Mathematical modeling and quantitative study of biological motility (in particular, of motility at microscopic scales) is producing new biophysical insight and is offering opportunities for new discoveries at the level of both fundamental science and technology. These range from the explanation of how complex behavior at the level of a single organism emerges from body architecture, to the understanding of collective phenomena in groups of organisms and tissues, and of how these forms of swarm intelligence can be controlled and harnessed in engineering applications, to the elucidation of processes of fundamental biological relevance at the cellular and sub-cellular level. In this paper, some of the most exciting new developments in the fields of locomotion of unicellular organisms, of soft adhesive locomotion across scales, of the study of pore translocation properties of knotted DNA, of the development of synthetic active solid sheets, of the mechanics of the unjamming transition in dense cell collectives, of the mechanics of cell sheet folding in volvocalean algae, and of the self-propulsion of topological defects in active matter are discussed. For each of these topics, we provide a brief state of the art, an example of recent achievements, and some directions for future research.

VL - 2 UR - http://dx.doi.org/10.3934/mine.2020011 ER - TY - JOUR T1 - Surface tension controls the onset of gyrification in brain organoids JF - Journal of the Mechanics and Physics of Solids Y1 - 2020 A1 - Davide Riccobelli A1 - Giulia Bevilacqua KW - Buckling KW - Embryogenesis KW - Morpho-elasticity KW - Post-buckling analysis KW - Surface tension AB -Understanding the mechanics of brain embryogenesis can provide insights on pathologies related to brain development, such as lissencephaly, a genetic disease which causes a reduction of the number of cerebral sulci. Recent experiments on brain organoids have confirmed that gyrification, i.e. the formation of the folded structures of the brain, is triggered by the inhomogeneous growth of the peripheral region. However, the rheology of these cellular aggregates and the mechanics of lissencephaly are still matter of debate. In this work, we develop a mathematical model of brain organoids based on the theory of morpho-elasticity. We describe them as non-linear elastic bodies, composed of a disk surrounded by a growing layer called cortex. The external boundary is subjected to a tissue surface tension due the intercellular adhesion forces. We show that the resulting surface energy is relevant at the small length scales of brain organoids and affects the mechanics of cellular aggregates. We perform a linear stability analysis of the radially symmetric configuration and we study the post-buckling behaviour through finite element simulations. We find that the process of gyrification is triggered by the cortex growth and modulated by the competition between two length scales: the radius of the organoid and the capillary length generated by surface tension. We show that a solid model can reproduce the results of the in-vitro experiments. Furthermore, we prove that the lack of brain sulci in lissencephaly is caused by a reduction of the cell stiffness: the softening of the organoid strengthens the role of surface tension, delaying or even inhibiting the onset of a mechanical instability at the free boundary.

VL - 134 UR - http://www.sciencedirect.com/science/article/pii/S0022509619304065 ER - TY - JOUR T1 - Activation of a muscle as a mapping of stress–strain curves JF - Extreme Mech. Lett. Y1 - 2019 A1 - Davide Riccobelli A1 - D. Ambrosi PB - Elsevier BV VL - 28 ER - TY - JOUR T1 - Benamou–Brenier and duality formulas for the entropic cost on RCD*(K,N) spaces JF - Probability Theory and Related Fields Y1 - 2019 A1 - Nicola Gigli A1 - Luca Tamanini AB -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 Schrödinger problem) admits:A threefold dynamical variational representation, in the spirit of the Benamou–Brenier formula for the Wasserstein distance; A Hamilton–Jacobi–Bellman dual representation, in line with Bobkov–Gentil–Ledoux and Otto–Villani results on the duality between Hamilton–Jacobi and continuity equation for optimal transport;A Kantorovich-type duality formula, where the Hopf–Lax semigroup is replaced by a suitable `entropic' counterpart.We thus provide a complete and unifying picture of the equivalent variational representations of the Schrödinger 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.

UR - https://doi.org/10.1007/s00440-019-00909-1 ER - TY - JOUR T1 - BlackNUFFT: Modular customizable black box hybrid parallelization of type 3 NUFFT in 3D JF - Computer Physics Communications Y1 - 2019 A1 - Nicola Giuliani KW - C++ KW - Extensibility KW - FFT KW - Modularity KW - MPI KW - MRI image processing KW - NUFFT type 3 KW - TBB AB -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.

VL - 235 UR - http://www.sciencedirect.com/science/article/pii/S0010465518303539 ER - TY - CONF T1 - A complete data-driven framework for the efficient solution of parametric shape design and optimisation in naval engineering problems T2 - VIII International Conference on Computational Methods in Marine Engineering Y1 - 2019 A1 - Nicola Demo A1 - Marco Tezzele A1 - Andrea Mola A1 - Gianluigi Rozza AB -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 –- assuming the topology is inaltered by the deformation –-, 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.

JF - VIII International Conference on Computational Methods in Marine Engineering ER - TY - RPRT T1 - A continuous dependence result for a dynamic debonding model in dimension one Y1 - 2019 A1 - Filippo Riva AB -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’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.

PB - SISSA UR - http://preprints.sissa.it/xmlui/handle/1963/35329 U1 - 35640 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Differential structure associated to axiomatic Sobolev spaces JF - Expositiones Mathematicae Y1 - 2019 A1 - Nicola Gigli A1 - Enrico Pasqualetto KW - Axiomatic Sobolev space KW - Cotangent module KW - Locality of differentials AB -The aim of this note is to explain in which sense an axiomatic Sobolev space over a general metric measure space (à la Gol’dshtein–Troyanov) induces – under suitable locality assumptions – a first-order differential structure.

UR - http://www.sciencedirect.com/science/article/pii/S0723086918300975 ER - TY - RPRT T1 - A dynamic model for viscoelastic materials with prescribed growing cracks Y1 - 2019 A1 - Maicol Caponi A1 - Francesco Sapio AB -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.

UR - http://preprints.sissa.it:8180/xmlui/handle/1963/35334 ER - TY - CONF T1 - Efficient Reduction in Shape Parameter Space Dimension for Ship Propeller Blade Design T2 - VIII International Conference on Computational Methods in Marine Engineering Y1 - 2019 A1 - Andrea Mola A1 - Marco Tezzele A1 - Mahmoud Gadalla A1 - Valdenazzi, Federica A1 - Grassi, Davide A1 - Padovan, Roberta A1 - Gianluigi Rozza AB -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.

JF - VIII International Conference on Computational Methods in Marine Engineering ER - TY - JOUR T1 - An entropic interpolation proof of the HWI inequality JF - Stochastic Processes and their Applications Y1 - 2019 A1 - Ivan Gentil A1 - Christian Léonard A1 - Luigia Ripani A1 - Luca Tamanini KW - Entropic interpolations KW - Fisher information KW - Relative entropy KW - Schrödinger problem KW - Wasserstein distance AB -The HWI inequality is an “interpolation”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 Schrödinger problem. Our approach consists in making rigorous the Otto–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.

UR - http://www.sciencedirect.com/science/article/pii/S0304414918303454 ER - TY - JOUR T1 - On the existence of elastic minimizers for initially stressed materials JF - Phil. Trans. R. Soc. A Y1 - 2019 A1 - Davide Riccobelli A1 - A. Agosti A1 - Pasquale Ciarletta PB - The Royal Society VL - 377 ER - TY - JOUR T1 - Ground state energy of mixture of Bose gases JF - Reviews in Mathematical Physics Y1 - 2019 A1 - Alessandro Michelangeli A1 - Phan Thanh Nam A1 - Alessandro Olgiati AB -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–Pitaevskii energy functional and that the many-body ground state fully condensates on the Gross–Pitaevskii minimizers. In the mean-field regime, when the interaction length scale is O(1), we are able to verify Bogoliubov’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.

VL - 31 UR - https://doi.org/10.1142/S0129055X19500053 ER - TY - JOUR T1 - Isomonodromy deformations at an irregular singularity with coalescing eigenvalues JF - Duke Math. J. Y1 - 2019 A1 - Giordano Cotti A1 - Boris Dubrovin A1 - Davide Guzzetti AB -We consider an n×n linear system of ODEs with an irregular singularity of Poincar\'e rank 1 at z=∞, holomorphically depending on parameter t within a polydisc in Cn centred at t=0. The eigenvalues of the leading matrix at z=∞ coalesce along a locus Δ contained in the polydisc, passing through t=0. Namely, z=∞ 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.

PB - Duke University Press VL - 168 UR - https://doi.org/10.1215/00127094-2018-0059 ER - TY - JOUR T1 - Local well-posedness for quasi-linear NLS with large Cauchy data on the circle JF - Annales de l'Institut Henri Poincaré C, Analyse non linéaire Y1 - 2019 A1 - Roberto Feola A1 - Felice Iandoli KW - Dispersive equations KW - Energy method KW - Local wellposedness KW - NLS KW - Para-differential calculus KW - Quasi-linear PDEs AB -We prove local in time well-posedness for a large class of quasilinear Hamiltonian, or parity preserving, Schrödinger 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.

VL - 36 UR - http://www.sciencedirect.com/science/article/pii/S0294144918300428 ER - TY - JOUR T1 - Minimality of the ball for a model of charged liquid droplets JF - arXiv preprint arXiv:1912.07092 Y1 - 2019 A1 - Ekaterina Mukoseeva A1 - Vescovo, Giulia ER - TY - JOUR T1 - N=2 gauge theories on unoriented/open four-manifolds and their AGT counterparts JF - JHEP Y1 - 2019 A1 - Aditya Bawane A1 - Benvenuti, Sergio A1 - Giulio Bonelli A1 - Muteeb, Nouman A1 - Alessandro Tanzini VL - 07 UR - http://inspirehep.net/record/1631219/ ER - TY - JOUR T1 - A Note About the Strong Maximum Principle on RCD Spaces JF - Canadian Mathematical Bulletin Y1 - 2019 A1 - Nicola Gigli A1 - Chiara Rigoni AB -We give a direct proof of the strong maximum principle on finite dimensional RCD spaces based on the Laplacian comparison of the squared distance.

PB - Canadian Mathematical Society VL - 62 ER - TY - JOUR T1 - On the Number of Flats Tangent to Convex Hypersurfaces in Random Position JF - Discrete & Computational Geometry Y1 - 2019 A1 - Khazhgali Kozhasov A1 - Antonio Lerario UR - https://doi.org/10.1007/s00454-019-00067-0 ER - TY - JOUR T1 - Nutations in growing plant shoots: The role of elastic deformations due to gravity loading JF - Journal of the Mechanics and Physics of Solids Y1 - 2019 A1 - Daniele Agostinelli A1 - Alessandro Lucantonio A1 - Giovanni Noselli A1 - Antonio DeSimone KW - Circumnutations KW - Flutter instability KW - Gravitropism KW - Hopf bifurcation AB -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’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.

UR - https://doi.org/10.1016/j.jmps.2019.103702 ER - TY - JOUR T1 - Point-Like Perturbed Fractional Laplacians Through Shrinking Potentials of Finite Range JF - Complex Analysis and Operator Theory Y1 - 2019 A1 - Alessandro Michelangeli A1 - Raffaele Scandone AB -We construct the rank-one, singular (point-like) perturbations of the d-dimensional fractional Laplacian in the physically meaningful norm-resolvent limit of fractional Schrödinger 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 Schrödinger operators formed by a fractional Laplacian and a regular potential.

UR - https://doi.org/10.1007/s11785-019-00927-w ER - TY - RPRT T1 - Quasi-continuous vector fields on RCD spaces Y1 - 2019 A1 - Clément Debin A1 - Nicola Gigli A1 - Enrico Pasqualetto ER - TY - JOUR T1 - The Real Polynomial Eigenvalue Problem is Well Conditioned on the Average JF - Foundations of Computational Mathematics Y1 - 2019 A1 - Carlos Beltrán A1 - Khazhgali Kozhasov AB -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.

UR - https://doi.org/10.1007/s10208-019-09414-2 ER - TY - JOUR T1 - Reducibility of first order linear operators on tori via Moser's theorem JF - Journal of Functional Analysis Y1 - 2019 A1 - Roberto Feola A1 - Filippo Giuliani A1 - Riccardo Montalto A1 - Michela Procesi KW - Hyperbolic PDEs KW - KAM theory KW - Nash–Moser KW - Reducibility AB -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'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.

VL - 276 UR - http://www.sciencedirect.com/science/article/pii/S0022123618303793 ER - TY - JOUR T1 - On the relaxed area of the graph of discontinuous maps from the plane to the plane taking three values with no symmetry assumptions JF - Annali di Matematica Pura ed Applicata (1923 -) Y1 - 2019 A1 - Giovanni Bellettini A1 - Alaa Elshorbagy A1 - Maurizio Paolini A1 - Riccardo Scala AB -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 ``fill the hole'' 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.

UR - https://doi.org/10.1007/s10231-019-00887-0 ER - TY - JOUR T1 - The Serre–Swan theorem for normed modules JF - Rendiconti del Circolo Matematico di Palermo Series 2 Y1 - 2019 A1 - Danka Lučić A1 - Enrico Pasqualetto VL - 68 UR - https://doi.org/10.1007/s12215-018-0366-6 ER - TY - CONF T1 - Shape optimization through proper orthogonal decomposition with interpolation and dynamic mode decomposition enhanced by active subspaces T2 - VIII International Conference on Computational Methods in Marine Engineering Y1 - 2019 A1 - Marco Tezzele A1 - Nicola Demo A1 - Gianluigi Rozza AB -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.

JF - VIII International Conference on Computational Methods in Marine Engineering ER - TY - RPRT T1 - The sharp quantitative isocapacitary inequality Y1 - 2019 A1 - Guido De Philippis A1 - Michele Marini A1 - Ekaterina Mukoseeva JF - arXiv preprint arXiv:1901.11309 ER - TY - RPRT T1 - On the square distance function from a manifold with boundary Y1 - 2019 A1 - Giovanni Bellettini A1 - Alaa Elshorbagy AB -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.

UR - http://cvgmt.sns.it/media/doc/paper/4260/manif_with_bound_dist.pdf ER - TY - JOUR T1 - Strong Novikov conjecture for low degree cohomology and exotic group C*-algebras JF - arXiv e-prints Y1 - 2019 A1 - Paolo Antonini A1 - Buss, Alcides A1 - Engel, Alexander A1 - Siebenand , Timo KW - Mathematics - K-Theory and Homology KW - Mathematics - Operator Algebras AB -We strengthen a result of Hanke–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.

ER - TY - RPRT T1 - On the topological degree of planar maps avoiding normal cones Y1 - 2019 A1 - Alessandro Fonda A1 - Giuliano Klun AB - The classical Poincaré–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 ±1. PB - SISSA UR - http://preprints.sissa.it/handle/1963/35330 U1 - 35641 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Two-Dimensional Yang–Mills Theory on Surfaces with Corners in Batalin–Vilkovisky Formalism JF - Communications in Mathematical Physics Y1 - 2019 A1 - Riccardo Iraso A1 - Mnev, P. AB -In this paper we recover the non-perturbative partition function of 2D Yang–Mills theory from the perturbative path integral. To achieve this goal, we study the perturbative path integral quantization for 2D Yang–Mills theory on surfaces with boundaries and corners in the Batalin–Vilkovisky formalism (or, more precisely, in its adaptation to the setting with boundaries, compatible with gluing and cutting–-the BV-BFV formalism). We prove that cutting a surface (e.g. a closed one) into simple enough pieces–-building blocks–-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–Mills theory.

UR - https://doi.org/10.1007/s00220-019-03392-w ER - TY - RPRT T1 - Zero modes and low-energy resolvent expansion for three dimensional Schrodinger operators with point interactions Y1 - 2019 A1 - Raffaele Scandone UR - https://arxiv.org/abs/1901.02449 ER - TY - JOUR T1 - Accelerating the iterative solution of convection-diffusion problems using singular value decomposition JF - NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS Y1 - 2018 A1 - Giuseppe Pitton A1 - Luca Heltai UR - https://arxiv.org/abs/1807.09467 ER - TY - JOUR T1 - Analysis of a Dynamic Peeling Test with Speed-Dependent Toughness JF - SIAM Journal on Applied Mathematics Y1 - 2018 A1 - Giuliano Lazzaroni A1 - Lorenzo Nardini AB -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'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.

VL - 78 UR - https://doi.org/10.1137/17M1147354 ER - TY - JOUR T1 - An authenticated theoretical modeling of electrified fluid jet in core–shell nanofibers production JF - JOURNAL OF INDUSTRIAL TEXTILES Y1 - 2018 A1 - Rafiei, S. A1 - Noroozi, B. A1 - Luca Heltai A1 - Haghi, A. K. VL - 47 ER - TY - JOUR T1 - The Baum–Connes conjecture localised at the unit element of a discrete group JF - ArXiv e-prints Y1 - 2018 A1 - Paolo Antonini A1 - Azzali, S. A1 - Skandalis, G. KW - 19K35 KW - 46L80 KW - 46L85 KW - 58J22 KW - Mathematics - K-Theory and Homology KW - Mathematics - Operator Algebras ER - TY - RPRT T1 - Canonical Surfaces and Hypersurfaces in Abelian Varieties Y1 - 2018 A1 - Luca Cesarano UR - https://arxiv.org/abs/1808.05302 ER - TY - RPRT T1 - On the Cauchy problem for the wave equation on time-dependent domains Y1 - 2018 A1 - Gianni Dal Maso A1 - Rodica Toader AB - 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. PB - SISSA UR - http://preprints.sissa.it/handle/1963/35314 U1 - 35622 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Certified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models JF - Journal of Scientific Computing Y1 - 2018 A1 - Immanuel Martini A1 - Bernard Haasdonk A1 - Gianluigi Rozza VL - 74 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85017156114&doi=10.1007%2fs10915-017-0430-y&partnerID=40&md5=023ef0bb95713f4442d1fa374c92a964 ER - TY - RPRT T1 - Characteristic boundary layers for mixed hyperbolic systems in one space dimension and applications to the Navier-Stokes and MHD equations Y1 - 2018 A1 - Stefano Bianchini A1 - Laura Spinolo AB - 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. PB - SISSA UR - http://preprints.sissa.it/handle/1963/35325 U1 - 35635 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Cohesive fracture with irreversibility: Quasistatic evolution for a model subject to fatigue JF - Mathematical Models and Methods in Applied Sciences Y1 - 2018 A1 - Vito Crismale A1 - Giuliano Lazzaroni A1 - Gianluca Orlando AB -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.

VL - 28 UR - https://doi.org/10.1142/S0218202518500379 ER - TY - CHAP T1 - Combined parameter and model reduction of cardiovascular problems by means of active subspaces and POD-Galerkin methods T2 - Mathematical and Numerical Modeling of the Cardiovascular System and Applications Y1 - 2018 A1 - Marco Tezzele A1 - Francesco Ballarin A1 - Gianluigi Rozza JF - Mathematical and Numerical Modeling of the Cardiovascular System and Applications PB - Springer ER - TY - JOUR T1 - A Comparison Between Active Strain and Active Stress in Transversely Isotropic Hyperelastic Materials JF - J. Elast. Y1 - 2018 A1 - Giulia Giantesio A1 - Alessandro Musesti A1 - Davide Riccobelli PB - Springer Nature ER - TY - CHAP T1 - Computational methods in cardiovascular mechanics T2 - Cardiovascular Mechanics Y1 - 2018 A1 - Auricchio, Ferdinando A1 - Conti, Michele A1 - Lefieux, Adrian A1 - Morganti, Simone A1 - Alessandro Reali A1 - Gianluigi Rozza A1 - Veneziani, Alessandro ED - Michel F. Labrosse AB -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.

JF - Cardiovascular Mechanics PB - CRC Press UR - https://www.taylorfrancis.com/books/e/9781315280288/chapters/10.1201%2Fb21917-5 ER - TY - RPRT T1 - On the continuity of the trace operator in GSBV (Ω) and GSBD (Ω) Y1 - 2018 A1 - Emanuele Tasso AB - 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. UR - http://preprints.sissa.it/handle/1963/35324 N1 - 27 pages U1 - 35634 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - deal2lkit: A toolkit library for high performance programming in deal.II JF - SOFTWAREX Y1 - 2018 A1 - Alberto Sartori A1 - Nicola Giuliani A1 - Mauro Bardelloni A1 - Luca Heltai VL - 7 ER - TY - JOUR T1 - The deal.II Library, Version 9.0 JF - JOURNAL OF NUMERICAL MATHEMATICS Y1 - 2018 A1 - Giovanni Alzetta A1 - Arndt, Daniel A1 - W. Bangerth A1 - Boddu, Vishal A1 - Brands, Benjamin A1 - Denis Davydov A1 - Gassmöller, Rene A1 - Timo Heister A1 - Luca Heltai A1 - Kormann, Katharina A1 - Martin Kronbichler A1 - Matthias Maier A1 - Pelteret, Jean-Paul A1 - B. Turcksin A1 - David Wells UR - https://doi.org/10.1515/jnma-2018-0054 ER - TY - RPRT T1 - Differential of metric valued Sobolev maps Y1 - 2018 A1 - Nicola Gigli A1 - Enrico Pasqualetto A1 - Elefterios Soultanis ER - TY - RPRT T1 - Dimension reduction for thin films with transversally varying prestrain: the oscillatory and the non-oscillatory case Y1 - 2018 A1 - Marta Lewicka A1 - Danka Lučić ER - TY - JOUR T1 - Dimension reduction in heterogeneous parametric spaces with application to naval engineering shape design problems JF - Advanced Modeling and Simulation in Engineering Sciences Y1 - 2018 A1 - Marco Tezzele A1 - Filippo Salmoiraghi A1 - Andrea Mola A1 - Gianluigi Rozza AB -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.

VL - 5 ER - TY - JOUR T1 - Discriminant circle bundles over local models of Strebel graphs and Boutroux curves JF - Teoret. Mat. Fiz. Y1 - 2018 A1 - Marco Bertola A1 - Korotkin, D. A. VL - 197 UR - https://doi.org/10.4213/tmf9513 ER - TY - CHAP T1 - A distributed lagrange formulation of the finite element immersed boundary method for fluids interacting with compressible solids T2 - Mathematical and Numerical Modeling of the Cardiovascular System and Applications Y1 - 2018 A1 - Boffi, Daniele A1 - Gastaldi, Lucia A1 - Luca Heltai JF - Mathematical and Numerical Modeling of the Cardiovascular System and Applications PB - Springer International Publishing CY - Cham VL - 16 UR - https://arxiv.org/abs/1712.02545v1 ER - TY - JOUR T1 - Effective non-linear spinor dynamics in a spin-1 Bose–Einstein condensate JF - Journal of Physics A: Mathematical and Theoretical Y1 - 2018 A1 - Alessandro Michelangeli A1 - Alessandro Olgiati AB -We derive from first principles the experimentally observed effective dynamics of a spinor Bose gas initially prepared as a Bose–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–spin interaction. The effective dynamics is well-known to be governed by a system of coupled semi-linear Schrödinger 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.

PB - IOP Publishing VL - 51 UR - https://doi.org/10.1088%2F1751-8121%2Faadbc2 ER - TY - Generic T1 - An efficient shape parametrisation by free-form deformation enhanced by active subspace for hull hydrodynamic ship design problems in open source environment T2 - The 28th International Ocean and Polar Engineering Conference Y1 - 2018 A1 - Nicola Demo A1 - Marco Tezzele A1 - Andrea Mola A1 - Gianluigi Rozza KW - Active subspaces KW - Boundary element method KW - Dynamic mode decomposition KW - Fluid structure interaction KW - Free form deformation KW - Fully nonlinear potential KW - Numerical towing tank AB - 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. JF - The 28th International Ocean and Polar Engineering Conference PB - International Society of Offshore and Polar Engineers CY - Sapporo, Japan UR - https://www.onepetro.org/conference-paper/ISOPE-I-18-481 ER - TY - ABST T1 - The Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: from Laminar to Turbulent Flows Y1 - 2018 A1 - Saddam Hijazi A1 - Shafqat Ali A1 - Giovanni Stabile A1 - Francesco Ballarin A1 - Gianluigi Rozza ER - TY - RPRT T1 - Energy-dissipation balance of a smooth moving crack Y1 - 2018 A1 - Maicol Caponi A1 - Ilaria Lucardesi A1 - Emanuele Tasso AB - 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. UR - http://preprints.sissa.it/handle/1963/35320 U1 - 35630 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Existence and uniqueness of dynamic evolutions for a one dimensional debonding model with damping Y1 - 2018 A1 - Lorenzo Nardini A1 - Filippo Riva AB -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'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's criterion.

UR - http://preprints.sissa.it/xmlui/handle/1963/35319 U1 - 35629 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Existence for elastodynamic Griffith fracture with a weak maximal dissipation condition Y1 - 2018 A1 - Gianni Dal Maso A1 - Cristopher J. Larsen A1 - Rodica Toader AB - 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. UR - http://preprints.sissa.it/handle/1963/35308 U1 - 35616 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - Existence of solutions to a phase field model of dynamic fracture with a crack dependent dissipation Y1 - 2018 A1 - Maicol Caponi AB - 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's criterion. UR - http://preprints.sissa.it/handle/1963/35307 U1 - 35614 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - EZyRB: Easy Reduced Basis method JF - The Journal of Open Source Software Y1 - 2018 A1 - Nicola Demo A1 - Marco Tezzele A1 - Gianluigi Rozza VL - 3 UR - https://joss.theoj.org/papers/10.21105/joss.00661 ER - TY - CHAP T1 - Failure of the Chain Rule in the Non Steady Two-Dimensional Setting T2 - Current Research in Nonlinear Analysis: In Honor of Haim Brezis and Louis Nirenberg Y1 - 2018 A1 - Stefano Bianchini A1 - Paolo Bonicatto ED - Rassias, Themistocles M. JF - Current Research in Nonlinear Analysis: In Honor of Haim Brezis and Louis Nirenberg PB - Springer International Publishing CY - Cham SN - 978-3-319-89800-1 UR - https://doi.org/10.1007/978-3-319-89800-1_2 ER - TY - JOUR T1 - Finite volume POD-Galerkin stabilised reduced order methods for the parametrised incompressible Navier-Stokes equations JF - Computers & Fluids Y1 - 2018 A1 - Giovanni Stabile A1 - Gianluigi Rozza PB - Elsevier {BV} UR - https://doi.org/10.1016/j.compfluid.2018.01.035 ER - TY - RPRT T1 - Foldable structures made of hydrogel bilayers Y1 - 2018 A1 - Virginia Agostiniani A1 - Antonio DeSimone A1 - Alessandro Lucantonio A1 - Danka Lučić ER - TY - JOUR T1 - Fractional powers and singular perturbations of quantum differential Hamiltonians JF - Journal of Mathematical Physics Y1 - 2018 A1 - Alessandro Michelangeli A1 - Andrea Ottolini A1 - Raffaele Scandone AB -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 Schrödinger equations for the corresponding operators, we outline a programme of relevant questions that deserve being investigated.

VL - 59 UR - https://doi.org/10.1063/1.5033856 ER - TY - JOUR T1 - On fractional powers of singular perturbations of the Laplacian JF - Journal of Functional Analysis Y1 - 2018 A1 - Vladimir Georgiev A1 - Alessandro Michelangeli A1 - Raffaele Scandone KW - Point interactions KW - Regular and singular component of a point-interaction operator KW - Singular perturbations of the Laplacian AB -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.

VL - 275 UR - http://www.sciencedirect.com/science/article/pii/S0022123618301046 ER - TY - JOUR T1 - Framed symplectic sheaves on surfaces JF - International Journal of Mathematics Y1 - 2018 A1 - Jacopo Vittorio Scalise AB -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.

VL - 29 UR - https://doi.org/10.1142/S0129167X18500076 ER - TY - JOUR T1 - Free-form deformation, mesh morphing and reduced-order methods: enablers for efficient aerodynamic shape optimisation JF - International Journal of Computational Fluid Dynamics Y1 - 2018 A1 - Filippo Salmoiraghi A1 - Scardigli, Angela A1 - Telib, Haysam A1 - Gianluigi Rozza AB -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–Stokes equations.

PB - Taylor & Francis VL - 32 ER - TY - JOUR T1 - On fully real eigenconfigurations of tensors JF - SIAM Journal on Applied Algebra and Geometry Y1 - 2018 A1 - Khazhgali Kozhasov AB -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.

PB - SIAM VL - 2 UR - https://epubs.siam.org/doi/pdf/10.1137/17M1145902 ER - TY - RPRT T1 - On Geometric Quantum Confinement in Grushin-Like Manifolds Y1 - 2018 A1 - Matteo Gallone A1 - Alessandro Michelangeli A1 - Eugenio Pozzoli AB - 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's analysis in each fibre, thus fully characterising the regimes of presence and absence of essential self-adjointness of the associated Laplace-Beltrami operator. UR - http://preprints.sissa.it/handle/1963/35322 N1 - 16 pages U1 - 35632 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Global, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials JF - Zeitschrift für angewandte Mathematik und Physik Y1 - 2018 A1 - Paolo Antonelli A1 - Alessandro Michelangeli A1 - Raffaele Scandone AB -We prove the existence of weak solutions in the space of energy for a class of nonlinear Schrödinger 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.

VL - 69 UR - https://doi.org/10.1007/s00033-018-0938-5 ER - TY - JOUR T1 - Heterogeneous elastic plates with in-plane modulation of the target curvature and applications to thin gel sheets JF - ESAIM: Control, Optimisation and Calculus of Variations Y1 - 2018 A1 - Virginia Agostiniani A1 - Alessandro Lucantonio A1 - Danka Lučić PB - EDP Sciences ER - TY - RPRT T1 - Hydrogenoid Spectra with Central Perturbations Y1 - 2018 A1 - Matteo Gallone A1 - Alessandro Michelangeli AB - Through the Kreĭn-Višik-Birman extension scheme, unlike the previous classical analysis based on von Neumann'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 Schördinger 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 Kreĭn-Višik-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. UR - http://preprints.sissa.it/handle/1963/35321 N1 - Mathematics Subject Classification (2010) 34L10 . 34L15 . 34L16 . 47B15 . 47B25 . 47N20 . 81Q10 . 81Q80 U1 - 35631 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Iterative map-making with two-level preconditioning for polarized cosmic microwave background data sets. A worked example for ground-based experiments JF - ASTRONOMY & ASTROPHYSICS Y1 - 2018 A1 - Puglisi, Giuseppe A1 - Poletti, Davide A1 - Fabbian, Giulio A1 - Baccigalupi, Carlo A1 - Luca Heltai A1 - Stompor, Radek VL - 618 UR - https://arxiv.org/abs/1801.08937 ER - TY - RPRT T1 - On Krylov solutions to infinite-dimensional inverse linear problems Y1 - 2018 A1 - Noe Caruso A1 - Alessandro Michelangeli A1 - Paolo Novati AB - 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. PB - SISSA UR - http://preprints.sissa.it/handle/1963/35327 U1 - 35638 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Local moduli of semisimple Frobenius coalescent structures Y1 - 2018 A1 - Giordano Cotti A1 - Boris Dubrovin A1 - Davide Guzzetti AB -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.

PB - SISSA UR - http://preprints.sissa.it/handle/1963/35304 U1 - 35610 U2 - Mathematics U4 - 1 U5 - MAT/03 ER - TY - JOUR T1 - A Localized Reduced-Order Modeling Approach for PDEs with Bifurcating Solutions JF - ArXiv e-prints Y1 - 2018 A1 - Martin W. Hess A1 - A. Alla A1 - Annalisa Quaini A1 - Gianluigi Rozza A1 - M. Gunzburger KW - Mathematics - Numerical Analysis ER - TY - RPRT T1 - Long time existence for fully nonlinear NLS with small Cauchy data on the circle Y1 - 2018 A1 - Feola Roberto A1 - Felice Iandoli ER - TY - JOUR T1 - Lp-Boundedness of Wave Operators for the Three-Dimensional Multi-Centre Point Interaction JF - Annales Henri Poincaré Y1 - 2018 A1 - Gianfausto Dell'Antonio A1 - Alessandro Michelangeli A1 - Raffaele Scandone A1 - Kenji Yajima AB -We prove that, for arbitrary centres and strengths, the wave operators for three-dimensional Schrödinger operators with multi-centre local point interactions are bounded in Lp(R3)for 1<p<3 and unbounded otherwise.

VL - 19 UR - https://doi.org/10.1007/s00023-017-0628-4 ER - TY - RPRT T1 - A minimization approach to the wave equation on time-dependent domains Y1 - 2018 A1 - Gianni Dal Maso A1 - Lucia De Luca AB - 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. PB - SISSA UR - http://preprints.sissa.it/handle/1963/35318 U1 - 35627 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Minimizing movements for mean curvature flow of droplets with prescribed contact angle JF - Journal de Mathématiques Pures et Appliquées Y1 - 2018 A1 - Giovanni Bellettini A1 - Matteo Novaga A1 - Shokhrukh Kholmatov KW - Capillary functional KW - Mean curvature flow with prescribed contact angle KW - Minimizing movements KW - Sets of finite perimeter AB -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–Taylor–Wang and Luckhaus–Sturzenhecker, we show the existence of a weak evolution, and its compatibility with a distributional solution. We also prove various comparison results. Résumé Nous étudions le mouvement par courbure moyenne d'une goutte qui glisse par courbure moyenne sur un hyperplan horizontal avec un angle de contact prescrit éventuellement non constant. En utilisant les solutions construites comme limites d'un algorithme d'approximation dû à Almgren, Taylor et Wang et Luckhaus et Sturzenhecker, nous montrons l'existence d'une évolution faible, et sa compatibilité avec une solution au sens des distributions. Nous démontrons également plusieurs résultats de comparaison.

VL - 117 UR - http://www.sciencedirect.com/science/article/pii/S0021782418300825 ER - TY - JOUR T1 - Minimizing Movements for Mean Curvature Flow of Partitions JF - SIAM Journal on Mathematical Analysis Y1 - 2018 A1 - Giovanni Bellettini A1 - Shokhrukh Kholmatov AB -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.

VL - 50 UR - https://doi.org/10.1137/17M1159294 ER - TY - CONF T1 - Model Order Reduction by means of Active Subspaces and Dynamic Mode Decomposition for Parametric Hull Shape Design Hydrodynamics T2 - Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship & Maritime Research Y1 - 2018 A1 - Marco Tezzele A1 - Nicola Demo A1 - Mahmoud Gadalla A1 - Andrea Mola A1 - Gianluigi Rozza AB - 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. JF - Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship & Maritime Research PB - IOS Press CY - Trieste, Italy UR - http://ebooks.iospress.nl/publication/49270 ER - TY - JOUR T1 - Model Reduction for Parametrized Optimal Control Problems in Environmental Marine Sciences and Engineering JF - SIAM Journal on Scientific Computing Y1 - 2018 A1 - Maria Strazzullo A1 - Francesco Ballarin A1 - Mosetti, R. A1 - Gianluigi Rozza VL - 40 UR - https://doi.org/10.1137/17M1150591 ER - TY - JOUR T1 - Morpho-elastic model of the tortuous tumour vessels JF - Int. J. Non-Linear Mech. Y1 - 2018 A1 - Davide Riccobelli A1 - Pasquale Ciarletta PB - Elsevier BV VL - 107 ER - TY - JOUR T1 - Noncommutative Painlevé Equations and Systems of Calogero Type JF - Comm. Math. Phys Y1 - 2018 A1 - Marco Bertola A1 - Mattia Cafasso A1 - V. Rubtsov ER - TY - RPRT T1 - Non-linear Gross-Pitaevskii dynamics of a 2D binary condensate: a numerical analysis Y1 - 2018 A1 - Alessandro Michelangeli A1 - Giuseppe Pitton AB - 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. UR - http://preprints.sissa.it/handle/1963/35323 U1 - 35633 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - On the notion of parallel transport on RCD spaces Y1 - 2018 A1 - Nicola Gigli A1 - Enrico Pasqualetto ER - TY - JOUR T1 - A novel reduced order model for vortex induced vibrations of long flexible cylinders Y1 - 2018 A1 - Giovanni Stabile A1 - Hermann G. Matthies A1 - Claudio Borri PB - Elsevier {BV} VL - 156 UR - https://doi.org/10.1016/j.oceaneng.2018.02.064 ER - TY - JOUR T1 - Numerical study of the Kadomtsev-Petviashvili equation and dispersive shock waves JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Y1 - 2018 A1 - Tamara Grava A1 - Christian Klein A1 - Giuseppe Pitton AB -A detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev–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 Schrödinger equation in the semiclassical limit.

VL - 474 UR - https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2017.0458 ER - TY - JOUR T1 - NURBS-SEM: A hybrid spectral element method on NURBS maps for the solution of elliptic PDEs on surfaces JF - COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Y1 - 2018 A1 - Giuseppe Pitton A1 - Luca Heltai VL - 338 UR - https://arxiv.org/abs/1804.08271 ER - TY - RPRT T1 - Observables in the equivariant A-model Y1 - 2018 A1 - Bonechi, F. A1 - Cattaneo, A.S. A1 - Riccardo Iraso A1 - Maxim Zabzine UR - https://arxiv.org/abs/1807.08659 ER - TY - JOUR T1 - Painlevé IV Critical Asymptotics for Orthogonal Polynomials in the Complex Plane JF - Symmetry, Integrability and Geometry. Methods and Applications Y1 - 2018 A1 - Marco Bertola A1 - José Gustavo Elias Rebelo A1 - Tamara Grava AB -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´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´e transcendent is pole-free on a semiaxis.

PB - National Academy of Sciences of Ukraine VL - 14 ER - TY - JOUR T1 - Peristaltic Waves as Optimal Gaits in Metameric Bio-Inspired Robots JF - Frontiers in Robotics and AI Y1 - 2018 A1 - Daniele Agostinelli A1 - François Alouges A1 - Antonio DeSimone KW - Biomimetic robots KW - Crawling motility KW - Lumbricus terrestris KW - Metameric robots KW - Optimization KW - Peristalsis KW - Self-propulsion KW - Soft robotics AB -*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 “phase coordination” 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''+(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.

PB - American Mathematical Society UR - http://urania.sissa.it/xmlui/handle/1963/35264 N1 - AMS Subject Classification: 34B15, 34B18, 34C25, 34C28, 47H11. U1 - 35568 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Positive subharmonic solutions to nonlinear ODEs with indefinite weight JF - Communications in Contemporary Mathematics Y1 - 2018 A1 - Alberto Boscaggin A1 - Guglielmo Feltrin AB -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) 467–477]. The proof, which applies to a larger class of indefinite equations, combines coincidence degree theory (yielding a positive harmonic solution) with the Poincaré–Birkhoff fixed point theorem (giving subharmonic solutions oscillating around it).

VL - 20 UR - https://doi.org/10.1142/S0219199717500213 ER - TY - JOUR T1 - Predicting and Optimizing Microswimmer Performance from the Hydrodynamics of Its Components: The Relevance of Interactions JF - SOFT ROBOTICS Y1 - 2018 A1 - Nicola Giuliani A1 - Luca Heltai A1 - Antonio DeSimone VL - 5 UR - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6094362/ ER - TY - JOUR T1 - PyDMD: Python Dynamic Mode Decomposition JF - The Journal of Open Source Software Y1 - 2018 A1 - Nicola Demo A1 - Marco Tezzele A1 - Gianluigi Rozza VL - 3 UR - https://joss.theoj.org/papers/734e4326edd5062c6e8ee98d03df9e1d ER - TY - JOUR T1 - On the Quasistatic Limit of Dynamic Evolutions for a Peeling Test in Dimension One JF - Journal of Nonlinear Science Y1 - 2018 A1 - Giuliano Lazzaroni A1 - Lorenzo Nardini AB -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'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's (quasistatic) criterion does not hold in general, thus the limit evolution is not rate-independent.

VL - 28 UR - https://doi.org/10.1007/s00332-017-9407-0 ER - TY - RPRT T1 - On real resonances for the three-dimensional, multi-centre point interaction Y1 - 2018 A1 - Alessandro Michelangeli A1 - Raffaele Scandone ER - TY - JOUR T1 - Recognizing the flat torus among RCD*(0,N) spaces via the study of the first cohomology group JF - Calculus of Variations and Partial Differential Equations Y1 - 2018 A1 - Nicola Gigli A1 - Chiara Rigoni AB -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.

VL - 57 UR - https://doi.org/10.1007/s00526-018-1377-z ER - TY - ABST T1 - A Reduced Basis approach for PDEs on parametrized geometries based on the Shifted Boundary Finite Element Method and application to fluid dynamics Y1 - 2018 A1 - Efthymios N. Karatzas A1 - Giovanni Stabile A1 - Leo Nouveau A1 - Guglielmo Scovazzi A1 - Gianluigi Rozza ER - TY - ABST T1 - A Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries Y1 - 2018 A1 - Efthymios N. Karatzas A1 - Giovanni Stabile A1 - N. Atallah A1 - Guglielmo Scovazzi A1 - Gianluigi Rozza ER - TY - RPRT T1 - Reducibility for a class of weakly dispersive linear operators arising from the Degasperis Procesi equation Y1 - 2018 A1 - Roberto Feola A1 - Filippo Giuliani A1 - Michela Procesi ER - TY - JOUR T1 - Regularity estimates for scalar conservation laws in one space dimension JF - Journal of Hyperbolic Differential Equations Y1 - 2018 A1 - Elio Marconi AB -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′∘ 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.

VL - 15 UR - https://doi.org/10.1142/S0219891618500200 ER - TY - JOUR T1 - Second order differentiation formula on RCD(K, N) spaces JF - Rendiconti Lincei-Matematica e Applicazioni Y1 - 2018 A1 - Nicola Gigli A1 - Luca Tamanini VL - 29 ER - TY - RPRT T1 - Second order differentiation formula on RCD*(K,N) spaces Y1 - 2018 A1 - Nicola Gigli A1 - Luca Tamanini ER - TY - CONF T1 - Shape Optimization by means of Proper Orthogonal Decomposition and Dynamic Mode Decomposition T2 - Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship & Maritime Research Y1 - 2018 A1 - Nicola Demo A1 - Marco Tezzele A1 - Gianluca Gustin A1 - Gianpiero Lavini A1 - Gianluigi Rozza AB - 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. JF - Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship & Maritime Research PB - IOS Press CY - Trieste, Italy UR - http://ebooks.iospress.nl/publication/49229 ER - TY - JOUR T1 - Shape transitions in a soft incompressible sphere with residual stresses JF - Math. Mech. Solids Y1 - 2018 A1 - Davide Riccobelli A1 - Pasquale Ciarletta PB - SAGE Publications Sage UK: London, England VL - 23 ER - TY - JOUR T1 - Singular Hartree equation in fractional perturbed Sobolev spaces JF - Journal of Nonlinear Mathematical Physics Y1 - 2018 A1 - Alessandro Michelangeli A1 - Alessandro Olgiati A1 - Raffaele Scandone AB -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 Schrödinger 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.

PB - Taylor & Francis VL - 25 UR - https://doi.org/10.1080/14029251.2018.1503423 ER - TY - RPRT T1 - On some rigorous aspects of fragmented condensation Y1 - 2018 A1 - Daniele Dimonte A1 - Marco Falconi A1 - Alessandro Olgiati UR - https://arxiv.org/abs/1809.03586 ER - TY - JOUR T1 - Spectral triples on the Jiang-Su algebra JF - Journal of Mathematical Physics Y1 - 2018 A1 - Jacopo Bassi A1 - Ludwik Dabrowski VL - 59 UR - https://doi.org/10.1063/1.5026311 ER - TY - RPRT T1 - Stochastic homogenisation of free-discontinuity problems Y1 - 2018 A1 - Filippo Cagnetti A1 - Gianni Dal Maso A1 - Lucia Scardia A1 - Caterina Ida Zeppieri AB - 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. UR - http://preprints.sissa.it/handle/1963/35309 U1 - 35617 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Symplectic invariants for parabolic orbits and cusp singularities of integrable systems JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Y1 - 2018 A1 - Alexey Bolsinov A1 - Lorenzo Guglielmi A1 - Elena Kudryavtseva AB -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 ‘Finite dimensional integrable systems: new trends and methods’.

VL - 376 UR - https://royalsocietypublishing.org/doi/abs/10.1098/rsta.2017.0424 ER - TY - RPRT T1 - Transmission conditions obtained by homogenisation Y1 - 2018 A1 - Gianni Dal Maso A1 - Giovanni Franzina A1 - Davide Zucco AB - 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. UR - http://preprints.sissa.it/handle/1963/35310 U1 - 35618 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - Truncation and convergence issues for bounded linear inverse problems in Hilbert space Y1 - 2018 A1 - Noe Caruso A1 - Alessandro Michelangeli A1 - Paolo Novati AB - 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. PB - SISSA UR - http://preprints.sissa.it/handle/1963/35326 U1 - 35637 U2 - Mathematics U4 - 1 ER - TY - CONF T1 - On Uniqueness of Weak Solutions to Transport Equation with Non-smooth Velocity Field T2 - Theory, Numerics and Applications of Hyperbolic Problems I Y1 - 2018 A1 - Paolo Bonicatto ED - Klingenberg, Christian ED - Westdickenberg, Michael JF - Theory, Numerics and Applications of Hyperbolic Problems I PB - Springer International Publishing CY - Cham SN - 978-3-319-91545-6 UR - https://link.springer.com/chapter/10.1007/978-3-319-91545-6_15 ER - TY - RPRT T1 - Weak formulation of elastodynamics in domains with growing cracks Y1 - 2018 A1 - Emanuele Tasso AB - 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'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. PB - SISSA UR - http://preprints.sissa.it/handle/1963/35328 U1 - 35639 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - π-BEM : A flexible parallel implementation for adaptive , geometry aware , and high order boundary element methods JF - Advances in Engineering Software Y1 - 2018 A1 - Nicola Giuliani A1 - Andrea Mola A1 - Luca Heltai VL - 121 ER - TY - RPRT T1 - On the 1D wave equation in time-dependent domains and the problem of debond initiation Y1 - 2017 A1 - Giuliano Lazzaroni A1 - Lorenzo Nardini AB -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.

PB - SISSA UR - http://preprints.sissa.it/handle/1963/35302 U1 - 35608 U2 - Mathematics ER - TY - JOUR T1 - Advances in Reduced order modelling for CFD: vortex shedding around a circular cylinder using a POD-Galerkin method JF - Communication in Applied Industrial Mathematics Y1 - 2017 A1 - Giovanni Stabile A1 - Saddam Hijazi A1 - Stefano Lorenzi A1 - Andrea Mola A1 - Gianluigi Rozza KW - finite volume, CFD KW - Reduced order methods AB -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.

UR - https://arxiv.org/abs/1701.03424 ER - TY - RPRT T1 - Almost global existence of solutions for capillarity-gravity water waves equations with periodic spatial boundary conditions Y1 - 2017 A1 - Massimiliano Berti A1 - Jean-Marc Delort AB - 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. UR - http://preprints.sissa.it/handle/1963/35285 U1 - 35590 U2 - Mathematics ER - TY - JOUR T1 - Analytic geometry of semisimple coalescent Frobenius structures JF - Random Matrices: Theory and Applications Y1 - 2017 A1 - Giordano Cotti A1 - Davide Guzzetti AB -We present some results of a joint paper with Dubrovin (see references), as exposed at the Workshop “Asymptotic and Computational Aspects of Complex Differential Equations” 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.

VL - 06 UR - https://doi.org/10.1142/S2010326317400044 ER - TY - JOUR T1 - An application of coincidence degree theory to cyclic feedback type systems associated with nonlinear differential operators JF - Topol. Methods Nonlinear Anal. Y1 - 2017 A1 - Guglielmo Feltrin A1 - Fabio Zanolin PB - Nicolaus Copernicus University, Juliusz P. Schauder Centre for Nonlinear Studies VL - 50 UR - https://doi.org/10.12775/TMNA.2017.038 ER - TY - JOUR T1 - On the Application of Reduced Basis Methods to Bifurcation Problems in Incompressible Fluid Dynamics JF - Journal of Scientific Computing Y1 - 2017 A1 - Giuseppe Pitton A1 - Gianluigi Rozza AB -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.

ER - TY - JOUR T1 - An avoiding cones condition for the Poincaré–Birkhoff Theorem JF - Journal of Differential Equations Y1 - 2017 A1 - Alessandro Fonda A1 - Paolo Gidoni KW - Avoiding cones condition KW - Hamiltonian systems KW - Periodic solutions KW - Poincaré–Birkhoff theorem AB -We provide a geometric assumption which unifies and generalizes the conditions proposed in [11], [12], so to obtain a higher dimensional version of the Poincaré–Birkhoff fixed point Theorem for Poincaré maps of Hamiltonian systems.

VL - 262 UR - http://www.sciencedirect.com/science/article/pii/S0022039616303278 ER - TY - CHAP T1 - Certified Reduced Basis Method for Affinely Parametric Isogeometric Analysis NURBS Approximation T2 - Spectral and High Order Methods for Partial Differential Equations Y1 - 2017 A1 - Denis Devaud A1 - Gianluigi Rozza AB -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.

JF - Spectral and High Order Methods for Partial Differential Equations PB - Springer CY - Heildeberg VL - 119 SN - 978-3-319-65869-8 ER - TY - JOUR T1 - On a certified smagorinsky reduced basis turbulence model JF - SIAM Journal on Numerical Analysis Y1 - 2017 A1 - Rebollo, T.C. A1 - E.D. Ávila A1 - Marmol, M.G. A1 - Francesco Ballarin A1 - Gianluigi Rozza VL - 55 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85039928218&doi=10.1137%2f17M1118233&partnerID=40&md5=221d9cd2bcc74121fcef93efd9d3d76c ER - TY - JOUR T1 - Clifford Tori and the singularly perturbed Cahn–Hilliard equation JF - Journal of Differential Equations Y1 - 2017 A1 - Matteo Rizzi KW - Cahn–Hilliard equation KW - Clifford Torus KW - Lyapunov–Schmidt reduction KW - Willmore surface AB -In this paper we construct entire solutions uε to the Cahn–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→1 as ε→0, whose nodal set approaches the Clifford Torus, that is the Torus with radii of ratio 1/2 embedded in R3, as ε→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–Schmidt reduction and on careful geometric expansions of the Laplacian.

VL - 262 UR - http://www.sciencedirect.com/science/article/pii/S0022039617300530 ER - TY - RPRT T1 - Complex Friedrichs systems and applications Y1 - 2017 A1 - Nenad Antonić A1 - Krešimir Burazin A1 - Ivana Crnjac A1 - Marko Erceg AB - 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. UR - http://urania.sissa.it/xmlui/handle/1963/35270 U1 - 35576 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Computational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: Applications to Coanda effect in cardiology JF - Journal of Computational Physics Y1 - 2017 A1 - Giuseppe Pitton A1 - Annalisa Quaini A1 - Gianluigi Rozza KW - Parametrized Navier–Stokes equations KW - Reduced basis method KW - Stability of flows KW - Symmetry breaking bifurcation AB -We focus on reducing the computational costs associated with the hydrodynamic stability of solutions of the incompressible Navier–Stokes equations for a Newtonian and viscous fluid in contraction–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.

VL - 344 UR - http://www.sciencedirect.com/science/article/pii/S002199911730356X ER - TY - RPRT T1 - On contact interactions realised as Friedrichs systems Y1 - 2017 A1 - Marko Erceg A1 - Alessandro Michelangeli AB - 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. UR - http://preprints.sissa.it/handle/1963/35298 U1 - 35604 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Curvature terms in small time heat kernel expansion for a model class of hypoelliptic Hörmander operators JF - Nonlinear Analysis Y1 - 2017 A1 - Davide Barilari A1 - Elisa Paoli KW - Curvature KW - Hypoelliptic heat equation KW - Small time asymptotics AB -We consider the heat equation associated with a class of second order hypoelliptic Hörmander 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.

VL - 164 UR - http://www.sciencedirect.com/science/article/pii/S0362546X17302298 ER - TY - JOUR T1 - Curvature-adapted remeshing of CAD surfaces JF - Engineering with Computers Y1 - 2017 A1 - Franco Dassi A1 - Andrea Mola A1 - Hang Si PB - Springer Nature VL - 34 UR - https://doi.org/10.1007/s00366-017-0558-2 ER - TY - JOUR T1 - The deal.II Library, Version 8.5 JF - JOURNAL OF NUMERICAL MATHEMATICS Y1 - 2017 A1 - Arndt, Daniel A1 - W. Bangerth A1 - Denis Davydov A1 - Timo Heister A1 - Luca Heltai A1 - Martin Kronbichler A1 - Matthias Maier A1 - Pelteret, Jean-Paul A1 - B. Turcksin A1 - David Wells VL - 25 UR - https://www.dealii.org/deal85-preprint.pdf ER - TY - RPRT T1 - Derivation of a rod theory from lattice systems with interactions beyond nearest neighbours Y1 - 2017 A1 - Roberto Alicandro A1 - Giuliano Lazzaroni A1 - Mariapia Palombaro AB - 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. UR - http://urania.sissa.it/xmlui/handle/1963/35269 U1 - 35575 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Discrete spectra for critical Dirac-Coulomb Hamiltonians Y1 - 2017 A1 - Matteo Gallone A1 - Alessandro Michelangeli AB - 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’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’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. UR - http://preprints.sissa.it/handle/1963/35300 U1 - 35606 U2 - Mathematics U4 - 1 ER - TY - CHAP T1 - Dispersive Estimates for Schrödinger Operators with Point Interactions in ℝ3 T2 - Advances in Quantum Mechanics: Contemporary Trends and Open Problems Y1 - 2017 A1 - Felice Iandoli A1 - Raffaele Scandone ED - Alessandro Michelangeli ED - Gianfausto Dell'Antonio AB -The study of dispersive properties of Schrödinger 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 Schrödinger 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 $q \geq 3$.

