of \\\"physical\\\" networks of interactions among genes or gene products. Results: This paper gives a comprehensive overview of which of these networks emerge significantly when reverse engineering large collections of gene expression data for two model organisms, E.coli and S.cerevisiae, without any prior information. For the first organism the pattern of co-expression is shown to reflect in fine detail both the operonal structure of the DNA and the regulatory effects exerted by the gene products when co-participating in a protein complex. For the second organism we find that direct transcriptional control (e.g., transcription factor-binding site interactions) has little statistical significance in comparison to the other regulatory mechanisms (such as co-sharing a protein complex, colocalization on a metabolic pathway or compartment), which are however resolved at a lower level of detail than in E.coli. Conclusion: The gene co-expression patterns deduced from compendia of profiling experiments tend to unveil functional categories that are mainly associated to stable bindings rather than transient interactions. The inference power of this systematic analysis is substantially reduced when passing from E.coli to S.cerevisiae. This extensive analysis provides a way to describe the different complexity between the two organisms and discusses the critical limitations affecting this type of methodologies.}, doi = {10.1371/journal.pone.0002981}, url = {http://hdl.handle.net/1963/2722}, author = {Mattia Zampieri and Nicola Soranzo and Daniele Bianchini and Claudio Altafini} } @article {Berti2008601, title = {On periodic elliptic equations with gradient dependence}, journal = {Communications on Pure and Applied Analysis}, volume = {7}, number = {3}, year = {2008}, note = {cited By (since 1996)1}, pages = {601-615}, abstract = {We construct entire solutions of Δu = f(x, u, ∇u) which are superpositions of odd, periodic functions and linear ones, with prescribed integer or rational slope.}, issn = {15340392}, author = {Massimiliano Berti and Matzeu, M and Enrico Valdinoci} } @article {mercuri2008positive, title = {Positive solutions of nonlinear Schr{\"o}dinger-Poisson systems with radial potentials vanishing at infinity}, journal = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl}, volume = {19}, number = {3}, year = {2008}, pages = {211{\textendash}227}, publisher = {Citeseer}, abstract = {We deal with a weighted nonlinear Schr{\textasciidieresis}odinger-Poisson system, allowing the potentials to vanish at infinity.

}, doi = {10.1.1.510.3635}, url = {http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.510.3635\&rep=rep1\&type=pdf}, author = {Mercuri, Carlo} } @article {2008, title = {Relaxation of some transversally isotropic energies and applications to smectic A elastomers}, journal = {Math. Models Methods Appl. Sci. 18 (2008) 1-20}, number = {SISSA;01/2007/M}, year = {2008}, doi = {10.1142/S0218202508002693}, url = {http://hdl.handle.net/1963/1912}, author = {James Adams and Sergio Conti and Antonio DeSimone and Georg Dolzmann} } @article {2008, title = {A second order minimality condition for the Mumford-Shah functional}, journal = {Calc. Var. Partial Differential Equations 33 (2008) 37-74}, number = {SISSA;82/2006/M}, year = {2008}, abstract = {A new necessary minimality condition for the Mumford-Shah functional is derived by means of second order variations. It is expressed in terms of a sign condition for a nonlocal quadratic form on $H^1_0(\\\\Gamma)$, $\\\\Gamma$ being a submanifold of the regular part of the discontinuity set of the critical point. Two equivalent formulations are provided: one in terms of the first eigenvalue of a suitable compact operator, the other involving a sort of nonlocal capacity of $\\\\Gamma$. A sufficient condition for minimality is also deduced. Finally, an explicit example is discussed, where a complete characterization of the domains where the second variation is nonnegative can be given.}, doi = {10.1007/s00526-007-0152-3}, url = {http://hdl.handle.net/1963/1955}, author = {Filippo Cagnetti and Maria Giovanna Mora and Massimiliano Morini} } @article {2008, title = {On semistable principal bundles over a complex projective manifold}, journal = {Int. Math. Res. Not. vol. 2008, article ID rnn035}, number = {arXiv.org;0803.4042v1}, year = {2008}, publisher = {Oxford University Press}, abstract = {Let G be a simple linear algebraic group defined over the complex numbers. Fix a proper parabolic subgroup P of G and a nontrivial antidominant character \\\\chi of P. We prove that a holomorphic principal G-bundle E over a connected complex projective manifold M is semistable and the second Chern class of its adjoint bundle vanishes in rational cohomology if and only if the line bundle over E/P defined by \\\\chi is numerically effective. Similar results remain valid for principal bundles with a reductive linear algebraic group as the structure group. These generalize an earlier work of Y. Miyaoka where he gave a characterization of semistable vector bundles over a smooth projective curve. Using these characterizations one can also produce similar criteria for the semistability of parabolic principal bundles over a compact Riemann surface.}, doi = {10.1093/imrn/rnn035}, url = {http://hdl.handle.net/1963/3418}, author = {Indranil Biswas and Ugo Bruzzo} } @article {2008, title = {Solitons of linearly coupled systems of semilinear non-autonomous equations on Rn}, journal = {J. Funct. Anal. 254 (2008) 2816-2845}, number = {SISSA;73/2007/M}, year = {2008}, abstract = {Using concentration compactness type arguments, we prove some results about the existence of positive ground and bound state of linearly coupled systems of nonlinear Schr{\"o}dinger equations.}, doi = {10.1016/j.jfa.2007.11.013}, url = {http://hdl.handle.net/1963/2175}, author = {Antonio Ambrosetti and Giovanna Cerami and David Ruiz} } @article {2008, title = {Stability of planar switched systems: the nondiagonalizable case}, journal = {Commun. Pure Appl. Anal. 7 (2008) 1-21}, number = {SISSA;44/2006/M}, year = {2008}, doi = {10.3934/cpaa.2008.7.1}, url = {http://hdl.handle.net/1963/1857}, author = {Ugo Boscain and Moussa Balde} } @article {2008, title = {Symmetric obstruction theories and Hilbert schemes of points on threefolds}, journal = {Algebra Number Theory 2 (2008) 313-345}, number = {arXiv.org;math/0512556v1}, year = {2008}, abstract = {In an earlier paper by one of us (Behrend), Donaldson-Thomas type invariants were expressed as certain weighted Euler characteristics of the moduli space. The Euler characteristic is weighted by a certain canonical\\nZ-valued constructible function on the moduli space. This constructible function associates to\\nany point of the moduli space a certain invariant of the singularity of the space at the point. Here we evaluate this invariant for the case of a singularity that is an isolated point of a C*-action and that admits a symmetric obstruction theory compatible with the C*-action. The answer is (-1)d, where d\\nis the dimension of the Zariski tangent space. We use this result to prove that for any threefold, proper or not, the weighted Euler characteristic of the Hilbert scheme of n points on the threefold is, up to sign, equal to the usual Euler characteristic. For the case of a projective Calabi-Yau threefold, we deduce that the Donaldson-Thomas invariant of the Hilbert scheme of n points is, up to sign, equal to the Euler characteristic. This proves a conjecture of Maulik, Nekrasov, Okounkov and Pandharipande.}, url = {http://hdl.handle.net/1963/2709}, author = {Kai Behrend and Barbara Fantechi} } @mastersthesis {2008, title = {Symmetries of noncommutative spaces and equivariant cohomology}, year = {2008}, school = {SISSA}, abstract = {As the title suggests, the main subject of this thesis is the study of symmetries of noncommutative spaces and related equivariant cohomologies. We focus on deformations of classical geometries coming from the action of some symmetry. A close relation between the deformation of the symmetry and the deformation of the space on which it acts is at the heart of our approach; we will use this idea to generate noncommutative geometries, and to de{\textasciimacron}ne algebraic models for the equivariant cohomology of such actions.}, keywords = {Noncommutative spaces}, url = {http://hdl.handle.net/1963/5254}, author = {Lucio Cirio} } @article {2008, title = {Topological Gauge Theories on Local Spaces and Black Hole Entropy Countings}, journal = {Adv. Theor. Math. Phys. 12 (2008) 1429-1446}, number = {SISSA;43/2007/EP}, year = {2008}, abstract = {We study cohomological gauge theories on total spaces of holomorphic line bundles over complex manifolds and obtain their reduction to the base manifold by U(1) equivariant localization of the path integral. We exemplify this general mechanism by proving via exact path integral localization a reduction for local curves conjectured in hep-th/0411280, relevant to the calculation of black hole entropy/Gromov-Witten invariants. Agreement with the four-dimensional gauge theory is recovered by taking into account in the latter non-trivial contributions coming from one-loop fluctuations determinants at the boundary of the total space. We also study a class of abelian gauge theories on Calabi-Yau local surfaces, describing the quantum foam for the A-model, relevant to the calculation of Donaldson-Thomas invariants.}, url = {http://hdl.handle.net/1963/1992}, author = {Giulio Bonelli and Alessandro Tanzini} } @article {2008, title = {Topological methods for an elliptic equation with exponential nonlinearities}, journal = {Discrete Contin. Dyn. Syst. 21 (2008) 277-294}, year = {2008}, abstract = {We consider a class of variational equations with exponential nonlinearities on compact surfaces. From considerations involving the Moser-Trudinger inequality, we characterize some sublevels of the Euler-Lagrange functional in terms of the topology of the surface and of the data of the equation. This is used together with a min-max argument to obtain existence results.}, doi = {10.3934/dcds.2008.21.277}, url = {http://hdl.handle.net/1963/2594}, author = {Andrea Malchiodi} } @article {2008, title = {Transition layer for the heterogeneous Allen-Cahn equation}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 25 (2008) 609-631}, number = {arXiv.org;math/0702878v1}, year = {2008}, abstract = {We consider the equation $\\\\e^{2}\\\\Delta u=(u-a(x))(u^2-1)$ in $\\\\Omega$, $\\\\frac{\\\\partial u}{\\\\partial \\\\nu} =0$ on $\\\\partial \\\\Omega$, where $\\\\Omega$ is a smooth and bounded domain in $\\\\R^n$, $\\\\nu$ the outer unit normal to $\\\\pa\\\\Omega$, and $a$ a smooth function satisfying $-10} and {a<0}. Assuming $\\\\nabla a \\\\neq 0$ on $K$ and $a\\\\ne 0$ on $\\\\partial \\\\Omega$, we show that there exists a sequence $\\\\e_j \\\\to 0$ such that the above equation has a solution $u_{\\\\e_j}$ which converges uniformly to $\\\\pm 1$ on the compact sets of $\\\\O_{\\\\pm}$ as $j \\\\to + \\\\infty$.}, doi = {10.1016/j.anihpc.2007.03.008}, url = {http://hdl.handle.net/1963/2656}, author = {Fethi Mahmoudi and Andrea Malchiodi and Juncheng Wei} } @inbook {2008, title = {Transport Rays and Applications to Hamilton{\textendash}Jacobi Equations}, booktitle = {Nonlinear PDE{\textquoteright}s and Applications : C.I.M.E. Summer School, Cetraro, Italy 2008 / Stefano Bianchini, Eric A. Carlen, Alexander Mielke, C{\'e}dric Villani. Eds. Luigi Ambrosio, Giuseppe Savar{\'e}. - Berlin : Springer, 2011. - (Lecture Notes in Mathematics ; 20}, year = {2008}, note = {This volume collects the notes of the CIME course Nonlinear PDE{\textquoteright}s and\\r\\napplications held in Cetraro (Italy) on June 23{\textendash}28, 2008. The school consisted\\r\\nin 5 series of lectures, delivered by Stefano Bianchini (SISSA, Trieste), Eric A. Carlen (Rutgers University), Alexander Mielke (WIAS, Berlin), Felix Otto (Bonn University), Cedric Villani (Ecole Normale Superieure de Lyon).}, publisher = {Springer}, organization = {Springer}, abstract = {The aim of these notes is to introduce the readers to the use of the Disintegration Theorem for measures as an effective tool for reducing problems in transport equations to simpler ones. The basic idea is to partition Rd into one dimensional sets, on which the problem under consideration becomes one space dimensional (and thus much easier, hopefully).}, isbn = {978-3-642-21718-0}, doi = {10.1007/978-3-642-21861-3_1}, url = {http://hdl.handle.net/1963/5463}, author = {Stefano Bianchini and Matteo Gloyer} } @article {2008, title = {A vanishing viscosity approach to quasistatic evolution in plasticity with softening}, journal = {Arch. Ration. Mech. Anal. 189 (2008) 469-544}, number = {SISSA;38/2006/M}, year = {2008}, abstract = {We deal with quasistatic evolution problems in plasticity with softening, in the framework of small strain associative elastoplasticity. The presence of a nonconvex term due to the softening phenomenon requires a nontrivial extension of the variational framework for rate-independent problems to the case of a nonconvex energy functional. We argue that, in this case, the use of global minimizers in the corresponding incremental problems is not justified from the mechanical point of view. Thus, we analize a different selection criterion for the solutions of the quasistatic evolution problem, based on a viscous approximation. This leads to a generalized formulation in terms of Young measures, developed in the first part of the paper. In the second part we apply our approach to some concrete examples.}, doi = {10.1007/s00205-008-0117-5}, url = {http://hdl.handle.net/1963/1844}, author = {Gianni Dal Maso and Antonio DeSimone and Maria Giovanna Mora and Massimiliano Morini} } @article {Berti2008391, title = {Variational methods for Hamiltonian PDEs}, journal = {NATO Science for Peace and Security Series B: Physics and Biophysics}, year = {2008}, note = {cited By (since 1996)0}, pages = {391-420}, abstract = {We present recent existence results of periodic solutions for completely resonant nonlinear wave equations in which both "small divisor" difficulties and infinite dimensional bifurcation phenomena occur. These results can be seen as generalizations of the classical finite-dimensional resonant center theorems of Weinstein-Moser and Fadell-Rabinowitz. The proofs are based on variational bifurcation theory: after a Lyapunov-Schmidt reduction, the small divisor problem in the range equation is overcome with a Nash-Moser implicit function theorem for a Cantor set of non-resonant parameters. Next, the infinite dimensional bifurcation equation, variational in nature, possesses minimax mountain-pass critical points. The big difficulty is to ensure that they are not in the "Cantor gaps". This is proved under weak non-degeneracy conditions. Finally, we also discuss the existence of forced vibrations with rational frequency. This problem requires variational methods of a completely different nature, such as constrained minimization and a priori estimates derivable from variational inequalities. {\textcopyright} 2008 Springer Science + Business Media B.V.}, isbn = {9781402069628}, issn = {18746500}, doi = {10.1007/978-1-4020-6964-2-16}, author = {Massimiliano Berti} } @article {2007, title = {Asymptotic behaviour of smooth solutions for partially dissipative hyperbolic systems with a convex entropy}, journal = {Comm. Pure Appl. Math. 60 (2007) 1559-1622}, number = {SISSA;83/2005/M}, year = {2007}, abstract = {We study the asymptotic time behavior of global smooth solutions to general entropy dissipative hyperbolic systems of balance law in m space dimensions, under the Shizuta-Kawashima condition.}, doi = {10.1002/cpa.20195}, url = {http://hdl.handle.net/1963/1780}, author = {Stefano Bianchini and Bernard Hanouzet and Roberto Natalini} } @article {2007, title = {The Asymptotic Behaviour of the Fourier Transforms of Orthogonal Polynomials II: L.I.F.S. Measures and Quantum Mechanics}, journal = {Ann. Henri Poincar{\textasciiacute}e 8 (2007), 301{\textendash}336}, year = {2007}, publisher = {2007 Birkh{\textasciidieresis}auser Verlag Basel/Switzerland}, abstract = {We study measures generated by systems of linear iterated functions,\r\ntheir Fourier transforms, and those of their orthogonal polynomials. We\r\ncharacterize the asymptotic behaviours of their discrete and continuous averages.\r\nFurther related quantities are analyzed, and relevance of this analysis\r\nto quantum mechanics is briefly discussed}, doi = {10.1007/s00023-006-0309-1}, author = {Davide Guzzetti and Giorgio Mantica} } @article {2007, title = {Asymptotic variational wave equations}, journal = {Arch. Ration. Mech. Anal. 183 (2007) 163-185}, number = {arXiv.org;math/0502124v1}, year = {2007}, abstract = {We investigate the equation $(u_t + (f(u))_x)_x = f\\\'\\\'(u) (u_x)^2/2$ where $f(u)$ is a given smooth function. Typically $f(u)= u^2/2$ or $u^3/3$. This equation models unidirectional and weakly nonlinear waves for the variational wave equation $u_{tt} - c(u) (c(u)u_x)_x =0$ which models some liquid crystals with a natural sinusoidal $c$. The equation itself is also the Euler-Lagrange equation of a variational problem. Two natural classes of solutions can be associated with this equation. A conservative solution will preserve its energy in time, while a dissipative weak solution loses energy at the time when singularities appear. Conservative solutions are globally defined, forward and backward in time, and preserve interesting geometric features, such as the Hamiltonian structure. On the other hand, dissipative solutions appear to be more natural from the physical point of view.\\nWe establish the well-posedness of the Cauchy problem within the class of conservative solutions, for initial data having finite energy and assuming that the flux function $f$ has Lipschitz continuous second-order derivative. In the case where $f$ is convex, the Cauchy problem is well-posed also within the class of dissipative solutions. However, when $f$ is not convex, we show that the dissipative solutions do not depend continuously on the initial data.}, doi = {10.1007/s00205-006-0014-8}, url = {http://hdl.handle.net/1963/2182}, author = {Alberto Bressan and Zhang Ping and Zheng Yuxi} } @article {Bertola:LOPs, title = {Biorthogonal Laurent polynomials, T{\"o}plitz determinants, minimal Toda orbits and isomonodromic tau functions}, journal = {Constr. Approx.}, volume = {26}, number = {3}, year = {2007}, pages = {383{\textendash}430}, issn = {0176-4276}, author = {Marco Bertola and Gekhtman, M.} } @article {Bertola:semiclassBOPsJAT, title = {Biorthogonal polynomials for two-matrix models with semiclassical potentials}, journal = {J. Approx. Theory}, volume = {144}, number = {2}, year = {2007}, pages = {162{\textendash}212}, issn = {0021-9045}, author = {Marco Bertola} } @article {2007, title = {Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory}, number = {SISSA;61/2006/FM}, year = {2007}, abstract = {We study the relationship between instanton counting in N=4 Yang-Mills theory on a generic four-dimensional toric orbifold and the semi-classical expansion of q-deformed Yang-Mills theory on the blowups of the minimal resolution of the orbifold singularity, with an eye to clarifying the recent proposal of using two-dimensional gauge theories to count microstates of black holes in four dimensions. We describe explicitly the instanton contributions to the counting of D-brane bound states which are captured by the two-dimensional gauge theory. We derive an intimate relationship between the two-dimensional Yang-Mills theory and Chern-Simons theory on generic Lens spaces, and use it to show that the correct instanton counting is only reproduced when the Chern-Simons contributions are treated as non-dynamical boundary conditions in the D4-brane gauge theory. We also use this correspondence to discuss the counting of instantons on higher genus ruled Riemann surfaces.