The success of mass vaccination campaigns may be jeopardized by human risky behaviors. For example, high level of vaccination coverage may induce early relaxation of social distancing. In this paper, we focus on the mutual influence between the decline in prevalence, due to the rise in the overall immunization coverage, and the consequent decrease in the compliance to social distancing measures. We consider an epidemic model where both the vaccination rate and the disease transmission rate are influenced by human behavior, which in turn depends on the current and past information about the spread of the disease. We highlight the impact of the information-related parameters on the transient and asymptotic behavior of the system that is on the early stage of the epidemic and its final outcome. Among the main results, we evidence that sustained oscillations may be triggered by the behavioral memory in the prevalence-dependent vaccination rate. However, the relaxation of social distancing may induce a switch from a cyclic regime to damped oscillations.The success of mass vaccination campaigns may be jeopardized by human risky behaviors. For example, high level of vaccination coverage may induce early relaxation of social distancing. In this paper, we focus on the mutual influence between the decline in prevalence, due to the rise in the overall immunization coverage, and the consequent decrease in the compliance to social distancing measures. We consider an epidemic model where both the vaccination rate and the disease transmission rate are influenced by human behavior, which in turn depends on the current and past information about the spread of the disease. We highlight the impact of the information-related parameters on the transient and asymptotic behavior of the system that is on the early stage of the epidemic and its final outcome. Among the main results, we evidence that sustained oscillations may be triggered by the behavioral memory in the prevalence-dependent vaccination rate. However, the relaxation of social distancing may induce a switch from a cyclic regime to damped oscillations.

%B Journal of Biological SystemsJournal of Biological Systems %V 30 %P 1 - 25 %8 2022/03/01 %@ 0218-3390 %G eng %U https://doi.org/10.1142/S0218339022500085 %N 01 %! J. Biol. Syst. %0 Journal Article %J ETNA - Electronic Transactions on Numerical Analysis %D 2022 %T A comparison of reduced-order modeling approaches using artificial neural networks for PDEs with bifurcating solutions %A Martin W. Hess %A Annalisa Quaini %A Gianluigi Rozza %B ETNA - Electronic Transactions on Numerical Analysis %V 56 %P 52–65 %G eng %R 10.1553/etna_vol56s52 %0 Generic %D 2022 %T Data-Driven Enhanced Model Reduction for Bifurcating Models in Computational Fluid Dynamics %A Martin W. Hess %A Annalisa Quaini %A Gianluigi Rozza %G eng %0 Generic %D 2022 %T A Data-Driven Surrogate Modeling Approach for Time-Dependent Incompressible Navier-Stokes Equations with Dynamic Mode Decomposition and Manifold Interpolation %A Martin W. Hess %A Annalisa Quaini %A Gianluigi Rozza %G eng %0 Journal Article %J ESAIM: M2AN %D 2022 %T Driving bifurcating parametrized nonlinear PDEs by optimal control strategies: application to Navier–Stokes equations with model order reduction %A Federico Pichi %A Maria Strazzullo %A F. Ballarin %A Gianluigi Rozza %B ESAIM: M2AN %V 56 %P 1361 - 1400 %8 2022/// %G eng %U https://doi.org/10.1051/m2an/2022044 %N 4 %0 Journal Article %J Mathematical Methods in the Applied SciencesMathematical Methods in the Applied SciencesMath Meth Appl Sci %D 2022 %T Mathematical modelling of oscillating patterns for chronic autoimmune diseases %A Rossella Della Marca %A Maria da Piedade Machado Ramos %A Carolina Ribeiro %A Ana Jacinta Soares %K autoimmune diseases %K cellular interactions %K Dynamical systems %K Hopf bifurcation %K kinetic theory %K mathematical biology %XMany autoimmune diseases are chronic in nature, so that in general, patients experience periods of recurrence and remission of the symptoms characterizing their specific autoimmune ailment. In order to describe this very important feature of autoimmunity, we construct a mathematical model of kinetic type describing the immune system cellular interactions in the context of autoimmunity exhibiting recurrent dynamics. The model equations constitute a nonlinear system of integro-differential equations with quadratic terms that describe the interactions between self-antigen presenting cells, self-reactive T cells, and immunosuppressive cells. We consider a constant input of self-antigen presenting cells, due to external environmental factors that are believed to trigger autoimmunity in people with predisposition for this condition. We also consider the natural death of all cell populations involved in our model, caused by their interaction with cells of the host environment. We derive the macroscopic analogue and show positivity and well-posedness of the solution and then we study the equilibria of the corresponding dynamical system and their stability properties. By applying dynamical system theory, we prove that steady oscillations may arise due to the occurrence of a Hopf bifurcation. We perform some numerical simulations for our model, and we observe a recurrent pattern in the solutions of both the kinetic description and its macroscopic analogue, which leads us to conclude that this model is able to capture the chronic behaviour of many autoimmune diseases.

%B Mathematical Methods in the Applied SciencesMathematical Methods in the Applied SciencesMath Meth Appl Sci %V n/a %8 2022/04/01 %@ 0170-4214 %G eng %U https://doi.org/10.1002/mma.8229 %N n/a %! Mathematical Methods in the Applied Sciences %0 Journal Article %J International Journal for Numerical Methods in FluidsInternational Journal for Numerical Methods in FluidsInt J Numer Meth Fluids %D 2022 %T Model order reduction for bifurcating phenomena in fluid-structure interaction problems %A Moaad Khamlich %A Federico Pichi %A Gianluigi Rozza %K Bifurcation theory %K Coandă effect %K continuum mechanics %K fluid dynamics %K monolithic method %K parametrized fluid-structure interaction problem %K Proper orthogonal decomposition %K reduced order modeling %XAbstract This work explores the development and the analysis of an efficient reduced order model for the study of a bifurcating phenomenon, known as the Coand? effect, in a multi-physics setting involving fluid and solid media. Taking into consideration a fluid-structure interaction problem, we aim at generalizing previous works towards a more reliable description of the physics involved. In particular, we provide several insights on how the introduction of an elastic structure influences the bifurcating behavior. We have addressed the computational burden by developing a reduced order branch-wise algorithm based on a monolithic proper orthogonal decomposition. We compared different constitutive relations for the solid, and we observed that a nonlinear hyper-elastic law delays the bifurcation w.r.t. the standard model, while the same effect is even magnified when considering linear elastic solid.

%B International Journal for Numerical Methods in FluidsInternational Journal for Numerical Methods in FluidsInt J Numer Meth Fluids %V n/a %8 2022/05/23 %@ 0271-2091 %G eng %U https://doi.org/10.1002/fld.5118 %N n/a %! International Journal for Numerical Methods in Fluids %0 Unpublished Work %D 2022 %T Model Reduction Using Sparse Polynomial Interpolation for the Incompressible Navier-Stokes Equations %A Martin W. Hess %A Gianluigi Rozza %G eng %0 Journal Article %J Computer Methods in Applied Mechanics and Engineering %D 2022 %T The Neural Network shifted-proper orthogonal decomposition: A machine learning approach for non-linear reduction of hyperbolic equations %A Davide Papapicco %A Nicola Demo %A Michele Girfoglio %A Giovanni Stabile %A Gianluigi Rozza %K Advection %K Computational complexity %K Deep neural network %K Deep neural networks %K Linear subspace %K Multiphase simulations %K Non linear %K Nonlinear hyperbolic equation %K Partial differential equations %K Phase space methods %K Pre-processing %K Principal component analysis %K reduced order modeling %K Reduced order modelling %K Reduced-order model %K Shifted-POD %XModels with dominant advection always posed a difficult challenge for projection-based reduced order modelling. Many methodologies that have recently been proposed are based on the pre-processing of the full-order solutions to accelerate the Kolmogorov N−width decay thereby obtaining smaller linear subspaces with improved accuracy. These methods however must rely on the knowledge of the characteristic speeds in phase space of the solution, limiting their range of applicability to problems with explicit functional form for the advection field. In this work we approach the problem of automatically detecting the correct pre-processing transformation in a statistical learning framework by implementing a deep-learning architecture. The purely data-driven method allowed us to generalise the existing approaches of linear subspace manipulation to non-linear hyperbolic problems with unknown advection fields. The proposed algorithm has been validated against simple test cases to benchmark its performances and later successfully applied to a multiphase simulation. © 2022 Elsevier B.V.

%B Computer Methods in Applied Mechanics and Engineering %V 392 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85124488633&doi=10.1016%2fj.cma.2022.114687&partnerID=40&md5=12f82dcaba04c4a7c44f8e5b20101997 %R 10.1016/j.cma.2022.114687 %0 Journal Article %D 2022 %T A POD-Galerkin reduced order model for the Navier–Stokes equations in stream function-vorticity formulation %A Michele Girfoglio %A Annalisa Quaini %A Gianluigi Rozza %K Galerkin projection %K Navier–Stokes equations %K Proper orthogonal decomposition %K Reduced order model %K Stream function-vorticity formulation %XWe develop a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for the efficient numerical simulation of the parametric Navier–Stokes equations in the stream function-vorticity formulation. Unlike previous works, we choose different reduced coefficients for the vorticity and stream function fields. In addition, for parametric studies we use a global POD basis space obtained from a database of time dependent full order snapshots related to sample points in the parameter space. We test the performance of our ROM strategy with the well-known vortex merger benchmark and a more complex case study featuring the geometry of the North Atlantic Ocean. Accuracy and efficiency are assessed for both time reconstruction and physical parametrization.

%P 105536 %8 2022/06/14/ %@ 0045-7930 %G eng %U https://www.sciencedirect.com/science/article/pii/S0045793022001645 %! Computers & Fluids %0 Generic %D 2022 %T Projection based semi–implicit partitioned Reduced Basis Method for non parametrized and parametrized Fluid–Structure Interaction problems %A Monica Nonino %A Francesco Ballarin %A Gianluigi Rozza %A Yvon Maday %XThe goal of this manuscript is to present a partitioned Model Order Reduction method that is based on a semi-implicit projection scheme to solve multiphysics problems. We implement a Reduced Order Method based on a Proper Orthogonal Decomposition, with the aim of addressing both time-dependent and time-dependent, parametrized Fluid-Structure Interaction problems, where the fluid is incompressible and the structure is thick and two dimensional.

%G eng %0 Generic %D 2022 %T A Proper Orthogonal Decomposition approach for parameters reduction of Single Shot Detector networks %A Laura Meneghetti %A Nicola Demo %A Gianluigi Rozza %K Computer Vision and Pattern Recognition (cs.CV) %K FOS: Computer and information sciences %K FOS: Mathematics %K Machine Learning (cs.LG) %K Numerical Analysis (math.NA) %G eng %U https://arxiv.org/abs/2207.13551 %R 10.48550/ARXIV.2207.13551 %0 Journal Article %J Networks and Heterogeneous Media %D 2022 %T An SIR–like kinetic model tracking individuals' viral load %A Rossella Della Marca %A Nadia Loy %A Andrea Tosin %B Networks and Heterogeneous Media %P - %G eng %0 Unpublished Work %D 2021 %T An artificial neural network approach to bifurcating phenomena in computational fluid dynamics %A Federico Pichi %A Francesco Ballarin %A Gianluigi Rozza %A Jan S Hesthaven %G eng %0 Journal Article %J Comptes Rendus. Mécanique %D 2021 %T Asymptotic approach to a rotational Taylor swimming sheet %A Giovanni Corsi %B Comptes Rendus. Mécanique %V 349 %P 103–116 %G eng %R 10.5802/crmeca.75 %0 Journal Article %J Software Impacts %D 2021 %T ATHENA: Advanced Techniques for High dimensional parameter spaces to Enhance Numerical Analysis %A Francesco Romor %A Marco Tezzele %A Gianluigi Rozza %B Software Impacts %V 10 %P 100133 %G eng %R 10.1016/j.simpa.2021.100133 %0 Unpublished Work %D 2021 %T A CERTIFIED REDUCED BASIS Method FOR LINEAR PARAMETRIZED PARABOLIC OPTIMAL CONTROL PROBLEMS IN SPACE-TIME FORMULATION %A Maria Strazzullo %A Francesco Ballarin %A Gianluigi Rozza %G eng %0 Journal Article %J Computers & Fluids %D 2021 %T On the comparison of LES data-driven reduced order approaches for hydroacoustic analysis %A Mahmoud Gadalla %A Marta Cianferra %A Marco Tezzele %A Giovanni Stabile %A Andrea Mola %A Gianluigi Rozza %K Dynamic mode decomposition %K Ffowcs Williams and Hawkings %K Hydroacoustics %K Large eddy simulation %K Model reduction %K Proper orthogonal decomposition %XIn this work, Dynamic Mode Decomposition (DMD) and Proper Orthogonal Decomposition (POD) methodologies are applied to hydroacoustic dataset computed using Large Eddy Simulation (LES) coupled with Ffowcs Williams and Hawkings (FWH) analogy. First, a low-dimensional description of the flow fields is presented with modal decomposition analysis. Sensitivity towards the DMD and POD bases truncation rank is discussed, and extensive dataset is provided to demonstrate the ability of both algorithms to reconstruct the flow fields with all the spatial and temporal frequencies necessary to support accurate noise evaluation. Results show that while DMD is capable to capture finer coherent structures in the wake region for the same amount of employed modes, reconstructed flow fields using POD exhibit smaller magnitudes of global spatiotemporal errors compared with DMD counterparts. Second, a separate set of DMD and POD modes generated using half the snapshots is employed into two data-driven reduced models respectively, based on DMD mid cast and POD with Interpolation (PODI). In that regard, results confirm that the predictive character of both reduced approaches on the flow fields is sufficiently accurate, with a relative superiority of PODI results over DMD ones. This infers that, discrepancies induced due to interpolation errors in PODI is relatively low compared with errors induced by integration and linear regression operations in DMD, for the present setup. Finally, a post processing analysis on the evaluation of FWH acoustic signals utilizing reduced fluid dynamic fields as input demonstrates that both DMD and PODI data-driven reduced models are efficient and sufficiently accurate in predicting acoustic noises.

%B Computers & Fluids %V 216 %P 104819 %G eng %U https://www.sciencedirect.com/science/article/pii/S0045793020303893 %R https://doi.org/10.1016/j.compfluid.2020.104819 %0 Unpublished Work %D 2021 %T Consistency of the full and reduced order models for Evolve-Filter-Relax Regularization of Convection-Dominated, Marginally-Resolved Flows %A Maria Strazzullo %A Michele Girfoglio %A Francesco Ballarin %A T. Iliescu %A Gianluigi Rozza %G eng %0 Unpublished Work %D 2021 %T A data-driven partitioned approach for the resolution of time-dependent optimal control problems with dynamic mode decomposition %A Eleonora Donadini %A Maria Strazzullo %A Marco Tezzele %A Gianluigi Rozza %G eng %0 Journal Article %D 2021 %T A Differential Perspective on Gradient Flows on CAT(K)-Spaces and Applications %A Nicola Gigli %A Francesco Nobili %XWe review the theory of Gradient Flows in the framework of convex and lower semicontinuous functionals on $$\textsf {CAT} (\kappa )$$-spaces and prove that they can be characterized by the same differential inclusion $$y_t'\in -\partial ^-\textsf {E} (y_t)$$one uses in the smooth setting and more precisely that $$y_t'$$selects the element of minimal norm in $$-\partial ^-\textsf {E} (y_t)$$. This generalizes previous results in this direction where the energy was also assumed to be Lipschitz. We then apply such result to the Korevaar–Schoen energy functional on the space of $$L^2$$and CAT(0) valued maps: we define the Laplacian of such $$L^2$$map as the element of minimal norm in $$-\partial ^-\textsf {E} (u)$$, provided it is not empty. The theory of gradient flows ensures that the set of maps admitting a Laplacian is $$L^2$$-dense. Basic properties of this Laplacian are then studied.

%V 31 %P 11780 - 11818 %8 2021/12/01 %@ 1559-002X %G eng %U https://doi.org/10.1007/s12220-021-00701-5 %N 12 %! The Journal of Geometric Analysis %0 Generic %D 2021 %T A Dimensionality Reduction Approach for Convolutional Neural Networks %A Laura Meneghetti %A Nicola Demo %A Gianluigi Rozza %G eng %0 Report %D 2021 %T On Dini derivatives of real functions %A Giuliano Klun %A Alessandro Fonda %A Andrea Sfecci %G eng %0 Conference Paper %B Numerical Mathematics and Advanced Applications ENUMATH 2019 %D 2021 %T Discontinuous Galerkin Model Order Reduction of Geometrically Parametrized Stokes Equation %A Nirav Shah %A Martin W. Hess %A Gianluigi Rozza %E Vermolen, Fred J. %E Vuik, Cornelis %XThe present work focuses on the geometric parametrization and the reduced order modeling of the Stokes equation. We discuss the concept of a parametrized geometry and its application within a reduced order modeling technique. The full order model is based on the discontinuous Galerkin method with an interior penalty formulation. We introduce the broken Sobolev spaces as well as the weak formulation required for an affine parameter dependency. The operators are transformed from a fixed domain to a parameter dependent domain using the affine parameter dependency. The proper orthogonal decomposition is used to obtain the basis of functions of the reduced order model. By using the Galerkin projection the linear system is projected onto the reduced space. During this process, the offline-online decomposition is used to separate parameter dependent operations from parameter independent operations. Finally this technique is applied to an obstacle test problem.The numerical outcomes presented include experimental error analysis, eigenvalue decay and measurement of online simulation time.

%B Numerical Mathematics and Advanced Applications ENUMATH 2019 %I Springer International Publishing %C Cham %8 2021// %@ 978-3-030-55874-1 %G eng %0 Journal Article %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2021 %T Displacement convexity of Entropy and the distance cost Optimal Transportation %A Fabio Cavalletti %A Nicola Gigli %A Flavia Santarcangelo %B Annales de la Faculté des sciences de Toulouse : Mathématiques %V Ser. 6, 30 %P 411–427 %G eng %U https://afst.centre-mersenne.org/articles/10.5802/afst.1679/ %R 10.5802/afst.1679 %0 Journal Article %J arXiv preprint arXiv:2110.09155 %D 2021 %T A dynamic mode decomposition extension for the forecasting of parametric dynamical systems %A Francesco Andreuzzi %A Nicola Demo %A Gianluigi Rozza %B arXiv preprint arXiv:2110.09155 %G eng %0 Journal Article %D 2021 %T A dynamic model for viscoelasticity in domains with time-dependent cracks %A Francesco Sapio %XIn this paper, we prove the existence of solutions for a class of viscoelastic dynamic systems on time-dependent cracking domains.

%V 28 %P 67 %8 2021/10/01 %@ 1420-9004 %G eng %U https://doi.org/10.1007/s00030-021-00729-0 %N 6 %! Nonlinear Differential Equations and Applications NoDEA %0 Journal Article %J Advances in Computational Mathematics %D 2021 %T Efficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method %A Moreno Pintore %A Federico Pichi %A Martin W. Hess %A Gianluigi Rozza %A Claudio Canuto %XThe majority of the most common physical phenomena can be described using partial differential equations (PDEs). However, they are very often characterized by strong nonlinearities. Such features lead to the coexistence of multiple solutions studied by the bifurcation theory. Unfortunately, in practical scenarios, one has to exploit numerical methods to compute the solutions of systems of PDEs, even if the classical techniques are usually able to compute only a single solution for any value of a parameter when more branches exist. In this work, we implemented an elaborated deflated continuation method that relies on the spectral element method (SEM) and on the reduced basis (RB) one to efficiently compute bifurcation diagrams with more parameters and more bifurcation points. The deflated continuation method can be obtained combining the classical continuation method and the deflation one: the former is used to entirely track each known branch of the diagram, while the latter is exploited to discover the new ones. Finally, when more than one parameter is considered, the efficiency of the computation is ensured by the fact that the diagrams can be computed during the online phase while, during the offline one, one only has to compute one-dimensional diagrams. In this work, after a more detailed description of the method, we will show the results that can be obtained using it to compute a bifurcation diagram associated with a problem governed by the Navier-Stokes equations.

%B Advances in Computational Mathematics %V 47 %G eng %R 10.1007/s10444-020-09827-6 %0 Journal Article %J Bolletino dell Unione Matematica Italiana %D 2021 %T An efficient computational framework for naval shape design and optimization problems by means of data-driven reduced order modeling techniques %A Nicola Demo %A Giulio Ortali %A Gianluca Gustin %A Gianluigi Rozza %A Gianpiero Lavini %XThis contribution describes the implementation of a data-driven shape optimization pipeline in a naval architecture application. We adopt reduced order models in order to improve the efficiency of the overall optimization, keeping a modular and equation-free nature to target the industrial demand. We applied the above mentioned pipeline to a realistic cruise ship in order to reduce the total drag. We begin by defining the design space, generated by deforming an initial shape in a parametric way using free form deformation. The evaluation of the performance of each new hull is determined by simulating the flux via finite volume discretization of a two-phase (water and air) fluid. Since the fluid dynamics model can result very expensive—especially dealing with complex industrial geometries—we propose also a dynamic mode decomposition enhancement to reduce the computational cost of a single numerical simulation. The real-time computation is finally achieved by means of proper orthogonal decomposition with Gaussian process regression technique. Thanks to the quick approximation, a genetic optimization algorithm becomes feasible to converge towards the optimal shape.

%B Bolletino dell Unione Matematica Italiana %V 14 %P 211-230 %G eng %R 10.1007/s40574-020-00263-4 %0 Journal Article %D 2021 %T An existence result for the fractional Kelvin–Voigt’s model on time-dependent cracked domains %A Maicol Caponi %A Francesco Sapio %XWe prove an existence result for the fractional Kelvin–Voigt’s model involving Caputo’s derivative on time-dependent cracked domains. We first show the existence of a solution to a regularized version of this problem. Then, we use a compactness argument to derive that the fractional Kelvin–Voigt’s model admits a solution which satisfies an energy-dissipation inequality. Finally, we prove that when the crack is not moving, the solution is unique.

%8 2021/06/04 %@ 1424-3202 %G eng %U https://doi.org/10.1007/s00028-021-00713-2 %! Journal of Evolution Equations %0 Unpublished Work %D 2021 %T AN EXTENDED PHYSICS INFORMED NEURAL NETWORK FOR PRELIMINARY ANALYSIS OF PARAMETRIC OPTIMAL CONTROL PROBLEMS %A Nicola Demo %A Maria Strazzullo %A Gianluigi Rozza %G eng %0 Generic %D 2021 %T A first-order condition for the independence on p of weak gradients %A Nicola Gigli %A Francesco Nobili %G eng %0 Journal Article %J Multiscale Modeling and Simulation %D 2021 %T Hierarchical model reduction techniques for flow modeling in a parametrized setting %A Matteo Zancanaro %A F. Ballarin %A Simona Perotto %A Gianluigi Rozza %XIn this work we focus on two different methods to deal with parametrized partial differential equations in an efficient and accurate way. Starting from high fidelity approximations built via the hierarchical model reduction discretization, we consider two approaches, both based on a projection model reduction technique. The two methods differ for the algorithm employed during the construction of the reduced basis. In particular, the former employs the proper orthogonal decomposition, while the latter relies on a greedy algorithm according to the certified reduced basis technique. The two approaches are preliminarily compared on two-dimensional scalar and vector test cases.

%B Multiscale Modeling and Simulation %V 19 %P 267-293 %G eng %R 10.1137/19M1285330 %0 Journal Article %J Journal of Marine Science and Engineering %D 2021 %T Hull Shape Design Optimization with Parameter Space and Model Reductions, and Self-Learning Mesh Morphing %A Nicola Demo %A Marco Tezzele %A Andrea Mola %A Gianluigi Rozza %XIn the field of parametric partial differential equations, shape optimization represents a challenging problem due to the required computational resources. In this contribution, a data-driven framework involving multiple reduction techniques is proposed to reduce such computational burden. Proper orthogonal decomposition (POD) and active subspace genetic algorithm (ASGA) are applied for a dimensional reduction of the original (high fidelity) model and for an efficient genetic optimization based on active subspace property. The parameterization of the shape is applied directly to the computational mesh, propagating the generic deformation map applied to the surface (of the object to optimize) to the mesh nodes using a radial basis function (RBF) interpolation. Thus, topology and quality of the original mesh are preserved, enabling application of POD-based reduced order modeling techniques, and avoiding the necessity of additional meshing steps. Model order reduction is performed coupling POD and Gaussian process regression (GPR) in a data-driven fashion. The framework is validated on a benchmark ship.

%B Journal of Marine Science and Engineering %V 9 %P 185 %G eng %U https://www.mdpi.com/2077-1312/9/2/185 %R 10.3390/jmse9020185 %0 Journal Article %J Fluids %D 2021 %T Hybrid Neural Network Reduced Order Modelling for Turbulent Flows with Geometric Parameters %A Matteo Zancanaro %A Markus Mrosek %A Giovanni Stabile %A Carsten Othmer %A Gianluigi Rozza %B Fluids %I MDPI AG %V 6 %P 296 %G eng %U https://doi.org/10.3390/fluids6080296 %R 10.3390/fluids6080296 %0 Journal Article %J Trans. Amer. Math. Soc. %D 2021 %T Independence of synthetic curvature dimension conditions on transport distance exponent %A Afiny Akdemir %A Andrew Colinet %A Robert McCann %A Fabio Cavalletti %A Flavia Santarcangelo %B Trans. Amer. Math. Soc. %V 374 %P 5877–5923 %G eng %U https://doi.org/10.1090/tran/8413 %R 10.1090/tran/8413 %0 Unpublished Work %D 2021 %T A local approach to parameter space reduction for regression and classification tasks %A Francesco Romor %A Marco Tezzele %A Gianluigi Rozza %B arXiv preprint arXiv:2107.10867 %G eng %0 Generic %D 2021 %T On master test plans for the space of BV functions %A Francesco Nobili %A Enrico Pasqualetto %A Timo Schultz %G eng %0 Journal Article %J Fluids %D 2021 %T A Monolithic and a Partitioned, Reduced Basis Method for Fluid–Structure Interaction Problems %A Monica Nonino %A F. Ballarin %A Gianluigi Rozza %XThe aim of this work is to present an overview about the combination of the Reduced Basis Method (RBM) with two different approaches for Fluid–Structure Interaction (FSI) problems, namely a monolithic and a partitioned approach. We provide the details of implementation of two reduction procedures, and we then apply them to the same test case of interest. We first implement a reduction technique that is based on a monolithic procedure where we solve the fluid and the solid problems all at once. We then present another reduction technique that is based on a partitioned (or segregated) procedure: the fluid and the solid problems are solved separately and then coupled using a fixed point strategy. The toy problem that we consider is based on the Turek–Hron benchmark test case, with a fluid Reynolds number Re=100.

%B Fluids %V 6 %P 229 %G eng %U https://www.mdpi.com/2311-5521/6/6/229 %R 10.3390/fluids6060229 %0 Generic %D 2021 %T Monotonicity formulas for harmonic functions in RCD(0,N) spaces %A Nicola Gigli %A Ivan Yuri Violo %XWe generalize to the RCD(0,N) setting a family of monotonicity formulas by Colding and Minicozzi for positive harmonic functions in Riemannian manifolds with non-negative Ricci curvature. Rigidity and almost rigidity statements are also proven, the second appearing to be new even in the smooth setting. Motivated by the recent work in [AFM] we also introduce the notion of electrostatic potential in RCD spaces, which also satisfies our monotonicity formulas. Our arguments are mainly based on new estimates for harmonic functions in RCD(K,N) spaces and on a new functional version of the `(almost) outer volume cone implies (almost) outer metric cone' theorem.

%G eng %0 Conference Paper %B Proceedings in Applied Mathematics & Mechanics %D 2021 %T Multi-fidelity data fusion for the approximation of scalar functions with low intrinsic dimensionality through active subspaces %A Francesco Romor %A Marco Tezzele %A Gianluigi Rozza %B Proceedings in Applied Mathematics & Mechanics %I Wiley Online Library %V 20 %G eng %R 10.1002/pamm.202000349 %0 Journal Article %J arXiv preprint arXiv:2110.14396 %D 2021 %T Multi-fidelity data fusion through parameter space reduction with applications to automotive engineering %A Francesco Romor %A Marco Tezzele %A Markus Mrosek %A Carsten Othmer %A Gianluigi Rozza %B arXiv preprint arXiv:2110.14396 %G eng %0 Journal Article %J Acta Mechanica Sinica %D 2021 %T Non-intrusive data-driven ROM framework for hemodynamics problems %A Michele Girfoglio %A Leonardo Scandurra %A Francesco Ballarin %A Giuseppe Infantino %A Francesca Nicolò %A Andrea Montalto %A Gianluigi Rozza %A Roberto Scrofani %A Marina Comisso %A Francesco Musumeci %B Acta Mechanica Sinica %V 37 %P 1183–1191 %G eng %0 Journal Article %J Communications in Contemporary MathematicsCommunications in Contemporary Mathematics %D 2021 %T Non-well-ordered lower and upper solutions for semilinear systems of PDEs %A Alessandro Fonda %A Giuliano Klun %A Andrea Sfecci %XWe prove existence results for systems of boundary value problems involving elliptic second-order differential operators. The assumptions involve lower and upper solutions, which may be either well-ordered, or not at all. The results are stated in an abstract framework, and can be translated also for systems of parabolic type.We prove existence results for systems of boundary value problems involving elliptic second-order differential operators. The assumptions involve lower and upper solutions, which may be either well-ordered, or not at all. The results are stated in an abstract framework, and can be translated also for systems of parabolic type.

%B Communications in Contemporary MathematicsCommunications in Contemporary Mathematics %P 2150080 %8 2021/08/27 %@ 0219-1997 %G eng %U https://doi.org/10.1142/S0219199721500802 %! Commun. Contemp. Math. %0 Journal Article %J Phil. Trans. R. Soc. A %D 2021 %T Nutations in growing plant shoots as a morphoelastic flutter instability %A Daniele Agostinelli %A Giovanni Noselli %A Antonio DeSimone %XGrowing plant shoots exhibit spontaneous oscillations that Darwin observed, and termed "circumnutations". Recently, they have received renewed attention for the design and optimal actuation of bioinspired robotic devices. We discuss a possible interpretation of these spontaneous oscillations as a Hopf-type bifurcation in a growing morphoelastic rod. Using a three-dimensional model and numerical simulations, we analyse the salient features of this flutter-like phenomenon (e.g. the characteristic period of the oscillations) and their dependence on the model details (in particular, the impact of choosing different growth models) finding that, overall, these features are robust with respect to changes in the details of the growth model adopted.

%B Phil. Trans. R. Soc. A %V 379 %G eng %U https://doi.org/10.1098/rsta.2020.0116 %9 Journal article %R 10.1098/rsta.2020.0116 %0 Journal Article %J Frontiers in Plant Science %D 2021 %T Nutations in plant shoots: Endogenous and exogenous factors in the presence of mechanical deformations %A Daniele Agostinelli %A Antonio DeSimone %A Giovanni Noselli %XWe present a three-dimensional morphoelastic rod model capable to describe the morphogenesis of growing plant shoots driven by differential growth. We discuss the evolution laws for endogenous oscillators, straightening mechanisms, and reorientations to directional cues, such as gravitropic reactions governed by the avalanche dynamics of statoliths. We use this model to investigate the role of elastic deflections due to gravity loading in circumnutating plant shoots. We show that, in the absence of endogenous cues, pendular and circular oscillations arise as a critical length is attained, thus suggesting the occurrence of an instability triggered by exogenous factors. When also oscillations due to endogenous cues are present, their weight relative to those associated with the instability varies in time as the shoot length and other biomechanical properties change. Thanks to the simultaneous occurrence of these two oscillatory mechanisms, we are able to reproduce a variety of complex behaviors, including trochoid-like patterns, which evolve into circular orbits as the shoot length increases, and the amplitude of the exogenous oscillations becomes dominant.

%B Frontiers in Plant Science %I Cold Spring Harbor Laboratory %V 12 %G eng %U https://www.frontiersin.org/article/10.3389/fpls.2021.608005 %9 Journal article %R 10.3389/fpls.2021.608005 %0 Generic %D 2021 %T Parallel transport on non-collapsed $\mathsfRCD(K,N)$ spaces %A Emanuele Caputo %A Nicola Gigli %A Enrico Pasqualetto %XWe provide a general theory for parallel transport on non-collapsed RCD spaces obtaining both existence and uniqueness results. Our theory covers the case of geodesics and, more generally, of curves obtained via the flow of sufficiently regular time dependent vector fields: the price that we pay for this generality is that we cannot study parallel transport along a single such curve, but only along almost all of these (in a sense related to the notions of Sobolev vector calculus and Regular Lagrangian Flow in the nonsmooth setting).

The class of ncRCD spaces contains finite dimensional Alexandrov spaces with curvature bounded from below, thus our construction provides a way of speaking about parallel transport in this latter setting alternative to the one proposed by Petrunin (1998). The precise relation between the two approaches is yet to be understood.

We prove the existence of periodic solutions of some infinite-dimensional systems by the use of the lower/upper solutions method. Both the well-ordered and non-well-ordered cases are treated, thus generalizing to systems some well-established results for scalar equations.

%V 18 %P 223 %8 2021/09/07 %@ 1660-5454 %G eng %U https://doi.org/10.1007/s00009-021-01857-8 %N 5 %! Mediterranean Journal of Mathematics %0 Journal Article %J Journal of Computational Physics %D 2021 %T A POD-Galerkin reduced order model for a LES filtering approach %A Michele Girfoglio %A Annalisa Quaini %A Gianluigi Rozza %XWe propose a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for an implementation of the Leray model that combines a two-step algorithm called Evolve-Filter (EF) with a computationally efficient finite volume method. The main novelty of the proposed approach relies in applying spatial filtering both for the collection of the snapshots and in the reduced order model, as well as in considering the pressure field at reduced level. In both steps of the EF algorithm, velocity and pressure fields are approximated by using different POD basis and coefficients. For the reconstruction of the pressures fields, we use a pressure Poisson equation approach. We test our ROM on two benchmark problems: 2D and 3D unsteady flow past a cylinder at Reynolds number 0≤Re≤100. The accuracy of the reduced order model is assessed against results obtained with the full order model. For the 2D case, a parametric study with respect to the filtering radius is also presented.

%B Journal of Computational Physics %V 436 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85102138957&doi=10.1016%2fj.jcp.2021.110260&partnerID=40&md5=73115708267e80754f343561c26f4744 %R 10.1016/j.jcp.2021.110260 %0 Journal Article %J Applied Mathematical Modelling %D 2021 %T A POD-Galerkin reduced order model of a turbulent convective buoyant flow of sodium over a backward-facing step %A Kelbij Star %A Giovanni Stabile %A Gianluigi Rozza %A Joris Degroote %XA Finite-Volume based POD-Galerkin reduced order modeling strategy for steady-state Reynolds averaged Navier–Stokes (RANS) simulation is extended for low-Prandtl number flow. The reduced order model is based on a full order model for which the effects of buoyancy on the flow and heat transfer are characterized by varying the Richardson number. The Reynolds stresses are computed with a linear eddy viscosity model. A single gradient diffusion hypothesis, together with a local correlation for the evaluation of the turbulent Prandtl number, is used to model the turbulent heat fluxes. The contribution of the eddy viscosity and turbulent thermal diffusivity fields are considered in the reduced order model with an interpolation based data-driven method. The reduced order model is tested for buoyancy-aided turbulent liquid sodium flow over a vertical backward-facing step with a uniform heat flux applied on the wall downstream of the step. The wall heat flux is incorporated with a Neumann boundary condition in both the full order model and the reduced order model. The velocity and temperature profiles predicted with the reduced order model for the same and new Richardson numbers inside the range of parameter values are in good agreement with the RANS simulations. Also, the local Stanton number and skin friction distribution at the heated wall are qualitatively well captured. Finally, the reduced order simulations, performed on a single core, are about 105 times faster than the RANS simulations that are performed on eight cores.

%B Applied Mathematical Modelling %V 89 %P 486-503 %G eng %R 10.1016/j.apm.2020.07.029 %0 Journal Article %D 2021 %T Quadratic Life Span of Periodic Gravity-capillary Water Waves %A Massimiliano Berti %A Roberto Feola %A Luca Franzoi %XWe consider the gravity-capillary water waves equations for a bi-dimensional fluid with a periodic one-dimensional free surface. We prove a rigorous reduction of this system to Birkhoff normal form up to cubic degree. Due to the possible presence of three-wave resonances for general values of gravity, surface tension, and depth, such normal form may be not trivial and exhibit a chaotic dynamics (Wilton ripples). Nevertheless, we prove that for all the values of gravity, surface tension, and depth, initial data that are of size $$ \varepsilon $$in a sufficiently smooth Sobolev space leads to a solution that remains in an $$ \varepsilon $$-ball of the same Sobolev space up times of order $$ \varepsilon ^{-2}$$. We exploit that the three-wave resonances are finitely many, and the Hamiltonian nature of the Birkhoff normal form.

%V 3 %P 85 - 115 %8 2021/04/01 %@ 2523-3688 %G eng %U https://doi.org/10.1007/s42286-020-00036-8 %N 1 %! Water Waves %0 Journal Article %D 2021 %T Quasistatic Limit of a Dynamic Viscoelastic Model with Memory %A Gianni Dal Maso %A Francesco Sapio %XWe study the behaviour of the solutions to a dynamic evolution problem for a viscoelastic model with long memory, when the rate of change of the data tends to zero. We prove that a suitably rescaled version of the solutions converges to the solution of the corresponding stationary problem.

%8 2021/11/30 %@ 1424-9294 %G eng %U https://doi.org/10.1007/s00032-021-00343-w %! Milan Journal of Mathematics %0 Journal Article %J Computer & Mathematics With Applications %D 2021 %T A Reduced Order Cut Finite Element method for geometrically parametrized steady and unsteady Navier–Stokes problems %A Efthymios N Karatzas %A Monica Nonino %A F. Ballarin %A Gianluigi Rozza %K Cut Finite Element Method %K Navier–Stokes equations %K Parameter–dependent shape geometry %K Reduced Order Models %K Unfitted mesh %XWe focus on steady and unsteady Navier–Stokes flow systems in a reduced-order modeling framework based on Proper Orthogonal Decomposition within a levelset geometry description and discretized by an unfitted mesh Finite Element Method. This work extends the approaches of [1], [2], [3] to nonlinear CutFEM discretization. We construct and investigate a unified and geometry independent reduced basis which overcomes many barriers and complications of the past, that may occur whenever geometrical morphings are taking place. By employing a geometry independent reduced basis, we are able to avoid remeshing and transformation to reference configurations, and we are able to handle complex geometries. This combination of a fixed background mesh in a fixed extended background geometry with reduced order techniques appears beneficial and advantageous in many industrial and engineering applications, which could not be resolved efficiently in the past.

%B Computer & Mathematics With Applications %8 2021/08/12/ %@ 0898-1221 %G eng %U https://www.sciencedirect.com/science/article/pii/S0898122121002790 %! Computers & Mathematics with Applications %0 Conference Paper %B Numerical Mathematics and Advanced Applications ENUMATH 2019 %D 2021 %T Reduced Order Methods for Parametrized Non-linear and Time Dependent Optimal Flow Control Problems, Towards Applications in Biomedical and Environmental Sciences %A Maria Strazzullo %A Zakia Zainib %A F. Ballarin %A Gianluigi Rozza %E Fred J Vermolen %E Cornelis Vuik %XWe introduce reduced order methods as an efficient strategy to solve parametrized non-linear and time dependent optimal flow control problems governed by partial differential equations. Indeed, the optimal control problems require a huge computational effort in order to be solved, most of all in physical and/or geometrical parametrized settings. Reduced order methods are a reliable and suitable approach, increasingly gaining popularity, to achieve rapid and accurate optimal solutions in several fields, such as in biomedical and environmental sciences. In this work, we employ a POD-Galerkin reduction approach over a parametrized optimality system, derived from the Karush-Kuhn-Tucker conditions. The methodology presented is tested on two boundary control problems, governed respectively by (1) time dependent Stokes equations and (2) steady non-linear Navier-Stokes equations.

%B Numerical Mathematics and Advanced Applications ENUMATH 2019 %I Springer International Publishing %C Cham %8 2021// %@ 978-3-030-55874-1 %G eng %U https://www.springerprofessional.de/en/reduced-order-methods-for-parametrized-non-linear-and-time-depen/19122676 %R https://doi.org/10.1007/978-3-030-55874-1_83 %0 Generic %D 2021 %T A remark on two notions of flatness for sets in the Euclidean space %A Ivan Yuri Violo %XIn this note we compare two ways of measuring the n-dimensional "flatness" of a set S⊂Rd, where n∈N and d>n. The first one is to consider the classical Reifenberg-flat numbers α(x,r) (x∈S, r>0), which measure the minimal scaling-invariant Hausdorff distances in Br(x) between S and n-dimensional affine subspaces of Rd. The second is an `intrinsic' approach in which we view the same set S as a metric space (endowed with the induced Euclidean distance). Then we consider numbers a(x,r)'s, that are the scaling-invariant Gromov-Hausdorff distances between balls centered at x of radius r in S and the n-dimensional Euclidean ball of the same radius. As main result of our analysis we make rigorous a phenomenon, first noted by David and Toro, for which the numbers a(x,r)'s behaves as the square of the numbers α(x,r)'s. Moreover we show how this result finds application in extending the Cheeger-Colding intrinsic-Reifenberg theorem to the biLipschitz case. As a by-product of our arguments, we deduce analogous results also for the Jones' numbers β's (i.e. the one-sided version of the numbers α's).

%G eng %0 Generic %D 2021 %T Rigidity and almost rigidity of Sobolev inequalities on compact spaces with lower Ricci curvature bounds %A Francesco Nobili %A Ivan Yuri Violo %X

We prove that if M is a closed n-dimensional Riemannian manifold, n≥3, with Ric≥n−1 and for which the optimal constant in the critical Sobolev inequality equals the one of the n-dimensional sphere Sn, then M is isometric to Sn. An almost-rigidity result is also established, saying that if equality is almost achieved, then M is close in the measure Gromov-Hausdorff sense to a spherical suspension. These statements are obtained in the RCD-setting of (possibly non-smooth) metric measure spaces satisfying synthetic lower Ricci curvature bounds.%G eng %0 Journal Article %J Revista Matematica Iberoamericana %D 2021 %T The sharp quantitative isocapacitary inequality %A Guido De Philippis %A Michele Marini %A Ekaterina Mukoseeva %K Fraenkel asymmetry %K isocapacitary inequality %K Stability estimates %X

An independent result of our analysis is the characterization of the best constant in the Sobolev inequality on any compact CD space, extending to the non-smooth setting a classical result by Aubin. Our arguments are based on a new concentration compactness result for mGH-converging sequences of RCD spaces and on a Polya-Szego inequality of Euclidean-type in CD spaces.

As an application of the technical tools developed we prove both an existence result for the Yamabe equation and the continuity of the generalized Yamabe constant under measure Gromov-Hausdorff convergence, in the RCD-setting.

We prove a sharp quantitative form of the classical isocapacitary inequality. Namely, we show that the difference between the capacity of a set and that of a ball with the same volume bounds the square of the Fraenkel asymmetry of the set. This provides a positive answer to a conjecture of Hall, Hayman, and Weitsman (J. Analyse Math.'91). © 2021 Real Sociedad Matemática Española

%B Revista Matematica Iberoamericana %V 37 %P 2191 - 2228 %8 2021 %@ 02132230 (ISSN) %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85104691573&doi=10.4171%2frmi%2f1259&partnerID=40&md5=5f88bc37b87a9eea7a502ea63523ff57 %N 6 %! Rev. Mat. Iberoam. %0 Journal Article %J Advances in Calculus of Variations %D 2021 %T The sharp quantitative isocapacitary inequality (the case of p-capacity) %A Ekaterina Mukoseeva %K isocapacitary inequality %K Stability estimates %XWe prove a sharp quantitative form of isocapacitary inequality in the case of a general p. This work is a generalization of the author's paper with Guido De Philippis and Michele Marini, where we treated the case of 2-capacity. © 2021 Walter de Gruyter GmbH, Berlin/Boston 2021.

%B Advances in Calculus of Variations %8 2021 %@ 18648258 (ISSN) %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85106363307&doi=10.1515%2facv-2020-0106&partnerID=40&md5=26dbcad781b68c1d873512e272f0e7f4 %! Adv. Calc. Var. %0 Journal Article %J SIAM Journal on Scientific Computing %D 2021 %T A supervised learning approach involving active subspaces for an efficient genetic algorithm in high-dimensional optimization problems %A Nicola Demo %A Marco Tezzele %A Gianluigi Rozza %XIn this work, we present an extension of the genetic algorithm (GA) which exploits the active subspaces (AS) property to evolve the individuals on a lower dimensional space. In many cases, GA requires in fact more function evaluations than others optimization method to converge to the optimum. Thus, complex and high-dimensional functions may result intractable with the standard algorithm. To address this issue, we propose to linearly map the input parameter space of the original function onto its AS before the evolution, performing the mutation and mate processes in a lower dimensional space. In this contribution, we describe the novel method called ASGA, presenting differences and similarities with the standard GA method. We test the proposed method over n-dimensional benchmark functions – Rosenbrock, Ackley, Bohachevsky, Rastrigin, Schaffer N. 7, and Zakharov – and finally we apply it to an aeronautical shape optimization problem.

