A parametric, hybrid reduced order model approach based on the Proper Orthogonal Decomposition with both Galerkin projection and interpolation based on Radial Basis Functions method is presented. This method is tested against a case of turbulent non-isothermal mixing in a T-junction pipe, a common ow arrangement found in nuclear reactor cooling systems. The reduced order model is derived from the 3D unsteady, incompressible Navier-Stokes equations weakly coupled with the energy equation. For high Reynolds numbers, the eddy viscosity and eddy diffusivity are incorporated into the reduced order model with a Proper Orthogonal Decomposition (nested and standard) with Interpolation (PODI), where the interpolation is performed using Radial Basis Functions. The reduced order solver, obtained using a k-ω SST URANS full order model, is tested against the full order solver in a 3D T-junction pipe with parametric velocity inlet boundary conditions.

%B Computers & Fluids %V 208 %P 104615 %G eng %U https://arxiv.org/abs/1906.08725 %R 10.1016/j.compfluid.2020.104615 %0 Journal Article %J Probability Theory and Related Fields %D 2019 %T Benamou–Brenier and duality formulas for the entropic cost on RCD*(K,N) spaces %A Nicola Gigli %A Luca Tamanini %XIn 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.

%B Probability Theory and Related Fields %8 Apr %G eng %U https://doi.org/10.1007/s00440-019-00909-1 %R 10.1007/s00440-019-00909-1 %0 Journal Article %J Computer Physics Communications %D 2019 %T BlackNUFFT: Modular customizable black box hybrid parallelization of type 3 NUFFT in 3D %A Nicola Giuliani %K C++ %K Extensibility %K FFT %K Modularity %K MPI %K MRI image processing %K NUFFT type 3 %K TBB %XMany 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.

%B Computer Physics Communications %V 235 %P 324 - 335 %G eng %U http://www.sciencedirect.com/science/article/pii/S0010465518303539 %R https://doi.org/10.1016/j.cpc.2018.10.005 %0 Journal Article %J Journal of Numerical Mathematics %D 2019 %T The deal.II Library, Version 9.1 %A Arndt, Daniel %A Bangerth, Wolfgang %A Clevenger, Thomas C. %A Davydov, Denis %A Fehling, Marc %A Garcia-Sanchez, Daniel %A Harper, Graham %A Heister, Timo %A Heltai, Luca %A Kronbichler, Martin %A Maguire Kynch, Ross %A Maier, Matthias %A Pelteret, Jean Paul %A Turcksin, Bruno %A Wells, David %X This paper provides an overview of the new features of the finite element library deal.II, version 9.1. %B Journal of Numerical Mathematics %G eng %R 10.1515/jnma-2019-0064 %0 Journal Article %J Expositiones Mathematicae %D 2019 %T Differential structure associated to axiomatic Sobolev spaces %A Nicola Gigli %A Enrico Pasqualetto %K Axiomatic Sobolev space %K Cotangent module %K Locality of differentials %XThe 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.

%B Expositiones Mathematicae %G eng %U http://www.sciencedirect.com/science/article/pii/S0723086918300975 %R https://doi.org/10.1016/j.exmath.2019.01.002 %0 Conference Paper %B VIII International Conference on Computational Methods in Marine Engineering %D 2019 %T Efficient Reduction in Shape Parameter Space Dimension for Ship Propeller Blade Design %A Mola, Andrea %A Tezzele, Marco %A Gadalla, Mahmoud %A Valdenazzi, Federica %A Grassi, Davide %A Padovan, Roberta %A Rozza, Gianluigi %XIn 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.

%B VIII International Conference on Computational Methods in Marine Engineering %G eng %U https://arxiv.org/abs/1905.09815 %0 Journal Article %J Stochastic Processes and their Applications %D 2019 %T An entropic interpolation proof of the HWI inequality %A Ivan Gentil %A Christian Léonard %A Luigia Ripani %A Luca Tamanini %K Entropic interpolations %K Fisher information %K Relative entropy %K Schrödinger problem %K Wasserstein distance %XThe 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.

%B Stochastic Processes and their Applications %G eng %U http://www.sciencedirect.com/science/article/pii/S0304414918303454 %R https://doi.org/10.1016/j.spa.2019.04.002 %0 Journal Article %J Computers & Fluids %D 2019 %T A Finite Volume approximation of the Navier-Stokes equations with nonlinear filtering stabilization %A Girfoglio, Michele %A Quaini, Annalisa %A Rozza, Gianluigi %XWe consider a Leray model with a nonlinear differential low-pass filter for the simulation of incompressible fluid flow at moderately large Reynolds number (in the range of a few thousands) with under-refined meshes. For the implementation of the model, we adopt the three-step algorithm Evolve-Filter-Relax (EFR). The Leray model has been extensively applied within a Finite Element (FE) framework. Here, we propose to combine the EFR algorithm with a computationally efficient Finite Volume (FV) method. Our approach is validated against numerical data available in the literature for the 2D flow past a cylinder and against experimental measurements for the 3D fluid flow in an idealized medical device, as recommended by the U.S. Food and Drug Administration. We will show that for similar levels of mesh refinement FV and FE methods provide significantly different results. Through our numerical experiments, we are able to provide practical directions to tune the parameters involved in the model. Furthermore, we are able to investigate the impact of mesh features (element type, non-orthogonality, local refinement, and element aspect ratio) and the discretization method for the convective term on the agreement between numerical solutions and experimental data.

%B Computers & Fluids %V 187 %P 27-45 %G eng %U https://arxiv.org/abs/1901.05251 %R 10.1016/j.compfluid.2019.05.001 %0 Journal Article %J Duke Math. J. %D 2019 %T Isomonodromy deformations at an irregular singularity with coalescing eigenvalues %A Giordano Cotti %A Boris Dubrovin %A Davide Guzzetti %XWe 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.

%B Duke Math. J. %I Duke University Press %V 168 %P 967–1108 %8 04 %G eng %U https://doi.org/10.1215/00127094-2018-0059 %R 10.1215/00127094-2018-0059 %0 Journal Article %J Computer Methods in Applied Mechanics and Engineering %D 2019 %T A Localized Reduced-Order Modeling Approach for PDEs with Bifurcating Solutions %A Hess, Martin %A Alla, Alessandro %A Quaini, Annalisa %A Rozza, Gianluigi %A Gunzburger, Max %XReduced-order modeling (ROM) commonly refers to the construction, based on a few solutions (referred to as snapshots) of an expensive discretized partial differential equation (PDE), and the subsequent application of low-dimensional discretizations of partial differential equations (PDEs) that can be used to more efficiently treat problems in control and optimization, uncertainty quantification, and other settings that require multiple approximate PDE solutions. In this work, a ROM is developed and tested for the treatment of nonlinear PDEs whose solutions bifurcate as input parameter values change. In such cases, the parameter domain can be subdivided into subregions, each of which corresponds to a different branch of solutions. Popular ROM approaches such as proper orthogonal decomposition (POD), results in a global low-dimensional basis that does no respect not take advantage of the often large differences in the PDE solutions corresponding to different subregions. Instead, in the new method, the k-means algorithm is used to cluster snapshots so that within cluster snapshots are similar to each other and are dissimilar to those in other clusters. This is followed by the construction of local POD bases, one for each cluster. The method also can detect which cluster a new parameter point belongs to, after which the local basis corresponding to that cluster is used to determine a ROM approximation. Numerical experiments show the effectiveness of the method both for problems for which bifurcation cause continuous and discontinuous changes in the solution of the PDE.

%B Computer Methods in Applied Mechanics and Engineering %V 351 %P 379-403 %G eng %U https://arxiv.org/abs/1807.08851 %R 10.1016/j.cma.2019.03.050 %0 Journal Article %J Canadian Mathematical Bulletin %D 2019 %T A Note About the Strong Maximum Principle on RCD Spaces %A Nicola Gigli %A Chiara Rigoni %XWe give a direct proof of the strong maximum principle on finite dimensional RCD spaces based on the Laplacian comparison of the squared distance.

%B Canadian Mathematical Bulletin %I Canadian Mathematical Society %V 62 %P 259–266 %G eng %R 10.4153/CMB-2018-022-9 %0 Journal Article %J Communications in Computational Physics %D 2019 %T Parametric POD-Galerkin Model Order Reduction for Unsteady-State Heat Transfer Problems %A Sokratia Georgaka %A Giovanni Stabile %A Gianluigi Rozza %A Michael J. Bluck %XA parametric reduced order model based on proper orthogonal decom- position with Galerkin projection has been developed and applied for the modeling of heat transport in T-junction pipes which are widely found in nuclear power plants. Thermal mixing of different temperature coolants in T-junction pipes leads to tem- perature fluctuations and this could potentially cause thermal fatigue in the pipe walls. The novelty of this paper is the development of a parametric ROM considering the three dimensional, incompressible, unsteady Navier-Stokes equations coupled with the heat transport equation in a finite volume approximation. Two different paramet- ric cases are presented in this paper: parametrization of the inlet temperatures and parametrization of the kinematic viscosity. Different training spaces are considered and the results are compared against the full order model.

%B Communications in Computational Physics %V 27 %P 1–32 %G eng %U https://arxiv.org/abs/1808.05175 %R 10.4208/cicp.OA-2018-0207 %0 Report %D 2019 %T Quasi-continuous vector fields on RCD spaces %A Clément Debin %A Nicola Gigli %A Enrico Pasqualetto %G eng %0 Journal Article %J Journal of Functional Analysis %D 2019 %T Reducibility of first order linear operators on tori via Moser's theorem %A Roberto Feola %A Filippo Giuliani %A Riccardo Montalto %A Michela Procesi %K Hyperbolic PDEs %K KAM theory %K Nash–Moser %K Reducibility %XIn 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.

%B Journal of Functional Analysis %V 276 %P 932 - 970 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022123618303793 %R https://doi.org/10.1016/j.jfa.2018.10.009 %0 Journal Article %J J. Elast. %D 2018 %T A Comparison Between Active Strain and Active Stress in Transversely Isotropic Hyperelastic Materials %A Giulia Giantesio %A Alessandro Musesti %A Davide Riccobelli %B J. Elast. %I Springer Nature %G eng %0 Journal Article %J SOFTWAREX %D 2018 %T deal2lkit: A toolkit library for high performance programming in deal.II %A Alberto Sartori %A Nicola Giuliani %A Mauro Bardelloni %A Luca Heltai %B SOFTWAREX %V 7 %P 318–327 %G eng %R 10.1016/j.softx.2018.09.004 %0 Journal Article %J JOURNAL OF NUMERICAL MATHEMATICS %D 2018 %T The deal.II Library, Version 9.0 %A Giovanni Alzetta %A Arndt, Daniel %A W. Bangerth %A Boddu, Vishal %A Brands, Benjamin %A Denis Davydov %A Gassmöller, Rene %A Timo Heister %A Luca Heltai %A Kormann, Katharina %A Martin Kronbichler %A Matthias Maier %A Pelteret, Jean-Paul %A B. Turcksin %A David Wells %B JOURNAL OF NUMERICAL MATHEMATICS %G eng %U https://doi.org/10.1515/jnma-2018-0054 %R 10.1515/jnma-2018-0054 %0 Report %D 2018 %T Differential of metric valued Sobolev maps %A Nicola Gigli %A Enrico Pasqualetto %A Elefterios Soultanis %G eng %0 Book Section %B Mathematical and Numerical Modeling of the Cardiovascular System and Applications %D 2018 %T A distributed lagrange formulation of the finite element immersed boundary method for fluids interacting with compressible solids %A Boffi, Daniele %A Gastaldi, Lucia %A Luca Heltai %B Mathematical and Numerical Modeling of the Cardiovascular System and Applications %I Springer International Publishing %C Cham %V 16 %P 1–21 %G eng %U https://arxiv.org/abs/1712.02545v1 %R 10.1007/978-3-319-96649-6_1 %0 Journal Article %J Journal of Functional Analysis %D 2018 %T On fractional powers of singular perturbations of the Laplacian %A Vladimir Georgiev %A Alessandro Michelangeli %A Raffaele Scandone %K Point interactions %K Regular and singular component of a point-interaction operator %K Singular perturbations of the Laplacian %XWe 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.

%B Journal of Functional Analysis %V 275 %P 1551 - 1602 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022123618301046 %R https://doi.org/10.1016/j.jfa.2018.03.007 %0 Report %D 2018 %T On Geometric Quantum Confinement in Grushin-Like Manifolds %A Matteo Gallone %A Alessandro Michelangeli %A Eugenio Pozzoli %X 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. %G en %U http://preprints.sissa.it/handle/1963/35322 %1 35632 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-09-19T07:05:15Z No. of bitstreams: 1 GMP-Grushin-SISSApreprint.pdf: 390608 bytes, checksum: c4bbb299a3b07668840d185c315c1a29 (MD5) %0 Report %D 2018 %T Hydrogenoid Spectra with Central Perturbations %A Matteo Gallone %A Alessandro Michelangeli %X 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. %G en %U http://preprints.sissa.it/handle/1963/35321 %1 35631 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-08-27T06:42:30Z No. of bitstreams: 1 GM-hydrogenoid-2018-SISSA-Preprint.pdf: 480482 bytes, checksum: 228ebe556a2688a43dcbbd1edeeaa5c4 (MD5) %0 Report %D 2018 %T Local moduli of semisimple Frobenius coalescent structures %A Giordano Cotti %A Boris Dubrovin %A Davide Guzzetti %XThere 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.