JF - Advances in Quantum Mechanics: Contemporary Trends and Open Problems PB - Springer International Publishing CY - Cham SN - 978-3-319-58904-6 UR - https://doi.org/10.1007/978-3-319-58904-6_11 ER - TY - RPRT T1 - On the effect of interactions beyond nearest neighbours on non-convex lattice systems Y1 - 2017 A1 - Roberto Alicandro A1 - Giuliano Lazzaroni A1 - Mariapia Palombaro AB - 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. UR - http://urania.sissa.it/xmlui/handle/1963/35268 U1 - 35574 U2 - Mathematics U4 - 1 ER - TY - CHAP T1 - Effective Non-linear Dynamics of Binary Condensates and Open Problems T2 - Advances in Quantum Mechanics: Contemporary Trends and Open Problems Y1 - 2017 A1 - Alessandro Olgiati ED - Alessandro Michelangeli ED - Gianfausto Dell'Antonio AB -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 Schödinger 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.

JF - Advances in Quantum Mechanics: Contemporary Trends and Open Problems PB - Springer International Publishing CY - Cham SN - 978-3-319-58904-6 UR - https://doi.org/10.1007/978-3-319-58904-6_14 ER - TY - RPRT T1 - Elliptic diffeomorphisms of symplectic 4-manifolds Y1 - 2017 A1 - Vsevolod Shevchishin A1 - Gleb Smirnov UR - https://arxiv.org/pdf/1708.01518.pdf ER - TY - JOUR T1 - Energy release rate and quasi-static evolution via vanishing viscosity in a fracture model depending on the crack opening JF - ESAIM: Control, Optimisation and Calculus of Variations Y1 - 2017 A1 - Stefano Almi AB -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’s criterion.

PB - EDP Sciences VL - 23 UR - https://www.esaim-cocv.org/component/article?access=doi&doi=10.1051/cocv/2016014 ER - TY - RPRT T1 - Friedrichs systems in a Hilbert space framework: solvability and multiplicity Y1 - 2017 A1 - Nenad Antonić A1 - Marko Erceg A1 - Alessandro Michelangeli AB - 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 Antonić 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. UR - http://preprints.sissa.it/handle/1963/35280 U1 - 35587 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Gamma-Convergence of Free-discontinuity problems Y1 - 2017 A1 - Filippo Cagnetti A1 - Gianni Dal Maso A1 - Lucia Scardia A1 - Caterina Ida Zeppieri AB - 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. PB - SISSA UR - http://preprints.sissa.it/handle/1963/35276 U1 - 35583 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Gauge theories on compact toric surfaces, conformal field theories and equivariant Donaldson invariants JF - Journal of Geometry and Physics Y1 - 2017 A1 - Mikhail Bershtein A1 - Giulio Bonelli A1 - Massimiliano Ronzani A1 - Alessandro Tanzini KW - AGT KW - Donaldson invariants KW - Equivariant localization KW - Exact partition function KW - Supersymmetry KW - Virasoro conformal blocks AB -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 — in honor of Ugo Bruzzo’s 60th birthday 17–22 August 2015, Guarujá, São Paulo, Brazil, mostly based on Bawane et al. (0000) and Bershtein et al. (0000).

VL - 118 UR - http://www.sciencedirect.com/science/article/pii/S0393044017300165 N1 - Interactions between Geometry and Physics. A Special Issue in Honor of Ugo Bruzzo’s 60th Birthday ER - TY - JOUR T1 - On the genesis of directional friction through bristle-like mediating elements JF - ESAIM: COCV Y1 - 2017 A1 - Paolo Gidoni A1 - Antonio DeSimone AB -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–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.

VL - 23 UR - https://doi.org/10.1051/cocv/2017030 ER - TY - JOUR T1 - Globally stable quasistatic evolution for strain gradient plasticity coupled with damage JF - Annali di Matematica Pura ed Applicata (1923 -) Y1 - 2017 A1 - Vito Crismale AB -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–Anand formulation (J Mech Phys Solids 53:1624–1649, 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'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).

VL - 196 UR - https://doi.org/10.1007/s10231-016-0590-7 ER - TY - JOUR T1 - Gross-Pitaevskii non-linear dynamics for pseudo-spinor condensates JF - Journal of Nonlinear Mathematical Physics Y1 - 2017 A1 - Alessandro Michelangeli A1 - Alessandro Olgiati AB -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 Schrödinger 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 Schrödinger equations coupled among themselves through linear (Rabi) terms. The proof relies on an adaptation to the spinor setting of Pickl’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.

PB - Taylor & Francis VL - 24 UR - https://doi.org/10.1080/14029251.2017.1346348 ER - TY - JOUR T1 - Homotopically invisible singular curves JF - Calculus of Variations and Partial Differential Equations Y1 - 2017 A1 - Andrei A. Agrachev A1 - Francesco Boarotto A1 - Antonio Lerario VL - 56 UR - https://doi.org/10.1007/s00526-017-1203-z ER - TY - JOUR T1 - Homotopy properties of horizontal path spaces and a theorem of Serre in subriemannian geometry JF - Communications in Analysis and Geometry Y1 - 2017 A1 - Francesco Boarotto A1 - Antonio Lerario PB - International Press of Boston VL - 25 ER - TY - JOUR T1 - The injectivity radius of Lie manifolds JF - ArXiv e-prints Y1 - 2017 A1 - Paolo Antonini A1 - Guido De Philippis A1 - Nicola Gigli KW - (58J40) KW - 53C21 KW - Mathematics - Differential Geometry AB -We prove in a direct, geometric way that for any compatible Riemannian metric on a Lie manifold the injectivity radius is positive

UR - https://arxiv.org/pdf/1707.07595.pdf ER - TY - JOUR T1 - Integrability of dominated decompositions on three-dimensional manifolds JF - Ergodic Theory and Dynamical Systems Y1 - 2017 A1 - Stefano Luzzatto A1 - Sina Türeli A1 - Khadim Mbacke War AB -

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.

UR - https://arxiv.org/pdf/1707.04855.pdf ER - TY - JOUR T1 - The Kontsevich matrix integral: convergence to the Painlevé hierarchy and Stokes' phenomenon JF - Comm. Math. Phys Y1 - 2017 A1 - Marco Bertola A1 - Mattia Cafasso VL - DOI 10.1007/s00220-017-2856-3 UR - http://arxiv.org/abs/1603.06420 ER - TY - RPRT T1 - Krein-Visik-Birman self-adjoint extension theory revisited Y1 - 2017 A1 - Matteo Gallone A1 - Alessandro Michelangeli A1 - Andrea Ottolini AB - 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. UR - http://preprints.sissa.it/handle/1963/35286 U1 - 35591 U2 - Mathematics ER - TY - RPRT T1 - A Lagrangian approach for scalar multi-d conservation laws Y1 - 2017 A1 - Stefano Bianchini A1 - Paolo Bonicatto A1 - Elio Marconi UR - http://preprints.sissa.it/handle/1963/35290 U1 - 35596 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Lagrangian representations for linear and nonlinear transport JF - Contemporary Mathematics. Fundamental Directions Y1 - 2017 A1 - Stefano Bianchini A1 - Paolo Bonicatto A1 - Elio Marconi AB -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.

PB - Peoples' Friendship University of Russia VL - 63 UR - http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=cmfd&paperid=327&option_lang=eng ER - TY - JOUR T1 - Limit of viscous dynamic processes in delamination as the viscosity and inertia vanish JF - ESAIM: COCV Y1 - 2017 A1 - Riccardo Scala AB -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 “local” 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) 101–126], where no viscosity in the adhesive is taken into account.

VL - 23 UR - https://doi.org/10.1051/cocv/2016006 ER - TY - RPRT T1 - Linear hyperbolic systems in domains with growing cracks Y1 - 2017 A1 - Maicol Caponi AB - 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. UR - http://urania.sissa.it/xmlui/handle/1963/35271 U1 - 35577 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Linearisation of multiwell energies Y1 - 2017 A1 - Roberto Alicandro A1 - Gianni Dal Maso A1 - Giuliano Lazzaroni A1 - Mariapia Palombaro AB - 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. UR - http://preprints.sissa.it/handle/1963/35288 U1 - 35594 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Lower semicontinuity of a class of integral functionals on the space of functions of bounded deformation JF - Advances in Calculus of Variations Y1 - 2017 A1 - Gianni Dal Maso A1 - Gianluca Orlando A1 - Rodica Toader AB -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.

PB - De Gruyter VL - 10 ER - TY - JOUR T1 - A lower semicontinuity result for a free discontinuity functional with a boundary term JF - Journal de Mathématiques Pures et Appliquées Y1 - 2017 A1 - Stefano Almi A1 - Gianni Dal Maso A1 - Rodica Toader AB -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.

VL - 108 UR - http://hdl.handle.net/20.500.11767/15979 IS - 6 U1 - 34731 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - The Malgrange form and Fredholm determinants JF - SIGMA Symmetry Integrability Geom. Methods Appl. Y1 - 2017 A1 - Marco Bertola VL - 13 UR - http://dx.doi.org/10.3842/SIGMA.2017.046 ER - TY - JOUR T1 - Maximal amplitudes of finite-gap solutions for the focusing Nonlinear Schrödinger Equation JF - Comm. Math. Phys. Y1 - 2017 A1 - Marco Bertola A1 - Alexander Tovbis VL - 354 UR - http://dx.doi.org/10.1007/s00220-017-2895-9 ER - TY - JOUR T1 - Mean-field quantum dynamics for a mixture of Bose–Einstein condensates JF - Analysis and Mathematical Physics Y1 - 2017 A1 - Alessandro Michelangeli A1 - Alessandro Olgiati AB -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 Schrödinger dynamics is effectively described by a system of coupled cubic non-linear Schrödinger equations, one for each component.

VL - 7 UR - https://doi.org/10.1007/s13324-016-0147-3 ER - TY - JOUR T1 - Minimizers of anisotropic perimeters with cylindrical norms JF - Communications on Pure & Applied Analysis Y1 - 2017 A1 - Giovanni Bellettini A1 - Matteo Novaga A1 - Shokhrukh Kholmatov KW - anisotropic Bernstein problem; KW - minimal cones KW - Non parametric minimal surfaces KW - Sets of finite perimeter AB -We study various regularity properties of minimizers of the Φ–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.

VL - 16 UR - http://aimsciences.org//article/id/47054f15-00c7-40b7-9da1-4c0b1d0a103d ER - TY - CHAP T1 - Model Reduction Methods T2 - Encyclopedia of Computational Mechanics Second Edition Y1 - 2017 A1 - Francisco Chinesta A1 - Antonio Huerta A1 - Gianluigi Rozza A1 - Karen Willcox AB -This chapter presents an overview of model order reduction – 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 – 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

JF - Encyclopedia of Computational Mechanics Second Edition PB - John Wiley & Sons ER - TY - RPRT T1 - Moduli of semistable sheaves as quiver moduli Y1 - 2017 A1 - Andrea Maiorana AB -In the 1980s Drézet 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×P1.

UR - https://arxiv.org/abs/1709.05555 ER - TY - JOUR T1 - Multiple positive solutions of a sturm-liouville boundary value problem with conflicting nonlinearities JF - Communications on Pure & Applied Analysis Y1 - 2017 A1 - Guglielmo Feltrin KW - Leray-Schauder topological degree; KW - positive solutions KW - Sturm-Liouville boundary conditions KW - Superlinear indefinite problems AB -We study the second order nonlinear differential equation

\begindocument $ u'' + \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.

VL - 16 UR - http://aimsciences.org//article/id/1163b042-0c64-4597-b25c-3494b268e5a1 ER - TY - JOUR T1 - Multiplicity of positive periodic solutions in the superlinear indefinite case via coincidence degree JF - Journal of Differential Equations Y1 - 2017 A1 - Guglielmo Feltrin A1 - Fabio Zanolin KW - Coincidence degree KW - Multiplicity results KW - Neumann boundary value problems KW - Positive periodic solutions KW - subharmonic solutions KW - Superlinear indefinite problems AB -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'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'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.

VL - 262 UR - http://www.sciencedirect.com/science/article/pii/S0022039617300219 ER - TY - JOUR T1 - A natural framework for isogeometric fluid-structure interaction based on BEM-shell coupling JF - COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Y1 - 2017 A1 - Luca Heltai A1 - Kiendl, J. A1 - Antonio DeSimone A1 - Alessandro Reali VL - 316 UR - http://cdsads.u-strasbg.fr/abs/2017CMAME.316..522H ER - TY - JOUR T1 - A note on a fixed point theorem on topological cylinders JF - Ann. Mat. Pura Appl. Y1 - 2017 A1 - Guglielmo Feltrin AB -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’skii ones.

PB - Springer Verlag UR - http://urania.sissa.it/xmlui/handle/1963/35263 N1 - AMS Subject Classification: 47H10, 37C25, 47H11, 54H25. U1 - 35567 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - A Note on the Convergence of Singularly Perturbed Second Order Potential-Type Equations JF - Journal of Dynamics and Differential Equations Y1 - 2017 A1 - Lorenzo Nardini VL - 29 UR - https://doi.org/10.1007/s10884-015-9461-y ER - TY - JOUR T1 - Numerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts JF - Biomechanics and Modeling in Mechanobiology Y1 - 2017 A1 - Francesco Ballarin A1 - Elena Faggiano A1 - Andrea Manzoni A1 - Alfio Quarteroni A1 - Gianluigi Rozza A1 - Sonia Ippolito A1 - Roberto Scrofani VL - 16 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85015065851&doi=10.1007%2fs10237-017-0893-7&partnerID=40&md5=c388f20bd5de14187bad9ed7d9affbd0 ER - TY - JOUR T1 - POD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder JF - Communications in Applied and Industrial Mathematics Y1 - 2017 A1 - Giovanni Stabile A1 - Saddam Hijazi A1 - Andrea Mola A1 - Stefano Lorenzi A1 - Gianluigi Rozza PB - Walter de Gruyter {GmbH} VL - 8 UR - https://doi.org/10.1515/caim-2017-0011 ER - TY - JOUR T1 - Quasi-periodic solutions for quasi-linear generalized KdV equations JF - Journal of Differential Equations Y1 - 2017 A1 - Filippo Giuliani KW - KAM for PDE's KW - KdV KW - Nash–Moser theory KW - Quasi-linear PDE's KW - Quasi-periodic solutions AB -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–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.

VL - 262 UR - http://www.sciencedirect.com/science/article/pii/S0022039617300487 ER - TY - JOUR T1 - Quasistatic crack growth based on viscous approximation: a model with branching and kinking JF - Nonlinear Differential Equations and Applications NoDEA Y1 - 2017 A1 - Vito Crismale A1 - Giuliano Lazzaroni AB -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.

VL - 24 UR - https://doi.org/10.1007/s00030-016-0426-6 ER - TY - RPRT T1 - Random spectrahedra Y1 - 2017 A1 - Paul Breiding A1 - Khazhgali Kozhasov A1 - Antonio Lerario ER - TY - JOUR T1 - Rayleigh–Taylor instability in soft elastic layers JF - Phil. Trans. R. Soc. A Y1 - 2017 A1 - Davide Riccobelli A1 - Pasquale Ciarletta PB - The Royal Society VL - 375 ER - TY - JOUR T1 - Real topological string amplitudes JF - Journal of High Energy Physics Y1 - 2017 A1 - Narain, K. S. A1 - Nicolò Piazzalunga A1 - Alessandro Tanzini AB -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 $g'= −\chi+ 1$. 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 $\mathcal{F}_g$.

VL - 2017 UR - https://doi.org/10.1007/JHEP03(2017)080 ER - TY - JOUR T1 - Reduced Basis Methods for Uncertainty Quantification JF - SIAM/ASA Journal on Uncertainty Quantification Y1 - 2017 A1 - Peng Chen A1 - Alfio Quarteroni A1 - Gianluigi Rozza AB -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. Babuška, 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–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.

JF - Model Reduction of Parametrized Systems PB - Springer International Publishing ER - TY - RPRT T1 - Regularity estimates for scalar conservation laws in one space dimension Y1 - 2017 A1 - Elio Marconi AB - 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 ƒ has on the entropy solution. More precisely, if the set ⟨w : ƒ " (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 ƒ. If moreover the set ⟨w : ƒ " (w) = 0⟩ is finite, under the additional polynomial degeneracy condition at the inflection points, we prove that ƒ' 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. UR - http://preprints.sissa.it/handle/1963/35291 U1 - 35597 U2 - Mathematics U4 - 1 ER - TY - CHAP T1 - Remarks on the Derivation of Gross-Pitaevskii Equation with Magnetic Laplacian T2 - Advances in Quantum Mechanics: Contemporary Trends and Open Problems Y1 - 2017 A1 - Alessandro Olgiati ED - Alessandro Michelangeli ED - Gianfausto Dell'Antonio AB -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 ``projection counting'' scheme.

JF - Advances in Quantum Mechanics: Contemporary Trends and Open Problems PB - Springer International Publishing CY - Cham SN - 978-3-319-58904-6 UR - https://doi.org/10.1007/978-3-319-58904-6_15 ER - TY - RPRT T1 - Second order differentiation formula on compact RCD*(K,N) spaces Y1 - 2017 A1 - Nicola Gigli A1 - Luca Tamanini ER - TY - RPRT T1 - Self-Adjoint Extensions of Dirac Operator with Coulomb Potential Y1 - 2017 A1 - Matteo Gallone AB - 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) = Ø(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. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/35273 U1 - 35579 U4 - 1 ER - TY - RPRT T1 - Self-adjoint realisations of the Dirac-Coulomb Hamiltonian for heavy nuclei Y1 - 2017 A1 - Matteo Gallone A1 - Alessandro Michelangeli AB - 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 KreĬn-Višik- Birman extension scheme, or also on Grubb'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. UR - http://preprints.sissa.it/handle/1963/35287 U1 - 35592 U2 - Mathematics ER - TY - RPRT T1 - Semistable Higgs Bundles on Calabi-Yau Manifolds Y1 - 2017 A1 - Ugo Bruzzo A1 - Valeriano Lanza A1 - Alessio Lo Giudice AB - 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. UR - http://preprints.sissa.it/handle/1963/35295 U1 - 35601 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Small Time Asymptotics on the Diagonal for Hörmander's Type Hypoelliptic Operators JF - Journal of Dynamical and Control Systems Y1 - 2017 A1 - Elisa Paoli AB -We compute the small time asymptotics of the fundamental solution of Hörmander'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.

VL - 23 UR - https://doi.org/10.1007/s10883-016-9321-z ER - TY - JOUR T1 - Solid tumors are poroelastic solids with a chemo-mechanical feedback on growth JF - J. Elast. Y1 - 2017 A1 - D. Ambrosi A1 - Pezzuto, S. A1 - Davide Riccobelli A1 - Stylianopoulos, T. A1 - Pasquale Ciarletta PB - Springer Netherlands VL - 129 ER - TY - CONF T1 - A Spectral Element Reduced Basis Method in Parametric CFD T2 - Numerical Mathematics and Advanced Applications - ENUMATH 2017, Springer, in press Y1 - 2017 A1 - Martin W. Hess A1 - Gianluigi Rozza JF - Numerical Mathematics and Advanced Applications - ENUMATH 2017, Springer, in press ER - TY - CHAP T1 - A Spectral Element Reduced Basis Method in Parametric CFD T2 - Numerical Mathematics and Advanced Applications - ENUMATH 2017 Y1 - 2017 A1 - Martin W. Hess A1 - Gianluigi Rozza AB -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.

JF - Numerical Mathematics and Advanced Applications - ENUMATH 2017 PB - Springer VL - 126 ER - TY - JOUR T1 - Spectral Properties of the 2+1 Fermionic Trimer with Contact Interactions Y1 - 2017 A1 - Simon Becker A1 - Alessandro Michelangeli A1 - Andrea Ottolini AB - 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. PB - SISSA UR - http://preprints.sissa.it/handle/1963/35303 N1 - 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.). U1 - 35609 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Stasis domains and slip surfaces in the locomotion of a bio-inspired two-segment crawler JF - Meccanica Y1 - 2017 A1 - Paolo Gidoni A1 - Antonio DeSimone AB -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.

VL - 52 UR - https://doi.org/10.1007/s11012-016-0408-0 ER - TY - JOUR T1 - Symplectic geometry of the moduli space of projective structures in homological coordinates JF - Inventiones Mathematicae Y1 - 2017 A1 - Marco Bertola A1 - Dmitry Korotkin A1 - Chaya Norton UR - https://arxiv.org/abs/1506.07918 ER - TY - RPRT T1 - Time quasi-periodic gravity water waves in finite depth Y1 - 2017 A1 - P Baldi A1 - Massimiliano Berti A1 - Emanuele Haus A1 - Riccardo Montalto AB - 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. UR - http://preprints.sissa.it/handle/1963/35296 U1 - 35602 U2 - Mathematics ER - TY - RPRT T1 - A uniqueness result for the decomposition of vector fields in Rd Y1 - 2017 A1 - Stefano Bianchini A1 - Paolo Bonicatto AB -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.

PB - SISSA UR - http://preprints.sissa.it/handle/1963/35274 U1 - 35581 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Universality of the matrix Airy and Bessel functions at spectral edges of unitary ensembles JF - Random Matrices Theory Appl. Y1 - 2017 A1 - Marco Bertola A1 - Mattia Cafasso VL - 6 UR - http://dx.doi.org/10.1142/S2010326317500101 ER - TY - JOUR T1 - Universality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schrödinger Equation JF - Phys. Rev. Lett. Y1 - 2017 A1 - Tikan, Alexey A1 - Billet, Cyril A1 - Gennady El A1 - Alexander Tovbis A1 - Marco Bertola A1 - Sylvestre, Thibaut A1 - Gustave, Francois A1 - Randoux, Stephane A1 - Genty, Goëry A1 - Suret, Pierre A1 - Dudley, John M. PB - American Physical Society VL - 119 UR - https://link.aps.org/doi/10.1103/PhysRevLett.119.033901 ER - TY - JOUR T1 - Wet and Dry Transom Stern Treatment for Unsteady and Nonlinear Potential Flow Model for Naval Hydrodynamics Simulations JF - Journal of Ship Research Y1 - 2017 A1 - Andrea Mola A1 - Luca Heltai A1 - Antonio DeSimone AB -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.

VL - 61 ER - TY - CONF T1 - Advances in geometrical parametrization and reduced order models and methods for computational fluid dynamics problems in applied sciences and engineering: overview and perspectives T2 - Proceedings of the ECCOMAS Congress 2016, VII European Conference on Computational Methods in Applied Sciences and Engineering, Y1 - 2016 A1 - Filippo Salmoiraghi A1 - Francesco Ballarin A1 - Giovanni Corsi A1 - Andrea Mola A1 - Marco Tezzele A1 - Gianluigi Rozza ED - Papadrakakis, M. ED - Papadopoulos, V. ED - Stefanou, G. ED - Plevris, V. AB -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.

JF - Proceedings of the ECCOMAS Congress 2016, VII European Conference on Computational Methods in Applied Sciences and Engineering, PB - ECCOMAS CY - Crete, Greece U1 - 35466 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - On the area of the graph of a piecewise smooth map from the plane to the plane with a curve discontinuity JF - ESAIM: COCV Y1 - 2016 A1 - Giovanni Bellettini A1 - Lucia Tealdi A1 - Maurizio Paolini KW - Area functional AB -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'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.

VL - 22 UR - https://www.esaim-cocv.org/articles/cocv/abs/2016/01/cocv140065/cocv140065.html IS - 1 U1 - 7257 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - On asymptotic regimes of orthogonal polynomials with complex varying quartic exponential weight JF - SIGMA Symmetry Integrability Geom. Methods Appl. Y1 - 2016 A1 - Marco Bertola A1 - Alexander Tovbis VL - 12 UR - http://dx.doi.org/10.3842/SIGMA.2016.118 ER - TY - RPRT T1 - Behaviour of the reference measure on RCD spaces under charts Y1 - 2016 A1 - Nicola Gigli A1 - Enrico Pasqualetto ER - TY - RPRT T1 - Coalescence Phenomenon of Quantum Cohomology of Grassmannians and the Distribution of Prime Numbers Y1 - 2016 A1 - Giordano Cotti ER - TY - JOUR T1 - Comparing Poisson Sigma Model with A-model JF - Journal of High Energy Physics Y1 - 2016 A1 - Bonechi, F. A1 - Cattaneo, A.S. A1 - Riccardo Iraso AB -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.

VL - 2016 UR - https://doi.org/10.1007/JHEP10(2016)133 ER - TY - JOUR T1 - On the concentration of entropy for scalar conservation laws JF - Discrete & Continuous Dynamical Systems - S Y1 - 2016 A1 - Stefano Bianchini A1 - Elio Marconi KW - concentration KW - Conservation laws KW - entropy solutions KW - Lagrangian representation KW - shocks AB -We prove that the entropy for an $L^∞$-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.

VL - 9 UR - http://aimsciences.org//article/id/ce4eb91e-9553-4e8d-8c4c-868f07a315ae ER - TY - JOUR T1 - Confinement of dislocations inside a crystal with a prescribed external strain Y1 - 2016 A1 - Ilaria Lucardesi A1 - Marco Morandotti A1 - Riccardo Scala A1 - Davide Zucco AB - 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. UR - http://urania.sissa.it/xmlui/handle/1963/35247 N1 - Preprint SISSA 20/2016/MATE U1 - 35558 U2 - Mathematics ER - TY - JOUR T1 - Conformal Equivalence of 3D Contact Structures on Lie Groups JF - Journal of Dynamical and Control Systems Y1 - 2016 A1 - Francesco Boarotto AB -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 $SU(2,1)$.

VL - 22 UR - https://doi.org/10.1007/s10883-015-9273-8 ER - TY - JOUR T1 - Construction of Real-Valued Localized Composite Wannier Functions for Insulators JF - Annales Henri Poincaré Y1 - 2016 A1 - Domenico Fiorenza A1 - Domenico Monaco A1 - Gianluca Panati AB -We consider a real periodic Schrödinger 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.

VL - 17 UR - https://doi.org/10.1007/s00023-015-0400-6 ER - TY - JOUR T1 - Correlation functions of the KdV hierarchy and applications to intersection numbers over $\overline\CalM_g,n$ JF - Phys. D Y1 - 2016 A1 - Marco Bertola A1 - Boris Dubrovin A1 - Di Yang VL - 327 UR - http://dx.doi.org/10.1016/j.physd.2016.04.008 ER - TY - JOUR T1 - CORRIGENDUM: The dependence on the monodromy data of the isomonodromic tau function Y1 - 2016 A1 - Marco Bertola UR - http://arxiv.org/abs/1601.04790 ER - TY - JOUR T1 - Critical points of a perturbed Otha-Kawasaki functional JF - arXiv preprint arXiv:1601.07093 Y1 - 2016 A1 - Matteo Rizzi ER - TY - JOUR T1 - Currents and dislocations at the continuum scale JF - Methods and Applications of Analysis Y1 - 2016 A1 - Riccardo Scala A1 - Nicolas Van Goethem AB -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.

PB - International Press of Boston VL - 23 ER - TY - JOUR T1 - The deal.II Library, Version 8.3 JF - ARCHIVE OF NUMERICAL SOFTWARE Y1 - 2016 A1 - W. Bangerth A1 - Timo Heister A1 - Luca Heltai A1 - G. Kanschat A1 - Martin Kronbichler A1 - Matthias Maier A1 - B. Turcksin VL - 4 UR - http://nbn-resolving.de/urn:nbn:de:bsz:16-ans-231226 ER - TY - JOUR T1 - The deal.II library, Version 8.4 JF - JOURNAL OF NUMERICAL MATHEMATICS Y1 - 2016 A1 - W. Bangerth A1 - Denis Davydov A1 - Timo Heister A1 - Luca Heltai A1 - G. Kanschat A1 - Martin Kronbichler A1 - Matthias Maier A1 - B. Turcksin A1 - David Wells VL - 24 UR - https://www.math.clemson.edu/ heister/preprints/deal84-preprint.pdf ER - TY - RPRT T1 - Equivalence of two different notions of tangent bundle on rectifiable metric measure spaces Y1 - 2016 A1 - Nicola Gigli A1 - Enrico Pasqualetto ER - TY - JOUR T1 - Error Estimates of B-spline based finite-element method for the wind-driven ocean circulation JF - JOURNAL OF SCIENTIFIC COMPUTING Y1 - 2016 A1 - Rotundo, N. A1 - Kim, T. -Y. A1 - Jiang, W. A1 - Luca Heltai A1 - Fried, E. VL - 69 ER - TY - RPRT T1 - Eulerian, Lagrangian and Broad continuous solutions to a balance law with non convex flux II Y1 - 2016 A1 - Giovanni Alberti A1 - Stefano Bianchini A1 - Laura Caravenna UR - http://urania.sissa.it/xmlui/handle/1963/35197 U1 - 35494 U2 - Mathematics ER - TY - JOUR T1 - Eulerian, Lagrangian and Broad continuous solutions to a balance law with non-convex flux I JF - Journal of Differential Equations, vol. 261, issue 8 (2016): 4298-4337 Y1 - 2016 A1 - Giovanni Alberti A1 - Stefano Bianchini A1 - Laura Caravenna PB - Elsevier UR - http://urania.sissa.it/xmlui/handle/1963/35207 U1 - 35507 U2 - Mathematics ER - TY - JOUR T1 - Exact results for N=2 supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants JF - Journal of High Energy Physics Y1 - 2016 A1 - Mikhail Bershtein A1 - Giulio Bonelli A1 - Massimiliano Ronzani A1 - Alessandro Tanzini AB -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.

VL - 2016 UR - https://doi.org/10.1007/JHEP07(2016)023 ER - TY - JOUR T1 - Existence and non-existence results for the SU(3) singular Toda system on compact surfaces JF - Journal of Functional Analysis Y1 - 2016 A1 - Luca Battaglia A1 - Andrea Malchiodi KW - Liouville-type equations KW - Min–max solutions KW - Non-existence results KW - Toda system AB -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 Pohožaev-type identities."

VL - 270 UR - http://www.sciencedirect.com/science/article/pii/S0022123615004942 ER - TY - JOUR T1 - Existence and uniqueness of dynamic evolutions for a peeling test in dimension one JF - Journal of Differential Equations Y1 - 2016 A1 - Gianni Dal Maso A1 - Giuliano Lazzaroni A1 - Lorenzo Nardini KW - Dynamic debonding KW - Dynamic energy release rate KW - Dynamic fracture KW - Griffith's criterion KW - Maximum dissipation principle KW - Wave equation in time-dependent domains AB -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.

VL - 261 UR - http://www.sciencedirect.com/science/article/pii/S0022039616301772 ER - TY - RPRT T1 - A fast virtual surgery platform for many scenarios haemodynamics of patient-specific coronary artery bypass grafts Y1 - 2016 A1 - Francesco Ballarin A1 - Elena Faggiano A1 - Andrea Manzoni A1 - Gianluigi Rozza A1 - Alfio Quarteroni A1 - Sonia Ippolito A1 - Roberto Scrofani A1 - Carlo Antona AB - 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. PB - Submitted UR - http://urania.sissa.it/xmlui/handle/1963/35240 U1 - 35545 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - Fracture models for elasto-plastic materials as limits of gradient damage models coupled with plasticity: the antiplane case JF - Calculus of Variations and Partial Differential Equations Y1 - 2016 A1 - Gianni Dal Maso A1 - Gianluca Orlando A1 - Rodica Toader AB -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.

VL - 55 UR - https://doi.org/10.1007/s00526-016-0981-z ER - TY - THES T1 - Frames symplectic sheaves on surfaces and their ADHM data Y1 - 2016 A1 - Jacopo Vittorio Scalise KW - moduli spaces AB - 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. PB - SISSA U1 - 35517 U2 - Mathematics U4 - 1 U5 - MAT/03 ER - TY - JOUR T1 - A Frobenius theorem for corank-1 continuous distributions in dimensions two and three JF - International Journal of Mathematics Y1 - 2016 A1 - Stefano Luzzatto A1 - Sina Türeli A1 - Khadim Mbacke War AB -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.

VL - 27 UR - https://doi.org/10.1142/S0129167X16500610 ER - TY - JOUR T1 - Generalizing the Poincaré–Miranda theorem: the avoiding cones condition JF - Annali di Matematica Pura ed Applicata (1923 -) Y1 - 2016 A1 - Alessandro Fonda A1 - Paolo Gidoni AB -After proposing a variant of the Poincaré–Bohl theorem, we extend the Poincaré–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 \$\$±1. An illustrative application is provided for the study of functionals having degenerate multi-saddle points.

VL - 195 UR - https://doi.org/10.1007/s10231-015-0519-6 ER - TY - JOUR T1 - Globally stable quasistatic evolution for a coupled elastoplastic–damage model JF - ESAIM: Control, Optimisation and Calculus of Variations Y1 - 2016 A1 - Vito Crismale AB -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.

PB - EDP Sciences VL - 22 UR - https://www.esaim-cocv.org/articles/cocv/abs/2016/03/cocv150037/cocv150037.html ER - TY - JOUR T1 - The Gysin sequence for quantum lens spaces JF - Journal of Noncommutative Geometry Y1 - 2016 A1 - Francesca Arici A1 - Simon Brain A1 - Giovanni Landi AB -We define quantum lens spaces as ‘direct sums of line bundles’ and exhibit them as ‘total spaces’ 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 ‘line bundles’ over quantum lens spaces and generically define ‘torsion classes’. We work out explicit examples of these classes.

VL - 9 ER - TY - JOUR T1 - Hankel determinant approach to generalized Vorob'ev-Yablonski polynomials and their roots JF - Constr. Approx. Y1 - 2016 A1 - Ferenc Balogh A1 - Marco Bertola A1 - Thomas Bothner VL - 44 UR - http://dx.doi.org/10.1007/s00365-016-9328-4 ER - TY - THES T1 - Instanton counting on compact manifolds Y1 - 2016 A1 - Massimiliano Ronzani KW - Supersymmetry AB - 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. • 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 × 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. • 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. • 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. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/35219 U1 - 35521 U2 - Mathematics U4 - 1 U5 - MAT/07 ER - TY - JOUR T1 - Integrability of C1 invariant splittings JF - Dynamical Systems Y1 - 2016 A1 - Stefano Luzzatto A1 - Sina Türeli A1 - Khadim Mbacke War AB -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.

PB - Taylor & Francis VL - 31 UR - https://doi.org/10.1080/14689367.2015.1057480 ER - TY - THES T1 - Integrability of continuous bundles and applications to dynamical systems Y1 - 2016 A1 - Khadim Mbacke War AB - In this dissertation we study the problem of integrability of bundles with low regularities. PB - SISSA U1 - 35529 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - Isogeometric analysis-based reduced order modelling for incompressible linear viscous flows in parametrized shapes Y1 - 2016 A1 - Filippo Salmoiraghi A1 - Francesco Ballarin A1 - Luca Heltai A1 - Gianluigi Rozza AB - 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. PB - Springer, AMOS Advanced Modelling and Simulation in Engineering Sciences UR - http://urania.sissa.it/xmlui/handle/1963/35199 U1 - 35493 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - RPRT T1 - Large KAM tori for perturbations of the dNLS equation Y1 - 2016 A1 - Massimiliano Berti A1 - Thomas Kappeler A1 - Riccardo Montalto AB - 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 2×2 block diagonal ones with constant coefficients together with sharp asymptotic estimates of their eigenvalues. UR - http://preprints.sissa.it/handle/1963/35284 U1 - 35589 U2 - Mathematics ER - TY - JOUR T1 - LinearOperator – a generic, high-level expression syntax for linear algebra JF - COMPUTERS & MATHEMATICS WITH APPLICATIONS Y1 - 2016 A1 - Matthias Maier A1 - Mauro Bardelloni A1 - Luca Heltai VL - 72 ER - TY - RPRT T1 - A model for the quasistatic growth of cracks with fractional dimension Y1 - 2016 A1 - Gianni Dal Maso A1 - Marco Morandotti AB - 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. UR - http://urania.sissa.it/xmlui/handle/1963/35175 U1 - 35459 U2 - Mathematics ER - TY - CHAP T1 - Model Order Reduction: a survey T2 - Wiley Encyclopedia of Computational Mechanics, 2016 Y1 - 2016 A1 - Francisco Chinesta A1 - Antonio Huerta A1 - Gianluigi Rozza A1 - Karen Willcox JF - Wiley Encyclopedia of Computational Mechanics, 2016 PB - Wiley UR - http://urania.sissa.it/xmlui/handle/1963/35194 U1 - 35470 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - Moser–Trudinger inequalities for singular Liouville systems JF - Mathematische Zeitschrift Y1 - 2016 A1 - Luca Battaglia AB -In this paper we prove a Moser–Trudinger inequality for the Euler–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, Pohožaev-type identities and blow-up analysis.

VL - 282 UR - https://doi.org/10.1007/s00209-015-1584-7 ER - TY - JOUR T1 - Motion planning and motility maps for flagellar microswimmers JF - The European Physical Journal E Y1 - 2016 A1 - Giancarlo Cicconofri A1 - Antonio DeSimone AB -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.

VL - 39 UR - https://doi.org/10.1140/epje/i2016-16072-y ER - TY - JOUR T1 - A multi-physics reduced order model for the analysis of Lead Fast Reactor single channel JF - Annals of Nuclear Energy, 87, 2 (2016): pp. 198-208 Y1 - 2016 A1 - Alberto Sartori A1 - Antonio Cammi A1 - Lelio Luzzi A1 - Gianluigi Rozza AB - 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. PB - Elsevier VL - 87 UR - http://urania.sissa.it/xmlui/handle/1963/35191 U1 - 35471 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - RPRT T1 - Multiplicity of self-adjoint realisations of the (2+1)-fermionic model of Ter-Martirosyan--Skornyakov type Y1 - 2016 A1 - Alessandro Michelangeli A1 - Andrea Ottolini AB - 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 Kreĭn, Višiik, and Birman. We identify the explicit `Kreĭn-Višik-Birman extension param- eter' as an operator on the `space of charges' for this model (the `Kreĭn space') 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. UR - http://urania.sissa.it/xmlui/handle/1963/35267 U1 - 35573 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - New existence results for the mean field equation on compact surfaces via degree theory JF - Rend. Sem. Mat. Univ. Padova Y1 - 2016 A1 - Aleks Jevnikar VL - 136 ER - TY - RPRT T1 - Non-linear Schrödinger system for the dynamics of a binary condensate: theory and 2D numerics Y1 - 2016 A1 - Alessandro Michelangeli A1 - Giuseppe Pitton AB - 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. UR - http://urania.sissa.it/xmlui/handle/1963/35266 U1 - 35572 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - A note on a multiplicity result for the mean field equation on compact surfaces JF - Advanced Nonlinear Studies Y1 - 2016 A1 - Aleks Jevnikar PB - De Gruyter VL - 16 ER - TY - JOUR T1 - Pairs of positive periodic solutions of nonlinear ODEs with indefinite weight: a topological degree approach for the super-sublinear case JF - Proc. Roy. Soc. Edinburgh Sect. A 146 (2016), 449–474. Y1 - 2016 A1 - Alberto Boscaggin A1 - Guglielmo Feltrin A1 - Fabio Zanolin AB -We study the periodic and Neumann boundary value problems associated with the second order nonlinear differential equation u''+cu'+λa(t)g(u)=0, where g:[0,+∞[→[0,+∞[ 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's coincidence degree theory and index computations.

PB - Cambridge University Press UR - http://urania.sissa.it/xmlui/handle/1963/35262 N1 - AMS Subject Classification: Primary 34B18; 34C25; Secondary 34B15; 47H11; U1 - 35566 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Periodic perturbations of Hamiltonian systems JF - Advances in Nonlinear Analysis Y1 - 2016 A1 - Alessandro Fonda A1 - Maurizio Garrione A1 - Paolo Gidoni AB -We prove existence and multiplicity results for periodic solutions of Hamiltonian systems, by the use of a higher dimensional version of the Poincaré–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.

PB - De Gruyter VL - 5 ER - TY - CHAP T1 - Pimsner Algebras and Circle Bundles T2 - Noncommutative Analysis, Operator Theory and Applications Y1 - 2016 A1 - Francesca Arici A1 - Francesco D'Andrea A1 - Giovanni Landi ED - Alpay, Daniel ED - Cipriani, Fabio ED - Colombo, Fabrizio ED - Guido, Daniele ED - Sabadini, Irene ED - Sauvageot, Jean-Luc AB -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.

JF - Noncommutative Analysis, Operator Theory and Applications PB - Springer International Publishing CY - Cham SN - 978-3-319-29116-1 UR - https://doi.org/10.1007/978-3-319-29116-1_1 ER - TY - JOUR T1 - Pimsner algebras and Gysin sequences from principal circle actions JF - Journal of Noncommutative Geometry Y1 - 2016 A1 - Francesca Arici A1 - Jens Kaad A1 - Giovanni Landi VL - 10 UR - http://hdl.handle.net/2066/162951 ER - TY - JOUR T1 - POD-Galerkin Method for Finite Volume Approximation of Navier-Stokes and RANS Equations Y1 - 2016 A1 - Stefano Lorenzi A1 - Antonio Cammi A1 - Lelio Luzzi A1 - Gianluigi Rozza AB - 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 – Reduced Order Model (POD – 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. PB - Computer Methods in Applied Mechanics and Engineering, Elsevier U1 - 35502 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - POD–Galerkin monolithic reduced order models for parametrized fluid-structure interaction problems JF - International Journal Numerical Methods for Fluids Y1 - 2016 A1 - Francesco Ballarin A1 - Gianluigi Rozza AB - 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)–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–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 PB - Wiley U1 - 35465 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - RPRT T1 - On point interactions realised as Ter-Martirosyan-Skornyakov Hamiltonians Y1 - 2016 A1 - Alessandro Michelangeli A1 - Andrea Ottolini AB - 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 ``Ter-Martirosyan--Skornyakov condition'' 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. UR - http://urania.sissa.it/xmlui/handle/1963/35195 U1 - 35489 U2 - Mathematics U4 - 1 U5 - MAT/07 ER - TY - THES T1 - Positive solutions to indefinite problems: a topological approach Y1 - 2016 A1 - Guglielmo Feltrin KW - positive solutions AB - 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'' + a(t) g(u) = 0, where g : [0,+∞[→[0,+∞[ is a continuous nonlinearity and a : [0,T]→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 Gómez‐Reñasco and López‐Gómez (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'' + 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'' + cu' + a(t) g(u) = 0. Meanwhile, more general operators in the one-dimensional case and problems involving PDEs will be subjects of future investigations. PB - SISSA N1 - The research work described in this Ph.D. thesis has produced 10 papers. U1 - 35528 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - A quadratic interaction estimate for conservation laws: motivations, techniques and open problems JF - Bulletin of the Brazilian Mathematical Society, New Series Y1 - 2016 A1 - Stefano Modena AB -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.

VL - 47 UR - https://doi.org/10.1007/s00574-016-0171-9 ER - TY - JOUR T1 - Quadratic interaction estimate for hyperbolic conservation laws, an overview JF - Contemporary Mathematics. Fundamental Directions Y1 - 2016 A1 - Stefano Modena PB - Peoples' Friendship University of Russia VL - 59 ER - TY - THES T1 - Qualitative properties and construction of solutions to some semilinear elliptic PDEs Y1 - 2016 A1 - Matteo Rizzi KW - moving planes method, maximum principle, Lyapunov-Schmidt reduction, Willmore surfaces, Otha-Kawasaki functional AB - 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. PB - SISSA U1 - 35500 U5 - MAT/05 ER - TY - RPRT T1 - Quasi-static hydraulic crack growth driven by Darcy's law Y1 - 2016 A1 - Stefano Almi AB -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’s law. We show the existence of such an evolution, and we prove that it satisfies a weak notion of the so-called Griffith’s criterion.

UR - http://urania.sissa.it/xmlui/handle/1963/35198 U1 - 35492 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - A Reduced Basis Approach for Modeling the Movement of Nuclear Reactor Control Rods JF - NERS-14-1062; ASME J of Nuclear Rad Sci, 2, 2 (2016) 021019 Y1 - 2016 A1 - Alberto Sartori A1 - Antonio Cammi A1 - Lelio Luzzi A1 - Gianluigi Rozza AB - 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 “classical” 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. PB - ASME VL - 2 UR - http://urania.sissa.it/xmlui/handle/1963/35192 IS - 2 N1 - 8 pages U1 - 35473 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Reduced basis approaches in time-dependent noncoercive settings for modelling the movement of nuclear reactor control rods JF - Communications in Computational Physics Y1 - 2016 A1 - Alberto Sartori A1 - Antonio Cammi A1 - Lelio Luzzi A1 - Gianluigi Rozza AB -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 “staircase” 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 “truth” solutions. At the same time, the computational speed-up in the Online phase, with respect to the fine “truth” 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.

PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/34963 IS - in press U1 - 35188 U2 - Mathematics ER - TY - JOUR T1 - Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries JF - Computers and Mathematics with Applications Y1 - 2016 A1 - Laura Iapichino A1 - Alfio Quarteroni A1 - Gianluigi Rozza AB - 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. PB - Elsevier VL - 71 IS - 1 U1 - 35187 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - Refined node polynomials via long edge graphs JF - Communications in Number Theory and Physics Y1 - 2016 A1 - Lothar Göttsche A1 - Benjamin Kipkirui Kikwai AB -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.

PB - International Press of Boston VL - 10 UR - http://dx.doi.org/10.4310/CNTP.2016.v10.n2.a2 ER - TY - JOUR T1 - Renormalization for Autonomous Nearly Incompressible BV Vector Fields in Two Dimensions JF - SIAM Journal on Mathematical Analysis Y1 - 2016 A1 - Stefano Bianchini A1 - Paolo Bonicatto A1 - N.A. Gusev AB -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's superposition principle [4].

VL - 48 UR - https://doi.org/10.1137/15M1007380 ER - TY - JOUR T1 - Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation JF - Proc. A. Y1 - 2016 A1 - Marco Bertola A1 - Gennady El A1 - Alexander Tovbis VL - 472 UR - http://dx.doi.org/10.1098/rspa.2016.0340 ER - TY - RPRT T1 - Second-order structured deformations Y1 - 2016 A1 - Ana Cristina Barroso A1 - Jose Matias A1 - Marco Morandotti A1 - David R. Owen PB - SISSA U1 - 35497 U2 - Mathematics U4 - 1 ER - TY - CONF T1 - Ship Sinkage and Trim Predictions Based on a CAD Interfaced Fully Nonlinear Potential Model T2 - The 26th International Ocean and Polar Engineering Conference Y1 - 2016 A1 - Andrea Mola A1 - Luca Heltai A1 - Antonio DeSimone A1 - Massimiliano Berti JF - The 26th International Ocean and Polar Engineering Conference PB - International Society of Offshore and Polar Engineers VL - 3 ER - TY - JOUR T1 - Simple Lie Algebras and Topological ODEs JF - Int. Math. Res. Not. Y1 - 2016 A1 - Marco Bertola A1 - Boris Dubrovin A1 - Di Yang VL - 2016 ER - TY - JOUR T1 - On Sobolev instability of the interior problem of tomography JF - Journal of Mathematical Analysis and Applications Y1 - 2016 A1 - Marco Bertola A1 - Alexander Katsevich A1 - Alexander Tovbis ER - TY - THES T1 - Some results on quasistatic evolution problems for unidirectional processes Y1 - 2016 A1 - Vito Crismale PB - SISSA U1 - 35522 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - THES T1 - Some results on the mathematical analysis of crack problems with forces applied on the fracture lips Y1 - 2016 A1 - Stefano Almi KW - Fracture mechanics AB - 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'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. PB - SISSA U1 - 35503 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Spectral analysis and the Aharonov-Bohm effect on certain almost-Riemannian manifolds JF - Communications in Partial Differential Equations Y1 - 2016 A1 - Ugo Boscain A1 - Dario Prandi A1 - M. Seri AB -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'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.

PB - Taylor & Francis VL - 41 UR - https://doi.org/10.1080/03605302.2015.1095766 ER - TY - RPRT T1 - On the structure of $L^\infty$-entropy solutions to scalar conservation laws in one-space dimension Y1 - 2016 A1 - Stefano Bianchini A1 - Elio Marconi AB -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 $f''=0$. 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.

PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/35209 U1 - 35508 U2 - Mathematics U5 - MAT/05 ER - TY - JOUR T1 - Symmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index JF - Journal of High Energy Physics Y1 - 2016 A1 - Benvenuti, Sergio A1 - Giulio Bonelli A1 - Massimiliano Ronzani A1 - Alessandro Tanzini AB -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.

VL - 2016 UR - https://doi.org/10.1007/JHEP09(2016)053 ER - TY - JOUR T1 - Symmetry properties of some solutions to some semilinear elliptic equations JF - Annali della Scuola Normale Superiore di Pisa. Classe di scienze Y1 - 2016 A1 - Farina, Alberto A1 - Andrea Malchiodi A1 - Matteo Rizzi PB - Classe di Scienze VL - 16 ER - TY - JOUR T1 - On the third critical speed for rotating Bose-Einstein condensates JF - Correggi, M., Dimonte, D., 2016. On the third critical speed for rotating Bose-Einstein condensates. J. Math. Phys. 57, 71901 Y1 - 2016 A1 - Daniele Dimonte A1 - Michele Correggi AB - 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. PB - AIP Publisher UR - http://urania.sissa.it/xmlui/handle/1963/35246 U1 - 35557 U2 - Mathematics ER - TY - JOUR T1 - Towards a gauge theory interpretation of the real topological string JF - Phys. Rev. D Y1 - 2016 A1 - Hayashi, Hirotaka A1 - Nicolò Piazzalunga A1 - Uranga, Angel M. AB -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’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.

PB - American Physical Society VL - 93 UR - https://link.aps.org/doi/10.1103/PhysRevD.93.066001 ER - TY - JOUR T1 - t-Structures are Normal Torsion Theories JF - Applied Categorical Structures Y1 - 2016 A1 - Domenico Fiorenza A1 - Fosco Loregian AB -We characterize $t$-structures in stable ∞-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.

VL - 24 UR - https://doi.org/10.1007/s10485-015-9393-z ER - TY - THES T1 - t-structures on stable (infinity,1)-categories Y1 - 2016 A1 - Fosco Loregian KW - category theory, higher category theory, factorization system, torsion theory, homological algebra, higher algebra AB - 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 Rosický, Tholen, and Cassidy-Hébert-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. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/35202 U1 - 35477 U2 - Mathematics U4 - 1 U5 - MAT/03 ER - TY - THES T1 - Two explorations in Dynamical Systems and Mechanics Y1 - 2016 A1 - Paolo Gidoni KW - Poincaré-Birkhoff Theorem AB - 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". PB - SISSA U1 - 35527 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Viscous approximation of quasistatic evolutions for a coupled elastoplastic-damage model JF - Calculus of Variations and Partial Differential Equations Y1 - 2016 A1 - Vito Crismale A1 - Giuliano Lazzaroni AB -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.

VL - 55 UR - https://doi.org/10.1007/s00526-015-0947-6 ER - TY - JOUR T1 - Volume geodesic distortion and Ricci curvature for Hamiltonian dynamics JF - arXiv preprint arXiv:1602.08745 Y1 - 2016 A1 - Andrei A. Agrachev A1 - Davide Barilari A1 - Elisa Paoli ER - TY - JOUR T1 - Young towers for product systems JF - Discrete & Continuous Dynamical Systems - A Y1 - 2016 A1 - Stefano Luzzatto A1 - Marks Ruziboev AB -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, Hénon maps and partially hyperbolic systems.

VL - 36 UR - http://aimsciences.org//article/id/18d4526e-470d-467e-967a-a0345ad4c642 ER - TY - JOUR T1 - Z2 Invariants of Topological Insulators as Geometric Obstructions JF - Communications in Mathematical Physics Y1 - 2016 A1 - Domenico Fiorenza A1 - Domenico Monaco A1 - Gianluca Panati AB -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.

VL - 343 UR - https://doi.org/10.1007/s00220-015-2552-0 ER - TY - JOUR T1 - Anisotropic mean curvature on facets and relations with capillarity Y1 - 2015 A1 - Stefano Amato A1 - Lucia Tealdi A1 - Giovanni Bellettini AB -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.

PB - de Gruyter UR - http://urania.sissa.it/xmlui/handle/1963/34481 U1 - 34663 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Asymptotics of orthogonal polynomials with complex varying quartic weight: global structure, critical point behavior and the first Painlevé equation JF - Constr. Approx. Y1 - 2015 A1 - Marco Bertola A1 - Alexander Tovbis VL - 41 UR - http://dx.doi.org/10.1007/s00365-015-9288-0 ER - TY - JOUR T1 - Benchmarking the Immersed Finite Element Method for Fluid-Structure Interaction Problems JF - Computers and Mathematics with Applications 69 (2015) 1167–1188 Y1 - 2015 A1 - Roy Saswati A1 - Luca Heltai A1 - Francesco Costanzo AB - 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. U1 - 34633 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - RPRT T1 - A bridging mechanism in the homogenisation of brittle composites with soft inclusions Y1 - 2015 A1 - Marco Barchiesi A1 - Giuliano Lazzaroni A1 - Caterina Ida Zeppieri AB - 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. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7492 U1 - 7621 ER - TY - BOOK T1 - Certified Reduced Basis Methods for Parametrized Partial Differential Equations T2 - Springer Briefs in Mathematics Y1 - 2015 A1 - Jan S Hesthaven A1 - Gianluigi Rozza A1 - Benjamin Stamm KW - a posteriori error bounds KW - empirical interpolation KW - parametrized partial differential equations KW - reduced basis methods, greedy algorithms AB -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.

JF - Springer Briefs in Mathematics PB - Springer CY - Switzerland SN - 978-3-319-22469-5 ER - TY - RPRT T1 - A class of Hamiltonians for a three-particle fermionic system at unitarity Y1 - 2015 A1 - Michele Correggi A1 - Gianfausto Dell'Antonio A1 - Domenico Finco A1 - Alessandro Michelangeli A1 - Alessandro Teta AB - 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. UR - http://urania.sissa.it/xmlui/handle/1963/34469 N1 - This SISSA preprint is composed of 29 pages and is recorded in PDF format U1 - 34644 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - A compatible-incompatible decomposition of symmetric tensors in Lp with application to elasticity JF - Mathematical Methods in the Applied Sciences Y1 - 2015 A1 - Maggiani, Giovanni Battista A1 - Riccardo Scala A1 - Nicolas Van Goethem KW - 35J58 KW - 35Q74 KW - compatibility conditions KW - elasticity KW - Korn inequality KW - strain decomposition KW - subclass74B05 AB -In this paper, we prove the Saint-Venant compatibility conditions in $L^p$ for $p\in(1,∞)$, 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 $p\in(1,∞)$. Copyright © 2015 John Wiley & Sons, Ltd.