%B SIAM Journal on Scientific Computing %V 43 %G eng %U https://arxiv.org/abs/2006.07282 %N 3 %& B831 %R https://doi.org/10.1137/20M1345219 %0 Journal Article %D 2021 %T Traveling Quasi-periodic Water Waves with Constant Vorticity %A Massimiliano Berti %A Luca Franzoi %A Alberto Maspero %XWe prove the first bifurcation result of time quasi-periodic traveling wave solutions for space periodic water waves with vorticity. In particular, we prove the existence of small amplitude time quasi-periodic solutions of the gravity-capillary water waves equations with constant vorticity, for a bidimensional fluid over a flat bottom delimited by a space-periodic free interface. These quasi-periodic solutions exist for all the values of depth, gravity and vorticity, and restrict the surface tension to a Borel set of asymptotically full Lebesgue measure.

%V 240 %P 99 - 202 %8 2021/04/01 %@ 1432-0673 %G eng %U https://doi.org/10.1007/s00205-021-01607-w %N 1 %! Archive for Rational Mechanics and Analysis %0 Journal Article %D 2021 %T A vanishing-inertia analysis for finite-dimensional rate-independent systems with nonautonomous dissipation and an application to soft crawlers %A Paolo Gidoni %A Filippo Riva %XWe study the approximation of finite-dimensional rate-independent quasistatic systems, via a vanishing-inertia asymptotic analysis of dynamic evolutions. We prove the uniform convergence of dynamic solutions to a rate-independent one, employing the variational concept of energetic solution. Motivated by applications in soft locomotion, we allow time-dependence of the dissipation potential, and translation invariance of the potential energy.

%V 60 %P 191 %8 2021/08/03 %@ 1432-0835 %G eng %U https://doi.org/10.1007/s00526-021-02067-6 %N 5 %! Calculus of Variations and Partial Differential Equations %0 Journal Article %J Computers and Mathematics with Applications %D 2021 %T A weighted POD-reduction approach for parametrized PDE-constrained optimal control problems with random inputs and applications to environmental sciences %A G. Carere %A Maria Strazzullo %A Francesco Ballarin %A Gianluigi Rozza %A R. Stevenson %B Computers and Mathematics with Applications %V 102 %P 261-276 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85117948561&doi=10.1016%2fj.camwa.2021.10.020&partnerID=40&md5=cb57d59a6975a35315b2cf5d0e3a6001 %R 10.1016/j.camwa.2021.10.020 %0 Journal Article %J Advanced Nonlinear Studies %D 2021 %T Well-Ordered and Non-Well-Ordered Lower and Upper Solutions for Periodic Planar Systems %A Alessandro Fonda %A Giuliano Klun %A Andrea Sfecci %B Advanced Nonlinear Studies %V 21 %P 397 - 419 %8 2021 %G eng %U https://doi.org/10.1515/ans-2021-2117 %N 2 %0 Conference Paper %B Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018 %D 2020 %T Advances in reduced order methods for parametric industrial problems in computational fluid dynamics %A Gianluigi Rozza %A M.H. Malik %A Nicola Demo %A Marco Tezzele %A Michele Girfoglio %A Giovanni Stabile %A Andrea Mola %XReduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of model order reduction techniques in various engineering and scientific applications including but not limited to mechanical, naval and aeronautical engineering. The focus here is kept limited to computational fluid mechanics and related applications. The advances in the reduced order modeling with proper orthogonal decomposition and reduced basis method are presented as well as a brief discussion of dynamic mode decomposition and also some present advances in the parameter space reduction. Here, an overview of the challenges faced and possible solutions are presented with examples from various problems.

%B Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075395686&partnerID=40&md5=fb0b1a3cfdfd35a104db9921bc9be675 %0 Journal Article %D 2020 %T On the Approximation of Quasistatic Evolutions for the Debonding of a Thin Film via Vanishing Inertia and Viscosity %A Filippo Riva %XIn this paper, we contribute to studying the issue of quasistatic limit in the context of Griffith’s theory by investigating a one-dimensional debonding model. It describes the evolution of a thin film partially glued to a rigid substrate and subjected to a vertical loading. Taking viscosity into account and under suitable assumptions on the toughness of the glue, we prove that, in contrast to what happens in the undamped case, dynamic solutions converge to the quasistatic one when inertia and viscosity go to zero, except for a possible discontinuity at the initial time. We then characterise the size of the jump by means of an asymptotic analysis of the debonding front.

%V 30 %P 903 - 951 %8 2020/06/01 %@ 1432-1467 %G eng %U https://doi.org/10.1007/s00332-019-09595-8 %N 3 %! Journal of Nonlinear Science %0 Book Section %B Model Order Reduction, Volume 2 Snapshot-Based Methods and Algorithms %D 2020 %T Basic ideas and tools for projection-based model reduction of parametric partial differential equations %A Gianluigi Rozza %A Martin W. Hess %A Giovanni Stabile %A Marco Tezzele %A F. Ballarin %B Model Order Reduction, Volume 2 Snapshot-Based Methods and Algorithms %I De Gruyter %C Berlin, Boston %P 1 - 47 %@ 9783110671490 %G eng %U https://www.degruyter.com/view/book/9783110671490/10.1515/9783110671490-001.xml %R https://doi.org/10.1515/9783110671490-001 %0 Journal Article %J Advances in Calculus of Variations %D 2020 %T On the blow-up of GSBV functions under suitable geometric properties of the jump set %A Emanuele Tasso %B Advances in Calculus of Variations %8 2020 %G eng %U https://doi.org/10.1515/acv-2019-0068 %0 Journal Article %J Computers and Mathematics with Applications %D 2020 %T Certified Reduced Basis VMS-Smagorinsky model for natural convection flow in a cavity with variable height %A F. Ballarin %A Rebollo, T.C. %A E.D. Ávila %A Marmol, M.G. %A Gianluigi Rozza %XIn this work we present a Reduced Basis VMS-Smagorinsky Boussinesq model, applied to natural convection problems in a variable height cavity, in which the buoyancy forces are involved. We take into account in this problem both physical and geometrical parametrizations, considering the Rayleigh number as a parameter, so as the height of the cavity. We perform an Empirical Interpolation Method to approximate the sub-grid eddy viscosity term that lets us obtain an affine decomposition with respect to the parameters. We construct an a posteriori error estimator, based upon the Brezzi–Rappaz–Raviart theory, used in the greedy algorithm for the selection of the basis functions. Finally we present several numerical tests for different parameter configuration.

%B Computers and Mathematics with Applications %V 80 %P 973-989 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85085843368&doi=10.1016%2fj.camwa.2020.05.013&partnerID=40&md5=7c6596865ec89651319c7dd97159dd77 %R 10.1016/j.camwa.2020.05.013 %0 Journal Article %J ESAIM: COCV %D 2020 %T On the continuity of the trace operator in GSBV (Ω) and GSBD (Ω) %A Emanuele Tasso %B ESAIM: COCV %V 26 %8 2020/// %G eng %U https://doi.org/10.1051/cocv/2019014 %0 Journal Article %J Journal of Computational Physics %D 2020 %T Data-driven POD-Galerkin reduced order model for turbulent flows %A Saddam Hijazi %A Giovanni Stabile %A Andrea Mola %A Gianluigi Rozza %XIn this work we present a Reduced Order Model which is specifically designed to deal with turbulent flows in a finite volume setting. The method used to build the reduced order model is based on the idea of merging/combining projection-based techniques with data-driven reduction strategies. In particular, the work presents a mixed strategy that exploits a data-driven reduction method to approximate the eddy viscosity solution manifold and a classical POD-Galerkin projection approach for the velocity and the pressure fields, respectively. The newly proposed reduced order model has been validated on benchmark test cases in both steady and unsteady settings with Reynolds up to $Re=O(10^5)$.

%B Journal of Computational Physics %V 416 %P 109513 %G eng %U https://arxiv.org/abs/1907.09909 %R 10.1016/j.jcp.2020.109513 %0 Journal Article %D 2020 %T A dynamic model for viscoelastic materials with prescribed growing cracks %A Maicol Caponi %A Francesco Sapio %XIn this paper, we prove the existence of solutions for a class of viscoelastic dynamic systems on time-dependent cracked domains, with possibly degenerate viscosity coefficients. Under stronger regularity assumptions, we also show a uniqueness result. Finally, we exhibit an example where the energy-dissipation balance is not satisfied, showing there is an additional dissipation due to the crack growth.

%V 199 %P 1263 - 1292 %8 2020/08/01 %@ 1618-1891 %G eng %U https://doi.org/10.1007/s10231-019-00921-1 %N 4 %! Annali di Matematica Pura ed Applicata (1923 -) %0 Journal Article %J Advances in Computational Mathematics %D 2020 %T Efficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method %A Moreno Pintore %A Federico Pichi %A Martin W. Hess %A Gianluigi Rozza %A Claudio Canuto %XThe majority of the most common physical phenomena can be described using partial differential equations (PDEs). However, they are very often characterized by strong nonlinearities. Such features lead to the coexistence of multiple solutions studied by the bifurcation theory. Unfortunately, in practical scenarios, one has to exploit numerical methods to compute the solutions of systems of PDEs, even if the classical techniques are usually able to compute only a single solution for any value of a parameter when more branches exist. In this work we implemented an elaborated deflated continuation method, that relies on the spectral element method (SEM) and on the reduced basis (RB) one, to efficiently compute bifurcation diagrams with more parameters and more bifurcation points. The deflated continuation method can be obtained combining the classical continuation method and the deflation one: the former is used to entirely track each known branch of the diagram, while the latter is exploited to discover the new ones. Finally, when more than one parameter is considered, the efficiency of the computation is ensured by the fact that the diagrams can be computed during the online phase while, during the offline one, one only has to compute one-dimensional diagrams. In this work, after a more detailed description of the method, we will show the results that can be obtained using it to compute a bifurcation diagram associated with a problem governed by the Navier-Stokes equations.

%B Advances in Computational Mathematics %G eng %U https://arxiv.org/abs/1912.06089 %0 Journal Article %J International Journal for Numerical Methods in Engineering %D 2020 %T Efficient Geometrical parametrization for finite-volume based reduced order methods %A Giovanni Stabile %A Matteo Zancanaro %A Gianluigi Rozza %XIn this work, we present an approach for the efficient treatment of parametrized geometries in the context of POD-Galerkin reduced order methods based on Finite Volume full order approximations. On the contrary to what is normally done in the framework of finite element reduced order methods, different geometries are not mapped to a common reference domain: the method relies on basis functions defined on an average deformed configuration and makes use of the Discrete Empirical Interpolation Method (D-EIM) to handle together non-affinity of the parametrization and non-linearities. In the first numerical example, different mesh motion strategies, based on a Laplacian smoothing technique and on a Radial Basis Function approach, are analyzed and compared on a heat transfer problem. Particular attention is devoted to the role of the non-orthogonal correction. In the second numerical example the methodology is tested on a geometrically parametrized incompressible Navier–Stokes problem. In this case, the reduced order model is constructed following the same segregated approach used at the full order level

%B International Journal for Numerical Methods in Engineering %V 121 %P 2655-2682 %G eng %U https://arxiv.org/abs/1901.06373 %R 10.1002/nme.6324 %0 Conference Paper %B Lecture Notes in Computational Science and Engineering %D 2020 %T The Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: from Laminar to Turbulent Flows %A Saddam Hijazi %A Shafqat Ali %A Giovanni Stabile %A F. Ballarin %A Gianluigi Rozza %XWe present in this double contribution two different reduced order strategies for incompressible parameterized Navier-Stokes equations characterized by varying Reynolds numbers. The first strategy deals with low Reynolds number (laminar flow) and is based on a stabilized finite element method during the offline stage followed by a Galerkin projection on reduced basis spaces generated by a greedy algorithm. The second methodology is based on a full order finite volume discretization. The latter methodology will be used for flows with moderate to high Reynolds number characterized by turbulent patterns. For the treatment of the mentioned turbulent flows at the reduced order level, a new POD-Galerkin approach is proposed. The new approach takes into consideration the contribution of the eddy viscosity also during the online stage and is based on the use of interpolation. The two methodologies are tested on classic benchmark test cases.

%B Lecture Notes in Computational Science and Engineering %I Springer International Publishing %C Cham %P 245–264 %@ 978-3-030-30705-9 %G eng %R 10.1007/978-3-030-30705-9_22 %0 Journal Article %D 2020 %T Energy-dissipation balance of a smooth moving crack %A Maicol Caponi %A Ilaria Lucardesi %A Emanuele Tasso %K Energy-dissipation balance %K Fracture dynamics %K Wave equation in time-dependent domains %XIn this paper we provide necessary and sufficient conditions in order to guarantee the energy-dissipation balance of a Mode III crack, growing on a prescribed smooth path. Moreover, we characterize the singularity of the displacement near the crack tip, generalizing the result in [10] valid for straight fractures.

%V 483 %P 123656 %8 2020/03/15/ %@ 0022-247X %G eng %U https://www.sciencedirect.com/science/article/pii/S0022247X19309242 %N 2 %! Journal of Mathematical Analysis and Applications %0 Journal Article %J Advanced Modeling and Simulation in Engineering Sciences %D 2020 %T Enhancing CFD predictions in shape design problems by model and parameter space reduction %A Marco Tezzele %A Nicola Demo %A Giovanni Stabile %A Andrea Mola %A Gianluigi Rozza %XIn this work we present an advanced computational pipeline for the approximation and prediction of the lift coefficient of a parametrized airfoil profile. The non-intrusive reduced order method is based on dynamic mode decomposition (DMD) and it is coupled with dynamic active subspaces (DyAS) to enhance the future state prediction of the target function and reduce the parameter space dimensionality. The pipeline is based on high-fidelity simulations carried out by the application of finite volume method for turbulent flows, and automatic mesh morphing through radial basis functions interpolation technique. The proposed pipeline is able to save 1/3 of the overall computational resources thanks to the application of DMD. Moreover exploiting DyAS and performing the regression on a lower dimensional space results in the reduction of the relative error in the approximation of the time-varying lift coefficient by a factor 2 with respect to using only the DMD.

%B Advanced Modeling and Simulation in Engineering Sciences %V 7 %G eng %U https://arxiv.org/abs/2001.05237 %N 40 %R https://doi.org/10.1186/s40323-020-00177-y %0 Journal Article %D 2020 %T Existence of solutions to a phase–field model of dynamic fracture with a crack–dependent dissipation %A Maicol Caponi %XWe propose a phase–field model of dynamic fracture based on the Ambrosio–Tortorelli’s approximation, which takes into account dissipative effects due to the speed of the crack tips. By adapting the time discretization scheme contained in Larsen et al. (Math Models Methods Appl Sci 20:1021–1048, 2010), we show the existence of a dynamic crack evolution satisfying an energy–dissipation balance, according to Griffith’s criterion. Finally, we analyze the dynamic phase–field model of Bourdin et al. (Int J Fract 168:133–143, 2011) and Larsen (in: Hackl (ed) IUTAM symposium on variational concepts with applications to the mechanics of materials, IUTAM Bookseries, vol 21. Springer, Dordrecht, 2010, pp 131–140) with no dissipative terms.

%V 27 %P 14 %8 2020/02/11 %@ 1420-9004 %G eng %U https://doi.org/10.1007/s00030-020-0617-z %N 2 %! Nonlinear Differential Equations and Applications NoDEA %0 Journal Article %J Annali di Matematica Pura ed Applicata (1923 -) %D 2020 %T On functions having coincident p-norms %A Giuliano Klun %XIn a measure space $(X,{\mathcal {A}},\mu )$, we consider two measurable functions $f,g:E\rightarrow {\mathbb {R}}$, for some $E\in {\mathcal {A}}$. We prove that the property of having equal p-norms when p varies in some infinite set $P\subseteq [1,+\infty )$ is equivalent to the following condition: $\begin{aligned} \mu (\{x\in E:|f(x)|>\alpha \})=\mu (\{x\in E:|g(x)|>\alpha \})\quad \text { for all } \alpha \ge 0. \end{aligned}$

%B Annali di Matematica Pura ed Applicata (1923 -) %V 199 %P 955-968 %G eng %U https://doi.org/10.1007/s10231-019-00907-z %R 10.1007/s10231-019-00907-z %0 Journal Article %J Computers & Fluids %D 2020 %T A hybrid reduced order method for modelling turbulent heat transfer problems %A Sokratia Georgaka %A Giovanni Stabile %A Kelbij Star %A Gianluigi Rozza %A Michael J. Bluck %XA 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 Book %D 2020 %T Kernel-based Active Subspaces with application to CFD parametric problems using Discontinuous Galerkin method %A Francesco Romor %A Marco Tezzele %A Lario, Andrea %A Gianluigi Rozza %G eng %0 Journal Article %J Mathematics in Engineering %D 2020 %T MicroMotility: State of the art, recent accomplishments and perspectives on the mathematical modeling of bio-motility at microscopic scales %A Daniele Agostinelli %A Roberto Cerbino %A Del Alamo, Juan C %A Antonio DeSimone %A Stephanie Höhn %A Cristian Micheletti %A Giovanni Noselli %A Eran Sharon %A Julia Yeomans %K active matter %K adhesive locomotion %K cell motility %K cell sheet folding %K knotted DNA %K topological defects %K unicellular swimmers %K unjamming transition %XMathematical modeling and quantitative study of biological motility (in particular, of motility at microscopic scales) is producing new biophysical insight and is offering opportunities for new discoveries at the level of both fundamental science and technology. These range from the explanation of how complex behavior at the level of a single organism emerges from body architecture, to the understanding of collective phenomena in groups of organisms and tissues, and of how these forms of swarm intelligence can be controlled and harnessed in engineering applications, to the elucidation of processes of fundamental biological relevance at the cellular and sub-cellular level. In this paper, some of the most exciting new developments in the fields of locomotion of unicellular organisms, of soft adhesive locomotion across scales, of the study of pore translocation properties of knotted DNA, of the development of synthetic active solid sheets, of the mechanics of the unjamming transition in dense cell collectives, of the mechanics of cell sheet folding in volvocalean algae, and of the self-propulsion of topological defects in active matter are discussed. For each of these topics, we provide a brief state of the art, an example of recent achievements, and some directions for future research.

%B Mathematics in Engineering %V 2 %P 230 %G eng %U http://dx.doi.org/10.3934/mine.2020011 %9 Perspective %R 10.3934/mine.2020011 %0 Generic %D 2020 %T MicroROM: An Efficient and Accurate Reduced Order Method to Solve Many-Query Problems in Micro-Motility %A Nicola Giuliani %A Martin W. Hess %A Antonio DeSimone %A Gianluigi Rozza %K FOS: Mathematics %K Numerical Analysis (math.NA) %G eng %U https://arxiv.org/abs/2006.13836 %R 10.48550/ARXIV.2006.13836 %0 Generic %D 2020 %T Minimality of the ball for a model of charged liquid droplets %A Ekaterina Mukoseeva %A Giulia Vescovo %G eng %0 Book Section %B Quantification of Uncertainty: Improving Efficiency and Technology: QUIET selected contributions %D 2020 %T Non-intrusive Polynomial Chaos Method Applied to Full-Order and Reduced Problems in Computational Fluid Dynamics: A Comparison and Perspectives %A Saddam Hijazi %A Giovanni Stabile %A Andrea Mola %A Gianluigi Rozza %XIn this work, Uncertainty Quantification (UQ) based on non-intrusive Polynomial Chaos Expansion (PCE) is applied to the CFD problem of the flow past an airfoil with parameterized angle of attack and inflow velocity. To limit the computational cost associated with each of the simulations required by the non-intrusive UQ algorithm used, we resort to a Reduced Order Model (ROM) based on Proper Orthogonal Decomposition (POD)-Galerkin approach. A first set of results is presented to characterize the accuracy of the POD-Galerkin ROM developed approach with respect to the Full Order Model (FOM) solver (OpenFOAM). A further analysis is then presented to assess how the UQ results are affected by substituting the FOM predictions with the surrogate ROM ones.

%B Quantification of Uncertainty: Improving Efficiency and Technology: QUIET selected contributions %I Springer International Publishing %C Cham %P 217–240 %@ 978-3-030-48721-8 %G eng %U https://doi.org/10.1007/978-3-030-48721-8_10 %R 10.1007/978-3-030-48721-8_10 %0 Journal Article %J NONLINEAR ANALYSIS %D 2020 %T Periodic solutions of nearly integrable Hamiltonian systems bifurcating from infinite-dimensional tori %A Alessandro Fonda %A Giuliano Klun %A Andrea Sfecci %XWe prove the existence of periodic solutions of some infinite-dimensional nearly integrable Hamiltonian systems, bifurcating from infinite-dimensional tori, by the use of a generalization of the Poincaré–Birkhoff Theorem.

%B NONLINEAR ANALYSIS %G eng %U https://doi.org/10.1016/j.na.2019.111720 %R 10.1016/j.na.2019.111720 %0 Unpublished Work %D 2020 %T POD-Galerkin Model Order Reduction for Parametrized Nonlinear Time Dependent Optimal Flow Control: an Application to Shallow Water Equations %A Maria Strazzullo %A F. Ballarin %A Gianluigi Rozza %XIn this work we propose reduced order methods as a reliable strategy to efficiently solve parametrized optimal control problems governed by shallow waters equations in a solution tracking setting. The physical parametrized model we deal with is nonlinear and time dependent: this leads to very time consuming simulations which can be unbearable e.g. in a marine environmental monitoring plan application. Our aim is to show how reduced order modelling could help in studying different configurations and phenomena in a fast way. After building the optimality system, we rely on a POD-Galerkin reduction in order to solve the optimal control problem in a low dimensional reduced space. The presented theoretical framework is actually suited to general nonlinear time dependent optimal control problems. The proposed methodology is finally tested with a numerical experiment: the reduced optimal control problem governed by shallow waters equations reproduces the desired velocity and height profiles faster than the standard model, still remaining accurate.

%G eng %0 Journal Article %J Journal of Scientific Computing %D 2020 %T POD–Galerkin Model Order Reduction for Parametrized Time Dependent Linear Quadratic Optimal Control Problems in Saddle Point Formulation %A Maria Strazzullo %A F. Ballarin %A Gianluigi Rozza %XIn this work we deal with parametrized time dependent optimal control problems governed by partial differential equations. We aim at extending the standard saddle point framework of steady constraints to time dependent cases. We provide an analysis of the well-posedness of this formulation both for parametrized scalar parabolic constraint and Stokes governing equations and we propose reduced order methods as an effective strategy to solve them. Indeed, on one hand, parametrized time dependent optimal control is a very powerful mathematical model which is able to describe several physical phenomena, on the other, it requires a huge computational effort. Reduced order methods are a suitable approach to have rapid and accurate simulations. We rely on POD–Galerkin reduction over the physical and geometrical parameters of the optimality system in a space-time formulation. Our theoretical results and our methodology are tested on two examples: a boundary time dependent optimal control for a Graetz flow and a distributed optimal control governed by time dependent Stokes equations. With these two test cases the convenience of the reduced order modelling is further extended to the field of time dependent optimal control.

%B Journal of Scientific Computing %V 83 %G eng %R 10.1007/s10915-020-01232-x %0 Journal Article %J Computers and Mathematics with Applications %D 2020 %T POD–Galerkin reduced order methods for combined Navier–Stokes transport equations based on a hybrid FV-FE solver %A S. Busto %A Giovanni Stabile %A Gianluigi Rozza %A M.E. Vázquez-Cendón %XThe purpose of this work is to introduce a novel POD–Galerkin strategy for the semi-implicit hybrid high order finite volume/finite element solver introduced in Bermúdez et al. (2014) and Busto et al. (2018). The interest is into the incompressible Navier–Stokes equations coupled with an additional transport equation. The full order model employed in this article makes use of staggered meshes. This feature will be conveyed to the reduced order model leading to the definition of reduced basis spaces in both meshes. The reduced order model presented herein accounts for velocity, pressure, and a transport-related variable. The pressure term at both the full order and the reduced order level is reconstructed making use of a projection method. More precisely, a Poisson equation for pressure is considered within the reduced order model. Results are verified against three-dimensional manufactured test cases. Moreover a modified version of the classical cavity test benchmark including the transport of a species is analysed.

%B Computers and Mathematics with Applications %V 79 %P 256-273 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85068068567&doi=10.1016%2fj.camwa.2019.06.026&partnerID=40&md5=a8dcce1b53b8ee872d174bbc4c20caa3 %R 10.1016/j.camwa.2019.06.026 %0 Journal Article %J Computers and Mathematics with Applications %D 2020 %T Projection-based reduced order models for a cut finite element method in parametrized domains %A Efthymios N Karatzas %A F. Ballarin %A Gianluigi Rozza %XThis work presents a reduced order modeling technique built on a high fidelity embedded mesh finite element method. Such methods, and in particular the CutFEM method, are attractive in the generation of projection-based reduced order models thanks to their capabilities to seamlessly handle large deformations of parametrized domains and in general to handle topological changes. The combination of embedded methods and reduced order models allows us to obtain fast evaluation of parametrized problems, avoiding remeshing as well as the reference domain formulation, often used in the reduced order modeling for boundary fitted finite element formulations. The resulting novel methodology is presented on linear elliptic and Stokes problems, together with several test cases to assess its capability. The role of a proper extension and transport of embedded solutions to a common background is analyzed in detail.

%B Computers and Mathematics with Applications %V 79 %P 833-851 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85070900852&doi=10.1016%2fj.camwa.2019.08.003&partnerID=40&md5=2d222ab9c7832955d155655d3c93e1b1 %R 10.1016/j.camwa.2019.08.003 %0 Journal Article %J International Journal of Computational Fluid Dynamics %D 2020 %T Reduced Basis Model Order Reduction for Navier-Stokes equations in domains with walls of varying curvature %A Martin W. Hess %A Annalisa Quaini %A Gianluigi Rozza %XWe consider the Navier-Stokes equations in a channel with a narrowing and walls of varying curvature. By applying the empirical interpolation method to generate an affine parameter dependency, the offline-online procedure can be used to compute reduced order solutions for parameter variations. The reduced order space is computed from the steady-state snapshot solutions by a standard POD procedure. The model is discretised with high-order spectral element ansatz functions, resulting in 4752 degrees of freedom. The proposed reduced order model produces accurate approximations of steady-state solutions for a wide range of geometries and kinematic viscosity values. The application that motivated the present study is the onset of asymmetries (i.e., symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the valve shape. Through our computational study, we found that the critical Reynolds number for the symmetry breaking increases as the wall curvature increases.

%B International Journal of Computational Fluid Dynamics %V 34 %P 119-126 %G eng %U https://arxiv.org/abs/1901.03708 %R 10.1080/10618562.2019.1645328 %0 Journal Article %J International Journal of Computational Fluid Dynamics %D 2020 %T Reduced basis model order reduction for Navier–Stokes equations in domains with walls of varying curvature %A Martin W. Hess %A Annalisa Quaini %A Gianluigi Rozza %XWe consider the Navier–Stokes equations in a channel with a narrowing and walls of varying curvature. By applying the empirical interpolation method to generate an affine parameter dependency, the offline-online procedure can be used to compute reduced order solutions for parameter variations. The reduced-order space is computed from the steady-state snapshot solutions by a standard POD procedure. The model is discretised with high-order spectral element ansatz functions, resulting in 4752 degrees of freedom. The proposed reduced-order model produces accurate approximations of steady-state solutions for a wide range of geometries and kinematic viscosity values. The application that motivated the present study is the onset of asymmetries (i.e. symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the valve shape. Through our computational study, we found that the critical Reynolds number for the symmetry breaking increases as the wall curvature increases.

%B International Journal of Computational Fluid Dynamics %V 34 %P 119-126 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85085233294&doi=10.1080%2f10618562.2019.1645328&partnerID=40&md5=e2ed8f24c66376cdc8b5485aa400efb0 %R 10.1080/10618562.2019.1645328 %0 Conference Paper %B IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22–25, 2018 %D 2020 %T A Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries %A Efthymios N Karatzas %A Giovanni Stabile %A Nabib Atallah %A Guglielmo Scovazzi %A Gianluigi Rozza %E Fehr, Jörg %E Bernard Haasdonk %XA model order reduction technique is combined with an embedded boundary finite element method with a POD-Galerkin strategy. The proposed methodology is applied to parametrized heat transfer problems and we rely on a sufficiently refined shape-regular background mesh to account for parametrized geometries. In particular, the employed embedded boundary element method is the Shifted Boundary Method (SBM) recently proposed. This approach is based on the idea of shifting the location of true boundary conditions to a surrogate boundary, with the goal of avoiding cut cells near the boundary of the computational domain. This combination of methodologies has multiple advantages. In the first place, since the Shifted Boundary Method always relies on the same background mesh, there is no need to update the discretized parametric domain. Secondly, we avoid the treatment of cut cell elements, which usually need particular attention. Thirdly, since the whole background mesh is considered in the reduced basis construction, the SBM allows for a smooth transition of the reduced modes across the immersed domain boundary. The performances of the method are verified in two dimensional heat transfer numerical examples.

%B IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22–25, 2018 %I Springer International Publishing %G eng %U https://arxiv.org/abs/1807.07753 %R 10.1007/978-3-030-21013-7_8 %0 Journal Article %J Lecture Notes in Computational Science and Engineering %D 2020 %T Reduced order isogeometric analysis approach for pdes in parametrized domains %A Fabrizio Garotta %A Nicola Demo %A Marco Tezzele %A Massimo Carraturo %A Alessandro Reali %A Gianluigi Rozza %XIn this contribution, we coupled the isogeometric analysis to a reduced order modelling technique in order to provide a computationally efficient solution in parametric domains. In details, we adopt the free-form deformation method to obtain the parametric formulation of the domain and proper orthogonal decomposition with interpolation for the computational reduction of the model. This technique provides a real-time solution for any parameter by combining several solutions, in this case computed using isogeometric analysis on different geometrical configurations of the domain, properly mapped into a reference configuration. We underline that this reduced order model requires only the full-order solutions, making this approach non-intrusive. We present in this work the results of the application of this methodology to a heat conduction problem inside a deformable collector pipe.

%B Lecture Notes in Computational Science and Engineering %V 137 %P 153-170 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85089615035&doi=10.1007%2f978-3-030-48721-8_7&partnerID=40&md5=7b15836ae65fa28dcfe8733788d7730c %R 10.1007/978-3-030-48721-8_7 %0 Journal Article %J International Journal for Numerical Methods in Biomedical EngineeringInternational Journal for Numerical Methods in Biomedical EngineeringInt J Numer Meth Biomed Engng %D 2020 %T Reduced order methods for parametric optimal flow control in coronary bypass grafts, toward patient-specific data assimilation %A Zakia Zainib %A F. Ballarin %A Stephen E. Fremes %A Piero Triverio %A Laura Jiménez-Juan %A Gianluigi Rozza %K coronary artery bypass grafts %K data assimilation %K flow control %K Galerkin methods %K hemodynamics modeling %K Optimization %K patient-specific simulations %K Proper orthogonal decomposition %K reduced order methods %XAbstract Coronary artery bypass grafts (CABG) surgery is an invasive procedure performed to circumvent partial or complete blood flow blockage in coronary artery disease. In this work, we apply a numerical optimal flow control model to patient-specific geometries of CABG, reconstructed from clinical images of real-life surgical cases, in parameterized settings. The aim of these applications is to match known physiological data with numerical hemodynamics corresponding to different scenarios, arisen by tuning some parameters. Such applications are an initial step toward matching patient-specific physiological data in patient-specific vascular geometries as best as possible. Two critical challenges that reportedly arise in such problems are: (a) lack of robust quantification of meaningful boundary conditions required to match known data as best as possible and (b) high computational cost. In this work, we utilize unknown control variables in the optimal flow control problems to take care of the first challenge. Moreover, to address the second challenge, we propose a time-efficient and reliable computational environment for such parameterized problems by projecting them onto a low-dimensional solution manifold through proper orthogonal decomposition-Galerkin.

%B International Journal for Numerical Methods in Biomedical EngineeringInternational Journal for Numerical Methods in Biomedical EngineeringInt J Numer Meth Biomed Engng %V n/a %P e3367 %8 2020/05/27 %@ 2040-7939 %G eng %U https://onlinelibrary.wiley.com/doi/10.1002/cnm.3367?af=R %N n/a %! International Journal for Numerical Methods in Biomedical Engineering %R https://doi.org/10.1002/cnm.3367 %0 Journal Article %J SIAM Journal on Scientific Computing %D 2020 %T A reduced order modeling technique to study bifurcating phenomena: Application to the gross-pitaevskii equation %A Federico Pichi %A Annalisa Quaini %A Gianluigi Rozza %XWe propose a computationally efficient framework to treat nonlinear partial differential equations having bifurcating solutions as one or more physical control parameters are varied. Our focus is on steady bifurcations. Plotting a bifurcation diagram entails computing multiple solutions of a parametrized, nonlinear problem, which can be extremely expensive in terms of computational time. In order to reduce these demanding computational costs, our approach combines a continuation technique and Newton's method with a reduced order modeling (ROM) technique, suitably supplemented with a hyperreduction method. To demonstrate the effectiveness of our ROM approach, we trace the steady solution branches of a nonlinear Schrödinger equation, called the Gross{Pitaevskii equation, as one or two physical parameters are varied. In the two-parameter study, we show that our approach is 60 times faster in constructing a bifurcation diagram than a standard full order method.

%B SIAM Journal on Scientific Computing %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85096768803&doi=10.1137%2f20M1313106&partnerID=40&md5=47d6012d10854c2f9a04b9737f870592 %R 10.1137/20M1313106 %0 Journal Article %J SIAM Journal on Scientific Computing %D 2020 %T A Reduced Order technique to study bifurcating phenomena: application to the Gross-Pitaevskii equation %A Federico Pichi %A Annalisa Quaini %A Gianluigi Rozza %XWe propose a computationally efficient framework to treat nonlinear partial differential equations having bifurcating solutions as one or more physical control parameters are varied. Our focus is on steady bifurcations. Plotting a bifurcation diagram entails computing multiple solutions of a parametrized, nonlinear problem, which can be extremely expensive in terms of computational time. In order to reduce these demanding computational costs, our approach combines a continuation technique and Newton's method with a Reduced Order Modeling (ROM) technique, suitably supplemented with a hyper-reduction method. To demonstrate the effectiveness of our ROM approach, we trace the steady solution branches of a nonlinear Schrödinger equation, called Gross-Pitaevskii equation, as one or two physical parameters are varied. In the two parameter study, we show that our approach is 60 times faster in constructing a bifurcation diagram than a standard Full Order Method.

%B SIAM Journal on Scientific Computing %G eng %U https://arxiv.org/abs/1907.07082 %R https://doi.org/10.1137/20M1313106 %0 Journal Article %J Computer Methods in Applied Mechanics and Engineering %D 2020 %T A reduced-order shifted boundary method for parametrized incompressible Navier–Stokes equations %A Efthymios N Karatzas %A Giovanni Stabile %A Leo Nouveau %A Guglielmo Scovazzi %A Gianluigi Rozza %XWe investigate a projection-based reduced order model of the steady incompressible Navier–Stokes equations for moderate Reynolds numbers. In particular, we construct an “embedded” reduced basis space, by applying proper orthogonal decomposition to the Shifted Boundary Method, a high-fidelity embedded method recently developed. We focus on the geometrical parametrization through level-set geometries, using a fixed Cartesian background geometry and the associated mesh. This approach avoids both remeshing and the development of a reference domain formulation, as typically done in fitted mesh finite element formulations. Two-dimensional computational examples for one and three parameter dimensions are presented to validate the convergence and the efficacy of the proposed approach.

%B Computer Methods in Applied Mechanics and Engineering %V 370 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85087886522&doi=10.1016%2fj.cma.2020.113273&partnerID=40&md5=d864e4808190b682ecb1c8b27cda72d8 %R 10.1016/j.cma.2020.113273 %0 Journal Article %J International Journal of Computational Fluid Dynamics %D 2020 %T Special Issue on Reduced Order Models in CFD %A Simona Perotto %A Gianluigi Rozza %B International Journal of Computational Fluid Dynamics %V 34 %P 91-92 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85084258805&doi=10.1080%2f10618562.2020.1756497&partnerID=40&md5=d9316aad9ba95f244e07379318ebbcba %R 10.1080/10618562.2020.1756497 %0 Journal Article %J Lecture Notes in Computational Science and Engineering %D 2020 %T A spectral element reduced basis method for navier–stokes equations with geometric variations %A Martin W. Hess %A Annalisa Quaini %A Gianluigi Rozza %XWe consider the Navier-Stokes equations in a channel with a narrowing of varying height. The model is discretized with high-order spectral element ansatz functions, resulting in 6372 degrees of freedom. The steady-state snapshot solutions define a reduced order space through a standard POD procedure. The reduced order space allows to accurately and efficiently evaluate the steady-state solutions for different geometries. In particular, we detail different aspects of implementing the reduced order model in combination with a spectral element discretization. It is shown that an expansion in element-wise local degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios.

%B Lecture Notes in Computational Science and Engineering %V 134 %P 561-571 %G eng %R 10.1007/978-3-030-39647-3_45 %0 Journal Article %J Computers and Mathematics with Applications %D 2020 %T Stabilized reduced basis methods for parametrized steady Stokes and Navier–Stokes equations %A Shafqat Ali %A F. Ballarin %A Gianluigi Rozza %XIt is well known in the Reduced Basis approximation of saddle point problems that the Galerkin projection on the reduced space does not guarantee the inf–sup approximation stability even if a stable high fidelity method was used to generate snapshots. For problems in computational fluid dynamics, the lack of inf–sup stability is reflected by the inability to accurately approximate the pressure field. In this context, inf–sup stability is usually recovered through the enrichment of the velocity space with suitable supremizer functions. The main goal of this work is to propose an alternative approach, which relies on the residual based stabilization techniques customarily employed in the Finite Element literature, such as Brezzi–Pitkaranta, Franca–Hughes, streamline upwind Petrov–Galerkin, Galerkin Least Square. In the spirit of offline–online reduced basis computational splitting, two such options are proposed, namely offline-only stabilization and offline–online stabilization. These approaches are then compared to (and combined with) the state of the art supremizer enrichment approach. Numerical results are discussed, highlighting that the proposed methodology allows to obtain smaller reduced basis spaces (i.e., neglecting supremizer enrichment) for which a modified inf–sup stability is still preserved at the reduced order level.

%B Computers and Mathematics with Applications %V 80 %P 2399-2416 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85083340115&doi=10.1016%2fj.camwa.2020.03.019&partnerID=40&md5=7ace96eee080701acb04d8155008dd7d %R 10.1016/j.camwa.2020.03.019 %0 Journal Article %J Journal of the Mechanics and Physics of Solids %D 2020 %T Surface tension controls the onset of gyrification in brain organoids %A Davide Riccobelli %A Giulia Bevilacqua %K Buckling %K Embryogenesis %K Morpho-elasticity %K Post-buckling analysis %K Surface tension %XUnderstanding the mechanics of brain embryogenesis can provide insights on pathologies related to brain development, such as lissencephaly, a genetic disease which causes a reduction of the number of cerebral sulci. Recent experiments on brain organoids have confirmed that gyrification, i.e. the formation of the folded structures of the brain, is triggered by the inhomogeneous growth of the peripheral region. However, the rheology of these cellular aggregates and the mechanics of lissencephaly are still matter of debate. In this work, we develop a mathematical model of brain organoids based on the theory of morpho-elasticity. We describe them as non-linear elastic bodies, composed of a disk surrounded by a growing layer called cortex. The external boundary is subjected to a tissue surface tension due the intercellular adhesion forces. We show that the resulting surface energy is relevant at the small length scales of brain organoids and affects the mechanics of cellular aggregates. We perform a linear stability analysis of the radially symmetric configuration and we study the post-buckling behaviour through finite element simulations. We find that the process of gyrification is triggered by the cortex growth and modulated by the competition between two length scales: the radius of the organoid and the capillary length generated by surface tension. We show that a solid model can reproduce the results of the in-vitro experiments. Furthermore, we prove that the lack of brain sulci in lissencephaly is caused by a reduction of the cell stiffness: the softening of the organoid strengthens the role of surface tension, delaying or even inhibiting the onset of a mechanical instability at the free boundary.

%B Journal of the Mechanics and Physics of Solids %V 134 %P 103745 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022509619304065 %R https://doi.org/10.1016/j.jmps.2019.103745 %0 Journal Article %J Journal of Applied Mechanics %D 2020 %T A theoretical study on the transient morphing of linear poroelastic plates %A Dario Andrini %A Alessandro Lucantonio %A Giovanni Noselli %XBased on their shape-shifting capabilities, soft active materials have enabled new possibilities for the engineering of sensing and actuation devices. While the relation between active strains and emergent equilibrium shapes has been fully characterized, the transient morphing of thin structures is a rather unexplored topic. Here, we focus on polymer gel plates and derive a reduced linear model to study their time-dependent response to changes in the fluid environment. We show that independent control of stretching and bending deformations in stress-free conditions allows to realize spherical shapes with prescribed geometry of the mid-plane. Furthermore, we demonstrate that tensile (compressive) membrane stresses delay (accelerate) swelling-induced shape transitions compared to the stress-free evolution. We believe that these effects should be considered for the accurate design of smart systems and may contribute to explain the complexity of natural shapes.

%B Journal of Applied Mechanics %V 88 %8 12 %G eng %U https://doi.org/10.1115/1.4048806 %R 10.1115/1.4048806 %0 Journal Article %D 2020 %T Weak formulation of elastodynamics in domains with growing cracks %A Emanuele Tasso %XIn this paper, we formulate and study the system of elastodynamics on domains with arbitrary growing cracks. This includes homogeneous Neumann conditions on the crack sets and mixed general Dirichlet–Neumann conditions on the boundary. The only assumptions on the crack sets are to be $$(n-1)$$-rectifiable with finite surface measure, and increasing in the sense of set inclusions. In particular, they might be dense; hence, the weak formulation must fall outside the usual context of Sobolev spaces and Korn’s inequality. We prove existence of a solution for both the damped and undamped systems, while in the damped case we are also able to prove uniqueness and an energy balance.

%V 199 %P 1571 - 1595 %8 2020/08/01 %@ 1618-1891 %G eng %U https://doi.org/10.1007/s10231-019-00932-y %N 4 %! Annali di Matematica Pura ed Applicata (1923 -) %0 Journal Article %J Extreme Mech. Lett. %D 2019 %T Activation of a muscle as a mapping of stress–strain curves %A Davide Riccobelli %A D. Ambrosi %B Extreme Mech. Lett. %I Elsevier BV %V 28 %P 37–42 %G eng %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 Conference Paper %B 8th International Conference on Computational Methods in Marine Engineering, MARINE 2019 %D 2019 %T A complete data-driven framework for the efficient solution of parametric shape design and optimisation in naval engineering problems %A Nicola Demo %A Marco Tezzele %A Andrea Mola %A Gianluigi Rozza %XIn the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples of the ROM application, in the naval field, can be found in [31, 24]. Mandatory ingredient for the ROM methods is the relation between the high-fidelity solutions and the parameters. Dealing with geometrical parameters, especially in the industrial context, this relation may be unknown and not trivial (simulations over hand morphed geometries) or very complex (high number of parameters or many nested morphing techniques). To overcome these scenarios, we propose in this contribution an efficient and complete data-driven framework involving ROM techniques for shape design and optimization, extending the pipeline presented in [7]. By applying the singular value decomposition (SVD) to the points coordinates defining the hull geometry — assuming the topology is inaltered by the deformation —, we are able to compute the optimal space which the deformed geometries belong to, hence using the modal coefficients as the new parameters we can reconstruct the parametric formulation of the domain. Finally the output of interest is approximated using the proper orthogonal decomposition with interpolation technique. To conclude, we apply this framework to a naval shape design problem where the bulbous bow is morphed to reduce the total resistance of the ship advancing in calm water.

%B 8th International Conference on Computational Methods in Marine Engineering, MARINE 2019 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075342565&partnerID=40&md5=d76b8a1290053e7a84fb8801c0e6bb3d %0 Conference Paper %B VIII International Conference on Computational Methods in Marine Engineering %D 2019 %T A complete data-driven framework for the efficient solution of parametric shape design and optimisation in naval engineering problems %A Nicola Demo %A Marco Tezzele %A Andrea Mola %A Gianluigi Rozza %XIn the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples of the ROM application, in the naval field, can be found in [31, 24]. Mandatory ingredient for the ROM methods is the relation between the high-fidelity solutions and the parameters. Dealing with geometrical parameters, especially in the industrial context, this relation may be unknown and not trivial (simulations over hand morphed geometries) or very complex (high number of parameters or many nested morphing techniques). To overcome these scenarios, we propose in this contribution an efficient and complete data-driven framework involving ROM techniques for shape design and optimization, extending the pipeline presented in [7]. By applying the singular value decomposition (SVD) to the points coordinates defining the hull geometry –- assuming the topology is inaltered by the deformation –-, we are able to compute the optimal space which the deformed geometries belong to, hence using the modal coefficients as the new parameters we can reconstruct the parametric formulation of the domain. Finally the output of interest is approximated using the proper orthogonal decomposition with interpolation technique. To conclude, we apply this framework to a naval shape design problem where the bulbous bow is morphed to reduce the total resistance of the ship advancing in calm water.