}, doi = {10.1016/j.nuclphysb.2007.02.030}, url = {http://hdl.handle.net/1963/1888}, author = {Luca Griguolo and Domenico Seminara and Richard J. Szabo and Alessandro Tanzini} } @article {2007, title = {Bose-Einstein condensation: analysis of problems and rigorous results}, number = {SISSA;70/2007/MP}, year = {2007}, url = {http://hdl.handle.net/1963/2189}, author = {Alessandro Michelangeli} } @article {2007, title = {Boundary interface for the Allen-Cahn equation}, journal = {J. Fixed Point Theory Appl. 1 (2007) 305-336}, year = {2007}, doi = {10.1007/s11784-007-0016-7}, url = {http://hdl.handle.net/1963/2027}, author = {Andrea Malchiodi and Juncheng Wei} } @article {2007, title = {Boundary-clustered interfaces for the Allen{\textendash}Cahn equation}, journal = {Pacific Journal of Mathematics 229 (2007), No. 2, 447{\textendash}468}, year = {2007}, publisher = {Mathematical Sciences Publishers}, url = {http://hdl.handle.net/1963/5089}, author = {Andrea Malchiodi and Wei-Ming Ni and Juncheng Wei} } @article {2007, title = {BV instability for the Lax-Friedrichs scheme}, number = {SISSA;100/2004/M}, year = {2007}, abstract = {It is proved that discrete shock profiles (DSPs) for the Lax-Friedrichs scheme for a system of conservation laws do not necessarily depend continuously in BV on their speed. We construct examples of $2 \\\\times 2$-systems for which there are sequences of DSPs with speeds converging to a rational number. Due to a resonance phenomenon, the difference between the limiting DSP and any DSP in the sequence will contain an order-one amount of variation.}, url = {http://hdl.handle.net/1963/2335}, author = {Paolo Baiti and Alberto Bressan and Helge Kristian Jenssen} } @article {2007, title = {Canonical structure and symmetries of the Schlesinger equations}, journal = {Comm. Math. Phys. 271 (2007) 289-373}, number = {arXiv.org;math/0311261v4}, year = {2007}, abstract = {The Schlesinger equations S (n,m) describe monodromy preserving deformations of order m Fuchsian systems with n+1 poles. They can be considered as a family of commuting time-dependent Hamiltonian systems on the direct product of n copies of m{\texttimes}m matrix algebras equipped with the standard linear Poisson bracket. In this paper we present a new canonical Hamiltonian formulation ofthe general Schlesinger equations S (n,m) for all n, m and we compute the action of the symmetries of the Schlesinger equations in these coordinates.}, doi = {10.1007/s00220-006-0165-3}, url = {http://hdl.handle.net/1963/1997}, author = {Boris Dubrovin and Marta Mazzocco} } @article {2007, title = {Chen-Ruan cohomology of ADE singularities}, journal = {International Journal of Mathematics. Volume 18, Issue 9, October 2007, Pages 1009-1059}, year = {2007}, note = {This is a short version of my Ph.D. Thesis math.AG/0510528. Version\r\n 2: chapters 2,3,4 and 5 has been rewritten using the language of groupoids; a\r\n link with the classical McKay correpondence is given. International Journal\r\n of Mathematics (to appear)}, publisher = {SISSA}, abstract = {We study Ruan\'s \\textit{cohomological crepant resolution conjecture} for\r\norbifolds with transversal ADE singularities. In the $A_n$-case we compute both\r\nthe Chen-Ruan cohomology ring $H^*_{\\rm CR}([Y])$ and the quantum corrected\r\ncohomology ring $H^*(Z)(q_1,...,q_n)$. The former is achieved in general, the\r\nlater up to some additional, technical assumptions. We construct an explicit\r\nisomorphism between $H^*_{\\rm CR}([Y])$ and $H^*(Z)(-1)$ in the $A_1$-case,\r\nverifying Ruan\'s conjecture. In the $A_n$-case, the family\r\n$H^*(Z)(q_1,...,q_n)$ is not defined for $q_1=...=q_n=-1$. This implies that\r\nthe conjecture should be slightly modified. We propose a new conjecture in the\r\n$A_n$-case which we prove in the $A_2$-case by constructing an explicit\r\nisomorphism.}, keywords = {Chen-Ruan cohomology, Ruan\'s conjecture, McKay correspondence}, doi = {10.1142/S0129167X07004436}, url = {http://hdl.handle.net/1963/6502}, author = {Fabio Perroni} } @article {2007, title = {The cohomological crepant resolution conjecture for P(1,3,4,4)}, number = {arXiv:0712.3248;}, year = {2007}, note = {11 pages, 1 figure}, publisher = {SISSA}, abstract = {We prove the cohomological crepant resolution conjecture of Ruan for the\r\nweighted projective space P(1,3,4,4). To compute the quantum corrected\r\ncohomology ring we combine the results of Coates-Corti-Iritani-Tseng on\r\nP(1,1,1,3) and our previous results.}, url = {http://hdl.handle.net/1963/6513}, author = {Samuel Boissiere and Fabio Perroni and Etienne Mann} } @article {2007, title = {Comparing association network algorithms for reverse engineering of large scale gene regulatory networks: synthetic vs real data}, journal = {Bioinformatics 23 (2007) 1640-1647}, year = {2007}, abstract = {Motivation: Inferring a gene regulatory network exclusively from microarray expression profiles is a difficult but important task. The aim of this work is to compare the predictive power of some of the most popular algorithms in different conditions (like data taken at equilibrium or time courses) and on both synthetic and real microarray data. We are in particular interested in comparing similarity measures both of linear type (like correlations and partial correlations) and of nonlinear type (mutual information and conditional mutual information), and in investigating the underdetermined case (less samples than genes). Results: In our simulations we see that all network inference algorithms obtain better performances from data produced with \\\"structural\\\" perturbations, like gene knockouts at steady state, than with any dynamical perturbation. The predictive power of all algorithms is confirmed on a reverse engineering problem from E. coli gene profiling data: the edges of the \\\"physical\\\" network of transcription factor-binding sites are significantly overrepresented among the highest weighting edges of the graph that we infer directly from the data without any structure supervision. Comparing synthetic and in vivo data on the same network graph allows us to give an indication of how much more complex a real transcriptional regulation program is with respect to an artificial model. Availability: Software and supplementary material are freely available at the URL http://people.sissa.it/~altafini/papers/SoBiAl07/}, doi = {10.1093/bioinformatics/btm163}, url = {http://hdl.handle.net/1963/2028}, author = {Nicola Soranzo and Ginestra Bianconi and Claudio Altafini} } @article {2007, title = {The complete one-loop spin chain for N=2 Super-Yang-Mills}, number = {SISSA;99/2004/FM}, year = {2007}, note = {Contributed to NATO Advanced Study Institute and EC Summer School on String Theory: From Gauge Interactions to Cosmology, Cargese, France, 7-19 Jun 2004.}, abstract = {We show that the complete planar one-loop mixing matrix of the N=2 Super Yang--Mills theory can be obtained from a reduction of that of the N=4 theory. For composite operators of scalar fields, this yields an anisotropic XXZ spin chain, whose spectrum of excitations displays a mass gap.}, url = {http://hdl.handle.net/1963/2309}, author = {Paolo Di Vecchia and Alessandro Tanzini} } @article {2007, title = {Computing Amplitudes in topological M-theory}, number = {SISSA;74/2006/FM}, year = {2007}, abstract = {We define a topological quantum membrane theory on a seven dimensional manifold of $G_2$ holonomy. We describe in detail the path integral evaluation for membrane geometries given by circle bundles over Riemann surfaces. We show that when the target space is $CY_3\\\\times S^1$ quantum amplitudes of non-local observables of membranes wrapping the circle reduce to the A-model amplitudes. \\nIn particular for genus zero we show that our model computes the Gopakumar-Vafa invariants. Moreover, for membranes wrapping calibrated homology spheres in the $CY_3$, we find that the amplitudes of our model are related to Joyce invariants.}, doi = {10.1088/1126-6708/2007/03/023}, url = {http://hdl.handle.net/1963/1901}, author = {Giulio Bonelli and Alessandro Tanzini and Maxim Zabzine} } @article {2007, title = {Concentration on minimal submanifolds for a singularly perturbed Neumann problem}, journal = {Adv. Math. 209 (2007) 460-525}, number = {arXiv.org;math/0611558}, year = {2007}, abstract = {We consider the equation $- \\\\e^2 \\\\D u + u= u^p$ in $\\\\Omega \\\\subseteq \\\\R^N$, where $\\\\Omega$ is open, smooth and bounded, and we prove concentration of solutions along $k$-dimensional minimal submanifolds of $\\\\partial \\\\O$, for $N \\\\geq 3$ and for $k \\\\in \\\\{1, ..., N-2\\\\}$. We impose Neumann boundary conditions, assuming $13 or with two inputs for n=4 and n=5, up to state-feedback transformations, preserving the affine structure. First using the Poincare series of moduli numbers we introduce the intrinsic numbers of functional moduli of each prescribed number of variables on which a classification problem depends. In order to classify affine systems with scalar input we associate with such a system the canonical frame by normalizing some structural functions in a commutative relation of the vector fields, which define our control system. Then, using this canonical frame, we introduce the canonical coordinates and find a complete system of state-feedback invariants of the system. It also gives automatically the micro-local (i.e. local in state-input space) classification of the generic non-affine n-dimensional control system with scalar input for n>2. Further we show how the problem of feedback-equivalence of affine systems with two-dimensional input in state space of dimensions 4 and 5 can be reduced to the same problem for affine systems with scalar input. In order to make this reduction we distinguish the subsystem of our control system, consisting of the directions of all extremals in dimension 4 and all abnormal extremals in dimension 5 of the time optimal problem, defined by the original control system. In each classification problem under consideration we find the intrinsic numbers of functional moduli of each prescribed number of variables according to its Poincare series.}, doi = {10.1137/050623711}, url = {http://hdl.handle.net/1963/2186}, author = {Andrei A. Agrachev and Igor Zelenko} } @article {2007, title = {Feedback control of spin systems}, number = {SISSA;01/2006/M}, year = {2007}, note = {Proc. of the 44th IEEE Conf. on Decision and Control,. Seville, Spain, December 2005 (to appear).}, abstract = {The feedback stabilization problem for ensembles of coupled spin 1/2 systems is discussed from a control theoretic perspective. The noninvasive nature of the bulk measurement allows for a fully unitary and deterministic closed loop. The Lyapunov-based feedback design presented does not require spins that are selectively addressable. With this method, it is possible to obtain control inputs also for difficult tasks, like suppressing undesired couplings in identical spin systems.}, doi = {10.1007/s11128-006-0038-x}, url = {http://hdl.handle.net/1963/1808}, author = {Claudio Altafini} } @article {2007, title = {Feedback stabilization of quantum ensembles: a global convergence analysis on complex flag manifolds}, journal = {45th IEEE Conference on Decision and Control (2007) 2471-2476}, number = {SISSA;65/2005/M}, year = {2007}, abstract = {In an N-level quantum mechanical system, the problem of unitary feedback stabilization of mixed density operators to periodic orbits admits a natural Lyapunov-based time-varying feedback design. A global description of the domain of attraction of the closed-loop system can be provided based on a \\\"root-space\\\"-like structure of the space of density operators. This convex set foliates as a complex flag manifold where each leaf is identified with the coadjoint orbit of the eigenvalues of the density operator. The converging conditions are time-independent but depend from the topology of the flag manifold: it is shown that the closed loop must have a number of equilibria at least equal to the Euler characteristic of the manifold, thus imposing obstructions of topological nature to global stabilizability.}, doi = {10.1109/CDC.2006.377774}, url = {http://hdl.handle.net/1963/1729}, author = {Claudio Altafini} } @article {2007, title = {On finite-dimensional projections of distributions for solutions of randomly forced PDE\\\'s}, journal = {Ann. Inst. Henri Poincare-Prob. Stat. 43 (2007) 399-415}, number = {arXiv.org;math/0603295}, year = {2007}, abstract = {The paper is devoted to studying the image of probability measures on a Hilbert space under finite-dimensional analytic maps. We establish sufficient conditions under which the image of a measure has a density with respect to the Lebesgue measure and continuously depends on the map. The results obtained are applied to the 2D Navier-Stokes equations perturbed by various random forces of low dimension.}, doi = {10.1016/j.anihpb.2006.06.001}, url = {http://hdl.handle.net/1963/2012}, author = {Andrei A. Agrachev and Sergei Kuksin and Andrey Sarychev and Armen Shirikyan} } @article {2007, title = {Gaussian estimates for hypoelliptic operators via optimal control}, journal = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 333-342}, number = {SISSA;45/2007/M}, year = {2007}, abstract = {We obtain Gaussian lower bounds for the fundamental solution of a class of hypoelliptic equations, by using repeatedly an invariant Harnack inequality. Our main result is given in terms of the value function of a suitable optimal control problem.}, doi = {10.4171/RLM/499}, url = {http://hdl.handle.net/1963/1994}, author = {Ugo Boscain and Sergio Polidoro} } @article {2007, title = {High-order angles in almost-Riemannian geometry}, number = {SISSA;59/2007/M}, year = {2007}, abstract = {Let X and Y be two smooth vector fields on a two-dimensional manifold M. If X and Y are everywhere linearly independent, then they define a Riemannian metric on M (the metric for which they are orthonormal) and they give to M the structure of metric space. If X and Y become linearly dependent somewhere on M, then the corresponding Riemannian metric has singularities, but under generic conditions the metric structure is still well defined. Metric structures that can be defined locally in this way are called almost-Riemannian structures. The main result of the paper is a generalization to almost-Riemannian structures of the Gauss-Bonnet formula for domains with piecewise-C2 boundary. The main feature of such formula is the presence of terms that play the role of high-order angles at the intersection points with the set of singularities.}, url = {http://hdl.handle.net/1963/1995}, author = {Ugo Boscain and Mario Sigalotti} } @article {2007, title = {The holomorphic anomaly for open string moduli}, journal = {JHEP 10 (2007) 060}, number = {SISSA;55/2007/EP}, year = {2007}, abstract = {We complete the holomorphic anomaly equations for topological strings with their dependence on open moduli. We obtain the complete system by standard path integral arguments generalizing the analysis of BCOV (Commun. Math. Phys. 165 (1994) 311) to strings with boundaries. We study both the anti-holomorphic dependence on open moduli and on closed moduli in presence of Wilson lines. By providing the compactification a\\\' la Deligne-Mumford of the moduli space of Riemann surfaces with boundaries, we show that the open holomorphic anomaly equations are structured on the (real codimension one) boundary components of this space.}, doi = {10.1088/1126-6708/2007/10/060}, url = {http://hdl.handle.net/1963/2113}, author = {Giulio Bonelli and Alessandro Tanzini} } @article {2007, title = {Luther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas}, journal = {Phys. Rev. Lett. 98 (2007) 030404}, number = {arXiv.org;cond-mat/0609346v1}, year = {2007}, abstract = {

The Luther-Emery liquid is a state of matter that is predicted to occur in one-dimensional systems of interacting fermions and is characterized by a gapless charge spectrum and a gapped spin spectrum. In this Letter we discuss a realization of the Luther-Emery phase in a trapped cold-atom gas. We study by means of the density-matrix renormalization-group technique a two-component atomic Fermi gas with attractive interactions subject to parabolic trapping inside an optical lattice. We demonstrate how this system exhibits compound phases characterized by the coexistence of spin pairing and atomic-density waves. A smooth crossover occurs with increasing magnitude of the atom-atom attraction to a state in which tightly bound spin-singlet dimers occupy the center of the trap. The existence of atomic-density waves could be detected in the elastic contribution to the light-scattering diffraction pattern.

}, doi = {10.1103/PhysRevLett.98.030404}, url = {http://hdl.handle.net/1963/2056}, author = {Gao Xianlong and Matteo Rizzi and Marco Polini and Rosario Fazio and Mario P. Tosi and Vivaldo L. Jr. Campo and Klaus Capelle} } @inbook {Bertola:MasslessdeSitter, title = {Massless scalar field in a two-dimensional de Sitter universe}, booktitle = {Rigorous quantum field theory}, series = {Progr. Math.}, volume = {251}, year = {2007}, pages = {27{\textendash}38}, publisher = {Birkh{\"a}user}, organization = {Birkh{\"a}user}, address = {Basel}, author = {Marco Bertola and Corbetta, Francesco and Moschella, Ugo} } @article {2007, title = {On the Maz\\\'ya inequalities: existence and multiplicity results for an elliptic problem involving cylindrical weights}, number = {SISSA;92/2007/M}, year = {2007}, url = {http://hdl.handle.net/1963/2522}, author = {Marita Gazzini and Roberta Musina} } @article {2007, title = {Metrics on semistable and numerically effective Higgs bundles}, journal = {J. Reine Angew. Math. 612 (2007) 59-79}, number = {SISSA;17/2006/FM}, year = {2007}, abstract = {We consider fibre metrics on Higgs vector bundles on compact K\\\\\\\"ahler manifolds, providing notions of numerical effectiveness and numerical flatness in terms of such metrics. We prove several properties of bundles satisfying such conditions and in particular we show that numerically flat Higgs bundles have vanishing Chern classes, and that they admit filtrations whose quotients are stable flat Higgs bundles. We compare these definitions with those previously given in the case of projective varieties. Finally we study the relations between numerically effectiveness and semistability, providing semistability criteria for Higgs bundles on projective manifolds of any dimension.}, doi = {10.1515/CRELLE.2007.084}, url = {http://hdl.handle.net/1963/1840}, author = {Ugo Bruzzo and Beatriz Grana-Otero} } @article {2007, title = {Multi-bump solitons to linearly coupled systems of nonlinear Schr{\"o}dinger equations}, number = {SISSA;29/2006/M}, year = {2007}, doi = {10.1007/s00526-006-0079-0}, url = {http://hdl.handle.net/1963/1835}, author = {Antonio Ambrosetti and Eduardo Colorado and David Ruiz} } @article {2007, title = {Nearly time optimal stabilizing patchy feedbacks}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 24 (2007) 279-310}, number = {arXiv.org;math/0512531v1}, year = {2007}, abstract = {We consider the time optimal stabilization problem for a nonlinear control system $\\\\dot x=f(x,u)$. Let $\\\\tau(y)$ be the minimum time needed to steer the system from the state $y\\\\in\\\\R^n$ to the origin, and call $\\\\A(T)$ the set of initial states that can be steered to the origin in time $\\\\tau(y)\\\\leq T$. Given any $\\\\ve>0$, in this paper we construct a patchy feedback $u=U(x)$ such that every solution of $\\\\dot x=f(x, U(x))$, $x(0)=y\\\\in \\\\A(T)$ reaches an $\\\\ve$-neighborhood of the origin within time $\\\\tau(y)+\\\\ve$.}, doi = {10.1016/j.anihpc.2006.03.010}, url = {http://hdl.handle.net/1963/2185}, author = {Fabio Ancona and Alberto Bressan} } @article {2007, title = {Necessary and sufficient conditions for the chainrule in W1,1loc(RN;Rd) and BVloc(RN;Rd)}, journal = {J. Eur. Math. Soc. (JEMS) 9 (2007) 219-252}, year = {2007}, abstract = {In this paper we prove necessary and sufficient conditions for the validity of the classical chain rule in Sobolev spaces and in the space of functions of bounded variation.