%I SISSA %G en %U http://preprints.sissa.it/handle/1963/35304 %1 35610 %2 Mathematics %4 1 %# MAT/03 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-01-16T11:11:03Z No. of bitstreams: 1 Preprint_Davide.pdf: 1242726 bytes, checksum: 527d898383b9f997856370b14965bbdc (MD5) %0 Conference Paper %B Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship & Maritime Research %D 2018 %T Model Order Reduction by means of Active Subspaces and Dynamic Mode Decomposition for Parametric Hull Shape Design Hydrodynamics %A Marco Tezzele %A Nicola Demo %A Mahmoud Gadalla %A Andrea Mola %A Gianluigi Rozza %X 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. %B Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship & Maritime Research %I IOS Press %C Trieste, Italy %G eng %U http://ebooks.iospress.nl/publication/49270 %R 10.3233/978-1-61499-870-9-569 %0 Report %D 2018 %T On the notion of parallel transport on RCD spaces %A Nicola Gigli %A Enrico Pasqualetto %G eng %0 Journal Article %J Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences %D 2018 %T Numerical study of the Kadomtsev-Petviashvili equation and dispersive shock waves %A Tamara Grava %A Christian Klein %A Giuseppe Pitton %XA 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.

%B Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences %V 474 %P 20170458 %G eng %U https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2017.0458 %R 10.1098/rspa.2017.0458 %0 Journal Article %J Symmetry, Integrability and Geometry. Methods and Applications %D 2018 %T Painlevé IV Critical Asymptotics for Orthogonal Polynomials in the Complex Plane %A Marco Bertola %A José Gustavo Elias Rebelo %A Tamara Grava %XWe 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.

%B Symmetry, Integrability and Geometry. Methods and Applications %I National Academy of Sciences of Ukraine %V 14 %G eng %R 10.3842/SIGMA.2018.091 %0 Journal Article %J SOFT ROBOTICS %D 2018 %T Predicting and Optimizing Microswimmer Performance from the Hydrodynamics of Its Components: The Relevance of Interactions %A Nicola Giuliani %A Luca Heltai %A Antonio DeSimone %B SOFT ROBOTICS %V 5 %P 410–424 %G eng %U https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6094362/ %R 10.1089/soro.2017.0099 %0 Journal Article %J Calculus of Variations and Partial Differential Equations %D 2018 %T Recognizing the flat torus among RCD*(0,N) spaces via the study of the first cohomology group %A Nicola Gigli %A Chiara Rigoni %XWe 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.

%B Calculus of Variations and Partial Differential Equations %V 57 %P 104 %8 Jun %G eng %U https://doi.org/10.1007/s00526-018-1377-z %R 10.1007/s00526-018-1377-z %0 Report %D 2018 %T Reducibility for a class of weakly dispersive linear operators arising from the Degasperis Procesi equation %A Roberto Feola %A Filippo Giuliani %A Michela Procesi %G eng %0 Journal Article %J Rendiconti Lincei-Matematica e Applicazioni %D 2018 %T Second order differentiation formula on RCD(K, N) spaces %A Nicola Gigli %A Luca Tamanini %B Rendiconti Lincei-Matematica e Applicazioni %V 29 %P 377–386 %G eng %0 Report %D 2018 %T Second order differentiation formula on RCD*(K,N) spaces %A Nicola Gigli %A Luca Tamanini %G eng %0 Conference Paper %B Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship & Maritime Research %D 2018 %T Shape Optimization by means of Proper Orthogonal Decomposition and Dynamic Mode Decomposition %A Nicola Demo %A Marco Tezzele %A Gianluca Gustin %A Gianpiero Lavini %A Gianluigi Rozza %X 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. %B Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship & Maritime Research %I IOS Press %C Trieste, Italy %G eng %U http://ebooks.iospress.nl/publication/49229 %& 212 %R 10.3233/978-1-61499-870-9-212 %0 Journal Article %J Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences %D 2018 %T Symplectic invariants for parabolic orbits and cusp singularities of integrable systems %A Alexey Bolsinov %A Lorenzo Guglielmi %A Elena Kudryavtseva %XWe 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’.

%B Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences %V 376 %P 20170424 %G eng %U https://royalsocietypublishing.org/doi/abs/10.1098/rsta.2017.0424 %R 10.1098/rsta.2017.0424 %0 Journal Article %J Advances in Engineering Software %D 2018 %T π-BEM : A flexible parallel implementation for adaptive , geometry aware , and high order boundary element methods %A Nicola Giuliani %A Andrea Mola %A Luca Heltai %B Advances in Engineering Software %V 121 %P 39–58 %G eng %0 Journal Article %J Random Matrices: Theory and Applications %D 2017 %T Analytic geometry of semisimple coalescent Frobenius structures %A Giordano Cotti %A Davide Guzzetti %XWe 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.

%B Random Matrices: Theory and Applications %V 06 %P 1740004 %G eng %U https://doi.org/10.1142/S2010326317400044 %R 10.1142/S2010326317400044 %0 Journal Article %J Journal of Differential Equations %D 2017 %T An avoiding cones condition for the Poincaré–Birkhoff Theorem %A Alessandro Fonda %A Paolo Gidoni %K Avoiding cones condition %K Hamiltonian systems %K Periodic solutions %K Poincaré–Birkhoff theorem %XWe 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.

%B Journal of Differential Equations %V 262 %P 1064 - 1084 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022039616303278 %R https://doi.org/10.1016/j.jde.2016.10.002 %0 Report %D 2017 %T Discrete spectra for critical Dirac-Coulomb Hamiltonians %A Matteo Gallone %A Alessandro Michelangeli %X 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. %G en %U http://preprints.sissa.it/handle/1963/35300 %1 35606 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-11-06T14:27:38Z No. of bitstreams: 1 SISSA_preprint_44-2017-MATE.pdf: 1573857 bytes, checksum: 728e94322471701d89ed5741cda85d99 (MD5) %0 Journal Article %J ESAIM: COCV %D 2017 %T On the genesis of directional friction through bristle-like mediating elements %A Paolo Gidoni %A Antonio DeSimone %XWe 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.

%B ESAIM: COCV %V 23 %P 1023-1046 %G eng %U https://doi.org/10.1051/cocv/2017030 %R 10.1051/cocv/2017030 %0 Journal Article %J ArXiv e-prints %D 2017 %T The injectivity radius of Lie manifolds %A Paolo Antonini %A Guido De Philippis %A Nicola Gigli %K (58J40) %K 53C21 %K Mathematics - Differential Geometry %XWe prove in a direct, geometric way that for any compatible Riemannian metric on a Lie manifold the injectivity radius is positive

%B ArXiv e-prints %G eng %U https://arxiv.org/pdf/1707.07595.pdf %0 Report %D 2017 %T Krein-Visik-Birman self-adjoint extension theory revisited %A Matteo Gallone %A Alessandro Michelangeli %A Andrea Ottolini %X 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. %G en %U http://preprints.sissa.it/handle/1963/35286 %1 35591 %2 Mathematics %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-05-31T08:18:47Z No. of bitstreams: 1 Gallone-Michelangeli-Ottolini-KVB.pdf: 675862 bytes, checksum: 325168fcaae89a9faedde0e5c32e69a7 (MD5) %0 Journal Article %J Journal of Differential Equations %D 2017 %T Quasi-periodic solutions for quasi-linear generalized KdV equations %A Filippo Giuliani %K KAM for PDE's %K KdV %K Nash–Moser theory %K Quasi-linear PDE's %K Quasi-periodic solutions %XWe 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.

%B Journal of Differential Equations %V 262 %P 5052 - 5132 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022039617300487 %R https://doi.org/10.1016/j.jde.2017.01.021 %0 Report %D 2017 %T Second order differentiation formula on compact RCD*(K,N) spaces %A Nicola Gigli %A Luca Tamanini %G eng %0 Report %D 2017 %T Self-Adjoint Extensions of Dirac Operator with Coulomb Potential %A Matteo Gallone %X 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. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/35273 %1 35579 %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-02-17T06:59:43Z No. of bitstreams: 1 Gallone_preprint2017.pdf: 186169 bytes, checksum: aa5eaaac65f07802fc5a3842ace968b4 (MD5) %0 Report %D 2017 %T Self-adjoint realisations of the Dirac-Coulomb Hamiltonian for heavy nuclei %A Matteo Gallone %A Alessandro Michelangeli %X 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. %G en %U http://preprints.sissa.it/handle/1963/35287 %1 35592 %2 Mathematics %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-06-05T06:42:39Z No. of bitstreams: 1 Coulomb_Gallone_Michelangeli_26_2017.pdf: 508858 bytes, checksum: 21c788d0de4fed88bee2e6fd5cd0849c (MD5) %0 Journal Article %J Meccanica %D 2017 %T Stasis domains and slip surfaces in the locomotion of a bio-inspired two-segment crawler %A Paolo Gidoni %A Antonio DeSimone %XWe 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.

%B Meccanica %V 52 %P 587–601 %8 Feb %G eng %U https://doi.org/10.1007/s11012-016-0408-0 %R 10.1007/s11012-016-0408-0 %0 Journal Article %J Phys. Rev. Lett. %D 2017 %T Universality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schrödinger Equation %A Tikan, Alexey %A Billet, Cyril %A Gennady El %A Alexander Tovbis %A Marco Bertola %A Sylvestre, Thibaut %A Gustave, Francois %A Randoux, Stephane %A Genty, Goëry %A Suret, Pierre %A Dudley, John M. %B Phys. Rev. Lett. %I American Physical Society %V 119 %P 033901 %8 Jul %G eng %U https://link.aps.org/doi/10.1103/PhysRevLett.119.033901 %R 10.1103/PhysRevLett.119.033901 %0 Report %D 2016 %T Behaviour of the reference measure on RCD spaces under charts %A Nicola Gigli %A Enrico Pasqualetto %G eng %0 Report %D 2016 %T Equivalence of two different notions of tangent bundle on rectifiable metric measure spaces %A Nicola Gigli %A Enrico Pasqualetto %G eng %0 Journal Article %J Annali di Matematica Pura ed Applicata (1923 -) %D 2016 %T Generalizing the Poincaré–Miranda theorem: the avoiding cones condition %A Alessandro Fonda %A Paolo Gidoni %XAfter 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.

%B Annali di Matematica Pura ed Applicata (1923 -) %V 195 %P 1347–1371 %8 Aug %G eng %U https://doi.org/10.1007/s10231-015-0519-6 %R 10.1007/s10231-015-0519-6 %0 Journal Article %J Advances in Nonlinear Analysis %D 2016 %T Periodic perturbations of Hamiltonian systems %A Alessandro Fonda %A Maurizio Garrione %A Paolo Gidoni %XWe 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.

%B Advances in Nonlinear Analysis %I De Gruyter %V 5 %P 367–382 %G eng %R 10.1515/anona-2015-0122 %0 Book Section %B Noncommutative Analysis, Operator Theory and Applications %D 2016 %T Pimsner Algebras and Circle Bundles %A Francesca Arici %A Francesco D'Andrea %A Giovanni Landi %E Alpay, Daniel %E Cipriani, Fabio %E Colombo, Fabrizio %E Guido, Daniele %E Sabadini, Irene %E Sauvageot, Jean-Luc %XWe 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.

%B Noncommutative Analysis, Operator Theory and Applications %I Springer International Publishing %C Cham %P 1–25 %@ 978-3-319-29116-1 %G eng %U https://doi.org/10.1007/978-3-319-29116-1_1 %R 10.1007/978-3-319-29116-1_1 %0 Journal Article %J Communications in Number Theory and Physics %D 2016 %T Refined node polynomials via long edge graphs %A Lothar Göttsche %A Benjamin Kipkirui Kikwai %XThe 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.

%B Communications in Number Theory and Physics %I International Press of Boston %V 10 %P 193–234 %G eng %U http://dx.doi.org/10.4310/CNTP.2016.v10.n2.a2 %R 10.4310/CNTP.2016.v10.n2.a2 %0 Journal Article %J SIAM Journal on Mathematical Analysis %D 2016 %T Renormalization for Autonomous Nearly Incompressible BV Vector Fields in Two Dimensions %A Stefano Bianchini %A Paolo Bonicatto %A N.A. Gusev %XGiven 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].