%B VIII International Conference on Computational Methods in Marine Engineering %G eng %U https://arxiv.org/abs/1905.05982 %0 Report %D 2019 %T A continuous dependence result for a dynamic debonding model in dimension one %A Filippo Riva %XIn this paper we address the problem of continuous dependence on initial and boundary data for a one-dimensional debonding model describing a thin ﬁlm peeled away from a substrate. The system underlying the process couples the weakly damped wave equation with a Griﬃth’s criterion which rules the evolution of the debonded region. We show that under general convergence assumptions on the data the corresponding solutions converge to the limit one with respect to diﬀerent natural topologies.

%I SISSA %G en %U http://preprints.sissa.it/xmlui/handle/1963/35329 %1 35640 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2019-03-07T10:11:29Z No. of bitstreams: 1 PREPRINT_A continuous dependence result_Riva.pdf: 414517 bytes, checksum: 2719ac30fe4051bca0f76f6e2f603b4c (MD5) %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 8th International Conference on Computational Methods in Marine Engineering, MARINE 2019 %D 2019 %T Efficient reduction in shape parameter space dimension for ship propeller blade design %A Andrea Mola %A Marco Tezzele %A Mahmoud Gadalla %A Valdenazzi, Federica %A Grassi, Davide %A Padovan, Roberta %A Gianluigi Rozza %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 8th International Conference on Computational Methods in Marine Engineering, MARINE 2019 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075395143&partnerID=40&md5=b6aa0fcedc2f88e78c295d0f437824d0 %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 Michele Girfoglio %A Annalisa Quaini %A Gianluigi Rozza %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 Computers and Fluids %D 2019 %T A Finite Volume approximation of the Navier-Stokes equations with nonlinear filtering stabilization %A Michele Girfoglio %A Annalisa Quaini %A Gianluigi Rozza %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 EFR algorithm. 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 and Fluids %V 187 %P 27-45 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85065471890&doi=10.1016%2fj.compfluid.2019.05.001&partnerID=40&md5=c982371b5b5d4b5664a676902aaa60f4 %R 10.1016/j.compfluid.2019.05.001 %0 Journal Article %D 2019 %T Isoperimetric inequality under Measure-Contraction property %A Fabio Cavalletti %A Flavia Santarcangelo %K Isoperimetric inequality %K Measure-Contraction property %K Optimal transport %K Ricci curvature %XWe prove that if (X,d,m) is an essentially non-branching metric measure space with m(X)=1, having Ricci curvature bounded from below by K and dimension bounded above by N∈(1,∞), understood as a synthetic condition called Measure-Contraction property, then a sharp isoperimetric inequality à la Lévy-Gromov holds true. Measure theoretic rigidity is also obtained.

%V 277 %P 2893 - 2917 %8 2019/11/01/ %@ 0022-1236 %G eng %U https://www.sciencedirect.com/science/article/pii/S0022123619302289 %N 9 %! Journal of Functional Analysis %0 Journal Article %J Annales de l'Institut Henri Poincaré C, Analyse non linéaire %D 2019 %T Local well-posedness for quasi-linear NLS with large Cauchy data on the circle %A Roberto Feola %A Felice Iandoli %K Dispersive equations %K Energy method %K Local wellposedness %K NLS %K Para-differential calculus %K Quasi-linear PDEs %XWe prove local in time well-posedness for a large class of quasilinear Hamiltonian, or parity preserving, Schrödinger equations on the circle. After a paralinearization of the equation, we perform several paradifferential changes of coordinates in order to transform the system into a paradifferential one with symbols which, at the positive order, are constant and purely imaginary. This allows to obtain a priori energy estimates on the Sobolev norms of the solutions.

%B Annales de l'Institut Henri Poincaré C, Analyse non linéaire %V 36 %P 119 - 164 %G eng %U http://www.sciencedirect.com/science/article/pii/S0294144918300428 %R https://doi.org/10.1016/j.anihpc.2018.04.003 %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 Martin W. Hess %A Alla, Alessandro %A Annalisa Quaini %A Gianluigi Rozza %A Max Gunzburger %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 Computer Methods in Applied Mechanics and Engineering %D 2019 %T A localized reduced-order modeling approach for PDEs with bifurcating solutions %A Martin W. Hess %A Alla, Alessandro %A Annalisa Quaini %A Gianluigi Rozza %A Max Gunzburger %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. Although ROMs have been successfully used in many settings, ROMs built specifically for the efficient treatment of PDEs having solutions that bifurcate as the values of input parameters change have not received much attention. 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 not respect the often large differences in the PDE solutions corresponding to different subregions. In this work, we develop and test a new ROM approach specifically aimed at bifurcation problems. 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://www.scopus.com/inward/record.uri?eid=2-s2.0-85064313505&doi=10.1016%2fj.cma.2019.03.050&partnerID=40&md5=8b095034b9e539995facc7ce7bafa9e9 %R 10.1016/j.cma.2019.03.050 %0 Journal Article %J Proceedings of the Royal Society A: Mathematical, Physical and Engineering SciencesProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences %D 2019 %T A neutrally stable shell in a Stokes flow: a rotational Taylor's sheet %A Giovanni Corsi %A Antonio DeSimone %A C. Maurini %A S. Vidoli %B Proceedings of the Royal Society A: Mathematical, Physical and Engineering SciencesProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences %V 475 %P 20190178 %8 2019/07/26 %G eng %U https://doi.org/10.1098/rspa.2019.0178 %N 2227 %! Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences %0 Journal Article %J Comptes Rendus - Mecanique %D 2019 %T A non-intrusive approach for the reconstruction of POD modal coefficients through active subspaces %A Nicola Demo %A Marco Tezzele %A Gianluigi Rozza %XReduced order modeling (ROM) provides an efficient framework to compute solutions of parametric problems. Basically, it exploits a set of precomputed high-fidelity solutions—computed for properly chosen parameters, using a full-order model—in order to find the low dimensional space that contains the solution manifold. Using this space, an approximation of the numerical solution for new parameters can be computed in real-time response scenario, thanks to the reduced dimensionality of the problem. In a ROM framework, the most expensive part from the computational viewpoint is the calculation of the numerical solutions using the full-order model. Of course, the number of collected solutions is strictly related to the accuracy of the reduced order model. In this work, we aim at increasing the precision of the model also for few input solutions by coupling the proper orthogonal decomposition with interpolation (PODI)—a data-driven reduced order method—with the active subspace (AS) property, an emerging tool for reduction in parameter space. The enhanced ROM results in a reduced number of input solutions to reach the desired accuracy. In this contribution, we present the numerical results obtained by applying this method to a structural problem and in a fluid dynamics one.

%B Comptes Rendus - Mecanique %V 347 %P 873-881 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075379471&doi=10.1016%2fj.crme.2019.11.012&partnerID=40&md5=dcb27af39dc14dc8c3a4a5f681f7d84b %R https://doi.org/10.1016/j.crme.2019.11.012 %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 Journal of the Mechanics and Physics of Solids %D 2019 %T Nutations in growing plant shoots: The role of elastic deformations due to gravity loading %A Daniele Agostinelli %A Alessandro Lucantonio %A Giovanni Noselli %A Antonio DeSimone %K Circumnutations %K Flutter instability %K Gravitropism %K Hopf bifurcation %XThe effect of elastic deformations induced by gravity loading on the active circumnutation movements of growing plant shoots is investigated. We consider first a discrete model (a gravitropic spring-pendulum system) and then a continuous rod model which is analyzed both analytically (under the assumption of small deformations) and numerically (in the large deformation regime). We find that, for a choice of material parameters consistent with values reported in the available literature on plant shoots, rods of sufficient length may exhibit lateral oscillations of increasing amplitude, which eventually converge to limit cycles. This behavior strongly suggests the occurrence of a Hopf bifurcation, just as for the gravitropic spring-pendulum system, for which this result is rigorously established. At least in this restricted set of material parameters, our analysis supports a view of Darwin’s circumnutations as a biological analogue to structural systems exhibiting flutter instabilities, i.e., spontaneous oscillations away from equilibrium configurations driven by non-conservative loads. Here, in the context of nutation movements of growing plant shoots, the energy needed to sustain oscillations is continuously supplied to the system by the internal biochemical machinery presiding the capability of plants to maintain a vertical pose.

%B Journal of the Mechanics and Physics of Solids %P 103702 %G eng %U https://doi.org/10.1016/j.jmps.2019.103702 %R 10.1016/j.jmps.2019.103702 %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 Journal Article %J International Journal for Numerical Methods in Engineering %D 2019 %T A POD-selective inverse distance weighting method for fast parametrized shape morphing %A F. Ballarin %A A. D'Amario %A Simona Perotto %A Gianluigi Rozza %XEfficient shape morphing techniques play a crucial role in the approximation of partial differential equations defined in parametrized domains, such as for fluid-structure interaction or shape optimization problems. In this paper, we focus on inverse distance weighting (IDW) interpolation techniques, where a reference domain is morphed into a deformed one via the displacement of a set of control points. We aim at reducing the computational burden characterizing a standard IDW approach without significantly compromising the accuracy. To this aim, first we propose an improvement of IDW based on a geometric criterion that automatically selects a subset of the original set of control points. Then, we combine this new approach with a dimensionality reduction technique based on a proper orthogonal decomposition of the set of admissible displacements. This choice further reduces computational costs. We verify the performances of the new IDW techniques on several tests by investigating the trade-off reached in terms of accuracy and efficiency.

%B International Journal for Numerical Methods in Engineering %V 117 %P 860-884 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85056396233&doi=10.1002%2fnme.5982&partnerID=40&md5=6aabcbdc9a0da25e36575a0ebfac034f %R 10.1002/nme.5982 %0 Journal Article %J Complex Analysis and Operator Theory %D 2019 %T Point-Like Perturbed Fractional Laplacians Through Shrinking Potentials of Finite Range %A Alessandro Michelangeli %A Raffaele Scandone %XWe construct the rank-one, singular (point-like) perturbations of the d-dimensional fractional Laplacian in the physically meaningful norm-resolvent limit of fractional Schrödinger operators with regular potentials centred around the perturbation point and shrinking to a delta-like shape. We analyse both possible regimes, the resonance-driven and the resonance-independent limit, depending on the power of the fractional Laplacian and the spatial dimension. To this aim, we also qualify the notion of zero-energy resonance for Schrödinger operators formed by a fractional Laplacian and a regular potential.

%B Complex Analysis and Operator Theory %8 May %G eng %U https://doi.org/10.1007/s11785-019-00927-w %R 10.1007/s11785-019-00927-w %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 Computer Methods in Applied Mechanics and Engineering %D 2019 %T A reduced basis approach for PDEs on parametrized geometries based on the shifted boundary finite element method and application to a Stokes flow %A Efthymios N Karatzas %A Giovanni Stabile %A Leo Nouveau %A Guglielmo Scovazzi %A Gianluigi Rozza %XWe propose a model order reduction technique integrating the Shifted Boundary Method (SBM) with a POD-Galerkin strategy. This approach allows to deal with complex parametrized domains in an efficient and straightforward way. The impact of the proposed approach is threefold. First, problems involving parametrizations of complex geometrical shapes and/or large domain deformations can be efficiently solved at full-order by means of the SBM. This unfitted boundary method permits to avoid remeshing and the tedious handling of cut cells by introducing an approximate surrogate boundary. Second, the computational effort is reduced by the development of a Reduced Order Model (ROM) technique based on a POD-Galerkin approach. Third, the SBM provides a smooth mapping from the true to the surrogate domain, and for this reason, the stability and performance of the reduced order basis are enhanced. This feature is the net result of the combination of the proposed ROM approach and the SBM. Similarly, the combination of the SBM with a projection-based ROM gives the great advantage of an easy and fast to implement algorithm considering geometrical parametrization with large deformations. The transformation of each geometry to a reference geometry (morphing) is in fact not required. These combined advantages will allow the solution of PDE problems more efficiently. We illustrate the performance of this approach on a number of two-dimensional Stokes flow problems.

%B Computer Methods in Applied Mechanics and Engineering %V 347 %P 568-587 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85060107322&doi=10.1016%2fj.cma.2018.12.040&partnerID=40&md5=1a3234f0cb000c91494d946428f8ebef %R 10.1016/j.cma.2018.12.040 %0 Journal Article %D 2019 %T Reduced basis approaches for parametrized bifurcation problems held by non-linear Von Kármán equations %A Federico Pichi %A Gianluigi Rozza %XThis work focuses on the computationally efficient detection of the buckling phenomena and bifurcation analysis of the parametric Von Kármán plate equations based on reduced order methods and spectral analysis. The computational complexity - due to the fourth order derivative terms, the non-linearity and the parameter dependence - provides an interesting benchmark to test the importance of the reduction strategies, during the construction of the bifurcation diagram by varying the parameter(s). To this end, together the state equations, we carry out also an analysis of the linearized eigenvalue problem, that allows us to better understand the physical behaviour near the bifurcation points, where we lose the uniqueness of solution. We test this automatic methodology also in the two parameter case, understanding the evolution of the first buckling mode. journal = Journal of Scientific Computing

%V 81 %P 112–135 %G eng %U https://arxiv.org/abs/1804.02014 %R 10.1007/s10915-019-01003-3 %0 Journal Article %J Journal of Scientific Computing %D 2019 %T Reduced Basis Approaches for Parametrized Bifurcation Problems held by Non-linear Von Kármán Equations %A Federico Pichi %A Gianluigi Rozza %XThis work focuses on the computationally efficient detection of the buckling phenomena and bifurcation analysis of the parametric Von Kármán plate equations based on reduced order methods and spectral analysis. The computational complexity—due to the fourth order derivative terms, the non-linearity and the parameter dependence—provides an interesting benchmark to test the importance of the reduction strategies, during the construction of the bifurcation diagram by varying the parameter(s). To this end, together the state equations, we carry out also an analysis of the linearized eigenvalue problem, that allows us to better understand the physical behaviour near the bifurcation points, where we lose the uniqueness of solution. We test this automatic methodology also in the two parameter case, understanding the evolution of the first buckling mode.

%B Journal of Scientific Computing %V 81 %P 112-135 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85068973907&doi=10.1007%2fs10915-019-01003-3&partnerID=40&md5=a09af83ce45183d6965cdb79d87a919b %R 10.1007/s10915-019-01003-3 %0 Journal Article %J Advances in Computational Mathematics %D 2019 %T A reduced order variational multiscale approach for turbulent flows %A Giovanni Stabile %A F. Ballarin %A G. Zuccarino %A Gianluigi Rozza %XThe purpose of this work is to present different reduced order model strategies starting from full order simulations stabilized using a residual-based variational multiscale (VMS) approach. The focus is on flows with moderately high Reynolds numbers. The reduced order models (ROMs) presented in this manuscript are based on a POD-Galerkin approach. Two different reduced order models are presented, which differ on the stabilization used during the Galerkin projection. In the first case, the VMS stabilization method is used at both the full order and the reduced order levels. In the second case, the VMS stabilization is used only at the full order level, while the projection of the standard Navier-Stokes equations is performed instead at the reduced order level. The former method is denoted as consistent ROM, while the latter is named non-consistent ROM, in order to underline the different choices made at the two levels. Particular attention is also devoted to the role of inf-sup stabilization by means of supremizers in ROMs based on a VMS formulation. Finally, the developed methods are tested on a numerical benchmark.

%B Advances in Computational Mathematics %V 45 %P 2349-2368 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85068076665&doi=10.1007%2fs10444-019-09712-x&partnerID=40&md5=af0142e6d13bbc2e88c6f31750aef6ad %R 10.1007/s10444-019-09712-x %0 Journal Article %D 2019 %T Reducibility for a fast-driven linear Klein–Gordon equation %A Luca Franzoi %A Alberto Maspero %XWe prove a reducibility result for a linear Klein–Gordon equation with a quasi-periodic driving on a compact interval with Dirichlet boundary conditions. No assumptions are made on the size of the driving; however, we require it to be fast oscillating. In particular, provided that the external frequency is sufficiently large and chosen from a Cantor set of large measure, the original equation is conjugated to a time-independent, diagonal one. We achieve this result in two steps. First, we perform a preliminary transformation, adapted to fast oscillating systems, which moves the original equation in a perturbative setting. Then, we show that this new equation can be put to constant coefficients by applying a KAM reducibility scheme, whose convergence requires a new type of Melnikov conditions.

%V 198 %P 1407 - 1439 %8 2019/08/01 %@ 1618-1891 %G eng %U https://doi.org/10.1007/s10231-019-00823-2 %N 4 %! Annali di Matematica Pura ed Applicata (1923 -) %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 Generic %D 2019 %T Regularity of minimizers for a model of charged droplets %A Guido De Philippis %A Jonas Hirsch %A Giulia Vescovo %G eng %0 Journal Article %J Annali di Matematica Pura ed Applicata (1923 -) %D 2019 %T On the relaxed area of the graph of discontinuous maps from the plane to the plane taking three values with no symmetry assumptions %A Giovanni Bellettini %A Alaa Elshorbagy %A Maurizio Paolini %A Riccardo Scala %XIn this paper, we estimate from above the area of the graph of a singular map u taking a disk to three vectors, the vertices of a triangle, and jumping along three $\mathcal{C}^2$-embedded curves that meet transversely at only one point of the disk. We show that the singular part of the relaxed area can be estimated from above by the solution of a Plateau-type problem involving three entangled nonparametric area-minimizing surfaces. The idea is to ``fill the hole'' in the graph of the singular map with a sequence of approximating smooth two-codimensional surfaces of graph-type, by imagining three minimal surfaces, placed vertically over the jump of u, coupled together via a triple point in the target triangle. Such a construction depends on the choice of a target triple point, and on a connection passing through it, which dictate the boundary condition for the three minimal surfaces. We show that the singular part of the relaxed area of u cannot be larger than what we obtain by minimizing over all possible target triple points and all corresponding connections.

%B Annali di Matematica Pura ed Applicata (1923 -) %8 Jul %G eng %U https://doi.org/10.1007/s10231-019-00887-0 %R 10.1007/s10231-019-00887-0 %0 Journal Article %J Rendiconti del Circolo Matematico di Palermo Series 2 %D 2019 %T The Serre–Swan theorem for normed modules %A Danka Lučić %A Enrico Pasqualetto %B Rendiconti del Circolo Matematico di Palermo Series 2 %V 68 %P 385–404 %8 Aug %G eng %U https://doi.org/10.1007/s12215-018-0366-6 %R 10.1007/s12215-018-0366-6 %0 Conference Paper %B 8th International Conference on Computational Methods in Marine Engineering, MARINE 2019 %D 2019 %T Shape optimization through proper orthogonal decomposition with interpolation and dynamic mode decomposition enhanced by active subspaces %A Marco Tezzele %A Nicola Demo %A Gianluigi Rozza %XWe propose a numerical pipeline for shape optimization in naval engineering involving two different non-intrusive reduced order method (ROM) techniques. Such methods are proper orthogonal decomposition with interpolation (PODI) and dynamic mode decomposition (DMD). The ROM proposed will be enhanced by active subspaces (AS) as a pre-processing tool that reduce the parameter space dimension and suggest better sampling of the input space. We will focus on geometrical parameters describing the perturbation of a reference bulbous bow through the free form deformation (FFD) technique. The ROM are based on a finite volume method (FV) to simulate the multi-phase incompressible flow around the deformed hulls. In previous works we studied the reduction of the parameter space in naval engineering through AS [38, 10] focusing on different parts of the hull. PODI and DMD have been employed for the study of fast and reliable shape optimization cycles on a bulbous bow in [9]. The novelty of this work is the simultaneous reduction of both the input parameter space and the output fields of interest. In particular AS will be trained computing the total drag resistance of a hull advancing in calm water and its gradients with respect to the input parameters. DMD will improve the performance of each simulation of the campaign using only few snapshots of the solution fields in order to predict the regime state of the system. Finally PODI will interpolate the coefficients of the POD decomposition of the output fields for a fast approximation of all the fields at new untried parameters given by the optimization algorithm. This will result in a non-intrusive data-driven numerical optimization pipeline completely independent with respect to the full order solver used and it can be easily incorporated into existing numerical pipelines, from the reference CAD to the optimal shape.

%B 8th International Conference on Computational Methods in Marine Engineering, MARINE 2019 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075390244&partnerID=40&md5=3e1f2e9a2539d34594caff13766c94b8 %0 Book Section %B Numerical Mathematics and Advanced Applications - ENUMATH 2017 %D 2019 %T A Spectral Element Reduced Basis Method in Parametric CFD %A Martin W. Hess %A Gianluigi Rozza %E Radu, Florin Adrian %E Kumar, Kundan %E Berre, Inga %E Nordbotten, Jan Martin %E Pop, Iuliu Sorin %XWe consider the Navier-Stokes equations in a channel with varying Reynolds numbers. The model is discretized with high-order spectral element ansatz functions, resulting in 14 259 degrees of freedom. The steady-state snapshot solu- tions define a reduced order space, which allows to accurately evaluate the steady- state solutions for varying Reynolds number with a reduced order model within a fixed-point iteration. In particular, we compare different aspects of implementing the reduced order model with respect to the use of a spectral element discretization. It is shown, how a multilevel static condensation in the pressure and velocity boundary degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios.

%B Numerical Mathematics and Advanced Applications - ENUMATH 2017 %I Springer International Publishing %V 126 %G eng %U https://arxiv.org/abs/1712.06432 %& A Spectral Element Reduced Basis Method in Parametric CFD %R 10.1007/978-3-319-96415-7_64 pages = 693–701 %0 Journal Article %J Lecture Notes in Computational Science and Engineering %D 2019 %T A spectral element reduced basis method in parametric CFD %A Martin W. Hess %A Gianluigi Rozza %XWe consider the Navier-Stokes equations in a channel with varying Reynolds numbers. The model is discretized with high-order spectral element ansatz functions, resulting in 14,259 degrees of freedom. The steady-state snapshot solutions define a reduced order space, which allows to accurately evaluate the steady-state solutions for varying Reynolds number with a reduced order model within a fixed-point iteration. In particular, we compare different aspects of implementing the reduced order model with respect to the use of a spectral element discretization. It is shown, how a multilevel static condensation (Karniadakis and Sherwin, Spectral/hp element methods for computational fluid dynamics, 2nd edn. Oxford University Press, Oxford, 2005) in the pressure and velocity boundary degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios.

%B Lecture Notes in Computational Science and Engineering %V 126 %P 693-701 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85060005503&doi=10.1007%2f978-3-319-96415-7_64&partnerID=40&md5=d1a900db8ddb92cd818d797ec212a4c6 %R 10.1007/978-3-319-96415-7_64 %0 Report %D 2019 %T On the square distance function from a manifold with boundary %A Giovanni Bellettini %A Alaa Elshorbagy %XWe characterize arbitrary codimensional smooth manifolds $\mathcal{M}$ with boundary embedded in $\mathbb{R}^n$ using the square distance function and the signed distance function from $\mathcal{M}$ and from its boundary. The results are localized in an open set.

%G eng %U http://cvgmt.sns.it/media/doc/paper/4260/manif_with_bound_dist.pdf %0 Journal Article %J TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS %D 2019 %T On the topological degree of planar maps avoiding normal cones %A Alessandro Fonda %A Giuliano Klun %XThe classical Poincaré-Bohl theorem provides the existence of a zero for a function avoiding external rays. When the domain is convex, the same holds true when avoiding normal cones.

We consider here the possibility of dealing with nonconvex sets having inward corners or cusps, in which cases the normal cone vanishes. This allows us to deal with situations where the topological degree may be strictly greater than $1$.

In this work we propose and analyze a weighted proper orthogonal decomposition method to solve elliptic partial differential equations depending on random input data, for stochastic problems that can be transformed into parametric systems. The algorithm is introduced alongside the weighted greedy method. Our proposed method aims to minimize the error in a L2 norm and, in contrast to the weighted greedy approach, it does not require the availability of an error bound. Moreover, we consider sparse discretization of the input space in the construction of the reduced model; for high-dimensional problems, provided the sampling is done accordingly to the parameters distribution, this enables a sensible reduction of computational costs, while keeping a very good accuracy with respect to high fidelity solutions. We provide many numerical tests to assess the performance of the proposed method compared to an equivalent reduced order model without weighting, as well as to the weighted greedy approach, in both low and high dimensional problems.

%B Journal of Scientific Computing %V 81 %P 136-153 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85053798049&doi=10.1007%2fs10915-018-0830-7&partnerID=40&md5=5cad501b6ef1955da55868807079ee5d %R 10.1007/s10915-018-0830-7 %0 Journal Article %J PoliTO Springer Series %D 2019 %T Weighted Reduced Order Methods for Parametrized Partial Differential Equations with Random Inputs %A L. Venturi %A D. Torlo %A F. Ballarin %A Gianluigi Rozza %XIn this manuscript we discuss weighted reduced order methods for stochastic partial differential equations. Random inputs (such as forcing terms, equation coefficients, boundary conditions) are considered as parameters of the equations. We take advantage of the resulting parametrized formulation to propose an efficient reduced order model; we also profit by the underlying stochastic assumption in the definition of suitable weights to drive to reduction process. Two viable strategies are discussed, namely the weighted reduced basis method and the weighted proper orthogonal decomposition method. A numerical example on a parametrized elasticity problem is shown.

%B PoliTO Springer Series %P 27-40 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85084009379&doi=10.1007%2f978-3-030-04870-9_2&partnerID=40&md5=446bcc1f331167bbba67bc00fb170150 %R 10.1007/978-3-030-04870-9_2 %0 Report %D 2019 %T Zero modes and low-energy resolvent expansion for three dimensional Schrodinger operators with point interactions %A Raffaele Scandone %G eng %U https://arxiv.org/abs/1901.02449 %0 Journal Article %J SIAM Journal on Applied Mathematics %D 2018 %T Analysis of a Dynamic Peeling Test with Speed-Dependent Toughness %A Giuliano Lazzaroni %A Lorenzo Nardini %XWe analyse a one-dimensional model of dynamic debonding for a thin film, where the local toughness of the glue between the film and the substrate also depends on the debonding speed. The wave equation on the debonded region is strongly coupled with Griffith's criterion for the evolution of the debonding front. We provide an existence and uniqueness result and find explicitly the solution in some concrete examples. We study the limit of solutions as inertia tends to zero, observing phases of unstable propagation, as well as time discontinuities, even though the toughness diverges at a limiting debonding speed.

%B SIAM Journal on Applied Mathematics %V 78 %P 1206-1227 %G eng %U https://doi.org/10.1137/17M1147354 %R 10.1137/17M1147354 %0 Report %D 2018 %T On the Cauchy problem for the wave equation on time-dependent domains %A Gianni Dal Maso %A Rodica Toader %X We introduce a notion of solution to the wave equation on a suitable class of time-dependent domains and compare it with a previous de nition. We prove an existence result for the solution of the Cauchy problem and present some additional conditions which imply uniqueness. %I SISSA %G en %U http://preprints.sissa.it/handle/1963/35314 %1 35622 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-04-23T06:03:52Z No. of bitstreams: 1 DM-Toa-18-sissa.pdf: 404543 bytes, checksum: 73bb5b0c57b574d05b3d6f33417016e0 (MD5) %0 Journal Article %J Journal of Scientific Computing %D 2018 %T Certified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models %A Immanuel Martini %A Bernard Haasdonk %A Gianluigi Rozza %B Journal of Scientific Computing %V 74 %P 197-219 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85017156114&doi=10.1007%2fs10915-017-0430-y&partnerID=40&md5=023ef0bb95713f4442d1fa374c92a964 %R 10.1007/s10915-017-0430-y %0 Report %D 2018 %T Characteristic boundary layers for mixed hyperbolic systems in one space dimension and applications to the Navier-Stokes and MHD equations %A Stefano Bianchini %A Laura Spinolo %X We provide a detailed analysis of the boundary layers for mixed hyperbolic-parabolic systems in one space dimension and small amplitude regimes. As an application of our results, we describe the solution of the so-called boundary Riemann problem recovered as the zero viscosity limit of the physical viscous approximation. In particular, we tackle the so called doubly characteristic case, which is considerably more demanding from the technical viewpoint and occurs when the boundary is characteristic for both the mixed hyperbolic-parabolic system and for the hyperbolic system obtained by neglecting the second order terms. Our analysis applies in particular to the compressible Navier-Stokes and MHD equations in Eulerian coordinates, with both positive and null conductivity. In these cases, the doubly characteristic case occurs when the velocity is close to 0. The analysis extends to non-conservative systems. %I SISSA %G en %U http://preprints.sissa.it/handle/1963/35325 %1 35635 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-10-16T11:48:42Z No. of bitstreams: 1 BiaSpiEuler116.pdf: 615669 bytes, checksum: 93b99e76a8c0a0f3e1753969d7170d1e (MD5) %0 Journal Article %J Mathematical Models and Methods in Applied Sciences %D 2018 %T Cohesive fracture with irreversibility: Quasistatic evolution for a model subject to fatigue %A Vito Crismale %A Giuliano Lazzaroni %A Gianluca Orlando %XIn this paper we prove the existence of quasistatic evolutions for a cohesive fracture on a prescribed crack surface, in small-strain antiplane elasticity. The main feature of the model is that the density of the energy dissipated in the fracture process depends on the total variation of the amplitude of the jump. Thus, any change in the crack opening entails a loss of energy, until the crack is complete. In particular this implies a fatigue phenomenon, i.e. a complete fracture may be produced by oscillation of small jumps. The first step of the existence proof is the construction of approximate evolutions obtained by solving discrete-time incremental minimum problems. The main difficulty in the passage to the continuous-time limit is that we lack of controls on the variations of the jump of the approximate evolutions. Therefore we resort to a weak formulation where the variation of the jump is replaced by a Young measure. Eventually, after proving the existence in this weak formulation, we improve the result by showing that the Young measure is concentrated on a function and coincides with the variation of the jump of the displacement.

%B Mathematical Models and Methods in Applied Sciences %V 28 %P 1371-1412 %G eng %U https://doi.org/10.1142/S0218202518500379 %R 10.1142/S0218202518500379 %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 Report %D 2018 %T Differential of metric valued Sobolev maps %A Nicola Gigli %A Enrico Pasqualetto %A Elefterios Soultanis %G eng %0 Report %D 2018 %T Dimension reduction for thin films with transversally varying prestrain: the oscillatory and the non-oscillatory case %A Marta Lewicka %A Danka Lučić %G eng %0 Report %D 2018 %T Existence and uniqueness of dynamic evolutions for a one dimensional debonding model with damping %A Lorenzo Nardini %A Filippo Riva %XIn this paper we analyse a one-dimensional debonding model for a thin film peeled from a substrate when friction is taken into account. It is described by the weakly damped wave equation whose domain, the debonded region, grows according to a Griffth's criterion. Firstly we prove that the equation admits a unique solution when the evolution of the debonding front is assigned. Finally we provide an existence and uniqueness result for the coupled problem given by the wave equation together with Griffth's criterion.

%G en %U http://preprints.sissa.it/xmlui/handle/1963/35319 %1 35629 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-07-16T13:11:24Z No. of bitstreams: 1 PREPRINT_28_2018_mate.pdf: 600708 bytes, checksum: 04321c1f671175dc8cf001c358699cba (MD5) %0 Report %D 2018 %T Existence for elastodynamic Griffith fracture with a weak maximal dissipation condition %A Gianni Dal Maso %A Cristopher J. Larsen %A Rodica Toader %X We consider a model of elastodynamics with fracture evolution, based on energy-dissipation balance and a maximal dissipation condition. We prove an existence result in the case of planar elasticity with a free crack path, where the maximal dissipation condition is satisfied among suitably regular competitor cracks. %G en %U http://preprints.sissa.it/handle/1963/35308 %1 35616 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-03-19T09:02:45Z No. of bitstreams: 1 DM-Lar-Toa-sissa.pdf: 429343 bytes, checksum: 82817f96da6dcabff29c2c322590fb66 (MD5) %0 Book Section %B Current Research in Nonlinear Analysis: In Honor of Haim Brezis and Louis Nirenberg %D 2018 %T Failure of the Chain Rule in the Non Steady Two-Dimensional Setting %A Stefano Bianchini %A Paolo Bonicatto %E Rassias, Themistocles M. %B Current Research in Nonlinear Analysis: In Honor of Haim Brezis and Louis Nirenberg %I Springer International Publishing %C Cham %P 33–60 %@ 978-3-319-89800-1 %G eng %U https://doi.org/10.1007/978-3-319-89800-1_2 %R 10.1007/978-3-319-89800-1_2 %0 Journal Article %J Computers and Fluids %D 2018 %T Finite volume POD-Galerkin stabilised reduced order methods for the parametrised incompressible Navier–Stokes equations %A Giovanni Stabile %A Gianluigi Rozza %XIn this work a stabilised and reduced Galerkin projection of the incompressible unsteady Navier–Stokes equations for moderate Reynolds number is presented. The full-order model, on which the Galerkin projection is applied, is based on a finite volumes approximation. The reduced basis spaces are constructed with a POD approach. Two different pressure stabilisation strategies are proposed and compared: the former one is based on the supremizer enrichment of the velocity space, and the latter one is based on a pressure Poisson equation approach.

%B Computers and Fluids %V 173 %P 273-284 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85043366603&doi=10.1016%2fj.compfluid.2018.01.035&partnerID=40&md5=c15435ea3b632e55450da19ba2bb6125 %R 10.1016/j.compfluid.2018.01.035 %0 Report %D 2018 %T Foldable structures made of hydrogel bilayers %A Virginia Agostiniani %A Antonio DeSimone %A Alessandro Lucantonio %A Danka Lučić %G eng %0 Journal Article %J Journal of Mathematical Physics %D 2018 %T Fractional powers and singular perturbations of quantum differential Hamiltonians %A Alessandro Michelangeli %A Andrea Ottolini %A Raffaele Scandone %XWe consider the fractional powers of singular (point-like) perturbations of the Laplacian and the singular perturbations of fractional powers of the Laplacian, and we compare two such constructions focusing on their perturbative structure for resolvents and on the local singularity structure of their domains. In application to the linear and non-linear Schrödinger equations for the corresponding operators, we outline a programme of relevant questions that deserve being investigated.

%B Journal of Mathematical Physics %V 59 %P 072106 %G eng %U https://doi.org/10.1063/1.5033856 %R 10.1063/1.5033856 %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 Journal Article %J Zeitschrift für angewandte Mathematik und Physik %D 2018 %T Global, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials %A Paolo Antonelli %A Alessandro Michelangeli %A Raffaele Scandone %XWe prove the existence of weak solutions in the space of energy for a class of nonlinear Schrödinger equations in the presence of a external, rough, time-dependent magnetic potential. Under our assumptions, it is not possible to study the problem by means of usual arguments like resolvent techniques or Fourier integral operators, for example. We use a parabolic regularisation, and we solve the approximating Cauchy problem. This is achieved by obtaining suitable smoothing estimates for the dissipative evolution. The total mass and energy bounds allow to extend the solution globally in time. We then infer sufficient compactness properties in order to produce a global-in-time finite energy weak solution to our original problem.

%B Zeitschrift für angewandte Mathematik und Physik %V 69 %P 46 %8 Mar %G eng %U https://doi.org/10.1007/s00033-018-0938-5 %R 10.1007/s00033-018-0938-5 %0 Journal Article %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %T Heterogeneous elastic plates with in-plane modulation of the target curvature and applications to thin gel sheets %A Virginia Agostiniani %A Alessandro Lucantonio %A Danka Lučić %B ESAIM: Control, Optimisation and Calculus of Variations %I EDP Sciences %G eng %R https://doi.org/10.1051/cocv/2018046 %0 Report %D 2018 %T Long time existence for fully nonlinear NLS with small Cauchy data on the circle %A Feola Roberto %A Felice Iandoli %G eng %0 Journal Article %J Annales Henri Poincaré %D 2018 %T Lp-Boundedness of Wave Operators for the Three-Dimensional Multi-Centre Point Interaction %A Gianfausto Dell'Antonio %A Alessandro Michelangeli %A Raffaele Scandone %A Kenji Yajima %XWe prove that, for arbitrary centres and strengths, the wave operators for three-dimensional Schrödinger operators with multi-centre local point interactions are bounded in Lp(R3)for 1<p<3 and unbounded otherwise.

%B Annales Henri Poincaré %V 19 %P 283–322 %8 Jan %G eng %U https://doi.org/10.1007/s00023-017-0628-4 %R 10.1007/s00023-017-0628-4 %0 Report %D 2018 %T A minimization approach to the wave equation on time-dependent domains %A Gianni Dal Maso %A Lucia De Luca %X We prove the existence of weak solutions to the homogeneous wave equation on a suitable class of time-dependent domains. Using the approach suggested by De Giorgi and developed by Serra and Tilli, such solutions are approximated by minimizers of suitable functionals in space-time. %I SISSA %G en %U http://preprints.sissa.it/handle/1963/35318 %1 35627 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-06-05T09:52:31Z No. of bitstreams: 1 DM-DeL-18-sissa.pdf: 301594 bytes, checksum: 0da772afb21ae49058bd3b54ae1dd432 (MD5) %0 Journal Article %J Journal de Mathématiques Pures et Appliquées %D 2018 %T Minimizing movements for mean curvature flow of droplets with prescribed contact angle %A Giovanni Bellettini %A Matteo Novaga %A Shokhrukh Kholmatov %K Capillary functional %K Mean curvature flow with prescribed contact angle %K Minimizing movements %K Sets of finite perimeter %XWe study the mean curvature motion of a droplet flowing by mean curvature on a horizontal hyperplane with a possibly nonconstant prescribed contact angle. Using the solutions constructed as a limit of an approximation algorithm of Almgren–Taylor–Wang and Luckhaus–Sturzenhecker, we show the existence of a weak evolution, and its compatibility with a distributional solution. We also prove various comparison results. Résumé Nous étudions le mouvement par courbure moyenne d'une goutte qui glisse par courbure moyenne sur un hyperplan horizontal avec un angle de contact prescrit éventuellement non constant. En utilisant les solutions construites comme limites d'un algorithme d'approximation dû à Almgren, Taylor et Wang et Luckhaus et Sturzenhecker, nous montrons l'existence d'une évolution faible, et sa compatibilité avec une solution au sens des distributions. Nous démontrons également plusieurs résultats de comparaison.

%B Journal de Mathématiques Pures et Appliquées %V 117 %P 1 - 58 %G eng %U http://www.sciencedirect.com/science/article/pii/S0021782418300825 %R https://doi.org/10.1016/j.matpur.2018.06.003 %0 Journal Article %J SIAM Journal on Mathematical Analysis %D 2018 %T Minimizing Movements for Mean Curvature Flow of Partitions %A Giovanni Bellettini %A Shokhrukh Kholmatov %XWe prove the existence of a weak global in time mean curvature flow of a bounded partition of space using the method of minimizing movements. The result is extended to the case when suitable driving forces are present. We also prove some consistency results for a minimizing movement solution with smooth and viscosity solutions when the evolution starts from a partition made by a union of bounded sets at a positive distance. In addition, the motion starting from the union of convex sets at a positive distance agrees with the classical mean curvature flow and is stable with respect to the Hausdorff convergence of the initial partitions.

%B SIAM Journal on Mathematical Analysis %V 50 %P 4117-4148 %G eng %U https://doi.org/10.1137/17M1159294 %R 10.1137/17M1159294 %0 Report %D 2018 %T Non-linear Gross-Pitaevskii dynamics of a 2D binary condensate: a numerical analysis %A Alessandro Michelangeli %A Giuseppe Pitton %X We present a numerical study of the two-dimensional Gross-Pitaevskii systems in a wide range of relevant regimes of population ratios and intra-species and inter-species interactions. Our numerical method is based on a Fourier collocation scheme in space combined with a fourth order integrating factor scheme in time. %G en %U http://preprints.sissa.it/handle/1963/35323 %1 35633 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-09-20T06:04:10Z No. of bitstreams: 1 SISSA_preprint_35-2018-MATE.pdf: 2536075 bytes, checksum: 323dca7431103028ecadfc71c052f4ed (MD5) %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 %D 2018 %T A novel reduced order model for vortex induced vibrations of long flexible cylinders %A Giovanni Stabile %A Hermann G. Matthies %A Claudio Borri %I Elsevier {BV} %V 156 %P 191–207 %8 may %G eng %U https://doi.org/10.1016/j.oceaneng.2018.02.064 %R 10.1016/j.oceaneng.2018.02.064 %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 Frontiers in Robotics and AI %D 2018 %T Peristaltic Waves as Optimal Gaits in Metameric Bio-Inspired Robots %A Daniele Agostinelli %A François Alouges %A Antonio DeSimone %K Biomimetic robots %K Crawling motility %K Lumbricus terrestris %K Metameric robots %K Optimization %K Peristalsis %K Self-propulsion %K Soft robotics %X*Peristalsis*, i.e., a motion pattern arising from the propagation of muscle contraction and expansion waves along the body, is a common locomotion strategy for limbless animals. Mimicking peristalsis in bio-inspired robots has attracted considerable attention in the literature. It has recently been observed that maximal velocity in a metameric earthworm-like robot is achieved by actuating the segments using a “phase coordination” principle. This paper shows that, in fact, peristalsis (which requires not only phase coordination, but also that all segments oscillate at same frequency and amplitude) emerges from optimization principles. More precisely, basing our analysis on the assumption of small deformations, we show that peristaltic waves provide the optimal actuation solution in the ideal case of a periodic infinite system, and that this is approximately true, modulo edge effects, for the real, finite length system. Therefore, this paper confirms the effectiveness of mimicking peristalsis in bio-inspired robots, at least in the small-deformation regime. Further research will be required to test the effectiveness of this strategy if large deformations are allowed.

We study the periodic boundary value problem associated with the second order nonlinear equation u''+(λa+(t)−μa−(t))g(u)=0, where g(u) has superlinear growth at zero and sublinear growth at infinity. For λ,μ positive and large, we prove the existence of 3^m−1 positive T-periodic solutions when the weight function a(t) has m positive humps separated by m negative ones (in a T-periodicity interval). As a byproduct of our approach we also provide abundance of positive subharmonic solutions and symbolic dynamics. The proof is based on coincidence degree theory for locally compact operators on open unbounded sets and also applies to Neumann and Dirichlet boundary conditions. Finally, we deal with radially symmetric positive solutions for the Neumann and the Dirichlet problems associated with elliptic PDEs.

%B Trans. Amer. Math. Soc. %I American Mathematical Society %G en %U http://urania.sissa.it/xmlui/handle/1963/35264 %1 35568 %2 Mathematics %4 1 %# MAT/05 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2016-11-21T07:53:44Z (GMT) No. of bitstreams: 0 %0 Journal Article %J Communications in Contemporary Mathematics %D 2018 %T Positive subharmonic solutions to nonlinear ODEs with indefinite weight %A Alberto Boscaggin %A Guglielmo Feltrin %XWe prove that the superlinear indefinite equation u″ + a(t)up = 0, where p > 1 and a(t) is a T-periodic sign-changing function satisfying the (sharp) mean value condition ∫0Ta(t)dt < 0, has positive subharmonic solutions of order k for any large integer k, thus providing a further contribution to a problem raised by Butler in its pioneering paper [Rapid oscillation, nonextendability, and the existence of periodic solutions to second order nonlinear ordinary differential equations, J. Differential Equations 22 (1976) 467–477]. The proof, which applies to a larger class of indefinite equations, combines coincidence degree theory (yielding a positive harmonic solution) with the Poincaré–Birkhoff fixed point theorem (giving subharmonic solutions oscillating around it).

%B Communications in Contemporary Mathematics %V 20 %P 1750021 %G eng %U https://doi.org/10.1142/S0219199717500213 %R 10.1142/S0219199717500213 %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 Journal of Nonlinear Science %D 2018 %T On the Quasistatic Limit of Dynamic Evolutions for a Peeling Test in Dimension One %A Giuliano Lazzaroni %A Lorenzo Nardini %XThe aim of this paper is to study the quasistatic limit of a one-dimensional model of dynamic debonding. We start from a dynamic problem that strongly couples the wave equation in a time-dependent domain with Griffith's criterion for the evolution of the domain. Passing to the limit as inertia tends to zero, we find that the limit evolution satisfies a stability condition; however, the activation rule in Griffith's (quasistatic) criterion does not hold in general, thus the limit evolution is not rate-independent.