}, doi = {10.4171/JEMS/78}, url = {http://hdl.handle.net/1963/2037}, author = {Giovanni Leoni and Massimiliano Morini} } @article {2007, title = {A new model for contact angle hysteresis}, number = {SISSA;37/2006/M}, year = {2007}, abstract = {We present a model which explains several experimental observations relating contact angle hysteresis with surface roughness. The model is based on the balance between released energy and dissipation, and it describes the stick-slip behavior of drops on a rough surface using ideas similar to those employed in dry friction, elasto-plasticity and fracture mechanics. The main results of our analysis are formulas giving the interval of stable contact angles as a function of the surface roughness. These formulas show that the difference between advancing and receding angles is much larger for a drop in complete contact with the substrate (Wenzel drop) than for one whose cavities are filled with air (Cassie-Baxter drop). This fact is used as the key tool to interpret the experimental evidence.}, url = {http://hdl.handle.net/1963/1848}, author = {Antonio DeSimone and Natalie Gruenewald and Felix Otto} } @mastersthesis {2007, title = {Noncommutative geometry and quantum group symmetries}, year = {2007}, school = {SISSA}, abstract = {It is a widespread belief that mathematics originates from the desire to understand (and eventually to formalize) some aspects of the real world. Quoting [Man07], {\guillemotleft}we are doing mathematics in order to understand, create, and handle things, and perhaps this understanding is mathematics{\guillemotright} . Let me thus begin with a brief discussion of the physical ideas that motivated the development of Noncommutative Geometry and Quantum Group Theory - the areas of mathematics to which this dissertation belongs. Some physicists believe, and Einstein himself expressed this view in [Ein98a], that physics progresses in stages: there is no {\textquoteleft}final\\\' theory of Nature, but simply a sequence of theories which provide more and more accurate descriptions of the real world...}, keywords = {Noncommutative geometry}, url = {http://hdl.handle.net/1963/5269}, author = {Francesco D{\textquoteright}Andrea} } @article {2007, title = {On a notion of unilateral slope for the Mumford-Shah functional}, journal = {NoDEA 13 (2007) 713-734}, number = {SISSA;78/2004/M}, year = {2007}, abstract = {In this paper we introduce a notion of unilateral slope for the Mumford-Shah functional, and provide an explicit formula in the case of smooth cracks. We show that the slope is not lower semicontinuous and study the corresponding relaxed functional.}, doi = {10.1007/s00030-006-4054-4}, url = {http://hdl.handle.net/1963/2059}, author = {Gianni Dal Maso and Rodica Toader} } @article {2007, title = {The number of eigenvalues of three-particle Schr{\"o}dinger operators on lattices}, journal = {J. Phys. A 40 (2007) 14819-14842}, number = {arXiv.org;math/0703191v1}, year = {2007}, abstract = {We consider the Hamiltonian of a system of three quantum mechanical particles (two identical fermions and boson)on the three-dimensional lattice $\\\\Z^3$ and interacting by means of zero-range attractive potentials. We describe the location and structure of the essential spectrum of the three-particle discrete Schr\\\\\\\"{o}dinger operator $H_{\\\\gamma}(K),$ $K$ being the total quasi-momentum and $\\\\gamma>0$ the ratio of the mass of fermion and boson.\\nWe choose for $\\\\gamma>0$ the interaction $v(\\\\gamma)$ in such a way the system consisting of one fermion and one boson has a zero energy resonance.\\nWe prove for any $\\\\gamma> 0$ the existence infinitely many eigenvalues of the operator $H_{\\\\gamma}(0).$ We establish for the number $N(0,\\\\gamma; z;)$ of eigenvalues lying below $z<0$ the following asymptotics $$ \\\\lim_{z\\\\to 0-}\\\\frac{N(0,\\\\gamma;z)}{\\\\mid \\\\log \\\\mid z\\\\mid \\\\mid}={U} (\\\\gamma) .$$ Moreover, for all nonzero values of the quasi-momentum $K \\\\in T^3 $ we establish the finiteness of the number $ N(K,\\\\gamma;\\\\tau_{ess}(K))$ of eigenvalues of $H(K)$ below the bottom of the essential spectrum and we give an asymptotics for the number $N(K,\\\\gamma;0)$ of eigenvalues below zero.}, doi = {10.1088/1751-8113/40/49/015}, url = {http://hdl.handle.net/1963/2576}, author = {Sergio Albeverio and Gianfausto Dell{\textquoteright}Antonio and Saidakhmat N. Lakaev} } @article {2007, title = {Numerical solution of the small dispersion limit of Korteweg de Vries and Whitham equations}, number = {SISSA;91/2005/FM}, year = {2007}, abstract = {The Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion of order $\\\\epsilon^2$, is characterized by the appearance of a zone of rapid modulated oscillations of wave-length of order $\\\\epsilon$. These oscillations are approximately described by the elliptic solution of KdV where the amplitude, wave-number and frequency are not constant but evolve according to the Whitham equations. In this manuscript we give a quantitative analysis of the discrepancy between the numerical solution of the KdV equation in the small dispersion limit and the corresponding approximate solution for values of $\\\\epsilon$ between $10^{-1}$ and $10^{-3}$. The numerical results are compatible with a difference of order $\\\\epsilon$ within the {\textquoteleft}interior\\\' of the Whitham oscillatory zone, of order $\\\\epsilon^{1/3}$ at the left boundary outside the Whitham zone and of order $\\\\epsilon^{1/2}$ at the right boundary outside the Whitham zone.}, doi = {10.1002/cpa.20183}, url = {http://hdl.handle.net/1963/1788}, author = {Tamara Grava and Christian Klein} } @article {2007, title = {Numerical study of a multiscale expansion of KdV and Camassa-Holm equation}, number = {arXiv.org;math-ph/0702038v1}, year = {2007}, abstract = {We study numerically solutions to the Korteweg-de Vries and Camassa-Holm equation close to the breakup of the corresponding solution to the dispersionless equation. The solutions are compared with the properly rescaled numerical solution to a fourth order ordinary differential equation, the second member of the Painlev\\\\\\\'e I hierarchy. It is shown that this solution gives a valid asymptotic description of the solutions close to breakup. We present a detailed analysis of the situation and compare the Korteweg-de Vries solution quantitatively with asymptotic solutions obtained via the solution of the Hopf and the Whitham equations. We give a qualitative analysis for the Camassa-Holm equation}, url = {http://hdl.handle.net/1963/2527}, author = {Tamara Grava and Christian Klein} } @article {2007, title = {Numerically flat Higgs vector bundles}, number = {SISSA;39/2005/FM}, year = {2007}, abstract = {After providing a suitable definition of numerical effectiveness for Higgs bundles, and a related notion of numerical flatness, in this paper we prove, together with some side results, that all Chern classes of a Higgs-numerically flat Higgs bundle vanish, and that a Higgs bundle is Higgs-numerically flat if and only if it is has a filtration whose quotients are flat stable Higgs bundles. We also study the relation between these numerical properties of Higgs bundles and (semi)stability.}, doi = {10.1142/S0219199707002526}, url = {http://hdl.handle.net/1963/1757}, author = {Ugo Bruzzo and Beatriz Grana-Otero} } @article {2007, title = {Parametrized curves in Lagrange Grassmannians}, journal = {C. R. Math. 345 (2007) 647-652}, number = {arXiv.org;0708.1100v1}, year = {2007}, doi = {10.1016/j.crma.2007.10.034}, url = {http://hdl.handle.net/1963/2560}, author = {Igor Zelenko and Li Chengbo} } @article {2007, title = {Perturbation techniques applied to the real vanishing viscosity approximation of an initial boundary value problem}, year = {2007}, institution = {SISSA}, url = {http://preprints.sissa.it/handle/1963/35315}, author = {Stefano Bianchini} } @article {2007, title = {Quasistatic crack growth for a cohesive zone model with prescribed crack path}, number = {SISSA;44/2005/M}, year = {2007}, abstract = {In this paper we study the quasistatic crack growth for a cohesive zone model. We assume that the crack path is prescribed and we study the time evolution of the crack in the framework of the variational theory of rate-independent processes.}, doi = {10.1017/S030821050500079X}, url = {http://hdl.handle.net/1963/1686}, author = {Gianni Dal Maso and Chiara Zanini} } @article {2007, title = {Quasistatic evolution problems for pressure-sensitive plastic materials}, journal = {Milan J. Math. 75 (2007) 117-134}, number = {SISSA;27/2007/M}, year = {2007}, abstract = {We study quasistatic evolution problems for pressure-sensitive plastic materials in the context of small strain associative perfect plasticity.}, doi = {10.1007/s00032-007-0071-y}, url = {http://hdl.handle.net/1963/1962}, author = {Gianni Dal Maso and Alexey Demyanov and Antonio DeSimone} } @article {2007, title = {Reciprocal transformations and flat metrics on Hurwitz spaces}, journal = {J. Phys. A 40 (2007) 10769-10790}, number = {arXiv.org;0704.1779v2}, year = {2007}, abstract = {We consider hydrodynamic systems which possess a local Hamiltonian structure of Dubrovin-Novikov type. To such a system there are also associated an infinite number of nonlocal Hamiltonian structures. We give necessary and sufficient conditions so that, after a nonlinear transformation of the independent variables, the reciprocal system still possesses a local Hamiltonian structure of Dubrovin-Novikov type. We show that, under our hypotheses, bi-hamiltonicity is preserved by the reciprocal transformation. Finally we apply such results to reciprocal systems of genus g Whitham-KdV modulation equations.}, doi = {10.1088/1751-8113/40/35/004}, url = {http://hdl.handle.net/1963/2210}, author = {Simonetta Abenda and Tamara Grava} } @article {2007, title = {Reduced density matrices and Bose-Einstein condensation}, number = {SISSA;39/2007/MP}, year = {2007}, abstract = {Emergence and applications of the ubiquitous tool of reduced density matrices in the rigorous analysis of Bose Einstein condensation is reviewed, and new related results are added. The need and the nature of scaling limits of infinitely many particles is discussed, which imposes that a physically meaningful and mathematically well-posed definition of asymptotic condensation is placed at the level of marginals.\\nThe topic of correlations in the condensed state is addressed in order to show their influence at this level of marginals, both in the true condensed state and in the suitable trial functions one introduces to approximate the many-body structure and energy. Complete condensation is shown to be equivalently defined at any fixed k-body level, both for pure and mixed states. Further, it is proven to be equivalent to some other characterizations in terms of asymptotic factorization of the many-body state, which are currently present in the literature.}, url = {http://hdl.handle.net/1963/1986}, author = {Alessandro Michelangeli} } @article {2007, title = {On the reductions and classical solutions of the Schlesinger equations}, journal = {Differential equations and quantum groups, IRMA Lect. Math. Theor. Phys. 9 (2007) 157-187}, year = {2007}, publisher = {SISSA}, abstract = {The Schlesinger equations S(n,m) describe monodromy preserving\\r\\ndeformations of order m Fuchsian systems with n+1 poles. They\\r\\ncan be considered as a family of commuting time-dependent Hamiltonian\\r\\nsystems on the direct product of n copies of m{\texttimes}m matrix algebras\\r\\nequipped with the standard linear Poisson bracket. In this paper we address\\r\\nthe problem of reduction of particular solutions of {\textquotedblleft}more complicated{\textquotedblright}\\r\\nSchlesinger equations S(n,m) to {\textquotedblleft}simpler{\textquotedblright} S(n',m') having n' < n\\r\\nor m' < m.}, url = {http://hdl.handle.net/1963/6472}, author = {Boris Dubrovin and Marta Mazzocco} } @article {2007, title = {On the regularity of weak solutions to H-systems}, journal = {Atti .Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 209-219}, number = {SISSA;36/2005/M}, year = {2007}, abstract = {Abstract. In this paper we prove that every weak solution to the H-surface equation is locally bounded, provided the prescibed mean curvatore H is asymptotic to a constant at infinity (with a suitable decay rate). No smoothness ssumptions are required on H. We consider also the Dirichlet problem....}, url = {http://hdl.handle.net/1963/1753}, author = {Roberta Musina} } @article {2007, title = {Role of scaling limits in the rigorous analysis of Bose-Einstein condensation}, journal = {J. Math. Phys. 48 (2007) 102102}, number = {SISSA;14/2007/MP}, year = {2007}, abstract = {In the context of the rigorous analysis of Bose-Einstein condensation, recent achievements have been obtained in the form of asymptotic results when some appropriate scaling is performed in the Hamiltonian, and the limit of infinite number of particles is taken. In particular, two modified thermodynamic limits of infinite dilution turned out to provide an insight in this analysis, the so-\\ncalled Gross-Pitaevskii limit and the related Tomas-Fermi limit. Here such scalings are discussed with respect to their physical and mathematical motivations, and to the currently known results obtained within this framework.}, doi = {10.1063/1.2783114}, url = {http://hdl.handle.net/1963/1984}, author = {Alessandro Michelangeli} } @article {2007, title = {Semistable principal Higgs bundles}, number = {SISSA;89/2007/MP}, year = {2007}, url = {http://hdl.handle.net/1963/2533}, author = {Ugo Bruzzo and Beatriz Grana-Otero} } @article {2007, title = {Smooth toric DM stacks}, number = {SISSA;64/2007/MP}, year = {2007}, abstract = {We give a new definition of smooth toric DM stacks in the same spirit of toric varieties. We show that our definition is equivalent to the one of Borisov, Chen and Smith in terms of stacky fans. In particular, we give a geometric interpretation of the combinatorial data contained in a stacky fan. We also give a bottom up classification in terms of simplicial toric varieties and fiber products of root stacks.}, url = {http://hdl.handle.net/1963/2120}, author = {Barbara Fantechi and Etienne Mann and Fabio Nironi} } @article {2007, title = {Soft elasticity and microstructure in smectic C elastomers}, number = {SISSA;05/2006/M}, year = {2007}, abstract = {Smectic C elastomers are layered materials exhibiting a solid-like elastic response along the layer normal and a rubbery one in the plane. The set of strains minimizing the elastic energy contains a one-parameter family of simple stretches associated with an internal degree of freedom, coming from the in-plane component of the director. We investigate soft elasticity and the corresponding microstructure by determining the quasiconvex hull of the set , and use this to propose experimental tests that should make the predicted soft response observable.}, doi = {10.1007/s00161-006-0031-8}, url = {http://hdl.handle.net/1963/1811}, author = {Antonio DeSimone and James Adams and Sergio Conti} } @article {2007, title = {Solutions of vectorial Hamilton-Jacobi equations and minimizers of nonquasiconvex functionals}, journal = {J. Math. Anal. Appl. 335 (2007) 1143-1160}, year = {2007}, abstract = {We provide a unified approach to prove existence results for the Dirichlet problem for Hamilton-Jacobi equations and for the minimum problem for nonquasiconvex functionals of the Calculus of Variations with affine boundary data. The idea relies on the definition of integro-extremal solutions introduced in the study of nonconvex scalar variational problem.}, doi = {10.1016/j.jmaa.2007.02.034}, url = {http://hdl.handle.net/1963/2763}, author = {Sandro Zagatti} } @article {2007, title = {Solutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part II: proof of the existence result}, number = {SISSA;52/2007/M}, year = {2007}, abstract = {We prove existence of a special class of solutions to the (elliptic) Nonlinear Schroedinger Equation $- \\\\epsilon^2 \\\\Delta \\\\psi + V(x) \\\\psi = |\\\\psi|^{p-1} \\\\psi$ on a manifold or in the Euclidean space. Here V represents the potential, p is an exponent greater than 1 and $\\\\epsilon$ a small parameter corresponding to the Planck constant. As $\\\\epsilon$ tends to zero (namely in the semiclassical limit) we prove existence of complex-valued solutions which concentrate along closed curves, and whose phase in highly oscillatory. Physically, these solutions carry quantum-mechanical momentum along the limit curves. In the first part of this work we identified the limit set and constructed approximate solutions, while here we give the complete proof of our main existence result.}, url = {http://hdl.handle.net/1963/2111}, author = {Fethi Mahmoudi and Andrea Malchiodi} } @article {2007, title = {Solutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part I: study of the limit set and approximate solutions}, number = {SISSA;51/2007/M}, year = {2007}, abstract = {We prove existence of a special class of solutions to the (elliptic) Nonlinear Schroeodinger Equation $- \\\\epsilon^2 \\\\Delta \\\\psi + V(x) \\\\psi = |\\\\psi|^{p-1} \\\\psi$, on a manifold or in the Euclidean space. Here V represents the potential, p an exponent greater than 1 and $\\\\epsilon$ a small parameter corresponding to the Planck constant. As $\\\\epsilon$ tends to zero (namely in the semiclassical limit) we prove existence of complex-valued solutions which concentrate along closed curves, and whose phase is highly oscillatory. Physically, these solutions carry quantum-mechanical momentum along the limit curves. In this first part we provide the characterization of the limit set, with natural stationarity and non-degeneracy conditions. We then construct an approximate solution up to order $\\\\epsilon^2$, showing that these conditions appear naturally in a Taylor expansion of the equation in powers of $\\\\epsilon$. Based on these, an existence result will be proved in the second part.}, url = {http://hdl.handle.net/1963/2112}, author = {Fethi Mahmoudi and Andrea Malchiodi and Marcelo Montenegro} } @article {2007, title = {Some existence results for the Toda system on closed surfaces}, journal = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 391-412}, number = {SISSA;75/2005/M}, year = {2007}, abstract = {Given a compact closed surface $\\\\Sig$, we consider the {\\\\em generalized Toda} system of equations on $\\\\Sig$: $- \\\\D u_i = \\\\sum_{j=1}^2 \\\\rho_j a_{ij} \\\\left( \\\\frac{h_j e^{u_j}}{\\\\int_\\\\Sig h_j e^{u_j} dV_g} - 1 \\\\right)$ for $i = 1, 2$, where $\\\\rho_1, \\\\rho_2$ are real parameters and $h_1, h_2$ are smooth positive functions. Exploiting the variational structure of the problem and using a new minimax scheme we prove existence of solutions for generic values of $\\\\rho_1$ and for $\\\\rho_2 < 4 \\\\pi$.}, doi = {10.4171/RLM/504}, url = {http://hdl.handle.net/1963/1775}, author = {Andrea Malchiodi and Cheikh Birahim Ndiaye} } @article {2007, title = {Stability of front tracking solutions to the initial and boundary value problem for systems of conservation laws}, journal = {NoDEA Nonlinear Differential Equations Appl. 14 (2007) 569-592}, number = {SISSA;68/2005/M}, year = {2007}, doi = {10.1007/s00030-007-5010-7}, url = {http://hdl.handle.net/1963/1769}, author = {Andrea Marson and Carlotta Donadello} } @article {2007, title = {Standing waves of some coupled Nonlinear Schr{\"o}dinger Equations}, number = {SISSA;02/2006/M}, year = {2007}, abstract = {We deal with a class of systems of NLS equations, proving the existence of bound and ground states provided the coupling parameter is small, respectively, large.