VL - 38 UR - https://onlinelibrary.wiley.com/doi/abs/10.1002/mma.3450 ER - TY - JOUR T1 - Complexity of Control-Affine Motion Planning JF - SIAM Journal on Control and Optimization Y1 - 2015 A1 - Jean, F. A1 - Dario Prandi AB -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.

VL - 53 UR - https://doi.org/10.1137/130950793 ER - TY - JOUR T1 - Constrained BV functions on double coverings for Plateau's type problems JF - Adv. Calc. Var. Y1 - 2015 A1 - Stefano Amato A1 - Giovanni Bellettini A1 - Maurizio Paolini AB -We link Brakke's "soap films" covering construction with the theory of finite perimeter sets, in order to study Plateau'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.

U1 - 7597 ER - TY - JOUR T1 - Convergence rate of the Glimm scheme JF - Bulletin of the Institute of Mathematics of Academia Sinica (New Series) Y1 - 2015 A1 - Stefano Modena A1 - Stefano Bianchini ER - TY - RPRT T1 - Convex combinations of low eigenvalues, Fraenkel asymmetries and attainable sets Y1 - 2015 A1 - Dario Mazzoleni A1 - Davide Zucco AB - 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 à 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. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/35140 U1 - 35378 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Deal2lkit: a Toolkit Library for High Performance Programming in deal.II Y1 - 2015 A1 - Alberto Sartori A1 - Nicola Giuliani A1 - Mauro Bardelloni A1 - Luca Heltai AB - 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. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/35006 U1 - 35235 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - The deal.II Library, Version 8.2 JF - Archive of Numerical Software, vol. 3, n. 100, (2015), pages : 1-8 Y1 - 2015 A1 - W. Bangerth A1 - Timo Heister A1 - Luca Heltai A1 - G. Kanschat A1 - Martin Kronbichler A1 - Matthias Maier A1 - B. Turcksin A1 - T. D. Young AB - This paper provides an overview of the new features of the finite element library deal.II version 8.2 UR - http://urania.sissa.it/xmlui/handle/1963/34464 U1 - 34637 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - Decay of correlations for invertible maps with non-Hölder observables JF - Dynamical Systems Y1 - 2015 A1 - Marks Ruziboev AB -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 Hénon maps and Solenoid maps with intermittency.

PB - Taylor & Francis VL - 30 UR - https://doi.org/10.1080/14689367.2015.1046816 ER - TY - JOUR T1 - A degeneration of two-phase solutions of the focusing nonlinear Schrödinger equation via Riemann-Hilbert problems JF - J. Math. Phys. Y1 - 2015 A1 - Marco Bertola A1 - Giavedoni, Pietro VL - 56 UR - http://dx.doi.org/10.1063/1.4922362 ER - TY - JOUR T1 - Dispersive deformations of the Hamiltonian structure of Euler's equations Y1 - 2015 A1 - Matteo Casati AB - Euler'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's equation and show that, up to the second order, they are trivial. U1 - 34700 U2 - Mathematics U4 - 1 U5 - MAT/07 ER - TY - RPRT T1 - Dynamics of screw dislocations: a generalised minimising-movements scheme approach Y1 - 2015 A1 - Giovanni A. Bonaschi A1 - Patrick Van Meurs A1 - Marco Morandotti AB - 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. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/34495 U1 - 34692 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Existence and multiplicity result for the singular Toda system JF - Journal of Mathematical Analysis and Applications Y1 - 2015 A1 - Luca Battaglia KW - Existence result KW - Liouville-type equations KW - Multiplicity result KW - PDEs on compact surfaces KW - Toda system AB -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's are allowed to be negative."

VL - 424 UR - http://www.sciencedirect.com/science/article/pii/S0022247X14010191 ER - TY - RPRT T1 - Existence for constrained dynamic Griffith fracture with a weak maximal dissipation condition Y1 - 2015 A1 - Gianni Dal Maso A1 - Cristopher J. Larsen A1 - Rodica Toader AB - 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. UR - http://urania.sissa.it/xmlui/handle/1963/35045 U1 - 35277 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Existence of positive solutions in the superlinear case via coincidence degree: the Neumann and the periodic boundary value problems JF - Adv. Differential Equations 20 (2015), 937–982. Y1 - 2015 A1 - Guglielmo Feltrin A1 - Fabio Zanolin AB -We prove the existence of positive periodic solutions for the second order nonlinear equation u'' + 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'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.

PB - Khayyam Publishing UR - http://projecteuclid.org/euclid.ade/1435064518 N1 - AMS Subject Classification: 34B18, 34B15, 34C25, 47H11. U1 - 35388 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Existence of positive solutions of a superlinear boundary value problem with indefinite weight JF - Conference Publications Y1 - 2015 A1 - Guglielmo Feltrin KW - boundary value problem KW - indefinite weight KW - Positive solution; existence result. KW - superlinear equation AB -We deal with the existence of positive solutions for a two-point boundary value problem associated with the nonlinear second order equation $u''+a(x)g(u)=0$. The weight $a(x)$ is allowed to change sign. We assume that the function $g\colon\mathopen[0,+∞\mathclose[\to\mathbb{R}$ 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.

VL - 2015 UR - http://aimsciences.org//article/id/b3c1c765-e8f5-416e-8130-05cc48478026 ER - TY - CONF T1 - Experience on vectorizing lattice Boltzmann kernels for multi-and many-core architectures T2 - International Conference on Parallel Processing and Applied Mathematics Y1 - 2015 A1 - Calore, Enrico A1 - Nicola Demo A1 - Schifano, Sebastiano Fabio A1 - Tripiccione, Raffaele JF - International Conference on Parallel Processing and Applied Mathematics PB - Springer ER - TY - RPRT T1 - Explicit formulas for relaxed disarrangement densities arising from structured deformations Y1 - 2015 A1 - Ana Cristina Barroso A1 - Jose Matias A1 - Marco Morandotti A1 - David R. Owen AB - 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’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’s results, and we establish additional explicit formulas for other measures of disarrangements. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/34492 U1 - 34687 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Extended affine Weyl groups of BCD type, Frobenius manifolds and their Landau-Ginzburg superpotentials Y1 - 2015 A1 - Boris Dubrovin A1 - Ian A.B. Strachan A1 - Youjin Zhang A1 - Dafeng Zuo AB - 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. PB - SISSA UR - http://preprints.sissa.it/handle/1963/35316 U1 - 35625 U2 - Mathematics U4 - 1 U5 - MAT/07 ER - TY - RPRT T1 - Fast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization Y1 - 2015 A1 - Francesco Ballarin A1 - Elena Faggiano A1 - Sonia Ippolito A1 - Andrea Manzoni A1 - Alfio Quarteroni A1 - Gianluigi Rozza A1 - Roberto Scrofani AB - 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–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. UR - http://urania.sissa.it/xmlui/handle/1963/34623 U1 - 34824 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - FEM SUPG stabilisation of mixed isoparametric BEMs: application to linearised free surface flows JF - Engineering Analysis with Boundary Elements 59 (2015), pp. 8-22 Y1 - 2015 A1 - Nicola Giuliani A1 - Andrea Mola A1 - Luca Heltai A1 - L. Formaggia AB -In finite element formulations, transport dominated problems are often stabilised through the Streamline-Upwind-Petrov–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.

UR - http://urania.sissa.it/xmlui/handle/1963/34466 U1 - 34640 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - A general existence result for the Toda system on compact surfaces JF - Advances in Mathematics Y1 - 2015 A1 - Luca Battaglia A1 - Aleks Jevnikar A1 - Andrea Malchiodi A1 - David Ruiz KW - Geometric PDEs KW - Min–max schemes KW - Variational methods AB -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–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."

VL - 285 UR - http://www.sciencedirect.com/science/article/pii/S0001870815003072 ER - TY - JOUR T1 - Geodesics and horizontal-path spaces in Carnot groups JF - Geometry & Topology Y1 - 2015 A1 - Andrei A. Agrachev A1 - Alessandro Gentile A1 - Antonio Lerario AB -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.

PB - Mathematical Sciences Publishers VL - 19 ER - TY - THES T1 - Geometric phases in graphene and topological insulators Y1 - 2015 A1 - Domenico Monaco KW - Geometric phases, graphene, topological insulators, Wannier functions, Bloch frames AB - 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. PB - SISSA U1 - 34702 U2 - Mathematics U4 - 1 U5 - MAT/07 ER - TY - THES T1 - Gibbs-Markov-Young Structures and Decay of Correlations Y1 - 2015 A1 - Marks Ruziboev KW - Decay of Correlations, GMY-towers AB - 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. PB - SISSA U1 - 34677 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Gli abachi: antichi strumenti precursori delle moderne macchine da calcolo Y1 - 2015 A1 - Giuliano Klun UR - http://hdl.handle.net/10077/10884 ER - TY - RPRT T1 - Global well-posedness of the magnetic Hartree equation with non-Strichartz external fields Y1 - 2015 A1 - Alessandro Michelangeli AB - 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. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/34440 U1 - 34567 ER - TY - JOUR T1 - Hilbert schemes of points of OP1(-n) as quiver varieties Y1 - 2015 A1 - Ugo Bruzzo AB - 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. PB - arXiv:1504.02987 [math.AG] UR - http://urania.sissa.it/xmlui/handle/1963/34487 U1 - 34673 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - Homogenization problems in the Calculus of Variations: an overview Y1 - 2015 A1 - Jose Matias A1 - Marco Morandotti AB - 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. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/34455 N1 - DEDICATED TO PROF. ORLANDO LOPES U1 - 34598 U2 - Mathematics U4 - 1 ER - TY - THES T1 - Integrability of Continuous Tangent Sub-bundles Y1 - 2015 A1 - Sina Türeli KW - Dynamical Systems, Global Analysis, Frobenius Theorem, Integrability AB - 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. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/34630 U1 - 34833 U2 - Mathematics U5 - MAT/05 ER - TY - THES T1 - Interaction functionals, Glimm approximations and Lagrangian structure of BV solutions for Hyperbolic Systems of Conservations Laws Y1 - 2015 A1 - Stefano Modena KW - Hyperbolic conservation laws AB - 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. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/34542 U1 - 34739 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Liquid crystal elastomer strips as soft crawlers JF - Journal of the Mechanics and Physics of Solids Y1 - 2015 A1 - Antonio DeSimone A1 - Paolo Gidoni A1 - Giovanni Noselli KW - Crawling motility KW - Directional surfaces KW - Frictional interactions KW - Liquid crystal elastomers KW - Soft biomimetic robots AB -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, ‘breathing-like’ 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.

VL - 84 UR - http://www.sciencedirect.com/science/article/pii/S0022509615300430 ER - TY - THES T1 - Mathematical Models of Locomotion: Legged Crawling, Snake-like Motility, and Flagellar Swimming Y1 - 2015 A1 - Giancarlo Cicconofri KW - Motility PB - SISSA U1 - 34743 U2 - Mathematics U4 - 1 U5 - FIS/02 ER - TY - JOUR T1 - Meromorphic differentials with imaginary periods on degenerating hyperelliptic curves JF - Anal. Math. Phys. Y1 - 2015 A1 - Marco Bertola A1 - Alexander Tovbis VL - 5 UR - http://dx.doi.org/10.1007/s13324-014-0088-7 ER - TY - JOUR T1 - Model order reduction of parameterized systems (MoRePaS): Preface to the special issue of advances in computational mathematics JF - Advances in Computational Mathematics Y1 - 2015 A1 - Peter Benner A1 - Mario Ohlberger A1 - Anthony Patera A1 - Gianluigi Rozza A1 - Sorensen, D.C. A1 - Karsten Urban VL - 41 ER - TY - JOUR T1 - Motility of a model bristle-bot: A theoretical analysis JF - International Journal of Non-Linear Mechanics Y1 - 2015 A1 - Giancarlo Cicconofri A1 - Antonio DeSimone KW - Bristle-robots KW - Crawling motility KW - Frictional interactions AB -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.

VL - 76 UR - http://www.sciencedirect.com/science/article/pii/S0020746215000025 ER - TY - THES T1 - Multidimensional Poisson Vertex Algebras and Poisson cohomology of Hamiltonian operators of hydrodynamic type Y1 - 2015 A1 - Matteo Casati KW - Poisson Vertex Algebras, Poisson brackets, Hamiltonian operators, Integrable Systems AB - 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 → 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–Lichnerowicz cohomology. From this computations it follows, already in the particular case dim Σ = 2, that the cohomology is infinite dimensional. PB - SISSA N1 - 161 pages U1 - 34902 U2 - Mathematics U4 - 1 U5 - MAT/07 ER - TY - JOUR T1 - Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations JF - Numerische Mathematik, (2015), 36 p. Article in Press Y1 - 2015 A1 - Gianluigi Rozza A1 - Peng Chen A1 - Alfio Quarteroni AB - 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. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34491 U1 - 34680 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - Multiple positive solutions for a superlinear problem: a topological approach JF - J. Differential Equations 259 (2015), 925–963. Y1 - 2015 A1 - Guglielmo Feltrin A1 - Fabio Zanolin AB -We study the multiplicity of positive solutions for a two-point boundary value problem associated to the nonlinear second order equation u''+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→0^+ and above λ_1 as s→+∞. 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'' + 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.

PB - Elsevier UR - http://urania.sissa.it/xmlui/handle/1963/35147 N1 - Work presented at the "Special Session 21" of the "10th AIMS Conference on Dynamical Systems, Differential Equations and Applications" (Madrid, July 7-11, 2014). U1 - 35387 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - N=2 supersymmetric gauge theories on S^2xS^2 and Liouville Gravity JF - Journal of High Energy Physics Y1 - 2015 A1 - Aditya Bawane A1 - Giulio Bonelli A1 - Massimiliano Ronzani A1 - Alessandro Tanzini AB -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.

VL - 2015 UR - https://doi.org/10.1007/JHEP07(2015)054 ER - TY - THES T1 - Normal matrix models and orthogonal polynomials for a class of potentials with discrete rotational symmetries Y1 - 2015 A1 - Dario Merzi KW - Mathematical Physics AB - 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} PB - SISSA U1 - 34938 U2 - Mathematics U4 - 1 U5 - MAT/07 ER - TY - JOUR T1 - A note on compactness properties of the singular Toda system JF - Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Y1 - 2015 A1 - Luca Battaglia A1 - Gabriele Mancini AB -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.

VL - 26 U1 - 34669 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Onofri-Type Inequalities for Singular Liouville Equations Y1 - 2015 A1 - Gabriele Mancini AB -We study the blow-up behavior of minimizing sequences for the singular Moser–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.

PB - Springer US U1 - 34668 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - The partition function of the extended $r$-reduced Kadomtsev-Petviashvili hierarchy JF - J. Phys. A Y1 - 2015 A1 - Marco Bertola A1 - Di Yang VL - 48 UR - http://dx.doi.org/10.1088/1751-8113/48/19/195205 ER - TY - JOUR T1 - A permanence theorem for local dynamical systems JF - Nonlinear Analysis: Theory, Methods & Applications Y1 - 2015 A1 - Alessandro Fonda A1 - Paolo Gidoni KW - Lotka–Volterra KW - permanence KW - Predator–prey KW - Uniform persistence AB -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–Volterra predator–prey model with intraspecific competition.

VL - 121 UR - http://www.sciencedirect.com/science/article/pii/S0362546X14003332 N1 - Nonlinear Partial Differential Equations, in honor of Enzo Mitidieri for his 60th birthday ER - TY - JOUR T1 - The phototransduction machinery in the rod outer segment has a strong efficacy gradient Y1 - 2015 A1 - Monica Mazzolini A1 - Giuseppe Facchetti A1 - L. Andolfi A1 - R. Proietti Zaccaria A1 - S. Tuccio A1 - J. Treud A1 - Claudio Altafini A1 - Enzo M. Di Fabrizio A1 - Marco Lazzarino A1 - G. Rapp A1 - Vincent Torre PB - National Academy of Sciences UR - http://urania.sissa.it/xmlui/handle/1963/35157 N1 - Open Access article U1 - 35382 U2 - Neuroscience ER - TY - RPRT T1 - Poisson cohomology of scalar multidimensional Dubrovin-Novikov brackets Y1 - 2015 A1 - Guido Carlet A1 - Matteo Casati A1 - Sergey Shadrin AB - 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. U1 - 35389 U2 - Mathematics U4 - 1 U5 - MAT/03 ER - TY - THES T1 - Principal circle bundles, Pimsner algebras and Gysin sequences Y1 - 2015 A1 - Francesca Arici AB - 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 `base space’ 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. PB - SISSA U1 - 34744 U2 - Mathematics U4 - 1 U5 - MAT/07 ER - TY - JOUR T1 - Quadratic Interaction Functional for General Systems of Conservation Laws JF - Communications in Mathematical Physics Y1 - 2015 A1 - Stefano Bianchini A1 - Stefano Modena AB -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;

VL - 338 ER - TY - JOUR T1 - Reduced basis approximation and a-posteriori error estimation for the coupled Stokes-Darcy system JF - Advances in Computational Mathematics Y1 - 2015 A1 - Immanuel Martini A1 - Gianluigi Rozza A1 - Bernard Haasdonk KW - Domain decomposition KW - Error estimation KW - Non-coercive problem KW - Porous medium equation KW - Reduced basis method KW - Stokes flow AB -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.

VL - special issue for MoRePaS 2012 IS - in press ER - TY - JOUR T1 - Reduced basis approximation of parametrized advection-diffusion PDEs with high Péclet number JF - Lecture Notes in Computational Science and Engineering Y1 - 2015 A1 - Pacciarini, P. A1 - Gianluigi Rozza AB -In this work we show some results about the reduced basis approximation of advection dominated parametrized problems, i.e. advection-diffusion problems with high Péclet 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.

VL - 103 ER - TY - JOUR T1 - Reduced basis approximation of parametrized optimal flow control problems for the Stokes equations JF - Computers and Mathematics with Applications Y1 - 2015 A1 - Federico Negri A1 - Andrea Manzoni A1 - Gianluigi Rozza AB -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.

VL - 69 ER - TY - JOUR T1 - Reduced Basis Isogeometric Methods (RB-IGA) for the real-time simulation of potential flows about parametrized NACA airfoils JF - Comput Methods Appl Mech Eng. 2015;284:1147–1180 Y1 - 2015 A1 - Andrea Manzoni A1 - Filippo Salmoiraghi A1 - Luca Heltai AB - 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. U1 - 34587 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - THES T1 - The relaxed area of maps from the plane to the plane with a line discontinuity, and the role of semicartesian surfaces. Y1 - 2015 A1 - Lucia Tealdi KW - Area functional AB - 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. PB - SISSA U1 - 34732 U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - Results on the minimization of the Dirichlet functional among semicartesian parametrizations Y1 - 2015 A1 - Lucia Tealdi A1 - Giovanni Bellettini A1 - Maurizio Paolini AB -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'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.

UR - http://urania.sissa.it/xmlui/handle/1963/34488 N1 - The article is compsed of 18 pages and is recorded in PDF format U1 - 34671 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - Rigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires Y1 - 2015 A1 - Giuliano Lazzaroni A1 - Mariapia Palombaro A1 - Anja Schlomerkemper AB - 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 PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7494 U1 - 7623 ER - TY - RPRT T1 - Schödinger operators on half-line with shrinking potentials at the origin Y1 - 2015 A1 - Gianfausto Dell'Antonio A1 - Alessandro Michelangeli AB - We discuss the general model of a Schrödinger 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. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/34439 U1 - 34566 ER - TY - RPRT T1 - Semicartesian surfaces and the relaxed area of maps from the plane to the plane with a line discontinuity Y1 - 2015 A1 - Lucia Tealdi A1 - Giovanni Bellettini A1 - Maurizio Paolini AB -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.

UR - http://urania.sissa.it/xmlui/handle/1963/34483 N1 - The preprint is compsed of 37 pages and is recorded in PDF format U1 - 34670 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - THES T1 - Sharp Inequalities and Blow-up Analysis for Singular Moser-Trudinger Embeddings. Y1 - 2015 A1 - Gabriele Mancini KW - Moser-Trudinger AB - 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. PB - SISSA U1 - 34738 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - Singular Liouville Equations on S^2: Sharp Inequalities and Existence Results Y1 - 2015 A1 - Gabriele Mancini AB -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.

UR - http://urania.sissa.it/xmlui/handle/1963/34489 U1 - 34672 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - THES T1 - Some results on anisotropic mean curvature and other phase-transition problems Y1 - 2015 A1 - Stefano Amato KW - Anisotropic mean curvature AB - The present thesis is divided into three parts. In the first part, we analyze a suitable regularization — which we call nonlinear multidomain model — 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’s type problems based on the theory of coverings and of BV functions. PB - SISSA U1 - 34733 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - Stability of closed gaps for the alternating Kronig-Penney Hamiltonian Y1 - 2015 A1 - Alessandro Michelangeli A1 - Domenico Monaco AB - 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. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/34460 U1 - 34629 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Stability of the (2+2)-fermionic system with zero-range interaction Y1 - 2015 A1 - Alessandro Michelangeli A1 - Paul Pfeiffer AB - 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. UR - http://urania.sissa.it/xmlui/handle/1963/34474 N1 - This SISSA preprint has 17 pages and recorded in PDF format U1 - 34649 U2 - Mathematics U4 - 1 U5 - MAT/07 ER - TY - JOUR T1 - Stable regular critical points of the Mumford-Shah functional are local minimizers JF - Annales de l'Institut Henri Poincare (C) Non Linear Analysis Y1 - 2015 A1 - Marco Bonacini A1 - Massimiliano Morini KW - Mumford-Shah functional AB -In this paper it is shown that any regular critical point of the Mumford–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.

VL - 471 UR - https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2015.0054 ER - TY - JOUR T1 - Supremizer stabilization of POD-Galerkin approximation of parametrized Navier-Stokes equations Y1 - 2015 A1 - Francesco Ballarin A1 - Andrea Manzoni A1 - Alfio Quarteroni A1 - Gianluigi Rozza AB - In this work, we present a stable proper orthogonal decomposition–Galerkin approximation for parametrized steady incompressible Navier–Stokes equations with low Reynolds number. PB - Wiley UR - http://urania.sissa.it/xmlui/handle/1963/34701 U1 - 34915 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - Symmetry and localization in periodic crystals: triviality of Bloch bundles with a fermionic time-reversal symmetry JF - Acta Applicandae Mathematicae, vol. 137, Issue 1, 2015, pages: 185-203 Y1 - 2015 A1 - Domenico Monaco A1 - Gianluca Panati AB -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 rôle 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.

PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34468 N1 - The article is composed of 23 pages and recorded in PDF format U1 - 34642 U2 - Mathematics U4 - 1 U5 - MAT/07 ER - TY - JOUR T1 - Three-sphere low-Reynolds-number swimmer with a passive elastic arm Y1 - 2015 A1 - Alessandro Montino A1 - Antonio DeSimone AB - 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's geometry. Our results can provide valuable conceptual guidance in the engineering of robotic microswimmers. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34530 U1 - 34735 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - A topological join construction and the Toda system on compact surfaces of arbitrary genus JF - Analysis & PDE Y1 - 2015 A1 - Aleks Jevnikar A1 - Kallel, Sadok A1 - Andrea Malchiodi PB - Mathematical Sciences Publishers VL - 8 ER - TY - RPRT T1 - Translation and adaptation of Birman's paper "On the theory of self-adjoint extensions of positive definite operators" (1956) Y1 - 2015 A1 - Mikhail Khotyakov A1 - Alessandro Michelangeli AB - 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. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/34443 U1 - 34570 ER - TY - JOUR T1 - Universality Conjecture and Results for a Model of Several Coupled Positive-Definite Matrices JF - Commun. Math. Phys. Y1 - 2015 A1 - Marco Bertola A1 - Thomas Bothner VL - 337 UR - http://link.springer.com/article/10.1007/s00220-015-2327-7 ER - TY - THES T1 - Variational aspects of Liouville equations and systems Y1 - 2015 A1 - Aleks Jevnikar KW - Toda system PB - SISSA N1 - The PHD thesis is composed of 112 pages and is recorded in PDF format U1 - 34676 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - THES T1 - Variational aspects of singular Liouville systems Y1 - 2015 A1 - Luca Battaglia KW - Variational methods, Liouville systems, Moser-Trudinger inequalities, min-max methods AB - 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. PB - SISSA U1 - 34737 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - THES T1 - Volume variation and heat kernel for affine control problems Y1 - 2015 A1 - Elisa Paoli KW - Heat kernel asymptotics AB - 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 Hörmander 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. PB - SISSA U1 - 35290 U2 - Mathematics U4 - -1 U5 - MAT/05 ER - TY - RPRT T1 - The wave equation on domains with cracks growing on a prescribed path: existence, uniqueness, and continuous dependence on the data Y1 - 2015 A1 - Gianni Dal Maso A1 - Ilaria Lucardesi AB - 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. UR - http://urania.sissa.it/xmlui/handle/1963/34629 U1 - 34832 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - An Abstract Nash–Moser Theorem and Quasi-Periodic Solutions for NLW and NLS on Compact Lie Groups and Homogeneous Manifolds Y1 - 2014 A1 - Massimiliano Berti A1 - Livia Corsi A1 - Michela Procesi AB - 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. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34651 U1 - 34858 U2 - Mathematics ER - TY - JOUR T1 - Achieving unanimous opinions in signed social networks Y1 - 2014 A1 - Claudio Altafini A1 - Gabriele Lini AB - 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. PB - Institute of Electrical and Electronics Engineers Inc. UR - http://urania.sissa.it/xmlui/handle/1963/34935 U1 - 35137 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Adler-Gelfand-Dickey approach to classical W-algebras within the theory of Poisson vertex algebras Y1 - 2014 A1 - Alberto De Sole A1 - Victor G. Kac A1 - Daniele Valeri AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/7242 N1 - 45 pages ER - TY - JOUR T1 - Approximate Hermitian–Yang–Mills structures on semistable principal Higgs bundles Y1 - 2014 A1 - Ugo Bruzzo A1 - Beatriz Grana-Otero AB - 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. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34645 U1 - 34849 U2 - Mathematics ER - TY - JOUR T1 - Approximate Hitchin-Kobayashi correspondence for Higgs G-bundles Y1 - 2014 A1 - Ugo Bruzzo A1 - Beatriz Graña Otero AB - We announce a result about the extension of the Hitchin-Kobayashi correspondence to principal Higgs bundles. A principal Higgs bundle on a compact Kähler manifold, with structure group a connected linear algebraic reductive group, is semistable if and only if it admits an approximate Hermitian-Yang-Mills structure. PB - World Scientific Publishing UR - http://urania.sissa.it/xmlui/handle/1963/35095 U1 - 35350 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Buckling dynamics of a solvent-stimulated stretched elastomeric sheet Y1 - 2014 A1 - Alessandro Lucantonio A1 - Matthieu Roché A1 - Paola Nardinocchi A1 - Howard A. Stone AB - 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. PB - Royal Society of Chemistry UR - http://urania.sissa.it/xmlui/handle/1963/34967 U1 - 35197 U2 - Physics U4 - 1 ER - TY - JOUR T1 - Cauchy-Laguerre two-matrix model and the Meijer-G random point field JF - Comm. Math. Phys. Y1 - 2014 A1 - Marco Bertola A1 - Gekhtman, M. A1 - Szmigielski, J. VL - 326 UR - http://dx.doi.org/10.1007/s00220-013-1833-8 ER - TY - JOUR T1 - Classical W-algebras and generalized Drinfeld-Sokolov hierarchies for minimal and short nilpotents JF - Communications in Mathematical Physics 331, nr. 2 (2014) 623-676 Y1 - 2014 A1 - Alberto De Sole A1 - Victor G. Kac A1 - Daniele Valeri AB - 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'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. PB - SISSA UR - http://hdl.handle.net/1963/6979 N1 - 46 pages U1 - 6967 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Comparison between reduced basis and stochastic collocation methods for elliptic problems Y1 - 2014 A1 - Peng Chen A1 - Alfio Quarteroni A1 - Gianluigi Rozza AB - The stochastic collocation method (Babuška 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. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34727 U1 - 34916 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Comparison of a Modal Method and a Proper Orthogonal Decomposition approach for multi-group time-dependent reactor spatial kinetics JF - Annals of Nuclear Energy Y1 - 2014 A1 - Alberto Sartori A1 - Davide Baroli A1 - Antonio Cammi A1 - Davide Chiesa A1 - Lelio Luzzi A1 - Roberto R. Ponciroli A1 - Ezio Previtali A1 - Marco E. Ricotti A1 - Gianluigi Rozza A1 - Monica Sisti AB -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.

PB - Elsevier VL - 71 UR - http://urania.sissa.it/xmlui/handle/1963/35039 U1 - 35270 U2 - Physics U4 - 1 ER - TY - JOUR T1 - Conformal invariants from nodal sets. I. negative eigenvalues and curvature prescription Y1 - 2014 A1 - Rod R. Gover A1 - Yaiza Canzani A1 - Dmitry Jakobson A1 - Raphaël Ponge A1 - Andrea Malchiodi AB - 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'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. PB - Oxford University Press UR - http://urania.sissa.it/xmlui/handle/1963/35128 U1 - 35366 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - On conjugate times of LQ optimal control problems Y1 - 2014 A1 - Andrei A. Agrachev A1 - Luca Rizzi A1 - Pavel Silveira KW - Optimal control, Lagrange Grassmannian, Conjugate point AB - 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 $\vec{H}$. PB - Springer UR - http://hdl.handle.net/1963/7227 N1 - 14 pages, 1 figure U1 - 7261 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - A correction and an extension of Stampacchia's work on the geometric BVP Y1 - 2014 A1 - Giovanni Vidossich AB - 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. PB - Advanced Nonlinear Studies UR - http://urania.sissa.it/xmlui/handle/1963/35023 U1 - 35263 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Crawling on directional surfaces JF - International Journal of Non-Linear Mechanics Y1 - 2014 A1 - Paolo Gidoni A1 - Giovanni Noselli A1 - Antonio DeSimone KW - Bio-mimetic micro-robots KW - Cell migration KW - Crawling motility KW - Directional surfaces KW - Self-propulsion AB -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 ‘along the grain’, and high resistance when sliding ‘against the grain’. 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.

VL - 61 UR - http://www.sciencedirect.com/science/article/pii/S0020746214000213 ER - TY - JOUR T1 - Critical points of the Moser-Trudinger functional on a disk Y1 - 2014 A1 - Andrea Malchiodi A1 - Luca Martinazzi AB - 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. PB - European Mathematical Society UR - http://hdl.handle.net/1963/6560 N1 - 16 pages U1 - 6487 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - THES T1 - The curvature of optimal control problems with applications to sub-Riemannian geometry Y1 - 2014 A1 - Luca Rizzi KW - Sub-Riemannian geometry AB - 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's volume and are also investigated. PB - SISSA UR - http://hdl.handle.net/1963/7321 N1 - The PhD thesis is composed of 211 pages and is recorded in PDF format U1 - 7367 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Curvature-adapted remeshing of CAD surfaces JF - Procedia Engineering Y1 - 2014 A1 - Franco Dassi A1 - Andrea Mola A1 - Hang Si AB -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 Lévy 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.

PB - Elsevier VL - 82 UR - https://doi.org/10.1016/j.proeng.2014.10.388 N1 - This is an open access article under the CC BY-NC-ND license U1 - 35220 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Darboux Transformations and Random Point Processes JF - IMRN Y1 - 2014 A1 - Marco Bertola A1 - Mattia Cafasso VL - rnu122 ER - TY - THES T1 - The decomposition of optimal transportation problems with convex cost Y1 - 2014 A1 - Mauro Bardelloni KW - Optimal Transportation PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7475 U1 - 7570 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - The decomposition of optimal transportation problems with convex cost Y1 - 2014 A1 - Stefano Bianchini A1 - Mauro Bardelloni PB - SISSA UR - http://hdl.handle.net/1963/7433 U1 - 7527 ER - TY - JOUR T1 - A density result for GSBD and its application to the approximation of brittle fracture energies Y1 - 2014 A1 - Flaviana Iurlano AB -We present an approximation result for functions u: Ω → 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 → 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).

PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34647 U1 - 34851 U2 - Mathematics ER - TY - JOUR T1 - Dirac operators on noncommutative principal circle bundles Y1 - 2014 A1 - Andrzej Sitarz A1 - Alessandro Zucca A1 - Ludwik Dabrowski AB - 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 → S2. PB - World Scientific Publishing UR - http://urania.sissa.it/xmlui/handle/1963/35125 U1 - 35363 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Dirac reduction for Poisson vertex algebras JF - Communications in Mathematical Physics 331, nr. 3 (2014) 1155-1190 Y1 - 2014 A1 - Alberto De Sole A1 - Victor G. Kac A1 - Daniele Valeri AB - We construct an analogue of Dirac'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's reduction of an arbitrary non-local Poisson structure. We apply this construction to an example of a generalized Drinfeld-Sokolov hierarchy. PB - SISSA UR - http://hdl.handle.net/1963/6980 N1 - 31 pages U1 - 6968 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Discrete one-dimensional crawlers on viscous substrates: achievable net displacements and their energy cost Y1 - 2014 A1 - Giovanni Noselli A1 - Amabile Tatone A1 - Antonio DeSimone KW - Cell migration AB - 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. PB - Elsevier UR - http://urania.sissa.it/xmlui/handle/1963/34449 U1 - 34591 U2 - Mathematics ER - TY - RPRT T1 - Dislocations at the continuum scale: functional setting and variational properties Y1 - 2014 A1 - Riccardo Scala A1 - Nicolas Van Goethem UR - http://cvgmt.sns.it/paper/2294/ ER - TY - RPRT T1 - Donagi–Markman cubic for the generalised Hitchin system Y1 - 2014 A1 - Ugo Bruzzo A1 - Peter Dalakov KW - Generalized Hitchin system, Donagi-Markman cubic, algebraically completely integrable systems, moduli space of Higgs G-bundles AB - 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–Pantev formula holds on maximal rank symplectic leaves of the G-generalised Hitchin system. UR - http://hdl.handle.net/1963/7253 U1 - 7294 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - RPRT T1 - Dynamics on a graph as the limit of the dynamics on a "fat graph" Y1 - 2014 A1 - Gianfausto Dell'Antonio A1 - Alessandro Michelangeli AB - 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. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7485 U1 - 7598 ER - TY - JOUR T1 - Editorial Y1 - 2014 A1 - Ciro Ciliberto A1 - Gianni Dal Maso A1 - Pasquale Vetro PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34712 U1 - 34926 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - An effective model for nematic liquid crystal composites with ferromagnetic inclusions Y1 - 2014 A1 - Maria Carme Calderer A1 - Antonio DeSimone A1 - Dmitry Golovaty A1 - Alexander Panchenko AB - 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. PB - Society for Industrial and Applied Mathematics Publications UR - http://urania.sissa.it/xmlui/handle/1963/34940 U1 - 35194 U2 - Physics U4 - 1 ER - TY - RPRT T1 - An efficient computational framework for reduced basis approximation and a posteriori error estimation of parametrized Navier-Stokes flows Y1 - 2014 A1 - Andrea Manzoni KW - Reduced Basis Method, parametrized Navier-Stokes equations, steady incompressible fluids, a posteriori error estimation, approximation stability AB - 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. U1 - 7291 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems JF - International Journal of Computational Fluid Dynamics Y1 - 2014 A1 - Forti, D. A1 - Gianluigi Rozza AB - We present some recent advances and improvements in shape parametrisation techniques of interfaces for reduced-order modelling with special attention to fluid–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–structure applications in several fields. The examples provided deal with aeronautics and wind engineering. VL - 28 ER - TY - JOUR T1 - Existence and uniqueness of the gradient flow of the Entropy in the space of probability measures Y1 - 2014 A1 - Stefano Bianchini A1 - Alexander Dabrowski AB - 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. PB - EUT Edizioni Universita di Trieste UR - http://urania.sissa.it/xmlui/handle/1963/34693 N1 - This paper resumes the main part of the Bachelor thesis of the second author, discussed in 2013 at the University of Trieste. U1 - 34907 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds JF - Mathematische Annalen Y1 - 2014 A1 - Kuwert, Ernst A1 - Andrea Mondino A1 - Johannes Schygulla AB -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.

VL - 359 UR - https://doi.org/10.1007/s00208-013-1005-3 ER - TY - JOUR T1 - Existence of immersed spheres minimizing curvature functionals in non-compact 3-manifolds JF - Annales de l'Institut Henri Poincare (C) Non Linear Analysis Y1 - 2014 A1 - Andrea Mondino A1 - Johannes Schygulla KW - Direct methods in the calculus of variations KW - General Relativity KW - Geometric measure theory KW - second fundamental form KW - Willmore functional AB -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.

VL - 31 UR - http://www.sciencedirect.com/science/article/pii/S0294144913000851 ER - TY - JOUR T1 - Existence of integral m-varifolds minimizing $\int |A|^p $ and $\int |H|^p$ , p>m, in Riemannian manifolds JF - Calculus of Variations and Partial Differential Equations Y1 - 2014 A1 - Andrea Mondino AB -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.

VL - 49 UR - https://doi.org/10.1007/s00526-012-0588-y ER - TY - JOUR T1 - Finite dimensional Kadomtsev-Petviashvili τ-functions. I. Finite Grassmannians Y1 - 2014 A1 - Ferenc Balogh A1 - Tiago Fonseca A1 - John P. Harnad AB - 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 Plücker coordinates appearing as coefficients in the Schur function expansion of the τ-function. PB - American Institute of Physics Inc. UR - http://urania.sissa.it/xmlui/handle/1963/34952 U1 - 35153 U2 - Mathematics U4 - 1 ER - TY - Generic T1 - A fully nonlinear potential model for ship hydrodynamics directly interfaced with CAD data structures T2 - Proceedings of the 24th International Ocean and Polar Engineering Conference, Busan, 2014 Y1 - 2014 A1 - Andrea Mola A1 - Luca Heltai A1 - Antonio DeSimone KW - ship hydrodynamics AB - 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. JF - Proceedings of the 24th International Ocean and Polar Engineering Conference, Busan, 2014 PB - SISSA U1 - 7357 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - CHAP T1 - Fundamentals of Reduced Basis Method for problems governed by parametrized PDEs and applications T2 - Separated representations and PGD-based model reduction : fundamentals and applications Y1 - 2014 A1 - Gianluigi Rozza KW - reduced basis method, linear elasticity, heat transfer, error bounds, parametrized PDEs AB -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.

JF - Separated representations and PGD-based model reduction : fundamentals and applications T3 - CISM International Centre for Mechanical Sciences PB - Springer CY - Wien VL - 554 ER - TY - THES T1 - Geometry and analysis of control-affine systems: motion planning, heat and Schrödinger evolution Y1 - 2014 A1 - Dario Prandi KW - control theory AB - 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 Schrödinger 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–Bohm-type perturbation. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7474 U1 - 7576 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Global Structure of Admissible BV Solutions to Piecewise Genuinely Nonlinear, Strictly Hyperbolic Conservation Laws in One Space Dimension Y1 - 2014 A1 - Stefano Bianchini A1 - Lei Yu AB -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.

PB - Taylor & Francis UR - http://urania.sissa.it/xmlui/handle/1963/34694 U1 - 34908 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Hölder equivalence of the value function for control-affine systems JF - ESAIM: Control, Optimisation and Calculus of Variations Y1 - 2014 A1 - Dario Prandi PB - EDP Sciences VL - 20 ER - TY - THES T1 - Holomorphically symplectic varieties with Prym Lagrangian fibrations Y1 - 2014 A1 - Tommaso Matteini KW - Holomorphically symplectic varieties AB - 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. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7434 U1 - 7511 U2 - Mathematics U4 - 1 U5 - MAT/03 ER - TY - RPRT T1 - Homogenization of functional with linear growth in the context of A-quasiconvexity Y1 - 2014 A1 - Jose Matias A1 - Marco Morandotti A1 - Pedro M. Santos AB - 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. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7436 U1 - 7528 ER - TY - JOUR T1 - Homology computation for a class of contact structures on T3 Y1 - 2014 A1 - Ali Maalaoui A1 - Vittorio Martino AB - 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. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34649 U1 - 34856 U2 - Mathematics ER - TY - JOUR T1 - An improvement on geometrical parameterizations by transfinite maps JF - Comptes Rendus Mathematique Y1 - 2014 A1 - Jäggli, C. A1 - Laura Iapichino A1 - Gianluigi Rozza AB - 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. VL - 352 ER - TY - JOUR T1 - Infinite-dimensional Frobenius manifolds underlying the Toda lattice hierarchy Y1 - 2014 A1 - Chaozhong Wu A1 - Dafeng Zuo AB - 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. PB - Elsevier UR - http://urania.sissa.it/xmlui/handle/1963/35026 U1 - 35264 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Integrability of Dirac reduced bi-Hamiltonian equations Y1 - 2014 A1 - Alberto De Sole A1 - Victor G. Kac A1 - Daniele Valeri AB - 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's, obtained by Dirac reduction from some generalized Drinfeld-Sokolov hierarchies. PB - SISSA UR - http://hdl.handle.net/1963/7247 N1 - 15 pages U1 - 7286 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - RPRT T1 - An irreducible symplectic orbifold of dimension 6 with a Lagrangian Prym fibration Y1 - 2014 A1 - Tommaso Matteini KW - Irreducible symplectic variety, Lagrangian fibration, Prym variety, automorphism of symplectic varieties AB - 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. U1 - 7360 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - On an isomonodromy deformation equation without the Painlevé property Y1 - 2014 A1 - Boris Dubrovin A1 - Andrey Kapaev AB - 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. PB - Maik Nauka-Interperiodica Publishing UR - http://hdl.handle.net/1963/6466 N1 - 34 pages, 8 figures, references added U1 - 6410 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - KAM for quasi-linear and fully nonlinear forced perturbations of Airy equation JF - Mathematische Annalen Y1 - 2014 A1 - P Baldi A1 - Massimiliano Berti A1 - Riccardo Montalto AB - 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. © 2014 Springer-Verlag Berlin Heidelberg. N1 - cited By (since 1996)0; Article in Press ER - TY - THES T1 - KAM for quasi-linear and fully nonlinear perturbations of Airy and KdV equations Y1 - 2014 A1 - Riccardo Montalto PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7476 U1 - 7571 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - KAM for quasi-linear KdV JF - C. R. Math. Acad. Sci. Paris Y1 - 2014 A1 - P Baldi A1 - Massimiliano Berti A1 - Riccardo Montalto AB -We prove the existence and stability of Cantor families of quasi-periodic, small-amplitude solutions of quasi-linear autonomous Hamiltonian perturbations of KdV.

PB - Elsevier VL - 352 UR - http://urania.sissa.it/xmlui/handle/1963/35067 IS - 7-8 U1 - 35302 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - KAM for Reversible Derivative Wave Equations JF - Arch. Ration. Mech. Anal. Y1 - 2014 A1 - Massimiliano Berti A1 - Luca Biasco A1 - Michela Procesi AB -We prove the existence of Cantor families of small amplitude, analytic, linearly stable quasi-periodic solutions of reversible derivative wave equations.

PB - Springer VL - 212 UR - http://urania.sissa.it/xmlui/handle/1963/34646 IS - 3 U1 - 34850 U2 - Mathematics ER - TY - JOUR T1 - Laplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length Y1 - 2014 A1 - Gianni Dal Maso A1 - Gianluca Orlando A1 - Rodica Toader KW - cracked domains, energy release rate, higher order derivatives, asymptotic expansion of solutions AB -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.

PB - SISSA UR - http://hdl.handle.net/1963/7271 U1 - 7316 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - CHAP T1 - Lecture notes on gradient flows and optimal transport Y1 - 2014 A1 - Sara Daneri A1 - Giuseppe Savarè AB - 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. PB - Cambridge University Press UR - http://urania.sissa.it/xmlui/handle/1963/35093 N1 - Book title: Optimal transportation U1 - 35348 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Legendre duality on hypersurfaces in Kähler manifolds Y1 - 2014 A1 - Vittorio Martino AB - We give a sufficient condition on real strictly Levi-convex hypersurfaces M, embedded in four-dimensional Kähler 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. PB - Walter de Gruyter and Co. UR - http://urania.sissa.it/xmlui/handle/1963/34777 U1 - 34998 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Linearized plastic plate models as Γ-limits of 3D finite elastoplasticity JF - ESAIM: Control, Optimisation and Calculus of Variations Y1 - 2014 A1 - Elisa Davoli AB -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 Kármán plate theory and the linearized plate theory.

PB - EDP Sciences VL - 20 ER - TY - JOUR T1 - Lipschitz continuous viscosity solutions for a class of fully nonlinear equations on lie groups Y1 - 2014 A1 - Vittorio Martino A1 - Annamaria Montanari AB - 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. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34699 U1 - 34910 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Local and global minimality results for a nonlocal isoperimetric problem on R^N JF - SIAM Journal on Mathematical Analysis Y1 - 2014 A1 - Marco Bonacini A1 - Riccardo Cristoferi KW - Nonlocal isoperimetric problem AB -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.

PB - SIAM Publications VL - 46 UR - http://hdl.handle.net/1963/6984 IS - 4 U1 - 6976 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Local behavior of fractional p-minimizers Y1 - 2014 A1 - Agnese Di Castro A1 - Tuomo Kuusi A1 - Giampiero Palatucci KW - fractional Sobolev spaces AB -We extend the De Giorgi-Nash Moser theory to nonlocal, possibly degerate integro-differential operators

PB - SISSA U1 - 7301 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - On the Lp-differentiability of certain classes of functions Y1 - 2014 A1 - Giovanni Alberti A1 - Stefano Bianchini A1 - Gianluca Crippa AB - 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. PB - European Mathematical Society UR - http://urania.sissa.it/xmlui/handle/1963/34695 U1 - 34909 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Maximal generalized solution of eikonal equation Y1 - 2014 A1 - Sandro Zagatti AB - 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∞(Ω) for which the problem admits a (maximal) generalized solution, providing a generalization of the notion of viscosity solution. PB - Elsevier UR - http://urania.sissa.it/xmlui/handle/1963/34642 U1 - 34846 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Minimal Liouville gravity correlation numbers from Douglas string equation Y1 - 2014 A1 - Alexander Belavin A1 - Boris Dubrovin A1 - Baur Mukhametzhanov AB - 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}. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34588 U1 - 34795 U2 - Physics U4 - 2 ER - TY - JOUR T1 - A model for crack growth with branching and kinking JF - Asymptotic Analysis Y1 - 2014 A1 - Simone Racca KW - quasistatic crack evolution, branching, kinking, Griffith\\\'s criterion AB -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's theory, in terms of the energy release rate, when the crack grows at least at one point of its front.

PB - SISSA VL - 89 UR - https://content.iospress.com/articles/asymptotic-analysis/asy1233 IS - 1-2 U1 - 6293 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Model Order Reduction in Fluid Dynamics: Challenges and Perspectives Y1 - 2014 A1 - Toni Lassila A1 - Andrea Manzoni A1 - Alfio Quarteroni A1 - Gianluigi Rozza AB - 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. PB - Springer U1 - 34923 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - A modular spectral triple for κ-Minkowski space Y1 - 2014 A1 - Marco Matassa AB - 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-Poincaré 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. PB - Elsevier UR - http://urania.sissa.it/xmlui/handle/1963/34895 U1 - 35180 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - A Moser-Trudinger inequality for the singular Toda system JF - Bull. Inst. Math. Acad. Sin. Y1 - 2014 A1 - Luca Battaglia A1 - Andrea Malchiodi VL - 9 ER - TY - JOUR T1 - M-theory interpretation of the real topological string JF - Journal of High Energy Physics Y1 - 2014 A1 - Nicolò Piazzalunga A1 - Uranga, Angel M. AB -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.

VL - 2014 UR - https://doi.org/10.1007/JHEP08(2014)054 ER - TY - JOUR T1 - N = 2 Quiver Gauge Theories on A-type ALE Spaces Y1 - 2014 A1 - Ugo Bruzzo A1 - Francesco Sala A1 - Richard J. Szabo AB - 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–Witten geometry. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34719 U1 - 34918 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - New results on Gamma-limits of integral functionals Y1 - 2014 A1 - Nadia Ansini A1 - Gianni Dal Maso A1 - Caterina Ida Zeppieri KW - Gamma-convergence PB - Elsevier UR - http://hdl.handle.net/1963/5880 U1 - 5745 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - THES T1 - Non-commutative integration for spectral triples associated to quantum groups Y1 - 2014 A1 - Marco Matassa KW - Non-commutative geometry AB - 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. PB - SISSA U1 - 7363 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Nonsingular Isogeometric Boundary Element Method for Stokes Flows in 3D Y1 - 2014 A1 - Luca Heltai A1 - Marino Arroyo A1 - Antonio DeSimone KW - Isogeometric Analysis AB - 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. PB - Elsevier UR - http://hdl.handle.net/1963/6326 U1 - 6250 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - Pfaffian representations of cubic surfaces Y1 - 2014 A1 - Fabio Tanturri AB -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.

PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34688 U1 - 34900 U2 - Mathematics U4 - 1 ER - TY - CONF T1 - Potential Model for Ship Hydrodynamics Simulations Directly Interfaced with CAD Data Structures T2 - The 24th International Ocean and Polar Engineering Conference Y1 - 2014 A1 - Andrea Mola A1 - Luca Heltai A1 - Antonio DeSimone A1 - Massimiliano Berti JF - The 24th International Ocean and Polar Engineering Conference PB - International Society of Offshore and Polar Engineers VL - 4 ER - TY - JOUR T1 - Pseudo-automorphisms of positive entropy on the blowups of products of projective spaces Y1 - 2014 A1 - Fabio Perroni A1 - Deqi Zhang AB - 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. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34714 U1 - 34921 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - On a quadratic functional for scalar conservation laws JF - Journal of Hyperbolic Differential Equations Y1 - 2014 A1 - Stefano Bianchini A1 - Stefano Modena AB -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.

PB - World Scientific Publishing VL - 11 UR - http://arxiv.org/abs/1311.2929 IS - 2 U1 - 34903 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Quadratic interaction functional for systems of conservation laws: a case study JF - Bulletin of the Institute of Mathematics of Academia Sinica (New Series) Y1 - 2014 A1 - Stefano Bianchini A1 - Stefano Modena VL - 9 UR - https://w3.math.sinica.edu.tw/bulletin_ns/20143/2014308.pdf ER - TY - JOUR T1 - Quantum dimension and quantum projective spaces Y1 - 2014 A1 - Marco Matassa AB - We show that the family of spectral triples for quantum projective spaces introduced by D'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. PB - Institute of Mathematics UR - http://urania.sissa.it/xmlui/handle/1963/34764 U1 - 34991 U2 - Physics U4 - 2 ER - TY - JOUR T1 - Quantum gauge symmetries in noncommutative geometry Y1 - 2014 A1 - Jyotishman Bhowmick A1 - Francesco D'Andrea A1 - Biswarup Krishna Das A1 - Ludwik Dabrowski AB - 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). PB - European Mathematical Society Publishing House UR - http://urania.sissa.it/xmlui/handle/1963/34897 U1 - 35182 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Quasi-static crack growth in hydraulic fracture JF - Nonlinear Analysis Y1 - 2014 A1 - Stefano Almi A1 - Gianni Dal Maso A1 - Rodica Toader AB -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.

PB - Elsevier VL - 109 UR - http://hdl.handle.net/20.500.11767/17350 IS - Nov U1 - 34741 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Quasistatic Evolution in Perfect Plasticity as Limit of Dynamic Processes JF - Journal of Dynamics and Differential Equations Y1 - 2014 A1 - Gianni Dal Maso A1 - Riccardo Scala AB -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.

VL - 26 UR - https://doi.org/10.1007/s10884-014-9409-7 ER - TY - JOUR T1 - Quasistatic evolution models for thin plates arising as low energy Γ-limits of finite plasticity JF - Mathematical Models and Methods in Applied Sciences Y1 - 2014 A1 - Elisa Davoli AB -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 Kármán and linearized Von Kármán 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 $\alpha$.

VL - 24 UR - https://doi.org/10.1142/S021820251450016X ER - TY - RPRT T1 - Rate-independent damage in thermo-viscoelastic materials with inertia Y1 - 2014 A1 - Giuliano Lazzaroni A1 - Riccarda Rossi A1 - Marita Thomas A1 - Rodica Toader AB - 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. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7444 U1 - 7542 ER - TY - THES T1 - Rational curves and instantons on the Fano threefold Y_5 Y1 - 2014 A1 - Giangiacomo Sanna KW - Moduli space of vector bundles AB - 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-Mülich 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. PB - arXiv preprint UR - http://urania.sissa.it/xmlui/handle/1963/7482 U1 - 7594 U2 - Mathematics U4 - 1 U5 - MAT/02 ER - TY - CONF T1 - Reduced basis method for the Stokes equations in decomposable domains using greedy optimization T2 - ECMI 2014 proceedings Y1 - 2014 A1 - Laura Iapichino A1 - Alfio Quarteroni A1 - Gianluigi Rozza A1 - Volkwein, Stefan JF - ECMI 2014 proceedings ER - TY - BOOK T1 - Reduced Order Methods for Modeling and Computational Reduction T2 - MS&A Y1 - 2014 A1 - Alfio Quarteroni A1 - Gianluigi Rozza KW - reduced order methods, MOR, ROM, POD, RB, greedy, CFD, Numerical Analysis AB -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.

JF - MS&A PB - Springer CY - Milano VL - 9 ER - TY - Generic T1 - A reduced order model for multi-group time-dependent parametrized reactor spatial kinetics T2 - 22nd International Conference on Nuclear Engineering ICONE22 Y1 - 2014 A1 - Alberto Sartori A1 - Davide Baroli A1 - Antonio Cammi A1 - Lelio Luzzi A1 - Gianluigi Rozza AB -

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.