%B SIAM Journal on Mathematical Analysis %V 48 %P 1-33 %G eng %U https://doi.org/10.1137/15M1007380 %R 10.1137/15M1007380 %0 Thesis %D 2016 %T Two explorations in Dynamical Systems and Mechanics %A Paolo Gidoni %K Poincaré-Birkhoff Theorem %X 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". %I SISSA %G en %1 35527 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Paolo Gidoni (pgidoni@sissa.it) on 2016-09-27T15:43:47Z No. of bitstreams: 1 PaoloGidoniDissertation.pdf: 3516967 bytes, checksum: 7ba7e59fb23b28fdd3ca2a95796a5827 (MD5) %0 Journal Article %D 2015 %T Deal2lkit: a Toolkit Library for High Performance Programming in deal.II %A Alberto Sartori %A Nicola Giuliani %A Mauro Bardelloni %A Luca Heltai %X 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. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/35006 %1 35235 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by asartori@sissa.it (asartori@sissa.it) on 2015-11-13T13:12:29Z No. of bitstreams: 1 paper_deal2lkit.pdf: 1085486 bytes, checksum: 1dc7e9b9790fe38d2ced7b5328633cd8 (MD5) %0 Journal Article %J J. Math. Phys. %D 2015 %T A degeneration of two-phase solutions of the focusing nonlinear Schrödinger equation via Riemann-Hilbert problems %A Marco Bertola %A Giavedoni, Pietro %B J. Math. Phys. %V 56 %P 061507, 17 %G eng %U http://dx.doi.org/10.1063/1.4922362 %R 10.1063/1.4922362 %0 Journal Article %J Engineering Analysis with Boundary Elements 59 (2015), pp. 8-22 %D 2015 %T FEM SUPG stabilisation of mixed isoparametric BEMs: application to linearised free surface flows %A Nicola Giuliani %A Andrea Mola %A Luca Heltai %A L. Formaggia %XIn 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.

%B Engineering Analysis with Boundary Elements 59 (2015), pp. 8-22 %G en_US %U http://urania.sissa.it/xmlui/handle/1963/34466 %1 34640 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by ngiuliani@sissa.it (ngiuliani@sissa.it) on 2015-05-04T12:32:04Z No. of bitstreams: 1 paper-free-surface.pdf: 888763 bytes, checksum: 68366266786e84b78a356acd6de50840 (MD5) %R 10.1016/j.enganabound.2015.04.006 %0 Journal Article %J Geometry & Topology %D 2015 %T Geodesics and horizontal-path spaces in Carnot groups %A Andrei A. Agrachev %A Alessandro Gentile %A Antonio Lerario %XWe 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.

%B Geometry & Topology %I Mathematical Sciences Publishers %V 19 %P 1569–1630 %G eng %R 10.2140/gt.2015.19.1569 %0 Journal Article %J Journal of the Mechanics and Physics of Solids %D 2015 %T Liquid crystal elastomer strips as soft crawlers %A Antonio DeSimone %A Paolo Gidoni %A Giovanni Noselli %K Crawling motility %K Directional surfaces %K Frictional interactions %K Liquid crystal elastomers %K Soft biomimetic robots %XIn 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.

%B Journal of the Mechanics and Physics of Solids %V 84 %P 254 - 272 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022509615300430 %R https://doi.org/10.1016/j.jmps.2015.07.017 %0 Journal Article %J Nonlinear Analysis: Theory, Methods & Applications %D 2015 %T A permanence theorem for local dynamical systems %A Alessandro Fonda %A Paolo Gidoni %K Lotka–Volterra %K permanence %K Predator–prey %K Uniform persistence %XWe 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.

%B Nonlinear Analysis: Theory, Methods & Applications %V 121 %P 73 - 81 %G eng %U http://www.sciencedirect.com/science/article/pii/S0362546X14003332 %R https://doi.org/10.1016/j.na.2014.10.011 %0 Journal Article %D 2014 %T Approximate Hermitian–Yang–Mills structures on semistable principal Higgs bundles %A Ugo Bruzzo %A Beatriz Grana-Otero %X 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. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34645 %1 34849 %2 Mathematics %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-10-14T16:50:03Z No. of bitstreams: 1 preprint2014.pdf: 191569 bytes, checksum: 33ef336bcd23cb79195af6fc13704f62 (MD5) %R 10.1007/s10455-014-9433-1 %0 Journal Article %J Comm. Math. Phys. %D 2014 %T Cauchy-Laguerre two-matrix model and the Meijer-G random point field %A Marco Bertola %A Gekhtman, M. %A Szmigielski, J. %B Comm. Math. Phys. %V 326 %P 111–144 %G eng %U http://dx.doi.org/10.1007/s00220-013-1833-8 %R 10.1007/s00220-013-1833-8 %0 Journal Article %D 2014 %T Conformal invariants from nodal sets. I. negative eigenvalues and curvature prescription %A Rod R. Gover %A Yaiza Canzani %A Dmitry Jakobson %A Raphaël Ponge %A Andrea Malchiodi %X 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. %I Oxford University Press %G en %U http://urania.sissa.it/xmlui/handle/1963/35128 %1 35366 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-12-02T16:09:57Z No. of bitstreams: 1 preprint2014.pdf: 356671 bytes, checksum: 20e817f9f20d9c72d717e04f94f86bd9 (MD5) %R 10.1093/imrn/rns295 %0 Journal Article %J International Journal of Non-Linear Mechanics %D 2014 %T Crawling on directional surfaces %A Paolo Gidoni %A Giovanni Noselli %A Antonio DeSimone %K Bio-mimetic micro-robots %K Cell migration %K Crawling motility %K Directional surfaces %K Self-propulsion %XIn 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.

%B International Journal of Non-Linear Mechanics %V 61 %P 65 - 73 %G eng %U http://www.sciencedirect.com/science/article/pii/S0020746214000213 %R https://doi.org/10.1016/j.ijnonlinmec.2014.01.012 %0 Journal Article %D 2014 %T An effective model for nematic liquid crystal composites with ferromagnetic inclusions %A Maria Carme Calderer %A Antonio DeSimone %A Dmitry Golovaty %A Alexander Panchenko %X 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. %I Society for Industrial and Applied Mathematics Publications %G en %U http://urania.sissa.it/xmlui/handle/1963/34940 %1 35194 %2 Physics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-11-09T09:28:26Z No. of bitstreams: 1 preprint2014.pdf: 284611 bytes, checksum: ef4123b4aefb1a36fa198c1207a6f021 (MD5) %R 10.1137/130910348 %0 Journal Article %D 2014 %T A Review of the Sixth Painlevé Equation %A Davide Guzzetti %X 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. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34658 %1 34868 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-10-20T13:13:55Z No. of bitstreams: 1 preprint2014.pdf: 283505 bytes, checksum: d5f401efb5eec8b4689b090dbcca6d84 (MD5) %R 10.1007/s00365-014-9250-6 %0 Journal Article %D 2014 %T Spontaneous division and motility in active nematic droplets %A Luca Giomi %A Antonio DeSimone %X 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. %I American Physical Society %G en %U http://urania.sissa.it/xmlui/handle/1963/34902 %1 35107 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-11-03T14:40:44Z No. of bitstreams: 1 preprint2014.pdf: 4005398 bytes, checksum: eebaadedd03c1077a9cb2a209b5abdcc (MD5) %R 10.1103/PhysRevLett.112.147802 %0 Report %D 2014 %T Steady nearly incompressible vector elds in 2D: chain rule and renormalization %A Stefano Bianchini %A N.A. Gusev %I SISSA %G en %1 7464 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-08-13T07:08:46Z No. of bitstreams: 1 main_stefano(1).pdf: 631783 bytes, checksum: 3ac150a4fb3cb33ebaf5273751dfdf27 (MD5) %0 Journal Article %J International Journal of Non-Linear Mechanics 56, 142-147 (2013) %D 2013 %T Crawlers in viscous environments: linear vs nonlinear rheology %A Antonio DeSimone %A Federica Guarnieri %A Giovanni Noselli %A Amabile Tatone %X 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. %B International Journal of Non-Linear Mechanics 56, 142-147 (2013) %I Elsevier %G en %1 34590 %2 Mathematics %$ Submitted by gnoselli@sissa.it (gnoselli@sissa.it) on 2015-03-07T17:29:52Z No. of bitstreams: 1 viscous_crawlers.pdf: 887755 bytes, checksum: 6022e4160d2eced97b51326bf51e0827 (MD5) %R 10.1016/j.ijnonlinmec.2013.02.007 %0 Report %D 2013 %T On critical behaviour in systems of Hamiltonian partial differential equations %A Boris Dubrovin %A Tamara Grava %A Christian Klein %A Antonio Moro %XWe 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.

%I SISSA %G en %1 7280 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Tamara Grava (grava@sissa.it) on 2014-01-14T18:10:19Z No. of bitstreams: 1 EHfinal_3.pdf: 7760169 bytes, checksum: 1e98e693fbceb1268a5acd269dd9b03e (MD5) %0 Report %D 2013 %T Defect annihilation and proliferation in active nematics %A Luca Giomi %A Mark J. Bowick %A Xu Ma %A M. Cristina Marchetti %X 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. %I SISSA %G en %U http://hdl.handle.net/1963/6566 %1 6517 %2 Mathematics %4 2 %# FIS/02 FISICA TEORICA, MODELLI E METODI MATEMATICI %$ Submitted by Luca Giomi (lgiomi@sissa.it) on 2013-04-04T08:03:17Z\nNo. of bitstreams: 1\n1303.4720v1.pdf: 2660135 bytes, checksum: 5fdf2d289b9b42a28ae3d000faee65fb (MD5) %0 Journal Article %J Topol. Methods Nonlinear Anal. %D 2013 %T Generalized Sturm-Liouville boundary conditions for first order differential systems in the plane %A Alessandro Fonda %A Maurizio Garrione %XWe 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.

%B Topol. Methods Nonlinear Anal. %I Nicolaus Copernicus University, Juliusz P. Schauder Centre for Nonlinear Studies %V 42 %P 293–325 %G eng %U https://projecteuclid.org:443/euclid.tmna/1461248981 %0 Journal Article %J Journal of Geometric Analysis %D 2013 %T Lipschitz Classification of Almost-Riemannian Distances on Compact Oriented Surfaces %A Ugo Boscain %A Grégoire Charlot %A Roberta Ghezzi %A Mario Sigalotti %XTwo-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.

%B Journal of Geometric Analysis %V 23 %P 438–455 %8 Jan %G eng %U https://doi.org/10.1007/s12220-011-9262-4 %R 10.1007/s12220-011-9262-4 %0 Journal Article %J Nonlinear Differential Equations and Applications NoDEA %D 2013 %T Planar Hamiltonian systems at resonance: the Ahmad–Lazer–Paul condition %A Alberto Boscaggin %A Maurizio Garrione %XWe 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.

%B Nonlinear Differential Equations and Applications NoDEA %V 20 %P 825–843 %8 Jun %G eng %U https://doi.org/10.1007/s00030-012-0181-2 %R 10.1007/s00030-012-0181-2 %0 Journal Article %D 2013 %T Softly Constrained Films %A Luca Giomi %X 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. %I SISSA %G en %U http://hdl.handle.net/1963/6563 %1 6518 %2 Mathematics %4 2 %# FIS/02 FISICA TEORICA, MODELLI E METODI MATEMATICI %$ Submitted by Luca Giomi (lgiomi@sissa.it) on 2013-04-04T08:04:08Z\nNo. of bitstreams: 1\n1304.1077v1.pdf: 4248769 bytes, checksum: c955d3de3233f3619d546d93dab34c63 (MD5) %0 Report %D 2013 %T The splitting theorem in non-smooth context %A Nicola Gigli %X 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. %G en %U http://preprints.sissa.it/handle/1963/35306 %1 35613 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-02-23T12:45:43Z No. of bitstreams: 1 Splittingmms-submitted.pdf: 826242 bytes, checksum: 0395e29f7f4d768880e012ef1a77073a (MD5) %0 Journal Article %J J. Math. Phys. %D 2013 %T Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two-matrix model %A Marco Bertola %A Gekhtman, M. %A Szmigielski, J. %B J. Math. Phys. %V 54 %P 043517, 25 %G eng %0 Report %D 2013 %T On the tritronquée solutions of P$_I^2$ %A Tamara Grava %A Andrey Kapaev %A Christian Klein %XFor 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.

%I SISSA %G en %1 7282 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Tamara Grava (grava@sissa.it) on 2014-01-14T18:35:53Z No. of bitstreams: 1 tritronquee_coeff.pdf: 753719 bytes, checksum: 812d268b2abe25ccbcc69eb40ff75f1f (MD5) %0 Journal Article %J SIAM J. Control Optim., 50 (2012) 559–582 %D 2012 %T On 2-step, corank 2 nilpotent sub-Riemannian metrics %A Davide Barilari %A Ugo Boscain %A Jean-Paul Gauthier %X 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. %B SIAM J. Control Optim., 50 (2012) 559–582 %I Society for Industrial and Applied Mathematics %G en %U http://hdl.handle.net/1963/6065 %1 5950 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-08-01T12:38:52Z\\nNo. of bitstreams: 1\\n1105.5766v2.pdf: 271835 bytes, checksum: 0836f63f262f14fbd4d44422b6c85686 (MD5) %R 10.1137/110835700 %0 Journal Article %J Journal of dynamical and control systems %D 2012 %T On a class of vector fields with discontinuity of divide-by-zero type and its applications %A Roberta Ghezzi %A Alexey O. Remizov %XWe 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.