%B Journal of Nonlinear Science %V 28 %P 269–304 %8 Feb %G eng %U https://doi.org/10.1007/s00332-017-9407-0 %R 10.1007/s00332-017-9407-0 %0 Report %D 2018 %T On real resonances for the three-dimensional, multi-centre point interaction %A Alessandro Michelangeli %A Raffaele Scandone %G eng %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 Book Section %B Numerical Methods for PDEs %D 2018 %T Reduced Basis Approximation and A Posteriori Error Estimation: Applications to Elasticity Problems in Several Parametric Settings %A Huynh, D. B. P. %A Federico Pichi %A Gianluigi Rozza %B Numerical Methods for PDEs %V 15 %G eng %U https://link.springer.com/chapter/10.1007/978-3-319-94676-4_8 %R https://doi.org/10.1007/978-3-319-94676-4_8 %0 Journal Article %J SEMA SIMAI Springer Series %D 2018 %T Reduced Basis Approximation and A Posteriori Error Estimation: Applications to Elasticity Problems in Several Parametric Settings %A D.B.P. Huynh %A Federico Pichi %A Gianluigi Rozza %XIn this work we consider (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for elasticity problems in affinely parametrized geometries. The essential ingredients of the methodology are: a Galerkin projection onto a low-dimensional space associated with a smooth “parametric manifold”—dimension reduction; an efficient and effective greedy sampling methods for identification of optimal and numerically stable approximations—rapid convergence; an a posteriori error estimation procedures—rigorous and sharp bounds for the functional outputs related with the underlying solution or related quantities of interest, like stress intensity factor; and Offline-Online computational decomposition strategies—minimum marginal cost for high performance in the real-time and many-query (e.g., design and optimization) contexts. We present several illustrative results for linear elasticity problem in parametrized geometries representing 2D Cartesian or 3D axisymmetric configurations like an arc-cantilever beam, a center crack problem, a composite unit cell or a woven composite beam, a multi-material plate, and a closed vessel. We consider different parametrization for the systems: either physical quantities—to model the materials and loads—and geometrical parameters—to model different geometrical configurations—with isotropic and orthotropic materials working in plane stress and plane strain approximation. We would like to underline the versatility of the methodology in very different problems. As last example we provide a nonlinear setting with increased complexity.

%B SEMA SIMAI Springer Series %V 15 %P 203-247 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85055036627&doi=10.1007%2f978-3-319-94676-4_8&partnerID=40&md5=e9c07038e7bcc6668ec702c0653410dc %R 10.1007/978-3-319-94676-4_8 %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 Journal of Hyperbolic Differential Equations %D 2018 %T Regularity estimates for scalar conservation laws in one space dimension %A Elio Marconi %XWe deal with the regularizing effect that, in scalar conservation laws in one space dimension, the nonlinearity of the flux function f has on the entropy solution. More precisely, if the set w : f″(w)≠0 is dense, the regularity of the solution can be expressed in terms of BVΦ spaces, where Φ depends on the nonlinearity of f. If moreover the set w : f″(w) = 0 is finite, under the additional polynomial degeneracy condition at the inflection points, we prove that f′∘ u(t) ∈BV loc(ℝ) for every t > 0 and that this can be improved to SBVloc(ℝ) regularity except an at most countable set of singular times. Finally, we present some examples that show the sharpness of these results and counterexamples to related questions, namely regularity in the kinetic formulation and a property of the fractional BV spaces.

%B Journal of Hyperbolic Differential Equations %V 15 %P 623-691 %G eng %U https://doi.org/10.1142/S0219891618500200 %R 10.1142/S0219891618500200 %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 Journal Article %J Journal of Nonlinear Mathematical Physics %D 2018 %T Singular Hartree equation in fractional perturbed Sobolev spaces %A Alessandro Michelangeli %A Alessandro Olgiati %A Raffaele Scandone %XWe establish the local and global theory for the Cauchy problem of the singular Hartree equation in three dimensions, that is, the modification of the non-linear Schrödinger equation with Hartree non-linearity, where the linear part is now given by the Hamiltonian of point interaction. The latter is a singular, self-adjoint perturbation of the free Laplacian, modelling a contact interaction at a fixed point. The resulting non-linear equation is the typical effective equation for the dynamics of condensed Bose gases with fixed point-like impurities. We control the local solution theory in the perturbed Sobolev spaces of fractional order between the mass space and the operator domain. We then control the global solution theory both in the mass and in the energy space.

%B Journal of Nonlinear Mathematical Physics %I Taylor & Francis %V 25 %P 558-588 %G eng %U https://doi.org/10.1080/14029251.2018.1503423 %R 10.1080/14029251.2018.1503423 %0 Journal Article %J International Journal of Mechanical Sciences %D 2018 %T Spontaneous morphing of equibiaxially pre-stretched elastic bilayers: The role of sample geometry %A Noe Caruso %A Aleksandar Cvetković %A Alessandro Lucantonio %A Giovanni Noselli %A Antonio DeSimone %K Bifurcation %K Elastic bilayer %K Pre-stretch %K Shape programming %XAn elastic bilayer, consisting of an equibiaxially pre-stretched sheet bonded to a stress-free one, spontaneously morphs into curved shapes in the absence of external loads or constraints. Using experiments and numerical simulations, we explore the role of geometry for square and rectangular samples in determining the equilibrium shape of the system, for a fixed pre-stretch. We classify the observed shapes over a wide range of aspect ratios according to their curvatures and compare measured and computed values, which show good agreement. In particular, as the bilayer becomes thinner, a bifurcation of the principal curvatures occurs, which separates two scaling regimes for the energy of the system. We characterize the transition between these two regimes and show the peculiar features that distinguish square from rectangular samples. The results for our model bilayer system may help explaining morphing in more complex systems made of active materials.

%B International Journal of Mechanical Sciences %V 149 %P 481-486 %G eng %U https://www.sciencedirect.com/science/article/pii/S0020740317311761 %R https://doi.org/10.1016/j.ijmecsci.2017.08.049 %0 Conference Paper %B Technology and Science for the Ships of the Future - Proceedings of NAV 2018: 19th International Conference on Ship and Maritime Research %D 2018 %T SRTP 2.0 - The evolution of the safe return to port concept %A D. Cangelosi %A A. Bonvicini %A M. Nardo %A Andrea Mola %A A. Marchese %A Marco Tezzele %A Gianluigi Rozza %XIn 2010 IMO (International Maritime Organisation) introduced new rules in SOLAS with the aim of intrinsically increase the safety of passenger ships. This requirement is achieved by providing safe areas for passengers and essential services for allowing ship to Safely Return to Port (SRtP). The entry into force of these rules has changed the way to design passenger ships. In this respect big effort in the research has been done by industry to address design issues related to the impact on failure analysis of the complex interactions among systems. Today the research activity is working to bring operational matters in the design stage. This change of research focus was necessary because human factor and the way to operate the ship itself after a casualty on board may have a big impact in the design of the ship/systems. Also the management of the passengers after a casualty is becoming a major topic for safety. This paper presents the state of the art of Italian knowledge in the field of system engineering applied to passenger ship address to safety improvement and design reliability. An overview of present tools and methodologies will be offered together with future focuses in the research activity.

%B Technology and Science for the Ships of the Future - Proceedings of NAV 2018: 19th International Conference on Ship and Maritime Research %G eng %R 10.3233/978-1-61499-870-9-665 %0 Journal Article %J SIAM-ASA Journal on Uncertainty Quantification %D 2018 %T Stabilized weighted reduced basis methods for parametrized advection dominated problems with random inputs %A D. Torlo %A F. Ballarin %A Gianluigi Rozza %XIn this work, we propose viable and eficient strategies for stabilized parametrized advection dominated problems, with random inputs. In particular, we investigate the combination of the wRB (weighted reduced basis) method for stochastic parametrized problems with the stabilized RB (reduced basis) method, which is the integration of classical stabilization methods (streamline/upwind Petrov-Galerkin (SUPG) in our case) in the ofine-online structure of the RB method. Moreover, we introduce a reduction method that selectively enables online stabilization; this leads to a sensible reduction of computational costs, while keeping a very good accuracy with respect to high-fdelity solutions. We present numerical test cases to assess the performance of the proposed methods in steady and unsteady problems related to heat transfer phenomena.

%B SIAM-ASA Journal on Uncertainty Quantification %V 6 %P 1475-1502 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85058246502&doi=10.1137%2f17M1163517&partnerID=40&md5=6c54e2f0eb727cb85060e988486b8ac8 %R 10.1137/17M1163517 %0 Report %D 2018 %T Stochastic homogenisation of free-discontinuity problems %A Filippo Cagnetti %A Gianni Dal Maso %A Lucia Scardia %A Caterina Ida Zeppieri %X In this paper we study the stochastic homogenisation of free-discontinuity functionals. Assuming stationarity for the random volume and surface integrands, we prove the existence of a homogenised random free-discontinuity functional, which is deterministic in the ergodic case. Moreover, by establishing a connection between the deterministic convergence of the functionals at any fixed realisation and the pointwise Subadditive Ergodic Theorem by Akcoglou and Krengel, we characterise the limit volume and surface integrands in terms of asymptotic cell formulas. %G en %U http://preprints.sissa.it/handle/1963/35309 %1 35617 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-03-19T09:16:27Z No. of bitstreams: 1 Cag-DM-Sca-Zep-Stochastic.pdf: 427225 bytes, checksum: 758a4e21e1c47b4a34c774f5d4bff8c2 (MD5) %0 Report %D 2018 %T Transmission conditions obtained by homogenisation %A Gianni Dal Maso %A Giovanni Franzina %A Davide Zucco %X We study the asymptotic behaviour of solutions to variational problems in perforated domains with Neumann boundary conditions. We consider perforations that in the limit concentrate on a smooth manifold. We characterise the limits of the solutions and show that they solve a variational problem with a transmission condition across the manifold. This is expressed through a measure on the manifold, vanishing on sets of capacity zero. Then, we prove that every such measure can be obtained by homogenising suitable perforations. Eventually, we provide an asymptotic formula for this measure by using some auxiliary minimum problems. %G en %U http://preprints.sissa.it/handle/1963/35310 %1 35618 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-03-19T09:23:08Z No. of bitstreams: 1 DM-Fra-Zuc-preprint.pdf: 420855 bytes, checksum: 1c4ce5133a6ab027c50e403c702aa690 (MD5) %0 Conference Paper %B Theory, Numerics and Applications of Hyperbolic Problems I %D 2018 %T On Uniqueness of Weak Solutions to Transport Equation with Non-smooth Velocity Field %A Paolo Bonicatto %E Klingenberg, Christian %E Westdickenberg, Michael %B Theory, Numerics and Applications of Hyperbolic Problems I %I Springer International Publishing %C Cham %P 191–203 %@ 978-3-319-91545-6 %G eng %U https://link.springer.com/chapter/10.1007/978-3-319-91545-6_15 %R 10.1007/978-3-319-91545-6_15 %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 Report %D 2017 %T On the 1D wave equation in time-dependent domains and the problem of debond initiation %A Giuliano Lazzaroni %A Lorenzo Nardini %XMotivated by a debonding model for a thin film peeled from a substrate, we analyse the one-dimensional wave equation, in a time-dependent domain which is degenerate at the initial time. In the first part of the paper we prove existence for the wave equation when the evolution of the domain is given; in the second part of the paper, the evolution of the domain is unknown and is governed by an energy criterion coupled with the wave equation. Our existence result for such coupled problem is a contribution to the study of crack initiation in dynamic fracture.

%I SISSA %G en %U http://preprints.sissa.it/handle/1963/35302 %1 35608 %2 Mathematics %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-12-04T07:54:16Z No. of bitstreams: 1 Laz-Nar-17b-initiation-preprint.pdf: 361257 bytes, checksum: faea0e34829456cb358a72d2020f0db4 (MD5) %0 Report %D 2017 %T Almost global existence of solutions for capillarity-gravity water waves equations with periodic spatial boundary conditions %A Massimiliano Berti %A Jean-Marc Delort %X The goal of this monograph is to prove that any solution of the Cauchy problem for the capillarity-gravity water waves equations, in one space dimension, with periodic, even in space, initial data of small size ϵ, is almost globally defined in time on Sobolev spaces, i.e. it exists on a time interval of length of magnitude ϵ−N for any N, as soon as the initial data are smooth enough, and the gravity-capillarity parameters are taken outside an exceptional subset of zero measure. In contrast to the many results known for these equations on the real line, with decaying Cauchy data, one cannot make use of dispersive properties of the linear flow. Instead, our method is based on a normal forms procedure, in order to eliminate those contributions to the Sobolev energy that are of lower degree of homogeneity in the solution. Since the water waves equations are a quasi-linear system, usual normal forms approaches would face the well known problem of losses of derivatives in the unbounded transformations. In this monograph, to overcome such a difficulty, after a paralinearization of the capillarity-gravity water waves equations, necessary to obtain energy estimates, and thus local existence of the solutions, we first perform several paradifferential reductions of the equations to obtain a diagonal system with constant coefficients symbols, up to smoothing remainders. Then we may start with a normal form procedure where the small divisors are compensated by the previous paradifferential regularization.The reversible structure of the water waves equations, and the fact that we look for solutions even in x, guarantees a key cancellation which prevents the growth of the Sobolev norms of the solutions. %G en %U http://preprints.sissa.it/handle/1963/35285 %1 35590 %2 Mathematics %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-05-30T09:17:49Z No. of bitstreams: 1 1702.04674.pdf: 2311619 bytes, checksum: 0765035340f77780899e30e93390092b (MD5) %0 Journal Article %J Topol. Methods Nonlinear Anal. %D 2017 %T An application of coincidence degree theory to cyclic feedback type systems associated with nonlinear differential operators %A Guglielmo Feltrin %A Fabio Zanolin %B Topol. Methods Nonlinear Anal. %I Nicolaus Copernicus University, Juliusz P. Schauder Centre for Nonlinear Studies %V 50 %P 683–726 %G eng %U https://doi.org/10.12775/TMNA.2017.038 %R 10.12775/TMNA.2017.038 %0 Journal Article %J Journal of Scientific Computing %D 2017 %T On the Application of Reduced Basis Methods to Bifurcation Problems in Incompressible Fluid Dynamics %A Giuseppe Pitton %A Gianluigi Rozza %XIn this paper we apply a reduced basis framework for the computation of flow bifurcation (and stability) problems in fluid dynamics. The proposed method aims at reducing the complexity and the computational time required for the construction of bifurcation and stability diagrams. The method is quite general since it can in principle be specialized to a wide class of nonlinear problems, but in this work we focus on an application in incompressible fluid dynamics at low Reynolds numbers. The validation of the reduced order model with the full order computation for a benchmark cavity flow problem is promising.

%B Journal of Scientific Computing %G eng %R 10.1007/s10915-017-0419-6 %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 Book Section %B Spectral and High Order Methods for Partial Differential Equations %D 2017 %T Certified Reduced Basis Method for Affinely Parametric Isogeometric Analysis NURBS Approximation %A Denis Devaud %A Gianluigi Rozza %XIn this work we apply reduced basis methods for parametric PDEs to an isogeometric formulation based on

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

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

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

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

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

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

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

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

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

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

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

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

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

%B Spectral and High Order Methods for Partial Differential Equations %7 Bittencourt, Dumont, Hesthaven. (Eds). %I Springer %C Heildeberg %V 119 %@ 978-3-319-65869-8 %G eng %0 Journal Article %J SIAM Journal on Numerical Analysis %D 2017 %T On a certified smagorinsky reduced basis turbulence model %A Rebollo, T.C. %A E.D. Ávila %A Marmol, M.G. %A F. Ballarin %A Gianluigi Rozza %B SIAM Journal on Numerical Analysis %V 55 %P 3047-3067 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85039928218&doi=10.1137%2f17M1118233&partnerID=40&md5=221d9cd2bcc74121fcef93efd9d3d76c %R 10.1137/17M1118233 %0 Journal Article %J Journal of Differential Equations %D 2017 %T Clifford Tori and the singularly perturbed Cahn–Hilliard equation %A Matteo Rizzi %K Cahn–Hilliard equation %K Clifford Torus %K Lyapunov–Schmidt reduction %K Willmore surface %XIn this paper we construct entire solutions uε to the Cahn–Hilliard equation −ε2Δ(−ε2Δu+W′(u))+W″(u)(−ε2Δu+W′(u))=ε4λε(1−uε), under the volume constraint ∫R3(1−uε)2dx=82π2cε, with cε→1 as ε→0, whose nodal set approaches the Clifford Torus, that is the Torus with radii of ratio 1/2 embedded in R3, as ε→0. It is crucial that the Clifford Torus is a Willmore hypersurface and it is non-degenerate, up to conformal transformations. The proof is based on the Lyapunov–Schmidt reduction and on careful geometric expansions of the Laplacian.

%B Journal of Differential Equations %V 262 %P 5306 - 5362 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022039617300530 %R https://doi.org/10.1016/j.jde.2017.01.026 %0 Journal Article %J Journal of Computational Physics %D 2017 %T Computational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: Applications to Coanda effect in cardiology %A Giuseppe Pitton %A Annalisa Quaini %A Gianluigi Rozza %K Parametrized Navier–Stokes equations %K Reduced basis method %K Stability of flows %K Symmetry breaking bifurcation %XWe focus on reducing the computational costs associated with the hydrodynamic stability of solutions of the incompressible Navier–Stokes equations for a Newtonian and viscous fluid in contraction–expansion channels. In particular, we are interested in studying steady bifurcations, occurring when non-unique stable solutions appear as physical and/or geometric control parameters are varied. The formulation of the stability problem requires solving an eigenvalue problem for a partial differential operator. An alternative to this approach is the direct simulation of the flow to characterize the asymptotic behavior of the solution. Both approaches can be extremely expensive in terms of computational time. We propose to apply Reduced Order Modeling (ROM) techniques to reduce the demanding computational costs associated with the detection of a type of steady bifurcations in fluid dynamics. The application that motivated the present study is the onset of asymmetries (i.e., symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the regurgitant mitral valve orifice shape.

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

%B Journal of Computational Physics %V 344 %P 247 - 259 %G eng %U http://www.sciencedirect.com/science/article/pii/S002199911730356X %R https://doi.org/10.1016/j.jcp.2017.04.068 %0 Journal Article %J Nonlinear Analysis %D 2017 %T Curvature terms in small time heat kernel expansion for a model class of hypoelliptic Hörmander operators %A Davide Barilari %A Elisa Paoli %K Curvature %K Hypoelliptic heat equation %K Small time asymptotics %XWe consider the heat equation associated with a class of second order hypoelliptic Hörmander operators with constant second order term and linear drift. We completely describe the small time heat kernel expansions on the diagonal giving a geometric characterization of the coefficients in terms of the divergence of the drift field and the curvature-like invariants of the optimal control problem associated with the diffusion operator.

%B Nonlinear Analysis %V 164 %P 118 - 134 %G eng %U http://www.sciencedirect.com/science/article/pii/S0362546X17302298 %R https://doi.org/10.1016/j.na.2017.09.002 %0 Report %D 2017 %T Derivation of a rod theory from lattice systems with interactions beyond nearest neighbours %A Roberto Alicandro %A Giuliano Lazzaroni %A Mariapia Palombaro %X We study continuum limits of discrete models for (possibly heterogeneous) nanowires. The lattice energy includes at least nearest and next-to-nearest neighbour interactions: the latter have the role of penalising changes of orientation. In the heterogeneous case, we obtain an estimate on the minimal energy spent to match different equilibria. This gives insight into the nucleation of dislocations in epitaxially grown heterostructured nanowires. %G en %U http://urania.sissa.it/xmlui/handle/1963/35269 %1 35575 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-01-16T12:46:44Z No. of bitstreams: 1 Lazzaroni_Preprint_58_2016.pdf: 305384 bytes, checksum: 9e6300f0e04681ca5ebd4b457ddea10e (MD5) %0 Book Section %B Advances in Quantum Mechanics: Contemporary Trends and Open Problems %D 2017 %T Dispersive Estimates for Schrödinger Operators with Point Interactions in ℝ3 %A Felice Iandoli %A Raffaele Scandone %E Alessandro Michelangeli %E Gianfausto Dell'Antonio %XThe study of dispersive properties of Schrödinger operators with point interactions is a fundamental tool for understanding the behavior of many body quantum systems interacting with very short range potential, whose dynamics can be approximated by non linear Schrödinger equations with singular interactions. In this work we proved that, in the case of one point interaction in $\mathbb{R}^3$, the perturbed Laplacian satisfies the same $L^p$−$L^q$ estimates of the free Laplacian in the smaller regime $q \in [2,3)$. These estimates are implied by a recent result concerning the Lpboundedness of the wave operators for the perturbed Laplacian. Our approach, however, is more direct and relatively simple, and could potentially be useful to prove optimal weighted estimates also in the regime $q \geq 3$.

%B Advances in Quantum Mechanics: Contemporary Trends and Open Problems %I Springer International Publishing %C Cham %P 187–199 %@ 978-3-319-58904-6 %G eng %U https://doi.org/10.1007/978-3-319-58904-6_11 %R 10.1007/978-3-319-58904-6_11 %0 Report %D 2017 %T On the effect of interactions beyond nearest neighbours on non-convex lattice systems %A Roberto Alicandro %A Giuliano Lazzaroni %A Mariapia Palombaro %X We analyse the rigidity of non-convex discrete energies where at least nearest and next-to-nearest neighbour interactions are taken into account. Our purpose is to show that interactions beyond nearest neighbours have the role of penalising changes of orientation and, to some extent, they may replace the positive-determinant constraint that is usually required when only nearest neighbours are accounted for. In a discrete to continuum setting, we prove a compactness result for a family of surface-scaled energies and we give bounds on its possible Gamma-limit in terms of interfacial energies that penalise changes of orientation. %G en %U http://urania.sissa.it/xmlui/handle/1963/35268 %1 35574 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-01-16T12:38:33Z No. of bitstreams: 1 Lazzaroni_preprint_57_2016.pdf: 249941 bytes, checksum: e60963aab015e1fc146068240f824f79 (MD5) %0 Journal Article %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %T Energy release rate and quasi-static evolution via vanishing viscosity in a fracture model depending on the crack opening %A Stefano Almi %XIn the setting of planar linearized elasticity, we study a fracture model depending on the crack opening. Assuming that the crack path is known a priori and sufficiently smooth, we prove that the energy release rate is well defined. Then, we consider the problem of quasi-static evolution for our model. Thanks to a vanishing viscosity approach, we show the existence of such an evolution satisfying a weak Griffith’s criterion.

%B ESAIM: Control, Optimisation and Calculus of Variations %I EDP Sciences %V 23 %P 791–826 %8 05/2017 %G eng %U https://www.esaim-cocv.org/component/article?access=doi&doi=10.1051/cocv/2016014 %R 10.1051/cocv/2016014 %0 Report %D 2017 %T Gamma-Convergence of Free-discontinuity problems %A Filippo Cagnetti %A Gianni Dal Maso %A Lucia Scardia %A Caterina Ida Zeppieri %X We study the Gamma-convergence of sequences of free-discontinuity functionals depending on vector-valued functions u which can be discontinuous across hypersurfaces whose shape and location are not known a priori. The main novelty of our result is that we work under very general assumptions on the integrands which, in particular, are not required to be periodic in the space variable. Further, we consider the case of surface integrands which are not bounded from below by the amplitude of the jump of u. We obtain three main results: compactness with respect to Gamma-convergence, representation of the Gamma-limit in an integral form and identification of its integrands, and homogenisation formulas without periodicity assumptions. In particular, the classical case of periodic homogenisation follows as a by-product of our analysis. Moreover, our result covers also the case of stochastic homogenisation, as we will show in a forthcoming paper. %I SISSA %G en %U http://preprints.sissa.it/handle/1963/35276 %1 35583 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-03-20T13:20:54Z No. of bitstreams: 1 Cag-DM-Sca-Zep-sissa.pdf: 494285 bytes, checksum: 0da567323c828153382b08fc0f967af4 (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 Annali di Matematica Pura ed Applicata (1923 -) %D 2017 %T Globally stable quasistatic evolution for strain gradient plasticity coupled with damage %A Vito Crismale %XWe consider evolutions for a material model which couples scalar damage with strain gradient plasticity, in small strain assumptions. For strain gradient plasticity, we follow the Gurtin–Anand formulation (J Mech Phys Solids 53:1624–1649, 2005). The aim of the present model is to account for different phenomena: On the one hand, the elastic stiffness reduces and the plastic yield surface shrinks due to material's degradation, on the other hand the dislocation density affects the damage growth. The main result of this paper is the existence of a globally stable quasistatic evolution (in the so-called energetic formulation). Furthermore, we study the limit model as the strain gradient terms tend to zero. Under stronger regularity assumptions, we show that the evolutions converge to the ones for the coupled elastoplastic damage model studied in Crismale (ESAIM Control Optim Calc Var 22:883-912, 2016).

%B Annali di Matematica Pura ed Applicata (1923 -) %V 196 %P 641–685 %8 Apr %G eng %U https://doi.org/10.1007/s10231-016-0590-7 %R 10.1007/s10231-016-0590-7 %0 Journal Article %J Calculus of Variations and Partial Differential Equations %D 2017 %T Homotopically invisible singular curves %A Andrei A. Agrachev %A Francesco Boarotto %A Antonio Lerario %B Calculus of Variations and Partial Differential Equations %V 56 %P 105 %8 Jul %G eng %U https://doi.org/10.1007/s00526-017-1203-z %R 10.1007/s00526-017-1203-z %0 Journal Article %J Communications in Analysis and Geometry %D 2017 %T Homotopy properties of horizontal path spaces and a theorem of Serre in subriemannian geometry %A Francesco Boarotto %A Antonio Lerario %B Communications in Analysis and Geometry %I International Press of Boston %V 25 %P 269–301 %G eng %R 10.4310/CAG.2017.v25.n2.a1 %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 A Lagrangian approach for scalar multi-d conservation laws %A Stefano Bianchini %A Paolo Bonicatto %A Elio Marconi %G en %U http://preprints.sissa.it/handle/1963/35290 %1 35596 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-08-08T08:57:31Z No. of bitstreams: 1 main.pdf: 427188 bytes, checksum: 8ab383e6ab2a6dcbf06a22d007db5dda (MD5) %0 Journal Article %J Contemporary Mathematics. Fundamental Directions %D 2017 %T Lagrangian representations for linear and nonlinear transport %A Stefano Bianchini %A Paolo Bonicatto %A Elio Marconi %XIn this note we present a unifying approach for two classes of first order partial differential equations: we introduce the notion of Lagrangian representation in the settings of continuity equation and scalar conservation laws. This yields, on the one hand, the uniqueness of weak solutions to transport equation driven by a two dimensional BV nearly incompressible vector field. On the other hand, it is proved that the entropy dissipation measure for scalar conservation laws in one space dimension is concentrated on countably many Lipschitz curves.

%B Contemporary Mathematics. Fundamental Directions %I Peoples' Friendship University of Russia %V 63 %P 418–436 %G eng %U http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=cmfd&paperid=327&option_lang=eng %R 10.22363/2413-3639-2017-63-3-418-436 %0 Journal Article %J ESAIM: COCV %D 2017 %T Limit of viscous dynamic processes in delamination as the viscosity and inertia vanish %A Riccardo Scala %XWe introduce a model of dynamic evolution of a delaminated visco-elastic body with viscous adhesive. We prove the existence of solutions of the corresponding system of PDEs and then study the behavior of such solutions when the data of the problem vary slowly. We prove that a rescaled version of the dynamic evolutions converge to a “local” quasistatic evolution, which is an evolution satisfying an energy inequality and a momentum balance at all times. In the one-dimensional case we give a more detailed description of the limit evolution and we show that it behaves in a very similar way to the limit of the solutions of the dynamic model in [T. Roubicek, SIAM J. Math. Anal. 45 (2013) 101–126], where no viscosity in the adhesive is taken into account.

%B ESAIM: COCV %V 23 %P 593-625 %G eng %U https://doi.org/10.1051/cocv/2016006 %R 10.1051/cocv/2016006 %0 Journal Article %D 2017 %T Linear Hyperbolic Systems in Domains with Growing Cracks %A Maicol Caponi %XWe consider the hyperbolic system ü$${ - {\rm div} (\mathbb{A} \nabla u) = f}$$in the time varying cracked domain $${\Omega \backslash \Gamma_t}$$, where the set $${\Omega \subset \mathbb{R}^d}$$is open, bounded, and with Lipschitz boundary, the cracks $${\Gamma_t, t \in [0, T]}$$, are closed subsets of $${\bar{\Omega}}$$, increasing with respect to inclusion, and $${u(t) : \Omega \backslash \Gamma_t \rightarrow \mathbb{R}^d}$$for every $${t \in [0, T]}$$. We assume the existence of suitable regular changes of variables, which reduce our problem to the transformed system v̈$${ - {\rm div} (\mathbb{B}\nabla v) + a\nabla v - 2 \nabla \dot{v}b = g}$$on the fixed domain $${\Omega \backslash \Gamma_0}$$. Under these assumptions, we obtain existence and uniqueness of weak solutions for these two problems. Moreover, we show an energy equality for the functions v, which allows us to prove a continuous dependence result for both systems. The same study has already been carried out in [3, 7] in the scalar case.

%V 85 %P 149 - 185 %8 2017/06/01 %@ 1424-9294 %G eng %U https://doi.org/10.1007/s00032-017-0268-7 %N 1 %! Milan Journal of Mathematics %0 Report %D 2017 %T Linearisation of multiwell energies %A Roberto Alicandro %A Gianni Dal Maso %A Giuliano Lazzaroni %A Mariapia Palombaro %X Linear elasticity can be rigorously derived from finite elasticity under the assumption of small loadings in terms of Gamma-convergence. This was first done in the case of one-well energies with super-quadratic growth and later generalised to different settings, in particular to the case of multi-well energies where the distance between the wells is very small (comparable to the size of the load). In this paper we study the case when the distance between the wells is independent of the size of the load. In this context linear elasticity can be derived by adding to the multi-well energy a singular higher order term which penalises jumps from one well to another. The size of the singular term has to satisfy certain scaling assumptions whose optimality is shown in most of the cases. Finally, the derivation of linear elasticty from a two-well discrete model is provided, showing that the role of the singular perturbation term is played in this setting by interactions beyond nearest neighbours. %G en %U http://preprints.sissa.it/handle/1963/35288 %1 35594 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-06-22T09:07:10Z No. of bitstreams: 1 ADMLP_linear.pdf: 364014 bytes, checksum: 305b4dcf6f1ee7c09e6747b7378ae58c (MD5) %0 Journal Article %J Advances in Calculus of Variations %D 2017 %T Lower semicontinuity of a class of integral functionals on the space of functions of bounded deformation %A Gianni Dal Maso %A Gianluca Orlando %A Rodica Toader %XWe study the lower semicontinuity of some free discontinuity functionals with linear growth defined on the space of functions with bounded deformation. The volume term is convex and depends only on the Euclidean norm of the symmetrized gradient. We introduce a suitable class of surface terms, which make the functional lower semicontinuous with respect to $L^1$ convergence.

%B Advances in Calculus of Variations %I De Gruyter %V 10 %P 183–207 %G eng %R 10.1515/acv-2015-0036 %0 Journal Article %J Journal de Mathématiques Pures et Appliquées %D 2017 %T A lower semicontinuity result for a free discontinuity functional with a boundary term %A Stefano Almi %A Gianni Dal Maso %A Rodica Toader %XWe study the lower semicontinuity in $GSBV^{p}(\Omega;\mathbb{R}^{m})$ of a free discontinuity functional $\mathcal{F}(u)$ that can be written as the sum of a crack term, depending only on the jump set $S_{u}$, and of a boundary term, depending on the trace of $u$ on $\partial\Omega$. We give sufficient conditions on the integrands for the lower semicontinuity of $\mathcal{F}$. Moreover, we prove a relaxation result, which shows that, if these conditions are not satisfied, the lower semicontinuous envelope of $\mathcal{F}$ can be represented by the sum of two integrals on $S_{u}$ and $\partial\Omega$, respectively.

%B Journal de Mathématiques Pures et Appliquées %V 108 %P 952-990 %G en %U http://hdl.handle.net/20.500.11767/15979 %N 6 %1 34731 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by salmi@sissa.it (salmi@sissa.it) on 2015-12-15T14:37:19Z No. of bitstreams: 1 Alm-DM-Toa-15-sissa.pdf: 351559 bytes, checksum: b6adddc4944478676c7d4b34028a347c (MD5) %& 952 %R 10.1016/j.matpur.2017.05.018 %0 Journal Article %J Communications on Pure & Applied Analysis %D 2017 %T Minimizers of anisotropic perimeters with cylindrical norms %A Giovanni Bellettini %A Matteo Novaga %A Shokhrukh Kholmatov %K anisotropic Bernstein problem; %K minimal cones %K Non parametric minimal surfaces %K Sets of finite perimeter %XWe study various regularity properties of minimizers of the Φ–perimeter, where Φ is a norm. Under suitable assumptions on Φ and on the dimension of the ambient space, we prove that the boundary of a cartesian minimizer is locally a Lipschitz graph out of a closed singular set of small Hausdorff dimension. Moreover, we show the following anisotropic Bernstein-type result: any entire cartesian minimizer is the subgraph of a monotone function depending only on one variable.

%B Communications on Pure & Applied Analysis %V 16 %P 1427 %G eng %U http://aimsciences.org//article/id/47054f15-00c7-40b7-9da1-4c0b1d0a103d %R 10.3934/cpaa.2017068 %0 Journal Article %J Communications on Pure & Applied Analysis %D 2017 %T Multiple positive solutions of a sturm-liouville boundary value problem with conflicting nonlinearities %A Guglielmo Feltrin %K Leray-Schauder topological degree; %K positive solutions %K Sturm-Liouville boundary conditions %K Superlinear indefinite problems %XWe study the second order nonlinear differential equation

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

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

%B Communications on Pure & Applied Analysis %V 16 %P 1083 %G eng %U http://aimsciences.org//article/id/1163b042-0c64-4597-b25c-3494b268e5a1 %R 10.3934/cpaa.2017052 %0 Journal Article %J Journal of Differential Equations %D 2017 %T Multiplicity of positive periodic solutions in the superlinear indefinite case via coincidence degree %A Guglielmo Feltrin %A Fabio Zanolin %K Coincidence degree %K Multiplicity results %K Neumann boundary value problems %K Positive periodic solutions %K subharmonic solutions %K Superlinear indefinite problems %XWe study the periodic boundary value problem associated with the second order nonlinear differential equationu″+cu′+(a+(t)−μa−(t))g(u)=0, where g(u) has superlinear growth at zero and at infinity, a(t) is a periodic sign-changing weight, c∈R and μ>0 is a real parameter. Our model includes (for c=0) the so-called nonlinear Hill's equation. We prove the existence of 2m−1 positive solutions when a(t) has m positive humps separated by m negative ones (in a periodicity interval) and μ is sufficiently large, thus giving a complete solution to a problem raised by G.J. Butler in 1976. The proof is based on Mawhin's coincidence degree defined in open (possibly unbounded) sets and applies also to Neumann boundary conditions. Our method also provides a topological approach to detect subharmonic solutions.

%B Journal of Differential Equations %V 262 %P 4255 - 4291 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022039617300219 %R https://doi.org/10.1016/j.jde.2017.01.009 %0 Journal Article %J Ann. Mat. Pura Appl. %D 2017 %T A note on a fixed point theorem on topological cylinders %A Guglielmo Feltrin %XWe present a fixed point theorem on topological cylinders in normed linear spaces for maps satisfying a property of stretching a space along paths. This result is a generalization of a similar theorem obtained by D. Papini and F. Zanolin. In view of the main result, we discuss the existence of fixed points for maps defined on different types of domains and we propose alternative proofs for classical fixed point theorems, as Brouwer, Schauder and Krasnosel’skii ones.

%B Ann. Mat. Pura Appl. %I Springer Verlag %G en %U http://urania.sissa.it/xmlui/handle/1963/35263 %1 35567 %2 Mathematics %4 1 %# MAT/05 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2016-11-21T07:45:03Z (GMT) No. of bitstreams: 0 %R 10.1007/s10231-016-0623-2 %0 Journal Article %J Journal of Dynamics and Differential Equations %D 2017 %T A Note on the Convergence of Singularly Perturbed Second Order Potential-Type Equations %A Lorenzo Nardini %B Journal of Dynamics and Differential Equations %V 29 %P 783–797 %8 Jun %G eng %U https://doi.org/10.1007/s10884-015-9461-y %R 10.1007/s10884-015-9461-y %0 Journal Article %J Biomechanics and Modeling in Mechanobiology %D 2017 %T Numerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts %A F. Ballarin %A Elena Faggiano %A Andrea Manzoni %A Alfio Quarteroni %A Gianluigi Rozza %A Sonia Ippolito %A Roberto Scrofani %B Biomechanics and Modeling in Mechanobiology %V 16 %P 1373-1399 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85015065851&doi=10.1007%2fs10237-017-0893-7&partnerID=40&md5=c388f20bd5de14187bad9ed7d9affbd0 %R 10.1007/s10237-017-0893-7 %0 Journal Article %J Communications in Applied and Industrial Mathematics %D 2017 %T POD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder %A Giovanni Stabile %A Saddam Hijazi %A Andrea Mola %A Stefano Lorenzi %A Gianluigi Rozza %XVortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. In this work a Reduced Order Model (ROM) of the incompressible flow around a circular cylinder, built performing a Galerkin projection of the governing equations onto a lower dimensional space is presented. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pressure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) for this purpose the projection of the Governing equations (momentum equation and Poisson equation for pressure) is performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework are presented. The accuracy of the reduced order model is assessed against full order results.

%B Communications in Applied and Industrial Mathematics %V 8 %P 210-236 %G eng %R 10.1515/caim-2017-0011 %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 Journal Article %J Nonlinear Differential Equations and Applications NoDEA %D 2017 %T Quasistatic crack growth based on viscous approximation: a model with branching and kinking %A Vito Crismale %A Giuliano Lazzaroni %XEmploying the technique of vanishing viscosity and time rescaling, we show the existence of quasistatic evolutions of cracks in brittle materials in the setting of antiplane shear. The crack path is not prescribed a priori and is chosen in an admissible class of piecewise regular sets that allows for branching and kinking.

%B Nonlinear Differential Equations and Applications NoDEA %V 24 %P 7 %8 Jan %G eng %U https://doi.org/10.1007/s00030-016-0426-6 %R 10.1007/s00030-016-0426-6 %0 Journal Article %J SIAM/ASA Journal on Uncertainty Quantification %D 2017 %T Reduced Basis Methods for Uncertainty Quantification %A Peng Chen %A Alfio Quarteroni %A Gianluigi Rozza %XIn this work we review a reduced basis method for the solution of uncertainty quantification problems. Based on the basic setting of an elliptic partial differential equation with random input, we introduce the key ingredients of the reduced basis method, including proper orthogonal decomposition and greedy algorithms for the construction of the reduced basis functions, a priori and a posteriori error estimates for the reduced basis approximations, as well as its computational advantages and weaknesses in comparison with a stochastic collocation method [I. Babuška, F. Nobile, and R. Tempone, *SIAM Rev.*, 52 (2010), pp. 317--355]. We demonstrate its computational efficiency and accuracy for a benchmark problem with parameters ranging from a few to a few hundred dimensions. Generalizations to more complex models and applications to uncertainty quantification problems in risk prediction, evaluation of statistical moments, Bayesian inversion, and optimal control under uncertainty are also presented to illustrate how to use the reduced basis method in practice. Further challenges, advancements, and research opportunities are outlined.

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

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

%B Model Reduction of Parametrized Systems %I Springer International Publishing %P 149–167 %G eng %& Reduced-order semi-implicit schemes for fluid-structure interaction problems %R 10.1007/978-3-319-58786-8_10 %0 Report %D 2017 %T Regularity estimates for scalar conservation laws in one space dimension %A Elio Marconi %X In this paper we deal with the regularizing effect that, in a scalar conservation laws in one space dimension, the nonlinearity of the flux function ƒ has on the entropy solution. More precisely, if the set ⟨w : ƒ " (w) ≠ 0⟩ is dense, the regularity of the solution can be expressed in terms of BV Ф spaces, where Ф depends on the nonlinearity of ƒ. If moreover the set ⟨w : ƒ " (w) = 0⟩ is finite, under the additional polynomial degeneracy condition at the inflection points, we prove that ƒ' 0 u(t) ∈ BVloc (R) for every t > 0 and that this can be improved to SBVloc (R) regularity except an at most countable set of singular times. Finally we present some examples that shows the sharpness of these results and counterexamples to related questions, namely regularity in the kinetic formulation and a property of the fractional BV spaces. %G en %U http://preprints.sissa.it/handle/1963/35291 %1 35597 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-08-16T06:45:14Z No. of bitstreams: 1 Regularity_preprint.pdf: 603969 bytes, checksum: 29e1eefa4da3dc5272a6e9c6119108a5 (MD5) %0 Report %D 2017 %T Second order differentiation formula on compact RCD*(K,N) spaces %A Nicola Gigli %A Luca Tamanini %G eng %0 Journal Article %J Journal of Dynamical and Control Systems %D 2017 %T Small Time Asymptotics on the Diagonal for Hörmander's Type Hypoelliptic Operators %A Elisa Paoli %XWe compute the small time asymptotics of the fundamental solution of Hörmander's type hypoelliptic operators with drift, on the diagonal at a point x0. We show that the order of the asymptotics depends on the controllability of an associated control problem and of its approximating system. If the control problem of the approximating system is controllable at x0, then so is also the original control problem, and in this case we show that the fundamental solution blows up as t−N/2\$\backslashphantom {\backslashdot {i}\backslash!}t^{-\backslashmathcal {N}/2}\$, where N\$\backslashphantom {\backslashdot {i}\backslash!}\backslashmathcal {N}\$is a number determined by the Lie algebra at x0 of the fields, that define the hypoelliptic operator.

%B Journal of Dynamical and Control Systems %V 23 %P 111–143 %8 Jan %G eng %U https://doi.org/10.1007/s10883-016-9321-z %R 10.1007/s10883-016-9321-z %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 Report %D 2017 %T Time quasi-periodic gravity water waves in finite depth %A P Baldi %A Massimiliano Berti %A Emanuele Haus %A Riccardo Montalto %X We prove the existence and the linear stability of Cantor families of small amplitude time quasi-periodic standing water wave solutions - namely periodic and even in the space variable x - of a bi-dimensional ocean with finite depth under the action of pure gravity. Such a result holds for all the values of the depth parameter in a Borel set of asymptotically full measure. This is a small divisor problem. The main difficulties are the quasi-linear nature of the gravity water waves equations and the fact that the linear frequencies grow just in a sublinear way at infinity. We overcome these problems by first reducing the linearized operators obtained at each approximate quasi-periodic solution along the Nash-Moser iteration to constant coefficients up to smoothing operators, using pseudo-differential changes of variables that are quasi-periodic in time. Then we apply a KAM reducibility scheme which requires very weak Melnikov non-resonance conditions (losing derivatives both in time and space), which we are able to verify for most values of the depth parameter using degenerate KAM theory arguments. %G en %U http://preprints.sissa.it/handle/1963/35296 %1 35602 %2 Mathematics %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-09-27T15:46:10Z No. of bitstreams: 1 1708.01517.pdf: 1909445 bytes, checksum: 71fc741593666cacf41187c00b092503 (MD5) %0 Report %D 2017 %T A uniqueness result for the decomposition of vector fields in Rd %A Stefano Bianchini %A Paolo Bonicatto %XGiven a vector field $\rho (1,\b) \in L^1_\loc(\R^+\times \R^{d},\R^{d+1})$ such that $\dive_{t,x} (\rho (1,\b))$ is a measure, we consider the problem of uniqueness of the representation $\eta$ of $\rho (1,\b) \mathcal L^{d+1}$ as a superposition of characteristics $\gamma : (t^-_\gamma,t^+_\gamma) \to \R^d$, $\dot \gamma (t)= \b(t,\gamma(t))$. We give conditions in terms of a local structure of the representation $\eta$ on suitable sets in order to prove that there is a partition of $\R^{d+1}$ into disjoint trajectories $\wp_\a$, $\a \in \A$, such that the PDE \begin{equation*} \dive_{t,x} \big( u \rho (1,\b) \big) \in \mathcal M(\R^{d+1}), \qquad u \in L^\infty(\R^+\times \R^{d}), \end{equation*} can be disintegrated into a family of ODEs along $\wp_\a$ with measure r.h.s.. The decomposition $\wp_\a$ is essentially unique. We finally show that $\b \in L^1_t(\BV_x)_\loc$ satisfies this local structural assumption and this yields, in particular, the renormalization property for nearly incompressible $\BV$ vector fields.