JF - 22nd International Conference on Nuclear Engineering ICONE22 PB - American Society of Mechanical Engineers (ASME) CY - Prague, Czech Republic SN - 978-079184595-0 UR - http://urania.sissa.it/xmlui/handle/1963/35123 N1 - 2014 22nd International Conference on Nuclear Engineering, ICONE 2014; Prague; Czech Republic; 7 July 2014 through 11 July 2014; Code 109131; U1 - 35360 U2 - Mathematics U4 - 1 ER - TY - CHAP T1 - Reduction on characteristics for continuous of a scalar balance law T2 - AIMS Series on Applied Mathematics, vol. 8 (2014): 399 - 406 Y1 - 2014 A1 - Giovanni Alberti A1 - Stefano Bianchini A1 - Laura Caravenna KW - Method of characteristics JF - AIMS Series on Applied Mathematics, vol. 8 (2014): 399 - 406 PB - SISSA UR - http://hdl.handle.net/1963/6562 U1 - 6516 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - A Review of the Sixth Painlevé Equation Y1 - 2014 A1 - Davide Guzzetti AB - For the Painlevé 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. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34658 U1 - 34868 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - A robotic crawler exploiting directional frictional interactions: experiments, numerics, and derivation of a reduced model JF - Proceedings of the Royal Society A 470, 20140333 (2014) Y1 - 2014 A1 - Giovanni Noselli A1 - Antonio DeSimone AB - We present experimental and numerical results for a model crawler which is able to extract net positional changes from reciprocal shape changes, i.e. ‘breathing-like’ 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. PB - Royal Society Publishing U1 - 34594 U2 - Mathematics ER - TY - JOUR T1 - SBV Regularity of Systems of Conservation Laws and Hamilton–Jacobi Equations Y1 - 2014 A1 - Stefano Bianchini AB - 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. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34691 U1 - 34904 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Second Order Asymptotic Development for the Anisotropic Cahn-Hilliard Functional Y1 - 2014 A1 - Gianni Dal Maso A1 - Irene Fonseca A1 - Giovanni Leoni KW - Gamma-convergence, Cahn-Hilliard functional, phase transitions AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/7390 N1 - This article is composed if 33 pages and recorded in PDF format U1 - 7439 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Semiclassical limit of focusing NLS for a family of square barrier initial data Y1 - 2014 A1 - Robert Jenkins A1 - Kenneth McLaughlin AB - The small dispersion limit of the focusing nonlinear Schrödinger 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. PB - Wiley Periodicals UR - http://urania.sissa.it/xmlui/handle/1963/35066 U1 - 35301 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Shape control of active surfaces inspired by the movement of euglenids Y1 - 2014 A1 - Marino Arroyo A1 - Antonio DeSimone AB - 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. PB - Elsevier UR - http://urania.sissa.it/xmlui/handle/1963/35118 U1 - 35375 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Shape Optimization by Free-Form Deformation: Existence Results and Numerical Solution for Stokes Flows Y1 - 2014 A1 - Francesco Ballarin A1 - Andrea Manzoni A1 - Gianluigi Rozza A1 - Sandro Salsa AB - 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. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34698 U1 - 34914 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Singular Value Decomposition of a Finite Hilbert Transform Defined on Several Intervals and the Interior Problem of Tomography: The Riemann-Hilbert Problem Approach JF - Comm. Pure Appl. Math. Y1 - 2014 A1 - Marco Bertola A1 - Alexander Katsevich A1 - Alexander Tovbis ER - TY - JOUR T1 - Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics Y1 - 2014 A1 - Giulio Bonelli A1 - Antonio Sciarappa A1 - Alessandro Tanzini A1 - Petr Vasko AB - 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. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34546 U1 - 34771 U2 - Physics U4 - 2 ER - TY - JOUR T1 - Smooth approximation of bi-Lipschitz orientation-preserving homeomorphisms JF - Annales de l'Institut Henri Poincare (C) Non Linear Analysis Y1 - 2014 A1 - Sara Daneri A1 - Aldo Pratelli AB -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.

VL - 31 UR - http://www.sciencedirect.com/science/article/pii/S0294144913000711 ER - TY - RPRT T1 - Some remarks on a model for rate-independent damage in thermo-visco-elastodynamics Y1 - 2014 A1 - Giuliano Lazzaroni A1 - Riccarda Rossi A1 - Marita Thomas A1 - Rodica Toader AB - 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. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7463 U1 - 7566 ER - TY - JOUR T1 - Some remarks on the seismic behaviour of embedded cantilevered retaining walls Y1 - 2014 A1 - Riccardo Conti A1 - F. Burali D'Arezzo A1 - Giulia M.B. Viggiani AB - 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. PB - Thomas Telford UR - http://urania.sissa.it/xmlui/handle/1963/35073 U1 - 35308 U2 - Physics U4 - 2 ER - TY - JOUR T1 - Spontaneous division and motility in active nematic droplets Y1 - 2014 A1 - Luca Giomi A1 - Antonio DeSimone AB - 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. PB - American Physical Society UR - http://urania.sissa.it/xmlui/handle/1963/34902 U1 - 35107 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Stability of equilibrium configurations for elastic films in two and three dimensions JF - Advances in Calculus of Variations Y1 - 2014 A1 - Marco Bonacini KW - Epitaxially strained elastic films AB -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.

PB - SISSA VL - 8 UR - https://www.degruyter.com/view/j/acv.2015.8.issue-2/acv-2013-0018/acv-2013-0018.xml IS - 2 U1 - 6997 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Stabilized reduced basis method for parametrized advection-diffusion PDEs JF - Computer Methods in Applied Mechanics and Engineering Y1 - 2014 A1 - Pacciarini, P. A1 - Gianluigi Rozza AB -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 ``double'' stabilization both in steady and unsteady problems, also related to heat transfer phenomena.

VL - 274 ER - TY - CONF T1 - Stabilized reduced basis method for parametrized scalar advection-diffusion problems at higher Péclet number: Roles of the boundary layers and inner fronts T2 - 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 Y1 - 2014 A1 - Pacciarini, P. A1 - Gianluigi Rozza AB -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.

JF - 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 UR - https://infoscience.epfl.ch/record/203327/files/ECCOMAS_PP_GR.pdf ER - TY - RPRT T1 - Steady nearly incompressible vector elds in 2D: chain rule and renormalization Y1 - 2014 A1 - Stefano Bianchini A1 - N.A. Gusev PB - SISSA U1 - 7464 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - The stringy instanton partition function Y1 - 2014 A1 - Giulio Bonelli A1 - Antonio Sciarappa A1 - Alessandro Tanzini A1 - Petr Vasko AB - 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. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34589 U1 - 34796 U2 - Physics U4 - 2 ER - TY - RPRT T1 - Structure of classical (finite and affine) W-algebras Y1 - 2014 A1 - Alberto De Sole A1 - Victor G. Kac A1 - Daniele Valeri AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/7314 N1 - 40 pages U1 - 7359 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Structure of entropy solutions to general scalar conservation laws in one space dimension JF - Journal of Mathematical Analysis and Applications Y1 - 2014 A1 - Stefano Bianchini A1 - Lei Yu PB - SISSA VL - 428 UR - https://www.sciencedirect.com/science/article/pii/S0022247X15002218 IS - 1 U1 - 7305 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - Swelling dynamics of a thin elastomeric sheet under uniaxial pre-stretch Y1 - 2014 A1 - Alessandro Lucantonio A1 - Paola Nardinocchi A1 - Howard A. Stone AB - 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. PB - American Institute of Physics UR - http://urania.sissa.it/xmlui/handle/1963/35113 U1 - 35370 U2 - Physics U4 - 1 ER - TY - JOUR T1 - Swelling-induced and controlled curving in layered gel beams Y1 - 2014 A1 - Alessandro Lucantonio A1 - Paola Nardinocchi A1 - Matteo Pezzulla AB - 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. PB - Royal Society of London UR - http://urania.sissa.it/xmlui/handle/1963/34987 U1 - 35229 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Topological Invariants of Eigenvalue Intersections and Decrease of Wannier Functions in Graphene JF - J. Stat. Phys 155 (2014) 1027-1071 Y1 - 2014 A1 - Domenico Monaco A1 - Gianluca Panati KW - Wannier functions, Bloch bundles, conical intersections, eigenspace vorticity, pseudospin winding number, graphene AB -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|→∞, both in monolayer and bilayer graphene.

PB - Journal of Statistical Physics U1 - 7368 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - The topology of a subspace of the Legendrian curves on a closed contact 3-manifold Y1 - 2014 A1 - Ali Maalaoui A1 - Vittorio Martino AB - 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. PB - Advanced Nonlinear Studies UR - http://urania.sissa.it/xmlui/handle/1963/35016 U1 - 35262 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - A uniqueness result for the continuity equation in two dimensions: dedicated to constantine dafermos on the occasion of his 70th birthday Y1 - 2014 A1 - Giovanni Alberti A1 - Stefano Bianchini A1 - Gianluca Crippa AB - 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. PB - European Mathematical Society; Springer Verlag UR - http://urania.sissa.it/xmlui/handle/1963/34692 U1 - 34906 U2 - Mathematics U4 - 1 ER - TY - THES T1 - A variational approach to statics and dynamics of elasto-plastic systems Y1 - 2014 A1 - Riccardo Scala KW - delamination AB - 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. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7471 U1 - 7583 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - A variational model for the quasi-static growth of fractional dimensional brittle fractures Y1 - 2014 A1 - Simone Racca A1 - Rodica Toader KW - Variational models AB -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.

PB - European Mathematical Society UR - http://hdl.handle.net/1963/6983 U1 - 6973 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - Vortex Partition Functions, Wall Crossing and Equivariant Gromov–Witten Invariants Y1 - 2014 A1 - Giulio Bonelli A1 - Antonio Sciarappa A1 - Alessandro Tanzini A1 - Petr Vasko AB - 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–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–Witten theory follow just by deforming the integration contour. In particular, we apply our formalism to compute Gromov–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. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34652 U1 - 34859 U2 - Physics ER - TY - JOUR T1 - A weighted empirical interpolation method: A priori convergence analysis and applications Y1 - 2014 A1 - Peng Chen A1 - Alfio Quarteroni A1 - Gianluigi Rozza AB - 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-Loève 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. PB - EDP Sciences UR - http://urania.sissa.it/xmlui/handle/1963/35021 U1 - 35253 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Weighted quantile correlation test for the logistic family Y1 - 2014 A1 - Ferenc Balogh A1 - Éva Krauczi AB - 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. PB - University of Szeged UR - http://urania.sissa.it/xmlui/handle/1963/35025 U1 - 35261 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Where best to place a Dirichlet condition in an anisotropic membrane? Y1 - 2014 A1 - Paolo Tilli A1 - Davide Zucco AB - 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. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7481 U1 - 7592 ER - TY - JOUR T1 - Zeros of Large Degree Vorob'ev-Yablonski Polynomials via a Hankel Determinant Identity JF - International Mathematics Research Notices Y1 - 2014 A1 - Marco Bertola A1 - Thomas Bothner VL - rnu239 ER - TY - RPRT T1 - Ambrosio-Tortorelli approximation of cohesive fracture models in linearized elasticity Y1 - 2013 A1 - Matteo Focardi A1 - Flaviana Iurlano KW - Functions of bounded deformation AB -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'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 $\gamma>0$.

PB - SISSA UR - http://hdl.handle.net/1963/6615 U1 - 6573 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Analytical validation of a continuum model for epitaxial growth with elasticity on vicinal surfaces Y1 - 2013 A1 - Gianni Dal Maso A1 - Irene Fonseca A1 - Giovanni Leoni KW - singular nonlinear parabolic equations, Hilbert transform, thin films AB - 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]. PB - Springer UR - http://hdl.handle.net/1963/7245 U1 - 7284 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - THES T1 - An Approximation Result for Generalised Functions of Bounded Deformation and Applications to Damage Problems Y1 - 2013 A1 - Flaviana Iurlano KW - Functions of bounded deformation PB - SISSA U1 - 7203 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Asymptotics of the first Laplace eigenvalue with Dirichlet regions of prescribed length Y1 - 2013 A1 - Paolo Tilli A1 - Davide Zucco AB - 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. PB - Society for Industrial and Applied Mathematics UR - http://urania.sissa.it/xmlui/handle/1963/35141 U1 - 35379 U2 - Physics U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - Attainment results for nematic elastomers Y1 - 2013 A1 - Virginia Agostiniani A1 - Gianni Dal Maso A1 - Antonio DeSimone AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/7174 U1 - 7201 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - THES T1 - Biregular and Birational Geometry of Algebraic Varieties Y1 - 2013 A1 - Alex Massarenti KW - Moduli spaces of curves, automorphisms, Hassett's moduli spaces, varieties of sums of powers AB - 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. PB - SISSA U1 - 6962 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Classical W-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras JF - Communications in Mathematical Physics 323, nr. 2 (2013) 663-711 Y1 - 2013 A1 - Alberto De Sole A1 - Victor G. Kac A1 - Daniele Valeri AB - 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. PB - Springer UR - http://hdl.handle.net/1963/6978 N1 - 43 pages. Second version with minor editing and corrections U1 - 6966 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - A combination between the reduced basis method and the ANOVA expansion: On the computation of sensitivity indices JF - Comptes Rendus Mathematique. Volume 351, Issue 15-16, August 2013, Pages 593-598 Y1 - 2013 A1 - Denis Devaud A1 - Andrea Manzoni A1 - Gianluigi Rozza KW - Partial differential equations AB -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.

PB - Elsevier UR - http://hdl.handle.net/1963/7389 U1 - 7434 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Common dynamical features of sensory adaptation in photoreceptors and olfactory sensory neurons. JF - Nature. Scientific Reports 3, Article number: 1251, Published : 13 February 2013 Y1 - 2013 A1 - Giovanna De Palo A1 - Giuseppe Facchetti A1 - Monica Mazzolini A1 - Anna Menini A1 - Vincent Torre A1 - Claudio Altafini AB -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.

PB - SISSA U1 - 6453 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Concentration of solutions for a singularly perturbed mixed problem in non-smooth domains JF - Journal of Differential Equations Y1 - 2013 A1 - Serena Dipierro KW - Finite-dimensional reductions KW - Local inversion KW - Singularly perturbed elliptic problems AB -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.

VL - 254 UR - http://www.sciencedirect.com/science/article/pii/S0022039612003312 ER - TY - JOUR T1 - The Conformal Willmore Functional: A Perturbative Approach JF - Journal of Geometric Analysis Y1 - 2013 A1 - Andrea Mondino AB -The conformal Willmore functional (which is conformal invariant in general Riemannian manifolds $(M,g)$ is studied with a perturbative method: the Lyapunov–Schmidt reduction. Existence of critical points is shown in ambient manifolds $(\mathbb{R}^3,g_\epsilon)$ – 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.

VL - 23 UR - https://doi.org/10.1007/s12220-011-9263-3 ER - TY - JOUR T1 - Connected Sum Construction for σk-Yamabe Metrics JF - Journal of Geometric Analysis 23, nr.2 (2013), pages 812-854 Y1 - 2013 A1 - Giovanni Catino A1 - Lorenzo Mazzieri AB - 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. PB - Springer UR - http://hdl.handle.net/1963/6441 N1 - This article has not yet been published. U1 - 6366 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - Crawlers in viscous environments: linear vs nonlinear rheology JF - International Journal of Non-Linear Mechanics 56, 142-147 (2013) Y1 - 2013 A1 - Antonio DeSimone A1 - Federica Guarnieri A1 - Giovanni Noselli A1 - Amabile Tatone AB - 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. PB - Elsevier U1 - 34590 U2 - Mathematics ER - TY - RPRT T1 - On critical behaviour in systems of Hamiltonian partial differential equations Y1 - 2013 A1 - Boris Dubrovin A1 - Tamara Grava A1 - Christian Klein A1 - Antonio Moro AB -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.

PB - SISSA U1 - 7280 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - RPRT T1 - The curvature: a variational approach Y1 - 2013 A1 - Andrei A. Agrachev A1 - Davide Barilari A1 - Luca Rizzi KW - Crurvature, subriemannian metric, optimal control problem AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/7226 N1 - 88 pages, 10 figures, (v2) minor typos corrected, (v3) added sections on Finsler manifolds, slow growth distributions, Heisenberg group U1 - 7260 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Curved noncommutative torus and Gauss--Bonnet JF - Journal of Mathematical Physics. Volume 54, Issue 1, 22 January 2013, Article number 013518 Y1 - 2013 A1 - Ludwik Dabrowski A1 - Andrzej Sitarz KW - Geometry AB - 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. PB - American Institute of Physics UR - http://hdl.handle.net/1963/7376 N1 - The article is composed of 13 pages and is recorded in PDF format U1 - 7424 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - RPRT T1 - The deal.II Library, Version 8.1 Y1 - 2013 A1 - W. Bangerth A1 - Timo Heister A1 - Luca Heltai A1 - G. Kanschat A1 - Martin Kronbichler A1 - Matthias Maier A1 - B. Turcksin A1 - T. D. Young AB - This paper provides an overview of the new features of the finite element library deal.II version 8.0. PB - SISSA UR - http://hdl.handle.net/1963/7236 N1 - 5 pages U1 - 7272 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - RPRT T1 - Defect annihilation and proliferation in active nematics Y1 - 2013 A1 - Luca Giomi A1 - Mark J. Bowick A1 - Xu Ma A1 - M. Cristina Marchetti AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/6566 N1 - 5 pages, 4 figures U1 - 6517 U2 - Mathematics U4 - 2 U5 - FIS/02 FISICA TEORICA, MODELLI E METODI MATEMATICI ER - TY - RPRT T1 - On deformations of multidimensional Poisson brackets of hydrodynamic type Y1 - 2013 A1 - Matteo Casati KW - Hamiltonian operator AB - 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'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. PB - SISSA UR - http://hdl.handle.net/1963/7235 U1 - 7271 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - THES T1 - On the desingularization of Kahler orbifolds with constant scalar curvature Y1 - 2013 A1 - Riccardo Lena PB - SISSA U1 - 7263 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Dirac operator on spinors and diffeomorphisms JF - Classical and Quantum Gravity. Volume 30, Issue 1, 7 January 2013, Article number 015006 Y1 - 2013 A1 - Ludwik Dabrowski A1 - Giacomo Dossena KW - gravity AB - 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. PB - IOP Publishing UR - http://hdl.handle.net/1963/7377 N1 - This article is composed of 13 pages and is recorded in PDF format U1 - 7425 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - RPRT T1 - Dislocation dynamics in crystals: a macroscopic theory in a fractional Laplace setting Y1 - 2013 A1 - Serena Dipierro A1 - Giampiero Palatucci A1 - Enrico Valdinoci KW - nonlocal Allen-Cahn equation AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/7124 U1 - 7124 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Early phase of plasticity-related gene regulation and SRF dependent transcription in the hippocampus JF - PloS one. Volume 8, Issue 7, July 2013 : e68078 Y1 - 2013 A1 - Giovanni Iacono A1 - Claudio Altafini A1 - Vincent Torre AB - 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 µM 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. PB - Public Library of Science UR - http://hdl.handle.net/1963/7287 N1 - The article is composed of 15 pages U1 - 7332 U2 - Neuroscience U4 - -1 ER - TY - JOUR T1 - Epitaxially strained elastic films: the case of anisotropic surface energies JF - ESAIM Control. Optim. Calc. Var. 19 (2013) 167-189 Y1 - 2013 A1 - Marco Bonacini AB -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.

PB - EDP Sciences UR - http://hdl.handle.net/1963/4268 U1 - 3999 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - RPRT T1 - Equilibrium measures for a class of potentials with discrete rotational symmetries Y1 - 2013 A1 - Ferenc Balogh A1 - Dario Merzi AB - 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 $s=1$.

PB - University of Catania U1 - 7318 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - An existence result for the mean-field equation on compact surfaces in a doubly supercritical regime JF - Proceedings of the Royal Society of Edinburgh: Section A Mathematics Y1 - 2013 A1 - Aleks Jevnikar PB - Royal Society of Edinburgh Scotland Foundation VL - 143 ER - TY - JOUR T1 - Expanded degenerations and pairs JF - Communications in Algebra. Volume 41, Issue 6, May 2013, Pages 2346-2386 Y1 - 2013 A1 - Dan Abramovich A1 - Charles Cadman A1 - Barbara Fantechi A1 - Jonathan Wise KW - Expanded pairs AB - Since Jun Li'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. PB - Taylor and Francis UR - http://hdl.handle.net/1963/7383 N1 - This article is composed of 41 pages and is recorded in PDF format U1 - 7431 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Fields of bounded deformation for mesoscopic dislocations Y1 - 2013 A1 - Nicolas Van Goethem AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/6378 U1 - 6311 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Fracture models as Gamma-limits of damage models JF - Communications on Pure and Applied Analysis 12 (2013) 1657-1686 Y1 - 2013 A1 - Gianni Dal Maso A1 - Flaviana Iurlano AB -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.

PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/4225 U1 - 3952 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Framed sheaves on projective stacks Y1 - 2013 A1 - Ugo Bruzzo A1 - Francesco Sala AB - 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 ``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 $A_k$. UR - http://urania.sissa.it/xmlui/handle/1963/7438 U1 - 7532 ER - TY - JOUR T1 - Free Form Deformation Techniques Applied to 3D Shape Optimization Problems JF - Communications in Applied and Industrial Mathematics Y1 - 2013 A1 - Anwar Koshakji A1 - Alfio Quarteroni A1 - Gianluigi Rozza AB - 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. ER - TY - JOUR T1 - The gap probabilities of the tacnode, Pearcey and Airy point processes, their mutual relationship and evaluation JF - Random Matrices: Theory and Applications Y1 - 2013 A1 - Marco Bertola A1 - Mattia Cafasso VL - 02 UR - http://www.worldscientific.com/doi/abs/10.1142/S2010326313500032 ER - TY - JOUR T1 - Generalized Sturm-Liouville boundary conditions for first order differential systems in the plane JF - Topol. Methods Nonlinear Anal. Y1 - 2013 A1 - Alessandro Fonda A1 - Maurizio Garrione AB -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 Fučík 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.

PB - Nicolaus Copernicus University, Juliusz P. Schauder Centre for Nonlinear Studies VL - 42 UR - https://projecteuclid.org:443/euclid.tmna/1461248981 ER - TY - JOUR T1 - Genus stabilization for moduli of curves with symmetries Y1 - 2013 A1 - Fabrizio Catanese A1 - Michael Lönne A1 - Fabio Perroni KW - group actions KW - mapping class group KW - Moduli space of curves KW - Teichmüller space AB - 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 $\\e$. PB - SISSA UR - http://hdl.handle.net/1963/6509 N1 - 21 pages, 2 figures U1 - 6461 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - An improved geometric inequality via vanishing moments, with applications to singular Liouville equations JF - Communications in Mathematical Physics 322, nr.2 (2013): 415-452 Y1 - 2013 A1 - Mauro Bardelloni A1 - Andrea Malchiodi PB - SISSA UR - http://hdl.handle.net/1963/6561 U1 - 6486 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Inversion formulae for the $\romancosh$-weighted Hilbert transform JF - Proc. Amer. Math. Soc. Y1 - 2013 A1 - Marco Bertola A1 - Katsevich, A. A1 - Alexander Tovbis VL - 141 UR - http://dx.doi.org/10.1090/S0002-9939-2013-11642-4 ER - TY - JOUR T1 - KAM theory for the Hamiltonian derivative wave equation JF - Annales Scientifiques de l'Ecole Normale Superieure Y1 - 2013 A1 - Massimiliano Berti A1 - Luca Biasco A1 - Michela Procesi AB -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. © 2013 Société Mathématique de France.

VL - 46 N1 - cited By (since 1996)4 ER - TY - JOUR T1 - Lipschitz Classification of Almost-Riemannian Distances on Compact Oriented Surfaces JF - Journal of Geometric Analysis Y1 - 2013 A1 - Ugo Boscain A1 - Grégoire Charlot A1 - Roberta Ghezzi A1 - Mario Sigalotti AB -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–Carathéodory 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.

VL - 23 UR - https://doi.org/10.1007/s12220-011-9262-4 ER - TY - JOUR T1 - Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations JF - ESAIM: Mathematical Modelling and Numerical Analysis Y1 - 2013 A1 - Cacace, S. A1 - Antonin Chambolle A1 - Antonio DeSimone A1 - Livio Fedeli PB - EDP Sciences VL - 47 ER - TY - RPRT T1 - Minimal partitions and image classification using a gradient-free perimeter approximation Y1 - 2013 A1 - Samuel Amstutz A1 - Nicolas Van Goethem A1 - Antonio André Novotny KW - Image classification, deblurring, optimal partitions, perimeter approximation AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/6976 U1 - 6964 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - THES T1 - Minimality and stability results for a class of free-discontinuity and nonlocal isoperimetric problems Y1 - 2013 A1 - Marco Bonacini KW - free-discontinuity problems PB - SISSA U1 - 7204 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Monads for framed sheaves on Hirzebruch surfaces Y1 - 2013 A1 - Claudio Bartocci A1 - Ugo Bruzzo A1 - Claudio L.S. Rava KW - Monads, framed sheaves, Hirzebruch surfaces AB - 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. U1 - 7292 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - The Monge Problem for Distance Cost in Geodesic Spaces JF - Communications in Mathematical Physics Y1 - 2013 A1 - Stefano Bianchini A1 - Fabio Cavalletti AB -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.

VL - 318 UR - https://doi.org/10.1007/s00220-013-1663-8 ER - TY - JOUR T1 - Multiplicity result for a nonhomogeneous Yamabe type equation involving the Kohn Laplacian JF - Journal of Mathematical Analysis and Applications. Volume 399, Issue 1, 1 March 2013, Pages 333-339 Y1 - 2013 A1 - Ali Maalaoui A1 - Vittorio Martino KW - CR-Yamabe PB - Elsevier UR - http://hdl.handle.net/1963/7374 N1 - The article is composed of 13 pages and is recorded in PDF format U1 - 7422 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae Y1 - 2013 A1 - Giulio Bonelli A1 - Kazunobu Maruyoshi A1 - Alessandro Tanzini A1 - Futoshi Yagi AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/6577 N1 - 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 U1 - 6522 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - A New Quadratic Potential for Scalar Conservation Laws JF - Oberwolfach Reports Y1 - 2013 A1 - Stefano Bianchini A1 - Stefano Modena VL - 29 ER - TY - JOUR T1 - Nonabelian Lie algebroid extensions Y1 - 2013 A1 - Ugo Bruzzo A1 - Igor Mencattini A1 - Pietro Tortella A1 - Vladimir Rubtsov KW - Lie algebroids, nonabelian extensions, spectral sequences AB -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 $d_2$

U1 - 7293 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Noncommutative circle bundles and new Dirac operators JF - Communications in Mathematical Physics. Volume 318, Issue 1, 2013, Pages 111-130 Y1 - 2013 A1 - Ludwik Dabrowski A1 - Andrzej Sitarz KW - Quantum principal bundles AB - 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. PB - Springer UR - http://hdl.handle.net/1963/7384 N1 - This article is composed of 25 pages and is recorded in PDF format U1 - 7432 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - The nonlinear multidomain model: a new formal asymptotic analysis. JF - Geometry Partial Differential Equations – proceedings, CRM Series (15), 2013. Y1 - 2013 A1 - Stefano Amato A1 - Giovanni Bellettini A1 - Maurizio Paolini KW - bidomain model, anisotropic mean curvature, star-shaped combination AB -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.

SN - 8876424724 U1 - 7259 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - A note on KAM theory for quasi-linear and fully nonlinear forced KdV JF - Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 24 (2013), no. 3: 437–450 Y1 - 2013 A1 - P Baldi A1 - Massimiliano Berti A1 - Riccardo Montalto KW - KAM for PDEs AB - 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. PB - European Mathematical Society U1 - 7268 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - A note on non-homogeneous hyperbolic operators with low-regularity coefficients Y1 - 2013 A1 - Ferruccio Colombini A1 - Francesco Fanelli AB -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 $t$.

ER - TY - JOUR T1 - One-dimensional swimmers in viscous fluids: dynamics, controllability, and existence of optimal controls Y1 - 2013 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Marco Morandotti AB -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.

PB - SISSA UR - http://hdl.handle.net/1963/6467 U1 - 6412 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Pairs of nodal solutions for a class of nonlinear problems with one-sided growth conditions JF - Advanced Nonlinear Studies Y1 - 2013 A1 - Alberto Boscaggin A1 - Fabio Zanolin PB - Advanced Nonlinear Studies, Inc. VL - 13 ER - TY - JOUR T1 - Periodic bouncing solutions for nonlinear impact oscillators JF - Advanced Nonlinear Studies Y1 - 2013 A1 - Alessandro Fonda A1 - Andrea Sfecci PB - Advanced Nonlinear Studies, Inc. VL - 13 ER - TY - JOUR T1 - Planar Hamiltonian systems at resonance: the Ahmad–Lazer–Paul condition JF - Nonlinear Differential Equations and Applications NoDEA Y1 - 2013 A1 - Alberto Boscaggin A1 - Maurizio Garrione AB -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–Lazer condition is analyzed, as well.

VL - 20 UR - https://doi.org/10.1007/s00030-012-0181-2 ER - TY - JOUR T1 - Quadratic cohomology Y1 - 2013 A1 - Andrei A. Agrachev AB - 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. PB - SISSA N1 - 24 pages U1 - 6456 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Quasi-periodic solutions with Sobolev regularity of NLS on Td with a multiplicative potential JF - Journal of the European Mathematical Society Y1 - 2013 A1 - Massimiliano Berti A1 - Philippe Bolle AB - We prove the existence of quasi-periodic solutions for Schrödinger 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∞ then the solutions are C∞. 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. © European Mathematical Society 2013. VL - 15 N1 - cited By (since 1996)5 ER - TY - JOUR T1 - A quasistatic evolution model for perfectly plastic plates derived by Γ-convergence JF - Annales de l'Institut Henri Poincare (C) Non Linear Analysis Y1 - 2013 A1 - Elisa Davoli A1 - Maria Giovanna Mora KW - -convergence KW - Perfect plasticity KW - Prandtl–Reuss plasticity KW - Quasistatic evolution KW - Rate-independent processes KW - Thin plates AB -The subject of this paper is the rigorous derivation of a quasistatic evolution model for a linearly elastic–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–Reuss elastoplasticity converge to a quasistatic evolution of a suitable reduced model. In this limiting model the admissible displacements are of Kirchhoff–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.

VL - 30 UR - http://www.sciencedirect.com/science/article/pii/S0294144912001035 ER - TY - JOUR T1 - Reduced basis approximation and a posteriori error estimation for Stokes flows in parametrized geometries: roles of the inf-sup stability constants JF - Numerische Mathematik, 2013 Y1 - 2013 A1 - Gianluigi Rozza A1 - Phuong Huynh A1 - Andrea Manzoni KW - parametrized Stokes equations AB - 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. PB - Springer UR - http://hdl.handle.net/1963/6339 U1 - 6269 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - CHAP T1 - Reduced Basis Approximation for the Structural-Acoustic Design based on Energy Finite Element Analysis (RB-EFEA) T2 - CEMRACS 2013 - Modelling and simulation of complex systems: stochastic and deterministic approaches Y1 - 2013 A1 - Denis Devaud A1 - Gianluigi Rozza JF - CEMRACS 2013 - Modelling and simulation of complex systems: stochastic and deterministic approaches VL - 48 ER - TY - JOUR T1 - Reduced basis method for parametrized elliptic optimal control problems JF - SIAM Journal on Scientific Computing Y1 - 2013 A1 - Federico Negri A1 - Gianluigi Rozza A1 - Andrea Manzoni A1 - Alfio Quarteroni AB - 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. VL - 35 ER - TY - RPRT T1 - A Reduced Computational and Geometrical Framework for Inverse Problems in Haemodynamics Y1 - 2013 A1 - Toni Lassila A1 - Andrea Manzoni A1 - Alfio Quarteroni A1 - Gianluigi Rozza PB - SISSA U1 - 6571 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - RPRT T1 - A reduced-order strategy for solving inverse Bayesian identification problems in physiological flows Y1 - 2013 A1 - Toni Lassila A1 - Andrea Manzoni A1 - Alfio Quarteroni A1 - Gianluigi Rozza PB - SISSA U1 - 6555 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - RPRT T1 - Reduction Strategies for Shape Dependent Inverse Problems in Haemodynamics Y1 - 2013 A1 - Toni Lassila A1 - Andrea Manzoni A1 - Gianluigi Rozza PB - SISSA U1 - 6554 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - Remarks on the Moser–Trudinger inequality JF - Advances in Nonlinear Analysis Y1 - 2013 A1 - Gabriele Mancini A1 - Luca Battaglia AB -We extend the Moser-Trudinger inequality to any Euclidean domain satisfying Poincaré'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.

PB - Advances in Nonlinear Analysis VL - 2 UR - http://edoc.unibas.ch/43974/ IS - 4 N1 - The article is composed of 32 pages inad recorded in PDF format U1 - 34666 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Self-adjoint extensions and stochastic completeness of the Laplace-Beltrami operator on conic and anticonic surfaces Y1 - 2013 A1 - Ugo Boscain A1 - Dario Prandi ER - TY - THES T1 - Semistability and Decorated Bundles Y1 - 2013 A1 - Andrea Pustetto KW - Decorated sheaves, semistability, moduli space, Mehta-Ramanathan, maximal destabilizing subsheaf AB - 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 “enclose” 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. PB - SISSA UR - http://hdl.handle.net/1963/7130 U1 - 7132 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Softly Constrained Films Y1 - 2013 A1 - Luca Giomi AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/6563 N1 - Review article, 21 pages, 16 figures, submitted to Soft Matter U1 - 6518 U2 - Mathematics U4 - 2 U5 - FIS/02 FISICA TEORICA, MODELLI E METODI MATEMATICI ER - TY - THES T1 - Some models of crack growth in brittle materials Y1 - 2013 A1 - Simone Racca KW - Quasi-static crack evolution PB - SISSA U1 - 7205 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Some open problems Y1 - 2013 A1 - Andrei A. Agrachev KW - Geometry AB - We discuss some challenging open problems in the geometric control theory and sub-Riemannian geometry. PB - SISSA UR - http://hdl.handle.net/1963/7070 U1 - 7064 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Some remarks on the viscous approximation of crack growth JF - Discrete Contin. Dyn. Syst. Ser. S Y1 - 2013 A1 - Giuliano Lazzaroni A1 - Rodica Toader KW - Variational models AB -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.

PB - SISSA VL - 6 UR - http://hdl.handle.net/1963/4206 U1 - 3945 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - THES T1 - Some topics on Higgs bundles over projective varieties and their moduli spaces Y1 - 2013 A1 - Alessio Lo Giudice KW - Algebraic Geometry, Moduli spaces, Vector bundles AB - 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. PB - SISSA U1 - 7134 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Spectra of random Hermitian matrices with a small-rank external source: the supercritical and subcritical regimes JF - J. Stat. Phys. Y1 - 2013 A1 - Marco Bertola A1 - Buckingham, R. A1 - Lee, S. Y. A1 - Pierce, V. VL - 153 UR - http://dx.doi.org/10.1007/s10955-013-0845-2 ER - TY - RPRT T1 - The splitting theorem in non-smooth context Y1 - 2013 A1 - Nicola Gigli AB - 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 ‘infinitesimally Hilbertian’ 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. UR - http://preprints.sissa.it/handle/1963/35306 U1 - 35613 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Stabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control JF - IEEE Transactions on Automatic Control. Volume 58, Issue 1, 2013, Article number6228517, Pages 74-85 Y1 - 2013 A1 - Claudio Altafini A1 - Francesco Ticozzi A1 - K. Nishio AB - 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 UR - http://hdl.handle.net/1963/6503 U1 - 6448 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - A stable and adaptive semi-Lagrangian potential model for unsteady and nonlinear ship-wave interactions JF - Engineering Analysis with Boundary Elements, 37(1):128 – 143, 2013. Y1 - 2013 A1 - Andrea Mola A1 - Luca Heltai A1 - Antonio DeSimone KW - Unsteady ship-wave interaction AB -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.

PB - SISSA UR - http://hdl.handle.net/1963/5669 U1 - 5457 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Stable determination of a body immersed in a fluid: the nonlinear stationary case JF - Applicable Analysis Y1 - 2013 A1 - Andrea Ballerini AB -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–Stokes equations, from a single measurement of force and velocity on a portion of the boundary. We obtain an estimate of stability of log–log type.

PB - Taylor & Francis VL - 92 UR - https://doi.org/10.1080/00036811.2011.628173 ER - TY - JOUR T1 - Stochastic optimal robin boundary control problems of advection-dominated elliptic equations JF - SIAM Journal on Numerical Analysis Y1 - 2013 A1 - Peng Chen A1 - Alfio Quarteroni A1 - Gianluigi Rozza AB - 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. VL - 51 ER - TY - JOUR T1 - Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two-matrix model JF - J. Math. Phys. Y1 - 2013 A1 - Marco Bertola A1 - Gekhtman, M. A1 - Szmigielski, J. VL - 54 ER - TY - THES T1 - The structure and regularity of admissible BV solutions to hyperbolic conservation laws in one space dimension Y1 - 2013 A1 - Lei Yu AB - 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: • SBV-like regularity of vanishing viscosity BV solutions to strict hyperbolic systems of conservation laws. • Global structure of admissible BV solutions to strict hyperbolic conservation laws. PB - SISSA U1 - 7210 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Subharmonic solutions for nonlinear second order equations in presence of lower and upper solutions JF - Discrete & Continuous Dynamical Systems - A Y1 - 2013 A1 - Alberto Boscaggin A1 - Fabio Zanolin KW - lower and upper solutions KW - parameter dependent equations KW - Periodic solutions KW - Poincaré-Birkhoff twist theorem KW - subharmonic solutions AB -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.

VL - 33 UR - http://aimsciences.org//article/id/3638a93e-4f3e-4146-a927-3e8a64e6863f ER - TY - RPRT T1 - On Sudakov's type decomposition of transference plans with norm costs Y1 - 2013 A1 - Stefano Bianchini A1 - Sara Daneri PB - SISSA UR - http://hdl.handle.net/1963/7206 U1 - 7234 U2 - Mathematics U4 - -1 ER - TY - RPRT T1 - Symplectic instanton bundles on P3 and 't Hooft instantons Y1 - 2013 A1 - Ugo Bruzzo A1 - Dimitri Markushevich A1 - Alexander Tikhomirov AB - 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 't Hooft instantons. PB - arXiv:1312.5554 [math.AG] UR - http://urania.sissa.it/xmlui/handle/1963/34486 N1 - 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. U1 - 34675 U2 - Mathematics U4 - 1 U5 - MAT/03 ER - TY - THES T1 - Topology of moduli spaces of framed sheaves Y1 - 2013 A1 - Gharchia Abdellaoui KW - Moduli spaces, framed sheaves, instantons PB - SISSA UR - http://hdl.handle.net/1963/7152 U1 - 7158 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - RPRT T1 - On the tritronquée solutions of P$_I^2$ Y1 - 2013 A1 - Tamara Grava A1 - Andrey Kapaev A1 - Christian Klein AB -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.

PB - SISSA U1 - 7282 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Universality for the focusing nonlinear Schrödinger equation at the gradient catastrophe point: rational breathers and poles of the \it Tritronquée solution to Painlevé I JF - Comm. Pure Appl. Math. Y1 - 2013 A1 - Marco Bertola A1 - Alexander Tovbis VL - 66 UR - http://dx.doi.org/10.1002/cpa.21445 ER - TY - JOUR T1 - A variational Analysis of the Toda System on Compact Surfaces JF - Communications on Pure and Applied Mathematics, Volume 66, Issue 3, March 2013, Pages 332-371 Y1 - 2013 A1 - Andrea Malchiodi A1 - David Ruiz AB - 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. PB - Wiley UR - http://hdl.handle.net/1963/6558 N1 - pre-peer version, to appear in Comm. Pure Applied Math U1 - 6489 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - A weighted reduced basis method for elliptic partial differential equations with random input data JF - SIAM Journal on Numerical Analysis Y1 - 2013 A1 - Peng Chen A1 - Alfio Quarteroni A1 - Gianluigi Rozza AB - 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. VL - 51 ER - TY - JOUR T1 - On 2-step, corank 2 nilpotent sub-Riemannian metrics JF - SIAM J. Control Optim., 50 (2012) 559–582 Y1 - 2012 A1 - Davide Barilari A1 - Ugo Boscain A1 - Jean-Paul Gauthier AB - 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. PB - Society for Industrial and Applied Mathematics UR - http://hdl.handle.net/1963/6065 U1 - 5950 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Asymptotics of the s-perimeter as s →0 JF - Discrete Contin. Dyn. Syst. 33, nr.7 (2012): 2777-2790 Y1 - 2012 A1 - Serena Dipierro A1 - Alessio Figalli A1 - Giampiero Palatucci A1 - Enrico Valdinoci AB -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.

PB - American Institute of Mathematical Sciences U1 - 7317 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - On the behaviour of flexible retaining walls under seismic actions JF - Geotechnique, Volume 62, Issue 12, December 2012, Pages 1081-1094 Y1 - 2012 A1 - Riccardo Conti A1 - G.S.P. Madabhushi A1 - Giulia M.B. Viggiani KW - Centrifuge modelling AB - 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. PB - ICE Publishing UR - http://hdl.handle.net/1963/6933 U1 - 6912 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty JF - Mathematical Modelling and Numerical Analysis, in press, 2012-13 Y1 - 2012 A1 - Toni Lassila A1 - Andrea Manzoni A1 - Alfio Quarteroni A1 - Gianluigi Rozza KW - shape optimization AB - 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. PB - Cambridge University Press UR - http://hdl.handle.net/1963/6337 U1 - 6267 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - On a class of vector fields with discontinuity of divide-by-zero type and its applications JF - Journal of dynamical and control systems Y1 - 2012 A1 - Roberta Ghezzi A1 - Alexey O. Remizov AB -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.

PB - Springer VL - 18 IS - 1 U1 - 7038 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - Classical double, R-operators, and negative flows of integrable hierarchies JF - Theoretical and Mathematical Physics. Volume 172, Issue 1, July 2012, Pages 911-931 Y1 - 2012 A1 - Boris Dubrovin A1 - Taras V. Skrypnyk AB - 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–Poisson bracket on g and its extensions. We consider examples of Lie algebras g with the “Adler–Kostant–Symes” 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–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. PB - SISSA UR - http://hdl.handle.net/1963/6468 U1 - 6413 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - A Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group. JF - Journal fur die Reine und Angewandte Mathematik, Issue 671, October 2012, Pages 131-198 Y1 - 2012 A1 - Andrea Malchiodi A1 - Paul Yang A1 - Jih-Hsin Cheng A1 - JennFang Hwang AB - 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 PB - SISSA UR - http://hdl.handle.net/1963/6556 U1 - 6490 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - CHAP T1 - Computing optimal strokes for low reynolds number swimmers T2 - Natural locomotion in fluids and on surfaces : swimming, flying, and sliding / editors Stephen Childress, Anette Hosoi, William W. Schultz, and Z. Jane Wang, editors, Y1 - 2012 A1 - Antonio DeSimone A1 - Luca Heltai A1 - François Alouges A1 - Lefebvre-Lepot Aline KW - Numerical analysis. AB -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.

JF - Natural locomotion in fluids and on surfaces : swimming, flying, and sliding / editors Stephen Childress, Anette Hosoi, William W. Schultz, and Z. Jane Wang, editors, PB - Springer SN - 9781461439967 UR - http://hdl.handle.net/1963/6445 U1 - 6381 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - Concentration on circles for nonlinear Schrödinger–Poisson systems with unbounded potentials vanishing at infinity JF - Communications in Contemporary Mathematics Y1 - 2012 A1 - Bonheure, Denis A1 - Di Cosmo, Jonathan A1 - Mercuri, Carlo AB -The present paper is devoted to weighted nonlinear Schrödinger–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.

PB - World Scientific VL - 14 UR - https://doi.org/10.1142/S0219199712500095 ER - TY - JOUR T1 - Conservation of Geometric Structures for Non-Homogeneous Inviscid Incompressible Fluids JF - Communications in Partial Differential Equations Y1 - 2012 A1 - Francesco Fanelli AB -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 Hölder regularity in the interior of a bounded domain.

PB - Taylor & Francis VL - 37 UR - https://doi.org/10.1080/03605302.2012.698343 ER - TY - JOUR T1 - Convergence of equilibria of thin elastic plates under physical growth conditions for the energy density Y1 - 2012 A1 - Maria Giovanna Mora A1 - Lucia Scardia AB -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 $\det F\to0$.

PB - Elsevier UR - http://hdl.handle.net/1963/3466 N1 - 21 pages U1 - 7112 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - Convex pencils of real quadratic forms JF - Discrete and Computational Geometry, Volume 48, Issue 4, December 2012, Pages 1025-1047 Y1 - 2012 A1 - Antonio Lerario AB - 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). PB - Springer UR - http://hdl.handle.net/1963/7099 N1 - Updated version to be published in DCG ; was published in : Discrete and Computational Geometry, Volume 48, Issue 4, December 2012, Pages 1025-1047 U1 - 7097 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Crawling motility through the analysis of model locomotors: two case studies JF - The European Physical Journal E, Volume 35, Issue 9, September 2012, Article number85 Y1 - 2012 A1 - Antonio DeSimone A1 - Amabile Tatone AB - 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. PB - Springer UR - http://hdl.handle.net/1963/7017 U1 - 7014 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - On the critical behavior in nonlinear evolutionary PDEs with small viscocity JF - Russian Journal of Mathematical Physics. Volume 19, Issue 4, December 2012, Pages 449-460 Y1 - 2012 A1 - Boris Dubrovin A1 - Maria Elaeva AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/6465 U1 - 6409 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Decompositions of large-scale biological systems based on dynamical properties JF - Bioinformatics (Oxford, England). 2012 Jan; 28(1):76-83 Y1 - 2012 A1 - Nicola Soranzo A1 - Fahimeh Ramezani A1 - Giovanni Iacono A1 - Claudio Altafini AB - 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. PB - Oxford University Press UR - http://hdl.handle.net/1963/5226 U1 - 5049 U2 - Physics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Deformed Lorentz symmetry and relative locality in a curved/expanding spacetime JF - Phys. Rev. D 86 (2012) 124035 Y1 - 2012 A1 - Giovanni Amelino-Camelia A1 - Antonino Marciano A1 - Marco Matassa A1 - Giacomo Rosati KW - Doubly special relativity AB - 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. PB - American Physical Society N1 - 12 pages, 5 figures U1 - 6496 U2 - Physics U4 - -1 ER - TY - JOUR T1 - Detection of transcriptional triggers in the dynamics of microbial growth: application to the respiratory-versatile bacterium Shewanella oneidensis JF - Nucleic Acids Research, Volume 40, Issue 15, August 2012, Pages 7132-7149 Y1 - 2012 A1 - Q Beg A1 - Mattia Zampieri A1 - N Klitgord A1 - S Collins A1 - M Serres A1 - Daniel Segrè A1 - Claudio Altafini AB - 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 PB - SISSA UR - http://hdl.handle.net/1963/6506 U1 - 6452 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - A dynamical feedback model for adaptation in the olfactory transduction pathway JF - Biophysical Journal. Volume 102, Issue 12, 20 June 2012, Pages 2677-2686 Y1 - 2012 A1 - Giovanna De Palo A1 - Anna Boccaccio A1 - Andrew Miri A1 - Anna Menini A1 - Claudio Altafini AB - 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. PB - Biophysical Society, Elsevier UR - http://hdl.handle.net/1963/7019 U1 - 7012 U2 - Neuroscience U4 - -1 ER - TY - JOUR T1 - Dynamics of opinion forming in structurally balanced social networks JF - PloS one. 2012 ; 7(6):e38135 Y1 - 2012 A1 - Claudio Altafini AB - 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. PB - PLoS UR - http://hdl.handle.net/1963/6051 U1 - 5942 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Exploring the low-energy landscape of large-scale signed social networks JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. Volume 86, Issue 3, 26 September 2012, Article number036116 Y1 - 2012 A1 - Giuseppe Facchetti A1 - Giovanni Iacono A1 - Claudio Altafini AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/6504 U1 - 6451 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - A formula for Popp\'s volume in sub-Riemannian geometry JF - Analysis and Geometry in Metric Spaces, vol. 1 (2012), pages : 42-57 Y1 - 2012 A1 - Luca Rizzi A1 - Davide Barilari KW - subriemannian, volume, Popp, control AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/6501 N1 - 16 pages, minor revisions U1 - 6446 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Fredholm determinants and pole-free solutions to the noncommutative Painlevé II equation JF - Comm. Math. Phys. Y1 - 2012 A1 - Marco Bertola A1 - Mattia Cafasso VL - 309 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00220-011-1383-x ER - TY - JOUR T1 - Frobenius manifold for the dispersionless Kadomtsev-Petviashvili equation JF - Communications in Mathematical Physics 311 (2012) 557-594 Y1 - 2012 A1 - Andrea Raimondo AB - 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. PB - Springer UR - http://hdl.handle.net/1963/6040 U1 - 5931 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - RPRT T1 - A Fully Coupled Immersed Finite Element Method for Fluid Structure Interaction via the Deal.II Library Y1 - 2012 A1 - Luca Heltai A1 - Saswati Roy A1 - Francesco Costanzo KW - Finite Element Method KW - Immersed Boundary Method KW - Immersed Finite Element Method AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/6255 N1 - 28 pages, 9 figures U1 - 6172 U2 - Mathematics U3 - Functional Analysis and Applications U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - Gamma-convergence and H-convergence of linear elliptic operators JF - Journal de Mathématiques Pures et Appliquées, Available online 12 September 2012 Y1 - 2012 A1 - Nadia Ansini A1 - Gianni Dal Maso A1 - Caterina Ida Zeppieri KW - Linear elliptic operators PB - Elsevier UR - http://hdl.handle.net/1963/5878 U1 - 5746 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Gauge Theories on ALE Space and Super Liouville Correlation Functions JF - Lett. Math. Phys. 101 (2012) 103-124 Y1 - 2012 A1 - Giulio Bonelli A1 - Kazunobu Maruyoshi A1 - Alessandro Tanzini AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/4305 N1 - 21 pages U1 - 4068 U2 - Physics U3 - Elementary Particle Theory U4 - -1 ER - TY - JOUR T1 - A general method for the existence of periodic solutions of differential systems in the plane JF - Journal of Differential Equations Y1 - 2012 A1 - Alessandro Fonda A1 - Andrea Sfecci KW - Nonlinear dynamics KW - Periodic solutions AB -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 “at resonance” are also considered, provided a Landesman–Lazer type of condition is assumed.

VL - 252 UR - http://www.sciencedirect.com/science/article/pii/S0022039611003196 ER - TY - CHAP T1 - Generalized reduced basis methods and n-width estimates for the approximation of the solution manifold of parametric PDEs T2 - Springer, Indam Series, Vol. 4, 2012 Y1 - 2012 A1 - Toni Lassila A1 - Andrea Manzoni A1 - Alfio Quarteroni A1 - Gianluigi Rozza KW - solution manifold AB - 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. JF - Springer, Indam Series, Vol. 4, 2012 PB - Springer UR - http://hdl.handle.net/1963/6340 U1 - 6270 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - On the genus two free energies for semisimple Frobenius manifolds JF - Russian Journal of Mathematical Physics. Volume 19, Issue 3, September 2012, Pages 273-298 Y1 - 2012 A1 - Boris Dubrovin A1 - Si-Qi Liu A1 - Youjin Zhang AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/6464 N1 - 36 pages, 3 figures U1 - 6411 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - On the Hausdorff volume in sub-Riemannian geometry JF - Calculus of Variations and Partial Differential Equations. Volume 43, Issue 3-4, March 2012, Pages 355-388 Y1 - 2012 A1 - Andrei A. Agrachev A1 - Davide Barilari A1 - Ugo Boscain AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/6454 U1 - 6399 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Hybridization in nanostructured DNA monolayers probed by AFM: theory versus experiment JF - Nanoscale. 2012 Mar; 4(5):1734-41 Y1 - 2012 A1 - Alessandro Bosco A1 - Fouzia Bano A1 - Pietro Parisse A1 - Loredana Casalis A1 - Antonio DeSimone A1 - Cristian Micheletti AB - 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. PB - Royal Society of Chemistry U1 - 6998 U2 - Physics U4 - -1 ER - TY - RPRT T1 - Introduction to Riemannian and sub-Riemannian geometry Y1 - 2012 A1 - Andrei A. Agrachev A1 - Davide Barilari A1 - Ugo Boscain PB - SISSA UR - http://hdl.handle.net/1963/5877 U1 - 5747 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - The KdV hierarchy: universality and a Painleve transcendent JF - International Mathematics Research Notices, vol. 22 (2012) , page 5063-5099 Y1 - 2012 A1 - Tom Claeys A1 - Tamara Grava KW - Small-Dispersion limit AB - 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. PB - Oxford University Press UR - http://hdl.handle.net/1963/6921 N1 - This article was published in "International Mathematics Research Notices, vol. 22 (2012) , page 5063-5099 U1 - 6902 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Linear elasticity obtained from finite elasticity by Gamma-convergence under weak coerciveness conditions JF - Ann. Inst. H. Poincare Anal. Non Lineaire Y1 - 2012 A1 - Virginia Agostiniani A1 - Gianni Dal Maso A1 - Antonio DeSimone KW - Nonlinear elasticity AB -The energy functional of linear elasticity is obtained as G-limit of suitable rescalings of the energies of finite elasticity...