}, doi = {10.1112/jlms/jdl020}, url = {http://hdl.handle.net/1963/1821}, author = {Antonio Ambrosetti and Eduardo Colorado} } @article {2007, title = {Strengthened convergence of marginals to the cubic nonlinear Schroedinger equation}, number = {SISSA;35/2007/MP}, year = {2007}, abstract = {We rewrite a recent derivation of the cubic non-linear Schroedinger equation by Adami, Golse, and Teta in the more natural formof the asymptotic factorisation of marginals at any fixed time and in the trace norm. This is the standard form in which the emergence of the\\nnon-linear effective dynamics of a large system of interacting bosons is\\nproved in the literature.}, url = {http://hdl.handle.net/1963/1977}, author = {Alessandro Michelangeli} } @article {2007, title = {Surfactants in Foam Stability: A Phase-Field Model}, journal = {Arch. Rational Mech. Anal. 183 (2007) 411-456}, year = {2007}, abstract = {The role of surfactants in stabilizing the formation of bubbles in foams is studied using a phase-field model. The analysis is centered on a van der Walls-Cahn-Hilliard-type energy with an added term accounting for the interplay between the presence of a surfactant density and the creation of interfaces. In particular, it is concluded that the surfactant segregates to the interfaces, and that the prescriptionof the distribution of surfactant will dictate the locus of interfaces, what is in agreement with experimentation.}, doi = {10.1007/s00205-006-0012-x}, url = {http://hdl.handle.net/1963/2035}, author = {Irene Fonseca and Massimiliano Morini and Valeriy Slastikov} } @article {2007, title = {Time optimal swing-up of the planar pendulum}, journal = {46th IEEE Conference on Decision and Control (2007) 5389 - 5394}, number = {SISSA;50/2006/M}, year = {2007}, abstract = {This paper presents qualitative and numerical results on the global structure of the time optimal trajectories of the planar pendulum on a cart.}, doi = {10.1109/CDC.2007.4434688}, url = {http://hdl.handle.net/1963/1867}, author = {Mireille E. Broucke and Paolo Mason and Benedetto Piccoli} } @article {2007, title = {Time-dependent systems of generalized Young measures}, number = {SISSA;98/2005/M}, year = {2007}, abstract = {In this paper some new tools for the study of evolution problems in the framework of Young measures are introduced. A suitable notion of time-dependent system of generalized Young measures is defined, which allows to extend the classical notions of total variation and absolute continuity with respect to time, as well as the notion of time derivative. The main results are a Helly type theorem for sequences of systems of generalized Young measures and a theorem about the existence of the time derivative for systems with bounded variation with respect to time.}, url = {http://hdl.handle.net/1963/1795}, author = {Gianni Dal Maso and Antonio DeSimone and Maria Giovanna Mora and Massimiliano Morini} } @article {2007, title = {Twisted noncommutative equivariant}, number = {SISSA;42/2007/MP}, year = {2007}, abstract = {We propose Weil and Cartan models for the equivariant cohomology of covariant actions on toric deformation manifolds. The construction is based on the noncommutative Weil algebra of Alekseev and Meinrenken; we show that one can implement a Drinfeld twist of their models in order to take into account the noncommutativity of the spaces we are acting on.}, url = {http://hdl.handle.net/1963/1991}, author = {Lucio Cirio} } @article {2007, title = {Uniqueness and continuous dependence on boundary data for integro-extremal minimizers of the functional of the gradient}, journal = {J. Convex Anal. 14 (2007) 705-727}, year = {2007}, abstract = {We study some qualitative properties of the integro-extremal minimizers of the functional of the gradient defined on Sobolev spaces with Dirichlet boundary conditions. We discuss their use in the non-convex case via viscosity methods and give conditions under which they are unique and depend continuously on boundary data.}, url = {http://hdl.handle.net/1963/2762}, author = {Sandro Zagatti} } @article {2007, title = {Viscosity solutions of Hamilton-Jacobi equations with discontinuous coefficients}, journal = {J. Hyperbolic Differ. Equ. 4 (2007) 771-795}, number = {SISSA;23/2003/M}, year = {2007}, publisher = {World Scientific}, abstract = {We consider Hamilton--Jacobi equations, where the Hamiltonian depends discontinuously on both the spatial and temporal location. Our main results are the existence and well--posedness of a viscosity solution to the Cauchy problem. We define a viscosity solution by treating the discontinuities in the coefficients analogously to \\\"internal boundaries\\\". By defining an appropriate penalization function, we prove that viscosity solutions are unique. The existence of viscosity solutions is established by showing that a sequence of front tracking approximations is compact in $L^\\\\infty$, and that the limits are viscosity solutions.}, doi = {10.1142/S0219891607001355}, url = {http://hdl.handle.net/1963/2907}, author = {Giuseppe Maria Coclite and Nils Henrik Risebro} } @article {2006, title = {2-d stability of the N{\'e}el wall}, journal = {Calc. Var. Partial Differential Equations 27 (2006) 233-253}, year = {2006}, abstract = {We are interested in thin-film samples in micromagnetism, where the magnetization m is a 2-d unit-length vector field. More precisely we are interested in transition layers which connect two opposite magnetizations, so called N{\'e}el walls.}, doi = {10.1007/s00526-006-0019-z}, url = {http://hdl.handle.net/1963/2194}, author = {Antonio DeSimone and Hans Knuepfer and Felix Otto} } @article {2006, title = {4e-condensation in a fully frustrated Josephson junction diamond chain}, journal = {Phys. Rev. B 73 (2006) 100502(R)}, number = {arXiv.org;cond-mat/0511423v1}, year = {2006}, abstract = {Fully frustrated one-dimensional diamond Josephson chains have been shown [B. Dou\\\\c{c}ot and J. Vidal, Phys. Rev. Lett. {\\\\bf 88}, 227005 (2002)] to posses a remarkable property: The superfluid phase occurs through the condensation of pairs of Cooper pairs. By means of Monte Carlo simulations we analyze quantitatively the Insulator to $4e$-Superfluid transition. We determine the location of the critical point and discuss the behaviour of the phase-phase correlators. For comparison we also present the case of a diamond chain at zero and 1/3 frustration where the standard $2e$-condensation is observed.

}, doi = {10.1103/PhysRevB.73.100502}, url = {http://hdl.handle.net/1963/2400}, author = {Matteo Rizzi and Vittorio Cataudella and Rosario Fazio} } @article {2006, title = {Almost Global Stochastic Feedback Stabilization of Conditional Quantum Dynamics}, number = {SISSA;80/2005/M}, year = {2006}, abstract = {We propose several parametrization-free solutions to the problem of quantum state reduction control by means of continuous measurement and smooth quantum feedback. In particular, we design a feedback law for which almost global stochastic feedback stabilization can be proved analytically by means of Lyapunov techinques. This synthesis arises very naturally from the physics of the problem, as it relies on the variance associated with the quantum filtering process.}, url = {http://hdl.handle.net/1963/1727}, author = {Claudio Altafini and Francesco Ticozzi} } @article {2006, title = {An artificial viscosity approach to quasistatic crack growth}, number = {SISSA;43/2006/M}, year = {2006}, abstract = {We introduce a new model of irreversible quasistatic crack growth in which the evolution of cracks is the limit of a suitably modified $\\\\epsilon$-gradient flow of the energy functional, as the \\\"viscosity\\\" parameter $\\\\epsilon$ tends to zero.}, url = {http://hdl.handle.net/1963/1850}, author = {Rodica Toader and Chiara Zanini} } @article {2006, title = {A Birkhoff-Lewis-Type Theorem for Some Hamiltonian PDEs}, journal = {SIAM J. Math. Anal. 37 (2006) 83-102}, number = {arXiv.org;math/0310182v1}, year = {2006}, abstract = {In this paper we give an extension of the Birkhoff--Lewis theorem to some semilinear PDEs. Accordingly we prove existence of infinitely many periodic orbits with large period accumulating at the origin. Such periodic orbits bifurcate from resonant finite dimensional invariant tori of the fourth order normal form of the system. Besides standard nonresonance and nondegeneracy assumptions, our main result is obtained assuming a regularizing property of the nonlinearity. We apply our main theorem to a semilinear beam equation and to a nonlinear Schr\\\\\\\"odinger equation with smoothing nonlinearity.}, doi = {10.1137/S0036141003436107}, url = {http://hdl.handle.net/1963/2159}, author = {Dario Bambusi and Massimiliano Berti} } @article {2006, title = {Born approximation in the problem of the rigorous derivation of the Gross-Pitaevskii equation}, number = {SISSA;13/2006/FM}, year = {2006}, abstract = {\\\"It has a flavour of Mathematical Physics...\\\"With these words, just few years ago, prof. Di Giacomo\\nused to introduce the topic of the Born approximation within a nonrelativistic potential theory, in his {\textquoteleft}oversize\\\' course of Theoretical Physics in Pisa. Something maybe too fictitious inside the formal theory of the scattering he was teaching us at that point of the course. Now that I\\\'m (studying to become) a Mathematical Physicist indeed, dealing with such an {\textquoteleft}exotic tasting\\\' topic, those words come back to the mind, into a new perspective. Here the very recent problem of the rigorous derivation of\\nthe cubic nonlinear Schr{\"o}dinger equation (the Gross-Pitaevski{\^\i} equation) is reviewed and discussed, with respect to the role of the Born approximation that one ends up with in an appropriate scaling limit}, url = {http://hdl.handle.net/1963/1819}, author = {Alessandro Michelangeli} } @article {2006, title = {Bound and ground states of coupled nonlinear Schr{\"o}dinger equations}, journal = {C. R. Acad. Sci. Paris, Ser. I 342 (2006) 453-458}, year = {2006}, abstract = {We prove existence of bound and ground states of some systems of coupled nonlinear Schrodinger equations.}, doi = {10.1016/j.crma.2006.01.024}, url = {http://hdl.handle.net/1963/2149}, author = {Antonio Ambrosetti and Eduardo Colorado} } @article {2006, title = {Bound states of Nonlinear Schroedinger Equations with Potentials Vanishing at Infinity}, journal = {J. Anal. Math. 98 (2006) 317-348}, number = {SISSA;18/2005/M}, year = {2006}, doi = {10.1007/BF02790279}, url = {http://hdl.handle.net/1963/1756}, author = {Antonio Ambrosetti and Andrea Malchiodi and David Ruiz} } @article {2006, title = {On Bressan\\\'s conjecture on mixing properties of vector fields}, journal = {Self-Similar Solutions of Nonlinear PDE / Ed. Piotr Biler and Grzegorz Karch. - Banach Center Publ. 74 (2006) 13-31}, number = {SISSA;70/2005/M}, year = {2006}, url = {http://hdl.handle.net/1963/1806}, author = {Stefano Bianchini} } @article {2006, title = {On a Camassa-Holm type equation with two dependent variables}, number = {SISSA;35/2005/FM}, year = {2006}, abstract = {We consider a generalization of the Camassa Holm (CH) equation with two dependent variables, called CH2, introduced in [16]. We briefly provide an alternative derivation of it based on the theory of Hamiltonian structures\\non (the dual of) a Lie Algebra. The Lie Algebra here involved is the same algebra underlying the NLS hierarchy. We study the structural properties of the CH2 hierarchy within the bihamiltonian theory of integrable PDEs, and\\nprovide its Lax representation. Then we explicitly discuss how to construct classes of solutions, both of peakon and of algebro-geometrical type. We finally sketch the construction of a class of singular solutions, defined by setting to zero one of the two dependent variables.}, doi = {10.1088/0305-4470/39/2/004}, url = {http://hdl.handle.net/1963/1721}, author = {Gregorio Falqui} } @article {2006, title = {A Canonical Frame for Nonholonomic Rank Two Distributions of Maximal Class}, number = {SISSA;25/2005/M}, year = {2006}, abstract = {In 1910 E. Cartan constructed the canonical frame and found the most symmetric case for maximally nonholonomic rank 2 distributions in R5. We solve the analogous problems for rank 2 distributions in Rn for arbitrary n > 5. Our method is a kind of symplectification of the problem and it is completely different from the Cartan method of equivalence.}, doi = {10.1016/j.crma.2006.02.010}, url = {http://hdl.handle.net/1963/1712}, author = {Boris Doubrov and Igor Zelenko} } @article {2006, title = {Cantor families of periodic solutions for completely resonant nonlinear wave equations}, journal = {Duke Math. J. 134 (2006) 359-419}, number = {arXiv.org;math/0410618v1}, year = {2006}, abstract = {We prove the existence of small amplitude, $2\\\\pi \\\\slash \\\\om$-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions, for any frequency $ \\\\om $ belonging to a Cantor-like set of positive measure and for a new set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem. In spite of the complete resonance of the equation we show that we can still reduce the problem to a {\\\\it finite} dimensional bifurcation equation. Moreover, a new simple approach for the inversion of the linearized operators required by the Nash-Moser scheme is developed. It allows to deal also with nonlinearities which are not odd and with finite spatial regularity.}, doi = {10.1215/S0012-7094-06-13424-5}, url = {http://hdl.handle.net/1963/2161}, author = {Massimiliano Berti and Philippe Bolle} } @article {2006, title = {Classification of stable time-optimal controls on 2-manifolds}, journal = {J. Math. Sci. 135 (2006) 3109-3124}, number = {SISSA;20/2004/M}, year = {2006}, doi = {10.1007/s10958-006-0148-0}, url = {http://hdl.handle.net/1963/2196}, author = {Ugo Boscain and Igor Nikolaev and Benedetto Piccoli} } @article {2006, title = {Common Polynomial Lyapunov Functions for Linear Switched Systems}, journal = {SIAM J. Control Optim. 45 (2006) 226-245}, number = {arXiv.org;math/0403209v2}, year = {2006}, abstract = {In this paper, we consider linear switched systems $\\\\dot x(t)=A_{u(t)} x(t)$, $x\\\\in\\\\R^n$, $u\\\\in U$, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching ({\\\\bf UAS} for short). We first prove that, given a {\\\\bf UAS} system, it is always possible to build a common polynomial Lyapunov function. Then our main result is that the degree of that common polynomial Lyapunov function is not uniformly bounded over all the {\\\\bf UAS} systems. This result answers a question raised by Dayawansa and Martin. A generalization to a class of piecewise-polynomial Lyapunov functions is given.}, doi = {10.1137/040613147}, url = {http://hdl.handle.net/1963/2181}, author = {Paolo Mason and Ugo Boscain and Yacine Chitour} } @article {2006, title = {Compactness of solutions to some geometric fourth-order equations}, journal = {J. Reine Angew. Math. 594 (2006) 137-174}, number = {arXiv.org;math/0410140v2}, year = {2006}, abstract = {We prove compactness of solutions to some fourth order equations with exponential nonlinearities on four manifolds. The proof is based on a refined bubbling analysis, for which the main estimates are given in integral form. Our result is used in a subsequent paper to find critical points (via minimax arguments) of some geometric functional, which give rise to conformal metrics of constant $Q$-curvature. As a byproduct of our method, we also obtain compactness of such metrics.}, doi = {10.1515/CRELLE.2006.038}, url = {http://hdl.handle.net/1963/2126}, author = {Andrea Malchiodi} } @article {2006, title = {Concentration at manifolds of arbitrary dimension for a singularly perturbed Neumann problem}, journal = {Atti Accad. Naz Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 17 (2006) 279-290}, year = {2006}, abstract = {We consider the equation $- \\\\e^2 \\\\D u + u = u^p$ in $\\\\O \\\\subseteq \\\\R^N$, where $\\\\O$ is open, smooth and bounded, and we prove concentration of solutions along $k$-dimensional minimal submanifolds of $\\\\pa \\\\O$, for $N \\\\geq 3$ and for $k \\\\in \\\\{1, \\\\dots, N-2\\\\}$. We impose Neumann boundary conditions, assuming $1<\\\\frac{N-k+2}{N-k-2}$ and $\\\\e \\\\to 0^+$. This result settles in full generality a phenomenon previously considered only in the particular case $N = 3$ and $k = 1$.}, url = {http://hdl.handle.net/1963/2170}, author = {Fethi Mahmoudi and Andrea Malchiodi} } @article {2006, title = {Conservative Solutions to a Nonlinear Variational Wave Equation}, journal = {Comm. Math. Phys. 266 (2006) 471-497}, number = {arXiv.org;math/0502058v1}, year = {2006}, abstract = {We establish the existence of a conservative weak solution to the Cauchy problem for the nonlinear variational wave equation $u_{tt} - c(u)(c(u)u_x)_x=0$, for initial data of finite energy. Here $c(\\\\cdot)$ is any smooth function with uniformly positive bounded values.}, doi = {10.1007/s00220-006-0047-8}, url = {http://hdl.handle.net/1963/2184}, author = {Alberto Bressan and Zheng Yuxi} } @article {2006, title = {A cyclic integral on k-Minkowski noncommutative space-time}, journal = {Int. J. Mod. Phys. A 21 (2006) 3133-3150}, number = {arXiv.org;hep-th/0407227v1}, year = {2006}, abstract = {We examine some alternative possibilities for an action functional for $\\\\kappa$-Minkowski noncommutative spacetime, with an approach which should be applicable to other spacetimes with coordinate-dependent commutators of the spacetime coordinates ($[x_\\\\mu,x_\\\\nu]=f_{\\\\mu,\\\\nu}(x)$). Early works on $\\\\kappa$-Minkowski focused on $\\\\kappa$-Poincar\\\\\\\'e covariance and the dependence of the action functional on the choice of Weyl map, renouncing to invariance under cyclic permutations of the factors composing the argument of the action functional. A recent paper (hep-th/0307149), by Dimitrijevic, Jonke, Moller, Tsouchnika, Wess and Wohlgenannt, focused on a specific choice of Weyl map and, setting aside the issue of $\\\\kappa$-Poincar\\\\\\\'e covariance of the action functional, introduced in implicit form a cyclicity-inducing measure. We provide an explicit formula for (and derivation of) a choice of measure which indeed ensures cyclicity of the action functional, and we show that the same choice of measure is applicable to all the most used choices of Weyl map. We find that this {\textquoteleft}{\textquoteleft}cyclicity-inducing measure\\\'\\\' is not covariant under $\\\\kappa$-Poincar\\\\\\\'e transformations. We also notice that the cyclicity-inducing measure can be straightforwardly derived using a map which connects the $\\\\kappa$-Minkowski spacetime coordinates and the spacetime coordinates of a {\textquoteleft}{\textquoteleft}canonical\\\'\\\' noncommutative spacetime, with coordinate-independent commutators.