%B Journal of dynamical and control systems %I Springer %V 18 %P 135-158 %G en %N 1 %1 7038 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-08-14T09:32:26Z No. of bitstreams: 1 1007.0912v1.pdf: 311033 bytes, checksum: 66a06c5e2764120aa6d9ac971a82baab (MD5) %R 10.1007/s10883-012-9137-4 %0 Journal Article %J International Mathematics Research Notices, vol. 22 (2012) , page 5063-5099 %D 2012 %T The KdV hierarchy: universality and a Painleve transcendent %A Tom Claeys %A Tamara Grava %K Small-Dispersion limit %X 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. %B International Mathematics Research Notices, vol. 22 (2012) , page 5063-5099 %I Oxford University Press %G en %U http://hdl.handle.net/1963/6921 %1 6902 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-05-29T08:08:55Z No. of bitstreams: 1 1101.2602v1.pdf: 327994 bytes, checksum: 5b5bbc9f9b74ce97c2bf5ae794698819 (MD5) %0 Journal Article %J Communications in Mathematical Physics, Volume 315, Issue 1, September 2012, Pages 1-37 %D 2012 %T Non-uniqueness results for critical metrics of regularized determinants in four dimensions %A Matthew Gursky %A Andrea Malchiodi %X 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. %B Communications in Mathematical Physics, Volume 315, Issue 1, September 2012, Pages 1-37 %I Springer %G en %U http://hdl.handle.net/1963/6559 %1 6488 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Andrea Malchiodi (malchiod@sissa.it) on 2013-03-14T10:25:46Z No. of bitstreams: 1 1105.3762v3.pdf: 658857 bytes, checksum: 2821cb9caed2f5cda3b406c745b73009 (MD5) %R 10.1007/s00220-012-1535-7 %0 Journal Article %J Physica D 241, nr. 23-24 (2012): 2246-2264 %D 2012 %T Numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions %A Tamara Grava %A Christian Klein %K Korteweg-de Vries equation %X 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. %B Physica D 241, nr. 23-24 (2012): 2246-2264 %I Elsevier %G en %1 7069 %2 Physics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-09-16T14:49:23Z No. of bitstreams: 1 1202.0962v2.pdf: 2652650 bytes, checksum: d8678338138745b35d8515af39f85d18 (MD5) %R 10.1016/j.physd.2012.04.001 %0 Journal Article %J Physica D: Nonlinear Phenomena, Volume 241, Issue 23-24, 1 December 2012, Pages 2188-2203 %D 2012 %T Poles Distribution of PVI Transcendents close to a Critical Point (summer 2011) %A Davide Guzzetti %K Painleve' equations %X 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. %B Physica D: Nonlinear Phenomena, Volume 241, Issue 23-24, 1 December 2012, Pages 2188-2203 %I Elsevier %G en %U http://hdl.handle.net/1963/6526 %1 6469 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Davide Guzzetti (guzzetti@sissa.it) on 2013-03-12T10:23:20Z No. of bitstreams: 1 1104.5066v3.pdf: 539839 bytes, checksum: 5e2f0aa0a56736f91219709b51d0a970 (MD5) %R doi:10.1016/j.physd.2012.02.015 %0 Journal Article %J Differential Integral Equations %D 2012 %T Resonance at the first eigenvalue for first-order systems in the plane: vanishing Hamiltonians and the Landesman-Lazer condition %A Maurizio Garrione %B Differential Integral Equations %I Khayyam Publishing, Inc. %V 25 %P 505–526 %8 05 %G eng %U https://projecteuclid.org:443/euclid.die/1356012676 %0 Journal Article %D 2012 %T A Review on The Sixth Painlevé Equation %A Davide Guzzetti %K Painlevé equation %XFor 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.

%I SISSA %G en %U http://hdl.handle.net/1963/6525 %1 6470 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Davide Guzzetti (guzzetti@sissa.it) on 2013-03-12T10:24:43Z\nNo. of bitstreams: 1\n1210.0311v1.pdf: 283505 bytes, checksum: d5f401efb5eec8b4689b090dbcca6d84 (MD5) %0 Journal Article %J Int Math Res Notices (2012) 2012 (6): 1352-1413 %D 2012 %T Solving the Sixth Painlevé Equation: Towards the Classification of all the Critical Behaviors and the Connection Formulae %A Davide Guzzetti %X 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. %B Int Math Res Notices (2012) 2012 (6): 1352-1413 %I Oxford University Press %G en %U http://hdl.handle.net/1963/6093 %1 5979 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-08-02T13:30:44Z\\nNo. of bitstreams: 1\\n1010.1895v3.pdf: 424524 bytes, checksum: b558cd4e4da76831f67255b275392840 (MD5) %R 10.1093/imrn/rnr071 %0 Journal Article %J Nonlinearity, Volume 25, Issue 12, December 2012, Pages 3235-3276 %D 2012 %T Tabulation of Painlevé 6 transcendents %A Davide Guzzetti %X 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. %B Nonlinearity, Volume 25, Issue 12, December 2012, Pages 3235-3276 %I IOP Publishing %G en %U http://hdl.handle.net/1963/6520 %1 6471 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Davide Guzzetti (guzzetti@sissa.it) on 2013-03-12T10:28:08Z No. of bitstreams: 1 1108.3401v3.pdf: 449170 bytes, checksum: f6436fe13133f97b3b49bb7d11e23004 (MD5) %R 10.1088/0951-7715/25/12/3235 %0 Journal Article %J J.Phys.A: Math.Theor. 44 (2011) 215203 %D 2011 %T An asymptotic reduction of a Painlevé VI equation to a Painlevé III %A Davide Guzzetti %X 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. %B J.Phys.A: Math.Theor. 44 (2011) 215203 %I IOP Publishing %G en %U http://hdl.handle.net/1963/5124 %1 4940 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-11-28T15:06:23Z\\nNo. of bitstreams: 1\\n1101.4705v1.pdf: 150593 bytes, checksum: 32af4569fb34ae6257486f096be0142b (MD5) %R 10.1088/1751-8113/44/21/215203 %0 Journal Article %J Proc. Amer. Math. Soc. 139 (2011), 1023-1032 %D 2011 %T Axial symmetry of some steady state solutions to nonlinear Schrödinger equations %A Changfeng Gui %A Andrea Malchiodi %A Haoyuan Xu %A Paul Yang %K Nonlinear Schrödinger equation %X 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. %B Proc. Amer. Math. Soc. 139 (2011), 1023-1032 %I American Mathematical Society %G en_US %U http://hdl.handle.net/1963/4100 %1 304 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-11-10T10:42:02Z\\r\\nNo. of bitstreams: 1\\r\\nGui_Malchiodi_75M.pdf: 196044 bytes, checksum: ed4d2f1be79209d4b3e7d428564d043a (MD5) %R 10.1090/S0002-9939-2010-10638-X %0 Journal Article %J Journal of Differential Equations %D 2011 %T Double resonance with Landesman–Lazer conditions for planar systems of ordinary differential equations %A Alessandro Fonda %A Maurizio Garrione %K Double resonance %K Landesman–Lazer conditions %K Nonlinear planar systems %XWe 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.

%B Journal of Differential Equations %V 250 %P 1052 - 1082 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022039610002901 %R https://doi.org/10.1016/j.jde.2010.08.006 %0 Journal Article %J Communications in Partial Differential Equations 36 (2011) 777-796 %D 2011 %T An Estimate on the Flow Generated by Monotone Operators %A Stefano Bianchini %A Matteo Gloyer %B Communications in Partial Differential Equations 36 (2011) 777-796 %I Taylor & Francis %G en_US %U http://hdl.handle.net/1963/3646 %1 658 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-06-10T13:06:54Z\\r\\nNo. of bitstreams: 1\\r\\n29_2009M.pdf: 209332 bytes, checksum: b30a32046e7a3c3c30436e84c03dc6d3 (MD5) %R 10.1080/03605302.2010.534224 %0 Journal Article %J Proceedings of the Steklov Institute of mathematics. vol. 273 (2011), page: 5-27 ; ISSN: 0081-5438 %D 2011 %T The geometry of Maximum Principle %A Andrei A. Agrachev %A Revaz Gamkrelidze %X An invariant formulation of the maximum principle in optimal control is presented, and some second-order invariants are discussed. %B Proceedings of the Steklov Institute of mathematics. vol. 273 (2011), page: 5-27 ; ISSN: 0081-5438 %G en %U http://hdl.handle.net/1963/6456 %1 6401 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-02-05T14:28:16Z\\nNo. of bitstreams: 0 %0 Journal Article %J Sports Engineering %D 2011 %T Multi-physics modelling and sensitivity analysis of olympic rowing boat dynamics %A Andrea Mola %A Mehdi Ghommem %A Muhammad R. Hajj %B Sports Engineering %I Springer Nature %V 14 %P 85–94 %8 nov %G eng %U https://doi.org/10.1007/s12283-011-0075-2 %R 10.1007/s12283-011-0075-2 %0 Journal Article %J Advanced Nonlinear Studies %D 2011 %T Nonlinear resonance: a comparison between Landesman-Lazer and Ahmad-Lazer-Paul conditions %A Alessandro Fonda %A Maurizio Garrione %XWe 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.

%B Advanced Nonlinear Studies %I Advanced Nonlinear Studies, Inc. %V 11 %P 391–404 %G eng %R 10.1515/ans-2011-0209 %0 Journal Article %J SIAM J. Appl. Math. 71 (2011) 983-1008 %D 2011 %T Numerical Study of breakup in generalized Korteweg-de Vries and Kawahara equations %A Boris Dubrovin %A Tamara Grava %A Christian Klein %X 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. %B SIAM J. Appl. Math. 71 (2011) 983-1008 %I SIAM %G en %U http://hdl.handle.net/1963/4951 %1 4732 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-27T12:18:45Z\\nNo. of bitstreams: 1\\n1101.0268v1.pdf: 522533 bytes, checksum: d9e2df220724f918ec3b888cef3593d4 (MD5) %R 10.1137/100819783 %0 Report %D 2011 %T Q-factorial Laurent rings %A Ugo Bruzzo %A Antonella Grassi %X 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. %I SISSA %G en %U http://hdl.handle.net/1963/4183 %1 3907 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-22T10:50:24Z\\nNo. of bitstreams: 1\\n1108.4116v1.pdf: 105862 bytes, checksum: e65647872af8c9b70f2fe8466f37669a (MD5) %0 Journal Article %J Le Matematiche %D 2011 %T Resonance and Landesman-Lazer conditions for first order systems in R^2 %A Maurizio Garrione %XThe 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].

%B Le Matematiche %V 66 %P 153–160 %G eng %0 Journal Article %J Nonlinear Analysis: Theory, Methods & Applications %D 2011 %T Resonance and rotation numbers for planar Hamiltonian systems: Multiplicity results via the Poincaré–Birkhoff theorem %A Alberto Boscaggin %A Maurizio Garrione %K Multiple periodic solutions %K Poincaré–Birkhoff theorem %K Resonance %K Rotation number %XIn 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.

%B Nonlinear Analysis: Theory, Methods & Applications %V 74 %P 4166 - 4185 %G eng %U http://www.sciencedirect.com/science/article/pii/S0362546X11001817 %R https://doi.org/10.1016/j.na.2011.03.051 %0 Journal Article %J Advances in Mathematics 226 (2011) 3655-3676 %D 2011 %T Semistable and numerically effective principal (Higgs) bundles %A Ugo Bruzzo %A Beatriz Grana-Otero %X 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. %B Advances in Mathematics 226 (2011) 3655-3676 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3638 %1 666 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-05-18T12:30:35Z\\r\\nNo. of bitstreams: 1\\r\\nBruzzo_Otero.pdf: 270209 bytes, checksum: 843961bd72149ca85c9b100395b70ed1 (MD5) %R 10.1016/j.aim.2010.10.026 %0 Book Section %B 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 %D 2011 %T Solving PVI by Isomonodromy Deformations %A Davide Guzzetti %K Painlevé Equations %X 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. %B 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 %I SISSA %@ 9783110275582 %G en %U http://hdl.handle.net/1963/6522 %1 6472 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Davide Guzzetti (guzzetti@sissa.it) on 2013-03-12T10:34:39Z\nNo. of bitstreams: 1\n17-StPeterburg12.pdf: 53422 bytes, checksum: a79d3d4bf7aa7e55c929d66671e31dfe (MD5) %0 Journal Article %J Journal of Dynamical and Control Systems %D 2011 %T The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry %A Bernard Bonnard %A Grégoire Charlot %A Roberta Ghezzi %A Gabriel Janin %XWe 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.