PB - Gauthier-Villars;Elsevier VL - 29 UR - http://hdl.handle.net/1963/4267 U1 - 3996 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - On localization in holomorphic equivariant cohomology JF - Central European Journal of Mathematics, Volume 10, Issue 4, August 2012, Pages 1442-1454 Y1 - 2012 A1 - Ugo Bruzzo A1 - Vladimir Rubtsov KW - Lie algebroids AB - 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's localization formulas. PB - Springer UR - http://hdl.handle.net/1963/6584 U1 - 6543 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - On the location of poles for the Ablowitz-Segur family of solutions to the second Painlevé equation JF - Nonlinearity Y1 - 2012 A1 - Marco Bertola VL - 25 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1088/0951-7715/25/4/1179 ER - TY - Generic T1 - Mathematical and numerical modeling of liquid crystal elastomer phase transition and deformation T2 - Materials Research Society Symposium Proceedings. Volume 1403, 2012, Pages 125-130 Y1 - 2012 A1 - Mariarita De Luca A1 - Antonio DeSimone KW - Artificial muscle AB - 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. JF - Materials Research Society Symposium Proceedings. Volume 1403, 2012, Pages 125-130 PB - Cambridge University Press SN - 9781605113807 UR - http://hdl.handle.net/1963/7020 U1 - 7011 U2 - Physics U4 - 1 ER - TY - JOUR T1 - Modeling and control of quantum systems: An introduction JF - IEEE Transactions on Automatic Control. Volume 57, Issue 8, 2012, Article number6189035, Pages 1898-1917 Y1 - 2012 A1 - Claudio Altafini A1 - Francesco Ticozzi AB - 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 PB - Institute of Electrical and Electronics Engineers UR - http://hdl.handle.net/1963/6505 U1 - 6449 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Moduli of symplectic instanton vector bundles of higher rank on projective space $\\mathbbP^3$ JF - Central European Journal of Mathematics 10, nr. 4 (2012) 1232 Y1 - 2012 A1 - Ugo Bruzzo A1 - Dimitri Markushevich A1 - Alexander Tikhomirov AB - 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 $4n(r+1)-r(2r+1)$. PB - SISSA UR - http://hdl.handle.net/1963/4656 N1 - 14 pages U1 - 4406 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Moduli spaces of noncommutative instantons: gauging away noncommutative parameters JF - Quarterly Journal of Mathematics (2012) 63 (1): 41-86 Y1 - 2012 A1 - Simon Brain A1 - Giovanni Landi AB - 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. PB - Oxford University Press UR - http://hdl.handle.net/1963/3777 U1 - 548 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - The Monge problem in Wiener space JF - Calculus of Variations and Partial Differential Equations Y1 - 2012 A1 - Fabio Cavalletti AB -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.

VL - 45 UR - https://doi.org/10.1007/s00526-011-0452-5 ER - TY - JOUR T1 - Nonlinear thin-walled beams with a rectangular cross-section-Part I JF - Math. Models Methods Appl. Sci. 22, 1150016 (2012) Y1 - 2012 A1 - Lorenzo Freddi A1 - Maria Giovanna Mora A1 - Roberto Paroni AB - 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. PB - World Scientific UR - http://hdl.handle.net/1963/4104 U1 - 300 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A nonresonance condition for radial solutions of a nonlinear Neumann elliptic problem JF - Nonlinear Analysis: Theory, Methods & Applications Y1 - 2012 A1 - Andrea Sfecci KW - Neumann problem KW - Nonresonance KW - Radial solutions KW - Time-map AB -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.

VL - 75 UR - http://www.sciencedirect.com/science/article/pii/S0362546X12002659 ER - TY - JOUR T1 - Non-uniqueness results for critical metrics of regularized determinants in four dimensions JF - Communications in Mathematical Physics, Volume 315, Issue 1, September 2012, Pages 1-37 Y1 - 2012 A1 - Matthew Gursky A1 - Andrea Malchiodi AB - 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'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. PB - Springer UR - http://hdl.handle.net/1963/6559 N1 - 35 pages, title changed, added determinant of half-torsion, references added. Comm. Math. Phys., to appear U1 - 6488 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Numerical modelling of installation effects for diaphragm walls in sand JF - Acta Geotechnica, Volume 7, Issue 3, September 2012, Pages 219-237 Y1 - 2012 A1 - Riccardo Conti A1 - Luca de Sanctis A1 - Giulia M.B. Viggiani KW - Constitutive relations AB - 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. PB - Springer UR - http://hdl.handle.net/1963/6934 U1 - 6916 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - Numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions JF - Physica D 241, nr. 23-24 (2012): 2246-2264 Y1 - 2012 A1 - Tamara Grava A1 - Christian Klein KW - Korteweg-de Vries equation AB - 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. PB - Elsevier U1 - 7069 U2 - Physics U4 - -1 ER - TY - JOUR T1 - Ogden-type energies for nematic elastomers JF - International Journal of Non-Linear mechanics Y1 - 2012 A1 - Virginia Agostiniani A1 - Antonio DeSimone KW - Nonlinear elasticity AB -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).

PB - Elsevier VL - 47 IS - 2 U1 - 6971 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - One-signed harmonic solutions and sign-changing subharmonic solutions to scalar second order differential equations JF - Advanced Nonlinear Studies Y1 - 2012 A1 - Alberto Boscaggin PB - Advanced Nonlinear Studies, Inc. VL - 12 ER - TY - JOUR T1 - Optimal Transport with Branching Distance Costs and the Obstacle Problem JF - SIAM Journal on Mathematical Analysis Y1 - 2012 A1 - Fabio Cavalletti VL - 44 UR - https://doi.org/10.1137/100801433 ER - TY - JOUR T1 - Pairs of positive periodic solutions of second order nonlinear equations with indefinite weight JF - Journal of Differential Equations Y1 - 2012 A1 - Alberto Boscaggin A1 - Fabio Zanolin KW - Critical points KW - Necessary conditions KW - Pairs of positive solutions KW - Periodic solutions AB -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.

VL - 252 UR - http://www.sciencedirect.com/science/article/pii/S0022039611003895 ER - TY - JOUR T1 - Periodic solutions of a system of coupled oscillators with one-sided superlinear retraction forces JF - Differential Integral Equations Y1 - 2012 A1 - Alessandro Fonda A1 - Andrea Sfecci PB - Khayyam Publishing, Inc. VL - 25 UR - https://projecteuclid.org:443/euclid.die/1356012248 ER - TY - JOUR T1 - Periodic solutions to superlinear planar Hamiltonian systems JF - Portugaliae Mathematica Y1 - 2012 A1 - Alberto Boscaggin AB -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.

PB - European Mathematical Society Publishing House VL - 69 ER - TY - JOUR T1 - Poles Distribution of PVI Transcendents close to a Critical Point (summer 2011) JF - Physica D: Nonlinear Phenomena, Volume 241, Issue 23-24, 1 December 2012, Pages 2188-2203 Y1 - 2012 A1 - Davide Guzzetti KW - Painleve' equations AB - The distribution of the poles of Painlevé 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. PB - Elsevier UR - http://hdl.handle.net/1963/6526 U1 - 6469 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Positive periodic solutions of second order nonlinear equations with indefinite weight: Multiplicity results and complex dynamics JF - Journal of Differential Equations Y1 - 2012 A1 - Alberto Boscaggin A1 - Fabio Zanolin KW - Complex dynamics KW - Poincaré map KW - Positive periodic solutions KW - Subharmonics AB -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.

VL - 252 UR - http://www.sciencedirect.com/science/article/pii/S0022039611003883 ER - TY - JOUR T1 - Predicting and characterizing selective multiple drug treatments for metabolic diseases and cancer. JF - BMC Systems Biology. 29 August 2012, Page 115 Y1 - 2012 A1 - Giuseppe Facchetti A1 - Claudio Altafini A1 - Mattia Zampieri AB - 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. PB - BioMed Central UR - http://hdl.handle.net/1963/6515 U1 - 6450 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Quasistatic evolution for Cam-Clay plasticity: properties of the viscosity solution JF - Calculus of variations and partial differential equations 44 (2012) 495-541 Y1 - 2012 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Francesco Solombrino AB -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.

PB - Springer UR - http://hdl.handle.net/1963/3900 U1 - 809 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic evolution in non-associative plasticity - the cap models JF - SIAM Journal on Mathematical Analysis 44, nr. 1 (2012) 245-292 Y1 - 2012 A1 - Jean-Francois Babadjian A1 - Gilles A. Francfort A1 - Maria Giovanna Mora KW - Elasto-plasticity AB - 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. PB - SIAM UR - http://hdl.handle.net/1963/4139 U1 - 3879 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - Generic T1 - Reduction strategies for PDE-constrained oprimization problems in Haemodynamics T2 - European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012) J. Eberhardsteiner et.al. (eds.), Vienna, Austria, 10-14 sept. 2012 Y1 - 2012 A1 - Gianluigi Rozza A1 - Andrea Manzoni A1 - Federico Negri KW - inverse problems AB - 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. JF - European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012) J. Eberhardsteiner et.al. (eds.), Vienna, Austria, 10-14 sept. 2012 UR - http://hdl.handle.net/1963/6338 U1 - 6268 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - Resonance at the first eigenvalue for first-order systems in the plane: vanishing Hamiltonians and the Landesman-Lazer condition JF - Differential Integral Equations Y1 - 2012 A1 - Maurizio Garrione PB - Khayyam Publishing, Inc. VL - 25 UR - https://projecteuclid.org:443/euclid.die/1356012676 ER - TY - JOUR T1 - Reverse engineering the euglenoid movement JF - Proceedings of the National Academy of Sciences of the United States of America. Volume 109, Issue 44, 30 October 2012, Pages 17874-17879 Y1 - 2012 A1 - Marino Arroyo A1 - Luca Heltai A1 - Daniel Millán A1 - Antonio DeSimone KW - microswimmers AB - 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. UR - http://hdl.handle.net/1963/6444 U1 - 6380 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - A Review on The Sixth Painlevé Equation Y1 - 2012 A1 - Davide Guzzetti KW - Painlevé equation AB -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.

PB - SISSA UR - http://hdl.handle.net/1963/6525 N1 - 31 pages, 10 figures U1 - 6470 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Riemann–Hilbert approach to multi-time processes: The Airy and the Pearcey cases JF - Physica D: Nonlinear Phenomena Y1 - 2012 A1 - Marco Bertola A1 - Mattia Cafasso KW - Integrable kernels VL - 241 UR - http://www.sciencedirect.com/science/article/pii/S0167278912000115 N1 - Integrable Systems in Pure and Applied Mathematics ER - TY - JOUR T1 - On robust Lie-algebraic stability conditions for switched linear systems JF - Systems and Control Letters. Volume 61, Issue 2, February 2012, Pages 347-353 Y1 - 2012 A1 - Andrei A. Agrachev A1 - Yurij Baryshnikov A1 - Daniel Liberzon AB - 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. UR - http://hdl.handle.net/1963/6455 U1 - 6400 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - SBV regularity for genuinely nonlinear, strictly hyperbolic systems of conservation laws in one space dimension JF - Communications in Mathematical Physics 313 (2012) 1-33 Y1 - 2012 A1 - Stefano Bianchini A1 - Laura Caravenna PB - Springer UR - http://hdl.handle.net/1963/4091 U1 - 313 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - SBV regularity for Hamilton-Jacobi equations with Hamiltonian depending on (t,x) JF - Siam Journal on Mathematical Analysis Y1 - 2012 A1 - Stefano Bianchini A1 - Daniela Tonon PB - SISSA VL - 44 UR - http://hdl.handle.net/20.500.11767/14066 IS - 3 U1 - 3890 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - SBV regularity of genuinely nonlinear hyperbolic systems of conservation laws in one space dimension JF - Acta Mathematica Scientia, Volume 32, Issue 1, January 2012, Pages 380-388 Y1 - 2012 A1 - Stefano Bianchini KW - Hyperbolic systems AB - 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 PB - Elsevier UR - http://hdl.handle.net/1963/6535 U1 - 6510 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - SBV-like regularity for general hyperbolic systems of conservation laws in one space dimension JF - Rend. Istit. Mat. Univ. Trieste Y1 - 2012 A1 - Stefano Bianchini A1 - Lei Yu VL - 44 ER - TY - JOUR T1 - SBV-like regularity for Hamilton-Jacobi equations with a convex Hamiltonian JF - Journal of Mathematical Analysis and Applications Y1 - 2012 A1 - Stefano Bianchini A1 - Daniela Tonon PB - SISSA VL - 391 UR - http://hdl.handle.net/20.500.11767/13909 IS - 1 U1 - 4352 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Second order approximations of quasistatic evolution problems in finite dimension JF - Discrete & Continuous Dynamical Systems - A Y1 - 2012 A1 - Virginia Agostiniani KW - discrete approximations KW - perturbation methods KW - saddle-node bifurcation KW - Singular perturbations KW - vanishing viscosity AB -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.

VL - 32 UR - http://aimsciences.org//article/id/560b82d9-f289-498a-a619-a4b132aaf9f8 ER - TY - JOUR T1 - Self-propelled micro-swimmers in a Brinkman fluid JF - Journal of Biological Dynamics Y1 - 2012 A1 - Marco Morandotti AB -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.

PB - Taylor & Francis VL - 6 UR - https://doi.org/10.1080/17513758.2011.611260 N1 - PMID: 22873677 ER - TY - JOUR T1 - Simulation-based uncertainty quantification of human arterial network hemodynamics JF - International Journal Numerical Methods Biomedical Engineering Y1 - 2012 A1 - Peng Chen A1 - Alfio Quarteroni A1 - Gianluigi Rozza KW - uncertainty quantification, mathematical modelling of the cardiovascular system, fluid-structure interaction AB - 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. PB - Wiley U1 - 6467 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - Sobolev quasi-periodic solutions of multidimensional wave equations with a multiplicative potential JF - Nonlinearity Y1 - 2012 A1 - Massimiliano Berti A1 - Philippe Bolle AB - 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 'separation properties' of the small divisors assuming weaker non-resonance conditions than in [11]. © 2012 IOP Publishing Ltd. VL - 25 N1 - cited By (since 1996)3 ER - TY - JOUR T1 - Solving the Sixth Painlevé Equation: Towards the Classification of all the Critical Behaviors and the Connection Formulae JF - Int Math Res Notices (2012) 2012 (6): 1352-1413 Y1 - 2012 A1 - Davide Guzzetti AB - 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. PB - Oxford University Press UR - http://hdl.handle.net/1963/6093 N1 - 53 pages, 2 figures U1 - 5979 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Some applications of the SBV Regularity Theorem for entropy solutions of 1D scalar conservation laws to ConvectionTheory and sticky particles JF - Riv. Mat. Univ. Parma Y1 - 2012 A1 - Daniela Tonon AB -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.

VL - 3 UR - https://hal.archives-ouvertes.fr/hal-00918409 ER - TY - THES T1 - Some aspects of spinors – classical and noncommutative Y1 - 2012 A1 - Giacomo Dossena PB - SISSA UR - http://hdl.handle.net/1963/6317 U1 - 6218 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Some remarks on quantum mechanics JF - International Journal of Geometric Methods in Modern Physics, Volume 9, Issue 2, March 2012, Article number1260018 Y1 - 2012 A1 - Gianfausto Dell'Antonio KW - Quantum mechanics AB - 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. PB - World Scientific Publishing UR - http://hdl.handle.net/1963/7018 U1 - 7013 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Spectra of random Hermitian matrices with a small-rank external source: the critical and near-critical regimes JF - J. Stat. Phys. Y1 - 2012 A1 - Marco Bertola A1 - Buckingham, R. A1 - Lee, S. Y. A1 - Pierce, V. VL - 146 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1007/s10955-011-0409-2 ER - TY - JOUR T1 - Stability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions JF - Rev. Math. Phys. 24 (2012), 1250017 Y1 - 2012 A1 - Michele Correggi A1 - Gianfausto Dell'Antonio A1 - Domenico Finco A1 - Alessandro Michelangeli A1 - Alessandro Teta AB - 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. PB - World Scientific UR - http://hdl.handle.net/1963/6069 U1 - 5955 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - CONF T1 - A stable semi-lagrangian potential method for the simulation of ship interaction with unsteady and nonlinear waves T2 - 17th Int. Conf. Ships Shipp. Res. Y1 - 2012 A1 - Andrea Mola A1 - Luca Heltai A1 - Antonio DeSimone JF - 17th Int. Conf. Ships Shipp. Res. ER - TY - JOUR T1 - Sub-Riemannian structures on 3D Lie groups JF - Journal of Dynamical and Control Systems. Volume 18, Issue 1, January 2012, Pages 21-44 Y1 - 2012 A1 - Andrei A. Agrachev A1 - Davide Barilari AB -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.

PB - SISSA UR - http://hdl.handle.net/1963/6453 U1 - 6397 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Systems of Quadratic Inequalities JF - Proceedings of the London Mathematical Society, Volume 105, Issue 3, September 2012, Pages 622-660 Y1 - 2012 A1 - Andrei A. Agrachev A1 - Antonio Lerario AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/7072 U1 - 7066 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Tabulation of Painlevé 6 transcendents JF - Nonlinearity, Volume 25, Issue 12, December 2012, Pages 3235-3276 Y1 - 2012 A1 - Davide Guzzetti AB - The critical and asymptotic behaviors of solutions of the sixth Painlev'e equation PVI, obtained in the framework of the monodromy preserving deformation method, and their explicit parametrization in terms of monodromy data, are tabulated. PB - IOP Publishing UR - http://hdl.handle.net/1963/6520 N1 - 30 pages, 1 figure; this article was published in "Nonlinearity" in 2012 U1 - 6471 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Thermodynamic phase transitions and shock singularities JF - Proc. R. Soc. A 8 March 2012 vol. 468 no. 2139 701-719 Y1 - 2012 A1 - Giuseppe De Nittis A1 - Antonio Moro AB - 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. PB - The Royal Society UR - http://hdl.handle.net/1963/6090 U1 - 5978 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - RPRT T1 - Topological sensitivity analysis for high order elliptic operators Y1 - 2012 A1 - Samuel Amstutz A1 - Antonio André Novotny A1 - Nicolas Van Goethem KW - Topological derivative, Elliptic operators, Polarization tensor AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/6343 U1 - 6272 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Variational implementation of immersed finite element methods JF - Computer Methods in Applied Mechanics and Engineering. Volume 229-232, 1 July 2012, Pages 110-127 Y1 - 2012 A1 - Luca Heltai A1 - Francesco Costanzo KW - Turbulent flow AB -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.

PB - Elsevier UR - http://hdl.handle.net/1963/6462 N1 - 42 pages, 5 figures, Revision 1 U1 - 6389 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Vertices, vortices & interacting surface operators JF - JHEP 06(2012)178 Y1 - 2012 A1 - Giulio Bonelli A1 - Alessandro Tanzini A1 - Zhao Jian AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/4134 N1 - 22 pages, 4 figures U1 - 3874 U2 - Physics U3 - Elementary Particle Theory U4 - -1 ER - TY - JOUR T1 - A Viscosity-driven crack evolution JF - Advances in Calculus of Variations 5 (2012) 433-483 Y1 - 2012 A1 - Simone Racca AB -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’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.

PB - SISSA UR - http://hdl.handle.net/1963/5130 U1 - 4944 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Weighted barycentric sets and singular Liouville equations on compact surfaces JF - Journal of Functional Analysis 262 (2012) 409-450 Y1 - 2012 A1 - Alessandro Carlotto A1 - Andrea Malchiodi AB - 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]). PB - Elsevier UR - http://hdl.handle.net/1963/5218 U1 - 5040 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Wild quiver gauge theories JF - JHEP 02(2012)031 Y1 - 2012 A1 - Giulio Bonelli A1 - Kazunobu Maruyoshi A1 - Alessandro Tanzini AB -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.

PB - SISSA UR - http://hdl.handle.net/1963/5184 N1 - 34 pages U1 - 4999 U2 - Physics U3 - Elementary Particle Theory U4 - -1 ER - TY - JOUR T1 - Adaptation as a genome-wide autoregulatory principle in the stress response of yeast. JF - IET systems biology. 2011 Jul; 5(4):269-79 Y1 - 2011 A1 - F Eduati A1 - B Di Camillo A1 - G Toffolo A1 - Claudio Altafini A1 - Giovanna De Palo A1 - Mattia Zampieri AB - 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. PB - The Institution of Engineering and Technology UR - http://hdl.handle.net/1963/5106 U1 - 4922 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - An asymptotic reduction of a Painlevé VI equation to a Painlevé III JF - J.Phys.A: Math.Theor. 44 (2011) 215203 Y1 - 2011 A1 - Davide Guzzetti AB - 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. PB - IOP Publishing UR - http://hdl.handle.net/1963/5124 U1 - 4940 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Axial symmetry of some steady state solutions to nonlinear Schrödinger equations JF - Proc. Amer. Math. Soc. 139 (2011), 1023-1032 Y1 - 2011 A1 - Changfeng Gui A1 - Andrea Malchiodi A1 - Haoyuan Xu A1 - Paul Yang KW - Nonlinear Schrödinger equation AB - 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. PB - American Mathematical Society UR - http://hdl.handle.net/1963/4100 U1 - 304 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Bishop and Laplacian Comparison Theorems on Three Dimensional Contact Subriemannian Manifolds with Symmetry Y1 - 2011 A1 - Andrei A. Agrachev A1 - Paul Lee AB - We prove a Bishop volume comparison theorem and a Laplacian comparison\r\ntheorem for three dimensional contact subriemannian manifolds with symmetry. PB - SISSA UR - http://hdl.handle.net/1963/6508 N1 - 25 pages U1 - 6455 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Boutroux curves with external field: equilibrium measures without a variational problem JF - Anal. Math. Phys. Y1 - 2011 A1 - Marco Bertola VL - 1 UR - http://dx.doi.org/10.1007/s13324-011-0012-3 ER - TY - JOUR T1 - Branching of Cantor Manifolds of Elliptic Tori and Applications to PDEs JF - Communications in Mathematical Physics Y1 - 2011 A1 - Massimiliano Berti A1 - Luca Biasco AB - 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. © 2011 Springer-Verlag. VL - 305 N1 - cited By (since 1996)8 ER - TY - JOUR T1 - A class of existence results for the singular Liouville equation JF - Comptes Rendus Mathematique 349 (2011) 161-166 Y1 - 2011 A1 - Alessandro Carlotto A1 - Andrea Malchiodi AB - 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–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. PB - Elsevier UR - http://hdl.handle.net/1963/5793 U1 - 5648 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Cluster solutions for the Schrödinger-Poisson-Slater problem around a local minimum of the potential JF - Rev. Mat. Iberoamericana Y1 - 2011 A1 - David Ruiz A1 - Giusi Vaira PB - Real Sociedad Matemática Española VL - 27 UR - https://projecteuclid.org:443/euclid.rmi/1296828834 ER - TY - RPRT T1 - Compactness by maximality Y1 - 2011 A1 - Sandro Zagatti AB - 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 $a$. UR - http://preprints.sissa.it/handle/1963/35317 U1 - 35626 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Computing global structural balance in large-scale signed social networks. JF - Proceedings of the National Academy of Sciences of the United States of America. Volume 108, Issue 52, 27 December 2011, Pages 20953-20958 Y1 - 2011 A1 - Giuseppe Facchetti A1 - Giovanni Iacono A1 - Claudio Altafini KW - Combinatorial optimization AB - 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.\\\" PB - National Academy of Sciences UR - http://hdl.handle.net/1963/6426 N1 - Free fulltext article in Pubmed Central U1 - 6362 U2 - Physics U4 - -1 ER - TY - JOUR T1 - Concentration of solutions for a singularly perturbed Neumann problem in non-smooth domains JF - Annales de l'I.H.P. Analyse non linéaire Y1 - 2011 A1 - Serena Dipierro PB - Elsevier VL - 28 UR - http://www.numdam.org/item/AIHPC_2011__28_1_107_0 ER - TY - JOUR T1 - Cones of divisors of blow-ups of projective spaces JF - Le Matematiche (Catania), volume 66, Issue no.2, (2011), pages : 153-187 Y1 - 2011 A1 - Alessio Lo Giudice A1 - Salvatore Cacciola A1 - M. Donten-Bury A1 - O. Dumitrescu A1 - J. Park KW - Mori dream space AB - 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. PB - Università degli Studi di Catania. Dipartimento di matematica UR - http://hdl.handle.net/1963/6613 U1 - 6462 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Covered by lines and Conic connected varieties JF - Le Matematiche 66 (2011) 137-151 Y1 - 2011 A1 - Simone Marchesi A1 - Alex Massarenti A1 - Saeed Tafazolian AB - 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. PB - Universita\\\' di Catania, Dipartimento di Matematica e Informatica UR - http://hdl.handle.net/1963/5788 U1 - 5641 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Crack growth with non-interpenetration : a simplified proof for the pure Neumann problem JF - Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1219-1231 Y1 - 2011 A1 - Gianni Dal Maso A1 - Giuliano Lazzaroni AB - 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. PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/3801 U1 - 526 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Crepant resolutions of weighted projective spaces and quantum deformations JF - 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) Y1 - 2011 A1 - Samuel Boissiere A1 - Etienne Mann A1 - Fabio Perroni AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/6514 N1 - 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) U1 - 6463 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - RPRT T1 - Critical points of the Moser-Trudinger functional Y1 - 2011 A1 - Francesca De Marchis A1 - Andrea Malchiodi A1 - Luca Martinazzi KW - Moser-Trudinger inequality PB - SISSA UR - http://hdl.handle.net/1963/4592 U1 - 4353 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Cytoskeletal actin networks in motile cells are critically self-organized systems synchronized by mechanical interactions JF - PNAS 108 (2011) 13978 Y1 - 2011 A1 - Luca Cardamone A1 - Alessandro Laio A1 - Rajesh Shahapure A1 - Antonio DeSimone PB - National Academy of Sciences UR - http://hdl.handle.net/1963/4358 U1 - 4066 U2 - Physics U3 - Functional Analysis and Applications U4 - -1 ER - TY - RPRT T1 - D-branes, surface operators, and ADHM quiver representations Y1 - 2011 A1 - Ugo Bruzzo A1 - Duiliu-Emanuel Diaconescu A1 - M. Yardim A1 - G. Pan A1 - Yi Zhang A1 - Chuang Wu-yen AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/4133 N1 - 45 pages, v2: minor corrections U1 - 3873 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - A Decomposition Theorem for BV functions JF - Communications on Pure and Applied Analysis Y1 - 2011 A1 - Stefano Bianchini A1 - Daniela Tonon PB - American Institute of Mathematical Sciences VL - 10 UR - http://hdl.handle.net/20.500.11767/14599 IS - 6 U1 - 693 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Degenerate KAM theory for partial differential equations JF - Journal of Differential Equations Y1 - 2011 A1 - Dario Bambusi A1 - Massimiliano Berti A1 - Elena Magistrelli AB - 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 Rüssmann type and an asymptotic behavior. An application to nonlinear wave equations is given. © 2010 Elsevier Inc. VL - 250 N1 - cited By (since 1996)3 ER - TY - THES T1 - Dimensional Reduction and Approximation of Measures and Weakly Differentiable Homeomorphisms Y1 - 2011 A1 - Sara Daneri AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/5348 U1 - 5178 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Double resonance with Landesman–Lazer conditions for planar systems of ordinary differential equations JF - Journal of Differential Equations Y1 - 2011 A1 - Alessandro Fonda A1 - Maurizio Garrione KW - Double resonance KW - Landesman–Lazer conditions KW - Nonlinear planar systems AB -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–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's results in Fabry (1995) [10], for scalar equations with double resonance with respect to the Dancer–Fučik spectrum.

VL - 250 UR - http://www.sciencedirect.com/science/article/pii/S0022039610002901 ER - TY - JOUR T1 - Embedding theorems and existence results for nonlinear Schrödinger–Poisson systems with unbounded and vanishing potentials JF - Journal of Differential Equations Y1 - 2011 A1 - Bonheure, Denis A1 - Mercuri, Carlo AB -Motivated by existence results for positive solutions of non-autonomous nonlinear Schrödinger–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.

PB - Elsevier VL - 251 UR - https://doi.org/10.1016/j.jde.2011.04.010 ER - TY - JOUR T1 - Energy release rate and stress intensity factor in antiplane elasticity JF - Journal de Mathematiques Pures et Appliquees 95 (2011) 565-584 Y1 - 2011 A1 - Giuliano Lazzaroni A1 - Rodica Toader AB - 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. PB - Elsevier UR - http://hdl.handle.net/1963/3780 U1 - 546 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Ennio De Giorgi and Γ-convergence JF - Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1017-1021 Y1 - 2011 A1 - Gianni Dal Maso AB - 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. PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/5308 U1 - 5138 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - An Estimate on the Flow Generated by Monotone Operators JF - Communications in Partial Differential Equations 36 (2011) 777-796 Y1 - 2011 A1 - Stefano Bianchini A1 - Matteo Gloyer PB - Taylor & Francis UR - http://hdl.handle.net/1963/3646 U1 - 658 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - An Existence and Uniqueness Result for the Motion of Self-Propelled Microswimmers JF - SIAM J. Math. Anal. Y1 - 2011 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Marco Morandotti AB -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.

PB - Society for Industrial and Applied Mathematics VL - 43 UR - http://hdl.handle.net/1963/3894 U1 - 815 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence for wave equations on domains with arbitrary growing cracks JF - Rend. Lincei Mat. Appl. 22 (2011) 387-408 Y1 - 2011 A1 - Gianni Dal Maso A1 - Cristopher J. Larsen KW - Wave equation AB - 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. PB - European Mathematical Society UR - http://hdl.handle.net/1963/4284 U1 - 4015 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Fracture and plastic models as Gamma-limits of damage models under different regimes JF - Advances in Calculus of Variations., to appear. Y1 - 2011 A1 - Flaviana Iurlano AB -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.

PB - Walter de Gruyter UR - http://hdl.handle.net/1963/5069 U1 - 4883 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Gamma-convergence of energies for nematic elastomers in the small strain limit JF - Continuum. Mech. Therm. Y1 - 2011 A1 - Virginia Agostiniani A1 - Antonio DeSimone KW - Liquid crystals AB -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.

PB - Springer VL - 23 UR - http://hdl.handle.net/1963/4141 U1 - 3882 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Generalised functions of bounded deformation JF - J. Eur. Math. Soc. (JEMS), to appear Y1 - 2011 A1 - Gianni Dal Maso KW - free discontinuity problems, special functions of bounded deformation, jump set, rec- tifiability, slicing, approximate differentiability AB -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.

PB - SISSA UR - http://hdl.handle.net/1963/6374 U1 - 6309 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Generalized matrix models and AGT correspondence at all genera JF - JHEP, Volume 2011, Issue 7, 2011, Article number055 Y1 - 2011 A1 - Giulio Bonelli A1 - Kazunobu Maruyoshi A1 - Alessandro Tanzini A1 - Futoshi Yagib AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/6568 N1 - This version is published in : Journal of High Energy Physics, Volume 2011, Issue 7, 2011, Article number055 U1 - 6530 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Generalized Ricci Curvature Bounds for Three Dimensional Contact Subriemannian manifolds Y1 - 2011 A1 - Andrei A. Agrachev A1 - Paul Lee PB - SISSA UR - http://hdl.handle.net/1963/6507 N1 - This is a revised extended version that contains new results. U1 - 6454 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - The geometry of Maximum Principle JF - Proceedings of the Steklov Institute of mathematics. vol. 273 (2011), page: 5-27 ; ISSN: 0081-5438 Y1 - 2011 A1 - Andrei A. Agrachev A1 - Revaz Gamkrelidze AB - An invariant formulation of the maximum principle in optimal control is presented, and some second-order invariants are discussed. UR - http://hdl.handle.net/1963/6456 U1 - 6401 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Holomorphic Cartan geometry on manifolds with numerically effective tangent bundle JF - Differential Geometry and its Applications 29 (2011) 147-153 Y1 - 2011 A1 - Indranil Biswas A1 - Ugo Bruzzo PB - Elsevier UR - http://hdl.handle.net/1963/3830 U1 - 497 U2 - Mathematics U3 - Mathematical Physics ER - TY - THES T1 - Homology invariants of quadratic maps Y1 - 2011 A1 - Antonio Lerario AB - 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... PB - SISSA UR - http://hdl.handle.net/1963/6245 U1 - 6145 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Infinite-dimensional Frobenius manifolds for 2 + 1 integrable systems JF - Matematische Annalen 349 (2011) 75-115 Y1 - 2011 A1 - Guido Carlet A1 - Boris Dubrovin A1 - Luca Philippe Mertens AB - 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. PB - Springer UR - http://hdl.handle.net/1963/3584 U1 - 716 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Infinitely many positive solutions for a Schrödinger–Poisson system JF - Nonlinear Analysis: Theory, Methods & Applications Y1 - 2011 A1 - Pietro d’Avenia A1 - Alessio Pomponio A1 - Giusi Vaira KW - Non-autonomous Schrödinger–Poisson system KW - Perturbation method AB -We are interested in the existence of infinitely many positive solutions of the Schrödinger–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

VL - 74 UR - http://www.sciencedirect.com/science/article/pii/S0362546X11003518 ER - TY - RPRT T1 - Instantons on ALE spaces and Super Liouville Conformal Field Theories Y1 - 2011 A1 - Giulio Bonelli A1 - Kazunobu Maruyoshi A1 - Alessandro Tanzini AB - 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). PB - SISSA UR - http://hdl.handle.net/1963/4262 N1 - 10 pages U1 - 3987 U2 - Physics U3 - Elementary Particle Theory U4 - -1 ER - TY - JOUR T1 - An Integro-Extremization Approach for Non Coercive and Evolution Hamilton-Jacobi Equations JF - Journal of Convex Analysis 18 (2011) 1141-1170 Y1 - 2011 A1 - Sandro Zagatti AB - 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 $F$. PB - Heldermann Verlag UR - http://hdl.handle.net/1963/5538 U1 - 5375 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Invariant manifolds for a singular ordinary differential equation JF - Journal of Differential Equations 250 (2011) 1788-1827 Y1 - 2011 A1 - Stefano Bianchini A1 - Laura Spinolo PB - Elsevier UR - http://hdl.handle.net/1963/2554 U1 - 1565 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Invariants, volumes and heat kernels in sub-Riemannian geometry Y1 - 2011 A1 - Davide Barilari KW - Sub-Riemannian geometry AB - 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]). PB - SISSA UR - http://hdl.handle.net/1963/6124 U1 - 6005 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Large Time Existence for Thin Vibrating Plates JF - Communication in Partial Differential Equations 36 (2011) 2062-2102 Y1 - 2011 A1 - Helmut Abels A1 - Maria Giovanna Mora A1 - Stefan Müller AB - 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. PB - Taylor & Francis UR - http://hdl.handle.net/1963/3755 U1 - 562 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Linearly degenerate Hamiltonian PDEs and a new class of solutions to the WDVV associativity equations JF - Functional Analysis and Its Applications. Volume 45, Issue 4, December 2011, Pages 278-290 Y1 - 2011 A1 - Boris Dubrovin A1 - M.V. Pavlov A1 - Sergei A. Zykov KW - Frobenius manifold AB - 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. PB - Springer UR - http://hdl.handle.net/1963/6430 U1 - 6367 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - The Liouville side of the vortex JF - JHEP 09(2011)096 Y1 - 2011 A1 - Giulio Bonelli A1 - Alessandro Tanzini A1 - Jian Zhao AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/4304 N1 - 25pages,11figures U1 - 4019 U2 - Physics U3 - Elementary Particle Theory U4 - -1 ER - TY - JOUR T1 - The matching property of infinitesimal isometries on elliptic surfaces and elasticity on thin shells JF - Archive for Rational Mechanics and Analysis 200 (2011) 1023-1050 Y1 - 2011 A1 - Marta Lewicka A1 - Maria Giovanna Mora A1 - Mohammad Reza Pakzad AB - 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. PB - Springer UR - http://hdl.handle.net/1963/3392 U1 - 940 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Metastable equilibria of capillary drops on solid surfaces: a phase field approach JF - Continuum Mechanics and Thermodynamics Y1 - 2011 A1 - Livio Fedeli A1 - Turco, Alessandro A1 - Antonio DeSimone AB -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–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.

VL - 23 UR - https://doi.org/10.1007/s00161-011-0189-6 ER - TY - JOUR T1 - A MODEL FOR CRACK PROPAGATION BASED ON VISCOUS APPROXIMATION JF - {MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES} Y1 - 2011 A1 - Giuliano Lazzaroni A1 - Rodica Toader KW - Brittle fracture KW - Crack propagation KW - energy derivative KW - energy release rate KW - free-discontinuity problems KW - Griffith's criterion KW - local minimizers KW - stress intensity factor} KW - vanishing viscosity KW - {Variational models AB -{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.}

PB - {WORLD SCIENTIFIC PUBL CO PTE LTD} CY - {5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE} VL - {21} ER - TY - JOUR T1 - Moduli of framed sheaves on projective surfaces JF - Doc. Math. 16 (2011) 399-410 Y1 - 2011 A1 - Ugo Bruzzo A1 - Dimitri Markushevich AB - 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. PB - Documenta Mathematica UR - http://hdl.handle.net/1963/5126 U1 - 4942 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - CONF T1 - The Monge Problem in Geodesic Spaces T2 - Nonlinear Conservation Laws and Applications Y1 - 2011 A1 - Stefano Bianchini A1 - Fabio Cavalletti ED - Alberto Bressan ED - Chen, Gui-Qiang G. ED - Marta Lewicka ED - Wang, Dehua AB -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.

JF - Nonlinear Conservation Laws and Applications PB - Springer US CY - Boston, MA SN - 978-1-4419-9554-4 ER - TY - JOUR T1 - Multi-physics modelling and sensitivity analysis of olympic rowing boat dynamics JF - Sports Engineering Y1 - 2011 A1 - Andrea Mola A1 - Mehdi Ghommem A1 - Muhammad R. Hajj PB - Springer Nature VL - 14 UR - https://doi.org/10.1007/s12283-011-0075-2 ER - TY - JOUR T1 - Multiplicity of solutions for a mean field equation on compact surfaces JF - Boll. Unione Mat. Ital.(9) Y1 - 2011 A1 - Francesca De Marchis AB -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.

VL - 4 ER - TY - JOUR T1 - New improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces JF - Geometric and Functional Analysis 21 (2011) 1196-1217 Y1 - 2011 A1 - Andrea Malchiodi A1 - David Ruiz AB - 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. PB - Springer UR - http://hdl.handle.net/1963/4099 U1 - 305 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Nonlinear resonance: a comparison between Landesman-Lazer and Ahmad-Lazer-Paul conditions JF - Advanced Nonlinear Studies Y1 - 2011 A1 - Alessandro Fonda A1 - Maurizio Garrione AB -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.

PB - Advanced Nonlinear Studies, Inc. VL - 11 ER - TY - RPRT T1 - Nonlinear thin-walled beams with a rectangular cross-section - Part II Y1 - 2011 A1 - Lorenzo Freddi A1 - Maria Giovanna Mora A1 - Roberto Paroni KW - Thin-walled cross-section beams AB - 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.. PB - SISSA UR - http://hdl.handle.net/1963/4169 U1 - 3891 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Nonlinear wave and Schrödinger equations on compact Lie groups and homogeneous spaces JF - Duke Mathematical Journal Y1 - 2011 A1 - Massimiliano Berti A1 - Michela Procesi AB - 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¨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. VL - 159 IS - 3 ER - TY - JOUR T1 - A note on a superlinear indefinite Neumann problem with multiple positive solutions JF - Journal of Mathematical Analysis and Applications Y1 - 2011 A1 - Alberto Boscaggin KW - Indefinite weight KW - Nonlinear boundary value problems KW - positive solutions KW - Shooting method AB -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.

VL - 377 UR - http://www.sciencedirect.com/science/article/pii/S0022247X10008796 ER - TY - JOUR T1 - On the number of eigenvalues of a model operator related to a system of three particles on lattices JF - J. Phys. A 44 (2011) 315302 Y1 - 2011 A1 - Gianfausto Dell'Antonio A1 - Zahriddin I. Muminov A1 - Y.M. Shermatova PB - IOP Publishing UR - http://hdl.handle.net/1963/5496 U1 - 5340 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Numerical Strategies for Stroke Optimization of Axisymmetric Microswimmers JF - Mathematical Models and Methods in Applied Sciences 21 (2011) 361-387 Y1 - 2011 A1 - François Alouges A1 - Antonio DeSimone A1 - Luca Heltai KW - Optimal swimming AB - 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. PB - World Scientific UR - http://hdl.handle.net/1963/3657 U1 - 648 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Numerical Study of breakup in generalized Korteweg-de Vries and Kawahara equations JF - SIAM J. Appl. Math. 71 (2011) 983-1008 Y1 - 2011 A1 - Boris Dubrovin A1 - Tamara Grava A1 - Christian Klein AB - This article is concerned with a conjecture in [B. Dubrovin, Comm. Math. Phys., 267 (2006), pp. 117–139] 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 Painlevé-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. PB - SIAM UR - http://hdl.handle.net/1963/4951 U1 - 4732 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Osservazioni sui teoremi di inversione globale JF - Rendiconti Lincei - Matematica e Applicazioni 22 (2011) 3-15 Y1 - 2011 A1 - Antonio Ambrosetti AB - Some global inversion theorems with applications to semilinear elliptic equation are discussed. PB - European Mathematical Society UR - http://hdl.handle.net/1963/4068 U1 - 334 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - A planar bi-Lipschitz extension Theorem Y1 - 2011 A1 - Sara Daneri A1 - Aldo Pratelli UR - http://arxiv.org/abs/1110.6124 ER - TY - JOUR T1 - Planar loops with prescribed curvature: existence, multiplicity and uniqueness results JF - Proceedings of the American Mathematical Society 139 (2011) 4445-4459 Y1 - 2011 A1 - Roberta Musina KW - Plane curves PB - American Mathematical Society UR - http://hdl.handle.net/1963/3842 U1 - 867 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Poincaré covariance and κ-Minkowski spacetime JF - Physics Letters A 375 (2011) 3496-3498 Y1 - 2011 A1 - Ludwik Dabrowski A1 - Gherardo Piacitelli AB - A fully Poincaré covariant model is constructed out of the k-Minkowski spacetime. Covariance is implemented by a unitary representation of the Poincaré group, and thus complies with the original Wigner approach to quantum symmetries. This provides yet another example (besides the DFR model), where Poincaré covariance is realised á 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 \\\"Poincaré covariance\\\". PB - Elsevier UR - http://hdl.handle.net/1963/3893 U1 - 816 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Poincaré polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces JF - Communications in Mathematical Physics 304 (2011) 395-409 Y1 - 2011 A1 - Ugo Bruzzo A1 - Rubik Poghossian A1 - Alessandro Tanzini AB -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.

PB - Springer VL - 304 UR - http://hdl.handle.net/1963/3738 IS - 2 U1 - 579 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Product of real spectral triples JF - International Journal of Geometric Methods in Modern Physics 8 (2011) 1833-1848 Y1 - 2011 A1 - Ludwik Dabrowski A1 - Giacomo Dossena AB - 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. PB - World Scientific UR - http://hdl.handle.net/1963/5510 N1 - Based on the talk given at the conference \\\"Noncommutative Geometry and Quantum Physics, Vietri sul Mare, Aug 31 - Sept 5, 2009\\\" U1 - 5345 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - A proof of Sudakov theorem with strictly convex norms JF - Mathematische Zeitschrift 268 (2011) 371-407 Y1 - 2011 A1 - Laura Caravenna AB - 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. PB - Springer UR - http://hdl.handle.net/1963/2967 U1 - 1733 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Q-factorial Laurent rings Y1 - 2011 A1 - Ugo Bruzzo A1 - Antonella Grassi AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/4183 N1 - 5 pages U1 - 3907 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Quantum Geometry on Quantum Spacetime: Distance, Area and Volume Operators JF - Commun. Math. Phys. 308 (2011) 567-589 Y1 - 2011 A1 - Dorothea Bahns A1 - Sergio Doplicher A1 - Klaus Fredenhagen A1 - Gherardo Piacitelli AB - We develop the first steps towards an analysis of geometry on the quantum\\r\\nspacetime proposed in Doplicher et al. (Commun Math Phys 172:187–220, 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. PB - Springer UR - http://hdl.handle.net/1963/5203 U1 - 5025 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - RPRT T1 - Quantum Hitchin Systems via beta-deformed Matrix Models Y1 - 2011 A1 - Giulio Bonelli A1 - Kazunobu Maruyoshi A1 - Alessandro Tanzini AB -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.

PB - SISSA UR - http://hdl.handle.net/1963/4181 N1 - 29 pages; v2. refs. added and typos corrected U1 - 3904 U2 - Physics U3 - Elementary Particle Theory U4 - -1 ER - TY - JOUR T1 - Quantum Isometries of the finite noncommutative geometry of the Standard Model JF - Commun. Math. Phys. 307:101-131, 2011 Y1 - 2011 A1 - Jyotishman Bhowmick A1 - Francesco D'Andrea A1 - Ludwik Dabrowski AB - 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. PB - Springer UR - http://hdl.handle.net/1963/4906 U1 - 4688 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Quasiconvex envelopes of energies for nematic elastomers in the small strain regime and applications JF - Journal of the Mechanics and Physics of Solids 59 (2011) 787-803 Y1 - 2011 A1 - Pierluigi Cesana A1 - Antonio DeSimone AB - 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. UR - http://hdl.handle.net/1963/4065 U1 - 337 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a Young measures approach JF - ESAIM: COCV 17 (2011) 1-27 Y1 - 2011 A1 - Filippo Cagnetti A1 - Rodica Toader AB - 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. PB - Cambridge University Press / EDP Sciences UR - http://hdl.handle.net/1963/2355 U1 - 1662 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic crack growth in finite elasticity with Lipschitz data JF - {ANNALI DI MATEMATICA PURA ED APPLICATA} Y1 - 2011 A1 - Giuliano Lazzaroni KW - Brittle fracture KW - Crack propagation KW - Energy minimization KW - Finite elasticity KW - free-discontinuity problems KW - Griffith's criterion KW - Non-interpenetration} KW - Polyconvexity KW - Quasistatic evolution KW - Rate-independent processes KW - {Variational models AB -{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.}

PB - {SPRINGER HEIDELBERG} CY - {TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY} VL - {190} ER - TY - JOUR T1 - Quasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling JF - Calculus of Variations and Partial Differential Equations 40 (2011) 125-181 Y1 - 2011 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Francesco Solombrino KW - Cam-Clay plasticity AB -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.

PB - Springer UR - http://hdl.handle.net/1963/3670 U1 - 635 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic evolution of sessile drops and contact angle hysteresis JF - Arch. Rational Mech. Anal. 202 (2011) 295-348 Y1 - 2011 A1 - Giovanni Alberti A1 - Antonio DeSimone AB - 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. PB - Springer UR - http://hdl.handle.net/1963/4912 U1 - 4693 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Resonance and Landesman-Lazer conditions for first order systems in R^2 JF - Le Matematiche Y1 - 2011 A1 - Maurizio Garrione AB -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].

VL - 66 ER - TY - JOUR T1 - Resonance and rotation numbers for planar Hamiltonian systems: Multiplicity results via the Poincaré–Birkhoff theorem JF - Nonlinear Analysis: Theory, Methods & Applications Y1 - 2011 A1 - Alberto Boscaggin A1 - Maurizio Garrione KW - Multiple periodic solutions KW - Poincaré–Birkhoff theorem KW - Resonance KW - Rotation number AB -In the general setting of a planar first order system (0.1)u′=G(t,u),u∈R2, with G:[0,T]×R2→R2, we study the relationships between some classical nonresonance conditions (including the Landesman–Lazer one) — at infinity and, in the unforced case, i.e. G(t,0)≡0, at zero — and the rotation numbers of “large” and “small” solutions of (0.1), respectively. Such estimates are then used to establish, via the Poincaré–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–Lazer condition, we obtain sharp conclusions when the system is resonant at infinity.

VL - 74 UR - http://www.sciencedirect.com/science/article/pii/S0362546X11001817 ER - TY - JOUR T1 - SBV regularity for Hamilton-Jacobi equations in R^n JF - Arch. Rational Mech. Anal. 200 (2011) 1003-1021 Y1 - 2011 A1 - Stefano Bianchini A1 - Camillo De Lellis A1 - Roger Robyr AB -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 $SBV_{loc}(\Omega)$.

PB - Springer UR - http://hdl.handle.net/1963/4911 U1 - 4695 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Semistable and numerically effective principal (Higgs) bundles JF - Advances in Mathematics 226 (2011) 3655-3676 Y1 - 2011 A1 - Ugo Bruzzo A1 - Beatriz Grana-Otero AB - 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–Yang–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. PB - Elsevier UR - http://hdl.handle.net/1963/3638 U1 - 666 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Singular perturbation models in phase transitions for second order materials JF - Indiana Univ. Math. J. 60 (2011) 367-409 Y1 - 2011 A1 - Milena Chermisi A1 - Gianni Dal Maso A1 - Irene Fonseca A1 - Giovanni Leoni AB - 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. PB - Indiana University UR - http://hdl.handle.net/1963/3858 U1 - 851 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - Solving PVI by Isomonodromy Deformations T2 - 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 Y1 - 2011 A1 - Davide Guzzetti KW - Painlevé Equations AB - 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. JF - 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 PB - SISSA SN - 9783110275582 UR - http://hdl.handle.net/1963/6522 N1 - 12 pages, 1 figurethis paper has been U1 - 6472 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - On the Space of Symmetric Operators with Multiple Ground States JF - Functional Analysis and its Applications, Volume 45, Issue 4, December 2011, Pages 241-251 Y1 - 2011 A1 - Andrei A. Agrachev KW - Multiple eigenvalue AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/7069 U1 - 6392 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry JF - Journal of Dynamical and Control Systems Y1 - 2011 A1 - Bernard Bonnard A1 - Grégoire Charlot A1 - Roberta Ghezzi A1 - Gabriel Janin AB -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.

PB - Springer VL - 17 UR - http://hdl.handle.net/1963/4914 U1 - 4692 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - RPRT T1 - Structure of level sets and Sard-type properties of Lipschitz maps Y1 - 2011 A1 - Giovanni Alberti A1 - Stefano Bianchini A1 - Gianluca Crippa PB - SISSA UR - http://hdl.handle.net/1963/4657 U1 - 4424 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Subharmonic solutions of planar Hamiltonian systems: a rotation number approach JF - Advanced Nonlinear Studies Y1 - 2011 A1 - Alberto Boscaggin PB - Advanced Nonlinear Studies, Inc. VL - 11 ER - TY - JOUR T1 - Subharmonic solutions of planar Hamiltonian systems via the Poincaré́-Birkhoff theorem JF - Le Matematiche Y1 - 2011 A1 - Alberto Boscaggin AB -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.

VL - 66 ER - TY - JOUR T1 - Supercritical conformal metrics on surfaces with conical singularities JF - Int Math Res Notices (2011) 2011 (24): 5625-5643 Y1 - 2011 A1 - Mauro Bardelloni A1 - Francesca De Marchis A1 - Andrea Malchiodi AB -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.

PB - Oxford University Press UR - http://hdl.handle.net/1963/4095 U1 - 309 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A system-level approach for deciphering the transcriptional response to prion infection JF - Bioinformatics (Oxford, England). 2011 Dec; 27(24):3407-14 Y1 - 2011 A1 - Mattia Zampieri A1 - Giuseppe Legname A1 - Daniel Segrè A1 - Claudio Altafini AB - 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. PB - Oxford University Press UR - http://hdl.handle.net/1963/5745 U1 - 5600 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - RPRT T1 - Thin-walled beams with a cross-section of arbitrary geometry: derivation of linear theories starting from 3D nonlinear elasticity Y1 - 2011 A1 - Elisa Davoli AB -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.

ER - TY - JOUR T1 - The time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity JF - Calculus of Variations and Partial Differential Equations 41 (2011) 241-259 Y1 - 2011 A1 - Helmut Abels A1 - Maria Giovanna Mora A1 - Stefan Müller AB - 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. PB - Springer UR - http://hdl.handle.net/1963/3835 U1 - 492 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The Transition between the Gap Probabilities from the Pearcey to the Airy Process–a Riemann-Hilbert Approach JF - International Mathematics Research Notices Y1 - 2011 A1 - Marco Bertola A1 - Mattia Cafasso VL - doi: 10.1093/imrn/rnr066 ER - TY - JOUR T1 - Uniqueness and nondegeneracy of the ground state for a quasilinear Schrödinger equation with a small parameter JF - Nonlinear Analysis: Theory, Methods & Applications Y1 - 2011 A1 - Alessandro Selvitella KW - Bifurcation theory KW - Nonlinear Schrödinger equations KW - Stationary solutions AB -We study least energy solutions of a quasilinear Schrödinger equation with a small parameter. We prove that the ground state is nondegenerate and unique up to translations and phase shifts using bifurcation theory.

VL - 74 UR - http://www.sciencedirect.com/science/article/pii/S0362546X10007613 ER - TY - RPRT T1 - A uniqueness result for the continuity equation in two dimensions Y1 - 2011 A1 - Giovanni Alberti A1 - Stefano Bianchini A1 - Gianluca Crippa PB - SISSA UR - http://hdl.handle.net/1963/4663 U1 - 4425 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - The well-posedness issue for the density-dependent Euler equations in endpoint Besov spaces JF - Journal de Mathématiques Pures et Appliquées Y1 - 2011 A1 - Raphaël Danchin A1 - Francesco Fanelli KW - Blow-up criterion KW - Critical regularity KW - Incompressible Euler equations KW - Lifespan KW - Nonhomogeneous inviscid fluids AB -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∞,rs embedded in the set of Lipschitz continuous functions, a functional framework which contains the particular case of Hölder spaces C1,α and of the endpoint Besov space B∞,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. Résumé Ce travail complète lʼarticle récent (Danchin, 2010) [9] consacré au système dʼEuler incompressible à densité variable. Lorsque lʼétat initial ne comporte pas de vide, on montre ici que le système est bien posé dans tous les espaces de Besov B∞,rs inclus dans lʼensemble des fonctions lipschitziennes. Ce cadre fonctionnel contient en particulier les espaces de Hölder C1,α et lʼespace de Besov limite B∞,11. On établit également un critère de prolongement dans lʼesprit de celui de Beale, Kato et Majda (1984) [2] pour le cas homogène. Dans la dernière partie de lʼarticle, on donne des minorations pour le temps de vie des solutions du système. En dimension deux, on montre que ce temps de vie tend vers lʼinfini lorsque la densité tend à être homogène. À notre connaissance, il sʼagit du premier résultat de ce type pour le système dʼEuler incompressible à densité variable.