%I SISSA %G en %U http://preprints.sissa.it/handle/1963/35274 %1 35581 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-03-16T09:52:48Z No. of bitstreams: 1 WeakBressanConj-BB.pdf: 1581291 bytes, checksum: fd43c78bcd9ad0384df44d3fdccbe294 (MD5) %0 Journal Article %J Journal of Ship Research %D 2017 %T Wet and Dry Transom Stern Treatment for Unsteady and Nonlinear Potential Flow Model for Naval Hydrodynamics Simulations %A Andrea Mola %A Luca Heltai %A Antonio DeSimone %XWe present a model for the fast evaluation of the total drag of ship hulls operating in both wet and dry transom stern conditions, in calm or wavy water, based on the combination of an unsteady semi-Lagrangian potential flow formulation with fully nonlinear free-surface treatment, experimental correlations, and simplified viscous drag modeling. The implementation is entirely based on open source libraries. The spatial discretization is solved using a streamline upwind Petrov‐Galerkin stabilization of an iso-parametric, collocation based, boundary element method, implemented using the open source library deal.II. The resulting nonlinear differential-algebraic system is integrated in time using implicit backward differentiation formulas, implemented in the open source library SUNDIALS. The Open CASCADE library is used to interface the model directly with computer-aided design data structures. The model accounts automatically for hulls with a transom stern, both in wet and dry regimes, by using a specific treatment of the free-surface nodes on the stern edge that automatically detects when the hull advances at low speeds. In this case, the transom stern is partially immersed, and a pressure patch is applied on the water surface detaching from the transom stern, to recover the gravity effect of the recirculating water on the underlying irrotational flow domain. The parameters of the model used to impose the pressure patch are approximated from experimental relations found in the literature. The test cases considered are those of the U.S. Navy Combatant DTMB-5415 and the National Physical Laboratory hull. Comparisons with experimental data on quasi-steady test cases for both water elevation and total hull drag are presented and discussed. The quality of the results obtained on quasi-steady simulations suggests that this model can represent a promising alternative to current unsteady solvers for simulations with Froude numbers below 0.35.

%B Journal of Ship Research %V 61 %P 1–14 %G eng %R https://doi.org/10.5957/JOSR.61.1.160016 %0 Conference Paper %B Proceedings of the ECCOMAS Congress 2016, VII European Conference on Computational Methods in Applied Sciences and Engineering, %D 2016 %T Advances in geometrical parametrization and reduced order models and methods for computational fluid dynamics problems in applied sciences and engineering: overview and perspectives %A Filippo Salmoiraghi %A F. Ballarin %A Giovanni Corsi %A Andrea Mola %A Marco Tezzele %A Gianluigi Rozza %E Papadrakakis, M. %E Papadopoulos, V. %E Stefanou, G. %E Plevris, V. %XSeveral problems in applied sciences and engineering require reduction techniques in order to allow computational tools to be employed in the daily practice, especially in iterative procedures such as optimization or sensitivity analysis. Reduced order methods need to face increasingly complex problems in computational mechanics, especially into a multiphysics setting. Several issues should be faced: stability of the approximation, efficient treatment of nonlinearities, uniqueness or possible bifurcations of the state solutions, proper coupling between fields, as well as offline-online computing, computational savings and certification of errors as measure of accuracy. Moreover, efficient geometrical parametrization techniques should be devised to efficiently face shape optimization problems, as well as shape reconstruction and shape assimilation problems. A related aspect deals with the management of parametrized interfaces in multiphysics problems, such as fluid-structure interaction problems, and also a domain decomposition based approach for complex parametrized networks. We present some illustrative industrial and biomedical problems as examples of recent advances on methodological developments.

%B Proceedings of the ECCOMAS Congress 2016, VII European Conference on Computational Methods in Applied Sciences and Engineering, %I ECCOMAS %C Crete, Greece %8 06/2016 %G en %1 35466 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2016-05-13T00:28:01Z No. of bitstreams: 1 eccomas2016_AROMA.pdf: 1846196 bytes, checksum: 9636e713df80de178d87fd2feff76f91 (MD5) %0 Journal Article %J ESAIM: COCV %D 2016 %T On the area of the graph of a piecewise smooth map from the plane to the plane with a curve discontinuity %A Giovanni Bellettini %A Lucia Tealdi %A Maurizio Paolini %K Area functional %XIn this paper we provide an estimate from above for the value of the relaxed area functional for a map defined on a bounded domain of the plane with values in the plane and discontinuous on a regular simple curve with two endpoints. We show that, under suitable assumptions, the relaxed area does not exceed the area of the regular part of the map, with the addition of a singular term measuring the area of a disk type solution of the Plateau's problem spanning the two traces of the map on the jump. The result is valid also when the area minimizing surface has self intersections. A key element in our argument is to show the existence of what we call a semicartesian parametrization of this surface, namely a conformal parametrization defined on a suitable parameter space, which is the identity in the first component. To prove our result, various tools of parametric minimal surface theory are used, as well as some result from Morse theory.

%B ESAIM: COCV %V 22 %P 29-63 %G en %U https://www.esaim-cocv.org/articles/cocv/abs/2016/01/cocv140065/cocv140065.html %N 1 %1 7257 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Lucia Tealdi (ltealdi@sissa.it) on 2013-11-29T13:51:49Z No. of bitstreams: 1 bellettini_paolini_tealdi_SISSAprprint.pdf: 705021 bytes, checksum: 98a550aeb5925de05f6b419569ccd283 (MD5) %R 10.1051/cocv/2014065 %0 Report %D 2016 %T Behaviour of the reference measure on RCD spaces under charts %A Nicola Gigli %A Enrico Pasqualetto %G eng %0 Journal Article %J Discrete & Continuous Dynamical Systems - S %D 2016 %T On the concentration of entropy for scalar conservation laws %A Stefano Bianchini %A Elio Marconi %K concentration %K Conservation laws %K entropy solutions %K Lagrangian representation %K shocks %XWe prove that the entropy for an $L^∞$-solution to a scalar conservation laws with continuous initial data is concentrated on a countably $1$-rectifiable set. To prove this result we introduce the notion of Lagrangian representation of the solution and give regularity estimates on the solution.

%B Discrete & Continuous Dynamical Systems - S %V 9 %P 73 %G eng %U http://aimsciences.org//article/id/ce4eb91e-9553-4e8d-8c4c-868f07a315ae %R 10.3934/dcdss.2016.9.73 %0 Journal Article %D 2016 %T Confinement of dislocations inside a crystal with a prescribed external strain %A Ilaria Lucardesi %A Marco Morandotti %A Riccardo Scala %A Davide Zucco %X We study screw dislocations in an isotropic crystal undergoing antiplane shear. In the framework of linear elasticity, by fixing a suitable boundary condition for the strain (prescribed non-vanishing boundary integral), we manage to confine the dislocations inside the material. More precisely, in the presence of an external strain with circulation equal to n times the lattice spacing, it is energetically convenient to have n distinct dislocations lying inside the crystal. The novelty of introducing a Dirichlet boundary condition for the tangential strain is crucial to the confinement: it is well known that, if Neumann boundary conditions are imposed, the dislocations tend to migrate to the boundary. The results are achieved using PDE techniques and Ƭ-convergence theory, in the framework of the so-called core radius approach. %G en %U http://urania.sissa.it/xmlui/handle/1963/35247 %1 35558 %2 Mathematics %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2016-10-20T11:44:46Z No. of bitstreams: 1 LMSZ-preprint.pdf: 547676 bytes, checksum: 5c7add921deefef560aac54da6a584cc (MD5) %0 Journal Article %J Journal of Dynamical and Control Systems %D 2016 %T Conformal Equivalence of 3D Contact Structures on Lie Groups %A Francesco Boarotto %XIn this paper, a conformal classification of three dimensional left-invariant sub-Riemannian contact structures is carried out; in particular, we will prove the following dichotomy: either a structure is locally conformal to the Heisenberg group $mathbbH^3$ or its conformal classification coincides with the metric one. If a structure is locally conformally flat, then its conformal group is locally isomorphic to $SU(2,1)$.

%B Journal of Dynamical and Control Systems %V 22 %P 251–283 %8 Apr %G eng %U https://doi.org/10.1007/s10883-015-9273-8 %R 10.1007/s10883-015-9273-8 %0 Journal Article %J arXiv preprint arXiv:1601.07093 %D 2016 %T Critical points of a perturbed Otha-Kawasaki functional %A Matteo Rizzi %B arXiv preprint arXiv:1601.07093 %G eng %0 Journal Article %J Methods and Applications of Analysis %D 2016 %T Currents and dislocations at the continuum scale %A Riccardo Scala %A Nicolas Van Goethem %XA striking geometric property of elastic bodies with dislocations is that the deformation tensor cannot be written as the gradient of a one-to-one immersion, its curl being nonzero and equal to the density of the dislocations, a measure concentrated in the dislocation lines. In this work, we discuss the mathematical properties of such constrained deformations and study a variational problem in finite-strain elasticity, where Cartesian maps allow us to consider deformations in $L^p$ with $1\leq p<2$, as required for dislocation-induced strain singularities. Firstly, we address the problem of mathematical modeling of dislocations. It is a key purpose of the paper to build a framework where dislocations are described in terms of integral 1-currents and to extract from this theoretical setting a series of notions having a mechanical meaning in the theory of dislocations. In particular, the paper aims at classifying integral 1-currents, with modeling purposes. In the second part of the paper, two variational problems are solved for two classes of dislocations, at the mesoscopic and at the continuum scale. By continuum it is here meant that a countable family of dislocations is considered, allowing for branching and cluster formation, with possible complex geometric patterns. Therefore, modeling assumptions of the defect part of the energy must also be provided, and discussed.

%B Methods and Applications of Analysis %I International Press of Boston %V 23 %P 1–34 %G eng %R 10.4310/MAA.2016.v23.n1.a1 %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 Journal of Differential Equations, vol. 261, issue 8 (2016): 4298-4337 %D 2016 %T Eulerian, Lagrangian and Broad continuous solutions to a balance law with non-convex flux I %A Giovanni Alberti %A Stefano Bianchini %A Laura Caravenna %B Journal of Differential Equations, vol. 261, issue 8 (2016): 4298-4337 %I Elsevier %G en %U http://urania.sissa.it/xmlui/handle/1963/35207 %1 35507 %2 Mathematics %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2016-09-05T15:06:32Z No. of bitstreams: 1 1512.04863v2_Caravenna.pdf: 1192837 bytes, checksum: 15e7fc975989af0ea19654f4eafd84a7 (MD5) %R 10.1016/j.jde.2016.06.026 %0 Report %D 2016 %T Eulerian, Lagrangian and Broad continuous solutions to a balance law with non convex flux II %A Giovanni Alberti %A Stefano Bianchini %A Laura Caravenna %G en %U http://urania.sissa.it/xmlui/handle/1963/35197 %1 35494 %2 Mathematics %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2016-06-21T11:33:07Z No. of bitstreams: 1 file2ABCottobre2015.pdf: 486411 bytes, checksum: cbdd0bce26d338707c03a61c42ec725e (MD5) %0 Journal Article %J Journal of Functional Analysis %D 2016 %T Existence and non-existence results for the SU(3) singular Toda system on compact surfaces %A Luca Battaglia %A Andrea Malchiodi %K Liouville-type equations %K Min–max solutions %K Non-existence results %K Toda system %XWe consider the SU(3) singular Toda system on a compact surface (Σ,g)−Δu1=2ρ1(h1eu1∫Σh1eu1dVg−1)−ρ2(h2eu2∫Σh2eu2dVg−1)−4π∑m=1Mα1m(δpm−1)−Δu2=2ρ2(h2eu2∫Σh2eu2dVg−1)−ρ1(h1eu1∫Σh1eu1dVg−1)−4π∑m=1Mα2m(δpm−1), where hi are smooth positive functions on Σ, ρi∈R+, pm∈Σ and αim>−1. We give both existence and non-existence results under some conditions on the parameters ρi and αim. Existence results are obtained using variational methods, which involve a geometric inequality of new type; non-existence results are obtained using blow-up analysis and localized Pohožaev-type identities."

%B Journal of Functional Analysis %V 270 %P 3750 - 3807 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022123615004942 %R https://doi.org/10.1016/j.jfa.2015.12.011 %0 Journal Article %J Journal of Differential Equations %D 2016 %T Existence and uniqueness of dynamic evolutions for a peeling test in dimension one %A Gianni Dal Maso %A Giuliano Lazzaroni %A Lorenzo Nardini %K Dynamic debonding %K Dynamic energy release rate %K Dynamic fracture %K Griffith's criterion %K Maximum dissipation principle %K Wave equation in time-dependent domains %XIn this paper we present a one-dimensional model of a dynamic peeling test for a thin film, where the wave equation is coupled with a Griffith criterion for the propagation of the debonding front. Our main results provide existence and uniqueness for the solution to this coupled problem under different assumptions on the data.

%B Journal of Differential Equations %V 261 %P 4897 - 4923 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022039616301772 %R https://doi.org/10.1016/j.jde.2016.07.012 %0 Report %D 2016 %T A fast virtual surgery platform for many scenarios haemodynamics of patient-specific coronary artery bypass grafts %A F. Ballarin %A Elena Faggiano %A Andrea Manzoni %A Gianluigi Rozza %A Alfio Quarteroni %A Sonia Ippolito %A Roberto Scrofani %A Carlo Antona %X A fast computational framework is devised to the study of several configurations of patient-specific coronary artery bypass grafts. This is especially useful to perform a sensitivity analysis of the haemodynamics for different flow conditions occurring in native coronary arteries and bypass grafts, the investigation of the progression of the coronary artery disease and the choice of the most appropriate surgical procedure. A complete pipeline, from the acquisition of patientspecific medical images to fast parametrized computational simulations, is proposed. Complex surgical configurations employed in the clinical practice, such as Y-grafts and sequential grafts, are studied. A virtual surgery platform based on model reduction of unsteady Navier Stokes equations for blood dynamics is proposed to carry out sensitivity analyses in a very rapid and reliable way. A specialized geometrical parametrization is employed to compare the effect of stenosis and anastomosis variation on the outcome of the surgery in several relevant cases. %I Submitted %G en %U http://urania.sissa.it/xmlui/handle/1963/35240 %1 35545 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2016-10-14T23:07:40Z No. of bitstreams: 1 BMMB_SISSA_report.pdf: 16374062 bytes, checksum: 7ee82fd9d989ed91bf9cc721ae2114a0 (MD5) %0 Journal Article %J Calculus of Variations and Partial Differential Equations %D 2016 %T Fracture models for elasto-plastic materials as limits of gradient damage models coupled with plasticity: the antiplane case %A Gianni Dal Maso %A Gianluca Orlando %A Rodica Toader %XWe study the asymptotic behavior of a variational model for damaged elasto-plastic materials in the case of antiplane shear. The energy functionals we consider depend on a small parameter $\varepsilon$, which forces damage concentration on regions of codimension one. We determine the $\Gamma$-limit as $\varepsilon$ tends to zero and show that it contains an energy term involving the crack opening.

%B Calculus of Variations and Partial Differential Equations %V 55 %P 45 %8 Apr %G eng %U https://doi.org/10.1007/s00526-016-0981-z %R 10.1007/s00526-016-0981-z %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 ESAIM: Control, Optimisation and Calculus of Variations %D 2016 %T Globally stable quasistatic evolution for a coupled elastoplastic–damage model %A Vito Crismale %XWe show the existence of globally stable quasistatic evolutions for a rate-independent material model with elastoplasticity and incomplete damage, in small strain assumptions. The main feature of our model is that the scalar internal variable which describes the damage affects both the elastic tensor and the plastic yield surface. It is also possible to require that the history of plastic strain up to the current state influences the future evolution of damage.

%B ESAIM: Control, Optimisation and Calculus of Variations %I EDP Sciences %V 22 %P 883–912 %G eng %U https://www.esaim-cocv.org/articles/cocv/abs/2016/03/cocv150037/cocv150037.html %R 10.1051/cocv/2015037 %0 Thesis %D 2016 %T Integrability of continuous bundles and applications to dynamical systems %A Khadim Mbacke War %X In this dissertation we study the problem of integrability of bundles with low regularities. %I SISSA %G en %1 35529 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by kmwar@sissa.it (kmwar@sissa.it) on 2016-09-28T12:10:43Z No. of bitstreams: 1 Thesis-Khadim.pdf: 510947 bytes, checksum: 66daf50c9c84de98301953af3433621e (MD5) %0 Report %D 2016 %T Isogeometric analysis-based reduced order modelling for incompressible linear viscous flows in parametrized shapes %A Filippo Salmoiraghi %A F. Ballarin %A Luca Heltai %A Gianluigi Rozza %X In this work we provide a combination of isogeometric analysis with reduced order modelling techniques, based on proper orthogonal decomposition, to guarantee computational reduction for the numerical model, and with free-form deformation, for versatile geometrical parametrization. We apply it to computational fluid dynamics problems considering a Stokes flow model. The proposed reduced order model combines efficient shape deformation and accurate and stable velocity and pressure approximation for incompressible viscous flows, computed with a reduced order method. Efficient offine-online computational decomposition is guaranteed in view of repetitive calculations for parametric design and optimization problems. Numerical test cases show the efficiency and accuracy of the proposed reduced order model. %I Springer, AMOS Advanced Modelling and Simulation in Engineering Sciences %G en %U http://urania.sissa.it/xmlui/handle/1963/35199 %1 35493 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2016-06-20T23:55:25Z No. of bitstreams: 1 MAIN_IGA_FFD_ROM.pdf: 1631282 bytes, checksum: b050e472f11943b95d8307915a50b6da (MD5) %0 Report %D 2016 %T Large KAM tori for perturbations of the dNLS equation %A Massimiliano Berti %A Thomas Kappeler %A Riccardo Montalto %X We prove that small, semi-linear Hamiltonian perturbations of the defocusing nonlinear Schr\"odinger (dNLS) equation on the circle have an abundance of invariant tori of any size and (finite) dimension which support quasi-periodic solutions. When compared with previous results the novelty consists in considering perturbations which do not satisfy any symmetry condition (they may depend on x in an arbitrary way) and need not be analytic. The main difficulty is posed by pairs of almost resonant dNLS frequencies. The proof is based on the integrability of the dNLS equation, in particular the fact that the nonlinear part of the Birkhoff coordinates is one smoothing. We implement a Newton-Nash-Moser iteration scheme to construct the invariant tori. The key point is the reduction of linearized operators, coming up in the iteration scheme, to 2×2 block diagonal ones with constant coefficients together with sharp asymptotic estimates of their eigenvalues. %G en %U http://preprints.sissa.it/handle/1963/35284 %1 35589 %2 Mathematics %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-05-30T09:09:35Z No. of bitstreams: 1 1603.09252.pdf: 1306610 bytes, checksum: 1e34137dcb21eb2e2a8e93d0c2d009a3 (MD5) %0 Report %D 2016 %T A model for the quasistatic growth of cracks with fractional dimension %A Gianni Dal Maso %A Marco Morandotti %X We study a variational model for the quasistatic growth of cracks with fractional dimension in brittle materials. We give a minimal set of properties of the collection of admissible cracks which ensure the existence of a quasistatic evolution. Both the antiplane and the planar cases are treated. %G en %U http://urania.sissa.it/xmlui/handle/1963/35175 %1 35459 %2 Mathematics %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2016-03-01T11:58:09Z No. of bitstreams: 1 DM-Mor-15-SISSA.pdf: 333769 bytes, checksum: f89da17dcba29091a91c253127244ede (MD5) %0 Book Section %B Wiley Encyclopedia of Computational Mechanics, 2016 %D 2016 %T Model Order Reduction: a survey %A Francisco Chinesta %A Antonio Huerta %A Gianluigi Rozza %A Karen Willcox %B Wiley Encyclopedia of Computational Mechanics, 2016 %I Wiley %G en %U http://urania.sissa.it/xmlui/handle/1963/35194 %1 35470 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2016-05-27T00:41:12Z No. of bitstreams: 1 ECM_MOR.pdf: 746542 bytes, checksum: 93d6252fe8a175c4378b96bd4192712c (MD5) %0 Journal Article %J Mathematische Zeitschrift %D 2016 %T Moser–Trudinger inequalities for singular Liouville systems %A Luca Battaglia %XIn this paper we prove a Moser–Trudinger inequality for the Euler–Lagrange functional of general singular Liouville systems on a compact surface. We characterize the values of the parameters which yield coercivity for the functional, hence the existence of energy-minimizing solutions for the system, and we give necessary conditions for boundedness from below. We also provide a sharp inequality under assuming the coefficients of the system to be non-positive outside the diagonal. The proofs use a concentration-compactness alternative, Pohožaev-type identities and blow-up analysis.

%B Mathematische Zeitschrift %V 282 %P 1169–1190 %8 Apr %G eng %U https://doi.org/10.1007/s00209-015-1584-7 %R 10.1007/s00209-015-1584-7 %0 Journal Article %J The European Physical Journal E %D 2016 %T Motion planning and motility maps for flagellar microswimmers %A Giancarlo Cicconofri %A Antonio DeSimone %XWe study two microswimmers consisting of a spherical rigid head and a passive elastic tail. In the first one the tail is clamped to the head, and the system oscillates under the action of an external torque. In the second one, head and tail are connected by a joint allowing the angle between them to vary periodically, as a result of an oscillating internal torque. Previous studies on these models were restricted to sinusoidal actuations, showing that the swimmers can propel while moving on average along a straight line, in the direction given by the symmetry axis around which beating takes place. We extend these results to motions produced by generic (non-sinusoidal) periodic actuations within the regime of small compliance of the tail. We find that modulation in the velocity of actuation can provide a mechanism to select different directions of motion. With velocity-modulated inputs, the externally actuated swimmer can translate laterally with respect to the symmetry axis of beating, while the internally actuated one is able to move along curved trajectories. The governing equations are analysed with an asymptotic perturbation scheme, providing explicit formulas, whose results are expressed through motility maps. Asymptotic approximations are further validated by numerical simulations.

%B The European Physical Journal E %V 39 %P 72 %8 Jul %G eng %U https://doi.org/10.1140/epje/i2016-16072-y %R 10.1140/epje/i2016-16072-y %0 Journal Article %J Annals of Nuclear Energy, 87, 2 (2016): pp. 198-208 %D 2016 %T A multi-physics reduced order model for the analysis of Lead Fast Reactor single channel %A Alberto Sartori %A Antonio Cammi %A Lelio Luzzi %A Gianluigi Rozza %X In this work, a Reduced Basis method, with basis functions sampled by a Proper Orthogonal Decomposition technique, has been employed to develop a reduced order model of a multi-physics parametrized Lead-cooled Fast Reactor single-channel. Being the first time that a reduced order model is developed in this context, the work focused on a methodological approach and the coupling between the neutronics and the heat transfer, where the thermal feedbacks on neutronics are explicitly taken into account, in time-invariant settings. In order to address the potential of such approach, two different kinds of varying parameters have been considered, namely one related to a geometric quantity (i.e., the inner radius of the fuel pellet) and one related to a physical quantity (i.e., the inlet lead velocity). The capabilities of the presented reduced order model (ROM) have been tested and compared with a high-fidelity finite element model (upon which the ROM has been constructed) on different aspects. In particular, the comparison focused on the system reactivity prediction (with and without thermal feedbacks on neutronics), the neutron flux and temperature field reconstruction, and on the computational time. The outcomes provided by the reduced order model are in good agreement with the high-fidelity finite element ones, and a computational speed-up of at least three orders of magnitude is achieved as well. %B Annals of Nuclear Energy, 87, 2 (2016): pp. 198-208 %I Elsevier %V 87 %P 208 %G en %U http://urania.sissa.it/xmlui/handle/1963/35191 %1 35471 %2 Mathematics %4 1 %# MAT/08 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2016-06-16T11:08:05Z (GMT) No. of bitstreams: 0 %& 198 %R doi:10.1016/j.anucene.2015.09.002 %0 Journal Article %J Rend. Sem. Mat. Univ. Padova %D 2016 %T New existence results for the mean field equation on compact surfaces via degree theory %A Aleks Jevnikar %B Rend. Sem. Mat. Univ. Padova %V 136 %P 11–17 %G eng %R 10.4171/RSMUP/136-2 %0 Report %D 2016 %T Non-linear Schrödinger system for the dynamics of a binary condensate: theory and 2D numerics %A Alessandro Michelangeli %A Giuseppe Pitton %X We present a comprehensive discussion of the mathematical framework for binary Bose-Einstein condensates and for the rigorous derivation of their effective dynamics, governed by a system of coupled non-linear Gross-Pitaevskii equations. We also develop in the 2D case a systematic numerical study of the Gross-Pitaevskii systems in a wide range of relevant regimes of population ratios and intra-species and inter-species interactions. Our numerical method is based on a Fourier collocation scheme in space combined with a fourth order integrating factor scheme in time. %G en %U http://urania.sissa.it/xmlui/handle/1963/35266 %1 35572 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-01-16T12:09:24Z No. of bitstreams: 1 SISSA_preprint_63-2016-MATE_Michelangeli-Pitton-2016.pdf: 6158349 bytes, checksum: ab11de2762ff510e6833474d0688a8b4 (MD5) %0 Journal Article %J Advanced Nonlinear Studies %D 2016 %T A note on a multiplicity result for the mean field equation on compact surfaces %A Aleks Jevnikar %B Advanced Nonlinear Studies %I De Gruyter %V 16 %P 221–229 %G eng %R 10.1515/ans-2015-5009 %0 Journal Article %J Proc. Roy. Soc. Edinburgh Sect. A 146 (2016), 449–474. %D 2016 %T Pairs of positive periodic solutions of nonlinear ODEs with indefinite weight: a topological degree approach for the super-sublinear case %A Alberto Boscaggin %A Guglielmo Feltrin %A Fabio Zanolin %XWe study the periodic and Neumann boundary value problems associated with the second order nonlinear differential equation u''+cu'+λa(t)g(u)=0, where g:[0,+∞[→[0,+∞[ is a sublinear function at infinity having superlinear growth at zero. We prove the existence of two positive solutions when ∫a(t)dt 0 is sufficiently large. Our approach is based on Mawhin's coincidence degree theory and index computations.

%B Proc. Roy. Soc. Edinburgh Sect. A 146 (2016), 449–474. %I Cambridge University Press %G en %U http://urania.sissa.it/xmlui/handle/1963/35262 %1 35566 %2 Mathematics %4 1 %# MAT/05 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2016-11-21T07:33:12Z (GMT) No. of bitstreams: 0 %R 10.1017/S0308210515000621 %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 Journal Article %D 2016 %T POD-Galerkin Method for Finite Volume Approximation of Navier-Stokes and RANS Equations %A Stefano Lorenzi %A Antonio Cammi %A Lelio Luzzi %A Gianluigi Rozza %X Numerical simulation of fluid flows requires important computational efforts but it is essential in engineering applications. Reduced Order Model (ROM) can be employed whenever fast simulations are required, or in general, whenever a trade-off between computational cost and solution accuracy is a preeminent issue as in process optimization and control. In this work, the efforts have been put to develop a ROM for Computational Fluid Dynamics (CFD) application based on Finite Volume approximation, starting from the results available in turbulent Reynold-Averaged Navier Stokes simulations in order to enlarge the application field of Proper Orthogonal Decomposition – Reduced Order Model (POD – ROM) technique to more industrial fields. The approach is tested in the classic benchmark of the numerical simulation of the 2D lid-driven cavity. In particular, two simulations at Re = 103 and Re = 105 have been considered in order to assess both a laminar and turbulent case. Some quantities have been compared with the Full Order Model in order to assess the performance of the proposed ROM procedure i.e., the kinetic energy of the system and the reconstructed quantities of interest (velocity, pressure and turbulent viscosity). In addition, for the laminar case, the comparison between the ROM steady-state solution and the data available in literature has been presented. The results have turned out to be very satisfactory both for the accuracy and the computational times. As a major outcome, the approach turns out not to be affected by the energy blow up issue characterizing the results obtained by classic turbulent POD-Galerkin methods. %I Computer Methods in Applied Mechanics and Engineering, Elsevier %G en %1 35502 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2016-08-06T00:39:18Z No. of bitstreams: 1 Manuscript_second_rev.pdf: 6749813 bytes, checksum: 08833a58f5485216e08c0597a7c13975 (MD5) %0 Journal Article %J International Journal Numerical Methods for Fluids %D 2016 %T POD–Galerkin monolithic reduced order models for parametrized fluid-structure interaction problems %A F. Ballarin %A Gianluigi Rozza %X In this paper we propose a monolithic approach for reduced order modelling of parametrized fluid-structure interaction problems based on a proper orthogonal decomposition (POD)–Galerkin method. Parameters of the problem are related to constitutive properties of the fluid or structural problem, or to geometrical parameters related to the domain configuration at the initial time. We provide a detailed description of the parametrized formulation of the multiphysics problem in its components, together with some insights on how to obtain an offline-online efficient computational procedure through the approximation of parametrized nonlinear tensors. Then, we present the monolithic POD–Galerkin method for the online computation of the global structural displacement, fluid velocity and pressure of the coupled problem. Finally, we show some numerical results to highlight the capabilities of the proposed reduced order method and its computational performances %B International Journal Numerical Methods for Fluids %I Wiley %G en %1 35465 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2016-05-13T00:02:12Z No. of bitstreams: 2 Navon75.pdf: 4121319 bytes, checksum: 70f177ea434e4e289b7df8f7aefe5534 (MD5) img.png: 368575 bytes, checksum: 8bdf24261b0824a8bbd57d499de78f41 (MD5) %R 10.1002/fld.4252 %0 Thesis %D 2016 %T Positive solutions to indefinite problems: a topological approach %A Guglielmo Feltrin %K positive solutions %X The present Ph.D. thesis is devoted to the study of positive solutions to indefinite problems. In particular, we deal with the second order nonlinear differential equation u'' + a(t) g(u) = 0, where g : [0,+∞[→[0,+∞[ is a continuous nonlinearity and a : [0,T]→R is a Lebesgue integrable sign-changing weight. We analyze the Dirichlet, Neumann and periodic boundary value problems on [0,T] associated with the equation and we provide existence, nonexistence and multiplicity results for positive solutions. In the first part of the manuscript, we investigate nonlinearities g(u) with a superlinear growth at zero and at infinity (including the classical superlinear case g(u)=u^p, with p>1). In particular, we prove that there exist 2^m-1 positive solutions when a(t) has m positive humps separated by negative ones and the negative part of a(t) is sufficiently large. Then, for the Dirichlet problem, we solve a conjecture by Gómez‐Reñasco and López‐Gómez (JDE, 2000) and, for the periodic problem, we give a complete answer to a question raised by Butler (JDE, 1976). In the second part, we study the super-sublinear case (i.e. g(u) is superlinear at zero and sublinear at infinity). If a(t) has m positive humps separated by negative ones, we obtain the existence of 3^m-1 positive solutions of the boundary value problems associated with the parameter-dependent equation u'' + λ a(t) g(u) = 0, when both λ>0 and the negative part of a(t) are sufficiently large. We propose a new approach based on topological degree theory for locally compact operators on open possibly unbounded sets, which applies for Dirichlet, Neumann and periodic boundary conditions. As a byproduct of our method, we obtain infinitely many subharmonic solutions and globally defined positive solutions with complex behavior, and we deal with chaotic dynamics. Moreover, we study positive radially symmetric solutions to the Dirichlet and Neumann problems associated with elliptic PDEs on annular domains. Furthermore, this innovative technique has the potential and the generality needed to deal with indefinite problems with more general differential operators. Indeed, our approach apply also for the non-Hamiltonian equation u'' + cu' + a(t) g(u) = 0. Meanwhile, more general operators in the one-dimensional case and problems involving PDEs will be subjects of future investigations. %I SISSA %G en %1 35528 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2016-09-27T16:35:29Z No. of bitstreams: 2 GFeltrin_PhDthesis.pdf: 2862403 bytes, checksum: f459a59342fc02fbb1cb3018037110ff (MD5) GFeltrin_PhDdefense.pdf: 1154181 bytes, checksum: f847c2ec71149b57133a19be81609634 (MD5) %0 Journal Article %J Bulletin of the Brazilian Mathematical Society, New Series %D 2016 %T A quadratic interaction estimate for conservation laws: motivations, techniques and open problems %A Stefano Modena %XIn a series of joint works with S. Bianchini [3, 4, 5], we proved a quadratic interaction estimate for general systems of conservation laws. Aim of this paper is to present the results obtained in the three cited articles [3, 4, 5], discussing how they are related with the general theory of hyperbolic conservation laws. To this purpose, first we explain why this quadratic estimate is interesting, then we give a brief overview of the techniques we used to prove it and finally we present some related open problems.

%B Bulletin of the Brazilian Mathematical Society, New Series %V 47 %P 589–604 %8 Jun %G eng %U https://doi.org/10.1007/s00574-016-0171-9 %R 10.1007/s00574-016-0171-9 %0 Journal Article %J Contemporary Mathematics. Fundamental Directions %D 2016 %T Quadratic interaction estimate for hyperbolic conservation laws, an overview %A Stefano Modena %B Contemporary Mathematics. Fundamental Directions %I Peoples' Friendship University of Russia %V 59 %P 148–172 %G eng %0 Thesis %D 2016 %T Qualitative properties and construction of solutions to some semilinear elliptic PDEs %A Matteo Rizzi %K moving planes method, maximum principle, Lyapunov-Schmidt reduction, Willmore surfaces, Otha-Kawasaki functional %X This thesis is devoted to the study of elliptic equations. On the one hand, we study some qualitative properties, such as symmetry of solutions, on the other hand we explicitly construct some solutions vanishing near some fixed manifold. The main techniques are the moving planes method, in order to investigate the qualitative properties and the Lyapunov-Schmidt reduction. %I SISSA %G en %1 35500 %# MAT/05 %$ Submitted by mrizzi@sissa.it (mrizzi@sissa.it) on 2016-07-11T13:48:21Z No. of bitstreams: 1 tesi_finale.pdf: 1142117 bytes, checksum: 481f2b0713509231cd3a6f8ead92bf59 (MD5) %0 Report %D 2016 %T Quasi-static hydraulic crack growth driven by Darcy's law %A Stefano Almi %XIn the framework of rate independent processes, we present a variational model of quasi-static crack growth in hydraulic fracture. We first introduce the energy functional and study the equilibrium conditions of an unbounded linearly elastic body subject to a remote strain ε ∈ R and with a sufficiently regular crack Γ filled by a volume V of incompressible fluid. In particular, we are able to find the pressure p of the fluid inside the crack as a function of Γ, V , and ε. Then, we study the problem of quasi-static evolution for our model, imposing that the fluid volume V and the fluid pressure p are related by Darcy’s law. We show the existence of such an evolution, and we prove that it satisfies a weak notion of the so-called Griffith’s criterion.

%G en %U http://urania.sissa.it/xmlui/handle/1963/35198 %1 35492 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by salmi@sissa.it (salmi@sissa.it) on 2016-06-18T13:27:56Z No. of bitstreams: 1 Almi-16.pdf: 469056 bytes, checksum: eeb8055150115033880a6c206e9d9fa8 (MD5) %0 Journal Article %J NERS-14-1062; ASME J of Nuclear Rad Sci, 2, 2 (2016) 021019 %D 2016 %T A Reduced Basis Approach for Modeling the Movement of Nuclear Reactor Control Rods %A Alberto Sartori %A Antonio Cammi %A Lelio Luzzi %A Gianluigi Rozza %X This work presents a reduced order model (ROM) aimed at simulating nuclear reactor control rods movement and featuring fast-running prediction of reactivity and neutron flux distribution as well. In particular, the reduced basis (RB) method (built upon a high-fidelity finite element (FE) approximation) has been employed. The neutronics has been modeled according to a parametrized stationary version of the multigroup neutron diffusion equation, which can be formulated as a generalized eigenvalue problem. Within the RB framework, the centroidal Voronoi tessellation is employed as a sampling technique due to the possibility of a hierarchical parameter space exploration, without relying on a “classical” a posteriori error estimation, and saving an important amount of computational time in the offline phase. Here, the proposed ROM is capable of correctly predicting, with respect to the high-fidelity FE approximation, both the reactivity and neutron flux shape. In this way, a computational speedup of at least three orders of magnitude is achieved. If a higher precision is required, the number of employed basis functions (BFs) must be increased. %B NERS-14-1062; ASME J of Nuclear Rad Sci, 2, 2 (2016) 021019 %I ASME %V 2 %P 8 %8 02/2016 %G en %U http://urania.sissa.it/xmlui/handle/1963/35192 %N 2 %1 35473 %2 Mathematics %4 1 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2016-05-30T00:18:10Z No. of bitstreams: 1 sartori_post-icone.pdf: 1377810 bytes, checksum: 5c09a1296518bbbd4b61b709ced8dbca (MD5) %R 10.1115/1.4031945 %0 Journal Article %J Computers and Mathematics with Applications %D 2016 %T Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries %A Laura Iapichino %A Alfio Quarteroni %A Gianluigi Rozza %X The aim of this work is to solve parametrized partial differential equations in computational domains represented by networks of repetitive geometries by combining reduced basis and domain decomposition techniques. The main idea behind this approach is to compute once, locally and for few reference shapes, some representative finite element solutions for different values of the parameters and with a set of different suitable boundary conditions on the boundaries: these functions will represent the basis of a reduced space where the global solution is sought for. The continuity of the latter is assured by a classical domain decomposition approach. Test results on Poisson problem show the flexibility of the proposed method in which accuracy and computational time may be tuned by varying the number of reduced basis functions employed, or the set of boundary conditions used for defining locally the basis functions. The proposed approach simplifies the pre-computation of the reduced basis space by splitting the global problem into smaller local subproblems. Thanks to this feature, it allows dealing with arbitrarily complex network and features more flexibility than a classical global reduced basis approximation where the topology of the geometry is fixed. %B Computers and Mathematics with Applications %I Elsevier %V 71 %P 430 %8 01/2016 %G en %N 1 %1 35187 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2015-11-05T14:59:46Z No. of bitstreams: 1 RDF2_reduced.pdf: 3254431 bytes, checksum: 508b8775e27dfb868f1b39c270cb4a6f (MD5) %& 408 %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 Report %D 2016 %T Second-order structured deformations %A Ana Cristina Barroso %A Jose Matias %A Marco Morandotti %A David R. Owen %I SISSA %G en %1 35497 %2 Mathematics %4 1 %$ Submitted by Lucio Lubiana (lubiana@sissa.it) on 2016-07-08T11:42:55Z No. of bitstreams: 1 Morandott-2oStD.pdf: 385787 bytes, checksum: 31ae44cb708c09f82aba2f6ea5e73248 (MD5) %0 Conference Paper %B The 26th International Ocean and Polar Engineering Conference %D 2016 %T Ship Sinkage and Trim Predictions Based on a CAD Interfaced Fully Nonlinear Potential Model %A Andrea Mola %A Luca Heltai %A Antonio DeSimone %A Massimiliano Berti %B The 26th International Ocean and Polar Engineering Conference %I International Society of Offshore and Polar Engineers %V 3 %P 511–518 %G eng %0 Thesis %D 2016 %T Some results on quasistatic evolution problems for unidirectional processes %A Vito Crismale %I SISSA %G en %1 35522 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by vcrisma@sissa.it (vcrisma@sissa.it) on 2016-09-18T20:26:55Z No. of bitstreams: 1 TesiPHD.pdf: 1721272 bytes, checksum: 95ef69bafc860616d3cdb08901da7ffb (MD5) %0 Thesis %D 2016 %T Some results on the mathematical analysis of crack problems with forces applied on the fracture lips %A Stefano Almi %K Fracture mechanics %X This thesis is devoted to the study of some models of fracture growth in elastic materials, characterized by the presence of forces acting on the crack lips. Working in the general framework of rate-independent processes, we first discuss a variational formulation of the problem of quasi-static crack evolution in hydraulic fracture. Then, we investigate the crack growth process in a cohesive fracture model, showing the existence of an evolution satisfying a weak Griffith's criterion. Finally, in the last chapter of this work we investigate, in the static case, the interaction between the energy spent in order to create a new fracture and the energy spent by the applied surface forces. This leads us to study the lower semicontinuity properties of a free discontinuity functional F(u) that can be written as the sum of a crack term, depending on the jump set of u, and of a boundary term, depending on the trace of u. %I SISSA %G en %1 35503 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by salmi@sissa.it (salmi@sissa.it) on 2016-08-09T10:34:01Z No. of bitstreams: 1 Almi-PhDThesis.pdf: 2060635 bytes, checksum: 5fab9efd5312430a0c9e57282df75694 (MD5) %0 Journal Article %J Communications in Partial Differential Equations %D 2016 %T Spectral analysis and the Aharonov-Bohm effect on certain almost-Riemannian manifolds %A Ugo Boscain %A Dario Prandi %A M. Seri %XWe study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. This operator contains first order diverging terms caused by the divergence of the volume. We get explicit descriptions of the spectrum and the eigenfunctions. In particular in both cases we get a Weyl's law with leading term Elog E. We then study the drastic effect of Aharonov-Bohm magnetic potentials on the spectral properties. Other generalized Riemannian structures including conic and anti-conic type manifolds are also studied. In this case, the Aharonov-Bohm magnetic potential may affect the self-adjointness of the Laplace-Beltrami operator.

%B Communications in Partial Differential Equations %I Taylor & Francis %V 41 %P 32-50 %G eng %U https://doi.org/10.1080/03605302.2015.1095766 %R 10.1080/03605302.2015.1095766 %0 Report %D 2016 %T On the structure of $L^\infty$-entropy solutions to scalar conservation laws in one-space dimension %A Stefano Bianchini %A Elio Marconi %XWe prove that if $u$ is the entropy solution to a scalar conservation law in one space dimension, then the entropy dissipation is a measure concentrated on countably many Lipschitz curves. This result is a consequence of a detailed analysis of the structure of the characteristics. In particular the characteristic curves are segments outside a countably 1-rectifiable set and the left and right traces of the solution exist in a $C^0$-sense up to the degeneracy due to the segments where $f''=0$. We prove also that the initial data is taken in a suitably strong sense and we give some counterexamples which show that these results are sharp.

%I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/35209 %1 35508 %2 Mathematics %# MAT/05 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2016-09-06T09:18:03Z No. of bitstreams: 1 1608.02811v1.pdf: 591028 bytes, checksum: 069b218b01f350df6db7904e245ef701 (MD5) %0 Journal Article %J Annali della Scuola Normale Superiore di Pisa. Classe di scienze %D 2016 %T Symmetry properties of some solutions to some semilinear elliptic equations %A Farina, Alberto %A Andrea Malchiodi %A Matteo Rizzi %B Annali della Scuola Normale Superiore di Pisa. Classe di scienze %I Classe di Scienze %V 16 %P 1209–1234 %G eng %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 %J Calculus of Variations and Partial Differential Equations %D 2016 %T Viscous approximation of quasistatic evolutions for a coupled elastoplastic-damage model %A Vito Crismale %A Giuliano Lazzaroni %XEmploying the technique of vanishing viscosity and time rescaling, we show the existence of quasistatic evolutions for elastoplastic materials with incomplete damage affecting both the elastic tensor and the plastic yield surface, in a softening framework and in small strain assumptions.

%B Calculus of Variations and Partial Differential Equations %V 55 %P 17 %8 Jan %G eng %U https://doi.org/10.1007/s00526-015-0947-6 %R 10.1007/s00526-015-0947-6 %0 Journal Article %J arXiv preprint arXiv:1602.08745 %D 2016 %T Volume geodesic distortion and Ricci curvature for Hamiltonian dynamics %A Andrei A. Agrachev %A Davide Barilari %A Elisa Paoli %B arXiv preprint arXiv:1602.08745 %G eng %0 Journal Article %J Discrete & Continuous Dynamical Systems - A %D 2016 %T Young towers for product systems %A Stefano Luzzatto %A Marks Ruziboev %XWe show that the direct product of maps with Young towers admits a Young tower whose return times decay at a rate which is bounded above by the slowest of the rates of decay of the return times of the component maps. An application of this result, together with other results in the literature, yields various statistical properties for the direct product of various classes of systems, including Lorenz-like maps, multimodal maps, piecewise $C^2$ interval maps with critical points and singularities, Hénon maps and partially hyperbolic systems.

%B Discrete & Continuous Dynamical Systems - A %V 36 %P 1465 %G eng %U http://aimsciences.org//article/id/18d4526e-470d-467e-967a-a0345ad4c642 %R 10.3934/dcds.2016.36.1465 %0 Journal Article %D 2015 %T Anisotropic mean curvature on facets and relations with capillarity %A Stefano Amato %A Lucia Tealdi %A Giovanni Bellettini %XWe discuss the relations between the anisotropic calibrability of a facet F of a solid crystal E, and the capillary problem on a capillary tube with base F. When F is parallel to a facet of the Wulff shape, calibrability is equivalent to show the existence of an anisotropic subunitary vector field in $F, with suitable normal trace on the boundary of the facet, and with constant divergence equal to the anisotropic mean curvature of F. When the Wulff shape is a cylynder, assuming E convex at F, and F (strictly) calibrable, such a vector field is obtained by solving the capillary problem on F in absence of gravity and with zero contact angle. We show some examples of facets for which it is possible, even without the strict calibrability assumption, to build one of these vector fields. The construction provides, at least for convex facets of class C^{1,1}, the solution of the total variation flow starting at 1_F.