%B Journal of Dynamical and Control Systems %I Springer %V 17 %P 141-161 %G en %U http://hdl.handle.net/1963/4914 %1 4692 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-25T09:38:15Z\\nNo. of bitstreams: 1\\n1009.2612v1.pdf: 263401 bytes, checksum: 0ddf4bcfd9663ee3c0da870233d119bb (MD5) %R 10.1007/s10883-011-9113-4 %0 Thesis %D 2010 %T Almost-Riemannian Geometry from a Control Theoretical Viewpoint %A Roberta Ghezzi %I SISSA %G en %U http://hdl.handle.net/1963/4705 %1 4482 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Davide Barilari (barilari@sissa.it) on 2011-10-13T08:13:37Z\\r\\nNo. of bitstreams: 1\\r\\nghezzi-PhD-thesis.pdf: 870834 bytes, checksum: 868d097fff7d3a6646b2bacc98dfeb4b (MD5) %0 Journal Article %J J. Approx. Theory %D 2010 %T Cauchy biorthogonal polynomials %A Marco Bertola %A Gekhtman, M. %A Szmigielski, J. %B J. Approx. Theory %V 162 %P 832–867 %G eng %U http://0-dx.doi.org.mercury.concordia.ca/10.1016/j.jat.2009.09.008 %R 10.1016/j.jat.2009.09.008 %0 Journal Article %J J. Geom. Phys. 60 (2010) 417-429 %D 2010 %T Chern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality %A Andrea Brini %A Luca Griguolo %A Domenico Seminara %A Alessandro Tanzini %X 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. %B J. Geom. Phys. 60 (2010) 417-429 %G en_US %U http://hdl.handle.net/1963/2938 %1 1762 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-12T16:01:18Z\\nNo. of bitstreams: 1\\n0809.1610v1.pdf: 287875 bytes, checksum: feadff501b37135585a6f62946b628de (MD5) %R 10.1016/j.geomphys.2009.11.006 %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 37-56 %D 2010 %T Concentration of solutions for some singularly perturbed mixed problems: Asymptotics of minimal energy solutions %A Jesus Garcia Azorero %A Andrea Malchiodi %A Luigi Montoro %A Ireneo Peral %X 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. %B Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 37-56 %G en_US %U http://hdl.handle.net/1963/3409 %1 926 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-08T11:10:32Z\\nNo. of bitstreams: 1\\nGMMPII.pdf: 324708 bytes, checksum: 4829f5449fac58672d6e7a8e42efb3c4 (MD5) %R 10.1016/j.anihpc.2009.06.005 %0 Journal Article %J Arch. Ration. Mech. Anal. 196 (2010) 907-950 %D 2010 %T Concentration of solutions for some singularly perturbed mixed problems. Part I: existence results %A Jesus Garcia Azorero %A Andrea Malchiodi %A Luigi Montoro %A Ireneo Peral %X 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. %B Arch. Ration. Mech. Anal. 196 (2010) 907-950 %G en_US %U http://hdl.handle.net/1963/3406 %1 927 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-08T11:03:36Z\\nNo. of bitstreams: 1\\nGMMPI.pdf: 466523 bytes, checksum: 004f66da4f9e531a535780337f19e185 (MD5) %R 10.1007/s00205-009-0259-0 %0 Journal Article %J Math. Z. 265 (2010) 889-923 %D 2010 %T On the Euler-Lagrange equation for a variational problem : the general case II %A Stefano Bianchini %A Matteo Gloyer %B Math. Z. 265 (2010) 889-923 %G en_US %U http://hdl.handle.net/1963/2551 %1 1568 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-01-14T09:52:10Z\\nNo. of bitstreams: 1\\ngeneralcase.final.pdf: 315418 bytes, checksum: dee89d593fb956f4a377db9221520eb6 (MD5) %R 10.1007/s00209-009-0547-2 %0 Journal Article %J The European journal of neuroscience. 2010 Oct; 32(8):1364-79 %D 2010 %T Gene expression analysis of the emergence of epileptiform activity after focal injection of kainic acid into mouse hippocampus. %A Dario Motti %A Caroline Le Duigou %A Nicole Chemaly %A Lucia Wittner %A Dejan Lazarevic %A Helena Krmac %A Troels Torben Marstrand %A Eivind Valen %A Remo Sanges %A Elia Stupka %A Albin Sandelin %A Enrico Cherubini %A Stefano Gustincich %A Richard Miles %XWe 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.

%B The European journal of neuroscience. 2010 Oct; 32(8):1364-79 %I Wiley %G en %U http://hdl.handle.net/1963/4480 %1 4244 %2 Neuroscience %3 Neurobiology %4 -1 %$ Approved for entry into archive by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-05T07:58:51Z (GMT) No. of bitstreams: 0 %R 10.1111/j.1460-9568.2010.07403.x %0 Journal Article %J Phys. Rev. A 81 (2010) 062335 %D 2010 %T Homogeneous binary trees as ground states of quantum critical Hamiltonians %A Pietro Silvi %A Vittorio Giovannetti %A Simone Montangero %A Matteo Rizzi %A J. Ignacio Cirac %A Rosario Fazio %XMany-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.

%B Phys. Rev. A 81 (2010) 062335 %I American Physical Society %G en_US %U http://hdl.handle.net/1963/3909 %1 800 %2 Physics %3 Condensed Matter Theory %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-07-27T07:32:21Z\\nNo. of bitstreams: 1\\n0912.0466v1.pdf: 336415 bytes, checksum: 7220d67cfb58f794aa50037140db23e6 (MD5) %R 10.1103/PhysRevA.81.062335 %0 Journal Article %J New J. Phys. 12 (2010) 075018 %D 2010 %T Homogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems %A Matteo Rizzi %A Simone Montangero %A Pietro Silvi %A Vittorio Giovannetti %A Rosario Fazio %XIn 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.

%B New J. Phys. 12 (2010) 075018 %I IOP Publishing %G en_US %U http://hdl.handle.net/1963/4067 %1 335 %2 Physics %3 Condensed Matter Theory %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-09-16T09:50:44Z\\nNo. of bitstreams: 1\\n10081611392421027.pdf: 1233170 bytes, checksum: 39da921aa8c098e7c8d6451b0ce08c15 (MD5) %R 10.1088/1367-2630/12/7/075018 %0 Journal Article %J Phys. Rev. D 81 (2010) 125024 %D 2010 %T Lorentz Covariant k-Minkowski Spacetime %A Ludwik Dabrowski %A Michal Godlinski %A Gherardo Piacitelli %X 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. %B Phys. Rev. D 81 (2010) 125024 %G en_US %U http://hdl.handle.net/1963/3829 %1 498 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-01-26T15:05:30Z\\nNo. of bitstreams: 1\\n0912.5451v2.pdf: 189407 bytes, checksum: e0a9a6af9e79410c0a199250cb168d04 (MD5) %R 10.1103/PhysRevD.81.125024 %0 Journal Article %J arXiv preprint arXiv:1008.5036 %D 2010 %T A normal form for generic 2-dimensional almost-Riemannian structures at a tangency point %A Ugo Boscain %A Grégoire Charlot %A Roberta Ghezzi %B arXiv preprint arXiv:1008.5036 %G eng %0 Report %D 2010 %T Numerical Solution of the Small Dispersion Limit of the Camassa-Holm and Whitham Equations and Multiscale Expansions %A Simonetta Abenda %A Tamara Grava %A Christian Klein %X 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.... %G en_US %U http://hdl.handle.net/1963/3840 %1 487 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-02-05T10:20:56Z\\nNo. of bitstreams: 1\\n0909.1020v1.pdf: 613403 bytes, checksum: be892250a6d664faff51d74b323fea67 (MD5) %0 Journal Article %J Comm. Pure Appl. Math. 63 (2010) 203-232 %D 2010 %T Painlevé II asymptotics near the leading edge of the oscillatory zone for the Korteweg-de Vries equation in the small-dispersion limit %A Tom Claeys %A Tamara Grava %X 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. %B Comm. Pure Appl. Math. 63 (2010) 203-232 %I Wiley %G en_US %U http://hdl.handle.net/1963/3799 %1 527 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-11-26T16:48:15Z\\nNo. of bitstreams: 1\\n0812.4142v1.pdf: 343118 bytes, checksum: 4bf2fa3751076c18466f29e1163acc09 (MD5) %R 10.1002/cpa.20277 %0 Report %D 2010 %T Picard group of hypersurfaces in toric varieties %A Ugo Bruzzo %A Antonella Grassi %X 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. %G en_US %U http://hdl.handle.net/1963/4103 %1 301 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-11-17T08:32:53Z\\nNo. of bitstreams: 1\\nBruzzo_78FM.pdf: 196280 bytes, checksum: 4025c3d0687d1cf714b24bdff1e33568 (MD5) %0 Journal Article %J Geom. Topol. 14 (2010) 83-115 %D 2010 %T Riemann-Roch theorems and elliptic genus for virtually smooth schemes %A Barbara Fantechi %A Lothar Göttsche %X 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. %B Geom. Topol. 14 (2010) 83-115 %I Mathematical Sciences Publishers %G en_US %U http://hdl.handle.net/1963/3888 %1 821 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-07-23T07:35:11Z\\nNo. of bitstreams: 1\\n0706.0988v1.pdf: 396801 bytes, checksum: 640403457a0a02c4166b8c684d8af419 (MD5) %R 10.2140/gt.2010.14.83 %0 Journal Article %J SIAM J. Math. Anal. 42 (2010) 2132-2154 %D 2010 %T Solitonic asymptotics for the Korteweg-de Vries equation in the small dispersion limit %A Tamara Grava %A Tom Claeys %X 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. %B SIAM J. Math. Anal. 42 (2010) 2132-2154 %G en_US %U http://hdl.handle.net/1963/3839 %1 488 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-02-05T10:12:44Z\\nNo. of bitstreams: 1\\n0911.5686v1.pdf: 311708 bytes, checksum: bfe41688febbfb066ebaae202e1e93b6 (MD5) %R 10.1137/090779103 %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire %D 2010 %T Two-dimensional almost-Riemannian structures with tangency points %A Andrei A. Agrachev %A Ugo Boscain %A Grégoire Charlot %A Roberta Ghezzi %A Mario Sigalotti %XTwo-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.