VL - 96 UR - http://www.sciencedirect.com/science/article/pii/S0021782411000511 ER - TY - JOUR T1 - An abstract Nash-Moser theorem with parameters and applications to PDEs JF - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis Y1 - 2010 A1 - Massimiliano Berti A1 - Philippe Bolle A1 - Michela Procesi KW - Abstracting KW - Aircraft engines KW - Finite dimensional KW - Hamiltonian PDEs KW - Implicit function theorem KW - Invariant tori KW - Iterative schemes KW - Linearized operators KW - Mathematical operators KW - Moser theorem KW - Non-Linearity KW - Nonlinear equations KW - Nonlinear wave equation KW - Periodic solution KW - Point of interest KW - Resonance phenomena KW - Small divisors KW - Sobolev KW - Wave equations AB - 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. © 2009 Elsevier Masson SAS. All rights reserved. VL - 27 N1 - cited By (since 1996)9 ER - TY - THES T1 - Almost-Riemannian Geometry from a Control Theoretical Viewpoint Y1 - 2010 A1 - Roberta Ghezzi PB - SISSA UR - http://hdl.handle.net/1963/4705 U1 - 4482 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - Generic T1 - Aspects of Quantum Field Theory on Quantum Spacetime T2 - PoS CNCFG2010:027,2010 Y1 - 2010 A1 - Gherardo Piacitelli AB - 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. JF - PoS CNCFG2010:027,2010 PB - SISSA UR - http://hdl.handle.net/1963/4171 N1 - 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 U1 - 3893 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - RPRT T1 - Canonical k-Minkowski Spacetime Y1 - 2010 A1 - Gherardo Piacitelli A1 - Ludwik Dabrowski AB - 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. UR - http://hdl.handle.net/1963/3863 U1 - 846 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Cauchy biorthogonal polynomials JF - J. Approx. Theory Y1 - 2010 A1 - Marco Bertola A1 - Gekhtman, M. A1 - Szmigielski, J. VL - 162 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1016/j.jat.2009.09.008 ER - TY - JOUR T1 - Chern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality JF - J. Geom. Phys. 60 (2010) 417-429 Y1 - 2010 A1 - Andrea Brini A1 - Luca Griguolo A1 - Domenico Seminara A1 - Alessandro Tanzini AB - 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. UR - http://hdl.handle.net/1963/2938 U1 - 1762 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Cohomology of Skew-holomorphic lie algebroids Y1 - 2010 A1 - Ugo Bruzzo A1 - Vladimir Rubtsov AB - 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. UR - http://hdl.handle.net/1963/3853 U1 - 856 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Concentration of solutions for some singularly perturbed mixed problems: Asymptotics of minimal energy solutions JF - Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 37-56 Y1 - 2010 A1 - Jesus Garcia Azorero A1 - Andrea Malchiodi A1 - Luigi Montoro A1 - Ireneo Peral AB - 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. UR - http://hdl.handle.net/1963/3409 U1 - 926 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Concentration of solutions for some singularly perturbed mixed problems. Part I: existence results JF - Arch. Ration. Mech. Anal. 196 (2010) 907-950 Y1 - 2010 A1 - Jesus Garcia Azorero A1 - Andrea Malchiodi A1 - Luigi Montoro A1 - Ireneo Peral AB - 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. UR - http://hdl.handle.net/1963/3406 U1 - 927 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Continuity of optimal control costs and its application to weak KAM theory JF - Calculus of Variations and Partial Differential Equations. Volume 39, Issue 1, 2010, Pages 213-232 Y1 - 2010 A1 - Andrei A. Agrachev A1 - Paul Lee AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/6459 N1 - 23 pages, 1 figures U1 - 6405 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - RPRT T1 - Convergence of equilibria of thin elastic rods under physical growth conditions for the energy density Y1 - 2010 A1 - Elisa Davoli A1 - Maria Giovanna Mora AB - 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 Kármán plate theory for rods, and the linear theory. UR - http://hdl.handle.net/1963/4086 U1 - 317 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The dependence on the monodromy data of the isomonodromic tau function JF - Comm. Math. Phys. Y1 - 2010 A1 - Marco Bertola VL - 294 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00220-009-0961-7 ER - TY - JOUR T1 - Dirac Operators on Quantum Projective Spaces JF - Comm. Math. Phys. 295 (2010) 731-790 Y1 - 2010 A1 - Francesco D'Andrea A1 - Ludwik Dabrowski AB - 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. UR - http://hdl.handle.net/1963/3622 U1 - 682 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Dynamics control by a time-varying feedback JF - Journal of Dynamical and Control Systems. Volume 16, Issue 2, April 2010, Pages :149-162 Y1 - 2010 A1 - Andrei A. Agrachev A1 - Marco Caponigro KW - Discrete-time dynamics AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/6461 U1 - 6407 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Effective Schroedinger dynamics on $ ε$-thin Dirichlet waveguides via Quantum Graphs I: star-shaped graphs JF - J. Phys. A 43 (2010) 474014 Y1 - 2010 A1 - Gianfausto Dell'Antonio A1 - Emanuele Costa AB - 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. PB - IOP Publishing UR - http://hdl.handle.net/1963/4106 U1 - 298 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Estimates on path functionals over Wasserstein Spaces JF - SIAM J. Math. Anal. 42 (2010) 1179-1217 Y1 - 2010 A1 - Stefano Bianchini A1 - Alessio Brancolini AB - 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. UR - http://hdl.handle.net/1963/3583 U1 - 717 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the Euler-Lagrange equation for a variational problem : the general case II JF - Math. Z. 265 (2010) 889-923 Y1 - 2010 A1 - Stefano Bianchini A1 - Matteo Gloyer UR - http://hdl.handle.net/1963/2551 U1 - 1568 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Exact reconstruction of damaged color images using a total variation model JF - Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 1291-1331 Y1 - 2010 A1 - Irene Fonseca A1 - Giovanni Leoni A1 - Francesco Maggi A1 - Massimiliano Morini AB - 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. PB - Elsevier UR - http://hdl.handle.net/1963/4039 U1 - 363 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence of planar curves minimizing length and curvature JF - Proc. Steklov Inst. Math. 270 (2010) 43-56 Y1 - 2010 A1 - Ugo Boscain A1 - Grégoire Charlot A1 - Francesco Rossi AB - 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. PB - Springer UR - http://hdl.handle.net/1963/4107 U1 - 297 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Feedback schemes for radiation damping suppression in NMR: a control-theoretical perspective JF - Systems and Control Letters, 59 (12):782-786, 2010 Y1 - 2010 A1 - Claudio Altafini A1 - Paola Cappellaro A1 - David Cory AB - 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. PB - Elsevier UR - http://hdl.handle.net/1963/4384 U1 - 4132 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - First colonization of a hard-edge in random matrix theory JF - Constr. Approx. Y1 - 2010 A1 - Marco Bertola A1 - Lee, S. Y. VL - 31 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00365-009-9052-4 ER - TY - JOUR T1 - Gauge theory: from physics to geometry JF - Rend. Istit. Mat. Univ. Trieste 42 (2010) 103-128 Y1 - 2010 A1 - Ugo Bruzzo AB - 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. PB - Istituto di matematica. Universita\\\' di Trieste UR - http://hdl.handle.net/1963/4105 U1 - 299 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Gene expression analysis of the emergence of epileptiform activity after focal injection of kainic acid into mouse hippocampus. JF - The European journal of neuroscience. 2010 Oct; 32(8):1364-79 Y1 - 2010 A1 - Dario Motti A1 - Caroline Le Duigou A1 - Nicole Chemaly A1 - Lucia Wittner A1 - Dejan Lazarevic A1 - Helena Krmac A1 - Troels Torben Marstrand A1 - Eivind Valen A1 - Remo Sanges A1 - Elia Stupka A1 - Albin Sandelin A1 - Enrico Cherubini A1 - Stefano Gustincich A1 - Richard Miles AB -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.

PB - Wiley UR - http://hdl.handle.net/1963/4480 U1 - 4244 U2 - Neuroscience U3 - Neurobiology U4 - -1 ER - TY - JOUR T1 - Generic multiplicity for a scalar field equation on compact surfaces JF - Journal of Functional Analysis Y1 - 2010 A1 - Francesca De Marchis KW - Generic multiplicity KW - Geometric PDE's KW - Morse inequalities KW - Scalar field equations AB -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.

VL - 259 UR - http://www.sciencedirect.com/science/article/pii/S0022123610002697 ER - TY - JOUR T1 - On the geometric origin of the bi-Hamiltonian structure of the Calogero-Moser system JF - Int. Math. Res. Not. (2010) 2010:279-296 Y1 - 2010 A1 - Claudio Bartocci A1 - Gregorio Falqui A1 - Igor Mencattini A1 - Giovanni Ortenzi A1 - Marco Pedroni AB - 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. PB - Oxford University Press UR - http://hdl.handle.net/1963/3800 U1 - 8 U2 - LISNU U3 - Interdisciplinary Laboratory for Advanced Studies ER - TY - RPRT T1 - The geometry emerging from the symmetries of a quantum system Y1 - 2010 A1 - Giuseppe De Nittis A1 - Gianluca Panati AB - 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. UR - http://hdl.handle.net/1963/3834 U1 - 493 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - A global compactness result for the p-Laplacian involving critical nonlinearities JF - Discrete & Continuous Dynamical Systems-A Y1 - 2010 A1 - Mercuri, Carlo A1 - Willem, Michel AB -We prove a representation theorem for Palais-Smale sequences involving the p-Laplacian and critical nonlinearities. Applications are given to a critical problem.VL - 28 UR - http://www.aimsciences.org/journals/displayArticles.jsp?paperID=5097 ER - TY - JOUR T1 - Hamiltonian PDEs: deformations, integrability, solutions JF - Journal of Physics A: Mathematical and Theoretical. Volume 43, Issue 43, 29 October 2010, Article number 434002 Y1 - 2010 A1 - Boris Dubrovin AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/6469 U1 - 6414 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Hitchin systems, N=2 gauge theories and W-gravity JF - Phys. Lett. B 691 (2010) 111-115 Y1 - 2010 A1 - Giulio Bonelli A1 - Alessandro Tanzini AB - 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. UR - http://hdl.handle.net/1963/3831 U1 - 496 U2 - Physics U3 - Elementary Particle Theory ER - TY - JOUR T1 - Homogeneous binary trees as ground states of quantum critical Hamiltonians JF - Phys. Rev. A 81 (2010) 062335 Y1 - 2010 A1 - Pietro Silvi A1 - Vittorio Giovannetti A1 - Simone Montangero A1 - Matteo Rizzi A1 - J. Ignacio Cirac A1 - Rosario Fazio AB -

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.

PB - American Physical Society UR - http://hdl.handle.net/1963/3909 U1 - 800 U2 - Physics U3 - Condensed Matter Theory ER - TY - JOUR T1 - Homogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems JF - New J. Phys. 12 (2010) 075018 Y1 - 2010 A1 - Matteo Rizzi A1 - Simone Montangero A1 - Pietro Silvi A1 - Vittorio Giovannetti A1 - Rosario Fazio AB -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.

PB - IOP Publishing UR - http://hdl.handle.net/1963/4067 U1 - 335 U2 - Physics U3 - Condensed Matter Theory ER - TY - JOUR T1 - Homogenization of fiber reinforced brittle material: the intermediate case JF - Adv. Calc. Var. 3 (2010) 345-370 Y1 - 2010 A1 - Gianni Dal Maso A1 - Caterina Ida Zeppieri AB - 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. PB - Walter de Gruyter UR - http://hdl.handle.net/1963/3607 U1 - 694 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Invariant Lagrange submanifolds of dissipative systems JF - Russian Mathematical Surveys. Volume 65, Issue 5, 2010, Pages: 977-978 Y1 - 2010 A1 - Andrei A. Agrachev AB - We study solutions of modified Hamilton-Jacobi equations H(du/dq,q) + cu(q) =\\r\\n0, q \\\\in M, on a compact manifold M . PB - SISSA UR - http://hdl.handle.net/1963/6457 U1 - 6403 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - A kinetic mechanism inducing oscillations in simple chemical reactions networks JF - Mathematical Biosciences and Engineering 7(2):301-312, 2010 Y1 - 2010 A1 - Julien Coatleven A1 - Claudio Altafini AB - 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. PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/2393 U1 - 2304 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Lorentz Covariant k-Minkowski Spacetime JF - Phys. Rev. D 81 (2010) 125024 Y1 - 2010 A1 - Ludwik Dabrowski A1 - Michal Godlinski A1 - Gherardo Piacitelli AB - 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. UR - http://hdl.handle.net/1963/3829 U1 - 498 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Monotonicity, frustration, and ordered response: an analysis of the energy landscape of perturbed large-scale biological networks JF - BMC Systems Biology 2010, 4:83 Y1 - 2010 A1 - Giovanni Iacono A1 - Claudio Altafini AB - 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. PB - BioMed Central UR - http://hdl.handle.net/1963/4055 U1 - 347 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Moore-Read Fractional Quantum Hall wavefunctions and SU(2) quiver gauge theories Y1 - 2010 A1 - Raoul Santachiara A1 - Alessandro Tanzini AB - 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. UR - http://hdl.handle.net/1963/3852 U1 - 857 U2 - Mathematics U3 - Mathematical Physics ER - TY - THES T1 - New approximation results for free discontinuity problems T2 - Università degli Studi di Trieste and SISSA Y1 - 2010 A1 - Flaviana Iurlano JF - Università degli Studi di Trieste and SISSA ER - TY - JOUR T1 - Nonlocal character of the reduced theory of thin films with higher order perturbations JF - Adv. Calc. Var. 3 (2010) 287-319 Y1 - 2010 A1 - Gianni Dal Maso A1 - Irene Fonseca A1 - Giovanni Leoni UR - http://hdl.handle.net/1963/3754 U1 - 563 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A normal form for generic 2-dimensional almost-Riemannian structures at a tangency point JF - arXiv preprint arXiv:1008.5036 Y1 - 2010 A1 - Ugo Boscain A1 - Grégoire Charlot A1 - Roberta Ghezzi ER - TY - RPRT T1 - On the number of positive solutions of some semilinear elliptic problems Y1 - 2010 A1 - Antonio Ambrosetti UR - http://hdl.handle.net/1963/4083 U1 - 320 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Numerical Solution of the Small Dispersion Limit of the Camassa-Holm and Whitham Equations and Multiscale Expansions Y1 - 2010 A1 - Simonetta Abenda A1 - Tamara Grava A1 - Christian Klein AB - 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.... UR - http://hdl.handle.net/1963/3840 U1 - 487 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - On optimality of c-cyclically monotone transference plans JF - Comptes Rendus Mathematique 348 (2010) 613-618 Y1 - 2010 A1 - Stefano Bianchini A1 - Laura Caravenna AB - 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. PB - Elsevier UR - http://hdl.handle.net/1963/4023 U1 - 379 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Optimally swimming Stokesian Robots Y1 - 2010 A1 - François Alouges A1 - Antonio DeSimone A1 - Luca Heltai A1 - Aline Lefebvre A1 - Benoit Merlet AB - 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. UR - http://hdl.handle.net/1963/3929 U1 - 472 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Painlevé II asymptotics near the leading edge of the oscillatory zone for the Korteweg-de Vries equation in the small-dispersion limit JF - Comm. Pure Appl. Math. 63 (2010) 203-232 Y1 - 2010 A1 - Tom Claeys A1 - Tamara Grava AB - 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. PB - Wiley UR - http://hdl.handle.net/1963/3799 U1 - 527 U2 - Mathematics U3 - Mathematical Physics ER - TY - CONF T1 - A Phase Field Approach to Wetting and Contact Angle Hysteresis Phenomena T2 - IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials Y1 - 2010 A1 - Antonio DeSimone A1 - Livio Fedeli A1 - Turco, Alessandro ED - Hackl, Klaus AB -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.

JF - IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials PB - Springer Netherlands CY - Dordrecht SN - 978-90-481-9195-6 ER - TY - RPRT T1 - Picard group of hypersurfaces in toric varieties Y1 - 2010 A1 - Ugo Bruzzo A1 - Antonella Grassi AB - 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. UR - http://hdl.handle.net/1963/4103 U1 - 301 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Poles of Integrale Tritronquee and Anharmonic Oscillators. Asymptotic localization from WKB analysis JF - Nonlinearity. vol. 23, (2010), page 2501-2507 Y1 - 2010 A1 - Davide Masoero AB -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.

UR - http://hdl.handle.net/1963/3841 U1 - 486 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Positive solutions for some non-autonomous Schrödinger–Poisson systems JF - Journal of Differential Equations Y1 - 2010 A1 - Giovanna Cerami A1 - Giusi Vaira PB - Academic Press VL - 248 ER - TY - JOUR T1 - Projective Reeds-Shepp car on $S^2$ with quadratic cost JF - ESAIM COCV 16 (2010) 275-297 Y1 - 2010 A1 - Ugo Boscain A1 - Francesco Rossi AB - 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. UR - http://hdl.handle.net/1963/2668 U1 - 1429 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Quantum Spacetime: a Disambiguation Y1 - 2010 A1 - Gherardo Piacitelli AB - 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. UR - http://hdl.handle.net/1963/3864 U1 - 845 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Quasistatic crack growth in elasto-plastic materials: the two-dimensional case JF - Arch. Ration. Mech. Anal. 196 (2010) 867-906 Y1 - 2010 A1 - Gianni Dal Maso A1 - Rodica Toader AB - 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. UR - http://hdl.handle.net/1963/2964 U1 - 1736 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic crack growth in finite elasticity with non-interpenetration JF - Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 257-290 Y1 - 2010 A1 - Gianni Dal Maso A1 - Giuliano Lazzaroni AB -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.

UR - http://hdl.handle.net/1963/3397 U1 - 935 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic evolution for Cam-Clay plasticity: the spatially homogeneous case JF - Netw. Heterog. Media 5 (2010) 97-132 Y1 - 2010 A1 - Gianni Dal Maso A1 - Francesco Solombrino KW - Cam-Clay plasticity AB -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.

UR - http://hdl.handle.net/1963/3671 U1 - 634 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic evolution for plasticity with softening: The spatially homogeneous case JF - Discrete & Continuous Dynamical Systems - A Y1 - 2010 A1 - Francesco Solombrino KW - plasticity with softening KW - rate independent processes AB -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'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.

VL - 27 UR - http://aimsciences.org//article/id/4c2301d8-f553-493e-b672-b4f76a3ede2f ER - TY - JOUR T1 - The reductions of the dispersionless 2D Toda hierarchy and their Hamiltonian structures JF - J. Phys. A 43 (2010) 045201 Y1 - 2010 A1 - Guido Carlet A1 - Paolo Lorenzoni A1 - Andrea Raimondo AB - 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. PB - IOP Publishing UR - http://hdl.handle.net/1963/3846 U1 - 863 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Riemann-Roch theorems and elliptic genus for virtually smooth schemes JF - Geom. Topol. 14 (2010) 83-115 Y1 - 2010 A1 - Barbara Fantechi A1 - Lothar Göttsche AB - 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. PB - Mathematical Sciences Publishers UR - http://hdl.handle.net/1963/3888 U1 - 821 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - The role of membrane viscosity in the dynamics of fluid membranes Y1 - 2010 A1 - Marino Arroyo A1 - Antonio DeSimone A1 - Luca Heltai AB - 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. UR - http://hdl.handle.net/1963/3930 U1 - 471 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Semiclassical evolution of two rotating solitons for the Nonlinear Schrödinger Equation with electric potential JF - Adv. Differential Equations Y1 - 2010 A1 - Alessandro Selvitella PB - Khayyam Publishing, Inc. VL - 15 UR - https://projecteuclid.org:443/euclid.ade/1355854752 ER - TY - JOUR T1 - On semistable principal bundles over complex projective manifolds, II JF - Geom. Dedicata 146 (2010) 27-41 Y1 - 2010 A1 - Indranil Biswas A1 - Ugo Bruzzo AB - 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. UR - http://hdl.handle.net/1963/3404 U1 - 928 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Sharp nonexistence results for a linear elliptic inequality involving Hardy and Leray potentials Y1 - 2010 A1 - Mouhamed Moustapha Fall A1 - Roberta Musina AB - 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. UR - http://hdl.handle.net/1963/3869 U1 - 840 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Shell theories arising as low energy Gamma-limit of 3d nonlinear elasticity JF - Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. IX (2010) 253-295 Y1 - 2010 A1 - Marta Lewicka A1 - Maria Giovanna Mora A1 - Mohammad Reza Pakzad AB - 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. UR - http://hdl.handle.net/1963/2601 U1 - 1521 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Sobolev periodic solutions of nonlinear wave equations in higher spatial dimensions JF - Archive for Rational Mechanics and Analysis Y1 - 2010 A1 - Massimiliano Berti A1 - Philippe Bolle AB - 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". © Springer-Verlag (2009). VL - 195 N1 - cited By (since 1996)6 ER - TY - JOUR T1 - Solitonic asymptotics for the Korteweg-de Vries equation in the small dispersion limit JF - SIAM J. Math. Anal. 42 (2010) 2132-2154 Y1 - 2010 A1 - Tamara Grava A1 - Tom Claeys AB - 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. UR - http://hdl.handle.net/1963/3839 U1 - 488 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Stable determination of an immersed body in a stationary Stokes fluid JF - Inverse Problems Y1 - 2010 A1 - Andrea Ballerini AB -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–log type.

PB - IOP Publishing VL - 26 UR - https://doi.org/10.1088%2F0266-5611%2F26%2F12%2F125015 ER - TY - JOUR T1 - Taming open/closed string duality with a Losev trick JF - JHEP 06(2010)063 Y1 - 2010 A1 - Giulio Bonelli A1 - Andrea Prudenziati A1 - Alessandro Tanzini AB - 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. UR - http://hdl.handle.net/1963/3855 U1 - 854 U2 - Physics U3 - Mathematical Physics ER - TY - JOUR T1 - A three-dimensional model for the dynamics and hydrodynamics of rowing boats JF - Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology Y1 - 2010 A1 - L. Formaggia A1 - Andrea Mola A1 - N Parolini A1 - M Pischiutta AB -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–-oars–-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.

VL - 224 UR - https://doi.org/10.1243/17543371jset46 ER - TY - JOUR T1 - A time-dependent perturbative analysis for a quantum particle in a cloud chamber JF - Annales Henri Poincare 11 (2010) 539-564 Y1 - 2010 A1 - Gianfausto Dell'Antonio A1 - Rodolfo Figari A1 - Alessandro Teta AB - 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. PB - Springer UR - http://hdl.handle.net/1963/3969 U1 - 432 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Twisted Covariance as a Non Invariant Restriction of the Fully Covariant DFR Model JF - Comm. Math. Phys. 295 (2010) 701-729 Y1 - 2010 A1 - Gherardo Piacitelli AB - 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. UR - http://hdl.handle.net/1963/3605 U1 - 696 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Two-dimensional almost-Riemannian structures with tangency points JF - Ann. Inst. H. Poincare Anal. Non Lineaire Y1 - 2010 A1 - Andrei A. Agrachev A1 - Ugo Boscain A1 - Grégoire Charlot A1 - Roberta Ghezzi A1 - Mario Sigalotti AB -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.

PB - Elsevier VL - 27 UR - http://hdl.handle.net/1963/3870 U1 - 839 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Uhlenbeck-Donaldson compactification for framed sheaves on projective surfaces Y1 - 2010 A1 - Ugo Bruzzo A1 - Dimitri Markushevich A1 - Alexander Tikhomirov AB - 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. UR - http://hdl.handle.net/1963/4049 U1 - 353 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Universality in the profile of the semiclassical limit solutions to the focusing nonlinear Schrödinger equation at the first breaking curve JF - Int. Math. Res. Not. IMRN Y1 - 2010 A1 - Marco Bertola A1 - Alexander Tovbis UR - http://0-dx.doi.org.mercury.concordia.ca/10.1093/imrn/rnp196 ER - TY - JOUR T1 - Well-posed infinite horizon variational problems on a compact manifold JF - Proceedings of the Steklov Institute of Mathematics. Volume 268, Issue 1, 2010, Pages 17-31 Y1 - 2010 A1 - Andrei A. Agrachev AB - 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 PB - SISSA UR - http://hdl.handle.net/1963/6458 U1 - 6404 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - 1D periodic potentials with gaps vanishing at k=0 JF - Mem. Differential Equations Math. Phys. 47 (2009) 133-158 Y1 - 2009 A1 - Alessandro Michelangeli A1 - Osvaldo Zagordi AB - 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 Schrödinger equation (Hill\\\'s equation). This result is placed in the perspective of the previous related results available in the literature. UR - http://hdl.handle.net/1963/1818 U1 - 2396 U2 - Mathematics U3 - Mathematical Physics ER - TY - CHAP T1 - Biological Fluid Dynamics, Non-linear Partial Differential Equations T2 - Encyclopedia of Complexity and Systems Science / Robert A. Meyers (ed.). - Springer, 2009, 548-554 Y1 - 2009 A1 - Antonio DeSimone A1 - François Alouges A1 - Aline Lefebvre JF - Encyclopedia of Complexity and Systems Science / Robert A. Meyers (ed.). - Springer, 2009, 548-554 UR - http://hdl.handle.net/1963/2630 U1 - 1493 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The boundary Riemann solver coming from the real vanishing viscosity approximation JF - Arch. Ration. Mech. Anal. 191 (2009) 1-96 Y1 - 2009 A1 - Stefano Bianchini A1 - Laura Spinolo AB - 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. UR - http://hdl.handle.net/1963/1831 U1 - 2385 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Bubbles with prescribed mean curvature: the variational approach Y1 - 2009 A1 - Paolo Caldiroli A1 - Roberta Musina UR - http://hdl.handle.net/1963/3659 N1 - H-systems, prescribed mean curvature equation, blowup U1 - 646 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The Cauchy two–matrix model JF - Comm. Math. Phys. Y1 - 2009 A1 - Marco Bertola A1 - M Gekhtman A1 - J Szmigielski VL - 287 ER - TY - JOUR T1 - Characterization of the time course of changes of the evoked electrical activity in a model of a chemically-induced neuronal plasticity JF - BMC Research Notes (2009) 2:13 Y1 - 2009 A1 - Frederic D. Broccard A1 - Silvia Pegoraro A1 - Maria Elisabetta Ruaro A1 - Claudio Altafini A1 - Vincent Torre AB - 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. PB - BioMed Central UR - http://hdl.handle.net/1963/3706 U1 - 599 U2 - Neuroscience U3 - Neurobiology ER - TY - JOUR T1 - Commuting difference operators, spinor bundles and the asymptotics of orthogonal polynomials with respect to varying complex weights JF - Adv. Math. Y1 - 2009 A1 - Marco Bertola A1 - Mo, M. Y. VL - 220 ER - TY - JOUR T1 - A connection between viscous profiles and singular ODEs JF - Rend. Istit. Mat. Univ. Trieste 41 (2009) 35-41 Y1 - 2009 A1 - Stefano Bianchini A1 - Laura Spinolo UR - http://hdl.handle.net/1963/2555 U1 - 1564 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Controllability and simultaneous controllability of isospectral bilinear control systems on complex flag manifolds JF - Systems Control Lett. 58 (2009) 213-216 Y1 - 2009 A1 - Claudio Altafini AB - 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. PB - Elsevier UR - http://hdl.handle.net/1963/3523 U1 - 741 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Controllability of the discrete-spectrum Schrodinger equation driven by an external field JF - Ann. Inst. H. Poincare Anal. Non Lineaire 26 (2009) 329-349 Y1 - 2009 A1 - Thomas Chambrion A1 - Paolo Mason A1 - Mario Sigalotti A1 - Ugo Boscain AB - 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. UR - http://hdl.handle.net/1963/2547 U1 - 1572 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Controllability on the group of diffeomorphisms JF - Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009) 2503-2509 Y1 - 2009 A1 - Andrei A. Agrachev A1 - Marco Caponigro AB - 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. UR - http://hdl.handle.net/1963/3396 U1 - 936 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the convergence of viscous approximations after shock interactions JF - Discrete Contin. Dyn. Syst. 23 (2009) 29-48 Y1 - 2009 A1 - Alberto Bressan A1 - Carlotta Donadello AB - 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. PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/3412 U1 - 923 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Cubic string boundary value problems and Cauchy biorthogonal polynomials JF - J. Phys. A Y1 - 2009 A1 - Marco Bertola A1 - Gekhtman, M. A1 - Szmigielski, J. VL - 42 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1088/1751-8113/42/45/454006 ER - TY - JOUR T1 - Decoupling A and B model in open string theory: topological adventures in the world of tadpoles JF - JHEP 06 (2009) 046 Y1 - 2009 A1 - Giulio Bonelli A1 - Andrea Prudenziati A1 - Alessandro Tanzini A1 - Yang Jie AB - 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. UR - http://hdl.handle.net/1963/3632 U1 - 672 U2 - Physics U3 - Mathematical Physics ER - TY - JOUR T1 - Differential geometry of curves in Lagrange Grassmannians with given Young diagram JF - Differential Geom. Appl. 27 (2009) 723-742 Y1 - 2009 A1 - Igor Zelenko A1 - Li Chengbo AB - 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. PB - Elsevier UR - http://hdl.handle.net/1963/3819 U1 - 508 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Discrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers JF - Netw. Heterog. Media 4 (2009) 667-708 Y1 - 2009 A1 - Marco Cicalese A1 - Antonio DeSimone A1 - Caterina Ida Zeppieri AB - 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. PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/3788 U1 - 538 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - The Disintegration Theorem and Applications to Optimal Mass Transportation Y1 - 2009 A1 - Laura Caravenna PB - SISSA UR - http://hdl.handle.net/1963/5900 U1 - 5750 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Equivariant cohomology and localization for Lie algebroids JF - Funct. Anal. Appl. 43 (2009) 18-29 Y1 - 2009 A1 - Ugo Bruzzo A1 - Lucio Cirio A1 - Paolo Rossi A1 - Vladimir Rubtsov AB - 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. SN - 978-981-270-377-4 UR - http://hdl.handle.net/1963/1724 U1 - 2427 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - ERNEST: a toolbox for chemical reaction network theory JF - Bioinformatics 25 (2009) 2853-2854 Y1 - 2009 A1 - Nicola Soranzo A1 - Claudio Altafini AB - 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. PB - Oxford University Press UR - http://hdl.handle.net/1963/3826 U1 - 501 U2 - Physics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Exact results for topological strings on resolved Yp,q singularities JF - Comm. Math. Phys. 289 (2009) 205-252 Y1 - 2009 A1 - Andrea Brini A1 - Alessandro Tanzini UR - http://hdl.handle.net/1963/2631 U1 - 1492 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Existence of extremals for the Maz\\\'ya and for the Caffarelli-Kohn-Nirenberg inequalities JF - Nonlinear Anal. 70 (2009) 3002-3007 Y1 - 2009 A1 - Roberta Musina AB - 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. UR - http://hdl.handle.net/1963/2739 U1 - 1961 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - An existence result for the Monge problem in R^n with norm cost Y1 - 2009 A1 - Laura Caravenna UR - http://hdl.handle.net/1963/3647 U1 - 657 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the extremality, uniqueness and optimality of transference plans JF - Bull. Inst. Math. Acad. Sin. (N.S.) 4 (2009) 353-458 Y1 - 2009 A1 - Stefano Bianchini A1 - Laura Caravenna AB - 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. UR - http://hdl.handle.net/1963/3692 U1 - 613 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Families of Monads and Instantons from a Noncommutative ADHM Construction Y1 - 2009 A1 - Simon Brain A1 - Giovanni Landi AB - 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 `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. UR - http://hdl.handle.net/1963/3478 U1 - 786 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - First colonization of a spectral outpost in random matrix theory JF - Constr. Approx. Y1 - 2009 A1 - Marco Bertola A1 - Lee, S. Y. VL - 30 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00365-008-9026-y ER - TY - JOUR T1 - Foliations of small tubes in Riemannian manifolds by capillary minimal discs JF - Nonlinear Analysis: Theory, Methods & Applications Y1 - 2009 A1 - Fall, Mouhamed Moustapha A1 - Mercuri, Carlo AB -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.

PB - Elsevier VL - 70 UR - https://doi.org/10.1016/j.na.2008.10.024 ER - TY - JOUR T1 - Gauged Laplacians on quantum Hopf bundles JF - Comm. Math. Phys. 287 (2009) 179-209 Y1 - 2009 A1 - Giovanni Landi A1 - Cesare Reina A1 - Alessandro Zampini AB - 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 `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. PB - Springer UR - http://hdl.handle.net/1963/3540 U1 - 1161 U2 - Mathematics U3 - Mathematical Physics ER - TY - CHAP T1 - Hamiltonian perturbations of hyperbolic PDEs: from classification results to the properties of solutions T2 - New Trends in Mathematical Physics : Selected contributions of the XVth International Congress on Mathematical Physics, Springer Netherlands, 2009, pp. 231-276. Y1 - 2009 A1 - Boris Dubrovin AB - 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. JF - New Trends in Mathematical Physics : Selected contributions of the XVth International Congress on Mathematical Physics, Springer Netherlands, 2009, pp. 231-276. PB - SISSA SN - 978-90-481-2810-5 UR - http://hdl.handle.net/1963/6470 U1 - 6415 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Hardy-Sobolev-Maz\\\'ja inequalities: symmetry and breaking symmetry of extremal functions JF - Commun. Contemp. Math. 11 (2009) 993-1007 Y1 - 2009 A1 - Marita Gazzini A1 - Roberta Musina UR - http://hdl.handle.net/1963/2569 U1 - 1551 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A higher order model for image restoration: the one dimensional case JF - SIAM J. Math. Anal. 40 (2009) 2351-2391 Y1 - 2009 A1 - Gianni Dal Maso A1 - Irene Fonseca A1 - Giovanni Leoni A1 - Massimiliano Morini AB - 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. UR - http://hdl.handle.net/1963/3174 U1 - 1127 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Holomorphic equivariant cohomology of Atiyah algebroids and localization Y1 - 2009 A1 - Ugo Bruzzo A1 - Vladimir Rubtsov UR - http://hdl.handle.net/1963/3774 U1 - 551 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Homogenization of fiber reinforced brittle materials: the extremal cases JF - SIAM J. Math. Anal. 41 (2009) 1874-1889 Y1 - 2009 A1 - Marco Barchiesi A1 - Gianni Dal Maso AB - 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. PB - SIAM UR - http://hdl.handle.net/1963/2705 U1 - 1396 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Initial value problem of the Whitham equations for the Camassa-Holm equation JF - Physica D 238 (2009) 55-66 Y1 - 2009 A1 - Tamara Grava A1 - Virgil U. Pierce A1 - Fei-Ran Tian AB - 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. PB - Elsevier UR - http://hdl.handle.net/1963/3429 U1 - 906 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups JF - J. Funct. Anal. 256 (2009) 2621-2655 Y1 - 2009 A1 - Andrei A. Agrachev A1 - Ugo Boscain A1 - Jean-Paul Gauthier A1 - Francesco Rossi AB - 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. UR - http://hdl.handle.net/1963/2669 U1 - 1428 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Investigating the Conformational Stability of Prion Strains through a Kinetic Replication Model JF - PLoS Comput Biol 2009;5(7): e1000420 Y1 - 2009 A1 - Mattia Zampieri A1 - Giuseppe Legname A1 - Claudio Altafini AB - 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. PB - PLoS UR - http://hdl.handle.net/1963/3989 U1 - 413 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Jacobi Equations and Comparison Theorems for Corank 1 Sub-Riemannian structures with symmetries Y1 - 2009 A1 - Li Chengbo A1 - Igor Zelenko AB - 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. UR - http://hdl.handle.net/1963/3736 U1 - 581 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Low-Frequency Variations of Force Coefficients on Square Cylinders with Sharp and Rounded Corners JF - Journal of Structural Engineering Y1 - 2009 A1 - Andrea Mola A1 - Giancarlo Bordonaro A1 - Muhammad R. Hajj PB - American Society of Civil Engineers ({ASCE}) VL - 135 UR - https://doi.org/10.1061/(asce)st.1943-541x.0000034 ER - TY - JOUR T1 - Mesoscopic colonization in a spectral band JF - J. Phys. A Y1 - 2009 A1 - Marco Bertola A1 - Lee, S. Y. A1 - Mo, M. Y. VL - 42 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1088/1751-8113/42/41/415204 ER - TY - JOUR T1 - Minimal disc-type surfaces embedded in a perturbed cylinder JF - Differential and Integral Equations Y1 - 2009 A1 - Fall, Mouhamed Moustapha A1 - Mercuri, Carlo AB -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.

PB - Khayyam Publishing, Inc. VL - 22 UR - https://projecteuclid.org/euclid.die/1356019407 ER - TY - JOUR T1 - A model for the dynamics of rowing boats JF - International Journal for Numerical Methods in Fluids Y1 - 2009 A1 - L. Formaggia A1 - Edie Miglio A1 - Andrea Mola A1 - Antonio Montano PB - Wiley VL - 61 UR - https://doi.org/10.1002/fld.1940 ER - TY - JOUR T1 - A model for the orbifold Chow ring of weighted projective spaces JF - Comm. Algebra 37 (2009) 503-514 Y1 - 2009 A1 - Samuel Boissiere A1 - Etienne Mann A1 - Fabio Perroni AB - 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. PB - Taylor and Francis UR - http://hdl.handle.net/1963/3589 U1 - 711 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Moment determinants as isomonodromic tau functions JF - Nonlinearity Y1 - 2009 A1 - Marco Bertola VL - 22 ER - TY - JOUR T1 - mRNA stability and the unfolding of gene expression in the long-period yeast metabolic cycle JF - BMC Systems Biology (2009) 3:18 Y1 - 2009 A1 - Nicola Soranzo A1 - Mattia Zampieri A1 - Lorenzo Farina A1 - Claudio Altafini AB - 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. PB - BioMed Central UR - http://hdl.handle.net/1963/3630 U1 - 674 U2 - Physics U3 - Statistical and Biological Physics ER - TY - JOUR T1 - A nonlinear theory for shells with slowly varying thickness JF - C. R. Math. 347 (2009) 211-216 Y1 - 2009 A1 - Marta Lewicka A1 - Maria Giovanna Mora A1 - Mohammad Reza Pakzad AB - We study the Γ-limit of 3d nonlinear elasticity for shells of small, variable thickness, around an arbitrary smooth 2d surface. UR - http://hdl.handle.net/1963/2632 U1 - 1491 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A note on the paper \\\"Optimizing improved Hardy inequalities\\\" by S. Filippas and A. Tertikas JF - J. Funct. Anal. 256 (2009) 2741-2745 Y1 - 2009 A1 - Roberta Musina UR - http://hdl.handle.net/1963/2698 U1 - 1402 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Optimal transportation under nonholonomic constraints JF - Trans. Amer. Math. Soc. 361 (2009) 6019-6047 Y1 - 2009 A1 - Andrei A. Agrachev A1 - Paul Lee AB - 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. UR - http://hdl.handle.net/1963/2176 U1 - 2068 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The partition function of the two-matrix model as an isomonodromic τ function JF - J. Math. Phys. Y1 - 2009 A1 - Marco Bertola A1 - Marchal, O. VL - 50 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1063/1.3054865 ER - TY - JOUR T1 - Quasistatic evolution for Cam-Clay plasticity: examples of spatially homogeneous solutions JF - Math. Models Methods Appl. Sci. 19 (2009) 1643-1711 Y1 - 2009 A1 - Gianni Dal Maso A1 - Antonio DeSimone AB - 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. UR - http://hdl.handle.net/1963/3395 U1 - 937 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic evolution problems for nonhomogeneous elastic plastic materials JF - J. Convex Anal. Y1 - 2009 A1 - Francesco Solombrino AB -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.

VL - 16 ER - TY - JOUR T1 - Regularity of a vector potential problem and its spectral curve JF - J. Approx. Theory Y1 - 2009 A1 - Ferenc Balogh A1 - Marco Bertola VL - 161 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1016/j.jat.2008.10.010 ER - TY - JOUR T1 - Relaxation dynamics of fluid membranes JF - Phys. Rev. E 79 (2009) 031915 Y1 - 2009 A1 - Marino Arroyo A1 - Antonio DeSimone AB - 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. PB - American Physical Society UR - http://hdl.handle.net/1963/3618 U1 - 686 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On a Sobolev type inequality related to the weighted p-Laplace operator JF - J. Math. Anal. Appl. 352 (2009) 99-111 Y1 - 2009 A1 - Marita Gazzini A1 - Roberta Musina UR - http://hdl.handle.net/1963/2613 U1 - 1510 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Solutions of the Schrödinger–Poisson problem concentrating on spheres, part I: necessary conditions JF - Mathematical Models and Methods in Applied Sciences Y1 - 2009 A1 - Ianni, Isabella A1 - Giusi Vaira AB -In this paper we study a coupled nonlinear Schrödinger–Poisson problem with radial functions. This system has been introduced as a model describing standing waves for the nonlinear Schrödinger 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.

VL - 19 UR - https://doi.org/10.1142/S0218202509003589 ER - TY - JOUR T1 - Some new entire solutions of semilinear elliptic equations on Rn JF - Adv. Math. 221 (2009) 1843-1909 Y1 - 2009 A1 - Andrea Malchiodi PB - Elsevier UR - http://hdl.handle.net/1963/3645 U1 - 659 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Strain-order coupling in nematic elastomers: equilibrium configurations JF - Math. Models Methods Appl. Sci. 19 (2009) 601-630 Y1 - 2009 A1 - Pierluigi Cesana A1 - Antonio DeSimone AB - 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. UR - http://hdl.handle.net/1963/2700 U1 - 1400 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Stratos: a code for 3D free surface flows with floating constraints Y1 - 2009 A1 - Antonio DeSimone A1 - B. Bianchi A1 - Luca Heltai AB - 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...... UR - http://hdl.handle.net/1963/3701 U1 - 604 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Tools for the Solution of PDEs Defined on Curved Manifolds with deal.II Y1 - 2009 A1 - Antonio DeSimone A1 - Luca Heltai A1 - Cataldo Manigrasso AB - 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. UR - http://hdl.handle.net/1963/3700 U1 - 605 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Topological branes, p-algebras and generalized Nahm equations JF - Phys. Lett. B 672 (2009) 390-395 Y1 - 2009 A1 - Giulio Bonelli A1 - Alessandro Tanzini A1 - Maxim Zabzine AB - 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 UR - http://hdl.handle.net/1963/2702 U1 - 1398 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Topological expansion for the Cauchy two-matrix model JF - J. Phys. A Y1 - 2009 A1 - Marco Bertola A1 - Ferrer, A. Prats VL - 42 UR - http://dx.doi.org/10.1088/1751-8113/42/33/335201 ER - TY - RPRT T1 - Twisted Covariance vs Weyl Quantisation Y1 - 2009 A1 - Gherardo Piacitelli AB - 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\\\"? UR - http://hdl.handle.net/1963/3451 U1 - 885 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - On universality of critical behaviour in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the \\\\it tritronquée solution to the Painlevé-I equation JF - J. Nonlinear Sci. 19 (2009) 57-94 Y1 - 2009 A1 - Boris Dubrovin A1 - Tamara Grava A1 - Christian Klein AB - We argue that the critical behaviour near the point of ``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. UR - http://hdl.handle.net/1963/2525 U1 - 1593 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Universality of the break-up profile for the KdV equation in the small dispersion limit using the Riemann-Hilbert approach JF - Comm. Math. Phys. 286 (2009) 979-1009 Y1 - 2009 A1 - Tamara Grava A1 - Tom Claeys AB - 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. UR - http://hdl.handle.net/1963/2636 U1 - 1487 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - A variational model for quasistatic crack growth in nonlinear elasticity: some qualitative properties of the solutions JF - Boll. Unione Mat. Ital. (9) 2 (2009) 371-390 Y1 - 2009 A1 - Gianni Dal Maso A1 - Alessandro Giacomini A1 - Marcello Ponsiglione UR - http://hdl.handle.net/1963/2675 U1 - 1425 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On viscosity solutions of Hamilton-Jacobi equations JF - Trans. Amer. Math. Soc. 361 (2009) 41-59 Y1 - 2009 A1 - Sandro Zagatti AB - 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. PB - American Mathematical Society UR - http://hdl.handle.net/1963/3420 U1 - 915 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Asymptotic evolution for the semiclassical nonlinear Schrödinger equation in presence of electric and magnetic fields JF - Journal of Differential Equations Y1 - 2008 A1 - Alessandro Selvitella AB -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.

VL - 245 UR - http://www.sciencedirect.com/science/article/pii/S002203960800243X ER - TY - JOUR T1 - Cantor families of periodic solutions for completely resonant wave equations JF - Frontiers of Mathematics in China Y1 - 2008 A1 - Massimiliano Berti A1 - Philippe Bolle AB - 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. © 2008 Higher Education Press. VL - 3 N1 - cited By (since 1996)0 ER - TY - JOUR T1 - Cantor families of periodic solutions for wave equations via a variational principle JF - Advances in Mathematics Y1 - 2008 A1 - Massimiliano Berti A1 - Philippe Bolle AB - 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. © 2007 Elsevier Inc. All rights reserved. VL - 217 N1 - cited By (since 1996)6 ER - TY - JOUR T1 - Cantor families of periodic solutions of wave equations with C k nonlinearities JF - Nonlinear Differential Equations and Applications Y1 - 2008 A1 - Massimiliano Berti A1 - Philippe Bolle AB - 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. © 2008 Birkhaueser. VL - 15 N1 - cited By (since 1996)10 ER - TY - JOUR T1 - Concentrating solutions of some singularly perturbed elliptic equations JF - Front. Math. China 3 (2008) 239-252 Y1 - 2008 A1 - Andrea Malchiodi AB - 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. UR - http://hdl.handle.net/1963/2657 U1 - 1466 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On concentration of positive bound states for the Schrödinger-Poisson problem with potentials JF - Advanced nonlinear studies Y1 - 2008 A1 - Ianni, Isabella A1 - Giusi Vaira AB -We study the existence of semiclassical states for a nonlinear Schrödinger-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.

PB - Advanced Nonlinear Studies, Inc. VL - 8 ER - TY - JOUR T1 - Convergence of equilibria of three-dimensional thin elastic beams JF - Proc. Roy. Soc. Edinburgh Sect. A 138 (2008) 873-896 Y1 - 2008 A1 - Maria Giovanna Mora A1 - Stefan Müller AB - 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 Müller 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. UR - http://hdl.handle.net/1963/1896 U1 - 2339 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Decomposition results for functions with bounded variation JF - Boll. Unione Mat. Ital. (9) 1 (2008) 497-505 Y1 - 2008 A1 - Gianni Dal Maso A1 - Rodica Toader PB - Unione Matematica Italiana UR - http://hdl.handle.net/1963/3535 U1 - 729 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Discerning static and causal interactions in genome-wide reverse engineering problems JF - Bioinformatics 24 (2008) 1510-1515 Y1 - 2008 A1 - Mattia Zampieri A1 - Nicola Soranzo A1 - Claudio Altafini AB - 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. UR - http://hdl.handle.net/1963/2757 U1 - 1943 U2 - Physics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Entire solutions of autonomous equations on Rn with nontrivial asymptotics JF - Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 19 (2008) 65-72 Y1 - 2008 A1 - Andrea Malchiodi AB - 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. UR - http://hdl.handle.net/1963/2640 U1 - 1483 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - An entropy based Glimm-type functional JF - J. Hyperbolic Differ. Equ. 5 (2008) 643-662 Y1 - 2008 A1 - Laura Caravenna PB - World Scientific UR - http://hdl.handle.net/1963/4051 U1 - 351 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Equivalent definitions of asymptotic 100% B.E.C. JF - Nuovo Cimento B 123 (2008) 181-192 Y1 - 2008 A1 - Alessandro Michelangeli AB - 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. UR - http://hdl.handle.net/1963/2546 U1 - 1573 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Eulerian calculus for the displacement convexity in the Wasserstein distance JF - SIAM J. Math. Anal. 40 (2008) 1104-1122 Y1 - 2008 A1 - Sara Daneri A1 - Giuseppe Savarè AB - 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. PB - SIAM UR - http://hdl.handle.net/1963/3413 U1 - 922 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence of conformal metrics with constant $Q$-curvature JF - Ann. of Math. 168 (2008) 813-858 Y1 - 2008 A1 - Zindine Djadli A1 - Andrea Malchiodi AB - 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. UR - http://hdl.handle.net/1963/2308 U1 - 1708 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Fluid–structure interaction problems in free surface flows: Application to boat dynamics JF - International Journal for Numerical Methods in Fluids Y1 - 2008 A1 - L. Formaggia A1 - Edie Miglio A1 - Andrea Mola A1 - N Parolini PB - Wiley VL - 56 UR - https://doi.org/10.1002/fld.1583 ER - TY - JOUR T1 - Forced Vibrations of a Nonhomogeneous String JF - SIAM J. Math. Anal. 40 (2008) 382-412 Y1 - 2008 A1 - P Baldi A1 - Massimiliano Berti AB - 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. UR - http://hdl.handle.net/1963/2643 U1 - 1480 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Frobenius Manifolds and Central Invariants for the Drinfeld - Sokolov Bihamiltonian Structures JF - Adv. Math. 219 (2008) 780-837 Y1 - 2008 A1 - Boris Dubrovin A1 - Liu Si-Qi A1 - Zhang Youjin AB - 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. UR - http://hdl.handle.net/1963/2523 U1 - 1595 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Fulde-Ferrell-Larkin-Ovchinnikov pairing in one-dimensional optical lattices JF - Phys. Rev. B 77 (2008) 245105 Y1 - 2008 A1 - Matteo Rizzi A1 - Marco Polini A1 - Miguel A. Cazalilla A1 - M.R. Bakhtiari A1 - Mario P. Tosi A1 - Rosario Fazio AB -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.

UR - http://hdl.handle.net/1963/2694 U1 - 1406 U2 - Physics U3 - Condensed Matter Theory ER - TY - JOUR T1 - A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds JF - Discrete Contin. Dyn. Syst. 20 (2008) 801-822 Y1 - 2008 A1 - Andrei A. Agrachev A1 - Ugo Boscain A1 - Mario Sigalotti AB - 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. UR - http://hdl.handle.net/1963/1869 U1 - 2353 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Globally stable quasistatic evolution in plasticity with softening JF - Netw. Heterog. Media 3 (2008) 567-614 Y1 - 2008 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Maria Giovanna Mora A1 - Massimiliano Morini AB - 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. UR - http://hdl.handle.net/1963/1965 U1 - 2228 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Gradient bounds for minimizers of free discontinuity problems related to cohesive zone models in fracture mechanics JF - Calc. Var. Partial Differential Equations 31 (2008) 137-145 Y1 - 2008 A1 - Gianni Dal Maso A1 - Adriana Garroni AB - 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. UR - http://hdl.handle.net/1963/1723 U1 - 2428 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Hamiltonian partial differential equations and Frobenius manifolds JF - Russian Mathematical Surveys. Volume 63, Issue 6, 2008, Pages 999-1010 Y1 - 2008 A1 - Boris Dubrovin AB - 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–de Vries, non-linear\\r\\nSchr¨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. PB - SISSA UR - http://hdl.handle.net/1963/6471 U1 - 6416 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Harish-Chandra integrals as nilpotent integrals JF - Int. Math. Res. Not. IMRN Y1 - 2008 A1 - Marco Bertola A1 - Ferrer, Aleix Prats ER - TY - RPRT T1 - Instanton counting on Hirzebruch surfaces Y1 - 2008 A1 - Ugo Bruzzo A1 - Rubik Poghossian A1 - Alessandro Tanzini AB - 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. UR - http://hdl.handle.net/1963/2852 U1 - 1848 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Invariant Carnot-Caratheodory metrics on S3, SO(3), SL(2) and Lens Spaces JF - SIAM J. Control Optim. 47 (2008) 1851-1878 Y1 - 2008 A1 - Ugo Boscain A1 - Francesco Rossi AB - 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). UR - http://hdl.handle.net/1963/2144 U1 - 2099 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Invariant Manifolds for Viscous Profiles of a Class of Mixed Hyperbolic-Parabolic Systems Y1 - 2008 A1 - Stefano Bianchini A1 - Laura Spinolo UR - http://hdl.handle.net/1963/3400 U1 - 932 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere JF - Comm. Math. Phys. 279 (2008) 77-116 Y1 - 2008 A1 - Francesco D'Andrea A1 - Ludwik Dabrowski A1 - Giovanni Landi AB - 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 `instanton\\\' projection. A real structure which satisfies all required properties modulo a suitable ideal of `infinitesimals\\\' is also introduced. UR - http://hdl.handle.net/1963/2567 U1 - 1553 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Limit Time Optimal Syntheses for a control-affine system on S² JF - SIAM J. Control Optim. 47 (2008) 111-143 Y1 - 2008 A1 - Paolo Mason A1 - Rebecca Salmoni A1 - Ugo Boscain A1 - Yacine Chitour AB - 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 $U_\\\\alpha$. UR - http://hdl.handle.net/1963/1862 U1 - 2360 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the Logarithmic Asymptotics of the Sixth Painleve\' Equation (Summer 2007) JF - J.Phys.A: Math.Theor. 41,(2008), 205201-205247 Y1 - 2008 A1 - Davide Guzzetti AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/6521 N1 - 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 → 0. 2). The title of the journal article is : The logarithmic asymptotics of the sixth Painlevé equation U1 - 6473 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Minimization of non quasiconvex functionals by integro-extremization method JF - Discrete Contin. Dyn. Syst. 21 (2008) 625-641 Y1 - 2008 A1 - Sandro Zagatti UR - http://hdl.handle.net/1963/2761 U1 - 1939 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Minimizers of non convex scalar functionals and viscosity solutions of Hamilton-Jacobi equations JF - Calc. Var. Partial Differential Equations 31 (2008) 511-519 Y1 - 2008 A1 - Sandro Zagatti UR - http://hdl.handle.net/1963/2760 U1 - 1940 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Morse theory and a scalar field equation on compact surfaces JF - Adv. Differential Equations 13 (2008) 1109-1129 Y1 - 2008 A1 - Andrea Malchiodi PB - Khayyam Publishing UR - http://hdl.handle.net/1963/3531 U1 - 733 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Multiple bound states for the Schroedinger-Poisson problem JF - Commun. Contemp. Math. 10 (2008) 391-404 Y1 - 2008 A1 - Antonio Ambrosetti A1 - David Ruiz UR - http://hdl.handle.net/1963/2679 U1 - 1421 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Noncommutative families of instantons JF - Int. Math. Res. Not. vol. 2008, Article ID rnn038 Y1 - 2008 A1 - Giovanni Landi A1 - Chiara Pagani A1 - Cesare Reina A1 - Walter van Suijlekom AB - 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 $Sp_\\\\theta(2)$. PB - Oxford University Press UR - http://hdl.handle.net/1963/3417 U1 - 918 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - The Noncommutative Geometry of the Quantum Projective Plane JF - Rev. Math. Phys. 20 (2008) 979-1006 Y1 - 2008 A1 - Francesco D'Andrea A1 - Ludwik Dabrowski A1 - Giovanni Landi AB - 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)). UR - http://hdl.handle.net/1963/2548 U1 - 1571 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - A note on the differentiability of Lipschitz functions and the chain rule in Sobolev spaces Y1 - 2008 A1 - Massimiliano Morini UR - http://hdl.handle.net/1963/2654 U1 - 1469 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Numerical study of a multiscale expansion of the Korteweg-de Vries equation and Painlevé-II equation JF - Proc. R. Soc. A 464 (2008) 733-757 Y1 - 2008 A1 - Tamara Grava A1 - Christian Klein AB - 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 $\\\\epsilon^{2/3}$. UR - http://hdl.handle.net/1963/2592 U1 - 1530 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Optimal Strokes for Low Reynolds Number Swimmers: An Example JF - J. Nonlinear Sci. 18 (2008) 277-302 Y1 - 2008 A1 - François Alouges A1 - Antonio DeSimone A1 - Aline Lefebvre AB - 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). PB - Springer UR - http://hdl.handle.net/1963/4006 U1 - 396 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Origin of Co-Expression Patterns in E.coli and S.cerevisiae Emerging from Reverse Engineering Algorithms JF - PLoS ONE 3 (2008) e2981 Y1 - 2008 A1 - Mattia Zampieri A1 - Nicola Soranzo A1 - Daniele Bianchini A1 - Claudio Altafini AB - 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. UR - http://hdl.handle.net/1963/2722 U1 - 1379 U2 - Physics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On periodic elliptic equations with gradient dependence JF - Communications on Pure and Applied Analysis Y1 - 2008 A1 - Massimiliano Berti A1 - Matzeu, M A1 - Enrico Valdinoci AB - 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. VL - 7 N1 - cited By (since 1996)1 ER - TY - JOUR T1 - Positive solutions of nonlinear Schrödinger-Poisson systems with radial potentials vanishing at infinity JF - Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl Y1 - 2008 A1 - Mercuri, Carlo AB -We deal with a weighted nonlinear Schr¨odinger-Poisson system, allowing the potentials to vanish at infinity.