%I de Gruyter %G en_US %U http://urania.sissa.it/xmlui/handle/1963/34481 %1 34663 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Stefano Amato (samato@sissa.it) on 2015-08-06T08:33:21Z No. of bitstreams: 1 amato_bellettini_tealdi.pdf: 561517 bytes, checksum: ee2370b8b8ae04078e1e8eae84d37bdd (MD5) %R 10.1515/geofl-2015-0005 %0 Journal Article %J Computers and Mathematics with Applications 69 (2015) 1167–1188 %D 2015 %T Benchmarking the Immersed Finite Element Method for Fluid-Structure Interaction Problems %A Roy Saswati %A Luca Heltai %A Francesco Costanzo %X We present an implementation of a fully variational formulation of an immersed methods for fluid-structure interaction problems based on the finite element method. While typical implementation of immersed methods are characterized by the use of approximate Dirac delta distributions, fully variational formulations of the method do not require the use of said distributions. In our implementation the immersed solid is general in the sense that it is not required to have the same mass density and the same viscous response as the surrounding fluid. We assume that the immersed solid can be either viscoelastic of differential type or hyperelastic. Here we focus on the validation of the method via various benchmarks for fluid-structure interaction numerical schemes. This is the first time that the interaction of purely elastic compressible solids and an incompressible fluid is approached via an immersed method allowing a direct comparison with established benchmarks. %B Computers and Mathematics with Applications 69 (2015) 1167–1188 %G en %1 34633 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Luca Heltai (heltai@sissa.it) on 2015-04-20T15:26:58Z No. of bitstreams: 1 rhc_feibm_validation-v3.pdf: 7039131 bytes, checksum: 705f28e17037504f00766fc4e84a10a4 (MD5) %R 10.1016/j.camwa.2015.03.012 %0 Report %D 2015 %T A bridging mechanism in the homogenisation of brittle composites with soft inclusions %A Marco Barchiesi %A Giuliano Lazzaroni %A Caterina Ida Zeppieri %X We provide a homogenisation result for the energy-functional associated with a purely brittle composite whose microstructure is characterised by soft periodic inclusions embedded in a stiffer matrix. We show that the two constituents as above can be suitably arranged on a microscopic scale ε to obtain, in the limit as ε tends to zero, a homogeneous macroscopic energy-functional explicitly depending on the opening of the crack. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/7492 %1 7621 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-01-26T14:21:23Z No. of bitstreams: 1 BarLazZep-soft-2015(1).pdf: 488285 bytes, checksum: 252f196c34b0c22b00f3de1f36190176 (MD5) %0 Book %B Springer Briefs in Mathematics %D 2015 %T Certified Reduced Basis Methods for Parametrized Partial Differential Equations %A Jan S Hesthaven %A Gianluigi Rozza %A Benjamin Stamm %K a posteriori error bounds %K empirical interpolation %K parametrized partial differential equations %K reduced basis methods, greedy algorithms %XThis book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.

%B Springer Briefs in Mathematics %7 1 %I Springer %C Switzerland %P 135 %@ 978-3-319-22469-5 %G eng %6 1 %0 Journal Article %J Mathematical Methods in the Applied Sciences %D 2015 %T A compatible-incompatible decomposition of symmetric tensors in Lp with application to elasticity %A Maggiani, Giovanni Battista %A Riccardo Scala %A Nicolas Van Goethem %K 35J58 %K 35Q74 %K compatibility conditions %K elasticity %K Korn inequality %K strain decomposition %K subclass74B05 %XIn this paper, we prove the Saint-Venant compatibility conditions in $L^p$ for $p\in(1,∞)$, in a simply connected domain of any space dimension. As a consequence, alternative, simple, and direct proofs of some classical Korn inequalities in Lp are provided. We also use the Helmholtz decomposition in $L^p$ to show that every symmetric tensor in a smooth domain can be decomposed in a compatible part, which is the symmetric part of a displacement gradient, and in an incompatible part, which is the incompatibility of a certain divergence-free tensor. Moreover, under a suitable Dirichlet boundary condition, this Beltrami-type decomposition is proved to be unique. This decomposition result has several applications, one of which being in dislocation models, where the incompatibility part is related to the dislocation density and where $1 < p < 2$. This justifies the need to generalize and prove these rather classical results in the Hilbertian case ($p = 2$), to the full range $p\in(1,∞)$. Copyright © 2015 John Wiley & Sons, Ltd.

%B Mathematical Methods in the Applied Sciences %V 38 %P 5217-5230 %G eng %U https://onlinelibrary.wiley.com/doi/abs/10.1002/mma.3450 %R 10.1002/mma.3450 %0 Journal Article %J SIAM Journal on Control and Optimization %D 2015 %T Complexity of Control-Affine Motion Planning %A Jean, F. %A Dario Prandi %XIn this paper we study the complexity of the motion planning problem for control-affine systems. Such complexities are already defined and rather well understood in the particular case of nonholonomic (or sub-Riemannian) systems. Our aim is to generalize these notions and results to systems with a drift. Accordingly, we present various definitions of complexity, as functions of the curve that is approximated, and of the precision of the approximation. Due to the lack of time-rescaling invariance of these systems, we consider geometric and parametrized curves separately. Then, we give some asymptotic estimates for these quantities. As a byproduct, we are able to treat the long time local controllability problem, giving quantitative estimates on the cost of stabilizing the system near a nonequilibrium point of the drift.

%B SIAM Journal on Control and Optimization %V 53 %P 816-844 %G eng %U https://doi.org/10.1137/130950793 %R 10.1137/130950793 %0 Journal Article %J Adv. Calc. Var. %D 2015 %T Constrained BV functions on double coverings for Plateau's type problems %A Stefano Amato %A Giovanni Bellettini %A Maurizio Paolini %XWe link Brakke's "soap films" covering construction with the theory of finite perimeter sets, in order to study Plateau's problem without fixing a priori the topology of the solution. The minimization is set up in the class of $BV$ functions defined on a double covering space of the complement of an $(n − 2)$-dimensional smooth compact manifold $S$ without boundary. The main novelty of our approach stands in the presence of a suitable constraint on the fibers, which couples together the covering sheets. The model allows to avoid all issues concerning the presence of the boundary $S$. The constraint is lifted in a natural way to Sobolev spaces, allowing also an approach based on $Γ$-convergence theory.

%B Adv. Calc. Var. %G en_US %1 7597 %$ Submitted by Stefano Amato (samato@sissa.it) on 2014-12-12T07:20:56Z No. of bitstreams: 1 bvcovering_gen.pdf: 520748 bytes, checksum: 7b3d78994ff2d2ae5cbbe87eaa5f0777 (MD5) %0 Journal Article %J Bulletin of the Institute of Mathematics of Academia Sinica (New Series) %D 2015 %T Convergence rate of the Glimm scheme %A Stefano Modena %A Stefano Bianchini %B Bulletin of the Institute of Mathematics of Academia Sinica (New Series) %G eng %0 Report %D 2015 %T Convex combinations of low eigenvalues, Fraenkel asymmetries and attainable sets %A Dario Mazzoleni %A Davide Zucco %X We consider the problem of minimizing convex combinations of the first two eigenvalues of the Dirichlet-Laplacian among open set of $R^N$ of fixed measure. We show that, by purely elementary arguments, based on the minimality condition, it is possible to obtain informations on the geometry of the minimizers of convex combinations: we study, in particular, when these minimizers are no longer convex, and the optimality of balls. As an application of our results we study the boundary of the attainable set for the Dirichlet spectrum. Our techniques involve symmetry results à la Serrin, explicit constants in quantitative inequalities, as well as a purely geometrical problem: the minimization of the Fraenkel 2-asymmetry among convex sets of fixed measure. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/35140 %1 35378 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Davide Zucco (dzucco@sissa.it) on 2015-12-03T12:26:59Z No. of bitstreams: 1 Mazzoleni_Zucco_preprint_SISSA.pdf: 437631 bytes, checksum: 990947c0f9a62d173c6e72d105297d19 (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 Archive of Numerical Software, vol. 3, n. 100, (2015), pages : 1-8 %D 2015 %T The deal.II Library, Version 8.2 %A Wolfgang Bangerth %A Timo Heister %A Luca Heltai %A G. Kanschat %A Martin Kronbichler %A Matthias Maier %A Bruno Turcksin %A T. D. Young %X This paper provides an overview of the new features of the finite element library deal.II version 8.2 %B Archive of Numerical Software, vol. 3, n. 100, (2015), pages : 1-8 %G en %U http://urania.sissa.it/xmlui/handle/1963/34464 %1 34637 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Luca Heltai (heltai@sissa.it) on 2015-04-20T15:40:46Z No. of bitstreams: 1 18031-44567-1-PB (1).pdf: 137014 bytes, checksum: 9a5fddeccfa389c32ca89a466e653074 (MD5) %R 10.11588/ans.2015.100.18031 %0 Journal Article %J Dynamical Systems %D 2015 %T Decay of correlations for invertible maps with non-Hölder observables %A Marks Ruziboev %XAn invertible dynamical system with some hyperbolic structure is considered. Upper estimates for the correlations of continuous observables are given in terms of modulus of continuity. The result is applied to certain Hénon maps and Solenoid maps with intermittency.

%B Dynamical Systems %I Taylor & Francis %V 30 %P 341-352 %G eng %U https://doi.org/10.1080/14689367.2015.1046816 %R 10.1080/14689367.2015.1046816 %0 Report %D 2015 %T Dynamics of screw dislocations: a generalised minimising-movements scheme approach %A Giovanni A. Bonaschi %A Patrick Van Meurs %A Marco Morandotti %X The gradient flow structure of the model introduced in [CG99] for the dynamics of screw dislocations is investigated by means of a generalised minimising-movements scheme approach. The assumption of a finite number of available glide directions, together with the "maximal dissipation criterion" that governs the equations of motion, results into solving a differential inclusion rather than an ODE. This paper addresses how the model in [CG99] is connected to a time-discrete evolution scheme which explicitly confines dislocations to move each time step along a single glide direction. It is proved that the time-continuous model in [CG99] is the limit of these time-discrete minimising-movement schemes when the time step converges to 0. The study presented here is a first step towards a generalization of the setting in [AGS08, Chap. 2 and 3] that allows for dissipations which cannot be described by a metric. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/34495 %1 34692 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-09-04T08:36:59Z No. of bitstreams: 1 BvMM_03_9_15-MM.pdf: 773084 bytes, checksum: 686749d206d2f9c676ab004b860799f4 (MD5) %0 Journal Article %J Journal of Mathematical Analysis and Applications %D 2015 %T Existence and multiplicity result for the singular Toda system %A Luca Battaglia %K Existence result %K Liouville-type equations %K Multiplicity result %K PDEs on compact surfaces %K Toda system %XWe consider the Toda system on a compact surface (Σ,g)−Δu1=2ρ1(h1eu1∫Σh1eu1dVg−1)−ρ2(h2eu2∫Σh2eu2dVg−1)−4π∑j=1Jα1j(δpj−1),−Δu2=2ρ2(h2eu2∫Σh2eu2dVg−1)−ρ1(h1eu1∫Σh1eu1dVg−1)−4π∑j=1Jα2j(δpj−1), where hi are smooth positive functions, ρi are positive real parameters, pj are given points on Σ and αij are numbers greater than −1. We give existence and multiplicity results, using variational and Morse-theoretical methods. It is the first existence result when some of the αij's are allowed to be negative."

%B Journal of Mathematical Analysis and Applications %V 424 %P 49 - 85 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022247X14010191 %R https://doi.org/10.1016/j.jmaa.2014.10.081 %0 Report %D 2015 %T Existence for constrained dynamic Griffith fracture with a weak maximal dissipation condition %A Gianni Dal Maso %A Cristopher J. Larsen %A Rodica Toader %X There are very few existence results for fracture evolution, outside of globally minimizing quasi-static evolutions. Dynamic evolutions are particularly problematic, due to the difficulty of showing energy balance, as well as of showing that solutions obey a maximal dissipation condition, or some similar condition that prevents stationary cracks from always being solutions. Here we introduce a new weak maximal dissipation condition and show that it is compatible with cracks constrained to grow smoothly on a smooth curve. In particular, we show existence of dynamic fracture evolutions satisfying this maximal dissipation condition, subject to the above smoothness constraints, and exhibit explicit examples to show that this maximal dissipation principle can indeed rule out stationary cracks as solutions. %G en %U http://urania.sissa.it/xmlui/handle/1963/35045 %1 35277 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2015-11-18T15:46:32Z No. of bitstreams: 1 DM-Lar-Toa-SISSA.pdf: 313034 bytes, checksum: 76419fd2c8c435ae7deeca773b424667 (MD5) %0 Journal Article %J Adv. Differential Equations 20 (2015), 937–982. %D 2015 %T Existence of positive solutions in the superlinear case via coincidence degree: the Neumann and the periodic boundary value problems %A Guglielmo Feltrin %A Fabio Zanolin %XWe prove the existence of positive periodic solutions for the second order nonlinear equation u'' + a(x) g(u) = 0, where g(u) has superlinear growth at zero and at infinity. The weight function a(x) is allowed to change its sign. Necessary and sufficient conditions for the existence of nontrivial solutions are obtained. The proof is based on Mawhin's coincidence degree and applies also to Neumann boundary conditions. Applications are given to the search of positive solutions for a nonlinear PDE in annular domains and for a periodic problem associated to a non-Hamiltonian equation.

%B Adv. Differential Equations 20 (2015), 937–982. %I Khayyam Publishing %G en %U http://projecteuclid.org/euclid.ade/1435064518 %1 35388 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-12-18T08:49:04Z No. of bitstreams: 1 FeltrinZanolin_ade2015.pdf: 321052 bytes, checksum: 38a45a1515a02fc86751b5f088bbfbfb (MD5) %0 Journal Article %J Conference Publications %D 2015 %T Existence of positive solutions of a superlinear boundary value problem with indefinite weight %A Guglielmo Feltrin %K boundary value problem %K indefinite weight %K Positive solution; existence result. %K superlinear equation %XWe deal with the existence of positive solutions for a two-point boundary value problem associated with the nonlinear second order equation $u''+a(x)g(u)=0$. The weight $a(x)$ is allowed to change sign. We assume that the function $g\colon\mathopen[0,+∞\mathclose[\to\mathbb{R}$ is continuous, $g(0)=0$ and satisfies suitable growth conditions, including the superlinear case $g(s)=s^p$, with $p>1$. In particular we suppose that $g(s)/s$ is large near infinity, but we do not require that $g(s)$ is non-negative in a neighborhood of zero. Using a topological approach based on the Leray-Schauder degree we obtain a result of existence of at least a positive solution that improves previous existence theorems.

%B Conference Publications %V 2015 %P 436 %G eng %U http://aimsciences.org//article/id/b3c1c765-e8f5-416e-8130-05cc48478026 %R 10.3934/proc.2015.0436 %0 Report %D 2015 %T Explicit formulas for relaxed disarrangement densities arising from structured deformations %A Ana Cristina Barroso %A Jose Matias %A Marco Morandotti %A David R. Owen %X Structured deformations provide a multiscale geometry that captures the contributions at the macrolevel of both smooth geometrical changes and non-smooth geometrical changes (disarrangements) at submacroscopic levels. For each (first-order) structured deformation (g,G) of a continuous body, the tensor field G is known to be a measure of deformations without disarrangements, and M:=∇g−G is known to be a measure of deformations due to disarrangements. The tensor fields G and M together deliver not only standard notions of plastic deformation, but M and its curl deliver the Burgers vector field associated with closed curves in the body and the dislocation density field used in describing geometrical changes in bodies with defects. Recently, Owen and Paroni [13] evaluated explicitly some relaxed energy densities arising in Choksi and Fonseca’s energetics of structured deformations [4] and thereby showed: (1) (trM)+ , the positive part of trM, is a volume density of disarrangements due to submacroscopic separations, (2) (trM)−, the negative part of trM, is a volume density of disarrangements due to submacroscopic switches and interpenetrations, and (3) trM, the absolute value of trM, is a volume density of all three of these non-tangential disarrangements: separations, switches, and interpenetrations. The main contribution of the present research is to show that a different approach to the energetics of structured deformations, that due to Ba\'{i}a, Matias, and Santos [1], confirms the roles of (trM)+, (trM)−, and trM established by Owen and Paroni. In doing so, we give an alternative, shorter proof of Owen and Paroni’s results, and we establish additional explicit formulas for other measures of disarrangements. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/34492 %1 34687 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-08-28T10:09:53Z No. of bitstreams: 1 SISSA_Preprint_37_2015_MATE.pdf: 315599 bytes, checksum: 2bd676c192205d3a2edd7c48bf53c11c (MD5) %0 Report %D 2015 %T Fast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization %A F. Ballarin %A Elena Faggiano %A Sonia Ippolito %A Andrea Manzoni %A Alfio Quarteroni %A Gianluigi Rozza %A Roberto Scrofani %X In this work a reduced-order computational framework for the study of haemodynamics in three-dimensional patient-specific configurations of coronary artery bypass grafts dealing with a wide range of scenarios is proposed. We combine several efficient algorithms to face at the same time both the geometrical complexity involved in the description of the vascular network and the huge computational cost entailed by time dependent patient-specific flow simulations. Medical imaging procedures allow to reconstruct patient-specific configurations from clinical data. A centerlines-based parametrization is proposed to efficiently handle geometrical variations. POD–Galerkin reduced-order models are employed to cut down large computational costs. This computational framework allows to characterize blood flows for different physical and geometrical variations relevant in the clinical practice, such as stenosis factors and anastomosis variations, in a rapid and reliable way. Several numerical results are discussed, highlighting the computational performance of the proposed framework, as well as its capability to perform sensitivity analysis studies, so far out of reach. %G en %U http://urania.sissa.it/xmlui/handle/1963/34623 %1 34824 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2015-10-07T00:30:27Z No. of bitstreams: 1 REPORT.pdf: 10426315 bytes, checksum: 6e5ddf4eb4cacdc7e803c2db1a540fc9 (MD5) %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 Advances in Mathematics %D 2015 %T A general existence result for the Toda system on compact surfaces %A Luca Battaglia %A Aleks Jevnikar %A Andrea Malchiodi %A David Ruiz %K Geometric PDEs %K Min–max schemes %K Variational methods %XIn this paper we consider the following Toda system of equations on a compact surface:−Δu1=2ρ1(h1eu1∫Σh1eu1dVg−1)−ρ2(h2eu2∫Σh2eu2dVg−1)−Δu1=−4π∑j=1mα1,j(δpj−1),−Δu2=2ρ2(h2eu2∫Σh2eu2dVg−1)−ρ1(h1eu1∫Σh1eu1dVg−1)−Δu2=−4π∑j=1mα2,j(δpj−1), which is motivated by the study of models in non-abelian Chern–Simons theory. Here h1,h2 are smooth positive functions, ρ1,ρ2 two positive parameters, pi points of the surface and α1,i,α2,j non-negative numbers. We prove a general existence result using variational methods. The same analysis applies to the following mean field equation−Δu=ρ1(heu∫ΣheudVg−1)−ρ2(he−u∫Σhe−udVg−1), which arises in fluid dynamics."

%B Advances in Mathematics %V 285 %P 937 - 979 %G eng %U http://www.sciencedirect.com/science/article/pii/S0001870815003072 %R https://doi.org/10.1016/j.aim.2015.07.036 %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 Thesis %D 2015 %T Gibbs-Markov-Young Structures and Decay of Correlations %A Marks Ruziboev %K Decay of Correlations, GMY-towers %X In this work we study mixing properties of discrete dynamical systems and related to them geometric structure. In the first chapter we show that the direct product of maps with Young towers admits a Young tower whose return times decay at a rate which is bounded above by the slowest of the rates of decay of the return times of the component maps. An application of this result, together with other results in the literature, yields various statistical properties for the direct product of various classes of systems, including Lorenz-like maps, multimodal maps, piecewise $C^2$ interval maps with critical points and singularities, H\'enon maps and partially hyperbolic systems. The second chapter is dedicated to the problem of decay of correlations for continuous observables. First we show that if the underlying system admits Young tower then the rate of decay of correlations for continuous observables can be estimated in terms of modulus of continuity and the decay rate of tail of Young tower. In the rest of the second chapter we study the relations between the rates of decay of correlations for smooth observables and continuous observables. We show that if the rates of decay of correlations is known for $C^r,$ observables ($r\ge 1$) then it is possible to obtain decay of correlations for continuous observables in terms of modulus of continuity. %I SISSA %G en %1 34677 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by mruziboe@sissa.it (mruziboe@sissa.it) on 2015-08-10T16:44:24Z No. of bitstreams: 1 ruziboev_thesis.pdf: 745751 bytes, checksum: 7743d9fe13df739ad5fe5dd9a0eed202 (MD5) %0 Report %D 2015 %T Homogenization problems in the Calculus of Variations: an overview %A Jose Matias %A Marco Morandotti %X In this note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundamental theoretical tools, both classical and modern. We conclude by mentioning some open problems. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/34455 %1 34598 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-03-18T12:11:41Z No. of bitstreams: 1 surveyhom1.pdf: 297678 bytes, checksum: be0ffd687370fdf3bf6a57d4f6dc61e4 (MD5) %0 Thesis %D 2015 %T Interaction functionals, Glimm approximations and Lagrangian structure of BV solutions for Hyperbolic Systems of Conservations Laws %A Stefano Modena %K Hyperbolic conservation laws %X This thesis is a contribution to the mathematical theory of Hyperbolic Conservation Laws. Three are the main results which we collect in this work. The first and the second result (denoted in the thesis by Theorem A and Theorem B respectively) deal with the following problem. The most comprehensive result about existence, uniqueness and stability of the solution to the Cauchy problem \begin{equation}\tag{$\mathcal C$} \label{E:abstract} \begin{cases} u_t + F(u)_x = 0, \\u(0, x) = \bar u(x), \end{cases} \end{equation} where $F: \R^N \to \R^N$ is strictly hyperbolic, $u = u(t,x) \in \R^N$, $t \geq 0$, $x \in \R$, $\TV(\bar u) \ll 1$, can be found in [Bianchini, Bressan 2005], where the well-posedness of \eqref{E:abstract} is proved by means of vanishing viscosity approximations. After the paper [Bianchini, Bressan 2005], however, it seemed worthwhile to develop a \emph{purely hyperbolic} theory (based, as in the genuinely nonlinear case, on Glimm or wavefront tracking approximations, and not on vanishing viscosity parabolic approximations) to prove existence, uniqueness and stability results. The reason of this interest can be mainly found in the fact that hyperbolic approximate solutions are much easier to study and to visualize than parabolic ones. Theorems A and B in this thesis are a contribution to this line of research. In particular, Theorem A proves an estimate on the change of the speed of the wavefronts present in a Glimm approximate solution when two of them interact; Theorem B proves the convergence of the Glimm approximate solutions to the weak admissible solution of \eqref{E:abstract} and provides also an estimate on the rate of convergence. Both theorems are proved in the most general setting when no assumption on $F$ is made except the strict hyperbolicity. The third result of the thesis, denoted by Theorem C, deals with the Lagrangian structure of the solution to \eqref{E:abstract}. The notion of Lagrangian flow is a well-established concept in the theory of the transport equation and in the study of some particular system of conservation laws, like the Euler equation. However, as far as we know, the general system of conservations laws \eqref{E:abstract} has never been studied from a Lagrangian point of view. This is exactly the subject of Theorem C, where a Lagrangian representation for the solution to the system \eqref{E:abstract} is explicitly constructed. The main reasons which led us to look for a Lagrangian representation of the solution of \eqref{E:abstract} are two: on one side, this Lagrangian representation provides the continuous counterpart in the exact solution of \eqref{E:abstract} to the well established theory of wavefront approximations; on the other side, it can lead to a deeper understanding of the behavior of the solutions in the general setting, when the characteristic field are not genuinely nonlinear or linearly degenerate. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/34542 %1 34739 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by smodena@sissa.it (smodena@sissa.it) on 2015-09-22T13:24:32Z No. of bitstreams: 1 Modena_tesi_2015_09_22.pdf: 1531188 bytes, checksum: 814a6709a4fcbf8b10bc95a9e3d155c7 (MD5) %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 Thesis %D 2015 %T Mathematical Models of Locomotion: Legged Crawling, Snake-like Motility, and Flagellar Swimming %A Giancarlo Cicconofri %K Motility %I SISSA %G en %1 34743 %2 Mathematics %4 1 %# FIS/02 %$ Submitted by cicconof@sissa.it (cicconof@sissa.it) on 2015-09-24T20:39:35Z No. of bitstreams: 1 TESI_Cicconofri.pdf: 4716549 bytes, checksum: 708afb866eb4c106392495f2a8e7c6a8 (MD5) %0 Journal Article %J International Journal of Non-Linear Mechanics %D 2015 %T Motility of a model bristle-bot: A theoretical analysis %A Giancarlo Cicconofri %A Antonio DeSimone %K Bristle-robots %K Crawling motility %K Frictional interactions %XBristle-bots are legged robots that can be easily made out of a toothbrush head and a small vibrating engine. Despite their simple appearance, the mechanism enabling them to propel themselves by exploiting friction with the substrate is far from trivial. Numerical experiments on a model bristle-bot have been able to reproduce such a mechanism revealing, in addition, the ability to switch direction of motion by varying the vibration frequency. This paper provides a detailed account of these phenomena through a fully analytical treatment of the model. The equations of motion are solved through an expansion in terms of a properly chosen small parameter. The convergence of the expansion is rigorously proven. In addition, the analysis delivers formulas for the average velocity of the robot and for the frequency at which the direction switch takes place. A quantitative description of the mechanism for the friction modulation underlying the motility of the bristle-bot is also provided.

%B International Journal of Non-Linear Mechanics %V 76 %P 233 - 239 %G eng %U http://www.sciencedirect.com/science/article/pii/S0020746215000025 %R https://doi.org/10.1016/j.ijnonlinmec.2014.12.010 %0 Journal Article %J Numerische Mathematik, (2015), 36 p. Article in Press %D 2015 %T Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations %A Gianluigi Rozza %A Peng Chen %A Alfio Quarteroni %X In this paper we develop and analyze a multilevel weighted reduced basis method for solving stochastic optimal control problems constrained by Stokes equations. We prove the analytic regularity of the optimal solution in the probability space under certain assumptions on the random input data. The finite element method and the stochastic collocation method are employed for the numerical approximation of the problem in the deterministic space and the probability space, respectively, resulting in many large-scale optimality systems to solve. In order to reduce the unaffordable computational effort, we propose a reduced basis method using a multilevel greedy algorithm in combination with isotropic and anisotropic sparse-grid techniques. A weighted a posteriori error bound highlights the contribution stemming from each method. Numerical tests on stochastic dimensions ranging from 10 to 100 demonstrate that our method is very efficient, especially for solving high-dimensional and large-scale optimization problems. %B Numerische Mathematik, (2015), 36 p. Article in Press %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34491 %1 34680 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2015-08-25T23:32:48Z No. of bitstreams: 1 06August2014_wRBM4SOC.pdf: 531409 bytes, checksum: d1a2f18b0de17872919c430779f7180c (MD5) %R 10.1007/s00211-015-0743-4 %0 Journal Article %J J. Differential Equations 259 (2015), 925–963. %D 2015 %T Multiple positive solutions for a superlinear problem: a topological approach %A Guglielmo Feltrin %A Fabio Zanolin %XWe study the multiplicity of positive solutions for a two-point boundary value problem associated to the nonlinear second order equation u''+f(x,u)=0. We allow x ↦ f(x,s) to change its sign in order to cover the case of scalar equations with indefinite weight. Roughly speaking, our main assumptions require that f(x,s)/s is below λ_1 as s→0^+ and above λ_1 as s→+∞. In particular, we can deal with the situation in which f(x,s) has a superlinear growth at zero and at infinity. We propose a new approach based on the topological degree which provides the multiplicity of solutions. Applications are given for u'' + a(x) g(u) = 0, where we prove the existence of 2^n-1 positive solutions when a(x) has n positive humps and a^-(x) is sufficiently large.

%B J. Differential Equations 259 (2015), 925–963. %I Elsevier %G en %U http://urania.sissa.it/xmlui/handle/1963/35147 %1 35387 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-12-17T09:31:06Z No. of bitstreams: 1 FeltrinZanolin_jde2015.pdf: 350880 bytes, checksum: 0e329b01081df570863ea2492ffefe0a (MD5) %R 10.1016/j.jde.2015.02.032 %0 Journal Article %J Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. %D 2015 %T A note on compactness properties of the singular Toda system %A Luca Battaglia %A Gabriele Mancini %XIn this note, we consider blow-up for solutions of the SU(3) Toda system on compact surfaces. In particular, we give a complete proof of a compactness result stated by Jost, Lin and Wang and we extend it to the case of singular systems. This is a necessary tool to find solutions through variational methods.

%B Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. %V 26 %P 299-307 %G en %1 34669 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by gmancini@sissa.it (gmancini@sissa.it) on 2015-08-07T16:01:01Z No. of bitstreams: 1 art3.pdf: 146803 bytes, checksum: 362923e2dd63f86658dd3bb0701ce05b (MD5) %R 10.4171/RLM/708 %0 Journal Article %D 2015 %T Onofri-Type Inequalities for Singular Liouville Equations %A Gabriele Mancini %XWe study the blow-up behavior of minimizing sequences for the singular Moser–Trudinger functional on compact surfaces. Assuming non-existence of minimum points, we give an estimate for the infimum value of the functional. This result can be applied to give sharp Onofri-type inequalities on the sphere in the presence of at most two singularities.

%I Springer US %G en %1 34668 %2 Mathematics %4 1 %# MAT/05 %R 10.1007/s12220-015-9589-3 %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 2015 %T The phototransduction machinery in the rod outer segment has a strong efficacy gradient %A Monica Mazzolini %A Giuseppe Facchetti %A L. Andolfi %A R. Proietti Zaccaria %A S. Tuccio %A J. Treud %A Claudio Altafini %A Enzo M. Di Fabrizio %A Marco Lazzarino %A G. Rapp %A Vincent Torre %I National Academy of Sciences %G en %U http://urania.sissa.it/xmlui/handle/1963/35157 %1 35382 %2 Neuroscience %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2016-01-21T09:29:28Z (GMT) No. of bitstreams: 0 %R 10.1073/pnas.1423162112 %0 Journal Article %J Communications in Mathematical Physics %D 2015 %T Quadratic Interaction Functional for General Systems of Conservation Laws %A Stefano Bianchini %A Stefano Modena %XFor the Glimm scheme approximation to the solution of the system of conservation laws in one space dimension with initial data u 0 with small total variation, we prove a quadratic (w.r.t. Tot. Var. ( u 0)) interaction estimate, which has been used in the literature for stability and convergence results. No assumptions on the structure of the flux f are made (apart from smoothness), and this estimate is the natural extension of the Glimm type interaction estimate for genuinely nonlinear systems. More precisely, we obtain the following results: a new analysis of the interaction estimates of simple waves;

%B Communications in Mathematical Physics %V 338 %P 1075–1152 %G eng %R 10.1007/s00220-015-2372-2 %0 Journal Article %J Advances in Computational Mathematics %D 2015 %T Reduced basis approximation and a-posteriori error estimation for the coupled Stokes-Darcy system %A Immanuel Martini %A Gianluigi Rozza %A Bernard Haasdonk %K Domain decomposition %K Error estimation %K Non-coercive problem %K Porous medium equation %K Reduced basis method %K Stokes flow %XThe coupling of a free flow with a flow through porous media has many potential applications in several fields related with computational science and engineering, such as blood flows, environmental problems or food technologies. We present a reduced basis method for such coupled problems. The reduced basis method is a model order reduction method applied in the context of parametrized systems. Our approach is based on a heterogeneous domain decomposition formulation, namely the Stokes-Darcy problem. Thanks to an offline/online-decomposition, computational times can be drastically reduced. At the same time the induced error can be bounded by fast evaluable a-posteriori error bounds. In the offline-phase the proposed algorithms make use of the decomposed problem structure. Rigorous a-posteriori error bounds are developed, indicating the accuracy of certain lifting operators used in the offline-phase as well as the accuracy of the reduced coupled system. Also, a strategy separately bounding pressure and velocity errors is extended. Numerical experiments dealing with groundwater flow scenarios demonstrate the efficiency of the approach as well as the limitations regarding a-posteriori error estimation.

%B Advances in Computational Mathematics %V special issue for MoRePaS 2012 %G eng %N in press %R 10.1007/s10444-014-9396-6 %0 Journal Article %J Computers and Mathematics with Applications %D 2015 %T Reduced basis approximation of parametrized optimal flow control problems for the Stokes equations %A Federico Negri %A Andrea Manzoni %A Gianluigi Rozza %XThis paper extends the reduced basis method for the solution of parametrized optimal control problems presented in Negri et al. (2013) to the case of noncoercive (elliptic) equations, such as the Stokes equations. We discuss both the theoretical properties-with particular emphasis on the stability of the resulting double nested saddle-point problems and on aggregated error estimates-and the computational aspects of the method. Then, we apply it to solve a benchmark vorticity minimization problem for a parametrized bluff body immersed in a two or a three-dimensional flow through boundary control, demonstrating the effectivity of the methodology.

%B Computers and Mathematics with Applications %V 69 %P 319–336 %G eng %R 10.1016/j.camwa.2014.12.010 %0 Journal Article %J Comput Methods Appl Mech Eng. 2015;284:1147–1180 %D 2015 %T Reduced Basis Isogeometric Methods (RB-IGA) for the real-time simulation of potential flows about parametrized NACA airfoils %A Andrea Manzoni %A Filippo Salmoiraghi %A Luca Heltai %X We present a Reduced Basis (RB) method based on Isogeometric Analysis (IGA) for the rapid and reliable evaluation of PDE systems characterized by complex geometrical features. At the current state of the art, this is the first case of coupling between RB and IGA methods. The construction of the RB method relies on an Isogeometric Boundary Element Method (IGA-BEM) as the high-fidelity technique, allowing a direct interface with Computer Aided Design (CAD) tools. A suitable Empirical Interpolation Method (EIM) ensures an efficient offline/online decomposition between the construction and the evaluation of the RB method. We consider the real-time simulation of potential flows past airfoils, parametrized with respect to the angle of attack and the NACA number identifying their shape, and we provide a validation of our methodology with respect to experimental data and reference numerical codes, showing in both cases a very good agreement.We present a Reduced Basis (RB) method based on Isogeometric Analysis (IGA) for the rapid and reliable evaluation of PDE systems characterized by complex geometrical features. At the current state of the art, this is the first case of coupling between RB and IGA methods. The construction of the RB method relies on an Isogeometric Boundary Element Method (IGA-BEM) as the high-fidelity technique, allowing a direct interface with Computer Aided Design (CAD) tools. A suitable Empirical Interpolation Method (EIM) ensures an efficient offline/online decomposition between the construction and the evaluation of the RB method. We consider the real-time simulation of potential flows past airfoils, parametrized with respect to the angle of attack and the NACA number identifying their shape, and we provide a validation of our methodology with respect to experimental data and reference numerical codes, showing in both cases a very good agreement. %B Comput Methods Appl Mech Eng. 2015;284:1147–1180 %G en %1 34587 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Luca Heltai (heltai@sissa.it) on 2015-03-03T16:15:31Z No. of bitstreams: 1 RB_IGA_BEM.pdf: 725470 bytes, checksum: e2fe6fabfdbe6118e9ef07fb185113af (MD5) %R 10.1016/j.cma.2014.11.037 %0 Thesis %D 2015 %T The relaxed area of maps from the plane to the plane with a line discontinuity, and the role of semicartesian surfaces. %A Lucia Tealdi %K Area functional %X In this thesis we study the relaxation of the area functional w.r.t. the L^1 topology of a map from a bounded planar domain with values in the plane and jumping on a segment. We estimate from above the singular contribution of this functional due to the presence of the jump in terms of the infimum of the area among a suitable family of surfaces that we call semicartesian surfaces. In our analysis, we also introduce a different notion of area, namely the relaxation of the area w.r.t. a convergence stronger than the L^1 convergence, whose singular contribution is completely characterized in terms of suitable semicartesian area minimizing problems. We propose also some examples of maps for which the two notions of relaxation are different: these examples underline the highly non-local behaviour of the L^1-relaxation, and justify the introduction of the other functional. Some result about the existence of a semicartesian area-minimizing surface is also provided. %I SISSA %G en %1 34732 %4 1 %# MAT/05 %$ Submitted by Lucia Tealdi (ltealdi@sissa.it) on 2015-09-21T12:23:44Z No. of bitstreams: 1 Tealdi_PhD_thesis.pdf: 917244 bytes, checksum: a6bfc90b8457a030be4c7314ee1f426f (MD5) %0 Report %D 2015 %T Results on the minimization of the Dirichlet functional among semicartesian parametrizations %A Lucia Tealdi %A Giovanni Bellettini %A Maurizio Paolini %XWe start to investigate the existence of conformal minimizers for the Dirichlet functional in the setting of the so-called semicartesian parametrizations, adapting to this context some techniques used in solving the classical Plateau's problem. The final goal is to find area minimizing semicartesian parametrizations spanning a Jordan curve obtained as union of two graphs; this problem appeared in the study of the relaxed area functional for maps from the plane to the plane jumping on a line.

%G en %U http://urania.sissa.it/xmlui/handle/1963/34488 %1 34671 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Lucia Tealdi (ltealdi@sissa.it) on 2015-08-07T16:12:37Z No. of bitstreams: 1 bellettini_paolini_tealdi_semicart.pdf: 338138 bytes, checksum: c689a5b64d30dc600fe0429b72996c7d (MD5) %0 Report %D 2015 %T Rigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires %A Giuliano Lazzaroni %A Mariapia Palombaro %A Anja Schlomerkemper %X In the context of nanowire heterostructures we perform a discrete to continuum limit of the corresponding free energy by means of Γ-convergence techniques. Nearest neighbours are identified by employing the notions of Voronoi diagrams and Delaunay triangulations. The scaling of the nanowire is done in such a way that we perform not only a continuum limit but a dimension reduction simultaneously. The main part of the proof is a discrete geometric rigidity result that we announced in an earlier work and show here in detail for a variety of three-dimensional lattices. We perform the passage from discrete to continuum twice: once for a system that compensates a lattice mismatch between two parts of the heterogeneous nanowire without defects and once for a system that creates dislocations. It turns out that we can verify the experimentally observed fact that the nanowires show dislocations when the radius of the specimen is large %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/7494 %1 7623 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-01-30T07:54:33Z No. of bitstreams: 1 LaPaSc-3dim.pdf: 249836 bytes, checksum: 8b8edddc952b9a4a084c1c0c85514051 (MD5) %0 Report %D 2015 %T Semicartesian surfaces and the relaxed area of maps from the plane to the plane with a line discontinuity %A Lucia Tealdi %A Giovanni Bellettini %A Maurizio Paolini %XWe address the problem of estimating the area of the graph of a map u, defined on a bounded planar domain O and taking values in the plane, jumping on a segment J, either compactly contained in O or having both the end points on the boundary of O. We define the relaxation of the area functional w.r.t. a sort of uniform convergence, and we characterize it in terms of the infimum of the area among those surfaces in the space spanning the graphs of the traces of u on the two side of J and having what we have called a semicartesian structure. We exhibit examples showing that the relaxed area functional w.r.t the L^1 convergence may depend also on the values of u far from J, and on the relative position of J w.r.t. the boundary of O; these examples confirm the non-local behaviour of the L^1 relaxed area functional, and justify the interest in studying the relaxation w.r.t. a stronger convergence. We prove also that the L^1 relaxed area functional in non-subadditive for a rather class of maps.

%G en %U http://urania.sissa.it/xmlui/handle/1963/34483 %1 34670 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Lucia Tealdi (ltealdi@sissa.it) on 2015-08-07T16:06:48Z No. of bitstreams: 1 bellettini_paolini_tealdi_semicartesian.pdf: 623410 bytes, checksum: 871f66c4686a39ad7d1bc996f0e2b0aa (MD5) %0 Thesis %D 2015 %T Sharp Inequalities and Blow-up Analysis for Singular Moser-Trudinger Embeddings. %A Gabriele Mancini %K Moser-Trudinger %X We investigate existence of solutions for a singular Liouville equation on S^2 and prove sharp Onofri-type inequalities for a Moser-Trudinger functional in the presence of singular potentials. As a consequence we obtain existence of extremal functions for the Moser-Trudinger embedding on compact surfaces with conical singularities. Finally we study the blow-up behavior for sequences of solutions Liouville-type systems and prove a compactness condition which plays an important role in the variational analysis of Toda systems. %I SISSA %G en %1 34738 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by gmancini@sissa.it (gmancini@sissa.it) on 2015-09-22T12:27:17Z No. of bitstreams: 1 tesi4.pdf: 1376221 bytes, checksum: cfc85996d91a3384e94546a64bf8c479 (MD5) %0 Report %D 2015 %T Singular Liouville Equations on S^2: Sharp Inequalities and Existence Results %A Gabriele Mancini %XWe prove a sharp Onofri-type inequality and non-existence of extremals for a Moser-Tudinger functional on S^2 in the presence of potentials having positive order singularities. We also investigate the existence of critical points and give some sufficient conditions under symmetry or nondegeneracy assumptions.