%B Ann. Inst. H. Poincare Anal. Non Lineaire %I Elsevier %V 27 %P 793-807 %G en_US %U http://hdl.handle.net/1963/3870 %1 839 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-05-31T14:15:39Z\\nNo. of bitstreams: 1\\n0908.2564v1.pdf: 302590 bytes, checksum: 15369151ee10bb886dc6678350dee7f5 (MD5) %R 10.1016/j.anihpc.2009.11.011 %0 Journal Article %J Comm. Math. Phys. %D 2009 %T The Cauchy two–matrix model %A Marco Bertola %A M Gekhtman %A J Szmigielski %B Comm. Math. Phys. %V 287 %P 983–1014 %G eng %0 Journal Article %J J. Phys. A %D 2009 %T Cubic string boundary value problems and Cauchy biorthogonal polynomials %A Marco Bertola %A Gekhtman, M. %A Szmigielski, J. %B J. Phys. A %V 42 %P 454006, 13 %G eng %U http://0-dx.doi.org.mercury.concordia.ca/10.1088/1751-8113/42/45/454006 %R 10.1088/1751-8113/42/45/454006 %0 Journal Article %J Commun. Contemp. Math. 11 (2009) 993-1007 %D 2009 %T Hardy-Sobolev-Maz\\\'ja inequalities: symmetry and breaking symmetry of extremal functions %A Marita Gazzini %A Roberta Musina %B Commun. Contemp. Math. 11 (2009) 993-1007 %G en_US %U http://hdl.handle.net/1963/2569 %1 1551 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-01-21T11:13:29Z\\nNo. of bitstreams: 1\\nGaMu2.pdf: 291392 bytes, checksum: 026cb4fccae5ac75b171e8a2923b84ca (MD5) %R 10.1142/S0219199709003636 %0 Journal Article %J Physica D 238 (2009) 55-66 %D 2009 %T Initial value problem of the Whitham equations for the Camassa-Holm equation %A Tamara Grava %A Virgil U. Pierce %A Fei-Ran Tian %X 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. %B Physica D 238 (2009) 55-66 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3429 %1 906 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-13T13:01:16Z\\nNo. of bitstreams: 1\\n0805.2558v1.pdf: 498872 bytes, checksum: 4d721f99d6ae9840be2332f3cc6a4118 (MD5) %R 10.1016/j.physd.2008.08.016 %0 Journal Article %J J. Funct. Anal. 256 (2009) 2621-2655 %D 2009 %T The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups %A Andrei A. Agrachev %A Ugo Boscain %A Jean-Paul Gauthier %A Francesco Rossi %X 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. %B J. Funct. Anal. 256 (2009) 2621-2655 %G en_US %U http://hdl.handle.net/1963/2669 %1 1428 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-06-11T11:38:01Z\\nNo. of bitstreams: 1\\n0806.0734v1.pdf: 494960 bytes, checksum: 640ace795ac663f09426814440b15432 (MD5) %R 10.1016/j.jfa.2009.01.006 %0 Journal Article %J J. Math. Anal. Appl. 352 (2009) 99-111 %D 2009 %T On a Sobolev type inequality related to the weighted p-Laplace operator %A Marita Gazzini %A Roberta Musina %B J. Math. Anal. Appl. 352 (2009) 99-111 %G en_US %U http://hdl.handle.net/1963/2613 %1 1510 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-04-03T10:13:10Z\\nNo. of bitstreams: 1\\nGaMu3.pdf: 298467 bytes, checksum: 6de8ed2f5202430d4c5b002c5f613347 (MD5) %R 10.1016/j.jmaa.2008.06.021 %0 Journal Article %J J. Nonlinear Sci. 19 (2009) 57-94 %D 2009 %T On universality of critical behaviour in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the \\\\it tritronquée solution to the Painlevé-I equation %A Boris Dubrovin %A Tamara Grava %A Christian Klein %X 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. %B J. Nonlinear Sci. 19 (2009) 57-94 %G en_US %U http://hdl.handle.net/1963/2525 %1 1593 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-11T13:11:26Z\\nNo. of bitstreams: 1\\n0704.0501v3.pdf: 568190 bytes, checksum: cf8471fc01eea53ce252339eda81b3cd (MD5) %R 10.1007/s00332-008-9025-y %0 Journal Article %J Comm. Math. Phys. 286 (2009) 979-1009 %D 2009 %T Universality of the break-up profile for the KdV equation in the small dispersion limit using the Riemann-Hilbert approach %A Tamara Grava %A Tom Claeys %X 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. %B Comm. Math. Phys. 286 (2009) 979-1009 %G en_US %U http://hdl.handle.net/1963/2636 %1 1487 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-04-22T10:17:48Z\\nNo. of bitstreams: 1\\n0801.2326v1.pdf: 375000 bytes, checksum: b00b6e0d823d47a002430b4fdecf8c7c (MD5) %R 10.1007/s00220-008-0680-5 %0 Journal Article %J Boll. Unione Mat. Ital. (9) 2 (2009) 371-390 %D 2009 %T A variational model for quasistatic crack growth in nonlinear elasticity: some qualitative properties of the solutions %A Gianni Dal Maso %A Alessandro Giacomini %A Marcello Ponsiglione %B Boll. Unione Mat. Ital. (9) 2 (2009) 371-390 %G en_US %U http://hdl.handle.net/1963/2675 %1 1425 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-06-26T15:44:13Z\\nNo. of bitstreams: 1\\nDM-Gia-Pon.pdf: 242504 bytes, checksum: 3b08c25331a3436a5766d41df8e937f7 (MD5) %0 Journal Article %J Calc. Var. Partial Differential Equations 31 (2008) 137-145 %D 2008 %T Gradient bounds for minimizers of free discontinuity problems related to cohesive zone models in fracture mechanics %A Gianni Dal Maso %A Adriana Garroni %X 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. %B Calc. Var. Partial Differential Equations 31 (2008) 137-145 %G en_US %U http://hdl.handle.net/1963/1723 %1 2428 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-01-26T12:52:13Z\\nNo. of bitstreams: 1\\nmath.AP0507088.pdf: 132125 bytes, checksum: 444c743b7852d0f6e97bb318f49b4467 (MD5) %R 10.1007/s00526-006-0084-3 %0 Journal Article %J J.Phys.A: Math.Theor. 41,(2008), 205201-205247 %D 2008 %T On the Logarithmic Asymptotics of the Sixth Painleve\' Equation (Summer 2007) %A Davide Guzzetti %X 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. %B J.Phys.A: Math.Theor. 41,(2008), 205201-205247 %I SISSA %G en %U http://hdl.handle.net/1963/6521 %1 6473 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Davide Guzzetti (guzzetti@sissa.it) on 2013-03-12T10:36:09Z\nNo. of bitstreams: 1\n0801.1157v4.pdf: 449572 bytes, checksum: 6c4042b70a0d361af61282bee96d84db (MD5) %R 10.1088/1751-8113/41/20/205201 %0 Journal Article %J Proc. R. Soc. A 464 (2008) 733-757 %D 2008 %T Numerical study of a multiscale expansion of the Korteweg-de Vries equation and Painlevé-II equation %A Tamara Grava %A Christian Klein %X 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 $\\\\epsilon^{2/3}$. %B Proc. R. Soc. A 464 (2008) 733-757 %G en_US %U http://hdl.handle.net/1963/2592 %1 1530 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-02-25T15:08:44Z\\nNo. of bitstreams: 1\\n0708.0638v3.pdf: 453744 bytes, checksum: 05291095860df236125f0d9f8c676fbb (MD5) %R 10.1098/rspa.2007.0249 %0 Book Section %B 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 %D 2008 %T Transport Rays and Applications to Hamilton–Jacobi Equations %A Stefano Bianchini %A Matteo Gloyer %X 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). %B 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 %I Springer %@ 978-3-642-21718-0 %G en %U http://hdl.handle.net/1963/5463 %1 5298 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-02-14T08:18:09Z\\nNo. of bitstreams: 1\\n20090907.pdf: 179195 bytes, checksum: bcdd57e58d4e0e0c4843018797e609bd (MD5) %R 10.1007/978-3-642-21861-3_1 %0 Journal Article %J Ann. Henri Poincar´e 8 (2007), 301–336 %D 2007 %T The Asymptotic Behaviour of the Fourier Transforms of Orthogonal Polynomials II: L.I.F.S. Measures and Quantum Mechanics %A Davide Guzzetti %A Giorgio Mantica %X 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 %B Ann. Henri Poincar´e 8 (2007), 301–336 %I 2007 Birkh¨auser Verlag Basel/Switzerland %G en %1 6480 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Davide Guzzetti (guzzetti@sissa.it) on 2013-03-13T10:11:23Z\nNo. of bitstreams: 1\n11-GuzMantica07.pdf: 924495 bytes, checksum: 5897cbac3fb5b378b02bf5cdae1273ea (MD5) %R 10.1007/s00023-006-0309-1 %0 Journal Article %J Constr. Approx. %D 2007 %T Biorthogonal Laurent polynomials, Töplitz determinants, minimal Toda orbits and isomonodromic tau functions %A Marco Bertola %A Gekhtman, M. %B Constr. Approx. %V 26 %P 383–430 %G eng %0 Report %D 2007 %T Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory %A Luca Griguolo %A Domenico Seminara %A Richard J. Szabo %A Alessandro Tanzini %X 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. %B Nucl. Phys. B 772 (2007) 1-24 %G en_US %U http://hdl.handle.net/1963/1888 %1 2347 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-11-09T10:57:35Z\\nNo. of bitstreams: 1\\nhep-th0610155.pdf: 340757 bytes, checksum: fb3e5bfec5e2a4c15d97a9ca6f2e8a0a (MD5) %R 10.1016/j.nuclphysb.2007.02.030 %0 Journal Article %J Int. Math. Res. Not. IMRN %D 2007 %T Effective inverse spectral problem for rational Lax matrices and applications %A Marco Bertola %A Gekhtman, M. %B Int. Math. Res. Not. IMRN %P Art. ID rnm103, 39 %G eng %0 Report %D 2007 %T On the Maz\\\'ya inequalities: existence and multiplicity results for an elliptic problem involving cylindrical weights %A Marita Gazzini %A Roberta Musina %G en_US %U http://hdl.handle.net/1963/2522 %1 1596 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-11T12:04:02Z\\nNo. of bitstreams: 1\\nGazzini.pdf: 266073 bytes, checksum: eb239636fd06715d381d38055d96481e (MD5) %0 Journal Article %J J. Reine Angew. Math. 612 (2007) 59-79 %D 2007 %T Metrics on semistable and numerically effective Higgs bundles %A Ugo Bruzzo %A Beatriz Grana-Otero %X 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. %B J. Reine Angew. Math. 612 (2007) 59-79 %G en_US %U http://hdl.handle.net/1963/1840 %1 2376 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-06-19T08:20:16Z\\nNo. of bitstreams: 1\\nmath.DG-0605659.pdf: 242976 bytes, checksum: b5e79cfd73f6c6533a0ae12bad3e3c90 (MD5) %R 10.1515/CRELLE.2007.084 %0 Report %D 2007 %T A new model for contact angle hysteresis %A Antonio DeSimone %A Natalie Gruenewald %A Felix Otto %X 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. %B Netw. Heterog. Media 2 (2007) 211-225 %G en_US %U http://hdl.handle.net/1963/1848 %1 2369 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-07-26T09:50:36Z\\nNo. of bitstreams: 1\\n37-2006M.pdf: 313357 bytes, checksum: ac507409dc660fba3ec468e50c4fe9b1 (MD5) %0 Report %D 2007 %T Numerical solution of the small dispersion limit of Korteweg de Vries and Whitham equations %A Tamara Grava %A Christian Klein %X 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. %B Comm. Pure Appl. Math. 60 (2007) 1623-1664 %G en_US %U http://hdl.handle.net/1963/1788 %1 2756 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-30T13:45:26Z\\nNo. of bitstreams: 1\\n91FM-2005.pdf: 905542 bytes, checksum: 8505fe7c8ac2e5f1da7248d62ae542b2 (MD5) %R 10.1002/cpa.20183 %0 Report %D 2007 %T Numerical study of a multiscale expansion of KdV and Camassa-Holm equation %A Tamara Grava %A Christian Klein %X 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 %G en_US %U http://hdl.handle.net/1963/2527 %1 1591 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-12T12:39:23Z\\nNo. of bitstreams: 1\\n0702038v1.pdf: 367188 bytes, checksum: f88c96f6ff42a7c5378de0118866d4bb (MD5) %0 Report %D 2007 %T Numerically flat Higgs vector bundles %A Ugo Bruzzo %A Beatriz Grana-Otero %X 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. %B Commun. Contemp. Math. 9 (2007) 437-446 %G en_US %U http://hdl.handle.net/1963/1757 %1 2787 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-21T15:59:56Z\\nNo. of bitstreams: 1\\n39_2005_fm.pdf: 192887 bytes, checksum: 1d32aff78ef27b80046dfc391135d55a (MD5) %R 10.1142/S0219199707002526 %0 Journal Article %J J. Phys. A 40 (2007) 10769-10790 %D 2007 %T Reciprocal transformations and flat metrics on Hurwitz spaces %A Simonetta Abenda %A Tamara Grava %X 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. %B J. Phys. A 40 (2007) 10769-10790 %G en_US %U http://hdl.handle.net/1963/2210 %1 2034 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-12T09:26:01Z\\nNo. of bitstreams: 1\\n0704.1779v2.pdf: 286756 bytes, checksum: 3d2d03a6f16be9191b242adb35638601 (MD5) %R 10.1088/1751-8113/40/35/004 %0 Report %D 2007 %T Semistable principal Higgs bundles %A Ugo Bruzzo %A Beatriz Grana-Otero %G en_US %U http://hdl.handle.net/1963/2533 %1 1585 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-17T09:52:22Z\\nNo. of bitstreams: 1\\nPrincHiggs-2.pdf: 197562 bytes, checksum: 44797463786b3c14408f7d1898531202 (MD5) %0 Journal Article %J Molecular pharmacology. 2006 Jul; 70(1):373-82 %D 2006 %T Experimental and modeling studies of desensitization of P2X3 receptors. %A Elena Sokolova %A Andrei Skorinkin %A Igor Moiseev %A Andrei A. Agrachev %A Andrea Nistri %A Rashid Giniatullin %X 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. %B Molecular pharmacology. 2006 Jul; 70(1):373-82 %I the American Society for Pharmacology and Experimental Therapeutics %G en %U http://hdl.handle.net/1963/4974 %1 4799 %2 Neuroscience %3 Neurobiology %4 -1 %$ Submitted by Alireza Alemi-neissi (alemi@sissa.it) on 2011-10-30T18:23:32Z\\nNo. of bitstreams: 0 %R 10.1124/mol.106.023564 %0 Report %D 2006 %T Large Parameter Behavior of Equilibrium Measures %A Tamara Grava %A Fei-Ran Tian %X 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). %B Commun. Math. Sci. 4 (2006) 551-573 %G en_US %U http://hdl.handle.net/1963/1789 %1 2755 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-30T13:50:45Z\\nNo. of bitstreams: 1\\n92FM-2005.pdf: 291341 bytes, checksum: 132e37e5c4fc64315d52903eed85753f (MD5) %0 Journal Article %J Journal of Physics A: Mathematical and General, Volume 39, Issue 39, 29 September 2006, Article numberS02, Pages 11973-12031 %D 2006 %T Matching Procedure for the Sixth Painlevé Equation (May 2006) %A Davide Guzzetti %X 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. %B Journal of Physics A: Mathematical and General, Volume 39, Issue 39, 29 September 2006, Article numberS02, Pages 11973-12031 %I SISSA %G en %U http://hdl.handle.net/1963/6524 %1 6474 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Davide Guzzetti (guzzetti@sissa.it) on 2013-03-12T10:58:15Z\nNo. of bitstreams: 1\n1010.1952v1.pdf: 554736 bytes, checksum: 574f14d78ead655022ad9c30ebed720f (MD5) %R doi:10.1088/0305-4470/39/39/S02 %0 Journal Article %J Lett. Math. Phys. 76 (2006) 187-214 %D 2006 %T Thomae type formulae for singular Z_N curves %A Victor Z. Enolski %A Tamara Grava %X 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. %B Lett. Math. Phys. 76 (2006) 187-214 %G en_US %U http://hdl.handle.net/1963/2125 %1 2118 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-18T08:04:36Z\\nNo. of bitstreams: 1\\n0602017v1.pdf: 315977 bytes, checksum: 2f5c46aa04d9dd6c02200ff627d69a00 (MD5) %R 10.1007/s11005-006-0073-7 %0 Journal Article %J SIAM J. Control Optim. 43 (2005) 1867-1887 %D 2005 %T Hybrid necessary principle %A Mauro Garavello %A Benedetto Piccoli %X 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. %B SIAM J. Control Optim. 43 (2005) 1867-1887 %I SIAM %G en %U http://hdl.handle.net/1963/1641 %1 2477 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:44Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002 %R 10.1137/S0363012903416219 %0 Journal Article %J Ann. Inst. Fourier (Grenoble) 55 (2005) 1803-1834 %D 2005 %T Modulation of the Camassa-Holm equation and reciprocal transformations %A Simonetta Abenda %A Tamara Grava %X 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. %B Ann. Inst. Fourier (Grenoble) 55 (2005) 1803-1834 %G en_US %U http://hdl.handle.net/1963/2305 %1 1711 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-29T10:50:29Z\\nNo. of bitstreams: 1\\n0506042v2.pdf: 305542 bytes, checksum: 045f6c919e0338003f17f6827528ad0d (MD5) %0 Journal Article %J SIAM J. Math. Anal. 36 (2005) 1862-1886 %D 2005 %T Traffic flow on a road network %A Giuseppe Maria Coclite %A Benedetto Piccoli %A Mauro Garavello %X 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. %B SIAM J. Math. Anal. 36 (2005) 1862-1886 %I SISSA Library %G en %U http://hdl.handle.net/1963/1584 %1 2534 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:54Z (GMT). No. of bitstreams: 1\\nmath.AP0202146.pdf: 256961 bytes, checksum: 51f64ff00e916dd87d3dd6df41903d23 (MD5)\\n Previous issue date: 2002 %R 10.1137/S0036141004402683 %0 Conference Proceedings %B 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 %D 2004 %T The elliptic representation of the sixth Painlevé equation. %A Davide Guzzetti %K Painlevé equation %X 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). %B 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 %I Societe Matematique de France %@ 978-2-85629-229-7 %G en %U http://hdl.handle.net/1963/6529 %1 6482 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Davide Guzzetti (guzzetti@sissa.it) on 2013-03-13T10:22:07Z\nNo. of bitstreams: 1\n10-SemCongSMF06.pdf: 299143 bytes, checksum: dc2b0ca561808604467132b9b5942fe3 (MD5) %0 Journal Article %J Int. Math. Res. Not. 2004, no. 32, 1619-1683 %D 2004 %T Singular Z_N curves, Riemann-Hilbert problem and modular solutions of the Schlesinger equation %A Victor Z. Enolski %A Tamara Grava %X 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. %B Int. Math. Res. Not. 2004, no. 32, 1619-1683 %G en_US %U http://hdl.handle.net/1963/2540 %1 1579 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-21T10:08:03Z\\nNo. of bitstreams: 1\\n0306050v2.pdf: 587970 bytes, checksum: 3d350364af41be2317176944f1d85868 (MD5) %R 10.1155/S1073792804132625 %0 Journal Article %J Electron. J. Differential Equations (2004) 94 %D 2004 %T Solitary waves for Maxwell Schrodinger equations %A Giuseppe Maria Coclite %A Vladimir Georgiev %X 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. %B Electron. J. Differential Equations (2004) 94 %I SISSA Library %G en %U http://hdl.handle.net/1963/1582 %1 2536 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:52Z (GMT). No. of bitstreams: 1\\nmath.AP0303142.pdf: 326987 bytes, checksum: 37c172f10800ae7a41e5398f6a0a0a0e (MD5)\\n Previous issue date: 2002 %0 Journal Article %J Int. J. Control 76 (2003) 1272-1284 %D 2003 %T Hybrid optimal control: case study of a car with gears %A Ciro D'Apice %A Mauro Garavello %A Rosanna Manzo %A Benedetto Piccoli %X 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. %B Int. J. Control 76 (2003) 1272-1284 %I Taylor and Francis %G en_US %U http://hdl.handle.net/1963/3022 %1 1311 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-02T15:37:32Z\\nNo. of bitstreams: 1\\ndgb.pdf: 374355 bytes, checksum: 5c6cc02be9e07396a29d5c6ff22db238 (MD5) %R 10.1080/0020717031000147520 %0 Journal Article %J Communications on Pure and Applied Mathematics, Volume 55, Issue 10, October 2002, Pages 1280-1363 %D 2002 %T The Elliptic Representation of the General Painlevé 6 Equation %A Davide Guzzetti %X We study the analytic properties and the critical behavior of the elliptic\r\nrepresentation of solutions of the Painlev\\\'e 6 equation. We solve the\r\nconnection problem for elliptic representation in the generic case and in a\r\nnon-generic case equivalent to WDVV equations of associativity. %B Communications on Pure and Applied Mathematics, Volume 55, Issue 10, October 2002, Pages 1280-1363 %I SISSA %G en %U http://hdl.handle.net/1963/6523 %1 6475 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Davide Guzzetti (guzzetti@sissa.it) on 2013-03-12T10:59:59Z\nNo. of bitstreams: 1\nmath_0108073v2.pdf: 604540 bytes, checksum: 7e39c5af49afe1e1539cb4c3140cca6e (MD5) %R 10.1002/cpa.10045 %0 Conference Proceedings %B Deformation of differential equations and asymptotic analysis / Yoshishige Haraoka. - Kyōto : Kyoto University, Research Institute for Mathematical Sciences, 2002. - RIMS kokyuroku, volume 1296 . - page: 112-123 %D 2002 %T The Elliptic Representation of the Painleve 6 Equation %A Davide Guzzetti %K Painleve equations %X We review our results on the elliptic representation of the sixth Painleve’ equation %B Deformation of differential equations and asymptotic analysis / Yoshishige Haraoka. - Kyōto : Kyoto University, Research Institute for Mathematical Sciences, 2002. - RIMS kokyuroku, volume 1296 . - page: 112-123 %I Kyoto University, Research Institute for Mathematical Sciences %G en %U http://hdl.handle.net/1963/6530 %1 6481 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Davide Guzzetti (guzzetti@sissa.it) on 2013-03-13T10:18:28Z\nNo. of bitstreams: 1\n07-RIMSKokyuroku02.pdf: 1194417 bytes, checksum: 4710ff5d2a123d59ae61aea637048ddc (MD5) %0 Journal Article %J J.Dynam. Control Systems 8 (2002),no.4, 547 %D 2002 %T On the K+P problem for a three-level quantum system: optimality implies resonance %A Ugo Boscain %A Thomas Chambrion %A Jean-Paul Gauthier %B J.Dynam. Control Systems 8 (2002),no.4, 547 %I SISSA Library %G en %U http://hdl.handle.net/1963/1601 %1 2517 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:08Z (GMT). No. of bitstreams: 1\\nmath.OC0204233.pdf: 252630 bytes, checksum: 14283368a7848e46caf6447b4bad85d4 (MD5)\\n Previous issue date: 2002 %R 10.1023/A:1020767419671 %0 Journal Article %J Proc. Steklov Inst. Math. 236 (2002) 395-414 %D 2002 %T The passage from nonconvex discrete systems to variational problems in Sobolev spaces: the one-dimensional case %A Andrea Braides %A Maria Stella Gelli %A Mario Sigalotti %B Proc. Steklov Inst. Math. 236 (2002) 395-414 %I MAIK Nauka/Interperiodica %G en_US %U http://hdl.handle.net/1963/3130 %1 1203 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-16T15:53:06Z\\nNo. of bitstreams: 1\\npassage.pdf: 242138 bytes, checksum: 1874bdb2ad8c185c3fe84d7deb988b5b (MD5) %0 Journal Article %J Mathematical Physics, Analysis and Geometry 4: 293–377, 2001 %D 2001 %T On the Critical Behavior, the Connection Problem and the Elliptic Representation of a Painlevé VI Equation %A Davide Guzzetti %K Painleve Equations, Isomonodromy deformations %X In this paper we find a class of solutions of the sixth Painlevé equation appearing in\r\nthe theory of WDVV equations. This class covers almost all the monodromy data associated to\r\nthe equation, except one point in the space of the data. We describe the critical behavior close to\r\nthe critical points in terms of two parameters and we find the relation among the parameters at\r\nthe different critical points (connection problem). We also study the critical behavior of Painlevé\r\ntranscendents in the elliptic representation. %B Mathematical Physics, Analysis and Geometry 4: 293–377, 2001 %I Kluwer Academic Publishers %G en %1 6477 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Davide Guzzetti (guzzetti@sissa.it) on 2013-03-13T09:51:54Z\nNo. of bitstreams: 1\n05-ElliptMu01.pdf: 612332 bytes, checksum: a0c74f3a94a9fc629c50e8bc47cb1939 (MD5) %R 10.1023/A:1014265919008 %0 Journal Article %J Proc. of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences 457 (2001): p. 2317-2335, OCT. 8, 2001 %D 2001 %T Dieletric breakdown: optimal bounds %A Adriana Garroni %A Vincenzo Nesi %A Marcello Ponsiglione %B Proc. of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences 457 (2001): p. 2317-2335, OCT. 8, 2001 %I SISSA Library %G en %U http://hdl.handle.net/1963/1569 %1 2549 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:17Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 2000 %0 Journal Article %J Proc. Royal Soc. Edinb. Ser. A 131 (2001), no. 3, 567-595 %D 2001 %T Finite Difference Approximation of Free Discontinuity Problems %A Massimo Gobbino %A Maria Giovanna Mora %B Proc. Royal Soc. Edinb. Ser. A 131 (2001), no. 3, 567-595 %I SISSA Library %G en %U http://hdl.handle.net/1963/1228 %1 2715 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:01Z (GMT). No. of bitstreams: 1\\nmath-FA0006059.pdf: 308143 bytes, checksum: 5fa8fcd8261bc58912f44f3981068d08 (MD5)\\n Previous issue date: 1999 %0 Journal Article %J Mathematical Physics, Analysis and Geometry 4: 245–291, 2001 %D 2001 %T Inverse Problem and Monodromy Data for Three-Dimensional Frobenius Manifolds %A Davide Guzzetti %K Frobenius Manifolds, Painleve Equations, Isomonodromy deformations %X We study the inverse problem for semi-simple Frobenius manifolds of dimension 3 and we\r\nexplicitly compute a parametric form of the solutions of theWDVV equations in terms of Painlevé VI\r\ntranscendents. We show that the solutions are labeled by a set of monodromy data. We use our parametric\r\nform to explicitly construct polynomial and algebraic solutions and to derive the generating\r\nfunction of Gromov–Witten invariants of the quantum cohomology of the two-dimensional projective\r\nspace. The procedure is a relevant application of the theory of isomonodromic deformations. %B Mathematical Physics, Analysis and Geometry 4: 245–291, 2001 %I RIMS, Kyoto University %G en %1 6479 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Davide Guzzetti (guzzetti@sissa.it) on 2013-03-13T10:02:25Z\nNo. of bitstreams: 1\n04-InvFrob01.pdf: 305277 bytes, checksum: 9371356f1496f5c30346ccf145b00fb8 (MD5) %R 10.1023/A:1012933622521 %0 Journal Article %J Rend. Mat. Appl. (7) %D 2001 %T Lie triple systems and warped products %A Marco Bertola %A Gouthier, D. %B Rend. Mat. Appl. (7) %V 21 %P 275–293 %G eng %0 Journal Article %J Ann. I. H. Poincare - An., 2001, 18, 359 %D 2001 %T On the subanalyticity of Carnot-Caratheodory distances %A Andrei A. Agrachev %A Jean-Paul Gauthier %B Ann. I. H. Poincare - An., 2001, 18, 359 %I SISSA Library %G en %U http://hdl.handle.net/1963/1483 %1 2680 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:03Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1016/S0294-1449(00)00064-0 %0 Journal Article %J Bol. Soc. Brasil. Mat. (N.S.) %D 2001 %T Warped products with special Riemannian curvature %A Marco Bertola %A Gouthier, Daniele %B Bol. Soc. Brasil. Mat. (N.S.) %V 32 %P 45–62 %G eng %0 Journal Article %J Nucl.Phys. B577 (2000) 547-608 %D 2000 %T 3D superconformal theories from Sasakian seven-manifolds: new nontrivial evidences for AdS_4/CFT_3 %A Davide Fabbri %A Pietro Fré %A Leonardo Gualtieri %A Cesare Reina %A Alessandro Tomasiello %A Alberto Zaffaroni %A Alessandro Zampa %B Nucl.Phys. B577 (2000) 547-608 %I SISSA Library %G en %U http://hdl.handle.net/1963/1327 %1 3128 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:56:21Z (GMT). No. of bitstreams: 1\\nhep-th9907219.pdf: 628836 bytes, checksum: c75d99f0a2296bdcc428232f3907ed15 (MD5)\\n Previous issue date: 1999 %R 10.1016/S0550-3213(00)00098-5 %0 Journal Article %J Nuclear Phys. B %D 2000 %T Decomposing quantum fields on branes %A Marco Bertola %A Bros, Jacques %A Gorini, Vittorio %A Moschella, Ugo %A Schaeffer, Richard %B Nuclear Phys. B %V 581 %P 575–603 %G eng %0 Journal Article %J J. Differential Equations 168 (2000), no. 1, 10--32 %D 2000 %T Elliptic variational problems in $ R\\\\sp N$ with critical growth %A Antonio Ambrosetti %A Jesus Garcia Azorero %A Ireneo Peral %B J. Differential Equations 168 (2000), no. 1, 10--32 %I SISSA Library %G en %U http://hdl.handle.net/1963/1258 %1 3197 %$ Made available in DSpace on 2004-09-01T12:55:25Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %R 10.1006/jdeq.2000.3875 %0 Journal Article %J Rend. Mat. Appl., 2000, 20, 167 %D 2000 %T Existence and multiplicity results for some nonlinear elliptic equations: a survey. %A Antonio Ambrosetti %A Jesus Garcia Azorero %A Ireneo Peral %B Rend. Mat. Appl., 2000, 20, 167 %I SISSA Library %G en %U http://hdl.handle.net/1963/1462 %1 3078 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:02:44Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %0 Journal Article %D 2000 %T Inverse problem for Semisimple Frobenius Manifolds Monodromy Data and the Painlevé VI Equation %A Davide Guzzetti %I SISSA Library %G en %U http://hdl.handle.net/1963/1557 %1 2561 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T13:04:06Z (GMT). No. of bitstreams: 1\\nmath.CV0010235.pdf: 1221345 bytes, checksum: 94b8360ca765cb56f658af63d2bf4f93 (MD5)\\n Previous issue date: 2000 %0 Journal Article %J Differential Integral Equations 13 (2000) 1503-1528 %D 2000 %T Stability of L^infty Solutions of Temple Class Systems %A Alberto Bressan %A Paola Goatin %XLet $u_t+f(u)_x=0$ be a strictly hyperbolic, genuinely nonlinear system of conservation laws of Temple class. In this paper, a continuous semigroup of solutions is constructed on a domain of $L^\infty$ functions, with possibly unbounded variation. Trajectories depend Lipschitz continuously on the initial data, in the $L^1$ distance. Moreover, we show that a weak solution of the Cauchy problem coincides with the corresponding semigroup trajectory if and only if it satisfies an entropy condition of Oleinik type, concerning the decay of positive waves.