}, doi = {10.1142/S0217751X06031077}, url = {http://hdl.handle.net/1963/2158}, author = {Alessandra Agostini and Giovanni Amelino-Camelia and Michele Arzano and Francesco D{\textquoteright}Andrea} } @article {2006, title = {The Dirichlet problem for H-systems with small boundary data: blowup phenomena and nonexistence results}, journal = {Arch. Ration. Mech. Anal. 181 (2006) 1-42}, number = {SISSA;79/2004/M}, year = {2006}, doi = {10.1007/s00205-005-0398-x}, url = {http://hdl.handle.net/1963/2252}, author = {Paolo Caldiroli and Roberta Musina} } @article {2006, title = {An estimation of the controllability time for single-input systems on compact Lie Groups}, journal = {ESAIM Control Optim. Calc. Var. 12 (2006) 409-441}, year = {2006}, abstract = {Geometric control theory and Riemannian techniques are used to describe the reachable set at time t of left invariant single-input control systems on semi-simple compact Lie groups and to estimate the minimal time needed to reach any point from identity. This method provides an effective way to give an upper and a lower bound for the minimal time needed to transfer a controlled quantum system with a drift from a given initial position to a given final position. The bounds include diameters of the flag manifolds; the latter are also explicitly computed in the paper.}, doi = {10.1051/cocv:2006007}, url = {http://hdl.handle.net/1963/2135}, author = {Andrei A. Agrachev and Thomas Chambrion} } @article {2006, title = {Experimental and modeling studies of desensitization of P2X3 receptors.}, journal = {Molecular pharmacology. 2006 Jul; 70(1):373-82}, number = {PMID:16627751;}, year = {2006}, publisher = {the American Society for Pharmacology and Experimental Therapeutics}, abstract = {The function of ATP-activated P2X3 receptors involved in pain sensation is modulated by desensitization, a phenomenon poorly understood. The present study used patch-clamp recording from cultured rat or mouse sensory neurons and kinetic modeling to clarify the properties of P2X3 receptor desensitization. Two types of desensitization were observed, a fast process (t1/2 = 50 ms; 10 microM ATP) following the inward current evoked by micromolar agonist concentrations, and a slow process (t1/2 = 35 s; 10 nM ATP) that inhibited receptors without activating them. We termed the latter high-affinity desensitization (HAD). Recovery from fast desensitization or HAD was slow and agonist-dependent. When comparing several agonists, there was analogous ranking order for agonist potency, rate of desensitization and HAD effectiveness, with 2-methylthioadenosine triphosphate the strongest and beta,gamma-methylene-ATP the weakest. HAD was less developed with recombinant (ATP IC50 = 390 nM) than native P2X3 receptors (IC50 = 2.3 nM). HAD could also be induced by nanomolar ATP when receptors seemed to be nondesensitized, indicating that resting receptors could express high-affinity binding sites. Desensitization properties were well accounted for by a cyclic model in which receptors could be desensitized from either open or closed states. Recovery was assumed to be a multistate process with distinct kinetics dependent on the agonist-dependent dissociation rate from desensitized receptors. Thus, the combination of agonist-specific mechanisms such as desensitization onset, HAD, and resensitization could shape responsiveness of sensory neurons to P2X3 receptor agonists. By using subthreshold concentrations of an HAD-potent agonist, it might be possible to generate sustained inhibition of P2X3 receptors for controlling chronic pain.}, doi = {10.1124/mol.106.023564}, url = {http://hdl.handle.net/1963/4974}, author = {Elena Sokolova and Andrei Skorinkin and Igor Moiseev and Andrei A. Agrachev and Andrea Nistri and Rashid Giniatullin} } @article {2006, title = {Extended affine Weyl groups and Frobenius manifolds -- II}, number = {SISSA;90/2005/FM}, year = {2006}, abstract = {For the root system of type $B_l$ and $C_l$, we generalize the result of \\\\cite{DZ1998} by showing the existence of a Frobenius manifold structure on the orbit space of the extended affine Weyl group that corresponds to any vertex of the Dynkin diagram instead of a particular choice of \\\\cite{DZ1998}.}, url = {http://hdl.handle.net/1963/1787}, author = {Boris Dubrovin and Zhang Youjin and Zuo Dafeng} } @article {2006, title = {Forced vibrations of wave equations with non-monotone nonlinearities}, journal = {Ann. Inst. H. Poincar{\'e} Anal. Non Lin{\'e}aire 23 (2006) 439-474}, number = {arXiv.org;math/0410619v1}, year = {2006}, abstract = {We prove existence and regularity of periodic in time solutions of completely resonant nonlinear forced wave equations with Dirichlet boundary conditions for a large class of non-monotone forcing terms. Our approach is based on a variational Lyapunov-Schmidt reduction. It turns out that the infinite dimensional bifurcation equation exhibits an intrinsic lack of compactness. We solve it via a minimization argument and a-priori estimate methods inspired to regularity theory of Rabinowitz.}, doi = {10.1016/j.anihpc.2005.05.004}, url = {http://hdl.handle.net/1963/2160}, author = {Massimiliano Berti and Luca Biasco} } @article {2006, title = {Fundamental form and Cartan tensor of (2,5)-distributions coincide}, journal = {J. Dyn. Control Syst. 12 (2006) 247-276}, number = {arXiv.org;math/0402195v2}, year = {2006}, abstract = {In our previous paper for generic rank 2 vector distributions on n-dimensional manifold (n greater or equal to 5) we constructed a special differential invariant, the fundamental form. In the case n=5 this differential invariant has the same algebraic nature, as the covariant binary biquadratic form, constructed by E.Cartan in 1910, using his {\textquoteleft}{\textquoteleft}reduction- prolongation\\\'\\\' procedure (we call this form Cartan\\\'s tensor). In the present paper we prove that our fundamental form coincides (up to constant factor -35) with Cartan\\\'s tensor. This result explains geometric reason for existence of Cartan\\\'s tensor (originally this tensor was obtained by very sophisticated algebraic manipulations) and gives the true analogs of this tensor in Riemannian geometry. In addition, as a part of the proof, we obtain a new useful formula for Cartan\\\'s tensor in terms of structural functions of any frame naturally adapted to the distribution.}, doi = {10.1007/s10450-006-0383-1}, url = {http://hdl.handle.net/1963/2187}, author = {Igor Zelenko} } @article {2006, title = {On geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on distributions of corank 1}, journal = {J. Math. Sci. 135 (2006) 3168-3194}, number = {arXiv.org;math/0406111v1}, year = {2006}, abstract = {The present paper is devoted to the problem of (local) geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on generic corank 1 distributions. Using Pontryagin Maximum Principle, we treat Riemannian and sub-Riemannian cases in an unified way and obtain some algebraic necessary conditions for the geodesic equivalence of (sub-)Riemannian metrics. In this way first we obtain a new elementary proof of classical Levi-Civita\\\'s Theorem about the classification of all Riemannian geodesically equivalent metrics in a neighborhood of so-called regular (stable) point w.r.t. these metrics. Secondly we prove that sub-Riemannian metrics on contact distributions are geodesically equivalent iff they are constantly proportional. Then we describe all geodesically equivalent sub-Riemannian metrics on quasi-contact distributions. Finally we make the classification of all pairs of geodesically equivalent Riemannian metrics on a surface, which proportional in an isolated point. This is the simplest case, which was not covered by Levi-Civita\\\'s Theorem.}, doi = {10.1007/s10958-006-0151-5}, url = {http://hdl.handle.net/1963/2205}, author = {Igor Zelenko} } @article {2006, title = {Glimm interaction functional for BGK schemes}, number = {SISSA;69/2005/M}, year = {2006}, url = {http://hdl.handle.net/1963/1770}, author = {Stefano Bianchini} } @article {2006, title = {On Hamiltonian perturbations of hyperbolic systems of conservation laws, II: universality of critical behaviour}, number = {SISSA;89/2005/FM}, year = {2006}, abstract = {Hamiltonian perturbations of the simplest hyperbolic equation $u_t + a(u) u_x=0$ are studied. We argue that the behaviour of solutions to the perturbed equation near the point of gradient catastrophe of the unperturbed one should be essentially independent on the choice of generic perturbation neither on the choice of generic solution. Moreover, this behaviour is described by a special solution to an integrable fourth order ODE.}, doi = {10.1007/s00220-006-0021-5}, url = {http://hdl.handle.net/1963/1786}, author = {Boris Dubrovin} } @article {2006, title = {On Hamiltonian perturbations of hyperbolic systems of conservation laws I: quasitriviality of bihamiltonian perturbations}, journal = {Comm. Pure Appl. Math. 59 (2006) 559-615}, number = {arXiv.org;math/0410027}, year = {2006}, abstract = {We study the general structure of formal perturbative solutions to the Hamiltonian perturbations of spatially one-dimensional systems of hyperbolic PDEs. Under certain genericity assumptions it is proved that any bihamiltonian perturbation can be eliminated in all orders of the perturbative expansion by a change of coordinates on the infinite jet space depending rationally on the derivatives. The main tools is in constructing of the so-called quasi-Miura transformation of jet coordinates eliminating an arbitrary deformation of a semisimple bihamiltonian structure of hydrodynamic type (the quasitriviality theorem). We also describe, following \\\\cite{LZ1}, the invariants of such bihamiltonian structures with respect to the group of Miura-type transformations depending polynomially on the derivatives.}, doi = {10.1002/cpa.20111}, url = {http://hdl.handle.net/1963/2535}, author = {Boris Dubrovin and Liu Si-Qi and Zhang Youjin} } @article {2006, title = {Homogeneous polynomial forms for simultaneous stabilizability of families of linear control systems: a tensor product approach}, journal = {IEEE Trans. Automat. Control 51 (2006) 1566-1571}, year = {2006}, abstract = {The paper uses the formalism of tensor products in order to deal with the problem of simultaneous\\nstabilizability of a family of linear control systems by means of Lyapunov functions which are homogeneous polynomial forms. While the feedback synthesis seems to be nonconvex, the simultaneous stability by means of homogeneous polynomial forms of the uncontrollable modes yields (convex) necessary but not sufficient conditions for simultaneous stabilizability.}, doi = {10.1109/TAC.2006.880811}, url = {http://hdl.handle.net/1963/2226}, author = {Claudio Altafini} } @article {2006, title = {A Hopf bundle over a quantum four-sphere from the symplectic group}, journal = {Commun. Math. Phys. 263 (2006) 65-88}, number = {arXiv.org;math/0407342v2}, year = {2006}, abstract = {We construct a quantum version of the SU(2) Hopf bundle $S^7 \\\\to S^4$. The quantum sphere $S^7_q$ arises from the symplectic group $Sp_q(2)$ and a quantum 4-sphere $S^4_q$ is obtained via a suitable self-adjoint idempotent $p$ whose entries generate the algebra $A(S^4_q)$ of polynomial functions over it. This projection determines a deformation of an (anti-)instanton bundle over the classical sphere $S^4$. We compute the fundamental $K$-homology class of $S^4_q$ and pair it with the class of $p$ in the $K$-theory getting the value -1 for the topological charge. There is a right coaction of $SU_q(2)$ on $S^7_q$ such that the algebra $A(S^7_q)$ is a non trivial quantum principal bundle over $A(S^4_q)$ with structure quantum group $A(SU_q(2))$.}, doi = {10.1007/s00220-005-1494-3}, url = {http://hdl.handle.net/1963/2179}, author = {Giovanni Landi and Chiara Pagani and Cesare Reina} } @article {2006, title = {Infinite Horizon Noncooperative Differential Games}, number = {SISSA;31/2005/M}, year = {2006}, abstract = {For a non-cooperative differential game, the value functions of the various players satisfy a system of Hamilton-Jacobi equations. In the present paper, we consider a class of infinite-horizon games with nonlinear costs exponentially discounted in time. By the analysis of the value\\nfunctions, we establish the existence of Nash equilibrium solutions in feedback form and provide results and counterexamples on their uniqueness and stability.}, doi = {10.1016/j.jde.2006.01.005}, url = {http://hdl.handle.net/1963/1720}, author = {Alberto Bressan and Fabio Simone Priuli} } @article {2006, title = {An instability of the Godunov scheme}, journal = {Comm. Pure Appl. Math. 59 (2006) 1604-1638}, number = {arXiv.org;math/0502125v1}, year = {2006}, abstract = {We construct a solution to a $2\\\\times 2$ strictly hyperbolic system of conservation laws, showing that the Godunov scheme \\\\cite{Godunov59} can produce an arbitrarily large amount of oscillations. This happens when the speed of a shock is close to rational, inducing a resonance with the grid. Differently from the Glimm scheme or the vanishing viscosity method, for systems of conservation laws our counterexample indicates that no a priori BV bounds or $L^1$ stability estimates can in general be valid for finite difference schemes.}, doi = {10.1002/cpa.20141}, url = {http://hdl.handle.net/1963/2183}, author = {Alberto Bressan and Helge Kristian Jenssen and Paolo Baiti} } @article {2006, title = {Large Parameter Behavior of Equilibrium Measures}, number = {SISSA;92/2005/FM}, year = {2006}, abstract = {We study the equilibrium measure for a logarithmic potential in the presence of an external field V*(x) + tp(x), where t is a parameter, V*(x) is a smooth function and p(x) a monic polynomial. When p(x) is of an odd degree, the equilibrium measure is shown to be supported on a single interval as |t| is sufficiently large. When p(x) is of an even degree, the equilibrium measure is supported on two disjoint intervals as t is negatively large; it is supported on a single interval for convex p(x) as t is positively large and is likely to be supported on multiple disjoint intervals for non-convex p(x).}, url = {http://hdl.handle.net/1963/1789}, author = {Tamara Grava and Fei-Ran Tian} } @article {2006, title = {Local Index Formula on the Equatorial Podles Sphere}, number = {SISSA;85/2005/FM}, year = {2006}, abstract = {We discuss spectral properties of the equatorial Podles sphere. As a preparation we also study the {\textquoteleft}degenerate\\\' (i.e. $q=0$) case (related to the quantum disk). We consider two different spectral triples: one related to the Fock representation of the Toeplitz algebra and the isopectral one....}, doi = {10.1007/s11005-005-0047-1}, url = {http://hdl.handle.net/1963/1782}, author = {Francesco D{\textquoteright}Andrea and Ludwik Dabrowski} } @article {2006, title = {Matching Procedure for the Sixth Painlev{\'e} Equation (May 2006)}, journal = {Journal of Physics A: Mathematical and General, Volume 39, Issue 39, 29 September 2006, Article numberS02, Pages 11973-12031}, number = {arXiv:1010.1952;}, year = {2006}, note = {This paper appeared in May 2006. I put it on the archive now, with more that four years of delay, for completeness sake. The paper is published in J.Phys.A: Math.Gen. 39 (2006), 11973-12031, with some modifications.}, publisher = {SISSA}, abstract = {We present a constructive procedure to obtain the critical behavior of\r\nPainleve\' VI transcendents and solve the connection problem. This procedure\r\nyields two and one parameter families of solutions, including trigonometric and\r\nlogarithmic behaviors, and three classes of solutions with Taylor expansion at\r\na critical point.}, doi = {doi:10.1088/0305-4470/39/39/S02}, url = {http://hdl.handle.net/1963/6524}, author = {Davide Guzzetti} } @article {2006, title = {N=1 superpotentials from multi-instanton calculus}, number = {SISSA;73/2005/FM}, year = {2006}, abstract = {In this paper we compute gaugino and scalar condensates in N = 1 supersymmetric gauge\\ntheories with and without massive adjoint matter, using localization formulae over the multi-instanton moduli space. Furthermore we compute the chiral ring relations among the correlators of the N = 1* theory and check this result against the multi-instanton computation finding agreement.}, doi = {10.1088/1126-6708/2006/01/031}, url = {http://hdl.handle.net/1963/1773}, author = {Francesco Fucito and Jose F. Morales and Rubik Poghossian and Alessandro Tanzini} } @article {2006, title = {Normal bundles to Laufer rational curves in local Calabi-Yau threefolds}, number = {SISSA;88/2005/FM}, year = {2006}, abstract = {We prove a conjecture by F. Ferrari. Let X be the total space of a nonlinear deformation of a rank 2 holomorphic vector bundle on a smooth rational curve, such that X has trivial canonical bundle and has sections. Then the normal bundle to such sections is computed in terms of the rank of the Hessian of a suitably defined superpotential at its critical points.}, doi = {10.1007/s11005-006-0057-7}, url = {http://hdl.handle.net/1963/1785}, author = {Ugo Bruzzo and Antonio Ricco} } @article {2006, title = {On Palais-Smale sequences for H-systems: some examples}, journal = {Adv. Differential Equations 11 (2006) 931-960}, number = {SISSA;32/2005/M}, year = {2006}, abstract = {We exhibit a series of examples of Palais-Smale sequences for the Dirichlet problem associated to the mean curvature equation with null boundary condition, and we show that in the case of nonconstant mean curvature functions different kinds of blow up phenomena appear and Palais-Smale sequences may have quite wild behaviour.}, url = {http://hdl.handle.net/1963/2157}, author = {Paolo Caldiroli and Roberta Musina} } @article {Bertola:PDEBOPs, title = {The PDEs of biorthogonal polynomials arising in the two-matrix model}, journal = {Math. Phys. Anal. Geom.}, volume = {9}, number = {1}, year = {2006}, pages = {23{\textendash}52}, issn = {1385-0172}, author = {Marco Bertola and B. Eynard} } @article {Baldi2006257, title = {Periodic solutions of nonlinear wave equations for asymptotically full measure sets of frequencies}, journal = {Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni}, volume = {17}, number = {3}, year = {2006}, note = {cited By (since 1996)5}, pages = {257-277}, abstract = {We prove existence and multiplicity of small amplitude periodic solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for asymptotically full measure sets of frequencies, extending the results of [7] to new types of nonlinearities.}, issn = {11206330}, author = {P Baldi and Massimiliano Berti} } @article {2006, title = {Q-curvature flow on S^4}, journal = {J. Differential Geom. 73 (2006) 1-44}, year = {2006}, url = {http://hdl.handle.net/1963/2193}, author = {Andrea Malchiodi and Michael Struwe} } @article {2006, title = {Quantisation of bending flows}, journal = {Czechoslovak Journal of Physics 56 (2006), n. 10-11, 1143-1148}, number = {arXiv.org;nlin/0610003}, year = {2006}, abstract = {We briefly review the Kapovich-Millson notion of Bending flows as an integrable system on the space of polygons in ${\\\\bf R}^3$, its connection with a specific Gaudin XXX system, as well as the generalisation to $su(r), r>2$. Then we consider the quantisation problem of the set of Hamiltonians pertaining to the problem, quite naturally called Bending Hamiltonians, and prove that their commutativity is preserved at the quantum level.