%G en %U http://urania.sissa.it/xmlui/handle/1963/34489 %1 34672 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by gmancini@sissa.it (gmancini@sissa.it) on 2015-08-11T09:06:30Z No. of bitstreams: 1 art4.pdf: 352978 bytes, checksum: 4e081003a6b037544c46954c3d44b826 (MD5) %0 Thesis %D 2015 %T Some results on anisotropic mean curvature and other phase-transition problems %A Stefano Amato %K Anisotropic mean curvature %X The present thesis is divided into three parts. In the first part, we analyze a suitable regularization — which we call nonlinear multidomain model — of the motion of a hypersurface under smooth anisotropic mean curvature flow. The second part of the thesis deals with crystalline mean curvature of facets of a solid set of R^3 . Finally, in the third part we study a phase-transition model for Plateau’s type problems based on the theory of coverings and of BV functions. %I SISSA %G en %1 34733 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Stefano Amato (samato@sissa.it) on 2015-09-21T12:36:18Z No. of bitstreams: 1 tesi.pdf: 1566254 bytes, checksum: be7cf105a787693fd374acc1afe44fc3 (MD5) %0 Journal Article %J Annales de l'Institut Henri Poincare (C) Non Linear Analysis %D 2015 %T Stable regular critical points of the Mumford-Shah functional are local minimizers %A Marco Bonacini %A Massimiliano Morini %K Mumford-Shah functional %XIn this paper it is shown that any regular critical point of the Mumford–Shah functional, with positive definite second variation, is an isolated local minimizer with respect to competitors which are sufficiently close in the $L^1$

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

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

%B Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences %V 471 %P 20150054 %G eng %U https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2015.0054 %R 10.1098/rspa.2015.0054 %0 Journal Article %D 2015 %T Supremizer stabilization of POD-Galerkin approximation of parametrized Navier-Stokes equations %A F. Ballarin %A Andrea Manzoni %A Alfio Quarteroni %A Gianluigi Rozza %X In this work, we present a stable proper orthogonal decomposition–Galerkin approximation for parametrized steady incompressible Navier–Stokes equations with low Reynolds number. %I Wiley %G en %U http://urania.sissa.it/xmlui/handle/1963/34701 %1 34915 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2015-10-22T11:39:58Z No. of bitstreams: 1 IJNME_2014.pdf: 6761966 bytes, checksum: ad65f2c4d2dbd30a4a1590ff42ee49a0 (MD5) %R 10.1002/nme.4772 %0 Journal Article %D 2015 %T Three-sphere low-Reynolds-number swimmer with a passive elastic arm %A Alessandro Montino %A Antonio DeSimone %X One of the simplest model swimmers at low Reynolds number is the three-sphere swimmer by Najafi and Golestanian. It consists of three spheres connected by two rods which change their lengths periodically in non-reciprocal fashion. Here we investigate a variant of this model in which one rod is periodically actuated while the other is replaced by an elastic spring. We show that the competition between the elastic restoring force and the hydrodynamic drag produces a delay in the response of the passive elastic arm with respect to the active one. This leads to non-reciprocal shape changes and self-propulsion. After formulating the equations of motion, we study their solutions qualitatively and numerically. The leading-order term of the solution is computed analytically. We then address questions of optimization with respect to both actuation frequency and swimmer's geometry. Our results can provide valuable conceptual guidance in the engineering of robotic microswimmers. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34530 %1 34735 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-09-22T07:16:17Z No. of bitstreams: 1 art_10.1140_epje_i2015-15042-3.pdf: 766953 bytes, checksum: 7c5396c7e15baff264376c63eaf2248b (MD5) %R 10.1140/epje/i2015-15042-3 %0 Journal Article %J Analysis & PDE %D 2015 %T A topological join construction and the Toda system on compact surfaces of arbitrary genus %A Aleks Jevnikar %A Kallel, Sadok %A Andrea Malchiodi %B Analysis & PDE %I Mathematical Sciences Publishers %V 8 %P 1963–2027 %G eng %R 10.2140/apde.2015.8.1963 %0 Thesis %D 2015 %T Variational aspects of Liouville equations and systems %A Aleks Jevnikar %K Toda system %I SISSA %G en %1 34676 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by ajevnika@sissa.it (ajevnika@sissa.it) on 2015-08-08T16:04:38Z No. of bitstreams: 1 tesi phd.pdf: 1034249 bytes, checksum: 6988a3a6220b4d1bbd38c3124f520655 (MD5) %0 Thesis %D 2015 %T Variational aspects of singular Liouville systems %A Luca Battaglia %K Variational methods, Liouville systems, Moser-Trudinger inequalities, min-max methods %X I studied singular Liouville systems on compact surfaces from a variational point of view. I gave sufficient and necessary conditions for the existence of globally minimizing solutions, then I found min-max solutions for some particular systems. Finally, I also gave some non-existence results. %I SISSA %G en %1 34737 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by lbatta@sissa.it (lbatta@sissa.it) on 2015-09-22T09:49:56Z No. of bitstreams: 1 thesis0.pdf: 1795685 bytes, checksum: e981358904223d6649e47eb70e6da429 (MD5) %0 Thesis %D 2015 %T Volume variation and heat kernel for affine control problems %A Elisa Paoli %K Heat kernel asymptotics %X In this thesis we study two main problems. The first one is the small-time heat kernel expansion on the diagonal for second order hypoelliptic opeartors. We consider operators that can depend on a drift field and that satisfy only the weak Hörmander condition. In a first work we use perturbation techniques to determine the exact order of decay of the heat kernel, that depends on the Lie algebra generated by the fields involved in the hypoelliptic operator. We generalize in particular some results already obtained in the sub-Riemannian setting. In a second work we consider a model class of hypoelliptic operators and we characterize geometrically all the coefficients in the on-the diagonal asymptotics at the equilibrium points of the drift field. The class of operators that we consider contains the linear hypoelliptic operators with constant second order part on the Euclidean space. We describe the coefficients in terms only of the divergence of the drift field and of curvature-like invariants, related to the minimal cost of geodesics of the associated optimal control problem. In the second part of the thesis we consider the variation of a smooth volume along a geodesic. The structure of the manifold is induced by a quadratic Hamiltonian and the geodesic in described as the projection of the Hamiltonian flow. We find an expansion similar to the classical Riemannian one. It depends on the curvature operator associated to the Hamiltonian, on the symbol of the geodesic and on a new metric-measure invariant determined by the symbol of the geodesic and by the given volume. %I SISSA %G en %1 35290 %2 Mathematics %4 -1 %# MAT/05 %$ Submitted by epaoli@sissa.it (epaoli@sissa.it) on 2015-11-26T08:47:31Z No. of bitstreams: 1 Paoli_thesis.pdf: 1061974 bytes, checksum: d273a57f7bf44214d5fc30460ece686a (MD5) %0 Report %D 2015 %T The wave equation on domains with cracks growing on a prescribed path: existence, uniqueness, and continuous dependence on the data %A Gianni Dal Maso %A Ilaria Lucardesi %X Given a bounded open set $\Omega \subset \mathbb R^d$ with Lipschitz boundary and an increasing family $\Gamma_t$, $t\in [0,T]$, of closed subsets of $\Omega$, we analyze the scalar wave equation $\ddot{u} - div (A \nabla u) = f$ in the time varying cracked domains $\Omega\setminus\Gamma_t$. Here we assume that the sets $\Gamma_t$ are contained into a prescribed $(d-1)$-manifold of class $C^2$. Our approach relies on a change of variables: recasting the problem on the reference configuration $\Omega\setminus \Gamma_0$, we are led to consider a hyperbolic problem of the form $\ddot{v} - div (B\nabla v) + a \cdot \nabla v - 2 b \cdot \nabla \dot{v} = g$ in $\Omega \setminus \Gamma_0$. Under suitable assumptions on the regularity of the change of variables that transforms $\Omega\setminus \Gamma_t$ into $\Omega\setminus \Gamma_0$, we prove existence and uniqueness of weak solutions for both formulations. Moreover, we provide an energy equality, which gives, as a by-product, the continuous dependence of the solutions with respect to the cracks. %G en %U http://urania.sissa.it/xmlui/handle/1963/34629 %1 34832 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by lucardes@sissa.it (lucardes@sissa.it) on 2015-10-12T09:08:37Z No. of bitstreams: 1 DM-Luc-15-SISSA.pdf: 376913 bytes, checksum: bfdcf0975c25c9366acb4195e0f08e79 (MD5) %0 Journal Article %D 2014 %T An Abstract Nash–Moser Theorem and Quasi-Periodic Solutions for NLW and NLS on Compact Lie Groups and Homogeneous Manifolds %A Massimiliano Berti %A Livia Corsi %A Michela Procesi %X We prove an abstract implicit function theorem with parameters for smooth operators defined on scales of sequence spaces, modeled for the search of quasi-periodic solutions of PDEs. The tame estimates required for the inverse linearised operators at each step of the iterative scheme are deduced via a multiscale inductive argument. The Cantor-like set of parameters where the solution exists is defined in a non inductive way. This formulation completely decouples the iterative scheme from the measure theoretical analysis of the parameters where the small divisors non-resonance conditions are verified. As an application, we deduce the existence of quasi-periodic solutions for forced NLW and NLS equations on any compact Lie group or manifold which is homogeneous with respect to a compact Lie group, extending previous results valid only for tori. A basic tool of harmonic analysis is the highest weight theory for the irreducible representations of compact Lie groups. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34651 %1 34858 %2 Mathematics %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-10-20T12:19:54Z No. of bitstreams: 1 preprint2014.pdf: 549502 bytes, checksum: 4896c2df9fba6a09abb33941adb07837 (MD5) %R 10.1007/s00220-014-2128-4 %0 Journal Article %D 2014 %T Achieving unanimous opinions in signed social networks %A Claudio Altafini %A Gabriele Lini %X Being able to predict the outcome of an opinion forming process is an important problem in social network theory. However, even for linear dynamics, this becomes a difficult task as soon as non-cooperative interactions are taken into account. Such interactions are naturally modeled as negative weights on the adjacency matrix of the social network. In this paper we show how the Perron-Frobenius theorem can be used for this task also beyond its standard formulation for cooperative systems. In particular we show how it is possible to associate the achievement of unanimous opinions with the existence of invariant cones properly contained in the positive orthant. These cases correspond to signed adjacency matrices having the eventual positivity property, i.e., such that in sufficiently high powers all negative entries have disappeared. More generally, we show how for social networks the achievement of a, possibily non-unanimous, opinion can be associated to the existence of an invariant cone fully contained in one of the orthants of n. %I Institute of Electrical and Electronics Engineers Inc. %G en %U http://urania.sissa.it/xmlui/handle/1963/34935 %1 35137 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-11-06T12:24:07Z (GMT) No. of bitstreams: 0 %R 10.1109/ECC.2014.6862161 %0 Journal Article %D 2014 %T Buckling dynamics of a solvent-stimulated stretched elastomeric sheet %A Alessandro Lucantonio %A Matthieu Roché %A Paola Nardinocchi %A Howard A. Stone %X When stretched uniaxially, a thin elastic sheet may exhibit buckling. The occurrence of buckling depends on the geometrical properties of the sheet and the magnitude of the applied strain. Here we show that an elastomeric sheet initially stable under uniaxial stretching can destabilize when exposed to a solvent that swells the elastomer. We demonstrate experimentally and computationally that the features of the buckling pattern depend on the magnitude of stretching, and this observation offers a new way for controlling the shape of a swollen homogeneous thin sheet. %I Royal Society of Chemistry %G en %U http://urania.sissa.it/xmlui/handle/1963/34967 %1 35197 %2 Physics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-11-10T09:50:41Z No. of bitstreams: 1 preprint2014.pdf: 2111018 bytes, checksum: 568652d2ca6c44cdad3e520342c8042d (MD5) %R 10.1039/c3sm52941j %0 Journal Article %D 2014 %T Comparison between reduced basis and stochastic collocation methods for elliptic problems %A Peng Chen %A Alfio Quarteroni %A Gianluigi Rozza %X The stochastic collocation method (Babuška et al. in SIAM J Numer Anal 45(3):1005-1034, 2007; Nobile et al. in SIAM J Numer Anal 46(5):2411-2442, 2008a; SIAM J Numer Anal 46(5):2309-2345, 2008b; Xiu and Hesthaven in SIAM J Sci Comput 27(3):1118-1139, 2005) has recently been applied to stochastic problems that can be transformed into parametric systems. Meanwhile, the reduced basis method (Maday et al. in Comptes Rendus Mathematique 335(3):289-294, 2002; Patera and Rozza in Reduced basis approximation and a posteriori error estimation for parametrized partial differential equations Version 1.0. Copyright MIT, http://augustine.mit.edu, 2007; Rozza et al. in Arch Comput Methods Eng 15(3):229-275, 2008), primarily developed for solving parametric systems, has been recently used to deal with stochastic problems (Boyaval et al. in Comput Methods Appl Mech Eng 198(41-44):3187-3206, 2009; Arch Comput Methods Eng 17:435-454, 2010). In this work, we aim at comparing the performance of the two methods when applied to the solution of linear stochastic elliptic problems. Two important comparison criteria are considered: (1), convergence results of the approximation error; (2), computational costs for both offline construction and online evaluation. Numerical experiments are performed for problems from low dimensions O (1) to moderate dimensions O (10) and to high dimensions O (100). The main result stemming from our comparison is that the reduced basis method converges better in theory and faster in practice than the stochastic collocation method for smooth problems, and is more suitable for large scale and high dimensional stochastic problems when considering computational costs. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34727 %1 34916 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-10-26T11:39:14Z (GMT) No. of bitstreams: 0 %R 10.1007/s10915-013-9764-2 %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 %D 2014 %T A correction and an extension of Stampacchia's work on the geometric BVP %A Giovanni Vidossich %X G. Stampacchia introduced the geometric boundary value problem for ODEs in his doctoral thesis and published four papers related to it. Here we point out that the proof of his last theorem on the subject is incorrect and we provide a substitute for it as well as a generalizations of some of his earlier results. %I Advanced Nonlinear Studies %G en %U http://urania.sissa.it/xmlui/handle/1963/35023 %1 35263 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-11-17T10:33:42Z (GMT) No. of bitstreams: 0 %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 Critical points of the Moser-Trudinger functional on a disk %A Andrea Malchiodi %A Luca Martinazzi %X On the 2-dimensional unit disk $B_1$ we study the Moser-Trudinger functional $$E(u)=\int_{B_1}(e^{u^2}-1)dx, u\in H^1_0(B_1)$$ and its restrictions to $M_\Lambda:=\{u \in H^1_0(B_1):\|u\|^2_{H^1_0}=\Lambda\}$ for $\Lambda>0$. We prove that if a sequence $u_k$ of positive critical points of $E|_{M_{\Lambda_k}}$ (for some $\Lambda_k>0$) blows up as $k\to\infty$, then $\Lambda_k\to 4\pi$, and $u_k\to 0$ weakly in $H^1_0(B_1)$ and strongly in $C^1_{\loc}(\bar B_1\setminus\{0\})$. Using this we also prove that when $\Lambda$ is large enough, then $E|_{M_\Lambda}$ has no positive critical point, complementing previous existence results by Carleson-Chang, M. Struwe and Lamm-Robert-Struwe. %I European Mathematical Society %G en %U http://hdl.handle.net/1963/6560 %1 6487 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Andrea Malchiodi (malchiod@sissa.it) on 2013-03-14T10:24:49Z No. of bitstreams: 1 1203.1077v1.pdf: 218315 bytes, checksum: 7e4a2900b082b373371033ed0196f5de (MD5) %R 10.4171/JEMS/450 %0 Journal Article %J Procedia Engineering %D 2014 %T Curvature-adapted remeshing of CAD surfaces %A Franco Dassi %A Andrea Mola %A Hang Si %XA common representation of surfaces with complicated topology and geometry is through composite parametric surfaces as is the case for most CAD modelers. A challenging problem is how to generate a mesh of such a surface that well approximates the geometry of the surface, preserves its topology and important geometric features, and contains nicely shaped elements. In this work, we present an optimization-based surface remeshing method that is able to satisfy many of these requirements simultaneously. This method is inspired by the recent work of Lévy and Bonneel (Proc. 21th International Meshing Roundtable, October 2012), which embeds a smooth surface into a high-dimensional space and remesh it uniformly in that embedding space. Our method works directly in the 3d spaces and uses an embedding space in R6 to evaluate mesh size and mesh quality. It generates a curvatureadapted anisotropic surface mesh that well represents the geometry of the surface with a low number of elements. We illustrate our approach through various examples.

%B Procedia Engineering %I Elsevier %V 82 %P 253–265 %G en %U https://doi.org/10.1016/j.proeng.2014.10.388 %1 35220 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-11-11T16:19:16Z No. of bitstreams: 1 art2014.pdf: 3913220 bytes, checksum: ba78b55b28c0eed195d2abc48bd7ca4b (MD5) %R 10.1016/j.proeng.2014.10.388 %0 Thesis %D 2014 %T The decomposition of optimal transportation problems with convex cost %A Mauro Bardelloni %K Optimal Transportation %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/7475 %1 7570 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Mauro Bardelloni (mbarde@sissa.it) on 2014-10-27T10:15:30Z No. of bitstreams: 1 Bardelloni-thesis.pdf: 1162347 bytes, checksum: f2b57d7f3054afe4fae1c207b090121f (MD5) %0 Report %D 2014 %T The decomposition of optimal transportation problems with convex cost %A Stefano Bianchini %A Mauro Bardelloni %I SISSA %G en_US %U http://hdl.handle.net/1963/7433 %1 7527 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-09-22T14:16:35Z No. of bitstreams: 1 sissa _45_2014_MATE.pdf: 893572 bytes, checksum: c4334710f599da624c2e1cfb56aac415 (MD5) %0 Journal Article %D 2014 %T A density result for GSBD and its application to the approximation of brittle fracture energies %A Flaviana Iurlano %XWe present an approximation result for functions u: Ω → ℝ^n belonging to the space GSBD(Ω) ∩ L2(Ω, ℝn) with e(u) square integrable and Hn-1(Ju) finite. The approximating functions uk are piecewise continuous functions such that uk → u in (Formula Presented). As an application, we provide the extension to the vector-valued case of the Γ-convergence result in GSBV(Ω) proved by Ambrosio and Tortorelli (Commun Pure Appl Math 43:999-1036, 1990; Boll. Un. Mat. Ital. B (7) 6:105-123, 1992).

%I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34647 %1 34851 %2 Mathematics %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-10-14T17:02:41Z No. of bitstreams: 1 preprint2014.pdf: 543013 bytes, checksum: 1d1170449f762ffdaf48812b31671bc2 (MD5) %R 10.1007/s00526-013-0676-7 %0 Journal Article %D 2014 %T Discrete one-dimensional crawlers on viscous substrates: achievable net displacements and their energy cost %A Giovanni Noselli %A Amabile Tatone %A Antonio DeSimone %K Cell migration %X We study model one-dimensional crawlers, namely, model mechanical systems that can achieve self-propulsion by controlled shape changes of their body (extension or contraction of portions of the body), thanks to frictional interactions with a rigid substrate. We evaluate the achievable net displacement and the related energetic cost for self-propulsion by discrete crawlers (i.e., whose body is made of a discrete number of contractile or extensile segments) moving on substrates with either a Newtonian (linear) or a Bingham-type (stick-slip) rheology. Our analysis is aimed at constructing the basic building blocks towards an integrative, multi-scale description of crawling cell motility. %I Elsevier %G en %U http://urania.sissa.it/xmlui/handle/1963/34449 %1 34591 %2 Mathematics %$ Submitted by gnoselli@sissa.it (gnoselli@sissa.it) on 2015-03-07T17:44:40Z No. of bitstreams: 1 N-link_crawlers.pdf: 1005838 bytes, checksum: 685d5b41e7de190ec65c60090d397f93 (MD5) %R 10.1016/j.mechrescom.2013.10.023 %0 Report %D 2014 %T Dislocations at the continuum scale: functional setting and variational properties %A Riccardo Scala %A Nicolas Van Goethem %G eng %U http://cvgmt.sns.it/paper/2294/ %0 Journal Article %D 2014 %T Editorial %A Ciro Ciliberto %A Gianni Dal Maso %A Pasquale Vetro %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34712 %1 34926 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-10-26T10:50:12Z (GMT) No. of bitstreams: 0 %R 10.1007/s12215-014-0172-8 %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 Report %D 2014 %T An efficient computational framework for reduced basis approximation and a posteriori error estimation of parametrized Navier-Stokes flows %A Andrea Manzoni %K Reduced Basis Method, parametrized Navier-Stokes equations, steady incompressible fluids, a posteriori error estimation, approximation stability %X We present the current Reduced Basis framework for the efficient numerical approximation of parametrized steady Navier-Stokes equations. We have extended the existing setting developed in the last decade (see e.g. [Deparis, Veroy & Patera, Quarteroni & Rozza] to more general affine and nonaffine parametrizations (such as volume-based techniques), to a simultaneous velocity-pressure error estimates and to a fully decoupled Offline/Online procedure in order to speedup the solution of the reduced-order problem. This is particularly suitable for real-time and many-query contexts, which are both part of our final goal. Furthermore, we present an efficient numerical implementation for treating nonlinear advection terms in a convenient way. A residual-based a posteriori error estimation with respect to a truth, full-order Finite Element approximation is provided for joint pressure/velocity errors, according to the Brezzi-Rappaz-Raviart stability theory. To do this, we take advantage of an extension of the Successive Constraint Method for the estimation of stability factors and of a suitable fixed-point algorithm for the approximation of Sobolev embedding constants. Finally, we present some numerical test cases, in order to show both the approximation properties and the computational efficiency of the derived framework. %G en %1 7291 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Andrea Manzoni (amanzoni@sissa.it) on 2014-02-12T17:36:11Z No. of bitstreams: 1 AM_2014_M2AN_preprint.pdf: 5678588 bytes, checksum: 9589729cb84fffc5229b4b071e5e69fb (MD5) %0 Journal Article %D 2014 %T Existence and uniqueness of the gradient flow of the Entropy in the space of probability measures %A Stefano Bianchini %A Alexander Dabrowski %X After a brief introduction on gradient flows in metric spaces and on geodesically convex functionals, we give an account of the proof (following the outline of [3, 7]) of the existence and uniqueness of the gradient flow of the Entropy in the space of Borel probability measures over a compact geodesic metric space with Ricci curvature bounded from below. %I EUT Edizioni Universita di Trieste %G en %U http://urania.sissa.it/xmlui/handle/1963/34693 %1 34907 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-10-22T09:22:40Z No. of bitstreams: 1 ExUniqGFEntropy.pdf: 344636 bytes, checksum: a918d50ab5d6b9ce9cb8683238f402e6 (MD5) %0 Journal Article %J Annales de l'Institut Henri Poincare (C) Non Linear Analysis %D 2014 %T Existence of immersed spheres minimizing curvature functionals in non-compact 3-manifolds %A Andrea Mondino %A Johannes Schygulla %K Direct methods in the calculus of variations %K General Relativity %K Geometric measure theory %K second fundamental form %K Willmore functional %XWe study curvature functionals for immersed 2-spheres in non-compact, three-dimensional Riemannian manifold $(M,h)$ without boundary. First, under the assumption that $(M,h)$ is the euclidean 3-space endowed with a semi-perturbed metric with perturbation small in $C^1$ norm and of compact support, we prove that if there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})>0$ then there exists a smooth embedding $ f:\mathbb{S}^2 \hookrightarrow M$ minimizing the Willmore functional $\frac{1}{4}\int |H|^2$, where $H$ is the mean curvature. Second, assuming that $(M,h)$ is of bounded geometry (i.e. bounded sectional curvature and strictly positive injectivity radius) and asymptotically euclidean or hyperbolic we prove that if there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})>6$ then there exists a smooth immersion $f:\mathbb{S}^2\hookrightarrow M$ minimizing the functional $\int (\frac{1}{2}|A|^2+1)$, where $A$ is the second fundamental form. Finally, adding the bound $K^M \leq 2$ to the last assumptions, we obtain a smooth minimizer $f:\mathbb{S}^2 \hookrightarrow M$ for the functional $\int \frac{1}{4}(|H|^2+1)$. The assumptions of the last two theorems are satisfied in a large class of 3-manifolds arising as spacelike timeslices solutions of the Einstein vacuum equation in case of null or negative cosmological constant.

%B Annales de l'Institut Henri Poincare (C) Non Linear Analysis %V 31 %P 707 - 724 %G eng %U http://www.sciencedirect.com/science/article/pii/S0294144913000851 %R https://doi.org/10.1016/j.anihpc.2013.07.002 %0 Journal Article %J Mathematische Annalen %D 2014 %T Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds %A Kuwert, Ernst %A Andrea Mondino %A Johannes Schygulla %XWe study curvature functionals for immersed 2-spheres in a compact, three-dimensional Riemannian manifold $M$. Under the assumption that the sectional curvature $K^M$ is strictly positive, we prove the existence of a smooth immersion $f:{\mathbb{S}}^2 \rightarrow M$ minimizing the $L^2$ integral of the second fundamental form. Assuming instead that $K^M \leq 2 $ and that there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})>6$, we obtain a smooth minimizer $f:{\mathbb{S}}^2 \rightarrow M$ for the functional $\int \frac{1}{4}|H|^2+1$, where $H$ is the mean curvature.

%B Mathematische Annalen %V 359 %P 379–425 %8 Jun %G eng %U https://doi.org/10.1007/s00208-013-1005-3 %R 10.1007/s00208-013-1005-3 %0 Journal Article %J Calculus of Variations and Partial Differential Equations %D 2014 %T Existence of integral m-varifolds minimizing $\int |A|^p $ and $\int |H|^p$ , p>m, in Riemannian manifolds %A Andrea Mondino %XWe prove existence of integral rectifiable $m$-dimensional varifolds minimizing functionals of the type $\int |H|^p$ and $\int |A|^p$ in a given Riemannian $n$-dimensional manifold $(N,g)$, $2 \leq m<n$ and $p>m$ under suitable assumptions on $N$ (in the end of the paper we give many examples of such ambient manifolds). To this aim we introduce the following new tools: some monotonicity formulas for varifolds in ${\mathbb{R }^S}$ involving $\int |H|^p$to avoid degeneracy of the minimizer, and a sort of isoperimetric inequality to bound the mass in terms of the mentioned functionals.

%B Calculus of Variations and Partial Differential Equations %V 49 %P 431–470 %8 Jan %G eng %U https://doi.org/10.1007/s00526-012-0588-y %R 10.1007/s00526-012-0588-y %0 Conference Proceedings %B Proceedings of the 24th International Ocean and Polar Engineering Conference, Busan, 2014 %D 2014 %T A fully nonlinear potential model for ship hydrodynamics directly interfaced with CAD data structures %A Andrea Mola %A Luca Heltai %A Antonio DeSimone %K ship hydrodynamics %X We present a model for ship hydrodynamics simulations currently under development at SISSA. The model employs potential flow theory and fully nonlinear free surface boundary conditions. The spatial discretization of the equations is performed by means of a collocation BEM. This gives rise to a Differential Algbraic Equations (DAE) system, solved using an implicit BDF scheme to time advance the solution. The model has been implemented into a C++ software able to automatically generate the computational grids from the CAD geometry of the hull. Numerical results on Kriso KCS and KVLCC2 hulls are presented and discussed. %B Proceedings of the 24th International Ocean and Polar Engineering Conference, Busan, 2014 %I SISSA %G en %1 7357 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Luca Heltai (heltai@sissa.it) on 2014-03-22T15:00:37Z No. of bitstreams: 1 MolaHeltaiDeSimone2014.pdf: 1241007 bytes, checksum: 1a56d909a08f1f470c7efc14018e37f8 (MD5) %0 Book Section %B Separated representations and PGD-based model reduction : fundamentals and applications %D 2014 %T Fundamentals of Reduced Basis Method for problems governed by parametrized PDEs and applications %A Gianluigi Rozza %K reduced basis method, linear elasticity, heat transfer, error bounds, parametrized PDEs %XIn this chapter we consider Reduced Basis (RB) approximations of parametrized Partial Differential Equations (PDEs). The the idea behind RB is to decouple the generation and projection stages (Offline/Online computational procedures) of the approximation process in order to solve parametrized PDEs in a fast, inexpensive and reliable way. The RB method, especially applied to 3D problems, allows great computational savings with respect to the classical Galerkin Finite Element (FE) Method. The standard FE method is typically ill suited to (i) iterative contexts like optimization, sensitivity analysis and many-queries in general, and (ii) real time evaluation. We consider for simplicity coercive PDEs. We discuss all the steps to set up a RB approximation, either from an analytical and a numerical point of view. Then we present an application of the RB method to a steady thermal conductivity problem in heat transfer with emphasis on geometrical and physical parameters.

%B Separated representations and PGD-based model reduction : fundamentals and applications %S CISM International Centre for Mechanical Sciences %I Springer %C Wien %V 554 %G eng %& 4 %R 10.1007/978-3-7091-1794-1_4 %0 Thesis %D 2014 %T Geometry and analysis of control-affine systems: motion planning, heat and Schrödinger evolution %A Dario Prandi %K control theory %X This thesis is dedicated to two problems arising from geometric control theory, regarding control-affine systems $\dot q= f_0(q)+\sum_{j=1}^m u_j f_j(q)$, where $f_0$ is called the drift. In the first part we extend the concept of complexity of non-admissible trajectories, well understood for sub-Riemannian systems, to this more general case, and find asymptotic estimates. In order to do this, we also prove a result in the same spirit as the Ball-Box theorem for sub-Riemannian systems, in the context of control-affine systems equipped with the L1 cost. Then, in the second part of the thesis, we consider a family of 2-dimensional driftless control systems. For these, we study how the set where the control vector fields become collinear affects the diffusion dynamics. More precisely, we study whether solutions to the heat and Schrödinger equations associated with this Laplace-Beltrami operator are able to cross this singularity, and how its the presence affects the spectral properties of the operator, in particular under a magnetic Aharonov–Bohm-type perturbation. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/7474 %1 7576 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by dprandi@sissa.it (dprandi@sissa.it) on 2014-10-28T17:03:22Z No. of bitstreams: 1 thesis_SISSA.pdf: 2610057 bytes, checksum: b1f6802988c3d34412407d628c7c1963 (MD5) %0 Journal Article %D 2014 %T Global Structure of Admissible BV Solutions to Piecewise Genuinely Nonlinear, Strictly Hyperbolic Conservation Laws in One Space Dimension %A Stefano Bianchini %A Lei Yu %XThe paper describes the qualitative structure of an admissible BV solution to a strictly hyperbolic system of conservation laws whose characteristic families are piecewise genuinely nonlinear. More precisely, we prove that there are a countable set of points Θ and a countable family of Lipschitz curves T{script} such that outside T{script} ∪ Θ the solution is continuous, and for all points in T{script}{set minus}Θ the solution has left and right limit. This extends the corresponding structural result in [7] for genuinely nonlinear systems. An application of this result is the stability of the wave structure of solution w.r.t. -convergence. The proof is based on the introduction of subdiscontinuities of a shock, whose behavior is qualitatively analogous to the discontinuities of the solution to genuinely nonlinear systems.

%I Taylor & Francis %G en %U http://urania.sissa.it/xmlui/handle/1963/34694 %1 34908 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-10-22T09:34:23Z No. of bitstreams: 1 global structure of solutions to PWGN hyperbolic conservation laws.pdf: 452219 bytes, checksum: 85bd51fc08fa53a087cee8aec2b9544a (MD5) %R 10.1080/03605302.2013.775153 %0 Journal Article %J ESAIM: Control, Optimisation and Calculus of Variations %D 2014 %T Hölder equivalence of the value function for control-affine systems %A Dario Prandi %B ESAIM: Control, Optimisation and Calculus of Variations %I EDP Sciences %V 20 %P 1224–1248 %G eng %R 10.1051/cocv/2014014 %0 Report %D 2014 %T Homogenization of functional with linear growth in the context of A-quasiconvexity %A Jose Matias %A Marco Morandotti %A Pedro M. Santos %X This work deals with the homogenization of functionals with linear growth in the context of A-quasiconvexity. A representation theorem is proved, where the new integrand function is obtained by solving a cell problem where the coupling between homogenization and the A-free condition plays a crucial role. This result extends some previous work to the linear case, thus allowing for concentration effects. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/7436 %1 7528 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-10-07T06:20:26Z No. of bitstreams: 1 Mat-Mor-San-14.pdf: 352795 bytes, checksum: de708e4c922915ea1f523eb23165cb83 (MD5) %0 Journal Article %D 2014 %T Homology computation for a class of contact structures on T3 %A Ali Maalaoui %A Vittorio Martino %X We consider a family of tight contact forms on the three-dimensional torus and we compute the relative Contact Homology by using the variational theory of critical points at infinity. We will also show local stability. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34649 %1 34856 %2 Mathematics %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-10-20T12:08:36Z No. of bitstreams: 1 preprint2014.pdf: 371632 bytes, checksum: abec6bf1b85cb6034662ab217f97c4b8 (MD5) %R 10.1007/s00526-013-0648-y %0 Thesis %D 2014 %T KAM for quasi-linear and fully nonlinear perturbations of Airy and KdV equations %A Riccardo Montalto %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/7476 %1 7571 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by rmontalt@sissa.it (rmontalt@sissa.it) on 2014-10-27T10:15:33Z No. of bitstreams: 1 Tesi-Phd-Montalto-Riccardo.pdf: 1843377 bytes, checksum: b4e504e6ad1860c3d3580beb4e24efff (MD5) %0 Journal Article %J C. R. Math. Acad. Sci. Paris %D 2014 %T KAM for quasi-linear KdV %A P Baldi %A Massimiliano Berti %A Riccardo Montalto %XWe prove the existence and stability of Cantor families of quasi-periodic, small-amplitude solutions of quasi-linear autonomous Hamiltonian perturbations of KdV.

%B C. R. Math. Acad. Sci. Paris %I Elsevier %V 352 %P 603-607 %G en %U http://urania.sissa.it/xmlui/handle/1963/35067 %N 7-8 %1 35302 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-11-30T15:30:40Z (GMT) No. of bitstreams: 0 %R 10.1016/j.crma.2014.04.012 %0 Journal Article %J Arch. Ration. Mech. Anal. %D 2014 %T KAM for Reversible Derivative Wave Equations %A Massimiliano Berti %A Luca Biasco %A Michela Procesi %XWe prove the existence of Cantor families of small amplitude, analytic, linearly stable quasi-periodic solutions of reversible derivative wave equations.

%B Arch. Ration. Mech. Anal. %I Springer %V 212 %P 905-955 %G en %U http://urania.sissa.it/xmlui/handle/1963/34646 %N 3 %1 34850 %2 Mathematics %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-10-14T16:55:00Z No. of bitstreams: 1 preprint2014.pdf: 620515 bytes, checksum: d1d981f350e63c9906f793bcfe66e972 (MD5) %R 10.1007/s00205-014-0726-0 %0 Journal Article %D 2014 %T Laplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length %A Gianni Dal Maso %A Gianluca Orlando %A Rodica Toader %K cracked domains, energy release rate, higher order derivatives, asymptotic expansion of solutions %XWe consider the weak solution of the Laplace equation in a planar domain with a straight crack, prescribing a homogeneous Neumann condition on the crack and a nonhomogeneous Dirichlet condition on the rest of the boundary. For every k we express the k-th derivative of the energy with respect to the crack length in terms of a finite number of coefficients of the asymptotic expansion of the solution near the crack tip and of a finite number of other parameters, which only depend on the shape of the domain.

%I SISSA %G en %U http://hdl.handle.net/1963/7271 %1 7316 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2014-03-11T15:17:50Z No. of bitstreams: 1 DM-Orl-Toa-sissa.pdf: 251851 bytes, checksum: 59273a217a11dcfc5a9ed89d2c34c6cd (MD5) %R 10.1007/s00030-014-0291-0 %0 Book Section %D 2014 %T Lecture notes on gradient flows and optimal transport %A Sara Daneri %A Giuseppe Savarè %X We present a short overview on the strongest variational formulation for gradient flows of geodesically λ-convex functionals in metric spaces, with applications to diffusion equations in Wasserstein spaces of probability measures. These notes are based on a series of lectures given by the second author for the Summer School "Optimal transportation: Theory and applications" in Grenoble during the week of June 22-26, 2009. %I Cambridge University Press %G en %U http://urania.sissa.it/xmlui/handle/1963/35093 %1 35348 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-12-02T11:28:52Z No. of bitstreams: 1 preprint2014.pdf: 448708 bytes, checksum: b8b01c6463b81dc26c42c74009c43406 (MD5) %R 10.1017/CBO9781107297296 %0 Journal Article %D 2014 %T Legendre duality on hypersurfaces in Kähler manifolds %A Vittorio Martino %X We give a sufficient condition on real strictly Levi-convex hypersurfaces M, embedded in four-dimensional Kähler manifolds V , such that Legendre duality can be performed. We consider the contact form onM whose kernel is the restriction of the holomorphic tangent space of V and show that if there exists a Legendrian Killing vector field v, then the dual form β(̇) := d(v, ̇) is a contact form on M with the same orientation than theta. %I Walter de Gruyter and Co. %G en %U http://urania.sissa.it/xmlui/handle/1963/34777 %1 34998 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-10-27T17:37:38Z No. of bitstreams: 1 preprint2014.pdf: 98700 bytes, checksum: 1187e3e70cd12ba31a32c4be8491bd32 (MD5) %R 10.1515/advgeom-2014-0016 %0 Journal Article %J ESAIM: Control, Optimisation and Calculus of Variations %D 2014 %T Linearized plastic plate models as Γ-limits of 3D finite elastoplasticity %A Elisa Davoli %XThe subject of this paper is the rigorous derivation of reduced models for a thin plate by means of $\Gamma$-convergence, in the framework of finite plasticity. Denoting by $\epsilon$ the thickness of the plate, we analyse the case where the scaling factor of the elasto-plastic energy per unit volume is of order $\epsilon^{2 \alpha -2}$, with $\alpha \geq 3$. According to the value of $\alpha$, partially or fully linearized models are deduced, which correspond, in the absence of plastic deformation, to the Von Kármán plate theory and the linearized plate theory.

%B ESAIM: Control, Optimisation and Calculus of Variations %I EDP Sciences %V 20 %P 725–747 %G eng %R 10.1051/cocv/2013081 %0 Journal Article %D 2014 %T Lipschitz continuous viscosity solutions for a class of fully nonlinear equations on lie groups %A Vittorio Martino %A Annamaria Montanari %X In this paper, we prove existence and uniqueness of Lipschitz continuous viscosity solutions for Dirichlet problems involving a class a fully non-linear operators on Lie groups. In particular, we consider the elementary symmetric functions of the eigenvalues of the Hessian built with left-invariant vector fields. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34699 %1 34910 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-10-22T10:28:16Z No. of bitstreams: 1 preprint2014.pdf: 418666 bytes, checksum: 959eed7adb8eeecee6c733f5ad7a136c (MD5) %R 10.1007/s12220-012-9332-2 %0 Journal Article %J SIAM Journal on Mathematical Analysis %D 2014 %T Local and global minimality results for a nonlocal isoperimetric problem on R^N %A Marco Bonacini %A Riccardo Cristoferi %K Nonlocal isoperimetric problem %XWe consider a nonlocal isoperimetric problem defined in the whole space R^N, whose nonlocal part is given by a Riesz potential with exponent $\alpha\in(0, N-1)$. We show that critical configurations with positive second variation are local minimizers and satisfy a quantitative inequality with respect to the L^1-norm. This criterion provides the existence of a (explicitly determined) critical threshold determining the interval of volumes for which the ball is a local minimizer, and allows to address several global minimality issues.

%B SIAM Journal on Mathematical Analysis %I SIAM Publications %V 46 %P 2310-2349 %G en %U http://hdl.handle.net/1963/6984 %N 4 %1 6976 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Marco Bonacini (mbonacin@sissa.it) on 2013-07-19T15:56:58Z No. of bitstreams: 1 boncri_fin.pdf: 567997 bytes, checksum: a24d4e9e6bbd6f176558b4d007dba6e3 (MD5) %R 10.1137/130929898 %0 Journal Article %D 2014 %T Local behavior of fractional p-minimizers %A Agnese Di Castro %A Tuomo Kuusi %A Giampiero Palatucci %K fractional Sobolev spaces %XWe extend the De Giorgi-Nash Moser theory to nonlocal, possibly degerate integro-differential operators

%I SISSA %G en %1 7301 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Giampiero Palatucci (palatucc@sissa.it) on 2014-03-03T08:54:40Z No. of bitstreams: 1 DKP.pdf: 459581 bytes, checksum: 58cf9e0f905a3932505ab467eefd39e9 (MD5) %0 Journal Article %D 2014 %T On the Lp-differentiability of certain classes of functions %A Giovanni Alberti %A Stefano Bianchini %A Gianluca Crippa %X We prove the Lp-differentiability at almost every point for convolution products on ℝd of the form K*μ, where μ is bounded measure and K is a homogeneous kernel of degree 1-d. From this result we derive the Lp-differentiability for vector fields on R d whose curl and divergence are measures, and also for vector fields with bounded deformation. %I European Mathematical Society %G en %U http://urania.sissa.it/xmlui/handle/1963/34695 %1 34909 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-10-22T09:44:25Z No. of bitstreams: 1 Alberti_Bianchini_50_M.pdf: 253000 bytes, checksum: 06381747f80814ced325966adefdec91 (MD5) %R 10.4171/rmi/782 %0 Journal Article %D 2014 %T Maximal generalized solution of eikonal equation %A Sandro Zagatti %X We study the Dirichlet problem for the eikonal equation: 1/2 |∇u(x)|^2-a(x)=0 in Ω u(x)=(x) on Ω, without continuity assumptions on the map a(.). We find a class of maps a(.) contained in the space L∞(Ω) for which the problem admits a (maximal) generalized solution, providing a generalization of the notion of viscosity solution. %I Elsevier %G en %U http://urania.sissa.it/xmlui/handle/1963/34642 %1 34846 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-10-21T08:38:44Z (GMT) No. of bitstreams: 0 %R 10.1016/j.jde.2014.04.001 %0 Journal Article %J Asymptotic Analysis %D 2014 %T A model for crack growth with branching and kinking %A Simone Racca %K quasistatic crack evolution, branching, kinking, Griffith\\\'s criterion %XWe study an evolution model for fractured elastic materials in the 2-dimensional case, for which the crack path is not assumed to be known a priori. We introduce some general assumptions on the structure of the fracture sets suitable to remove the restrictions on the regularity of the crack sets and to allow for kinking and branching to develop. In addition we define the front of the fracture and its velocity. By means of a time-discretization approach, we prove the existence of a continuous-time evolution that satisfies an energy inequality and a stability criterion. The energy balance also takes into account the energy dissipated at the front of the fracture. The stability criterion is stated in the framework of Griffith's theory, in terms of the energy release rate, when the crack grows at least at one point of its front.

%B Asymptotic Analysis %I SISSA %V 89 %P 63-110 %G en %U https://content.iospress.com/articles/asymptotic-analysis/asy1233 %N 1-2 %9 Research Article %1 6293 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Simone Racca (sracca@sissa.it) on 2012-12-27T14:51:21Z\\nNo. of bitstreams: 1\\nA model for crack growth with branching and kinking - Racca.pdf: 566327 bytes, checksum: c6cfc3165c0bfee387a9c6f8b1e5b4b1 (MD5) %& 63 %R 10.3233/ASY-141233 %0 Journal Article %D 2014 %T Model Order Reduction in Fluid Dynamics: Challenges and Perspectives %A Toni Lassila %A Andrea Manzoni %A Alfio Quarteroni %A Gianluigi Rozza %X This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities - which are mainly related either to nonlinear convection terms and/or some geometric variability - that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration. We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of inf-sup stability, certification through error estimation, computational issues and-in the unsteady case - long-time stability of the reduced model. Moreover, we provide an extensive list of literature references. %I Springer %G en %1 34923 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-10-22T15:11:51Z No. of bitstreams: 1 preprint2014.pdf: 287014 bytes, checksum: b195410aa3f63643829ed25f1adb6520 (MD5) %R 10.1007/978-3-319-02090-7_9 %0 Journal Article %J Bull. Inst. Math. Acad. Sin. %D 2014 %T A Moser-Trudinger inequality for the singular Toda system %A Luca Battaglia %A Andrea Malchiodi %B Bull. Inst. Math. Acad. Sin. %V 9 %P 1–23 %G eng %0 Journal Article %D 2014 %T New results on Gamma-limits of integral functionals %A Nadia Ansini %A Gianni Dal Maso %A Caterina Ida Zeppieri %K Gamma-convergence %I Elsevier %G en %U http://hdl.handle.net/1963/5880 %1 5745 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-05-30T12:48:08Z No. of bitstreams: 1 03M_2012_Ansini.pdf: 262251 bytes, checksum: 4e0dd5c07ab75bd2da8aa462f2ae8f0f (MD5) %R 10.1016/j.anihpc.2013.02.005 %0 Journal Article %D 2014 %T Nonsingular Isogeometric Boundary Element Method for Stokes Flows in 3D %A Luca Heltai %A Marino Arroyo %A Antonio DeSimone %K Isogeometric Analysis %X Isogeometric analysis (IGA) is emerging as a technology bridging Computer Aided Geometric Design (CAGD), most commonly based on Non-Uniform Rational B-Splines (NURBS) surfaces, and engineering analysis. In finite element and boundary element isogeometric methods (FE-IGA and IGA-BEM), the NURBS basis functions that de- scribe the geometry define also the approximation spaces. In the FE-IGA approach, the surfaces generated by the CAGD tools need to be extended to volumetric descriptions, a major open problem in 3D. This additional passage can be avoided in principle when the partial differential equations to be solved admit a formulation in terms of bound- ary integral equations, leading to Boundary Element Isogeometric Analysis (IGA-BEM). The main advantages of such an approach are given by the dimensionality reduction of the problem (from volumetric-based to surface-based), by the fact that the interface with CAGD tools is direct, and by the possibility to treat exterior problems, where the computational domain is infinite. By contrast, these methods produce system matrices which are full, and require the integration of singular kernels. In this paper we address the second point and propose a nonsingular formulation of IGA-BEM for 3D Stokes flows, whose convergence is carefully tested numerically. Standard Gaussian quadrature rules suffice to integrate the boundary integral equations, and carefully chosen known exact solutions of the interior Stokes problem are used to correct the resulting matrices, extending the work by Klaseboer et al. [27] to IGA-BEM. %I Elsevier %G en %U http://hdl.handle.net/1963/6326 %1 6250 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Luca Heltai (heltai@sissa.it) on 2012-12-03T08:19:28Z No. of bitstreams: 1 isogeo_stokes.pdf: 732320 bytes, checksum: 224ef57de6c49f03db0afaccdcb234f9 (MD5) %R 10.1016/j.cma.2013.09.017 %0 Journal Article %J Journal of Hyperbolic Differential Equations %D 2014 %T On a quadratic functional for scalar conservation laws %A Stefano Bianchini %A Stefano Modena %XWe prove a quadratic interaction estimate for approximate solutions to scalar conservation laws obtained by the wavefront tracking approximation or the Glimm scheme. This quadratic estimate has been used in the literature to prove the convergence rate of the Glimm scheme.

%B Journal of Hyperbolic Differential Equations %I World Scientific Publishing %V 11 %P 355-435 %G en %U http://arxiv.org/abs/1311.2929 %N 2 %1 34903 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-10-22T08:34:56Z No. of bitstreams: 1 31M_Bianchini_Modena.pdf: 710996 bytes, checksum: 8dd1a009996ca60b6c2f1dc96bb46f43 (MD5) %R 10.1142/S0219891614500118 %0 Journal Article %J Bulletin of the Institute of Mathematics of Academia Sinica (New Series) %D 2014 %T Quadratic interaction functional for systems of conservation laws: a case study %A Stefano Bianchini %A Stefano Modena %B Bulletin of the Institute of Mathematics of Academia Sinica (New Series) %V 9 %P 487-546 %G eng %U https://w3.math.sinica.edu.tw/bulletin_ns/20143/2014308.pdf %0 Journal Article %J Nonlinear Analysis %D 2014 %T Quasi-static crack growth in hydraulic fracture %A Stefano Almi %A Gianni Dal Maso %A Rodica Toader %XWe present a variational model for the quasi-static crack growth in hydraulic fracture in the framework of the energy formulation of rate-independent processes. The cracks are assumed to lie on a prescribed plane and to satisfy a very weak regularity assumption.

%B Nonlinear Analysis %I Elsevier %V 109 %P 301-318 %G en %U http://hdl.handle.net/20.500.11767/17350 %N Nov %9 Journal article %1 34741 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by salmi@sissa.it (salmi@sissa.it) on 2015-09-24T08:10:23Z No. of bitstreams: 1 A-DM-T-070714.pdf: 283645 bytes, checksum: 68056ef27e9dcfa246029148c0016c0f (MD5) %& 301 %R 10.1016/j.na.2014.07.009 %0 Journal Article %J Journal of Dynamics and Differential Equations %D 2014 %T Quasistatic Evolution in Perfect Plasticity as Limit of Dynamic Processes %A Gianni Dal Maso %A Riccardo Scala %XWe introduce a model of dynamic visco-elasto-plastic evolution in the linearly elastic regime and prove an existence and uniqueness result. Then we study the limit of (a rescaled version of) the solutions when the data vary slowly. We prove that they converge, up to a subsequence, to a quasistatic evolution in perfect plasticity.