%B Differential Integral Equations 13 (2000) 1503-1528 %I Khayyam Publishing %G en_US %U http://hdl.handle.net/1963/3256 %1 1445 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-11-06T13:16:51Z\\nNo. of bitstreams: 1\\nTemple.pdf: 221742 bytes, checksum: a13773198af84c04068cf3021f12d3c8 (MD5) %0 Book Section %B Rokko Lectures in Mathematics, Vol 7 [Issue title: Perspective of Painleve equations], (2000), pages : 101-109 %D 2000 %T Stokes Matrices for Frobenius Manifolds and the 6 Painlevé Equation %A Davide Guzzetti %K Painlevé equation %X These notes are a short review on the theory of Frobenius manifolds and its connection to problems of isomonodromy deformations and to Painlev'e equations. %B Rokko Lectures in Mathematics, Vol 7 [Issue title: Perspective of Painleve equations], (2000), pages : 101-109 %I Kobe University, Japan %@ 4-907719-07-8 %G en %U http://hdl.handle.net/1963/6546 %1 6478 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Davide Guzzetti (guzzetti@sissa.it) on 2013-03-13T09:57:27Z No. of bitstreams: 1 03-RokkoLect00.pdf: 95063 bytes, checksum: 1b6fe9d8f1fe70ec5b8dec97d78fc55c (MD5) %0 Journal Article %J Phys. Lett. B %D 1999 %T Correspondence between Minkowski and de Sitter quantum field theory %A Marco Bertola %A Gorini, Vittorio %A Moschella, Ugo %A Schaeffer, Richard %B Phys. Lett. B %V 462 %P 249–253 %G eng %0 Journal Article %J Nonlinear Analysis, Theory, Methods and Applications. Volume 37, Issue 6, September 1999, Pages 707-717 %D 1999 %T A Lipschitz selection from the set of minimizers of a nonconvex functional of the gradient %A Gianni Dal Maso %A Vladimir V. Goncharov %A Antonio Ornelas %X A constructive and improved version of the proof that there exist a continuous map that solves the convexified problem is presented. A Lipschitz continuous map is analyzed such that a map vector minimizes the functional at each vector satisfying Cellina\\\'s condition of existence of minimum. This map is explicitly given by a direct constructive algorithm. %B Nonlinear Analysis, Theory, Methods and Applications. Volume 37, Issue 6, September 1999, Pages 707-717 %I SISSA %G en %U http://hdl.handle.net/1963/6439 %1 6379 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-31T18:52:31Z\\nNo. of bitstreams: 1\\nDM-Gon-Orn-96-sissa.pdf: 182850 bytes, checksum: e2288b2be15f6e2f0d0dfc3fc74af3cd (MD5) %R 10.1016/S0362-546X(98)00067-4 %0 Journal Article %J J. Differential Equations 156 (1999), no. 1, 26--49 %D 1999 %T Oleinik type estimates and uniqueness for n x n conservation laws %A Alberto Bressan %A Paola Goatin %X Let $u_t+f(u)_x=0$ be a strictly hyperbolic $n\\\\times n$ system of conservation laws in one space dimension. Relying on the existence of a semigroup of solutions, we first establish the uniqueness of entropy admissible weak solutions to the Cauchy problem, under a mild assumption on the local oscillation of $u$ in a forward neighborhood of each point in the $t\\\\text{-}x$ plane. In turn, this yields the uniqueness of weak solutions which satisfy a decay estimate on positive waves of genuinely nonlinear families, thus extending a classical result proved by Oleĭnik in the scalar case. %B J. Differential Equations 156 (1999), no. 1, 26--49 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3375 %1 955 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-12-01T09:26:02Z\\nNo. of bitstreams: 1\\nOleinik_type.pdf: 1567166 bytes, checksum: ba588e7f2b587d26f5b613a53557bb2f (MD5) %R 10.1006/jdeq.1998.3606 %0 Journal Article %J J. Funct. Anal. 165 (1999) 117-149 %D 1999 %T Perturbation of $\Delta u+u^(N+2)/(N-2)=0$, the scalar curvature problem in $R^N$, and related topics %A Antonio Ambrosetti %A Jesus Garcia Azorero %A Ireneo Peral %XSome nonlinear elliptic equations on $R^N$ which arise perturbing the problem with the critical Sobolev exponent are studied. In particular, some results dealing with the scalar curvature problem in $R^N$ are given.