PB - Citeseer VL - 19 UR - http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.510.3635&rep=rep1&type=pdf ER - TY - JOUR T1 - Relaxation of some transversally isotropic energies and applications to smectic A elastomers JF - Math. Models Methods Appl. Sci. 18 (2008) 1-20 Y1 - 2008 A1 - James Adams A1 - Sergio Conti A1 - Antonio DeSimone A1 - Georg Dolzmann UR - http://hdl.handle.net/1963/1912 U1 - 2325 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A second order minimality condition for the Mumford-Shah functional JF - Calc. Var. Partial Differential Equations 33 (2008) 37-74 Y1 - 2008 A1 - Filippo Cagnetti A1 - Maria Giovanna Mora A1 - Massimiliano Morini AB - 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. UR - http://hdl.handle.net/1963/1955 U1 - 2318 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On semistable principal bundles over a complex projective manifold JF - Int. Math. Res. Not. vol. 2008, article ID rnn035 Y1 - 2008 A1 - Indranil Biswas A1 - Ugo Bruzzo AB - 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. PB - Oxford University Press UR - http://hdl.handle.net/1963/3418 U1 - 917 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Solitons of linearly coupled systems of semilinear non-autonomous equations on Rn JF - J. Funct. Anal. 254 (2008) 2816-2845 Y1 - 2008 A1 - Antonio Ambrosetti A1 - Giovanna Cerami A1 - David Ruiz AB - Using concentration compactness type arguments, we prove some results about the existence of positive ground and bound state of linearly coupled systems of nonlinear Schrödinger equations. UR - http://hdl.handle.net/1963/2175 U1 - 2069 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Stability of planar switched systems: the nondiagonalizable case JF - Commun. Pure Appl. Anal. 7 (2008) 1-21 Y1 - 2008 A1 - Ugo Boscain A1 - Moussa Balde UR - http://hdl.handle.net/1963/1857 U1 - 2361 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Symmetric obstruction theories and Hilbert schemes of points on threefolds JF - Algebra Number Theory 2 (2008) 313-345 Y1 - 2008 A1 - Kai Behrend A1 - Barbara Fantechi AB - 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. UR - http://hdl.handle.net/1963/2709 U1 - 1392 U2 - Mathematics U3 - Mathematical Physics ER - TY - THES T1 - Symmetries of noncommutative spaces and equivariant cohomology Y1 - 2008 A1 - Lucio Cirio KW - Noncommutative spaces AB - 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¯ne algebraic models for the equivariant cohomology of such actions. PB - SISSA UR - http://hdl.handle.net/1963/5254 U1 - 5077 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Topological Gauge Theories on Local Spaces and Black Hole Entropy Countings JF - Adv. Theor. Math. Phys. 12 (2008) 1429-1446 Y1 - 2008 A1 - Giulio Bonelli A1 - Alessandro Tanzini AB - 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. UR - http://hdl.handle.net/1963/1992 U1 - 2204 U2 - Physics U3 - Elementary Particle Theory ER - TY - JOUR T1 - Topological methods for an elliptic equation with exponential nonlinearities JF - Discrete Contin. Dyn. Syst. 21 (2008) 277-294 Y1 - 2008 A1 - Andrea Malchiodi AB - 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. UR - http://hdl.handle.net/1963/2594 U1 - 1528 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Transition layer for the heterogeneous Allen-Cahn equation JF - Ann. Inst. H. Poincare Anal. Non Lineaire 25 (2008) 609-631 Y1 - 2008 A1 - Fethi Mahmoudi A1 - Andrea Malchiodi A1 - Juncheng Wei AB - 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 $j \\\\to + \\\\infty$. UR - http://hdl.handle.net/1963/2656 U1 - 1467 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - Transport Rays and Applications to Hamilton–Jacobi Equations T2 - Nonlinear PDE’s and Applications : C.I.M.E. Summer School, Cetraro, Italy 2008 / Stefano Bianchini, Eric A. Carlen, Alexander Mielke, Cédric Villani. Eds. Luigi Ambrosio, Giuseppe Savaré. - Berlin : Springer, 2011. - (Lecture Notes in Mathematics ; 20 Y1 - 2008 A1 - Stefano Bianchini A1 - Matteo Gloyer AB - 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). JF - Nonlinear PDE’s and Applications : C.I.M.E. Summer School, Cetraro, Italy 2008 / Stefano Bianchini, Eric A. Carlen, Alexander Mielke, Cédric Villani. Eds. Luigi Ambrosio, Giuseppe Savaré. - Berlin : Springer, 2011. - (Lecture Notes in Mathematics ; 20 PB - Springer SN - 978-3-642-21718-0 UR - http://hdl.handle.net/1963/5463 N1 - This volume collects the notes of the CIME course Nonlinear PDE’s and\\r\\napplications held in Cetraro (Italy) on June 23–28, 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). U1 - 5298 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - A vanishing viscosity approach to quasistatic evolution in plasticity with softening JF - Arch. Ration. Mech. Anal. 189 (2008) 469-544 Y1 - 2008 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Maria Giovanna Mora A1 - Massimiliano Morini AB - 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. UR - http://hdl.handle.net/1963/1844 U1 - 2373 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Variational methods for Hamiltonian PDEs JF - NATO Science for Peace and Security Series B: Physics and Biophysics Y1 - 2008 A1 - Massimiliano Berti AB - 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. © 2008 Springer Science + Business Media B.V. SN - 9781402069628 N1 - cited By (since 1996)0 ER - TY - JOUR T1 - Asymptotic behaviour of smooth solutions for partially dissipative hyperbolic systems with a convex entropy JF - Comm. Pure Appl. Math. 60 (2007) 1559-1622 Y1 - 2007 A1 - Stefano Bianchini A1 - Bernard Hanouzet A1 - Roberto Natalini AB - 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. UR - http://hdl.handle.net/1963/1780 U1 - 2764 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The Asymptotic Behaviour of the Fourier Transforms of Orthogonal Polynomials II: L.I.F.S. Measures and Quantum Mechanics JF - Ann. Henri Poincar´e 8 (2007), 301–336 Y1 - 2007 A1 - Davide Guzzetti A1 - Giorgio Mantica AB - 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 PB - 2007 Birkh¨auser Verlag Basel/Switzerland U1 - 6480 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Asymptotic variational wave equations JF - Arch. Ration. Mech. Anal. 183 (2007) 163-185 Y1 - 2007 A1 - Alberto Bressan A1 - Zhang Ping A1 - Zheng Yuxi AB - 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. UR - http://hdl.handle.net/1963/2182 U1 - 2062 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Biorthogonal Laurent polynomials, Töplitz determinants, minimal Toda orbits and isomonodromic tau functions JF - Constr. Approx. Y1 - 2007 A1 - Marco Bertola A1 - Gekhtman, M. VL - 26 ER - TY - JOUR T1 - Biorthogonal polynomials for two-matrix models with semiclassical potentials JF - J. Approx. Theory Y1 - 2007 A1 - Marco Bertola VL - 144 ER - TY - RPRT T1 - Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory Y1 - 2007 A1 - Luca Griguolo A1 - Domenico Seminara A1 - Richard J. Szabo A1 - Alessandro Tanzini AB - 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. JF - Nucl. Phys. B 772 (2007) 1-24 UR - http://hdl.handle.net/1963/1888 U1 - 2347 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Bose-Einstein condensation: analysis of problems and rigorous results Y1 - 2007 A1 - Alessandro Michelangeli UR - http://hdl.handle.net/1963/2189 U1 - 2055 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Boundary interface for the Allen-Cahn equation JF - J. Fixed Point Theory Appl. 1 (2007) 305-336 Y1 - 2007 A1 - Andrea Malchiodi A1 - Juncheng Wei UR - http://hdl.handle.net/1963/2027 U1 - 2169 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Boundary-clustered interfaces for the Allen–Cahn equation JF - Pacific Journal of Mathematics 229 (2007), No. 2, 447–468 Y1 - 2007 A1 - Andrea Malchiodi A1 - Wei-Ming Ni A1 - Juncheng Wei PB - Mathematical Sciences Publishers UR - http://hdl.handle.net/1963/5089 U1 - 4905 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - RPRT T1 - BV instability for the Lax-Friedrichs scheme Y1 - 2007 A1 - Paolo Baiti A1 - Alberto Bressan A1 - Helge Kristian Jenssen AB - 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. UR - http://hdl.handle.net/1963/2335 U1 - 1681 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Canonical structure and symmetries of the Schlesinger equations JF - Comm. Math. Phys. 271 (2007) 289-373 Y1 - 2007 A1 - Boris Dubrovin A1 - Marta Mazzocco AB - 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×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. UR - http://hdl.handle.net/1963/1997 U1 - 2199 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Chen-Ruan cohomology of ADE singularities JF - International Journal of Mathematics. Volume 18, Issue 9, October 2007, Pages 1009-1059 Y1 - 2007 A1 - Fabio Perroni KW - Chen-Ruan cohomology, Ruan\'s conjecture, McKay correspondence AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/6502 N1 - 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) U1 - 6447 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - The cohomological crepant resolution conjecture for P(1,3,4,4) Y1 - 2007 A1 - Samuel Boissiere A1 - Fabio Perroni A1 - Etienne Mann AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/6513 N1 - 11 pages, 1 figure U1 - 6464 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Comparing association network algorithms for reverse engineering of large scale gene regulatory networks: synthetic vs real data JF - Bioinformatics 23 (2007) 1640-1647 Y1 - 2007 A1 - Nicola Soranzo A1 - Ginestra Bianconi A1 - Claudio Altafini AB - 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/ UR - http://hdl.handle.net/1963/2028 U1 - 2168 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - The complete one-loop spin chain for N=2 Super-Yang-Mills Y1 - 2007 A1 - Paolo Di Vecchia A1 - Alessandro Tanzini AB - 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. UR - http://hdl.handle.net/1963/2309 N1 - Contributed to NATO Advanced Study Institute and EC Summer School on String Theory: From Gauge Interactions to Cosmology, Cargese, France, 7-19 Jun 2004. U1 - 1707 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Computing Amplitudes in topological M-theory Y1 - 2007 A1 - Giulio Bonelli A1 - Alessandro Tanzini A1 - Maxim Zabzine AB - 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. JF - JHEP 03 (2007) 023 UR - http://hdl.handle.net/1963/1901 U1 - 2335 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Concentration on minimal submanifolds for a singularly perturbed Neumann problem JF - Adv. Math. 209 (2007) 460-525 Y1 - 2007 A1 - Fethi Mahmoudi A1 - Andrea Malchiodi AB - 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. UR - http://hdl.handle.net/1963/2186 U1 - 2058 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Feedback control of spin systems Y1 - 2007 A1 - Claudio Altafini AB - 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. JF - Quantum Inf. Process. 6 (2007) 9-36 UR - http://hdl.handle.net/1963/1808 N1 - Proc. of the 44th IEEE Conf. on Decision and Control,. Seville, Spain, December 2005 (to appear). U1 - 2406 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Feedback stabilization of quantum ensembles: a global convergence analysis on complex flag manifolds JF - 45th IEEE Conference on Decision and Control (2007) 2471-2476 Y1 - 2007 A1 - Claudio Altafini AB - 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. UR - http://hdl.handle.net/1963/1729 U1 - 2422 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On finite-dimensional projections of distributions for solutions of randomly forced PDE\\\'s JF - Ann. Inst. Henri Poincare-Prob. Stat. 43 (2007) 399-415 Y1 - 2007 A1 - Andrei A. Agrachev A1 - Sergei Kuksin A1 - Andrey Sarychev A1 - Armen Shirikyan AB - 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. UR - http://hdl.handle.net/1963/2012 U1 - 2184 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Gaussian estimates for hypoelliptic operators via optimal control JF - Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 333-342 Y1 - 2007 A1 - Ugo Boscain A1 - Sergio Polidoro AB - 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. UR - http://hdl.handle.net/1963/1994 U1 - 2202 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - High-order angles in almost-Riemannian geometry Y1 - 2007 A1 - Ugo Boscain A1 - Mario Sigalotti AB - 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. UR - http://hdl.handle.net/1963/1995 U1 - 2201 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The holomorphic anomaly for open string moduli JF - JHEP 10 (2007) 060 Y1 - 2007 A1 - Giulio Bonelli A1 - Alessandro Tanzini AB - 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. UR - http://hdl.handle.net/1963/2113 U1 - 2576 U2 - Physics U3 - Elementary Particle Theory ER - TY - JOUR T1 - Luther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas JF - Phys. Rev. Lett. 98 (2007) 030404 Y1 - 2007 A1 - Gao Xianlong A1 - Matteo Rizzi A1 - Marco Polini A1 - Rosario Fazio A1 - Mario P. Tosi A1 - Vivaldo L. Jr. Campo A1 - Klaus Capelle AB -

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.

UR - http://hdl.handle.net/1963/2056 U1 - 2140 U2 - Physics U3 - Condensed Matter Theory ER - TY - CHAP T1 - Massless scalar field in a two-dimensional de Sitter universe T2 - Rigorous quantum field theory Y1 - 2007 A1 - Marco Bertola A1 - Corbetta, Francesco A1 - Moschella, Ugo JF - Rigorous quantum field theory T3 - Progr. Math. PB - Birkhäuser CY - Basel VL - 251 ER - TY - RPRT T1 - On the Maz\\\'ya inequalities: existence and multiplicity results for an elliptic problem involving cylindrical weights Y1 - 2007 A1 - Marita Gazzini A1 - Roberta Musina UR - http://hdl.handle.net/1963/2522 U1 - 1596 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Metrics on semistable and numerically effective Higgs bundles JF - J. Reine Angew. Math. 612 (2007) 59-79 Y1 - 2007 A1 - Ugo Bruzzo A1 - Beatriz Grana-Otero AB - 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. UR - http://hdl.handle.net/1963/1840 U1 - 2376 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Multi-bump solitons to linearly coupled systems of nonlinear Schrödinger equations Y1 - 2007 A1 - Antonio Ambrosetti A1 - Eduardo Colorado A1 - David Ruiz JF - Calc. Var. Partial Differential Equations 30 (2007) 85-112 UR - http://hdl.handle.net/1963/1835 U1 - 2381 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Nearly time optimal stabilizing patchy feedbacks JF - Ann. Inst. H. Poincare Anal. Non Lineaire 24 (2007) 279-310 Y1 - 2007 A1 - Fabio Ancona A1 - Alberto Bressan AB - 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 $\\\\tau(y)+\\\\ve$. UR - http://hdl.handle.net/1963/2185 U1 - 2059 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Necessary and sufficient conditions for the chainrule in W1,1loc(RN;Rd) and BVloc(RN;Rd) JF - J. Eur. Math. Soc. (JEMS) 9 (2007) 219-252 Y1 - 2007 A1 - Giovanni Leoni A1 - Massimiliano Morini AB -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.

UR - http://hdl.handle.net/1963/2037 U1 - 2159 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - A new model for contact angle hysteresis Y1 - 2007 A1 - Antonio DeSimone A1 - Natalie Gruenewald A1 - Felix Otto AB - 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. JF - Netw. Heterog. Media 2 (2007) 211-225 UR - http://hdl.handle.net/1963/1848 U1 - 2369 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Noncommutative geometry and quantum group symmetries Y1 - 2007 A1 - Francesco D'Andrea KW - Noncommutative geometry AB - 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], «we are doing mathematics in order to understand, create, and handle things, and perhaps this understanding is mathematics» . 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 `final\\\' theory of Nature, but simply a sequence of theories which provide more and more accurate descriptions of the real world... PB - SISSA UR - http://hdl.handle.net/1963/5269 U1 - 5093 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - On a notion of unilateral slope for the Mumford-Shah functional JF - NoDEA 13 (2007) 713-734 Y1 - 2007 A1 - Gianni Dal Maso A1 - Rodica Toader AB - 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. UR - http://hdl.handle.net/1963/2059 U1 - 2137 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The number of eigenvalues of three-particle Schrödinger operators on lattices JF - J. Phys. A 40 (2007) 14819-14842 Y1 - 2007 A1 - Sergio Albeverio A1 - Gianfausto Dell'Antonio A1 - Saidakhmat N. Lakaev AB - 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. UR - http://hdl.handle.net/1963/2576 U1 - 1545 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Numerical solution of the small dispersion limit of Korteweg de Vries and Whitham equations Y1 - 2007 A1 - Tamara Grava A1 - Christian Klein AB - 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 `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. JF - Comm. Pure Appl. Math. 60 (2007) 1623-1664 UR - http://hdl.handle.net/1963/1788 U1 - 2756 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Numerical study of a multiscale expansion of KdV and Camassa-Holm equation Y1 - 2007 A1 - Tamara Grava A1 - Christian Klein AB - 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 UR - http://hdl.handle.net/1963/2527 U1 - 1591 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Numerically flat Higgs vector bundles Y1 - 2007 A1 - Ugo Bruzzo A1 - Beatriz Grana-Otero AB - 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. JF - Commun. Contemp. Math. 9 (2007) 437-446 UR - http://hdl.handle.net/1963/1757 U1 - 2787 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Parametrized curves in Lagrange Grassmannians JF - C. R. Math. 345 (2007) 647-652 Y1 - 2007 A1 - Igor Zelenko A1 - Li Chengbo UR - http://hdl.handle.net/1963/2560 U1 - 1559 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Perturbation techniques applied to the real vanishing viscosity approximation of an initial boundary value problem Y1 - 2007 A1 - Stefano Bianchini PB - SISSA UR - http://preprints.sissa.it/handle/1963/35315 U1 - 35623 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Quasistatic crack growth for a cohesive zone model with prescribed crack path Y1 - 2007 A1 - Gianni Dal Maso A1 - Chiara Zanini AB - 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. JF - Proc. Roy. Soc. Edinburgh Sect. A 137 (2007) 253-279 UR - http://hdl.handle.net/1963/1686 U1 - 2447 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic evolution problems for pressure-sensitive plastic materials JF - Milan J. Math. 75 (2007) 117-134 Y1 - 2007 A1 - Gianni Dal Maso A1 - Alexey Demyanov A1 - Antonio DeSimone AB - We study quasistatic evolution problems for pressure-sensitive plastic materials in the context of small strain associative perfect plasticity. UR - http://hdl.handle.net/1963/1962 U1 - 2231 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Reciprocal transformations and flat metrics on Hurwitz spaces JF - J. Phys. A 40 (2007) 10769-10790 Y1 - 2007 A1 - Simonetta Abenda A1 - Tamara Grava AB - 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. UR - http://hdl.handle.net/1963/2210 U1 - 2034 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Reduced density matrices and Bose-Einstein condensation Y1 - 2007 A1 - Alessandro Michelangeli AB - 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. UR - http://hdl.handle.net/1963/1986 U1 - 2210 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - On the reductions and classical solutions of the Schlesinger equations JF - Differential equations and quantum groups, IRMA Lect. Math. Theor. Phys. 9 (2007) 157-187 Y1 - 2007 A1 - Boris Dubrovin A1 - Marta Mazzocco AB - 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×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 “more complicated”\\r\\nSchlesinger equations S(n,m) to “simpler” S(n′,m′) having n′ < n\\r\\nor m′ < m. PB - SISSA UR - http://hdl.handle.net/1963/6472 U1 - 6418 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - On the regularity of weak solutions to H-systems JF - Atti .Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 209-219 Y1 - 2007 A1 - Roberta Musina AB - 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.... UR - http://hdl.handle.net/1963/1753 U1 - 2791 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Role of scaling limits in the rigorous analysis of Bose-Einstein condensation JF - J. Math. Phys. 48 (2007) 102102 Y1 - 2007 A1 - Alessandro Michelangeli AB - 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. UR - http://hdl.handle.net/1963/1984 U1 - 2212 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Semistable principal Higgs bundles Y1 - 2007 A1 - Ugo Bruzzo A1 - Beatriz Grana-Otero UR - http://hdl.handle.net/1963/2533 U1 - 1585 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Smooth toric DM stacks Y1 - 2007 A1 - Barbara Fantechi A1 - Etienne Mann A1 - Fabio Nironi AB - 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. UR - http://hdl.handle.net/1963/2120 U1 - 2123 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Soft elasticity and microstructure in smectic C elastomers Y1 - 2007 A1 - Antonio DeSimone A1 - James Adams A1 - Sergio Conti AB - 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. JF - Contin. Mech. Thermodyn. 18 (2007) 319-334 UR - http://hdl.handle.net/1963/1811 U1 - 2403 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Solutions of vectorial Hamilton-Jacobi equations and minimizers of nonquasiconvex functionals JF - J. Math. Anal. Appl. 335 (2007) 1143-1160 Y1 - 2007 A1 - Sandro Zagatti AB - 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. UR - http://hdl.handle.net/1963/2763 U1 - 1937 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Solutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part II: proof of the existence result Y1 - 2007 A1 - Fethi Mahmoudi A1 - Andrea Malchiodi AB - 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. UR - http://hdl.handle.net/1963/2111 U1 - 2578 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Solutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part I: study of the limit set and approximate solutions Y1 - 2007 A1 - Fethi Mahmoudi A1 - Andrea Malchiodi A1 - Marcelo Montenegro AB - 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. UR - http://hdl.handle.net/1963/2112 U1 - 2577 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Some existence results for the Toda system on closed surfaces JF - Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 391-412 Y1 - 2007 A1 - Andrea Malchiodi A1 - Cheikh Birahim Ndiaye AB - 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 $\\\\rho_2 < 4 \\\\pi$. UR - http://hdl.handle.net/1963/1775 U1 - 2769 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Stability of front tracking solutions to the initial and boundary value problem for systems of conservation laws JF - NoDEA Nonlinear Differential Equations Appl. 14 (2007) 569-592 Y1 - 2007 A1 - Andrea Marson A1 - Carlotta Donadello UR - http://hdl.handle.net/1963/1769 U1 - 2775 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Standing waves of some coupled Nonlinear Schrödinger Equations Y1 - 2007 A1 - Antonio Ambrosetti A1 - Eduardo Colorado AB - 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. JF - J. Lond. Math. Soc. 75 (2007) 67-82 UR - http://hdl.handle.net/1963/1821 U1 - 2393 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Strengthened convergence of marginals to the cubic nonlinear Schroedinger equation Y1 - 2007 A1 - Alessandro Michelangeli AB - 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. UR - http://hdl.handle.net/1963/1977 U1 - 2218 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Surfactants in Foam Stability: A Phase-Field Model JF - Arch. Rational Mech. Anal. 183 (2007) 411-456 Y1 - 2007 A1 - Irene Fonseca A1 - Massimiliano Morini A1 - Valeriy Slastikov AB - 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. UR - http://hdl.handle.net/1963/2035 U1 - 2161 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Time optimal swing-up of the planar pendulum JF - 46th IEEE Conference on Decision and Control (2007) 5389 - 5394 Y1 - 2007 A1 - Mireille E. Broucke A1 - Paolo Mason A1 - Benedetto Piccoli AB - This paper presents qualitative and numerical results on the global structure of the time optimal trajectories of the planar pendulum on a cart. UR - http://hdl.handle.net/1963/1867 U1 - 2355 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Time-dependent systems of generalized Young measures Y1 - 2007 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Maria Giovanna Mora A1 - Massimiliano Morini AB - 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. JF - Netw. Heterog. Media 2 (2007) 1-36 UR - http://hdl.handle.net/1963/1795 U1 - 2749 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Twisted noncommutative equivariant Y1 - 2007 A1 - Lucio Cirio AB - 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. UR - http://hdl.handle.net/1963/1991 U1 - 2205 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Uniqueness and continuous dependence on boundary data for integro-extremal minimizers of the functional of the gradient JF - J. Convex Anal. 14 (2007) 705-727 Y1 - 2007 A1 - Sandro Zagatti AB - 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. UR - http://hdl.handle.net/1963/2762 U1 - 1938 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Viscosity solutions of Hamilton-Jacobi equations with discontinuous coefficients JF - J. Hyperbolic Differ. Equ. 4 (2007) 771-795 Y1 - 2007 A1 - Giuseppe Maria Coclite A1 - Nils Henrik Risebro AB - 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. PB - World Scientific UR - http://hdl.handle.net/1963/2907 U1 - 1793 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - 2-d stability of the Néel wall JF - Calc. Var. Partial Differential Equations 27 (2006) 233-253 Y1 - 2006 A1 - Antonio DeSimone A1 - Hans Knuepfer A1 - Felix Otto AB - 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 Néel walls. UR - http://hdl.handle.net/1963/2194 U1 - 2050 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - 4e-condensation in a fully frustrated Josephson junction diamond chain JF - Phys. Rev. B 73 (2006) 100502(R) Y1 - 2006 A1 - Matteo Rizzi A1 - Vittorio Cataudella A1 - Rosario Fazio AB -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.

UR - http://hdl.handle.net/1963/2400 U1 - 2297 U2 - Physics U3 - Condensed Matter Theory ER - TY - RPRT T1 - Almost Global Stochastic Feedback Stabilization of Conditional Quantum Dynamics Y1 - 2006 A1 - Claudio Altafini A1 - Francesco Ticozzi AB - 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. UR - http://hdl.handle.net/1963/1727 U1 - 2424 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - An artificial viscosity approach to quasistatic crack growth Y1 - 2006 A1 - Rodica Toader A1 - Chiara Zanini AB - 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. UR - http://hdl.handle.net/1963/1850 U1 - 2367 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A Birkhoff-Lewis-Type Theorem for Some Hamiltonian PDEs JF - SIAM J. Math. Anal. 37 (2006) 83-102 Y1 - 2006 A1 - Dario Bambusi A1 - Massimiliano Berti AB - 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. UR - http://hdl.handle.net/1963/2159 U1 - 2085 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Born approximation in the problem of the rigorous derivation of the Gross-Pitaevskii equation Y1 - 2006 A1 - Alessandro Michelangeli AB - \\\"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 `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 `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 Schrödinger equation (the Gross-Pitaevskiî equation) is reviewed and discussed, with respect to the role of the Born approximation that one ends up with in an appropriate scaling limit UR - http://hdl.handle.net/1963/1819 U1 - 2395 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Bound and ground states of coupled nonlinear Schrödinger equations JF - C. R. Acad. Sci. Paris, Ser. I 342 (2006) 453-458 Y1 - 2006 A1 - Antonio Ambrosetti A1 - Eduardo Colorado AB - We prove existence of bound and ground states of some systems of coupled nonlinear Schrodinger equations. UR - http://hdl.handle.net/1963/2149 U1 - 2094 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Bound states of Nonlinear Schroedinger Equations with Potentials Vanishing at Infinity JF - J. Anal. Math. 98 (2006) 317-348 Y1 - 2006 A1 - Antonio Ambrosetti A1 - Andrea Malchiodi A1 - David Ruiz UR - http://hdl.handle.net/1963/1756 U1 - 2788 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On Bressan\\\'s conjecture on mixing properties of vector fields JF - Self-Similar Solutions of Nonlinear PDE / Ed. Piotr Biler and Grzegorz Karch. - Banach Center Publ. 74 (2006) 13-31 Y1 - 2006 A1 - Stefano Bianchini UR - http://hdl.handle.net/1963/1806 U1 - 2408 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - On a Camassa-Holm type equation with two dependent variables Y1 - 2006 A1 - Gregorio Falqui AB - 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. JF - J. Phys. A 39 (2006) 327-342 UR - http://hdl.handle.net/1963/1721 U1 - 2430 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - A Canonical Frame for Nonholonomic Rank Two Distributions of Maximal Class Y1 - 2006 A1 - Boris Doubrov A1 - Igor Zelenko AB - 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. JF - C. R. Math. Acad. Sci. Paris 342 (2006) 589-594 UR - http://hdl.handle.net/1963/1712 U1 - 2439 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Cantor families of periodic solutions for completely resonant nonlinear wave equations JF - Duke Math. J. 134 (2006) 359-419 Y1 - 2006 A1 - Massimiliano Berti A1 - Philippe Bolle AB - 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. UR - http://hdl.handle.net/1963/2161 U1 - 2083 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Classification of stable time-optimal controls on 2-manifolds JF - J. Math. Sci. 135 (2006) 3109-3124 Y1 - 2006 A1 - Ugo Boscain A1 - Igor Nikolaev A1 - Benedetto Piccoli UR - http://hdl.handle.net/1963/2196 U1 - 2048 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Common Polynomial Lyapunov Functions for Linear Switched Systems JF - SIAM J. Control Optim. 45 (2006) 226-245 Y1 - 2006 A1 - Paolo Mason A1 - Ugo Boscain A1 - Yacine Chitour AB - 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. UR - http://hdl.handle.net/1963/2181 U1 - 2063 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Compactness of solutions to some geometric fourth-order equations JF - J. Reine Angew. Math. 594 (2006) 137-174 Y1 - 2006 A1 - Andrea Malchiodi AB - 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. UR - http://hdl.handle.net/1963/2126 U1 - 2117 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Concentration at manifolds of arbitrary dimension for a singularly perturbed Neumann problem JF - Atti Accad. Naz Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 17 (2006) 279-290 Y1 - 2006 A1 - Fethi Mahmoudi A1 - Andrea Malchiodi AB - 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 $k = 1$. UR - http://hdl.handle.net/1963/2170 U1 - 2074 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Conservative Solutions to a Nonlinear Variational Wave Equation JF - Comm. Math. Phys. 266 (2006) 471-497 Y1 - 2006 A1 - Alberto Bressan A1 - Zheng Yuxi AB - 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. UR - http://hdl.handle.net/1963/2184 U1 - 2060 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A cyclic integral on k-Minkowski noncommutative space-time JF - Int. J. Mod. Phys. A 21 (2006) 3133-3150 Y1 - 2006 A1 - Alessandra Agostini A1 - Giovanni Amelino-Camelia A1 - Michele Arzano A1 - Francesco D'Andrea AB - 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 ``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 ``canonical\\\'\\\' noncommutative spacetime, with coordinate-independent commutators. UR - http://hdl.handle.net/1963/2158 U1 - 2086 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - The Dirichlet problem for H-systems with small boundary data: blowup phenomena and nonexistence results JF - Arch. Ration. Mech. Anal. 181 (2006) 1-42 Y1 - 2006 A1 - Paolo Caldiroli A1 - Roberta Musina UR - http://hdl.handle.net/1963/2252 U1 - 1995 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - An estimation of the controllability time for single-input systems on compact Lie Groups JF - ESAIM Control Optim. Calc. Var. 12 (2006) 409-441 Y1 - 2006 A1 - Andrei A. Agrachev A1 - Thomas Chambrion AB - 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. UR - http://hdl.handle.net/1963/2135 U1 - 2108 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Experimental and modeling studies of desensitization of P2X3 receptors. JF - Molecular pharmacology. 2006 Jul; 70(1):373-82 Y1 - 2006 A1 - Elena Sokolova A1 - Andrei Skorinkin A1 - Igor Moiseev A1 - Andrei A. Agrachev A1 - Andrea Nistri A1 - Rashid Giniatullin AB - 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. PB - the American Society for Pharmacology and Experimental Therapeutics UR - http://hdl.handle.net/1963/4974 U1 - 4799 U2 - Neuroscience U3 - Neurobiology U4 - -1 ER - TY - RPRT T1 - Extended affine Weyl groups and Frobenius manifolds -- II Y1 - 2006 A1 - Boris Dubrovin A1 - Zhang Youjin A1 - Zuo Dafeng AB - 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}. UR - http://hdl.handle.net/1963/1787 U1 - 2757 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Forced vibrations of wave equations with non-monotone nonlinearities JF - Ann. Inst. H. Poincaré Anal. Non Linéaire 23 (2006) 439-474 Y1 - 2006 A1 - Massimiliano Berti A1 - Luca Biasco AB - 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. UR - http://hdl.handle.net/1963/2160 U1 - 2084 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Fundamental form and Cartan tensor of (2,5)-distributions coincide JF - J. Dyn. Control Syst. 12 (2006) 247-276 Y1 - 2006 A1 - Igor Zelenko AB - 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 ``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. UR - http://hdl.handle.net/1963/2187 U1 - 2057 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on distributions of corank 1 JF - J. Math. Sci. 135 (2006) 3168-3194 Y1 - 2006 A1 - Igor Zelenko AB - 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. UR - http://hdl.handle.net/1963/2205 U1 - 2039 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Glimm interaction functional for BGK schemes Y1 - 2006 A1 - Stefano Bianchini UR - http://hdl.handle.net/1963/1770 U1 - 2774 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - On Hamiltonian perturbations of hyperbolic systems of conservation laws, II: universality of critical behaviour Y1 - 2006 A1 - Boris Dubrovin AB - 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. JF - Comm. Math. Phys. 267 (2006) 117-139 UR - http://hdl.handle.net/1963/1786 U1 - 2758 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - On Hamiltonian perturbations of hyperbolic systems of conservation laws I: quasitriviality of bihamiltonian perturbations JF - Comm. Pure Appl. Math. 59 (2006) 559-615 Y1 - 2006 A1 - Boris Dubrovin A1 - Liu Si-Qi A1 - Zhang Youjin AB - 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. UR - http://hdl.handle.net/1963/2535 U1 - 1583 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Homogeneous polynomial forms for simultaneous stabilizability of families of linear control systems: a tensor product approach JF - IEEE Trans. Automat. Control 51 (2006) 1566-1571 Y1 - 2006 A1 - Claudio Altafini AB - 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. UR - http://hdl.handle.net/1963/2226 U1 - 2018 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A Hopf bundle over a quantum four-sphere from the symplectic group JF - Commun. Math. Phys. 263 (2006) 65-88 Y1 - 2006 A1 - Giovanni Landi A1 - Chiara Pagani A1 - Cesare Reina AB - 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 $A(SU_q(2))$. UR - http://hdl.handle.net/1963/2179 U1 - 2065 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Infinite Horizon Noncooperative Differential Games Y1 - 2006 A1 - Alberto Bressan A1 - Fabio Simone Priuli AB - 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. JF - J. Differential Equations 227 (2006) 230-257 UR - http://hdl.handle.net/1963/1720 U1 - 2431 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - An instability of the Godunov scheme JF - Comm. Pure Appl. Math. 59 (2006) 1604-1638 Y1 - 2006 A1 - Alberto Bressan A1 - Helge Kristian Jenssen A1 - Paolo Baiti AB - 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. UR - http://hdl.handle.net/1963/2183 U1 - 2061 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Large Parameter Behavior of Equilibrium Measures Y1 - 2006 A1 - Tamara Grava A1 - Fei-Ran Tian AB - 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). JF - Commun. Math. Sci. 4 (2006) 551-573 UR - http://hdl.handle.net/1963/1789 U1 - 2755 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Local Index Formula on the Equatorial Podles Sphere Y1 - 2006 A1 - Francesco D'Andrea A1 - Ludwik Dabrowski AB - We discuss spectral properties of the equatorial Podles sphere. As a preparation we also study the `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.... JF - Lett. Math. Phys. 75 (2006) 235-254 UR - http://hdl.handle.net/1963/1782 U1 - 2762 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Matching Procedure for the Sixth Painlevé Equation (May 2006) JF - Journal of Physics A: Mathematical and General, Volume 39, Issue 39, 29 September 2006, Article numberS02, Pages 11973-12031 Y1 - 2006 A1 - Davide Guzzetti AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/6524 N1 - 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. U1 - 6474 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - RPRT T1 - N=1 superpotentials from multi-instanton calculus Y1 - 2006 A1 - Francesco Fucito A1 - Jose F. Morales A1 - Rubik Poghossian A1 - Alessandro Tanzini AB - 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. JF - JHEP01(2006)031 UR - http://hdl.handle.net/1963/1773 U1 - 2771 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Normal bundles to Laufer rational curves in local Calabi-Yau threefolds Y1 - 2006 A1 - Ugo Bruzzo A1 - Antonio Ricco AB - 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. JF - Lett. Math. Phys. 76 (2006) 57-63 UR - http://hdl.handle.net/1963/1785 U1 - 2759 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - On Palais-Smale sequences for H-systems: some examples JF - Adv. Differential Equations 11 (2006) 931-960 Y1 - 2006 A1 - Paolo Caldiroli A1 - Roberta Musina AB - 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. UR - http://hdl.handle.net/1963/2157 U1 - 2087 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The PDEs of biorthogonal polynomials arising in the two-matrix model JF - Math. Phys. Anal. Geom. Y1 - 2006 A1 - Marco Bertola A1 - B. Eynard VL - 9 ER - TY - JOUR T1 - Periodic solutions of nonlinear wave equations for asymptotically full measure sets of frequencies JF - Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni Y1 - 2006 A1 - P Baldi A1 - Massimiliano Berti AB - 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. VL - 17 N1 - cited By (since 1996)5 ER - TY - JOUR T1 - Q-curvature flow on S^4 JF - J. Differential Geom. 73 (2006) 1-44 Y1 - 2006 A1 - Andrea Malchiodi A1 - Michael Struwe UR - http://hdl.handle.net/1963/2193 U1 - 2051 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quantisation of bending flows JF - Czechoslovak Journal of Physics 56 (2006), n. 10-11, 1143-1148 Y1 - 2006 A1 - Gregorio Falqui A1 - Fabio Musso AB - 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. UR - http://hdl.handle.net/1963/2537 U1 - 1582 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Quasi-periodic solutions of completely resonant forced wave equations JF - Comm. Partial Differential Equations 31 (2006) 959 - 985 Y1 - 2006 A1 - Massimiliano Berti A1 - Michela Procesi AB - 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. UR - http://hdl.handle.net/1963/2234 U1 - 2010 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic evolution problems for linearly elastic-perfectly plastic materials JF - Arch. Ration. Mech. Anal. 180 (2006) 237-291 Y1 - 2006 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Maria Giovanna Mora AB - 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. UR - http://hdl.handle.net/1963/2129 U1 - 2114 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Radial solutions concentrating on spheres of nonlinear Schrödinger equations with vanishing potentials JF - Proc. Roy. Soc. Edinburgh Sect. A 136 (2006) 889-907 Y1 - 2006 A1 - Antonio Ambrosetti A1 - David Ruiz AB - 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. UR - http://hdl.handle.net/1963/1755 U1 - 2789 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - Recent analytical developments in micromagnetics T2 - The science of hysteresis / eds. Giorgio Bertotti, Isaak D. Mayergoyz. - Amsterdam: Elsevier, 2006. Vol.2, 269-381. Y1 - 2006 A1 - Antonio DeSimone A1 - Robert V. Kohn A1 - Stefan Müller A1 - Felix Otto JF - The science of hysteresis / eds. Giorgio Bertotti, Isaak D. Mayergoyz. - Amsterdam: Elsevier, 2006. Vol.2, 269-381. SN - 978-0-12-480874-4 UR - http://hdl.handle.net/1963/2230 U1 - 2014 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Reflection symmetries for multiqubit density operators JF - J. Math. Phys. 47 (2006) 032104 Y1 - 2006 A1 - Claudio Altafini A1 - Timothy F. Havel AB - 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. UR - http://hdl.handle.net/1963/2121 U1 - 2122 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Semiclassical orthogonal polynomials, matrix models and isomonodromic tau functions JF - Comm. Math. Phys. Y1 - 2006 A1 - Marco Bertola A1 - B. Eynard A1 - Harnad, J. VL - 263 ER - TY - JOUR T1 - Semistability vs. nefness for (Higgs) vector bundles JF - Differential Geom. Appl. 24 (2006) 403-416 Y1 - 2006 A1 - Ugo Bruzzo A1 - Daniel Hernandez Ruiperez AB - 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. UR - http://hdl.handle.net/1963/2237 U1 - 2007 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - On Separation of Variables for Homogeneous SL(r) Gaudin Systems Y1 - 2006 A1 - Gregorio Falqui A1 - Fabio Musso AB - 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. JF - Math. Phys. Anal. Geom. 9 (2006), n. 3, 233-262 (2007) UR - http://hdl.handle.net/1963/2538 U1 - 1581 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Spectral geometry of k-Minkowski space JF - J. Math. Phys. 47 (2006) 062105 Y1 - 2006 A1 - Francesco D'Andrea AB -After recalling Snyder'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'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.