}, doi = {10.1007/s10582-006-0415-9}, url = {http://hdl.handle.net/1963/2537}, author = {Gregorio Falqui and Fabio Musso} } @article {2006, title = {Quasi-periodic solutions of completely resonant forced wave equations}, journal = {Comm. Partial Differential Equations 31 (2006) 959 - 985}, number = {SISSA;106/2004/M}, year = {2006}, abstract = {We prove existence of quasi-periodic solutions with two frequencies of completely resonant, periodically forced nonlinear wave equations with periodic spatial boundary conditions. We consider both the cases the forcing frequency is: (Case A) a rational number and (Case B) an irrational number.}, doi = {10.1080/03605300500358129}, url = {http://hdl.handle.net/1963/2234}, author = {Massimiliano Berti and Michela Procesi} } @article {2006, title = {Quasistatic evolution problems for linearly elastic-perfectly plastic materials}, journal = {Arch. Ration. Mech. Anal. 180 (2006) 237-291}, number = {arXiv.org;math/0412212v1}, year = {2006}, abstract = {The problem of quasistatic evolution in small strain associative elastoplasticity is studied in the framework of the variational theory for rate-independent processes. Existence of solutions is proved through the use of incremental variational problems in spaces of functions with bounded deformation. This provides a new approximation result for the solutions of the quasistatic evolution problem, which are shown to be absolutely continuous in time. Four equivalent formulations of the problem in rate form are derived. A strong formulation of the flow rule is obtained by introducing a precise definition of the stress on the singular set of the plastic strain.}, doi = {10.1007/s00205-005-0407-0}, url = {http://hdl.handle.net/1963/2129}, author = {Gianni Dal Maso and Antonio DeSimone and Maria Giovanna Mora} } @article {2006, title = {Radial solutions concentrating on spheres of nonlinear Schr{\"o}dinger equations with vanishing potentials}, journal = {Proc. Roy. Soc. Edinburgh Sect. A 136 (2006) 889-907}, number = {SISSA;38/2005/M}, year = {2006}, abstract = {We prove the existence of radial solutions of 1.2) concentrating at a sphere for potentials which might be zero and might decay to zero at\\r\\ninfinity. The proofs use a perturbation technique in a variational setting, through a Lyapunov-Schmidt reduction.}, doi = {10.1017/S0308210500004789}, url = {http://hdl.handle.net/1963/1755}, author = {Antonio Ambrosetti and David Ruiz} } @inbook {2006, title = {Recent analytical developments in micromagnetics}, booktitle = {The science of hysteresis / eds. Giorgio Bertotti, Isaak D. Mayergoyz. - Amsterdam: Elsevier, 2006. Vol.2, 269-381.}, number = {SISSA;76/2004/M}, year = {2006}, isbn = {978-0-12-480874-4}, url = {http://hdl.handle.net/1963/2230}, author = {Antonio DeSimone and Robert V. Kohn and Stefan M{\"u}ller and Felix Otto} } @article {2006, title = {Reflection symmetries for multiqubit density operators}, journal = {J. Math. Phys. 47 (2006) 032104}, number = {arXiv.org;quant-ph/0405123v2}, year = {2006}, abstract = {For multiqubit density operators in a suitable tensorial basis, we show that a number of nonunitary operations used in the detection and synthesis of entanglement are classifiable as reflection symmetries, i.e., orientation changing rotations. While one-qubit reflections correspond to antiunitary symmetries, as is known for example from the partial transposition criterion, reflections on the joint density of two or more qubits are not accounted for by the Wigner Theorem and are well-posed only for sufficiently mixed states. One example of such nonlocal reflections is the unconditional NOT operation on a multiparty density, i.e., an operation yelding another density and such that the sum of the two is the identity operator. This nonphysical operation is admissible only for sufficiently mixed states.}, doi = {10.1063/1.2181827}, url = {http://hdl.handle.net/1963/2121}, author = {Claudio Altafini and Timothy F. Havel} } @article {Bertola:Semiiso, title = {Semiclassical orthogonal polynomials, matrix models and isomonodromic tau functions}, journal = {Comm. Math. Phys.}, volume = {263}, number = {2}, year = {2006}, pages = {401{\textendash}437}, issn = {0010-3616}, author = {Marco Bertola and B. Eynard and Harnad, J.} } @article {2006, title = {Semistability vs. nefness for (Higgs) vector bundles}, journal = {Differential Geom. Appl. 24 (2006) 403-416}, number = {arXiv.org;math/0310040v3}, year = {2006}, abstract = {According to Miyaoka, a vector bundle E on a smooth projective curve is semistable if and only if a certain numerical class in the projectivized bundle PE is nef. We establish a similar criterion for the semistability of Higgs bundles: namely, such a bundle is semistable if and only if for every integer s between 0 and the rank of E, a suitable numerical class in the scheme parametrizing the rank s locally-free Higgs quotients of E is nef. We also extend this result to higher-dimensional complex projective varieties by showing that the nefness of the above mentioned classes is equivalent to the semistability of the Higgs bundle E together with the vanishing of the discriminant of E.}, doi = {10.1016/j.difgeo.2005.12.007}, url = {http://hdl.handle.net/1963/2237}, author = {Ugo Bruzzo and Daniel Hernandez Ruiperez} } @article {2006, title = {On Separation of Variables for Homogeneous SL(r) Gaudin Systems}, number = {SISSA;106/2003/FM}, year = {2006}, abstract = {By means of a recently introduced bihamiltonian structure for the homogeneous Gaudin models, we find a new set of Separation Coordinates for the sl(r) case.}, doi = {10.1007/s11040-006-9012-1}, url = {http://hdl.handle.net/1963/2538}, author = {Gregorio Falqui and Fabio Musso} } @article {2006, title = {Spectral geometry of k-Minkowski space}, journal = {J. Math. Phys. 47 (2006) 062105}, number = {arXiv.org;hep-th/0503012v4}, year = {2006}, abstract = {After recalling Snyder{\textquoteright}s idea of using vector fields over a smooth manifold as "coordinates on a noncommutative space", we discuss a two dimensional toy-model whose "dual" noncommutative coordinates form a Lie algebra: this is the well known $\kappa$-Minkowski space. We show how to improve Snyder{\textquoteright}s idea using the tools of quantum groups and noncommutative geometry. We find a natural representation of the coordinate algebra of $\kappa$-Minkowski as linear operators on an Hilbert space study its "spectral properties" and discuss how to obtain a Dirac operator for this space. We describe two Dirac operators. The first is associated with a spectral triple. We prove that the cyclic integral of M. Dimitrijevic et al. can be obtained as Dixmier trace associated to this triple. The second Dirac operator is equivariant for the action of the quantum Euclidean group, but it has unbounded commutators with the algebra.

}, doi = {10.1063/1.2204808}, url = {http://hdl.handle.net/1963/2131}, author = {Francesco D{\textquoteright}Andrea} } @article {2006, title = {Stability of planar nonlinear switched systems}, number = {SISSA;04/2005/M}, year = {2006}, abstract = {We consider the time-dependent nonlinear system ˙ q(t) = u(t)X(q(t)) + (1 - u(t))Y (q(t)), where q ∈ R2, X and Y are two smooth vector fields, globally asymptotically stable at the origin and u : [0,$\infty$) {\textrightarrow} {0, 1} is an arbitrary measurable function. Analysing the topology of the set where X and Y are parallel, we give some sufficient and some necessary conditions for global asymptotic stability, uniform with respect to u(.). Such conditions can be verified without any integration or construction of a Lyapunov function, and they are robust under small perturbations of the vector fields.}, url = {http://hdl.handle.net/1963/1710}, author = {Ugo Boscain and Gr{\'e}goire Charlot and Mario Sigalotti} } @article {2006, title = {Thomae type formulae for singular Z_N curves}, journal = {Lett. Math. Phys. 76 (2006) 187-214}, number = {arXiv.org;math-ph/0602017v1}, year = {2006}, abstract = {We give an elementary and rigorous proof of the Thomae type formula for singular $Z_N$ curves. To derive the Thomae formula we use the traditional variational method which goes back to Riemann, Thomae and Fuchs. An important step of the proof is the use of the Szego kernel computed explicitly in algebraic form for non-singular 1/N-periods. The proof inherits principal points of Nakayashiki\\\'s proof [31], obtained for non-singular ZN curves.}, doi = {10.1007/s11005-006-0073-7}, url = {http://hdl.handle.net/1963/2125}, author = {Victor Z. Enolski and Tamara Grava} } @article {2006, title = {Time Minimal Trajectories for a Spin 1/2 Particle in a Magnetic field}, number = {SISSA;82/2005/M}, year = {2006}, abstract = {In this paper we consider the minimum time population transfer problem for the z-component\\nof the spin of a (spin 1/2) particle driven by a magnetic field, controlled along the x axis, with bounded amplitude. On the Bloch sphere (i.e. after a suitable Hopf projection), this problem can be attacked with techniques of optimal syntheses on 2-D manifolds. Let (-E,E) be the two energy levels, and |omega (t)| <= M the bound on the field amplitude. For each couple of values E and M, we determine the time optimal synthesis starting from the level -E and we provide the explicit expression of the time optimal trajectories steering the state one to the state two, in terms of a parameter that can be computed solving numerically a suitable equation. For M/E << 1, every time optimal trajectory is bang-bang and in particular the corresponding control is periodic with frequency of the order of the resonance frequency wR = 2E. On the other side, for M/E > 1, the time optimal trajectory steering the state one to the state two is bang-bang with exactly one switching. Fixed E we also prove that for M {\textrightarrow} $\infty$ the time needed to reach the state two tends to zero. In the case M/E > 1 there are time optimal trajectories containing a singular arc. Finally we compare these results with some known results of Khaneja, Brockett and Glaser and with those obtained by controlling the magnetic field both on the x and y directions (or with one external field, but in the rotating wave approximation). As byproduct we prove that the qualitative shape of the time optimal synthesis presents different patterns, that cyclically alternate as M/E {\textrightarrow} 0, giving a partial proof of a conjecture formulated in a previous paper.}, doi = {10.1063/1.2203236}, url = {http://hdl.handle.net/1963/1734}, author = {Ugo Boscain and Paolo Mason} } @article {2006, title = {On topological M-theory}, number = {SISSA;64/2005/FM}, year = {2006}, abstract = {We construct a gauge fixed action for topological membranes on G2-manifolds such that its bosonic part is the standard membrane theory in a particular gauge. We prove that quantum mechanically the path-integral in this gauge localizes on associative submanifolds.}, url = {http://hdl.handle.net/1963/1765}, author = {Giulio Bonelli and Alessandro Tanzini and Maxim Zabzine} } @article {2006, title = {Topological symmetry of forms, N=1 supersymmetry and S-duality on special manifolds}, journal = {J. Geom. Phys. 56 (2006) 2379-2401}, number = {arXiv.org;hep-th/0412014v2}, year = {2006}, abstract = {We study the quantization of a holomorphic two-form coupled to a Yang-Mills field on special manifolds in various dimensions, and we show that it yields twisted supersymmetric theories. The construction determines ATQFT\\\'s (Almost Topological Quantum Field Theories), that is, theories with observables that are invariant under changes of metrics belonging to restricted classes. For Kahler manifolds in four dimensions, our topological model is related to N=1 Super Yang-Mills theory. Extended supersymmetries are recovered by considering the coupling with chiral multiplets. We also analyse Calabi-Yau manifolds in six and eight dimensions, and seven dimensional G_2 manifolds of the kind recently discussed by Hitchin. We argue that the two-form field could play an interesting role for the study of the conjectured S-duality in topological string. We finally show that in the case of real forms in six dimensions the partition function of our topological model is related to the square of that of the holomorphic Chern-Simons theory, and we discuss the uplift to seven dimensions and its relation with the recent proposals for the topological M-theory.}, doi = {10.1016/j.geomphys.2005.12.006}, url = {http://hdl.handle.net/1963/2168}, author = {Laurent Baulieu and Alessandro Tanzini} } @article {Bertola:2MM_extendedWhitham, title = {Two-matrix model with semiclassical potentials and extended Whitham hierarchy}, journal = {J. Phys. A}, volume = {39}, number = {28}, year = {2006}, pages = {8823{\textendash}8855}, issn = {0305-4470}, author = {Marco Bertola} } @inbook {2006, title = {On universality of critical behaviour in Hamiltonian PDEs}, booktitle = {Geometry, topology, and mathematical physics : S.P. Novikov\\\'s seminar : 2006-2007 / V.M. Buchstaber, I.M. Krichever, editors. - Providence, R.I. : American Mathematical Society, 2008. - pages : 59-109}, number = {American Mathematical Society translations, ISSN 0065-9290;ser. 2;v. 224}, year = {2006}, publisher = {American Mathematical Society}, organization = {American Mathematical Society}, abstract = {Our main goal is the comparative study of singularities of solutions to\\r\\nthe systems of rst order quasilinear PDEs and their perturbations containing higher\\r\\nderivatives. The study is focused on the subclass of Hamiltonian PDEs with one\\r\\nspatial dimension. For the systems of order one or two we describe the local structure\\r\\nof singularities of a generic solution to the unperturbed system near the point of\\r\\n\\\\gradient catastrophe\\\" in terms of standard objects of the classical singularity theory;\\r\\nwe argue that their perturbed companions must be given by certain special solutions\\r\\nof Painlev e equations and their generalizations.}, isbn = {978-0-8218-4674-2}, url = {http://hdl.handle.net/1963/6491}, author = {Boris Dubrovin} } @article {2006, title = {On variational approach to differential invariants of rank two distributions}, journal = {Differential Geom. Appl. 24 (2006) 235-259}, number = {arXiv.org;math/0402171v2}, year = {2006}, abstract = {n the present paper we construct differential invariants for generic rank 2 vector distributions on n-dimensional manifold. In the case n=5 (the first case containing functional parameters) E. Cartan found in 1910 the covariant fourth-order tensor invariant for such distributions, using his \\\"reduction-prolongation\\\" procedure. After Cartan\\\'s work the following questions remained open: first the geometric reason for existence of Cartan\\\'s tensor was not clear; secondly it was not clear how to generalize this tensor to other classes of distributions; finally there were no explicit formulas for computation of Cartan\\\'s tensor. Our paper is the first in the series of papers, where we develop an alternative approach, which gives the answers to the questions mentioned above. It is based on the investigation of dynamics of the field of so-called abnormal extremals (singular curves) of rank 2 distribution and on the general theory of unparametrized curves in the Lagrange Grassmannian, developed in our previous works with A. Agrachev . In this way we construct the fundamental form and the projective Ricci curvature of rank 2 vector distributions for arbitrary n greater than 4.\\nFor n=5 we give an explicit method for computation of these invariants and demonstrate it on several examples. In our next paper we show that in the case n=5 our fundamental form coincides with Cartan\\\'s tensor.}, doi = {10.1016/j.difgeo.2005.09.004}, url = {http://hdl.handle.net/1963/2188}, author = {Igor Zelenko} } @article {2006, title = {Variational problems in fracture mechanics}, number = {SISSA;10/2006/M}, year = {2006}, abstract = {We present some recent existence results for the variational model of crack growth in brittle materials proposed by Francfort and Marigo in 1998. These results, obtained in collaboration with Francfort and Toader, cover the case of arbitrary space dimension with a general quasiconvex bulk energy and with prescribed boundary deformations and applied loads.}, url = {http://hdl.handle.net/1963/1816}, author = {Gianni Dal Maso} } @inbook {2006, title = {WDVV equations and Frobenius manifolds}, booktitle = {Encyclopedia of Mathematical Physics. Vol 1 A : A-C. Oxford: Elsevier, 2006, p. 438-447}, year = {2006}, publisher = {SISSA}, organization = {SISSA}, isbn = {0125126611}, url = {http://hdl.handle.net/1963/6473}, author = {Boris Dubrovin} } @article {2005, title = {Asymptotic Morse theory for the equation $\\\\Delta v=2v\\\\sb x\\\\wedge v\\\\sb y$}, journal = {Comm. Anal. Geom. 13 (2005) 187-252}, number = {arXiv.org;math/0205106v1}, year = {2005}, publisher = {International Press}, abstract = {Given a smooth bounded domain ${\\\\O}\\\\subseteq \\\\R^2$, we consider the equation $\\\\D v = 2 v_x \\\\wedge v_y$ in $\\\\O$, where $v: {\\\\O}\\\\to \\\\R^3$. We prescribe Dirichlet boundary datum, and consider the case in which this datum converges to zero. An asymptotic study of the corresponding Euler functional is performed, analyzing multiple-bubbling phenomena. This allows us to settle a particular case of a question raised by H. Brezis and J.M. Coron.}, url = {http://hdl.handle.net/1963/3533}, author = {Sagun Chanillo and Andrea Malchiodi} } @article {2005, title = {On the attainable set for Temple class systems with boundary controls}, journal = {SIAM J. Control Optim. 43 (2005) 2166-2190}, number = {SISSA;10/2002/M}, year = {2005}, publisher = {SISSA Library}, abstract = {Consider the initial-boundary value problem for a strictly hyperbolic, genuinely nonlinear, Temple class system of conservation laws \% $$ u_t+f(u)_x=0, \\\\qquad u(0,x)=\\\\ov u(x), \\\\qquad {{array}{ll} \&u(t,a)=\\\\widetilde u_a(t), \\\\noalign{\\\\smallskip} \&u(t,b)=\\\\widetilde u_b(t), {array}. \\\\eqno(1) $$ on the domain $\\\\Omega =\\\\{(t,x)\\\\in\\\\R^2 : t\\\\geq 0, a \\\\le x\\\\leq b\\\\}.$ We study the mixed problem (1) from the point of view of control theory, taking the initial data $\\\\bar u$ fixed, and regarding the boundary data $\\\\widetilde u_a, \\\\widetilde u_b$ as control functions that vary in prescribed sets $\\\\U_a, \\\\U_b$, of $\\\\li$ boundary controls. In particular, we consider the family of configurations $$ \\\\A(T) \\\\doteq \\\\big\\\\{u(T,\\\\cdot); ~ u {\\\\rm is a sol. to} (1), \\\\quad \\\\widetilde u_a\\\\in \\\\U_a, \\\\widetilde u_b \\\\in \\\\U_b \\\\big\\\\} $$ that can be attained by the system at a given time $T>0$, and we give a description of the attainable set $\\\\A(T)$ in terms of suitable Oleinik-type conditions. We also establish closure and compactness of the set $\\\\A(T)$ in the $lu$ topology.}, doi = {10.1137/S0363012902407776}, url = {http://hdl.handle.net/1963/1581}, author = {Fabio Ancona and Giuseppe Maria Coclite} } @article {2005, title = {On the Blow-up for a Discrete Boltzmann Equation in the Plane}, journal = {Discrete Contin. Dyn. Syst. 13 (2005) 1-12}, number = {arXiv.org;math/0403047v2}, year = {2005}, abstract = {We study the possibility of finite-time blow-up for a two dimensional Broadwell model. In a set of rescaled variables, we prove that no self-similar blow-up solution exists, and derive some a priori bounds on the blow-up rate. In the final section, a possible blow-up scenario is discussed.