%B J. Funct. Anal. 165 (1999) 117-149 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3255 %1 1446 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-11-06T13:02:46Z\\nNo. of bitstreams: 1\\nperturbation.pdf: 330668 bytes, checksum: 9e0dfad7ade47327768f2c94e44b4124 (MD5) %R 10.1006/jfan.1999.3390 %0 Journal Article %J Comm. Math. Phys. 207 (1999) 341-383 %D 1999 %T Stokes matrices and monodromy of the quantum cohomology of projective spaces %A Davide Guzzetti %X n this paper we compute Stokes matrices and monodromy of the quantum cohomology of projective spaces. This problem can be formulated in a \\\"classical\\\" framework, as the problem of computation of Stokes matrices and monodromy of differential equations with regular and irregular singularities. We prove that the Stokes\\\' matrix of the quantum cohomology coincides with the Gram matrix in the theory of derived categories of coherent sheaves. We also study the monodromy group of the quantum cohomology and we show that it is related to hyperbolic triangular groups. %B Comm. Math. Phys. 207 (1999) 341-383 %I Springer %G en_US %U http://hdl.handle.net/1963/3475 %1 789 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-29T17:01:09Z\\nNo. of bitstreams: 1\\n9904099v1.pdf: 477251 bytes, checksum: 6278f554f7fc5d2e100e89e3b236603a (MD5) %R 10.1007/s002200050729 %0 Journal Article %J Arch. Ration. Mech. Anal. 146 (1999), no. 1, 23--58 %D 1999 %T Variational formulation of softening phenomena in fracture mechanics. The one-dimensional case %A Andrea Braides %A Gianni Dal Maso %A Adriana Garroni %X Starting from experimental evidence, the authors justify a variational model for softening phenomena in fracture of one-dimensional bars where the energy is given by the contribution and interaction of two terms: a typical bulk energy term depending on elastic strain and a discrete part that depends upon the jump discontinuities that occur in fracture. A more formal, rigorous derivation of the model is presented by examining the $\\\\Gamma$-convergence of discrete energy functionals associated to an array of masses and springs. Close attention is paid to the softening and fracture regimes. \\nOnce the continuous model is derived, it is fully analyzed without losing sight of its discrete counterpart. In particular, the associated boundary value problem is studied and a detailed analysis of the stationary points under the presence of a dead load is performed. A final, interesting section on the scale effect on the model is included. %B Arch. Ration. Mech. Anal. 146 (1999), no. 1, 23--58 %I Springer %G en_US %U http://hdl.handle.net/1963/3371 %1 959 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-11-28T17:18:31Z\\nNo. of bitstreams: 1\\nVariational_formulation.pdf: 2100868 bytes, checksum: 88bfc4cfb6072391f1c6d7cd06e7b8ec (MD5) %R 10.1007/s002050050135 %0 Thesis %D 1998 %T On the Cauchy Problem for the Whitham Equations %A Tamara Grava %K Korteweg de Vries equation %I SISSA %G en %U http://hdl.handle.net/1963/5555 %1 5382 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-02-24T08:14:13Z\\nNo. of bitstreams: 1\\nPhD_Grava_Tamara.pdf: 3951334 bytes, checksum: 2a0b9e024dd0a2bc9c856a24c123e9c3 (MD5) %0 Journal Article %J Gravit. Cosmol. %D 1998 %T Generation of primordial fluctuations in curved spaces %A Schaeffer, Richard %A Moschella, Ugo %A Marco Bertola %A Gorini, Vittorio %B Gravit. Cosmol. %V 4 %P 121–127 %G eng %0 Journal Article %J NoDEA Nonlinear Differential Equations Appl. 5 (1998), no. 2, 219--243 %D 1998 %T Special functions with bounded variation and with weakly differentiable traces on the jump set %A Luigi Ambrosio %A Andrea Braides %A Adriana Garroni %B NoDEA Nonlinear Differential Equations Appl. 5 (1998), no. 2, 219--243 %I SISSA Library %G en %U http://hdl.handle.net/1963/1025 %1 2831 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:41:50Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Journal Article %J Discrete Contin. Dynam. Systems 3 (1997), no. 1, 35--58. %D 1997 %T Shift-differentiability of the flow generated by a conservation law %A Alberto Bressan %A Graziano Guerra %X The paper introduces a notion of \\\"shift-differentials\\\" for maps with values in the space BV. These differentials describe first order variations of a given functin $u$, obtained by horizontal shifts of the points of its graph. The flow generated by a scalar conservation law is proved to be generically shift-differentiable, according to the new definition. %B Discrete Contin. Dynam. Systems 3 (1997), no. 1, 35--58. %I SISSA Library %G en %U http://hdl.handle.net/1963/1033 %1 2823 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:41:57Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Thesis %D 1994 %T Asymptotic Behaviour of Dirichlet Problems in Perforated Domains %A Adriana Garroni %K Dirichlet problems %I SISSA %G en %U http://hdl.handle.net/1963/5714 %1 5566 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-04-16T10:54:30Z\\nNo. of bitstreams: 1\\nPhD_Garroni_Adriana.pdf: 8799112 bytes, checksum: 71df771317b5fd6f6add4ee83805d0e5 (MD5)