UR - http://hdl.handle.net/1963/2131 U1 - 2112 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Stability of planar nonlinear switched systems Y1 - 2006 A1 - Ugo Boscain A1 - Grégoire Charlot A1 - Mario Sigalotti AB - 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,∞) → {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. JF - Discrete Contin. Dyn. Syst. 15 (2006) 415-432 UR - http://hdl.handle.net/1963/1710 U1 - 2441 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Thomae type formulae for singular Z_N curves JF - Lett. Math. Phys. 76 (2006) 187-214 Y1 - 2006 A1 - Victor Z. Enolski A1 - Tamara Grava AB - 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. UR - http://hdl.handle.net/1963/2125 U1 - 2118 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Time Minimal Trajectories for a Spin 1/2 Particle in a Magnetic field Y1 - 2006 A1 - Ugo Boscain A1 - Paolo Mason AB - 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 → ∞ 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 → 0, giving a partial proof of a conjecture formulated in a previous paper. JF - Journal of Mathematical Physics 47, 062101 (2006) UR - http://hdl.handle.net/1963/1734 U1 - 2418 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - On topological M-theory Y1 - 2006 A1 - Giulio Bonelli A1 - Alessandro Tanzini A1 - Maxim Zabzine AB - 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. JF - Adv. Theor. Math. Phys. 10 (2006) 239-260 UR - http://hdl.handle.net/1963/1765 U1 - 2779 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Topological symmetry of forms, N=1 supersymmetry and S-duality on special manifolds JF - J. Geom. Phys. 56 (2006) 2379-2401 Y1 - 2006 A1 - Laurent Baulieu A1 - Alessandro Tanzini AB - 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. UR - http://hdl.handle.net/1963/2168 U1 - 2076 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Two-matrix model with semiclassical potentials and extended Whitham hierarchy JF - J. Phys. A Y1 - 2006 A1 - Marco Bertola VL - 39 ER - TY - CHAP T1 - On universality of critical behaviour in Hamiltonian PDEs T2 - 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 Y1 - 2006 A1 - Boris Dubrovin AB - 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. JF - 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 PB - American Mathematical Society SN - 978-0-8218-4674-2 UR - http://hdl.handle.net/1963/6491 U1 - 6417 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - On variational approach to differential invariants of rank two distributions JF - Differential Geom. Appl. 24 (2006) 235-259 Y1 - 2006 A1 - Igor Zelenko AB - 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. UR - http://hdl.handle.net/1963/2188 U1 - 2056 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Variational problems in fracture mechanics Y1 - 2006 A1 - Gianni Dal Maso AB - 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. UR - http://hdl.handle.net/1963/1816 U1 - 2398 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - WDVV equations and Frobenius manifolds T2 - Encyclopedia of Mathematical Physics. Vol 1 A : A-C. Oxford: Elsevier, 2006, p. 438-447 Y1 - 2006 A1 - Boris Dubrovin JF - Encyclopedia of Mathematical Physics. Vol 1 A : A-C. Oxford: Elsevier, 2006, p. 438-447 PB - SISSA SN - 0125126611 UR - http://hdl.handle.net/1963/6473 U1 - 6419 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Asymptotic Morse theory for the equation $\\\\Delta v=2v\\\\sb x\\\\wedge v\\\\sb y$ JF - Comm. Anal. Geom. 13 (2005) 187-252 Y1 - 2005 A1 - Sagun Chanillo A1 - Andrea Malchiodi AB - 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. PB - International Press UR - http://hdl.handle.net/1963/3533 U1 - 731 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the attainable set for Temple class systems with boundary controls JF - SIAM J. Control Optim. 43 (2005) 2166-2190 Y1 - 2005 A1 - Fabio Ancona A1 - Giuseppe Maria Coclite AB - 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. PB - SISSA Library UR - http://hdl.handle.net/1963/1581 U1 - 2537 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the Blow-up for a Discrete Boltzmann Equation in the Plane JF - Discrete Contin. Dyn. Syst. 13 (2005) 1-12 Y1 - 2005 A1 - Alberto Bressan A1 - Massimo Fonte AB - 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. UR - http://hdl.handle.net/1963/2244 U1 - 2000 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Commuting multiparty quantum observables and local compatibility JF - Phys. Rev. A 72 (2005) 012112 Y1 - 2005 A1 - Claudio Altafini AB - 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 ``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 ``Bell Theorem without inequalities\\\'\\\'. UR - http://hdl.handle.net/1963/2228 U1 - 2016 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - Complete systems of invariants for rank 1 curves in Lagrange Grassmannians T2 - Differential geometry and its applications, 367-382, Matfyzpress, Prague, 2005 Y1 - 2005 A1 - Igor Zelenko AB - 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. JF - Differential geometry and its applications, 367-382, Matfyzpress, Prague, 2005 UR - http://hdl.handle.net/1963/2310 N1 - Proceedings of 9th Conference on Differential Geometry and its Applications, Prague 2004 U1 - 1706 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Concentration at curves for a singularly perturbed Neumann problem in three-dimensional domains JF - Geometric and Functional Analysis 15 (6) 1162-1222 (2005) Y1 - 2005 A1 - Andrea Malchiodi AB - 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 → 0. PB - Springer UR - http://hdl.handle.net/1963/4866 U1 - 4645 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Conservation laws with time dependent discontinuous coefficients JF - SIAM J. Math. Anal. 36 (2005) 1293-1309 Y1 - 2005 A1 - Giuseppe Maria Coclite A1 - Nils Henrik Risebro AB - 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]. PB - SISSA Library UR - http://hdl.handle.net/1963/1666 U1 - 2452 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On curvatures and focal points of distributions of dynamical Lagrangian distributions and their reductions by first integrals JF - J. Dyn. Control Syst. 11 (2005) 297-327 Y1 - 2005 A1 - Andrei A. Agrachev A1 - Natalia N. Chtcherbakova A1 - Igor Zelenko AB - 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. UR - http://hdl.handle.net/1963/2254 U1 - 1993 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Decay of a bound state under a time-periodic perturbation: a toy case JF - J. Phys. A 38 (2005) 4769-4781 Y1 - 2005 A1 - Michele Correggi A1 - Gianfausto Dell'Antonio AB - 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 ``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. UR - http://hdl.handle.net/1963/2298 U1 - 1718 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - The Dirac operator on SU_q(2) JF - Commun. Math. Phys. 259 (2005) 729-759 Y1 - 2005 A1 - Ludwik Dabrowski A1 - Giovanni Landi A1 - Andrzej Sitarz A1 - Walter van Suijlekom A1 - Joseph C. Varilly AB - 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. PB - Springer UR - http://hdl.handle.net/1963/4425 N1 - v2: minor changes U1 - 4175 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Explicit Wei–Norman formulae for matrix Lie groups via Putzer\\\'s method JF - Systems and Control Letters, 54 (11):1121-1130, 2005 Y1 - 2005 A1 - Claudio Altafini AB - The Wei–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. PB - Elsevier UR - http://hdl.handle.net/1963/4538 U1 - 4299 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - A fourth order uniformization theorem on some four manifolds with large total Q-curvature JF - C. R. Acad. Sci. Paris, Ser. I 340 (2005) 341-346. Y1 - 2005 A1 - Zindine Djadli A1 - Andrea Malchiodi AB - 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. PB - Elsevier UR - http://hdl.handle.net/1963/4868 U1 - 4649 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - RPRT T1 - Gel\\\'fand-Zakharevich Systems and Algebraic Integrability: the Volterra Lattice Revisited Y1 - 2005 A1 - Gregorio Falqui A1 - Marco Pedroni AB - 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. JF - Regul. Chaotic Dyn. 10 (2005) 399-412 UR - http://hdl.handle.net/1963/1689 U1 - 2444 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Global solutions of the Hunter-Saxton equation JF - SIAM J. Math. Anal. 37 (2005) 996-1026 Y1 - 2005 A1 - Alberto Bressan A1 - Adrian Constantin AB - 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. UR - http://hdl.handle.net/1963/2256 U1 - 1991 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Ground states of nonlinear Schroedinger equations with potentials vanishing at infinity JF - J. Eur. Math. Soc. 7 (2005) 117-144 Y1 - 2005 A1 - Antonio Ambrosetti A1 - Veronica Felli A1 - Andrea Malchiodi AB - 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 $\\\\theta= (p+1)/(p-1)-1/2$. UR - http://hdl.handle.net/1963/2352 U1 - 1664 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Hybrid necessary principle JF - SIAM J. Control Optim. 43 (2005) 1867-1887 Y1 - 2005 A1 - Mauro Garavello A1 - Benedetto Piccoli AB - 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. PB - SIAM UR - http://hdl.handle.net/1963/1641 N1 - Proceedings of IFAC Conference on Analysis and Design of Hybrid Systems, Saint Malo, France U1 - 2477 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Ionization for Three Dimensional Time-dependent Point Interactions JF - Comm. Math. Phys. 257 (2005) 169-192 Y1 - 2005 A1 - Michele Correggi A1 - Gianfausto Dell'Antonio A1 - Rodolfo Figari A1 - Andrea Mantile AB - 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 ``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. UR - http://hdl.handle.net/1963/2297 U1 - 1719 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Isomonodromic deformation of resonant rational connections JF - IMRP Int. Math. Res. Pap. Y1 - 2005 A1 - Marco Bertola A1 - Mo, M. Y. ER - TY - JOUR T1 - The local index formula for SUq(2) JF - K-Theory 35 (2005) 375-394 Y1 - 2005 A1 - Walter van Suijlekom A1 - Ludwik Dabrowski A1 - Giovanni Landi A1 - Andrzej Sitarz A1 - Joseph C. Varilly AB - 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. UR - http://hdl.handle.net/1963/1713 U1 - 2438 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Minimal surfaces in pseudohermitian geometry JF - Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (5), 4 (2005) 129-177. Y1 - 2005 A1 - Jih-Hsin Cheng A1 - JennFang Hwang A1 - Andrea Malchiodi A1 - Paul Yang AB - 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. PB - Scuola Normale Superiore UR - http://hdl.handle.net/1963/4579 U1 - 4347 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - On the Minimum Problem for Nonconvex Scalar Functionals JF - SIAM J. Math. Anal. 37 (2005) 982-995 Y1 - 2005 A1 - Sandro Zagatti AB - 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. UR - http://hdl.handle.net/1963/2764 U1 - 1936 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Modulation of the Camassa-Holm equation and reciprocal transformations JF - Ann. Inst. Fourier (Grenoble) 55 (2005) 1803-1834 Y1 - 2005 A1 - Simonetta Abenda A1 - Tamara Grava AB - 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. UR - http://hdl.handle.net/1963/2305 U1 - 1711 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Multiple clustered layer solutions for semilinear Neumann problems on a ball JF - Ann. Inst. H. Poincare Anal. Non Lineaire 22 (2005) 143-163 Y1 - 2005 A1 - Andrea Malchiodi A1 - Wei-Ming Ni A1 - Juncheng Wei PB - Elsevier UR - http://hdl.handle.net/1963/3532 U1 - 732 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Nonisotropic 3-level quantum systems: complete solutions for minimum time and minimum energy JF - Discrete Contin. Dyn. Syst. Ser. B 5 (2005) 957-990 Y1 - 2005 A1 - Ugo Boscain A1 - Thomas Chambrion A1 - Grégoire Charlot AB - 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. UR - http://hdl.handle.net/1963/2259 U1 - 1988 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Nonlinear Schrödinger Equations with vanishing and decaying potentials Y1 - 2005 A1 - Antonio Ambrosetti A1 - Wang Zhi-Qiang JF - Differential Integral Equations 18 (2005), no. 12, 1321-1332 UR - http://hdl.handle.net/1963/1760 U1 - 2784 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - An Optimal Transportation Metric for Solutions of the Camassa-Holm Equation Y1 - 2005 A1 - Alberto Bressan A1 - Massimo Fonte AB - 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 · 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. JF - Methods Appl. Anal. 12 (2005) 191-219 UR - http://hdl.handle.net/1963/1719 U1 - 2432 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Orbifold Cohomology of ADE-singularities Y1 - 2005 A1 - Fabio Perroni KW - Orbifolds PB - SISSA UR - http://hdl.handle.net/1963/5298 U1 - 5126 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Periodic solutions of nonlinear wave equations with non-monotone forcing terms JF - Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 16 (2005), no. 2, 117-124 Y1 - 2005 A1 - Massimiliano Berti A1 - Luca Biasco PB - Accademia Nazionale dei Lincei UR - http://hdl.handle.net/1963/4581 U1 - 4349 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Principal fibrations from noncommutative spheres JF - Comm. Math. Phys. 260 (2005) 203-225 Y1 - 2005 A1 - Giovanni Landi A1 - Walter van Suijlekom AB - 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. UR - http://hdl.handle.net/1963/2284 U1 - 1732 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Quasi-periodic oscillations for wave equations under periodic forcing JF - Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 16 (2005), no. 2, 109-116 Y1 - 2005 A1 - Massimiliano Berti A1 - Michela Procesi PB - Accademia Nazionale dei Lincei UR - http://hdl.handle.net/1963/4583 U1 - 4350 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Quasistatic Crack Growth in Nonlinear Elasticity JF - Arch. Ration. Mech. Anal. 176 (2005) 165-225 Y1 - 2005 A1 - Gianni Dal Maso A1 - Gilles A. Francfort A1 - Rodica Toader AB - 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. UR - http://hdl.handle.net/1963/2293 U1 - 1723 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Regularity properties of optimal trajectories of single-input control systems in dimension three JF - Journal of Mathematical Sciences 126 (2005) 1561-1573 Y1 - 2005 A1 - Mario Sigalotti AB - 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. PB - Springer UR - http://hdl.handle.net/1963/4794 U1 - 4564 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Self-similar folding patterns and energy scaling in compressed elastic sheets JF - Comput. Methods Appl. Mech. Engrg. 194 (2005) 2534-2549 Y1 - 2005 A1 - Sergio Conti A1 - Antonio DeSimone A1 - Stefan Müller AB - 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. PB - Elsevier UR - http://hdl.handle.net/1963/3000 U1 - 1333 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - A short introduction to optimal control T2 - Contrôle non linéaire et applications: Cours donnés à l\\\'école d\\\'été du Cimpa de l\\\'Université de Tlemcen / Sari Tewfit [ed.]. - Paris: Hermann, 2005 Y1 - 2005 A1 - Ugo Boscain A1 - Benedetto Piccoli JF - Contrôle non linéaire et applications: Cours donnés à l\\\'école d\\\'été du Cimpa de l\\\'Université de Tlemcen / Sari Tewfit [ed.]. - Paris: Hermann, 2005 SN - 2 7056 6511 0 UR - http://hdl.handle.net/1963/2257 U1 - 1990 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - ABST T1 - Solutions of Neumann problems in domains with cracks and applications to fracture mechanics Y1 - 2005 A1 - Gianni Dal Maso UR - http://hdl.handle.net/1963/1684 U1 - 79 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The spectral geometry of the equatorial Podles sphere JF - C. R. Math. 340 (2005) 819-822 Y1 - 2005 A1 - Ludwik Dabrowski A1 - Giovanni Landi A1 - Mario Paschke A1 - Andrzej Sitarz AB - 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. UR - http://hdl.handle.net/1963/2275 U1 - 1972 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Stability of solutions of quasilinear parabolic equations JF - J. Math. Anal. Appl. 308 (2005) 221-239 Y1 - 2005 A1 - Giuseppe Maria Coclite A1 - Helge Holden AB - 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. PB - Elsevier UR - http://hdl.handle.net/1963/2892 U1 - 1808 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Stress-dilatancy based modelling of granular materials and extensions to soils with crushable grains JF - Int. J. Numer. Anal. Met. 29 (2005) 73-101 Y1 - 2005 A1 - Antonio DeSimone A1 - Claudio Tamagnini AB - 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. UR - http://hdl.handle.net/1963/2165 U1 - 2079 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Time minimal trajectories for two-level quantum systems with drift Y1 - 2005 A1 - Ugo Boscain A1 - Paolo Mason AB - 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. JF - Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC \\\'05. 44th IEEE Conference on UR - http://hdl.handle.net/1963/1688 U1 - 2445 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Time Optimal Synthesis for Left-Invariant Control Systems on SO(3) JF - SIAM J. Control Optim. 44 (2005) 111-139 Y1 - 2005 A1 - Ugo Boscain A1 - Yacine Chitour AB - 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. UR - http://hdl.handle.net/1963/2258 U1 - 1989 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Topological vector symmetry, topological gauge fixing of BRSTQFT and construction of maximal supersymmetry Y1 - 2005 A1 - Laurent Baulieu A1 - Guillaume Bossard A1 - Alessandro Tanzini AB - 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. Poincaré 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. JF - JHEP 0508 (2005) 037 UR - http://hdl.handle.net/1963/1741 U1 - 2411 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Traffic flow on a road network JF - SIAM J. Math. Anal. 36 (2005) 1862-1886 Y1 - 2005 A1 - Giuseppe Maria Coclite A1 - Benedetto Piccoli A1 - Mauro Garavello AB - 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. PB - SISSA Library UR - http://hdl.handle.net/1963/1584 U1 - 2534 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Vanishing viscosity solutions of nonlinear hyperbolic systems JF - Ann. of Math. 161 (2005) 223-342 Y1 - 2005 A1 - Stefano Bianchini A1 - Alberto Bressan AB - 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 $u_t+f(u)_x=0$. PB - Annals of Mathematics UR - http://hdl.handle.net/1963/3074 U1 - 1259 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Wetting of rough surfaces: a homogenization approach JF - Proc. R. Soc. Lon. Ser. A 461 (2005) 79-97 Y1 - 2005 A1 - Antonio DeSimone A1 - Giovanni Alberti AB - 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. UR - http://hdl.handle.net/1963/2253 U1 - 1994 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On almost duality for Frobenius manifolds JF - Amer. Math. Soc. Transl. 212 (2004)\\n75-132. Y1 - 2004 A1 - Boris Dubrovin AB - 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. UR - http://hdl.handle.net/1963/2543 U1 - 1576 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - On analytic families of invariant tori for PDEs JF - Astérisque. Issue 297, 2004, Pages 35-65 Y1 - 2004 A1 - Boris Dubrovin AB - 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. PB - SISSA UR - http://hdl.handle.net/1963/6474 U1 - 6420 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains JF - Ann. Inst. H. Poincaré. Anal. Non Linéaire 21 (2004), (4), p. 445-486. Y1 - 2004 A1 - Gianni Dal Maso A1 - Francois Murat AB - 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. PB - SISSA Library UR - http://hdl.handle.net/1963/1611 U1 - 2507 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Bifurcation of free vibrations for completely resonant wave equations JF - Boll. Unione Mat. Ital. Sez. B 7 (2004) 519-528 Y1 - 2004 A1 - Massimiliano Berti A1 - Philippe Bolle AB - We prove existence of small amplitude, 2 pi/omega -periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for any frequency omega belonging to a Cantor-like set of positive measure and for a generic set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem. UR - http://hdl.handle.net/1963/2245 U1 - 1999 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Blow-up solutions for the Schrödinger equation in dimension three with a concentrated nonlinearity JF - Ann. Inst. H. Poincare Anal. Non Lineaire 21 (2004) 121-137 Y1 - 2004 A1 - Riccardo Adami A1 - Gianfausto Dell'Antonio A1 - Rodolfo Figari A1 - Alessandro Teta AB - We present some results on the blow-up phenomenon for the Schroedinger equation in dimension three with a nonlinear term supported in a fixed point. We find sufficient conditions for the blow up exploiting the moment of inertia of the solution and the uncertainty principle. In the critical case, we discuss the additional symmetry of the equation and construct a family of explicit blow up solutions. PB - Elsevier UR - http://hdl.handle.net/1963/2998 U1 - 1335 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Calculation of impulsively started incompressible viscous flows JF - Int. J. Numer. Meth. Fluids Y1 - 2004 A1 - Marra, Andrea A1 - Andrea Mola A1 - Quartapelle, Luigi A1 - Riviello, Luca VL - 46 ER - TY - JOUR T1 - Coarse-grained models of materials with non-convex free-energy: two case studies JF - Computer methods in applied mechanics and engineering , 193 (2004) 5129-5141 Y1 - 2004 A1 - Antonio DeSimone AB - Bridging across length scales is one of the fundamental challenges in the computational modelling of material systems whose mechanical response is driven by rough energy landscapes. The typical feature of such systems is that of exhibiting fine scale microstructures. Two case studies, namely, nematic elastomers and ferromagnetic shape memory alloys, are presented to illustrate the use of modern techniques from (non-convex) calculus of variations in developing coarse-grained models of microstructure-driven material response. PB - Elsevier UR - http://hdl.handle.net/1963/4884 U1 - 4664 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Coherent control of open quantum dynamical systems JF - Phys. Rev. A 70 (2004) 062321 Y1 - 2004 A1 - Claudio Altafini AB - A systematic analysis of the behavior of the quantum Markovian master equation driven by coherent control fields is proposed. Its irreversible character is formalized using control-theoretic notions and the sets of states that can be reached via cohere nt controls are described. The analysis suggests to which extent (and how) it is possible to counteract the effect of dissipation. UR - http://hdl.handle.net/1963/2227 U1 - 2017 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the convergence rate of vanishing viscosity approximations JF - Comm. Pure Appl. Math. 57 (2004) 1075-1109 Y1 - 2004 A1 - Alberto Bressan A1 - Tong Yang AB - Given a strictly hyperbolic, genuinely nonlinear system of conservation laws, we prove the a priori bound $\\\\big\\\\|u(t,\\\\cdot)-u^\\\\ve(t,\\\\cdot)\\\\big\\\\|_{\\\\L^1}= \\\\O(1)(1+t)\\\\cdot \\\\sqrt\\\\ve|\\\\ln\\\\ve|$ on the distance between an exact BV solution $u$ and a viscous approximation $u^\\\\ve$, letting the viscosity coefficient $\\\\ve\\\\to 0$. In the proof, starting from $u$ we construct an approximation of the viscous solution $u^\\\\ve$ by taking a mollification $u*\\\\phi_{\\\\strut \\\\sqrt\\\\ve}$ and inserting viscous shock profiles at the locations of finitely many large shocks, for each fixed $\\\\ve$. Error estimates are then obtained by introducing new Lyapunov functionals which control shock interactions, interactions between waves of different families and by using sharp decay estimates for positive nonlinear waves. PB - Wiley UR - http://hdl.handle.net/1963/2915 U1 - 1785 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - Generic T1 - The elliptic representation of the sixth Painlevé equation. T2 - Théories asymptotiques et équations de Painlevé : [colloque], Angers, juin 2004 / édité par Éric Delabaere, Michèle Loday-Richaud. - Paris : Société mathématique de France, 2006. - Collection SMF. Séminaires et congrès. - page : 83-101 Y1 - 2004 A1 - Davide Guzzetti KW - Painlevé equation AB - We find a class of solutions of the sixth Painlev´e equation corresponding\r\nto almost all the monodromy data of the associated linear system; actually, all data\r\nbut one point in the space of data. We describe the critical behavior close to the\r\ncritical points by means of the elliptic representation, and we find the relation among\r\nthe parameters at the different critical points (connection problem). JF - Théories asymptotiques et équations de Painlevé : [colloque], Angers, juin 2004 / édité par Éric Delabaere, Michèle Loday-Richaud. - Paris : Société mathématique de France, 2006. - Collection SMF. Séminaires et congrès. - page : 83-101 PB - Societe Matematique de France SN - 978-2-85629-229-7 UR - http://hdl.handle.net/1963/6529 U1 - 6482 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Energetics and switching of quasi-uniform states in small ferromagnetic particles JF - M2AN Math. Model. Numer. Anal. 38 (2004) 235-248 Y1 - 2004 A1 - François Alouges A1 - Sergio Conti A1 - Antonio DeSimone A1 - Ivo Pokern AB - We present a numerical algorithm to solve the micromagnetic equations based on tangential-plane minimization for the magnetization update and a homothethic-layer decomposition of outer space for the computation of the demagnetization field. As a first application, detailed results on the flower-vortex transition in the cube of Micromagnetic Standard Problem number 3 are obtained, which confirm, with a different method, those already present in the literature, and validate our method and code. We then turn to switching of small cubic or almost-cubic particles, in the single-domain limit. Our data show systematic deviations from the Stoner-Wohlfarth model due to the non-ellipsoidal shape of the particle, and in particular a non-monotone dependence on the particle size. PB - EDP Sciences UR - http://hdl.handle.net/1963/2999 U1 - 1334 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence of H-bubbles in a perturbative setting JF - Rev. Mat. Iberoamericana 20 (2004) 611-626 Y1 - 2004 A1 - Paolo Caldiroli A1 - Roberta Musina AB - Given a $C^{1}$ function $H: \\\\mathbb{R}^3 \\\\to \\\\mathbb{R}$, we look for $H$-bubbles, i.e., surfaces in $\\\\mathbb{R}^3$ parametrized by the sphere $\\\\mathbb{S}^2$ with mean curvature $H$ at every regular point. Here we study the case $H(u)=H_{0}(u)+\\\\epsilon H_{1}(u)$ where $H_{0}$ is some \\\"good\\\" curvature (for which there exist $H_{0}$-bubbles with minimal energy, uniformly bounded in $L^{\\\\infty}$), $\\\\epsilon$ is the smallness parameter, and $H_{1}$ is {\\\\em any} $C^{1}$ function. PB - SISSA Library UR - http://hdl.handle.net/1963/1606 U1 - 2512 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The Extended Toda Hierarchy JF - Moscow Math. J. 4 (2004)\\n313-332. Y1 - 2004 A1 - Guido Carlet A1 - Boris Dubrovin A1 - Zhang Youjin UR - http://hdl.handle.net/1963/2542 U1 - 1577 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Fredholm modules for quantum euclidean spheres JF - J. Geom. Phys. 49 (2004) 272-293 Y1 - 2004 A1 - Eli Hawkins A1 - Giovanni Landi AB - The quantum Euclidean spheres, $S_q^{N-1}$, are (noncommutative) homogeneous spaces of quantum orthogonal groups, $\\\\SO_q(N)$. The *-algebra $A(S^{N-1}_q)$ of polynomial functions on each of these is given by generators and relations which can be expressed in terms of a self-adjoint, unipotent matrix. We explicitly construct complete sets of generators for the K-theory (by nontrivial self-adjoint idempotents and unitaries) and the K-homology (by nontrivial Fredholm modules) of the spheres $S_q^{N-1}$. We also construct the corresponding Chern characters in cyclic homology and cohomology and compute the pairing of K-theory with K-homology. On odd spheres (i. e., for N even) we exhibit unbounded Fredholm modules by means of a natural unbounded operator D which, while failing to have compact resolvent, has bounded commutators with all elements in the algebra $A(S^{N-1}_q)$. PB - SISSA Library UR - http://hdl.handle.net/1963/1636 U1 - 2482 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - A geometric approach to the separability of the Neumann-Rosochatius system JF - Differential Geom. Appl. 21 (2004) 349-360 Y1 - 2004 A1 - Claudio Bartocci A1 - Gregorio Falqui A1 - Marco Pedroni AB - We study the separability of the Neumann-Rosochatius system on the n-dimensional sphere using the geometry of bi-Hamiltonian manifolds. Its well-known separation variables are recovered by means of a separability condition relating the Hamiltonian with a suitable (1,1) tensor field on the sphere. This also allows us to iteratively construct the integrals of motion of the system. UR - http://hdl.handle.net/1963/2541 U1 - 1578 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - H-bubbles in a perturbative setting: the finite-dimensional reduction\\\'s method JF - Duke Math. J. 122 (2004), no. 3, 457--484 Y1 - 2004 A1 - Paolo Caldiroli A1 - Roberta Musina AB - Given a regular function $H\\\\colon\\\\mathbb{R}^{3}\\\\to\\\\mathbb{R}$, we look for $H$-bubbles, that is, regular surfaces in $\\\\mathbb{R}^{3}$ parametrized on the sphere $\\\\mathbb{S}+^{2}$ with mean curvature $H$ at every point. Here we study the case of $H(u)=H_{0}+\\\\varepsilon H_{1}(u)=:H_{\\\\varepsilon}(u)$, where $H_{0}$ is a nonzero constant, $\\\\varepsilon$ is the smallness parameter, and $H_{1}$ is any $C^{2}$-function. We prove that if $\\\\bar p\\\\in\\\\mathbb{R}^{3}$ is a ``good\\\'\\\' stationary point for the Melnikov-type function $\\\\Gamma(p)=-\\\\int_{|q-p|<|H_{0}|^{-1}}H_{1}(q)\\\\,dq$, then for $|\\\\varepsilon|$ small there exists an $H_{\\\\varepsilon}$-bubble $\\\\omega^{\\\\varepsilon}$ that converges to a sphere of radius $|H_{0}|^{-1}$ centered at $\\\\bar p$, as $\\\\varepsilon\\\\to 0$. PB - SISSA Library UR - http://hdl.handle.net/1963/1607 U1 - 2511 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Higher order quasiconvexity reduces to quasiconvexity JF - Arch. Ration. Mech. Anal. 171 (2004) 55-81 Y1 - 2004 A1 - Gianni Dal Maso A1 - Irene Fonseca A1 - Giovanni Leoni A1 - Massimiliano Morini AB - In this paper it is shown that higher order quasiconvex functions suitable in the variational treatment of problems involving second derivatives may be extended to the space of all matrices as classical quasiconvex functions. Precisely, it is proved that a smooth strictly 2-quasiconvex function with p-growth at infinity, p>1, is the restriction to symmetric matrices of a 1-quasiconvex function with the same growth. As a consequence, lower semicontinuity results for second-order variational problems are deduced as corollaries of well-known first order theorems. PB - Springer UR - http://hdl.handle.net/1963/2911 U1 - 1789 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - Generic T1 - On the minimal degree of a common Lyapunov function for planar switched systems T2 - 43rd IEEE Conference on Decision and Control, 2004, 2786 - 2791 Vol.3 Y1 - 2004 A1 - Paolo Mason A1 - Ugo Boscain A1 - Yacine Chitour AB - In this paper, we consider linear switched systems x(t) = Au(t)x(t), x ε Rn, u ε U, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching (UAS for short). We first prove that, given a UAS system, it is always possible to build a polynomial common Lyapunov function. Then our main result is that the degree of that the common polynomial Lyapunov function is not uniformly bounded over all the UAS systems. This result answers a question raised by Dayawansa and Martin. JF - 43rd IEEE Conference on Decision and Control, 2004, 2786 - 2791 Vol.3 PB - IEEE UR - http://hdl.handle.net/1963/4834 U1 - 4611 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Multidimensional boundary layers for a singularly perturbed Neumann problem JF - Duke Math. J. 124 (2004) 105-143 Y1 - 2004 A1 - Andrea Malchiodi A1 - Marcelo Montenegro PB - Duke University Press UR - http://hdl.handle.net/1963/2960 U1 - 1740 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Multiplicity of periodic solutions of nonlinear wave equations JF - Nonlinear Anal. 56 (2004) 1011-1046 Y1 - 2004 A1 - Massimiliano Berti A1 - Philippe Bolle PB - Elsevier UR - http://hdl.handle.net/1963/2974 U1 - 1359 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Periodic orbits close to elliptic tori and applications to the three-body problem JF - Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 3 (2004) 87-138 Y1 - 2004 A1 - Massimiliano Berti A1 - Luca Biasco A1 - Enrico Valdinoci AB - We prove, under suitable non-resonance and non-degeneracy ``twist\\\'\\\' conditions, a Birkhoff-Lewis type result showing the existence of infinitely many periodic solutions, with larger and larger minimal period, accumulating onto elliptic invariant tori (of Hamiltonian systems). We prove the applicability of this result to the spatial planetary three-body problem in the small eccentricity-inclination regime. Furthermore, we find other periodic orbits under some restrictions on the period and the masses of the ``planets\\\'\\\'. The proofs are based on averaging theory, KAM theory and variational methods. (Supported by M.U.R.S.T. Variational Methods and Nonlinear Differential Equations.) PB - Scuola Normale Superiore di Pisa UR - http://hdl.handle.net/1963/2985 U1 - 1348 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasi-static evolution in brittle fracture: the case of bounded solutions JF - Quad. Mat. Dip. Mat. Seconda Univ. Napoli 14 (2004) 245-266 Y1 - 2004 A1 - Gianni Dal Maso A1 - Gilles A. Francfort A1 - Rodica Toader AB - The main steps of the proof of the existence result for the quasi-static evolution of cracks in brittle materials, obtained in [7] in the vector case and for a general quasiconvex elastic energy, are presented here under the simplifying assumption that the minimizing sequences involved in the problem are uniformly bounded in $L^\\\\infty$. UR - http://hdl.handle.net/1963/2229 U1 - 2015 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Reduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite Riemannian metric JF - ESAIM: COCV 10 (2004) 526-548 Y1 - 2004 A1 - Claudio Altafini AB - For a Riemannian structure on a semidirect product of Lie groups, the variational problems can be reduced using the group symmetry. Choosing the Levi-Civita connection of a positive definite metric tensor, instead of any of the canonical connections for the Lie group, simplifies the reduction of the variations but complicates the expression for the Lie algebra valued covariant derivatives. The origin of the discrepancy is in the semidirect product structure, which implies that the Riemannian exponential map and the Lie group exponential map do not coincide. The consequence is that the reduced equations look more complicated than the original ones. The main scope of this paper is to treat the reduction of second order variational problems (corresponding to geometric splines) on such semidirect products of Lie groups. Due to the semidirect structure, a number of extra terms appears in the reduction, terms that are calculated explicitely. The result is used to compute the necessary conditions of an optimal control problem for a simple mechanical control system having invariant Lagrangian equal to the kinetic energy corresponding to the metric tensor. As an example, the case of a rigid body on the Special Euclidean group is considered in detail. PB - EDP Sciences UR - http://hdl.handle.net/1963/3521 U1 - 743 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Representing multiqubit unitary evolutions via Stokes tensors JF - Phys. Rev. A 70 (2004) 032331 Y1 - 2004 A1 - Claudio Altafini AB - For the Stokes tensor parametrization of a multiqubit density operator, we provide an explicit formulation of the corresponding unitary dynamics at the infinitesimal level. The main advantage of this formalism (clearly reminiscent of the ideas of ``coherences\\\'\\\' and ``coupling Hamiltonians\\\'\\\' of spin systems) is that the pattern of correlation between qubits and the pattern of infinitesimal correlation are highlighted simultaneously and can be used constructively for qubit manipulation. For example, it allows to compute explicitly a Rodrigues\\\' formula for the one-parameter orbits of nonlocal Hamiltonians. The result is easily generalizable to orbits of Cartan subalgebras and allows to express the Cartan decomposition of unitary propagators as a linear action directly in terms of the infinitesimal generators. UR - http://hdl.handle.net/1963/2307 U1 - 1709 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Resonance of minimizers for n-level quantum systems with an arbitrary cost JF - ESAIM COCV 10 (2004) 593-614 Y1 - 2004 A1 - Ugo Boscain A1 - Grégoire Charlot AB - We consider an optimal control problem describing a laser-induced population transfer on a $n$-level quantum system.\\nFor a convex cost depending only on the moduli of controls (i.e. the lasers intensities), we prove that there always exists a minimizer in resonance. This permits to justify some strategies used in experimental physics. It is also quite important because it permits to reduce remarkably the complexity of the problem (and extend some of our previous results for $n=2$ and $n=3$): instead of looking for minimizers on the sphere $S^{2n-1}\\\\subset\\\\C^n$ one is reduced to look just for minimizers on the sphere $S^{n-1}\\\\subset \\\\R^n$. Moreover, for the reduced problem, we investigate on the question of existence of strict abnormal minimizer. PB - EDP Sciences UR - http://hdl.handle.net/1963/2910 U1 - 1790 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The role of the spectrum of the Laplace operator on \\\\S2 in the H-bubble problem JF - J. Anal. Math. 94 (2004) 265-291 Y1 - 2004 A1 - Roberta Musina PB - Hebrew University Magnes Press UR - http://hdl.handle.net/1963/2894 U1 - 1806 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Rotating Singular Perturbations of the Laplacian JF - Ann. Henri Poincare 5 (2004) 773-808 Y1 - 2004 A1 - Michele Correggi A1 - Gianfausto Dell'Antonio AB - We study a system of a quantum particle interacting with a singular time-dependent uniformly rotating potential in 2 and 3 dimensions: in particular we consider an interaction with support on a point (rotating point interaction) and on a set of codimension 1 (rotating blade). We prove the existence of the Hamiltonians of such systems as suitable self-adjoint operators and we give an explicit expression for their unitary semigroups. Moreover we analyze the asymptotic limit of large angular velocity and we prove strong convergence of the time-dependent propagator to some one-parameter unitary group as (\\\\omega \\\\to \\\\infty). PB - Springer UR - http://hdl.handle.net/1963/2945 U1 - 1755 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Semiclassical analysis of constrained quantum systems JF - J. Phys. A 37 (2004) 5605-5624 Y1 - 2004 A1 - Gianfausto Dell'Antonio A1 - Lucattilio Tenuta AB - We study the dynamics of a quantum particle in R^(n+m) constrained by a strong potential force to stay within a distance of order hbar (in suitable units) from a smooth n-dimensional submanifold M. We prove that in the semiclassical limit the evolution of the wave function is approximated in norm, up to terms of order hbar^(1/2), by the evolution of a semiclassical wave packet centred on the trajectory of the corresponding classical constrained system. PB - IOP Publishing UR - http://hdl.handle.net/1963/2997 U1 - 1336 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Semi-cooperative strategies for differential games JF - Internat. J. Game Theory 32 (2004) 561-593 Y1 - 2004 A1 - Alberto Bressan A1 - Wen Shen AB - The paper is concerned with a non-cooperative differential game for two players. We first consider Nash equilibrium solutions in feedback form. In this case, we show that the Cauchy problem for the value functions is generically ill-posed. Looking at vanishing viscosity approximations, one can construct special solutions in the form of chattering controls, but these also appear to be unstable. In the second part of the paper we propose an alternative \\\"semi-cooperative\\\" pair of strategies for the two players, seeking a Pareto optimum instead of a Nash equilibrium. In this case, we prove that the corresponding Hamiltonian system for the value functions is always weakly hyperbolic. PB - Springer UR - http://hdl.handle.net/1963/2893 U1 - 1807 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A sharp decay estimate for positive nonlinear waves JF - SIAM J. Math. Anal. 36 (2004) 659-677 Y1 - 2004 A1 - Alberto Bressan A1 - Tong Yang AB - We consider a strictly hyperbolic, genuinely nonlinear system of conservation laws in one space dimension. A sharp decay estimate is proved for the positive waves in an entropy weak solution. The result is stated in terms of a partial ordering among positive measures, using symmetric rearrangements and a comparison with a solution of Burgers\\\' equation with impulsive sources. PB - SIAM UR - http://hdl.handle.net/1963/2916 U1 - 1784 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Singular Z_N curves, Riemann-Hilbert problem and modular solutions of the Schlesinger equation JF - Int. Math. Res. Not. 2004, no. 32, 1619-1683 Y1 - 2004 A1 - Victor Z. Enolski A1 - Tamara Grava AB - We are solving the classical Riemann-Hilbert problem of rank N>1 on the extended complex plane punctured in 2m+2 points, for NxN quasi-permutation monodromy matrices. Following Korotkin we solve the Riemann-Hilbert problem in terms of the Szego kernel of certain Riemann surfaces branched over the given 2m+2 points. These Riemann surfaces are constructed from a permutation representation of the symmetric group S_N to which the quasi-permutation monodromy representation has been reduced. The permutation representation of our problem generates the cyclic subgroup Z_N. For this reason the corresponding Riemann surfaces of genus N(m-1) have Z_N symmetry. This fact enables us to write the matrix entries of the solution of the NxN Riemann-Hilbert problem as a product of an algebraic function and theta-function quotients. The algebraic function turns out to be related to the Szego kernel with zero characteristics. From the solution of the Riemann- Hilbert problem we automatically obtain a particular solution of the Schlesinger system. The tau-function of the Schlesinger system is computed explicitly. The rank 3 problem with four singular points (0,t,1,\\\\infty) is studied in detail. The corresponding solution of the Riemann-Hilbert problem and the Schlesinger system is given in terms of Jacobi\\\'s theta-function with modulus T=T(t), Im(T)>0. The function T=T(t) is invertible if it belongs to the Siegel upper half space modulo the subgroup \\\\Gamma_0(3) of the modular group. The inverse function t=t(T) generates a solution of a general Halphen system. UR - http://hdl.handle.net/1963/2540 U1 - 1579 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Singularity perturbed elliptic equations with symmetry: existence of solutions concetrating on spheres, Part II JF - Indiana Univ. Math. J. 53 (2004) 297-392 Y1 - 2004 A1 - Antonio Ambrosetti A1 - Andrea Malchiodi A1 - Wei-Ming Ni PB - Indiana University Mathematics Journal UR - http://hdl.handle.net/1963/1663 U1 - 2455 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Small BV solutions of hyperbolic noncooperative differential games JF - SIAM J. Control Optim. 43 (2004) 194-215 Y1 - 2004 A1 - Alberto Bressan A1 - Wen Shen AB - The paper is concerned with an n-persons differential game in one space dimension. We state conditions for which the system of Hamilton-Jacobi equations for the value functions is strictly hyperbolic. In the positive case, we show that the weak solution of a corresponding system of conservation laws determines an n-tuple of feedback strategies. These yield a Nash equilibrium solution to the non-cooperative differential game. PB - SIAM UR - http://hdl.handle.net/1963/2917 U1 - 1783 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Solitary waves for Maxwell Schrodinger equations JF - Electron. J. Differential Equations (2004) 94 Y1 - 2004 A1 - Giuseppe Maria Coclite A1 - Vladimir Georgiev AB - In this paper we study solitary waves for the coupled system of Schrodinger-Maxwell equations in the three-dimensional space. We prove the existence of a sequence of radial solitary waves for these equations with a fixed L^2 norm. We study the asymptotic behavior and the smoothness of these solutions. We show also that the eigenvalues are negative and the first one is isolated. PB - SISSA Library UR - http://hdl.handle.net/1963/1582 U1 - 2536 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Solutions concentrating at curves for some singularly perturbed elliptic problems JF - C. R. Acad. Sci. Paris, Ser. I 338 (2004) 775-780 Y1 - 2004 A1 - Andrea Malchiodi PB - Elsevier UR - http://hdl.handle.net/1963/4869 U1 - 4647 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Soluzioni periodiche di PDEs Hamiltoniane JF - Bollettino dell\\\'Unione Matematica Italiana Serie 8 7-B (2004), p. 647-661 Y1 - 2004 A1 - Massimiliano Berti PB - Unione Matematica Italiana UR - http://hdl.handle.net/1963/4582 U1 - 4351 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Some remarks on multidimensional systems of conservation laws JF - Rend. Mat. Acc. Lincei, s. 9, v. 15 (2004) 3-4, pp. 225 - 233 Y1 - 2004 A1 - Alberto Bressan AB - This note is concerned with the Cauchy problem for hyperbolic systems of conservation\\nlaws in several space dimensions. We first discuss an example of ill-posedness, for a special system\\nhaving a radial symmetry property. Some conjectures are formulated, on the compactness of the set of\\nflow maps generated by vector fields with bounded variation. PB - Accademia Nazionale dei Lincei UR - http://hdl.handle.net/1963/3642 U1 - 662 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Stability rates for patchy vector fields JF - ESAIM COCV 10 (2004) 168-200 Y1 - 2004 A1 - Fabio Ancona A1 - Alberto Bressan AB - This paper is concerned with the stability of the set of trajectories of a patchy vector field, in the presence of impulsive perturbations. Patchy vector fields are discontinuous, piecewise smooth vector fields that were introduced in Ancona and Bressan (1999) to study feedback stabilization problems. For patchy vector fields in the plane, with polygonal patches in generic position, we show that the distance between a perturbed trajectory and an unperturbed one is of the same order of magnitude as the impulsive forcing term. PB - EDP Sciences UR - http://hdl.handle.net/1963/2959 U1 - 1741 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Superlocalization formulas and supersymmetric Yang-Mills theories JF - Nucl. Phys. B 678 (2004) 638-655 Y1 - 2004 A1 - Ugo Bruzzo A1 - Francesco Fucito AB - By using supermanifold techniques we prove a generalization of the localization formula in equivariant cohomology which is suitable for studying supersymmetric Yang-Mills theories in terms of ADHM data. With these techniques one can compute the reduced partition functions of topological super Yang-Mills theory with 4, 8 or 16 supercharges. More generally, the superlocalization formula can be applied to any topological field theory in any number of dimensions. PB - Elsevier UR - http://hdl.handle.net/1963/2886 U1 - 1814 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Tensor of coherences parametrization of multiqubit density operators for entanglement characterization JF - Phys. Rev. A 69 (2004) 012311 Y1 - 2004 A1 - Claudio Altafini AB - For multiqubit densities, the tensor of coherences (or Stokes tensor) is a real parameterization obtained by the juxtaposition of the affine Bloch vectors of each qubit. While it maintains the tensorial structure of the underlying space, it highlights the pattern of correlations, both classical and quantum, between the subsystems and, due to the affine parameterization, it contains in its components all reduced densities of all orders. The main purpose of our use of this formalism is to deal with entanglement. For example, the detection of bipartite entanglement is straightforward, as it is the synthesis of densities having positive partial transposes between desired qubits. In addition, finding explicit mixtures for families of separable states becomes a feasible issue for few qubit symmetric densities (we compute it for Werner states) and, more important, it provides some insight on the possible origin of entanglement for such densities. PB - American Physical Society UR - http://hdl.handle.net/1963/2845 U1 - 1855 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Time-dependent singular interactions Y1 - 2004 A1 - Michele Correggi KW - Rotating singular interactions PB - SISSA UR - http://hdl.handle.net/1963/5310 U1 - 5135 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Virasoro Symmetries of the Extended Toda Hierarchy JF - Comm. Math.\\nPhys. 250 (2004) 161-193. Y1 - 2004 A1 - Boris Dubrovin A1 - Zhang Youjin AB - We prove that the extended Toda hierarchy of \\\\cite{CDZ} admits nonabelian Lie algebra of infinitesimal symmetries isomorphic to the half of the Virasoro algebra. The generators $L_m$, $m\\\\geq -1$ of the Lie algebra act by linear differential operators onto the tau function of the hierarchy. We also prove that the tau function of a generic solution to the extended Toda hierarchy is annihilated by a combination of the Virasoro operators and the flows of the hierarchy. As an application we show that the validity of the Virasoro constraints for the $CP^1$ Gromov-Witten invariants and their descendents implies that their generating function is the logarithm of a particular tau function of the extended Toda hierarchy. UR - http://hdl.handle.net/1963/2544 U1 - 1575 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Well-posedness for general 2x2 systems of conservation laws JF - Mem. Amer. Math. Soc. 169 (2004), no. 801, x+170 pp. Y1 - 2004 A1 - Fabio Ancona A1 - Andrea Marson PB - SISSA Library UR - http://hdl.handle.net/1963/1241 U1 - 2702 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Autonomous integral functionals with discontinous nonconvex integrands: Lipschitz regularity of mimimizers, DuBois-Reymond necessary conditions and Hamilton-Jacobi equations JF - Applied Math.Optim. 48 (2003), no.1, p.39-66 Y1 - 2003 A1 - Gianni Dal Maso A1 - Helene Frankowska PB - SISSA Library UR - http://hdl.handle.net/1963/1625 U1 - 2493 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Bilinear semiclassical moment functionals and their integral representation JF - J. Approx. Theory Y1 - 2003 A1 - Marco Bertola VL - 121 ER - TY - JOUR T1 - The calibration method for the Mumford-Shah functional and free-discontinuity problems JF - Calc. Var. Partial Differential Equations 16 (2003) 299-333 Y1 - 2003 A1 - Giovanni Alberti A1 - Guy Bouchitte A1 - Gianni Dal Maso AB - We present a minimality criterion for the Mumford-Shah functional, and more generally for non convex variational integrals on SBV which couple a surface and a bulk term. This method provides short and easy proofs for several minimality results. PB - Springer UR - http://hdl.handle.net/1963/3051 U1 - 1282 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Control Problems for Systems of Conservation Laws Y1 - 2003 A1 - Giuseppe Maria Coclite KW - Asymptotic Stabilization PB - SISSA UR - http://hdl.handle.net/1963/5325 U1 - 5154 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Controllability properties for finite dimensional quantum Markovian master equations JF - J. Math. Phys. 44 (2003) 2357-2372 Y1 - 2003 A1 - Claudio Altafini AB - Various notions from geometric control theory are used to characterize the behavior of the Markovian master equation for N-level quantum mechanical systems driven by unitary control and to describe the structure of the sets of reachable states. It is shown that the system can be accessible but neither small-time controllable nor controllable in finite time. In particular, if the generators of quantum dynamical semigroups are unital, then the reachable sets admit easy characterizations as they monotonically grow in time. The two level case is treated in detail. PB - American Institute of Physics UR - http://hdl.handle.net/1963/2909 U1 - 1791 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Differential systems for biorthogonal polynomials appearing in 2-matrix models and the associated Riemann-Hilbert problem JF - Comm. Math. Phys. Y1 - 2003 A1 - Marco Bertola A1 - B. Eynard A1 - Harnad, J. VL - 243 ER - TY - JOUR T1 - Drift in phase space: a new variational mechanism with optimal diffusion time JF - J. Math. Pures Appl. 82 (2003) 613-664 Y1 - 2003 A1 - Massimiliano Berti A1 - Luca Biasco A1 - Philippe Bolle AB - We consider non-isochronous, nearly integrable, a-priori unstable Hamiltonian systems with a (trigonometric polynomial) $O(\\\\mu)$-perturbation which does not preserve the unperturbed tori. We prove the existence of Arnold diffusion with diffusion time $ T_d = O((1/ \\\\mu) \\\\log (1/ \\\\mu))$ by a variational method which does not require the existence of ``transition chains of tori\\\'\\\' provided by KAM theory. We also prove that our estimate of the diffusion time $T_d $ is optimal as a consequence of a general stability result derived from classical perturbation theory. PB - Elsevier UR - http://hdl.handle.net/1963/3020 U1 - 1313 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The duality of spectral curves that arises in two-matrix models JF - Teoret. Mat. Fiz. Y1 - 2003 A1 - Marco Bertola A1 - B. Eynard A1 - Kharnad, Dzh. VL - 134 ER - TY - JOUR T1 - Effective dynamics for Bloch electrons: Peierls substitution and beyond Y1 - 2003 A1 - Gianluca Panati A1 - Herbert Spohn A1 - Stefan Teufel AB - We consider an electron moving in a periodic potential and subject to an additional slowly varying external electrostatic potential, $\\\\phi(\\\\epsi x)$, and vector potential $A(\\\\epsi x)$, with $x \\\\in \\\\R^d$ and $\\\\epsi \\\\ll 1$. We prove that associated to an isolated family of Bloch bands there exists an almost invariant subspace of $L^2(\\\\R^d)$ and an effective Hamiltonian governing the evolution inside this subspace to all orders in $\\\\epsi$. To leading order the effective Hamiltonian is given through the Peierls substitution. We explicitly compute the first order correction. From a semiclassical analysis of this effective quantum Hamiltonian we establish the first order correction to the standard semiclassical model of solid state physics. PB - Springer UR - http://hdl.handle.net/1963/3040 U1 - 1293 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - A finite element approximation of the Griffith\\\'s model in fracture mechanics JF - Numer. Math., 2003, 95, 653 Y1 - 2003 A1 - Matteo Negri AB - The Griffith model for the mechanics of fractures in brittle materials is consider in the weak formulation of SBD spaces. We suggest an approximation, in the sense of Gamma-convergence, by a sequence of discrete functionals defined on finite elements spaces over structured and adaptive triangulations. The quasi-static evolution for boundary value problems is also taken into account and some numerical results are shown. PB - SISSA Library UR - http://hdl.handle.net/1963/1548 U1 - 2570 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Free energy of the two-matrix model/dToda tau-function JF - Nuclear Phys. B Y1 - 2003 A1 - Marco Bertola VL - 669 ER - TY - JOUR T1 - Gaudin models and bending flows: a geometrical point of view JF - J. Phys. A: Math. Gen. 36 (2003) 11655-11676 Y1 - 2003 A1 - Gregorio Falqui A1 - Fabio Musso AB - In this paper we discuss the bihamiltonian formulation of the (rational XXX) Gaudin models of spin-spin interaction, generalized to the case of sl(r)-valued spins. In particular, we focus on the homogeneous models. We find a pencil of Poisson brackets that recursively define a complete set of integrals of the motion, alternative to the set of integrals associated with the \\\'standard\\\' Lax representation of the Gaudin model. These integrals, in the case of su(2), coincide wih the Hamiltonians of the \\\'bending flows\\\' in the moduli space of polygons in Euclidean space introduced by Kapovich and Millson. We finally address the problem of separability of these flows and explicitly find separation coordinates and separation relations for the r=2 case. PB - IOP Publishing UR - http://hdl.handle.net/1963/2884 U1 - 1816 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Geometric motion control for a kinematically redundant robotic chain: application to a holonomic mobile manipulator JF - J. Robotic Syst. 20 (2003) 211-227 Y1 - 2003 A1 - Claudio Altafini AB - For kinematically redundant robotic manipulators, the extra degrees of freedom available allows freedom in the generation of the trajectories of the end-effector. In this paper, for this scope, we use techniques for motion control of rigid bodies on Riemannian manifolds (and Lie groups in particular) to design workspace control algorithms for the end-effector of the robotic chain and then to pull them back to joint space, all respecting the different geometric structures of the two underlying model spaces. The trajectory planner makes use of geometric splines. Examples of the different kinds of curves that are obtained via the De Casteljau algorithm in correspondence of different metric structures in SE(3) are reported. The feedback module, instead, consists of a Lyapunov based PD controller defined from a suitable notion of error distance on the Lie group. The motivating application of our work is a holonomic mobile manipulator for which simulation results are described in detail. PB - Wiley UR - http://hdl.handle.net/1963/3019 U1 - 1314 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Hybrid optimal control: case study of a car with gears JF - Int. J. Control 76 (2003) 1272-1284 Y1 - 2003 A1 - Ciro D'Apice A1 - Mauro Garavello A1 - Rosanna Manzo A1 - Benedetto Piccoli AB - The purpose of this paper is to show the use of some analytical tools for hybrid optimal control. We illustrate both the hybrid maximum principle and the hybrid necessary principle at work on a simple example of a car with gears. The model is sufficiently rich to generate non-trivial optimization problems and the obtained results match with intuition. Finally, computer simulations confirm the theoretical analysis. PB - Taylor and Francis UR - http://hdl.handle.net/1963/3022 U1 - 1311 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - An ill posed Cauchy problem for a hyperbolic system in two space dimensions Y1 - 2003 A1 - Alberto Bressan AB - The theory of weak solutions for nonlinear conservation laws is now well developed in the case of scalar equations [3] and for one-dimensional hyperbolic systems [1, 2]. For systems in several space dimensions, however, even the global existence of solutions to the Cauchy problem remains a challenging open question. In this note we construct a conterexample showing that, even for a simple class of hyperbolic systems, in two space dimensions the Cauchy problem can be ill posed. PB - Università di Padova UR - http://hdl.handle.net/1963/2913 U1 - 1787 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - An interior estimate for a nonlinear parabolic equation JF - J.Math.Anal.Appl. 284 (2003) no.1, 49 Y1 - 2003 A1 - Giuseppe Maria Coclite PB - SISSA Library UR - http://hdl.handle.net/1963/1622 U1 - 2496 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A lemma and a conjecture on the cost of rearrangements JF - Rend. Sem. Mat. Univ. Padova 110 (2003) 97-102 Y1 - 2003 A1 - Alberto Bressan AB - Consider a stack of books, containing both white and black books. Suppose that we want to sort them out, putting the white books on the right, and the black books on the left (fig.~1). This will be done by a finite sequence of elementary transpositions. In other words, if we have a stack of all black books of length $a$ followed by a stack of all white books of length $b$, we are allowed to reverse their order at the cost of $a+b$. We are interested in a lower bound on the total cost of the rearrangement. PB - Università di Padova UR - http://hdl.handle.net/1963/2914 U1 - 1786 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the local structure of optimal trajectories in R3 JF - SIAM J. Control Optim. 42 (2003) 513-531 Y1 - 2003 A1 - Andrei A. Agrachev A1 - Mario Sigalotti AB - We analyze the structure of a control function u(t) corresponding to an optimal trajectory for the system $\\\\dot q =f(q)+u\\\\, g(q)$ in a three-dimensional manifold, near a point where some nondegeneracy conditions are satisfied. The kind of optimality which is studied includes time-optimality. The control turns out to be the concatenation of some bang and some singular arcs. Studying the index of the second variation of the switching times, the number of such arcs is bounded by four. PB - SISSA Library UR - http://hdl.handle.net/1963/1612 U1 - 2506 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Mixed correlation functions of the two-matrix model JF - J. Phys. A Y1 - 2003 A1 - Marco Bertola A1 - B. Eynard VL - 36 ER - TY - JOUR T1 - Motion on submanifolds of noninvariant holonomic constraints for a kinematic control system evolving on a matrix Lie group JF - Syst. Control Lett. 50 (2003) 241-250 Y1 - 2003 A1 - Claudio Altafini A1 - Ruggero Frezza AB - For a control system on a matrix Lie group with one or more configuration constraints that are not left/right invariant, finding the combinations of (kinematic) control inputs satisfying the motion constraints is not a trivial problem. Two methods, one coordinate-dependent and the other coordinate-free are suggested. The first is based on the Wei-Norman formula; the second on the calculation of the annihilator of the coadjoint action of the constraint one-form at each point of the group manifold. The results are applied to a control system on SE(3) with a holonomic inertial constraint involving the noncommutative part in a nontrivial way. The difference in terms of compactness of the result between the two methods is considerable. PB - Elsevier UR - http://hdl.handle.net/1963/3018 U1 - 1315 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Multi-instanton calculus and equivariant cohomology JF - J.High Energy Phys. 2003,no.5,054,24 pp. Y1 - 2003 A1 - Ugo Bruzzo A1 - Jose F. Morales A1 - Francesco Fucito A1 - Alessandro Tanzini PB - SISSA Library UR - http://hdl.handle.net/1963/1645 U1 - 2473 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Non-linear sigma-models in noncommutative geometry: fields with values in finite spaces JF - Mod. Phys. Lett. A 18 (2003) 2371-2379 Y1 - 2003 A1 - Ludwik Dabrowski A1 - Thomas Krajewski A1 - Giovanni Landi AB - We study sigma-models on noncommutative spaces, notably on noncommutative tori. We construct instanton solutions carrying a nontrivial topological charge q and satisfying a Belavin-Polyakov bound. The moduli space of these instantons is conjectured to consists of an ordinary torus endowed with a complex structure times a projective space $CP^{q-1}$. PB - World Scientific UR - http://hdl.handle.net/1963/3215 U1 - 1086 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - A note on singular limits to hyperbolic systems of conservation laws JF - Commun. Pure Appl. Ana., 2003, 2, 51-64 Y1 - 2003 A1 - Stefano Bianchini AB - In this note we consider two different singular limits to hyperbolic system of conservation laws, namely the standard backward schemes for non linear semigroups and the semidiscrete scheme. \\nUnder the assumption that the rarefaction curve of the corresponding hyperbolic system are straight lines, we prove the stability of the solution and the convergence to the perturbed system to the unique solution of the limit system for initial data with small total variation. PB - SISSA Library UR - http://hdl.handle.net/1963/1542 U1 - 2621 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A note on the integral representation of functionals in the space SBD(O) JF - Rend. Mat. Appl. 23 (2003) 189-201 Y1 - 2003 A1 - Francois Ebobisse A1 - Rodica Toader AB - In this paper we study the integral representation in the space SBD(O) of special functions with bounded deformation of some L^1-norm lower semicontinuous functionals invariant with respect to rigid motions. PB - Rendiconti di Matematica UR - http://hdl.handle.net/1963/3064 U1 - 1269 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Parameter differentiation and quantum state decomposition for time varying Schrödinger equations JF - Rep. Math. Phys. 52 (2003) 381-400 Y1 - 2003 A1 - Claudio Altafini AB - For the unitary operator, solution of the Schroedinger equation corresponding to a time-varying Hamiltonian, the relation between the Magnus and the product of exponentials expansions can be expressed in terms of a system of first order differential equations in the parameters of the two expansions. A method is proposed to compute such differential equations explicitly and in a closed form. PB - Elsevier UR - http://hdl.handle.net/1963/3017 U1 - 1316 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Partition functions for matrix models and isomonodromic tau functions JF - J. Phys. A Y1 - 2003 A1 - Marco Bertola A1 - B. Eynard A1 - Harnad, J. VL - 36 N1 - Random matrix theory ER - TY - JOUR T1 - Periodic solutions of nonlinear wave equations with general nonlinearities JF - Comm.Math.Phys. 243 (2003) no.2, 315 Y1 - 2003 A1 - Massimiliano Berti A1 - Philippe Bolle PB - SISSA Library UR - http://hdl.handle.net/1963/1648 U1 - 2470 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Poisson Pencils, Integrability, and Separation of Variables Y1 - 2003 A1 - Gregorio Falqui AB - In this paper we will review a recently introduced method for solving the Hamilton-Jacobi equations by the method of Separation of Variables. This method is based on the notion of pencil of Poisson brackets and on the bihamiltonian approach to integrable systems. We will discuss how separability conditions can be intrinsically characterized within such a geometrical set-up, the definition of the separation coordinates being encompassed in the \\\\bih structure itself. We finally discuss these constructions studying in details a particular example, based on a generalization of the classical Toda Lattice. PB - SISSA UR - http://hdl.handle.net/1963/3026 U1 - 1307 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Positive solutions to a class of quasilinear elliptic equations on R JF - Discrete Contin.Dyn.Syst. 9 (2003), no.1, 55-68 Y1 - 2003 A1 - Antonio Ambrosetti A1 - Wang Zhi-Qiang AB - We discuss the existence of positive solutions of perturbation to a class of quasilinear elliptic equations on R. PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/1628 U1 - 2490 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Prescribing scalar and boundary mean curvature on the three dimensional half sphere JF - J. Geom. Anal. 13 (2003) 255-289 Y1 - 2003 A1 - Zindine Djadli A1 - Andrea Malchiodi A1 - Mohameden Ould Ahmedou AB - We consider the problem of prescribing the scalar curvature and the boundary mean curvature of the standard half three sphere, by deforming conformally its standard metric. Using blow up analysis techniques and minimax arguments, we prove some existence and compactness results. PB - Springer UR - http://hdl.handle.net/1963/3086 U1 - 1247 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quantum spin coverings and statistics JF - J. Phys. A 36 (2003), no. 13, 3829-3840 Y1 - 2003 A1 - Ludwik Dabrowski A1 - Cesare Reina AB - SL_q(2) at odd roots of unity q^l =1 is studied as a quantum cover of the complex rotation group SO(3,C), in terms of the associated Hopf algebras of (quantum) polynomial functions. We work out the irreducible corepresentations, the decomposition of their tensor products and a coquasitriangular structure, with the associated braiding (or statistics). As an example, the case l=3 is discussed in detail. PB - IOP Publishing UR - http://hdl.handle.net/1963/1667 U1 - 2451 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Second and third order observables of the two-matrix model JF - J. High Energy Phys. Y1 - 2003 A1 - Marco Bertola ER - TY - JOUR T1 - Separation of variables for Bi-Hamiltonian systems JF - Math. Phys. Anal. Geom. 6 (2003) 139-179 Y1 - 2003 A1 - Gregorio Falqui A1 - Marco Pedroni AB - We address the problem of the separation of variables for the Hamilton-Jacobi equation within the theoretical scheme of bi-Hamiltonian geometry. We use the properties of a special class of bi-Hamiltonian manifolds, called omega-N manifolds, to give intrisic tests of separability (and Staeckel separability) for Hamiltonian systems. The separation variables are naturally associated with the geometrical structures of the omega-N manifold itself. We apply these results to bi-Hamiltonian systems of the Gel\\\'fand-Zakharevich type and we give explicit procedures to find the separated coordinates and the separation relations. PB - SISSA Library UR - http://hdl.handle.net/1963/1598 U1 - 2520 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Sequences of Singularly Perturbed Functionals Generating Free-Discontinuity Problems JF - SIAM J. Math. Anal. 35 (2003) 759-805 Y1 - 2003 A1 - Massimiliano Morini AB - We prove that a wide class of singularly perturbed functionals generates as $\\\\Gamma$-limit a functional related to a free-discontinuity problem. Several applications of the result are shown. PB - SIAM UR - http://hdl.handle.net/1963/3071 U1 - 1262 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Single-Input Control Affine Systems: Local Regularity of Optimal Trajectories and a Geometric Controllability Problem Y1 - 2003 A1 - Mario Sigalotti PB - SISSA UR - http://hdl.handle.net/1963/5342 U1 - 5170 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Singularly perturb