}, url = {http://hdl.handle.net/1963/2244}, author = {Alberto Bressan and Massimo Fonte} } @article {2005, title = {Commuting multiparty quantum observables and local compatibility}, journal = {Phys. Rev. A 72 (2005) 012112}, number = {SISSA;93/2004/M}, year = {2005}, abstract = {A formula for the commutator of tensor product matrices is used to shows that, for qubits, compatibility of quantum multiparty observables almost never implies local compatibility at each site and to predict when this happens/does not happen in a concise manner. In particular, it is shown that two {\textquoteleft}{\textquoteleft}fully nontrivial\\\'\\\' $n$-qubit observables are compatible locally and globally if and only if they are equal up to sign. In addition, the formula gives insight into the construction of new paradoxes of the type of the Kochen-Specker Theorem, which can then be easily rephrased into proposals for new no hidden variable experiments of the type of the {\textquoteleft}{\textquoteleft}Bell Theorem without inequalities\\\'\\\'.}, doi = {10.1103/PhysRevA.72.012112}, url = {http://hdl.handle.net/1963/2228}, author = {Claudio Altafini} } @inbook {2005, title = {Complete systems of invariants for rank 1 curves in Lagrange Grassmannians}, booktitle = {Differential geometry and its applications, 367-382, Matfyzpress, Prague, 2005}, number = {SISSA;82/2004/M}, year = {2005}, note = {Proceedings of 9th Conference on Differential Geometry and its Applications, Prague 2004}, abstract = {Curves in Lagrange Grassmannians naturally appear when one studies intrinsically \\\"the Jacobi equations for extremals\\\", associated with control systems and geometric structures. In this way one reduces the problem of construction of the curvature-type invariants for these objects to the much more concrete problem of finding of invariants of curves in Lagrange Grassmannians w.r.t. the action of the linear Symplectic group. In the present paper we develop a new approach to differential geometry of so-called rank 1 curves in Lagrange Grassmannian, i.e., the curves with velocities being rank one linear mappings (under the standard identification of the tangent space to a point of the Lagrange Grassmannian with an appropriate space of linear mappings). The curves of this class are associated with \\\"the Jacobi equations for extremals\\\", corresponding to control systems with scalar control and to rank 2 vector distributions. In particular, we construct the tuple of m principal invariants, where m is equal to half of dimension of the ambient linear symplectic space, such that for a given tuple of arbitrary m smooth functions there exists the unique, up to a symplectic transformation, rank 1 curve having this tuple, as the tuple of the principal invariants. This approach extends and essentially simplifies some results of our previous paper (J. Dynamical and Control Systems, 8, 2002, No. 1, 93-140), where only the uniqueness part was proved and in rather cumbersome way. It is based on the construction of the new canonical moving frame with the most simple structural equation.}, url = {http://hdl.handle.net/1963/2310}, author = {Igor Zelenko} } @article {2005, title = {Concentration at curves for a singularly perturbed Neumann problem in three-dimensional domains}, journal = {Geometric and Functional Analysis 15 (6) 1162-1222 (2005)}, year = {2005}, publisher = {Springer}, abstract = {We prove new concentration phenomena for the equation -ɛ2 Δu + u = up in a smooth bounded domain R3 and with Neumann boundary conditions. Here p > 1 and ɛ > 0 is small. We show that concentration of solutions occurs at some geodesics of ∂Ω when ɛ {\textrightarrow} 0.}, doi = {10.1007/s00039-005-0542-7}, url = {http://hdl.handle.net/1963/4866}, author = {Andrea Malchiodi} } @article {2005, title = {Conservation laws with time dependent discontinuous coefficients}, journal = {SIAM J. Math. Anal. 36 (2005) 1293-1309}, number = {SISSA;96/2002/M}, year = {2005}, publisher = {SISSA Library}, abstract = {We consider scalar conservation laws where the flux function depends discontinuously on both the spatial and temporal location. Our main results are the existence and well-posedness of an entropy solution to the Cauchy problem. The existence is established by showing that a sequence of front tracking approximations is compact in L1, and that the limits are entropy solutions. Then, using the definition of an entropy solution taken form [11], we show that the solution operator is L1 contractive. These results generalize the corresponding results from [16] and [11].}, doi = {10.1137/S0036141002420005}, url = {http://hdl.handle.net/1963/1666}, author = {Giuseppe Maria Coclite and Nils Henrik Risebro} } @article {2005, title = {On curvatures and focal points of distributions of dynamical Lagrangian distributions and their reductions by first integrals}, journal = {J. Dyn. Control Syst. 11 (2005) 297-327}, number = {SISSA;58/2004/M}, year = {2005}, abstract = {Pairs (Hamiltonian system, Lagrangian distribution), called dynamical Lagrangian distributions, appear naturally in Differential Geometry, Calculus of Variations and Rational Mechanics. The basic differential invariants of a dynamical Lagrangian distribution w.r.t. the action of the group of symplectomorphisms of the ambient symplectic manifold are the curvature operator and the curvature form. These invariants can be seen as generalizations of the classical curvature tensor in Riemannian Geometry. In particular, in terms of these invariants one can localize the focal points along extremals of the corresponding variational problems. In the present paper we study the behavior of the curvature operator, the curvature form and the focal points of a dynamical Lagrangian distribution after its reduction by arbitrary first integrals in involution. The interesting phenomenon is that the curvature form of so-called monotone increasing Lagrangian dynamical distributions, which appear naturally in mechanical systems, does not decrease after reduction. It also turns out that the set of focal points to the given point w.r.t. the monotone increasing dynamical Lagrangian distribution and the corresponding set of focal points w.r.t. its reduction by one integral are alternating sets on the corresponding integral curve of the Hamiltonian system of the considered dynamical distributions. Moreover, the first focal point corresponding to the reduced Lagrangian distribution comes before any focal point related to the original dynamical distribution. We illustrate our results on the classical $N$-body problem.}, doi = {10.1007/s10883-005-6581-4}, url = {http://hdl.handle.net/1963/2254}, author = {Andrei A. Agrachev and Natalia N. Chtcherbakova and Igor Zelenko} } @article {2005, title = {Decay of a bound state under a time-periodic perturbation: a toy case}, journal = {J. Phys. A 38 (2005) 4769-4781}, number = {SISSA;54/2004/FM}, year = {2005}, abstract = {We study the time evolution of a three dimensional quantum particle, initially in a bound state, under the action of a time-periodic zero range interaction with {\textquoteleft}{\textquoteleft}strength\\\'\\\' (\\\\alpha(t)). Under very weak generic conditions on the Fourier coefficients of (\\\\alpha(t)), we prove complete ionization as (t \\\\to \\\\infty). We prove also that, under the same conditions, all the states of the system are scattering states.}, doi = {10.1088/0305-4470/38/22/002}, url = {http://hdl.handle.net/1963/2298}, author = {Michele Correggi and Gianfausto Dell{\textquoteright}Antonio} } @article {2005, title = {The Dirac operator on SU_q(2)}, journal = {Commun. Math. Phys. 259 (2005) 729-759}, number = {arXiv:math/0411609;}, year = {2005}, note = {v2: minor changes}, publisher = {Springer}, abstract = {We construct a 3^+ summable spectral triple (A(SU_q(2)),H,D) over the quantum group SU_q(2) which is equivariant with respect to a left and a right action of U_q(su(2)). The geometry is isospectral to the classical case since the spectrum of the operator D is the same as that of the usual Dirac operator on the 3-dimensional round sphere. The presence of an equivariant real structure J demands a modification in the axiomatic framework of spectral geometry, whereby the commutant and first-order properties need be satisfied only modulo infinitesimals of arbitrary high order.}, doi = {10.1007/s00220-005-1383-9}, url = {http://hdl.handle.net/1963/4425}, author = {Ludwik Dabrowski and Giovanni Landi and Andrzej Sitarz and Walter van Suijlekom and Joseph C. Varilly} } @article {2005, title = {Explicit Wei{\textendash}Norman formulae for matrix Lie groups via Putzer\\\'s method}, journal = {Systems and Control Letters, 54 (11):1121-1130, 2005}, year = {2005}, publisher = {Elsevier}, abstract = {The Wei{\textendash}Norman formula locally relates the Magnus solution of a system of linear time-varying ODEs with the solution expressed in terms of products of exponentials by means of a set of nonlinear differential equations in the parameters of the two types of solutions. A closed form expression of such formula is proposed based on the use of Putzer\\\'s method.}, doi = {10.1016/j.sysconle.2005.03.006}, url = {http://hdl.handle.net/1963/4538}, author = {Claudio Altafini} } @article {2005, title = {A fourth order uniformization theorem on some four manifolds with large total Q-curvature}, journal = {C. R. Acad. Sci. Paris, Ser. I 340 (2005) 341-346.}, year = {2005}, publisher = {Elsevier}, abstract = {Given a four-dimensional manifold (M,g), we study the existence of a conformal metric for which the Q-curvature, associated to a conformally invariant fourth-order operator (the Paneitz operator), is constant. Using a topological argument, we obtain a new result in cases which were still open.}, doi = {10.1016/j.crma.2005.01.013}, url = {http://hdl.handle.net/1963/4868}, author = {Zindine Djadli and Andrea Malchiodi} } @article {2005, title = {Gel\\\'fand-Zakharevich Systems and Algebraic Integrability: the Volterra Lattice Revisited}, number = {SISSA;29/2005/FM}, year = {2005}, abstract = {In this paper we will discuss some features of the bi-Hamiltonian method for solving the Hamilton-Jacobi (H-J) equations by Separation of Variables, and make contact with the theory of Algebraic Complete Integrability and, specifically, with the Veselov-Novikov notion of algebro-geometric (AG) Poisson brackets.}, doi = {10.1070/RD2005v010n04ABEH000322}, url = {http://hdl.handle.net/1963/1689}, author = {Gregorio Falqui and Marco Pedroni} } @article {2005, title = {Global solutions of the Hunter-Saxton equation}, journal = {SIAM J. Math. Anal. 37 (2005) 996-1026}, number = {SISSA;104/2004/M}, year = {2005}, abstract = {We construct a continuous semigroup of weak, dissipative solutions to a nonlinear partial differential equations modeling nematic liquid crystals. A new distance functional, determined by a problem of optimal transportation, yields sharp estimates on the continuity of solutions with respect to the initial data.}, doi = {10.1137/050623036}, url = {http://hdl.handle.net/1963/2256}, author = {Alberto Bressan and Adrian Constantin} } @article {2005, title = {Ground states of nonlinear Schroedinger equations with potentials vanishing at infinity}, journal = {J. Eur. Math. Soc. 7 (2005) 117-144}, number = {SISSA;16/2004/M}, year = {2005}, abstract = {We deal with a class on nonlinear Schr\\\\\\\"odinger equations \\\\eqref{eq:1} with potentials $V(x)\\\\sim |x|^{-\\\\a}$, $0<\\\\a<2$, and $K(x)\\\\sim |x|^{-\\\\b}$, $\\\\b>0$. Working in weighted Sobolev spaces, the existence of ground states $v_{\\\\e}$ belonging to $W^{1,2}(\\\\Rn)$ is proved under the assumption that $p$ satisfies \\\\eqref{eq:p}. Furthermore, it is shown that $v_{\\\\e}$ are {\\\\em spikes} concentrating at a minimum of ${\\\\cal A}=V^{\\\\theta}K^{-2/(p-1)}$, where $\\\\theta= (p+1)/(p-1)-1/2$.}, url = {http://hdl.handle.net/1963/2352}, author = {Antonio Ambrosetti and Veronica Felli and Andrea Malchiodi} } @article {2005, title = {Hybrid necessary principle}, journal = {SIAM J. Control Optim. 43 (2005) 1867-1887}, number = {SISSA;71/2002/M}, year = {2005}, note = {Proceedings of IFAC Conference on Analysis and Design of Hybrid Systems, Saint Malo, France}, publisher = {SIAM}, abstract = {We consider a hybrid control system and general optimal control problems for this system. We suppose that the switching strategy imposes restrictions on control sets and we provide necessary conditions for an optimal hybrid trajectory, stating a hybrid necessary principle (HNP). Our result generalizes various necessary principles available in the literature.}, doi = {10.1137/S0363012903416219}, url = {http://hdl.handle.net/1963/1641}, author = {Mauro Garavello and Benedetto Piccoli} } @article {2005, title = {Ionization for Three Dimensional Time-dependent Point Interactions}, journal = {Comm. Math. Phys. 257 (2005) 169-192}, number = {SISSA;11/2004/FM}, year = {2005}, abstract = {We study the time evolution of a three dimensional quantum particle under the action of a time-dependent point interaction fixed at the origin. We assume that the {\textquoteleft}{\textquoteleft}strength\\\'\\\' of the interaction (\\\\alpha(t)) is a periodic function with an arbitrary mean. Under very weak conditions on the Fourier coefficients of (\\\\alpha(t)), we prove that there is complete ionization as (t \\\\to \\\\infty), starting from a bound state at time (t = 0). Moreover we prove also that, under the same conditions, all the states of the system are scattering states.}, doi = {10.1007/s00220-005-1293-x}, url = {http://hdl.handle.net/1963/2297}, author = {Michele Correggi and Gianfausto Dell{\textquoteright}Antonio and Rodolfo Figari and Andrea Mantile} } @article {Bertola:Isomono_resonant, title = {Isomonodromic deformation of resonant rational connections}, journal = {IMRP Int. Math. Res. Pap.}, number = {11}, year = {2005}, pages = {565{\textendash}635}, issn = {1687-3017}, author = {Marco Bertola and Mo, M. Y.} } @article {2005, title = {The local index formula for SUq(2)}, journal = {K-Theory 35 (2005) 375-394}, number = {SISSA;01/2005/FM}, year = {2005}, abstract = {We discuss the local index formula of Connes-Moscovici for the isospectral noncommutative geometry that we have recently constructed on quantum SU(2). We work out the cosphere bundle and the dimension spectrum as well as the local cyclic cocycles yielding the index formula.}, doi = {10.1007/s10977-005-3116-4}, url = {http://hdl.handle.net/1963/1713}, author = {Walter van Suijlekom and Ludwik Dabrowski and Giovanni Landi and Andrzej Sitarz and Joseph C. Varilly} } @article {2005, title = {Minimal surfaces in pseudohermitian geometry}, journal = {Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (5), 4 (2005) 129-177.}, number = {arXiv:math/0401136;}, year = {2005}, publisher = {Scuola Normale Superiore}, abstract = {We consider surfaces immersed in three-dimensional pseudohermitian manifolds. We define the notion of (p-)mean curvature and of the associated (p-)minimal surfaces, extending some concepts previously given for the (flat) Heisenberg group. We interpret the p-mean curvature not only as the tangential sublaplacian of a defining function, but also as the curvature of a characteristic curve, and as a quantity in terms of calibration geometry. As a differential equation, the p-minimal surface equation is degenerate (hyperbolic and elliptic). To analyze the singular set, we formulate some {\em extension} theorems, which describe how the characteristic curves meet the singular set. This allows us to classify the entire solutions to this equation and to solve a Bernstein-type problem (for graphs over the $xy$-plane) in the Heisenberg group $H_1$. In $H_{1}$, identified with the Euclidean space $R^{3}$, the p-minimal surfaces are classical ruled surfaces with the rulings generated by Legendrian lines. We also prove a uniqueness theorem for the Dirichlet problem under a condition on the size of the singular set in two dimensions, and generalize to higher dimensions without any size control condition. We also show that there are no closed, connected, $C^{2}$ smoothly immersed constant p-mean curvature or p-minimal surfaces of genus greater than one in the standard $S^{3}.$ This fact continues to hold when $S^{3}$ is replaced by a general spherical pseudohermitian 3-manifold.}, doi = {10.2422/2036-2145.2005.1.05}, url = {http://hdl.handle.net/1963/4579}, author = {Jih-Hsin Cheng and JennFang Hwang and Andrea Malchiodi and Paul Yang} } @article {2005, title = {On the Minimum Problem for Nonconvex Scalar Functionals}, journal = {SIAM J. Math. Anal. 37 (2005) 982-995}, year = {2005}, abstract = {We study the minimum problem for scalar nonconvex functionals defined on Sobolev maps satisfying a Dirichlet boundary condition and refine well-known existence results under standard regularity assumptions.}, doi = {10.1137/040612506}, url = {http://hdl.handle.net/1963/2764}, author = {Sandro Zagatti} } @article {2005, title = {Modulation of the Camassa-Holm equation and reciprocal transformations}, journal = {Ann. Inst. Fourier (Grenoble) 55 (2005) 1803-1834}, number = {SISSA;107/2004/FM}, year = {2005}, abstract = {We derive the modulation equations or Whitham equations for the Camassa-Holm (CH) equation. We show that the modulation equations are hyperbolic and admit bi-Hamiltonian structure. Furthermore they are connected by a reciprocal transformation to the modulation equations of the first negative flow of the Korteweg de Vries (KdV) equation. The reciprocal transformation is generated by the Casimir of the second Poisson bracket of the KdV averaged flow. We show that the geometry of the bi-Hamiltonian structure of the KdV and CH modulation equations is quite different: indeed the KdV averaged bi-Hamiltonian structure can always be related to a semisimple Frobenius manifold while the CH one cannot.}, url = {http://hdl.handle.net/1963/2305}, author = {Simonetta Abenda and Tamara Grava} } @article {2005, title = {Multiple clustered layer solutions for semilinear Neumann problems on a ball}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 22 (2005) 143-163}, year = {2005}, publisher = {Elsevier}, doi = {10.1016/j.anihpc.2004.05.003}, url = {http://hdl.handle.net/1963/3532}, author = {Andrea Malchiodi and Wei-Ming Ni and Juncheng Wei} } @article {2005, title = {Nonisotropic 3-level quantum systems: complete solutions for minimum time and minimum energy}, journal = {Discrete Contin. Dyn. Syst. Ser. B 5 (2005) 957-990}, number = {SISSA;56/2004/M}, year = {2005}, abstract = {We apply techniques of subriemannian geometry on Lie groups and of optimal synthesis on 2-D manifolds to the population transfer problem in a three-level quantum system driven by two laser pulses, of arbitrary shape and frequency. In the rotating wave approximation, we consider a nonisotropic model i.e. a model in which the two coupling constants of the lasers are different. The aim is to induce transitions from the first to the third level, minimizing 1) the time of the transition (with bounded laser amplitudes),\\n2) the energy of lasers (with fixed final time). After reducing the problem to real variables, for the purpose 1) we develop a theory of time optimal syntheses for distributional problem on 2-D-manifolds, while for the purpose 2) we use techniques of subriemannian geometry on 3-D Lie groups. The complete optimal syntheses are computed.}, url = {http://hdl.handle.net/1963/2259}, author = {Ugo Boscain and Thomas Chambrion and Gr{\'e}goire Charlot} } @article {2005, title = {Nonlinear Schr{\"o}dinger Equations with vanishing and decaying potentials}, number = {SISSA;52/2005/M}, year = {2005}, url = {http://hdl.handle.net/1963/1760}, author = {Antonio Ambrosetti and Wang Zhi-Qiang} } @article {2005, title = {An Optimal Transportation Metric for Solutions of the Camassa-Holm Equation}, number = {SISSA;27/2005/M}, year = {2005}, abstract = {In this paper we construct a global, continuous flow of solutions to the Camassa-Holm equation on the entire space H1. Our solutions are conservative, in the sense that the total energy int[(u2 + u2x) dx] remains a.e. constant in time. Our new approach is based on a distance functional J(u, v), defined in terms of an optimal transportation problem, which satisfies d dtJ(u(t), v(t)) <= κ {\textperiodcentered} J(u(t), v(t)) for every couple of solutions. Using this new distance functional, we can construct arbitrary solutions as the uniform limit of multi-peakon solutions, and prove a general uniqueness result.}, url = {http://hdl.handle.net/1963/1719}, author = {Alberto Bressan and Massimo Fonte} } @mastersthesis {2005, title = {Orbifold Cohomology of ADE-singularities}, year = {2005}, school = {SISSA}, keywords = {Orbifolds}, url = {http://hdl.handle.net/1963/5298}, author = {Fabio Perroni} } @article {2005, title = {Periodic solutions of nonlinear wave equations with non-monotone forcing terms}, journal = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 16 (2005), no. 2, 117-124}, year = {2005}, publisher = {Accademia Nazionale dei Lincei}, url = {http://hdl.handle.net/1963/4581}, author = {Massimiliano Berti and Luca Biasco} } @article {2005, title = {Principal fibrations from noncommutative spheres}, journal = {Comm. Math. Phys. 260 (2005) 203-225}, number = {SISSA;68/2004/FM}, year = {2005}, abstract = {We construct noncommutative principal fibrations S_\\\\theta^7 \\\\to S_\\\\theta^4 which are deformations of the classical SU(2) Hopf fibration over the four sphere. We realize the noncommutative vector bundles associated to the irreducible representations of SU(2) as modules of coequivariant maps and construct corresponding projections. The index of Dirac operators with coefficients in the associated bundles is computed with the Connes-Moscovici local index formula. The algebra inclusion $A(S_\\\\theta^4) \\\\into A(S_\\\\theta^7)$ is an example of a not trivial quantum principal bundle.}, doi = {10.1007/s00220-005-1377-7}, url = {http://hdl.handle.net/1963/2284}, author = {Giovanni Landi and Walter van Suijlekom} } @article {2005, title = {Quasi-periodic oscillations for wave equations under periodic forcing}, journal = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 16 (2005), no. 2, 109-116}, year = {2005}, publisher = {Accademia Nazionale dei Lincei}, url = {http://hdl.handle.net/1963/4583}, author = {Massimiliano Berti and Michela Procesi} } @article {2005, title = {Quasistatic Crack Growth in Nonlinear Elasticity}, journal = {Arch. Ration. Mech. Anal. 176 (2005) 165-225}, number = {SISSA;2/2004/M}, year = {2005}, abstract = {In this paper, we prove a new existence result for a variational model of crack growth in brittle materials proposed in [15]. We consider the case of $n$-dimensional finite elasticity, for an arbitrary $n\\\\ge1$, with a quasiconvex bulk energy and with prescribed boundary deformations and applied loads, both depending on time.}, doi = {10.1007/s00205-004-0351-4}, url = {http://hdl.handle.net/1963/2293}, author = {Gianni Dal Maso and Gilles A. Francfort and Rodica Toader} } @article {2005, title = {Regularity properties of optimal trajectories of single-input control systems in dimension three}, journal = {Journal of Mathematical Sciences 126 (2005) 1561-1573}, year = {2005}, publisher = {Springer}, abstract = {Let q=f(q)+ug(q) be a smooth control system on a three-dimensional manifold. Given a point q 0 of the manifold at which the iterated Lie brackets of f and g satisfy some prescribed independence condition, we analyze the structure of a control function u(t) corresponding to a time-optimal trajectory lying in a neighborhood of q 0. The control turns out to be the concatenation of some bang-bang and some singular arcs. More general optimality criteria than time-optimality are considered. The paper is a step toward to the analysis of generic single-input systems affine in the control in dimension 3. The main techniques used are second-order optimality conditions and, in particular, the index of the second variation of the switching times for bang-bang trajectories.}, doi = {10.1007/s10958-005-0044-z}, url = {http://hdl.handle.net/1963/4794}, author = {Mario Sigalotti} } @article {2005, title = {Self-similar folding patterns and energy scaling in compressed elastic sheets}, journal = {Comput. Methods Appl. Mech. Engrg. 194 (2005) 2534-2549}, year = {2005}, publisher = {Elsevier}, abstract = {Thin elastic sheets under isotropic compression, such as for example blisters formed by thin films which debonded from the substrate, can exhibit remarkably complex folding patterns. We discuss the scaling of the elastic energy with respect to the film thickness, and show that in certain regimes the optimal energy scaling can be reached\\nby self-similar folding patterns that refine towards the boundary, in agreement with experimental observations. We then extend the analysis\\nto anisotropic compression, and discuss a simplified scalar model which suggests the presence of a transition between a regime where\\nthe deformation is governed by global properties of the domain and another one where the direction of maximal compression dominates and the scale of the folds is mainly determined by the distance to the boundary in the direction of the folds themselves.}, doi = {10.1016/j.cma.2004.07.044}, url = {http://hdl.handle.net/1963/3000}, author = {Sergio Conti and Antonio DeSimone and Stefan M{\"u}ller} } @inbook {2005, title = {A short introduction to optimal control}, booktitle = {Contr{\^o}le non lin{\'e}aire et applications: Cours donn{\'e}s {\`a} l\\\'{\'e}cole d\\\'{\'e}t{\'e} du Cimpa de l\\\'Universit{\'e} de Tlemcen / Sari Tewfit [ed.]. - Paris: Hermann, 2005}, number = {SISSA;10/2004/M}, year = {2005}, isbn = {2 7056 6511 0}, url = {http://hdl.handle.net/1963/2257}, author = {Ugo Boscain and Benedetto Piccoli} } @booklet {2005, title = {Solutions of Neumann problems in domains with cracks and applications to fracture mechanics}, number = {arXiv.org;math.AP/0105132}, year = {2005}, url = {http://hdl.handle.net/1963/1684}, author = {Gianni Dal Maso} } @article {2005, title = {The spectral geometry of the equatorial Podles sphere}, journal = {C. R. Math. 340 (2005) 819-822}, number = {SISSA;71/2004/FM}, year = {2005}, abstract = {We propose a slight modification of the properties of a spectral geometry a la Connes, which allows for some of the algebraic relations to be satisfied only modulo compact operators. On the equatorial Podles sphere we construct suq2-equivariant Dirac operator and real structure which satisfy these modified properties.}, doi = {10.1016/j.crma.2005.04.003}, url = {http://hdl.handle.net/1963/2275}, author = {Ludwik Dabrowski and Giovanni Landi and Mario Paschke and Andrzej Sitarz} } @article {2005, title = {Stability of solutions of quasilinear parabolic equations}, journal = {J. Math. Anal. Appl. 308 (2005) 221-239}, number = {SISSA;51/2003/M}, year = {2005}, publisher = {Elsevier}, abstract = {We bound the difference between solutions $u$ and $v$ of $u_t = a\\\\Delta u+\\\\Div_x f+h$ and $v_t = b\\\\Delta v+\\\\Div_x g+k$ with initial data $\\\\phi$ and $ \\\\psi$, respectively, by $\\\\Vert u(t,\\\\cdot)-v(t,\\\\cdot)\\\\Vert_{L^p(E)}\\\\le A_E(t)\\\\Vert \\\\phi-\\\\psi\\\\Vert_{L^\\\\infty(\\\\R^n)}^{2\\\\rho_p}+ B(t)(\\\\Vert a-b\\\\Vert_{\\\\infty}+ \\\\Vert \\\\nabla_x\\\\cdot f-\\\\nabla_x\\\\cdot g\\\\Vert_{\\\\infty}+ \\\\Vert f_u-g_u\\\\Vert_{\\\\infty} + \\\\Vert h-k\\\\Vert_{\\\\infty})^{\\\\rho_p} \\\\abs{E}^{\\\\eta_p}$. Here all functions $a$, $f$, and $h$ are smooth and bounded, and may depend on $u$, $x\\\\in\\\\R^n$, and $t$. The functions $a$ and $h$ may in addition depend on $\\\\nabla u$. Identical assumptions hold for the functions that determine the solutions $v$. Furthermore, $E\\\\subset\\\\R^n$ is assumed to be a bounded set, and $\\\\rho_p$ and $\\\\eta_p$ are fractions that depend on $n$ and $p$. The diffusion coefficients $a$ and $b$ are assumed to be strictly positive and the initial data are smooth.}, doi = {10.1016/j.jmaa.2005.01.026}, url = {http://hdl.handle.net/1963/2892}, author = {Giuseppe Maria Coclite and Helge Holden} } @article {2005, title = {Stress-dilatancy based modelling of granular materials and extensions to soils with crushable grains}, journal = {Int. J. Numer. Anal. Met. 29 (2005) 73-101}, number = {SISSA;74/2004/M}, year = {2005}, abstract = {Stress-dilatancy relations have played a crucial role in the understanding of the mechanical behaviour of soils and in the development of realistic constitutive models for their response. Recent investigations on the mechanical behaviour of materials with crushable grains have called into question the validity of classical relations such as those used in critical state soil mechanics.\\nIn this paper, a method to construct thermodynamically consistent (isotropic, three-invariant) elasto-plastic models based on a given stress-dilatancy relation is discussed. Extensions to cover the case of granular materials with crushable grains are also presented, based on the interpretation of some classical model parameters (e.g. the stress ratio at critical state) as internal variables that evolve according to suitable hardening laws.}, doi = {10.1002/nag.405}, url = {http://hdl.handle.net/1963/2165}, author = {Antonio DeSimone and Claudio Tamagnini} } @article {2005, title = {Time minimal trajectories for two-level quantum systems with drift}, number = {SISSA;5/2005/M}, year = {2005}, abstract = {On a two-level quantum system driven by an external field, we consider the population transfer problem from the first to the second level, minimizing the time of transfer, with bounded field amplitude. On the Bloch sphere (i.e. after a suitable Hopf projection), this problem can be attacked with techniques of optimal syntheses on 2-D manifolds.}, url = {http://hdl.handle.net/1963/1688}, author = {Ugo Boscain and Paolo Mason} } @article {2005, title = {Time Optimal Synthesis for Left-Invariant Control Systems on SO(3)}, journal = {SIAM J. Control Optim. 44 (2005) 111-139}, number = {SISSA;21/2004/M}, year = {2005}, abstract = {Consider the control system given by $\\\\dot x=x(f+ug)$, where $x\\\\in SO(3)$, $|u|\\\\leq 1$ and $f,g\\\\in so(3)$ define two perpendicular left-invariant vector fields normalized so that $\\\\|f\\\\|=\\\\cos(\\\\al)$ and $\\\\|g\\\\|=\\\\sin(\\\\al)$, $\\\\al\\\\in ]0,\\\\pi/4[$. In this paper, we provide an upper bound and a lower bound for $N(\\\\alpha)$, the maximum number of switchings for time-optimal trajectories. More precisely, we show that $N_S(\\\\al)\\\\leq N(\\\\al)\\\\leq N_S(\\\\al)+4$, where $N_S(\\\\al)$ is a suitable integer function of $\\\\al$ which for $\\\\al\\\\to 0$ is of order $\\\\pi/(4\\\\alpha).$ The result is obtained by studying the time optimal synthesis of a projected control problem on $R P^2$, where the projection is defined by an appropriate Hopf fibration. Finally, we study the projected control problem on the unit sphere $S^2$. It exhibits interesting features which will be partly rigorously derived and partially described by numerical simulations.}, doi = {10.1137/S0363012904441532}, url = {http://hdl.handle.net/1963/2258}, author = {Ugo Boscain and Yacine Chitour} } @article {2005, title = {Topological vector symmetry, topological gauge fixing of BRSTQFT and construction of maximal supersymmetry}, number = {SISSA;24/2005/FM}, year = {2005}, abstract = {The scalar and vector topological Yang-Mills symmetries determine a closed and consistent sector of Yang-Mills supersymmetry. We provide a geometrical construction of these symmetries, based on a horizontality condition on reducible manifolds. This yields globally well-defined scalar and vector topological BRST operators. These operators generate a subalgebra of maximally supersymmetric Yang-Mills theory, which is small enough to be closed off-shell with a finite set of auxiliary fields and large enough to determine the Yang-Mills supersymmetric theory. Poincar{\'e} supersymmetry is reached in the limit of flat manifolds. The arbitrariness of the gauge functions in BRSTQFTs is thus removed by the requirement of scalar and vector topological symmetry, which also determines the complete supersymmetry transformations in a twisted way. Provided additional Killing vectors exist on the manifold, an equivariant extension of our geometrical framework is provided, and the resulting \\\"equivariant topological field theory\\\" corresponds to the twist of super Yang-Mills theory on omega backgrounds.}, doi = {10.1088/1126-6708/2005/08/037}, url = {http://hdl.handle.net/1963/1741}, author = {Laurent Baulieu and Guillaume Bossard and Alessandro Tanzini} } @article {2005, title = {Traffic flow on a road network}, journal = {SIAM J. Math. Anal. 36 (2005) 1862-1886}, number = {SISSA;13/2002/M}, year = {2005}, publisher = {SISSA Library}, abstract = {This paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from conservation of the number of cars,\\ndefined on a road network that is a collection of roads with junctions. The evolution problem is underdetermined at junctions, hence we choose to have some fixed rules for the distribution of traffic plus an optimization criteria for the flux. We prove existence, uniqueness and stability of solutions to the Cauchy problem. Our method is based on wave front tracking approach, see [6], and works also for boundary data and time dependent coefficients of traffic distribution at junctions, so including traffic lights.}, doi = {10.1137/S0036141004402683}, url = {http://hdl.handle.net/1963/1584}, author = {Giuseppe Maria Coclite and Benedetto Piccoli and Mauro Garavello} } @article {2005, title = {Vanishing viscosity solutions of nonlinear hyperbolic systems}, journal = {Ann. of Math. 161 (2005) 223-342}, number = {SISSA;86/2001/M}, year = {2005}, publisher = {Annals of Mathematics}, abstract = {We consider the Cauchy problem for a strictly hyperbolic, $n\\\\times n$ system in one space dimension: $u_t+A(u)u_x=0$, assuming that the initial data has small total variation.\\nWe show that the solutions of the viscous approximations $u_t+A(u)u_x=\\\\ve u_{xx}$ are defined globally in time and satisfy uniform BV estimates, independent of $\\\\ve$. Moreover, they depend continuously on the initial data in the $\\\\L^1$ distance, with a Lipschitz constant independent of $t,\\\\ve$. Letting $\\\\ve\\\\to 0$, these viscous solutions converge to a unique limit, depending Lipschitz continuously on the initial data. In the conservative case where $A=Df$ is the Jacobian of some flux function $f:\\\\R^n\\\\mapsto\\\\R^n$, the vanishing viscosity limits are precisely the unique entropy weak solutions to the system of conservation laws $u_t+f(u)_x=0$.}, url = {http://hdl.handle.net/1963/3074}, author = {Stefano Bianchini and Alberto Bressan} } @article {2005, title = {Wetting of rough surfaces: a homogenization approach}, journal = {Proc. R. Soc. Lon. Ser. A 461 (2005) 79-97}, number = {SISSA;75/2004/M}, year = {2005}, abstract = {The contact angle of a drop in equilibrium on a solid is strongly affected by the roughness of the surface on which it rests. We study the roughness-induced enhancement of the hydrophobic or hydrophilic properties of a solid surface through homogenization theory. By relying on a variational formulation of the problem, we show that the macroscopic contact angle is associated with the solution of two cell problems, giving the minimal energy per unit macroscopic area for a transition layer between the rough solid surface and a liquid or vapor phase. Our results are valid for both chemically heterogeneous and homogeneous surfaces. In the latter case, a very transparent structure emerges from the variational\\napproach: the classical laws of Wenzel and Cassie-Baxter give bounds for the optimal energy, and configurations of minimal energy are those leading to the smallest macroscopic contact angle in the hydrophobic case, to the largest one in the hydrophilic case.}, doi = {10.1098/rspa.2004.1364}, url = {http://hdl.handle.net/1963/2253}, author = {Antonio DeSimone and Giovanni Alberti} } @article {2004, title = {On almost duality for Frobenius manifolds}, journal = {Amer. Math. Soc. Transl. 212 (2004)\\n75-132.}, number = {arXiv.org;math/0307374}, year = {2004}, abstract = {We present a universal construction of almost duality for Frobenius manifolds. The analytic setup of this construction is described in details for the case of semisimple Frobenius manifolds. We illustrate the general considerations by examples from the singularity theory, mirror symmetry, the theory of Coxeter groups and Shephard groups, from the Seiberg - Witten duality.}, url = {http://hdl.handle.net/1963/2543}, author = {Boris Dubrovin} } @article {2004, title = {On analytic families of invariant tori for PDEs}, journal = {Ast{\'e}risque. Issue 297, 2004, Pages 35-65}, year = {2004}, publisher = {SISSA}, abstract = {We propose to apply a version of the classical Stokes\\r\\nexpansion method to the perturbative construction of invariant tori for\\r\\nPDEs corresponding to solutions quasiperiodic in space and time variables.\\r\\nWe argue that, for integrable PDEs all but finite number of the\\r\\nsmall divisors arising in the perturbative analysis cancel. As an illustrative\\r\\nexample we establish such cancellations for the case of KP equation.\\r\\nIt is proved that, under mild assumptions about decay of the magnitude\\r\\nof the Fourier modes all analytic families of finite-dimensional invariant\\r\\ntori for KP are given by the Krichever construction in terms of thetafunctions\\r\\nof Riemann surfaces. We also present an explicit construction\\r\\nof infinite dimensional real theta-functions and corresponding quasiperiodic\\r\\nsolutions to KP as sums of infinite number of interacting plane\\r\\nwaves.}, url = {http://hdl.handle.net/1963/6474}, author = {Boris Dubrovin} } @article {2004, title = {Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains}, journal = {Ann. Inst. H. Poincar{\'e}. Anal. Non Lin{\'e}aire 21 (2004), (4), p. 445-486.}, number = {SISSA;40/2002/M}, year = {2004}, publisher = {SISSA Library}, abstract = {We consider a sequence of Dirichlet problems in varying domains (or, more generally, of relaxed Dirichlet problems involving measures in M_0) for second order linear elliptic operators in divergence form with varying matrices of coefficients. When the matrices H-converge to a matrix A^0, we prove that there exist a subsequence and a measure mu^0 in M_0 such that the limit problem is the relaxed Dirichlet problem corresponding to A^0 and mu^0. We also prove a corrector result which provides an explicit approximation of the solutions in the H^1-norm, and which is obtained by multiplying the corrector for the H-converging matrices by some special test function which depends both on the varying matrices and on the varying domains.}, url = {http://hdl.handle.net/1963/1611}, author = {Gianni Dal Maso and Francois Mu