%B Journal of Dynamics and Differential Equations %V 26 %P 915–954 %8 Dec %G eng %U https://doi.org/10.1007/s10884-014-9409-7 %R 10.1007/s10884-014-9409-7 %0 Journal Article %J Mathematical Models and Methods in Applied Sciences %D 2014 %T Quasistatic evolution models for thin plates arising as low energy Γ-limits of finite plasticity %A Elisa Davoli %XIn this paper we deduce by $\Gamma$-convergence some partially and fully linearized quasistatic evolution models for thin plates, in the framework of finite plasticity. Denoting by $\epsilon$ the thickness of the plate, we study the case where the scaling factor of the elasto-plastic energy is of order $\epsilon^{2 \alpha -2}$, with $\alpha\geq 3$. These scalings of the energy lead, in the absence of plastic dissipation, to the Von Kármán and linearized Von Kármán functionals for thin plates. We show that solutions to the three-dimensional quasistatic evolution problems converge, as the thickness of the plate tends to zero, to a quasistatic evolution associated to a suitable reduced model depending on $\alpha$.

%B Mathematical Models and Methods in Applied Sciences %V 24 %P 2085-2153 %G eng %U https://doi.org/10.1142/S021820251450016X %R 10.1142/S021820251450016X %0 Report %D 2014 %T Rate-independent damage in thermo-viscoelastic materials with inertia %A Giuliano Lazzaroni %A Riccarda Rossi %A Marita Thomas %A Rodica Toader %X We present a model for rate-independent, unidirectional, partial damage in visco-elastic materials with inertia and thermal effects. The damage process is modeled by means of an internal variable, governed by a rate-independent flow rule. The heat equation and the momentum balance for the displacements are coupled in a highly nonlinear way. Our assumptions on the corresponding energy functional also comprise the case of the Ambrosio-Tortorelli phase-field model (without passage to the brittle limit). We discuss a suitable weak formulation and prove an existence theorem obtained with the aid of a (partially) decoupled time-discrete scheme and variational convergence methods. We also carry out the asymptotic analysis for vanishing viscosity and inertia and obtain a fully rate-independent limit model for displacements and damage, which is Independent of temperature. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/7444 %1 7542 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-10-15T09:00:07Z No. of bitstreams: 1 LRTT-SISSA-preprint-14_10_15.pdf: 498065 bytes, checksum: 0de0c4a77dafb5df12747fd9947cec5c (MD5) %0 Conference Paper %B ECMI 2014 proceedings %D 2014 %T Reduced basis method for the Stokes equations in decomposable domains using greedy optimization %A Laura Iapichino %A Alfio Quarteroni %A Gianluigi Rozza %A Volkwein, Stefan %B ECMI 2014 proceedings %P 1–7 %G eng %0 Book %B MS&A %D 2014 %T Reduced Order Methods for Modeling and Computational Reduction %A Alfio Quarteroni %A Gianluigi Rozza %K reduced order methods, MOR, ROM, POD, RB, greedy, CFD, Numerical Analysis %XThis monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics.

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

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

%B MS&A %7 1 %I Springer %C Milano %V 9 %P 334 %G eng %6 1 %R 10.1007/978-3-319-02090-7 %0 Book Section %B AIMS Series on Applied Mathematics, vol. 8 (2014): 399 - 406 %D 2014 %T Reduction on characteristics for continuous of a scalar balance law %A Giovanni Alberti %A Stefano Bianchini %A Laura Caravenna %K Method of characteristics %B AIMS Series on Applied Mathematics, vol. 8 (2014): 399 - 406 %I SISSA %G en %U http://hdl.handle.net/1963/6562 %1 6516 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-04-03T07:48:04Z No. of bitstreams: 1 Alberti_11.pdf: 330968 bytes, checksum: a5f69e2a1d0afcfe139cf17ebcaf0f2d (MD5) %0 Journal Article %J Proceedings of the Royal Society A 470, 20140333 (2014) %D 2014 %T A robotic crawler exploiting directional frictional interactions: experiments, numerics, and derivation of a reduced model %A Giovanni Noselli %A Antonio DeSimone %X We present experimental and numerical results for a model crawler which is able to extract net positional changes from reciprocal shape changes, i.e. ‘breathing-like’ deformations, thanks to directional, frictional interactions with a textured solid substrate, mediated by flexible inclined feet. We also present a simple reduced model that captures the essential features of the kinematics and energetics of the gait, and compare its predictions with the results from experiments and from numerical simulations. %B Proceedings of the Royal Society A 470, 20140333 (2014) %I Royal Society Publishing %G en %1 34594 %2 Mathematics %$ Submitted by gnoselli@sissa.it (gnoselli@sissa.it) on 2015-03-07T18:10:10Z No. of bitstreams: 1 bristle_crawlers.pdf: 9309327 bytes, checksum: 10f6df9814dd01c888aa9ec7836f1dff (MD5) %R 10.1098/rspa.2014.0333 %0 Journal Article %D 2014 %T SBV Regularity of Systems of Conservation Laws and Hamilton–Jacobi Equations %A Stefano Bianchini %X We review the SBV regularity for solutions to hyperbolic systems of conservation laws and Hamilton-Jacobi equations. We give an overview of the techniques involved in the proof, and a collection of related problems concludes the paper. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34691 %1 34904 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-10-22T08:51:26Z No. of bitstreams: 1 proceeding.DFDE11.pdf: 401448 bytes, checksum: 0002408d841699f963dfb817ed96e577 (MD5) %R 10.1007/s10958-014-2022-9 %0 Journal Article %D 2014 %T Second Order Asymptotic Development for the Anisotropic Cahn-Hilliard Functional %A Gianni Dal Maso %A Irene Fonseca %A Giovanni Leoni %K Gamma-convergence, Cahn-Hilliard functional, phase transitions %X The asymptotic behavior of an anisotropic Cahn-Hilliard functional with prescribed mass and Dirichlet boundary condition is studied when the parameter $\varepsilon$ that determines the width of the transition layers tends to zero. The double-well potential is assumed to be even and equal to $|s-1|^\beta$ near $s=1$, with $1<\beta<2$. The first order term in the asymptotic development by $\Gamma$-convergence is well-known, and is related to a suitable anisotropic perimeter of the interface. Here it is shown that, under these assumptions, the second order term is zero, which gives an estimate on the rate of convergence of the minimum values. %I SISSA %G en %U http://hdl.handle.net/1963/7390 %1 7439 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2014-06-19T16:24:43Z No. of bitstreams: 1 DM-Fon-Leo-14-sissa.pdf: 409621 bytes, checksum: 40ba0baf0686b18dcd89582772f376b5 (MD5) %0 Journal Article %D 2014 %T Shape control of active surfaces inspired by the movement of euglenids %A Marino Arroyo %A Antonio DeSimone %X We examine a novel mechanism for active surface morphing inspired by the cell body deformations of euglenids. Actuation is accomplished through in-plane simple shear along prescribed slip lines decorating the surface. Under general non-uniform actuation, such local deformation produces Gaussian curvature, and therefore leads to shape changes. Geometrically, a deformation that realizes the prescribed local shear is an isometric embedding. We explore the possibilities and limitations of this bio-inspired shape morphing mechanism, by first characterizing isometric embeddings under axisymmetry, understanding the limits of embeddability, and studying in detail the accessibility of surfaces of zero and constant curvature. Modeling mechanically the active surface as a non-Euclidean plate (NEP), we further examine the mechanism beyond the geometric singularities arising from embeddability, where mechanics and buckling play a decisive role. We also propose a non-axisymmetric actuation strategy to accomplish large amplitude bending and twisting motions of elongated cylindrical surfaces. Besides helping understand how euglenids delicately control their shape, our results may provide the background to engineer soft machines. %I Elsevier %G en %U http://urania.sissa.it/xmlui/handle/1963/35118 %1 35375 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-12-03T09:19:38Z (GMT) No. of bitstreams: 0 %R 10.1016/j.jmps.2013.09.017 %0 Journal Article %D 2014 %T Shape Optimization by Free-Form Deformation: Existence Results and Numerical Solution for Stokes Flows %A F. Ballarin %A Andrea Manzoni %A Gianluigi Rozza %A Sandro Salsa %X Shape optimization problems governed by PDEs result from many applications in computational fluid dynamics. These problems usually entail very large computational costs and require also a suitable approach for representing and deforming efficiently the shape of the underlying geometry, as well as for computing the shape gradient of the cost functional to be minimized. Several approaches based on the displacement of a set of control points have been developed in the last decades, such as the so-called free-form deformations. In this paper we present a new theoretical result which allows to recast free-form deformations into the general class of perturbation of identity maps, and to guarantee the compactness of the set of admissible shapes. Moreover, we address both a general optimization framework based on the continuous shape gradient and a numerical procedure for solving efficiently three-dimensional optimal design problems. This framework is applied to the optimal design of immersed bodies in Stokes flows, for which we consider the numerical solution of a benchmark case study from literature. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34698 %1 34914 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-10-22T11:24:27Z (GMT) No. of bitstreams: 0 %R 10.1007/s10915-013-9807-8 %0 Journal Article %J Annales de l'Institut Henri Poincare (C) Non Linear Analysis %D 2014 %T Smooth approximation of bi-Lipschitz orientation-preserving homeomorphisms %A Sara Daneri %A Aldo Pratelli %X

We show that a planar bi-Lipschitz orientation-preserving homeomorphism can be approximated in the W1,p norm, together with its inverse, with an orientation-preserving homeomorphism which is piecewise affine or smooth.

%B Annales de l'Institut Henri Poincare (C) Non Linear Analysis %V 31 %P 567 - 589 %G eng %U http://www.sciencedirect.com/science/article/pii/S0294144913000711 %R https://doi.org/10.1016/j.anihpc.2013.04.007 %0 Report %D 2014 %T Some remarks on a model for rate-independent damage in thermo-visco-elastodynamics %A Giuliano Lazzaroni %A Riccarda Rossi %A Marita Thomas %A Rodica Toader %X This note deals with the analysis of a model for partial damage, where the rateindependent, unidirectional flow rule for the damage variable is coupled with the rate-dependent heat equation, and with the momentum balance featuring inertia and viscosity according to Kelvin-Voigt rheology. The results presented here combine the approach from Roubicek [1] with the methods from Lazzaroni/Rossi/Thomas/Toader [2] and extend the analysis to the setting of inhomogeneous time-dependent Dirichlet data. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/7463 %1 7566 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-10-23T09:01:52Z No. of bitstreams: 1 MURPHYS_LRTT14_SISSA-preprint(1).pdf: 246259 bytes, checksum: a67369f4eab98d39fb2165d882d97592 (MD5) %0 Journal Article %D 2014 %T Some remarks on the seismic behaviour of embedded cantilevered retaining walls %A Riccardo Conti %A F. Burali D'Arezzo %A Giulia M.B. Viggiani %X This paper is a numerical investigation of the physical phenomena that control the dynamic behaviour of embedded cantilevered retaining walls. Recent experimental observations obtained from centrifuge tests have shown that embedded cantilevered retaining walls experience permanent displacements even before the acceleration reaches its critical value, corresponding to full mobilisation of the soil strength. The motivation for this work stems from the need to incorporate these observations in simplified design procedures. A parametric study was carried out on a pair of embedded cantilevered walls in dry sand, subjected to real earthquakes scaled at different values of the maximum acceleration. The results of these analyses indicate that, for the geotechnical design of the wall, the equivalent acceleration to be used in pseudo-static calculations can be related to the maximum displacement that the structure can sustain, and can be larger than the maximum acceleration expected at the site. For the structural design of the wall, it is suggested that the maximum bending moments of the wall can be computed using a realistic distribution of contact stress and a conservative value of the pseudo-static acceleration, taking into account two-dimensional amplification effects near the walls. %I Thomas Telford %G en %U http://urania.sissa.it/xmlui/handle/1963/35073 %1 35308 %2 Physics %4 2 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-11-30T17:34:56Z No. of bitstreams: 1 art2014.pdf: 1304935 bytes, checksum: 2618504941effc8eed6dddb1077d8916 (MD5) %R 10.1680/geot.13.P.031 %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 Journal Article %J Advances in Calculus of Variations %D 2014 %T Stability of equilibrium configurations for elastic films in two and three dimensions %A Marco Bonacini %K Epitaxially strained elastic films %XWe establish a local minimality sufficiency criterion, based on the strict positivity of the second variation, in the context of a variational model for the epitaxial growth of elastic films. Our result holds also in the three-dimensional case and for a general class of nonlinear elastic energies. Applications to the study of the local minimality of flat morphologies are also shown.

%B Advances in Calculus of Variations %I SISSA %V 8 %P 117-153 %8 01/2014 %G en %U https://www.degruyter.com/view/j/acv.2015.8.issue-2/acv-2013-0018/acv-2013-0018.xml %N 2 %1 6997 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Marco Bonacini (mbonacin@sissa.it) on 2013-08-07T11:12:48Z No. of bitstreams: 1 films.pdf: 595689 bytes, checksum: 009553ee1f902e6e6984675ad0cf70b6 (MD5) %& 117 %R https://doi.org/10.1515/acv-2013-0018 %0 Journal Article %J Computer Methods in Applied Mechanics and Engineering %D 2014 %T Stabilized reduced basis method for parametrized advection-diffusion PDEs %A Pacciarini, P. %A Gianluigi Rozza %XIn this work, we propose viable and efficient strategies for the stabilization of the reduced basis approximation of an advection dominated problem. In particular, we investigate the combination of a classic stabilization method (SUPG) with the Offline-Online structure of the RB method. We explain why the stabilization is needed in both stages and we identify, analytically and numerically, which are the drawbacks of a stabilization performed only during the construction of the reduced basis (i.e. only in the Offline stage). We carry out numerical tests to assess the performances of the ``double'' stabilization both in steady and unsteady problems, also related to heat transfer phenomena.

%B Computer Methods in Applied Mechanics and Engineering %V 274 %P 1–18 %G eng %R 10.1016/j.cma.2014.02.005 %0 Conference Paper %B 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014 %D 2014 %T Stabilized reduced basis method for parametrized scalar advection-diffusion problems at higher Péclet number: Roles of the boundary layers and inner fronts %A Pacciarini, P. %A Gianluigi Rozza %XAdvection-dominated problems, which arise in many engineering situations, often require a fast and reliable approximation of the solution given some parameters as inputs. In this work we want to investigate the coupling of the reduced basis method - which guarantees rapidity and reliability - with some classical stabilization techiques to deal with the advection-dominated condition. We provide a numerical extension of the results presented in [1], focusing in particular on problems with curved boundary layers and inner fronts whose direction depends on the parameter.

%B 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014 %P 5614–5624 %G eng %U https://infoscience.epfl.ch/record/203327/files/ECCOMAS_PP_GR.pdf %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 Journal of Mathematical Analysis and Applications %D 2014 %T Structure of entropy solutions to general scalar conservation laws in one space dimension %A Stefano Bianchini %A Lei Yu %B Journal of Mathematical Analysis and Applications %I SISSA %V 428 %P 356-386 %8 08/2015 %G en %U https://www.sciencedirect.com/science/article/pii/S0022247X15002218 %N 1 %1 7305 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-03-10T11:39:18Z No. of bitstreams: 1 Global structure of entropy solutions to scalar conservation laws.ref.pdf: 464993 bytes, checksum: 9b83b6f3f845eda8eb202f0748617756 (MD5) %& 356 %R https://doi.org/10.1016/j.jmaa.2015.03.006 %0 Journal Article %D 2014 %T Swelling dynamics of a thin elastomeric sheet under uniaxial pre-stretch %A Alessandro Lucantonio %A Paola Nardinocchi %A Howard A. Stone %X It has been demonstrated experimentally that pre-stretch affects the swelling of an elastomeric membrane when it is exposed to a solvent. We study theoretically the one-dimensional swelling of a pre-stretched thin elastomeric sheet, bonded to an impermeable rigid substrate, to quantify the influence of pre-stretch. We show that the solvent uptake increases when pre-stretch increases, both at equilibrium and during the swelling transient, where it exhibits two different scaling regimes. The coupling between the solvent uptake and pre-stretch may be practically exploited to design soft actuators where the swelling-induced deformations can be controlled by varying the pre-stretch. %I American Institute of Physics %G en %U http://urania.sissa.it/xmlui/handle/1963/35113 %1 35370 %2 Physics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-12-02T16:28:53Z No. of bitstreams: 1 art2014.pdf: 777840 bytes, checksum: 2362b6250fd872264208d0d3b846a551 (MD5) %R 10.1063/1.4866576 %0 Journal Article %D 2014 %T Swelling-induced and controlled curving in layered gel beams %A Alessandro Lucantonio %A Paola Nardinocchi %A Matteo Pezzulla %X We describe swelling-driven curving in originally straight and non-homogeneous beams. We present and verify a structural model of swollen beams, based on a new point of view adopted to describe swelling-induced deformation processes in bilayered gel beams, that is based on the split of the swelling-induced deformation of the beam at equilibrium into two components, both depending on the elastic properties of the gel. The method allows us to: (i) determine beam stretching and curving, once assigned the characteristics of the solvent bath and of the non-homogeneous beam, and (ii) estimate the characteristics of non-homogeneous flat gel beams in such a way as to obtain, under free-swelling conditions, three-dimensional shapes. The study was pursued by means of analytical, semi-analytical and numerical tools; excellent agreement of the outcomes of the different techniques was found, thus confirming the strength of the method. %I Royal Society of London %G en %U http://urania.sissa.it/xmlui/handle/1963/34987 %1 35229 %2 Mathematics %4 1 %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2015-11-12T09:25:24Z (GMT) No. of bitstreams: 0 %R 10.1098/rspa.2014.0467 %0 Journal Article %D 2014 %T The topology of a subspace of the Legendrian curves on a closed contact 3-manifold %A Ali Maalaoui %A Vittorio Martino %X In this paper we study a subspace of the space of Legendrian loops and we show that the injection of this space into the full loop space is an S 1-equivariant homotopy equivalence. This space can be also seen as the space of zero Maslov index Legendrian loops and it shows up as a suitable space of variations in contact form geometry. %I Advanced Nonlinear Studies %G en %U http://urania.sissa.it/xmlui/handle/1963/35016 %1 35262 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-11-17T09:54:29Z No. of bitstreams: 1 preprint2014.pdf: 721147 bytes, checksum: 810ace1cc0879eac4e2e7b7f33a89751 (MD5) %0 Journal Article %D 2014 %T A uniqueness result for the continuity equation in two dimensions: dedicated to constantine dafermos on the occasion of his 70th birthday %A Giovanni Alberti %A Stefano Bianchini %A Gianluca Crippa %X We characterize the autonomous, divergence-free vector fields b on the plane such that the Cauchy problem for the continuity equation ∂tu +div(bu) = 0 admits a unique bounded solution (in the weak sense) for every bounded initial datum; the characterization is given in terms of a property of Sard type for the potential f associated to b. As a corollary we obtain uniqueness under the assumption that the curl of b is a measure. This result can be extended to certain nonautonomous vector fields b with bounded divergence. %I European Mathematical Society; Springer Verlag %G en %U http://urania.sissa.it/xmlui/handle/1963/34692 %1 34906 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-10-22T09:07:51Z No. of bitstreams: 1 Alberti_Bianchini_Crippa_52M.pdf: 318780 bytes, checksum: 556a1d21b44c58d90201b25b2c104744 (MD5) %R 10.4171/JEMS/431 %0 Thesis %D 2014 %T A variational approach to statics and dynamics of elasto-plastic systems %A Riccardo Scala %K delamination %X We prove some existence results for dynamic evolutions in elasto-plasticity and delamination. We study the limit as the data vary very slowly and prove convergence results to quasistatic evolutions. We model dislocations by mean of currents, we introduce the space of deformations in the presence of dislocations and study the graphs of these maps. We prove existence results for minimum problems. We study the properties of minimizers. %I SISSA %G en_US %U http://urania.sissa.it/xmlui/handle/1963/7471 %1 7583 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Riccardo Scala (rscala@sissa.it) on 2014-10-29T12:04:30Z No. of bitstreams: 1 tesi.pdf: 1322338 bytes, checksum: 5fcf0395d13a0dc16eac4edaef440913 (MD5) %0 Journal Article %D 2014 %T A variational model for the quasi-static growth of fractional dimensional brittle fractures %A Simone Racca %A Rodica Toader %K Variational models %XWe propose a variational model for the irreversible quasi-static evolution of brittle fractures having fractional Hausdorff dimension in the setting of two-dimensional antiplane and plane elasticity. The evolution along such irregular crack paths can be obtained as $\Gamma$-limit of evolutions along one-dimensional cracks when the fracture toughness tends to zero.

%I European Mathematical Society %G en %U http://hdl.handle.net/1963/6983 %1 6973 %2 Mathematics %4 -1 %$ Submitted by Simone Racca (sracca@sissa.it) on 2013-07-18T08:39:00Z No. of bitstreams: 1 Racca_Toader.pdf: 416939 bytes, checksum: cf459548a10944037e56b7504fe60f51 (MD5) %R 10.4171/IFB/328 %0 Journal Article %D 2014 %T A weighted empirical interpolation method: A priori convergence analysis and applications %A Peng Chen %A Alfio Quarteroni %A Gianluigi Rozza %X We extend the classical empirical interpolation method [M. Barrault, Y. Maday, N.C. Nguyen and A.T. Patera, An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations. Compt. Rend. Math. Anal. Num. 339 (2004) 667-672] to a weighted empirical interpolation method in order to approximate nonlinear parametric functions with weighted parameters, e.g. random variables obeying various probability distributions. A priori convergence analysis is provided for the proposed method and the error bound by Kolmogorov N-width is improved from the recent work [Y. Maday, N.C. Nguyen, A.T. Patera and G.S.H. Pau, A general, multipurpose interpolation procedure: the magic points. Commun. Pure Appl. Anal. 8 (2009) 383-404]. We apply our method to geometric Brownian motion, exponential Karhunen-Loève expansion and reduced basis approximation of non-affine stochastic elliptic equations. We demonstrate its improved accuracy and efficiency over the empirical interpolation method, as well as sparse grid stochastic collocation method. %I EDP Sciences %G en %U http://urania.sissa.it/xmlui/handle/1963/35021 %1 35253 %2 Mathematics %4 1 %# MAT/05 %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2015-11-17T10:26:06Z (GMT) No. of bitstreams: 0 %R 10.1051/m2an/2013128 %0 Report %D 2014 %T Where best to place a Dirichlet condition in an anisotropic membrane? %A Paolo Tilli %A Davide Zucco %X We study a shape optimization problem for the first eigenvalue of an elliptic operator in divergence form, with non constant coefficients, over a fixed domain $\Omega$. Dirichlet conditions are imposed along $\partial\Omega$ and, in addition, along a set $\Sigma$ of prescribed length ($1$-dimensional Hausdorff measure). We look for the best shape and position for the supplementary Dirichlet region $\Sigma$ in order to maximize the first eigenvalue. We characterize the limit distribution of the optimal sets, as their prescribed length tends to infinity, via $\Gamma$-convergence. %I SISSA %G en_US %U http://urania.sissa.it/xmlui/handle/1963/7481 %1 7592 %$ Submitted by dzucco@sissa.it (dzucco@sissa.it) on 2014-11-07T16:09:28Z No. of bitstreams: 1 Tilli_Zucco_varifold.pdf: 379650 bytes, checksum: 341cfa2d9d25e41789652de4c99c22fe (MD5) %0 Report %D 2013 %T Ambrosio-Tortorelli approximation of cohesive fracture models in linearized elasticity %A Matteo Focardi %A Flaviana Iurlano %K Functions of bounded deformation %XWe provide an approximation result in the sense of $\Gamma$-convergence for cohesive fracture energies of the form \[ \int_\Omega \mathscr{Q}_1(e(u))\,dx+a\,\mathcal{H}^{n-1}(J_u)+b\,\int_{J_u}\mathscr{Q}_0^{1/2}([u]\odot\nu_u)\,d\mathcal{H}^{n-1}, \] where $\Omega\subset{\mathbb R}^n$ is a bounded open set with Lipschitz boundary, $\mathscr{Q}_0$ and $\mathscr{Q}_1$ are coercive quadratic forms on ${\mathbb M}^{n\times n}_{sym}$, $a,\,b$ are positive constants, and $u$ runs in the space of fields $SBD^2(\Omega)$ , i.e., it's a special field with bounded deformation such that its symmetric gradient $e(u)$ is square integrable, and its jump set $J_u$ has finite $(n-1)$-Hausdorff measure in ${\mathbb R}^n$. The approximation is performed by means of Ambrosio-Tortorelli type elliptic regularizations, the prototype example being \[ \int_\Omega\Big(v|e(u)|^2+\frac{(1-v)^2}{\varepsilon}+{\gamma\,\varepsilon}|\nabla v|^2\Big)\,dx, \] where $(u,v)\in H^1(\Omega,{\mathbb R}^n){\times} H^1(\Omega)$, $\varepsilon\leq v\leq 1$ and $\gamma>0$.

%I SISSA %G en %U http://hdl.handle.net/1963/6615 %1 6573 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Flaviana Iurlano (iurlano@sissa.it) on 2013-05-13T11:26:04Z No. of bitstreams: 1 coesivo17_preprint_SISSA.pdf: 482275 bytes, checksum: 890efd398f9ff18a36d5b18fc90f8107 (MD5) %0 Journal Article %D 2013 %T Analytical validation of a continuum model for epitaxial growth with elasticity on vicinal surfaces %A Gianni Dal Maso %A Irene Fonseca %A Giovanni Leoni %K singular nonlinear parabolic equations, Hilbert transform, thin films %X In this paper it is shown existence of weak solutions of a variational inequality derived from the continuum model introduced by Xiang [7, formula (3.62)] (see also the work of Xiang and E [8] and Xu and Xiang [9]) to describe the self-organization of terraces and steps driven by misfit elasticity between a film and a substrate in heteroepitaxial growth. This model is obtained as a continuum limit of discrete theories of Duport, Politi, and Villain [3] and Tersoff, Phang, Zhang, and Lagally[6]. %I Springer %G en %U http://hdl.handle.net/1963/7245 %1 7284 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2014-01-15T08:47:14Z No. of bitstreams: 1 DM-Fon-Leo.pdf: 409459 bytes, checksum: 07429e936667a481a2c093217e585e84 (MD5) %R 10.1007/s00205-014-0730-4 %0 Thesis %D 2013 %T An Approximation Result for Generalised Functions of Bounded Deformation and Applications to Damage Problems %A Flaviana Iurlano %K Functions of bounded deformation %I SISSA %G en %1 7203 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Flaviana Iurlano (iurlano@sissa.it) on 2013-10-23T12:46:25Z No. of bitstreams: 1 Iurlano - PhD Thesis.pdf: 1234569 bytes, checksum: e031f9fd97f6a1662f96f1caf2bc564e (MD5) %0 Journal Article %D 2013 %T Asymptotics of the first Laplace eigenvalue with Dirichlet regions of prescribed length %A Paolo Tilli %A Davide Zucco %X We consider the problem of maximizing the first eigenvalue of the $p$-Laplacian (possibly with nonconstant coefficients) over a fixed domain $\Omega$, with Dirichlet conditions along $\partial\Omega$ and along a supplementary set $\Sigma$, which is the unknown of the optimization problem. The set $\Sigma$, which plays the role of a supplementary stiffening rib for a membrane $\Omega$, is a compact connected set (e.g., a curve or a connected system of curves) that can be placed anywhere in $\overline{\Omega}$ and is subject to the constraint of an upper bound $L$ to its total length (one-dimensional Hausdorff measure). This upper bound prevents $\Sigma$ from spreading throughout $\Omega$ and makes the problem well-posed. We investigate the behavior of optimal sets $\Sigma_L$ as $L\to\infty$ via $\Gamma$-convergence, and we explicitly construct certain asymptotically optimal configurations. We also study the behavior as $p\to\infty$ with $L$ fixed, finding connections with maximum-distance problems related to the principal frequency of the $\infty$-Laplacian. %I Society for Industrial and Applied Mathematics %G en %U http://urania.sissa.it/xmlui/handle/1963/35141 %1 35379 %2 Physics %4 1 %# MAT/05 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-12-09T16:12:39Z (GMT) No. of bitstreams: 0 %R 10.1137/130916825 %0 Report %D 2013 %T Attainment results for nematic elastomers %A Virginia Agostiniani %A Gianni Dal Maso %A Antonio DeSimone %X We consider a class of non-quasiconvex frame indifferent energy densities which includes Ogden-type energy densities for nematic elastomers. For the corresponding geometrically linear problem we provide an explicit minimizer of the energy functional satisfying a nontrivial boundary condition. Other attainment results, both for the nonlinear and the linearized model, are obtained by using the theory of convex integration introduced by Mueller and Sverak in the context of crystalline solids. %I SISSA %G en %U http://hdl.handle.net/1963/7174 %1 7201 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-10-22T14:32:26Z No. of bitstreams: 1 Ago-DM-DeS-13-sissa.pdf: 394672 bytes, checksum: d02690a6c7f206310d28d253ce53d0d3 (MD5) %0 Journal Article %J Comptes Rendus Mathematique. Volume 351, Issue 15-16, August 2013, Pages 593-598 %D 2013 %T A combination between the reduced basis method and the ANOVA expansion: On the computation of sensitivity indices %A Denis Devaud %A Andrea Manzoni %A Gianluigi Rozza %K Partial differential equations %XWe consider a method to efficiently evaluate in a real-time context an output based on the numerical solution of a partial differential equation depending on a large number of parameters. We state a result allowing to improve the computational performance of a three-step RB-ANOVA-RB method. This is a combination of the reduced basis (RB) method and the analysis of variations (ANOVA) expansion, aiming at compressing the parameter space without affecting the accuracy of the output. The idea of this method is to compute a first (coarse) RB approximation of the output of interest involving all the parameter components, but with a large tolerance on the a posteriori error estimate; then, we evaluate the ANOVA expansion of the output and freeze the least important parameter components; finally, considering a restricted model involving just the retained parameter components, we compute a second (fine) RB approximation with a smaller tolerance on the a posteriori error estimate. The fine RB approximation entails lower computational costs than the coarse one, because of the reduction of parameter dimensionality. Our result provides a criterion to avoid the computation of those terms in the ANOVA expansion that are related to the interaction between parameters in the bilinear form, thus making the RB-ANOVA-RB procedure computationally more feasible.

%B Comptes Rendus Mathematique. Volume 351, Issue 15-16, August 2013, Pages 593-598 %I Elsevier %G en %U http://hdl.handle.net/1963/7389 %1 7434 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-06-19T08:56:09Z No. of bitstreams: 1 Devaud_Manzoni_Rozza_2013.pdf: 564002 bytes, checksum: 4c93e74468534915513e6805d440dee9 (MD5) %R 10.1016/j.crma.2013.07.023 %0 Journal Article %J Nature. Scientific Reports 3, Article number: 1251, Published : 13 February 2013 %D 2013 %T Common dynamical features of sensory adaptation in photoreceptors and olfactory sensory neurons. %A Giovanna De Palo %A Giuseppe Facchetti %A Monica Mazzolini %A Anna Menini %A Vincent Torre %A Claudio Altafini %XSensory systems adapt, i.e., they adjust their sensitivity to external stimuli according to the ambient level. In this paper we show that single cell electrophysiological responses of vertebrate olfactory receptors and of photoreceptors to different input protocols exhibit several common features related to adaptation, and that these features can be used to investigate the dynamical structure of the feedback regulation responsible for the adaptation. In particular, we point out that two different forms of adaptation can be observed, in response to steps and to pairs of pulses. These two forms of adaptation appear to be in a dynamical trade-off: the more adaptation to a step is close to perfect, the slower is the recovery in adaptation to pulse pairs and viceversa. Neither of the two forms is explained by the dynamical models currently used to describe adaptation, such as the integral feedback model.

%B Nature. Scientific Reports 3, Article number: 1251, Published : 13 February 2013 %I SISSA %G en %1 6453 %2 Mathematics %4 1 %$ Submitted by Claudio Altafini (altafini@sissa.it) on 2013-02-27T14:00:21Z\nNo. of bitstreams: 0 %R 10.1038/srep01251 %0 Journal Article %J Journal of Differential Equations %D 2013 %T Concentration of solutions for a singularly perturbed mixed problem in non-smooth domains %A Serena Dipierro %K Finite-dimensional reductions %K Local inversion %K Singularly perturbed elliptic problems %XWe consider a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^n$ whose boundary has an $(n−2)$-dimensional singularity. Assuming $1<p<\frac{n+2}{n−2}$, we prove that, under suitable geometric conditions on the boundary of the domain, there exist solutions which approach the intersection of the Neumann and the Dirichlet parts as the singular perturbation parameter tends to zero.

%B Journal of Differential Equations %V 254 %P 30 - 66 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022039612003312 %R https://doi.org/10.1016/j.jde.2012.08.017 %0 Journal Article %J Journal of Geometric Analysis %D 2013 %T The Conformal Willmore Functional: A Perturbative Approach %A Andrea Mondino %XThe conformal Willmore functional (which is conformal invariant in general Riemannian manifolds $(M,g)$ is studied with a perturbative method: the Lyapunov–Schmidt reduction. Existence of critical points is shown in ambient manifolds $(\mathbb{R}^3,g_\epsilon)$ – where $g_\epsilon$ is a metric close and asymptotic to the Euclidean one. With the same technique a non-existence result is proved in general Riemannian manifolds $(M,g)$ of dimension three.

%B Journal of Geometric Analysis %V 23 %P 764–811 %8 Apr %G eng %U https://doi.org/10.1007/s12220-011-9263-3 %R 10.1007/s12220-011-9263-3 %0 Journal Article %J Journal of Geometric Analysis 23, nr.2 (2013), pages 812-854 %D 2013 %T Connected Sum Construction for σk-Yamabe Metrics %A Giovanni Catino %A Lorenzo Mazzieri %X In this paper we produce families of Riemannian metrics with positive constant $\sigma_k$-curvature equal to $2^{-k} {n \choose k}$ by performing the connected sum of two given compact {\em non degenerate} $n$--dimensional solutions $(M_1,g_1)$ and $(M_2,g_2)$ of the (positive) $\sigma_k$-Yamabe problem, provided $2 \leq 2k < n$. The problem is equivalent to solve a second order fully nonlinear elliptic equation. %B Journal of Geometric Analysis 23, nr.2 (2013), pages 812-854 %I Springer %G en %U http://hdl.handle.net/1963/6441 %1 6366 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-01-29T10:41:53Z No. of bitstreams: 1 0910.5353v2.pdf: 355177 bytes, checksum: 0fa7b4a369607d617c4c167617460165 (MD5) %R 10.1007/s12220-011-9265-1 %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 The curvature: a variational approach %A Andrei A. Agrachev %A Davide Barilari %A Luca Rizzi %K Crurvature, subriemannian metric, optimal control problem %X The curvature discussed in this paper is a rather far going generalization of the Riemannian sectional curvature. We define it for a wide class of optimal control problems: a unified framework including geometric structures such as Riemannian, sub-Riemannian, Finsler and sub-Finsler structures; a special attention is paid to the sub-Riemannian (or Carnot-Caratheodory) metric spaces. Our construction of the curvature is direct and naive, and it is similar to the original approach of Riemann. Surprisingly, it works in a very general setting and, in particular, for all sub-Riemannian spaces. %I SISSA %G en %U http://hdl.handle.net/1963/7226 %1 7260 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-12-03T08:46:32Z No. of bitstreams: 1 1306.5318v3.pdf: 991021 bytes, checksum: f99fb9f1455fa70fbca476e8fd2571af (MD5) %0 Report %D 2013 %T The deal.II Library, Version 8.1 %A Wolfgang Bangerth %A Timo Heister %A Luca Heltai %A G. Kanschat %A Martin Kronbichler %A Matthias Maier %A Bruno Turcksin %A T. D. Young %X This paper provides an overview of the new features of the finite element library deal.II version 8.0. %I SISSA %G en %U http://hdl.handle.net/1963/7236 %1 7272 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Luca Heltai (heltai@sissa.it) on 2013-12-10T10:43:08Z No. of bitstreams: 1 1312.2266v1.pdf: 245445 bytes, checksum: e00fcd6d7d9ac6e2076208958b07eef3 (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 Report %D 2013 %T Dislocation dynamics in crystals: a macroscopic theory in a fractional Laplace setting %A Serena Dipierro %A Giampiero Palatucci %A Enrico Valdinoci %K nonlocal Allen-Cahn equation %X We consider an evolution equation arising in the Peierls-Nabarro model for crystal dislocation. We study the evolution of such dislocation function and show that, at a macroscopic scale, the dislocations have the tendency to concentrate at single points of the crystal, where the size of the slip coincides with the natural periodicity of the medium. These dislocation points evolve according to the external stress and an interior repulsive potential. %I SISSA %G en %U http://hdl.handle.net/1963/7124 %1 7124 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Giampiero Palatucci (palatucc@sissa.it) on 2013-09-23T12:18:14Z No. of bitstreams: 1 Dipierro-Palatucci-Valdinoci.pdf: 651692 bytes, checksum: 839508f3ff7cdc4417c33991ebf3a9f3 (MD5) %0 Journal Article %J PloS one. Volume 8, Issue 7, July 2013 : e68078 %D 2013 %T Early phase of plasticity-related gene regulation and SRF dependent transcription in the hippocampus %A Giovanni Iacono %A Claudio Altafini %A Vincent Torre %X Hippocampal organotypic cultures are a highly reliable in vitro model for studying neuroplasticity: in this paper, we analyze the early phase of the transcriptional response induced by a 20 µM gabazine treatment (GabT), a GABA-Ar antagonist, by using Affymetrix oligonucleotide microarray, RT-PCR based time-course and chromatin-immuno-precipitation. The transcriptome profiling revealed that the pool of genes up-regulated by GabT, besides being strongly related to the regulation of growth and synaptic transmission, is also endowed with neuro-protective and pro-survival properties. By using RT-PCR, we quantified a time-course of the transient expression for 33 of the highest up-regulated genes, with an average sampling rate of 10 minutes and covering the time interval [10:90] minutes. The cluster analysis of the time-course disclosed the existence of three different dynamical patterns, one of which proved, in a statistical analysis based on results from previous works, to be significantly related with SRF-dependent regulation (p-value<0.05). The chromatin immunoprecipitation (chip) assay confirmed the rich presence of working CArG boxes in the genes belonging to the latter dynamical pattern and therefore validated the statistical analysis. Furthermore, an in silico analysis of the promoters revealed the presence of additional conserved CArG boxes upstream of the genes Nr4a1 and Rgs2. The chip assay confirmed a significant SRF signal in the Nr4a1 CArG box but not in the Rgs2 CArG box. %B PloS one. Volume 8, Issue 7, July 2013 : e68078 %I Public Library of Science %G en %U http://hdl.handle.net/1963/7287 %1 7332 %2 Neuroscience %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-03-14T11:26:18Z No. of bitstreams: 1 journal.pone.0068078.pdf: 1188661 bytes, checksum: 29e83864b33fd1a072fe4ab4da6fcc17 (MD5) %R 10.1371/journal.pone.0068078 %0 Journal Article %J ESAIM Control. Optim. Calc. Var. 19 (2013) 167-189 %D 2013 %T Epitaxially strained elastic films: the case of anisotropic surface energies %A Marco Bonacini %XIn the context of a variational model for the epitaxial growth of strained elastic films, we study the effects of the presence of anisotropic surface energies in the determination of equilibrium configurations. We show that the threshold effect that describes the stability of flat morphologies in the isotropic case remains valid for weak anisotropies, but is no longer present in the case of highly anisotropic surface energies, where we show that the flat configuration is always a local minimizer of the total energy. The main tool used to obtain these results is a minimality criterion based on the positivity of the second variation.

%B ESAIM Control. Optim. Calc. Var. 19 (2013) 167-189 %I EDP Sciences %G en %U http://hdl.handle.net/1963/4268 %1 3999 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-26T15:17:45Z\\r\\nNo. of bitstreams: 1\\r\\nbonacini_31_M.pdf: 278252 bytes, checksum: ae2b293dfe841dc6e68fcdf2bea68578 (MD5) %R 10.1051/cocv/2012003 %0 Journal Article %J Le Matematiche (Catania), Vol. 68 (2013), no. 1: 201-216 %D 2013 %T Existence and symmetry results for a Schrodinger type problem involving the fractional Laplacian %A Serena Dipierro %A Giampiero Palatucci %A Enrico Valdinoci %XThis paper deals with the following class of nonlocal Schr\"odinger equations $$ \displaystyle (-\Delta)^s u + u = |u|^{p-1}u \ \ \text{in} \ \mathbb{R}^N, \quad \text{for} \ s\in (0,1). $$ We prove existence and symmetry results for the solutions $u$ in the fractional Sobolev space $H^s(\mathbb{R}^N)$. Our results are in clear accordance with those for the classical local counterpart, that is when $s=1$.

%B Le Matematiche (Catania), Vol. 68 (2013), no. 1: 201-216 %I University of Catania %G en %1 7318 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-03-11T16:07:36Z No. of bitstreams: 1 1202.0576v1.pdf: 219939 bytes, checksum: 822c73753d6d4194cf48cb0ff9ad0e48 (MD5) %0 Journal Article %J Proceedings of the Royal Society of Edinburgh: Section A Mathematics %D 2013 %T An existence result for the mean-field equation on compact surfaces in a doubly supercritical regime %A Aleks Jevnikar %B Proceedings of the Royal Society of Edinburgh: Section A Mathematics %I Royal Society of Edinburgh Scotland Foundation %V 143 %P 1021–1045 %G eng %R 10.1017/S030821051200042X %0 Journal Article %D 2013 %T Fields of bounded deformation for mesoscopic dislocations %A Nicolas Van Goethem %X In this paper we discuss the consequences of the distributional approach to dislocations in terms of the mathematical properties\\r\\nof the auxiliary model fields such as displacement and displacement gradient which are obtained directly from \\r\\nthe main model field here considered as the linear strain. We show that these fields cannot be introduced rigourously without \\r\\nthe introduction of gauge fields, or equivalently, without cuts in the Riemann foliation associated to the dislocated crystal.\\r\\nIn a second step we show that the space of bounded deformations follows from the distributional approach in a natural way and \\r\\ndiscuss the reasons why it is adequate to model dislocations. The case of dislocation clusters is also addressed, as it represents an important issue in industrial crystal growth while from a mathematical point of view, peculiar phenomena might appear at the set of accumulation points. \\r\\nThe elastic-plastic decomposition of the strain within this approach is also given a precise meaning. %I SISSA %G en %U http://hdl.handle.net/1963/6378 %1 6311 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Nicolas Van Goethem (vangoeth@sissa.it) on 2013-01-14T21:21:32Z\\nNo. of bitstreams: 1\\nFBDMD.pdf: 330187 bytes, checksum: 50e746906921ab10755a58da683b979d (MD5) %0 Journal Article %J Communications on Pure and Applied Analysis 12 (2013) 1657-1686 %D 2013 %T Fracture models as Gamma-limits of damage models %A Gianni Dal Maso %A Flaviana Iurlano %XWe analyze the asymptotic behavior of a variational model for damaged elastic materials. This model depends on two small parameters, which govern the width of the damaged regions and the minimum elasticity constant attained in the damaged regions. When these parameters tend to zero, we find that the corresponding functionals Gamma-converge to a functional related to fracture mechanics. The corresponding problem is brittle or cohesive, depending on the asymptotic ratio of the two parameters.

%B Communications on Pure and Applied Analysis 12 (2013) 1657-1686 %I American Institute of Mathematical Sciences %G en %U http://hdl.handle.net/1963/4225 %1 3952 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-23T11:09:07Z\\r\\nNo. of bitstreams: 1\\r\\nDalMaso_Iurlano_25_M.pdf: 360594 bytes, checksum: a0e0909b1c483748ede26b7e785a1d79 (MD5) %R 10.3934/cpaa.2013.12.1657 %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 Communications in Mathematical Physics 322, nr.2 (2013): 415-452 %D 2013 %T An improved geometric inequality via vanishing moments, with applications to singular Liouville equations %A Mauro Bardelloni %A Andrea Malchiodi %B Communications in Mathematical Physics 322, nr.2 (2013): 415-452 %I SISSA %G en %U http://hdl.handle.net/1963/6561 %1 6486 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Andrea Malchiodi (malchiod@sissa.it) on 2013-03-14T10:23:46Z No. of bitstreams: 2 1206.0225v2.pdf: 376591 bytes, checksum: 84aab361b9f74c6f00164ed271fe2cfd (MD5) 1206.0225v2.pdf: 376591 bytes, checksum: 84aab361b9f74c6f00164ed271fe2cfd (MD5) %R 10.1007/s00220-013-1731-0 %0 Journal Article %J Annales Scientifiques de l'Ecole Normale Superieure %D 2013 %T KAM theory for the Hamiltonian derivative wave equation %A Massimiliano Berti %A Luca Biasco %A Michela Procesi %XWe prove an infinite dimensional KAM theorem which implies the existence of Can- tor families of small-amplitude, reducible, elliptic, analytic, invariant tori of Hamiltonian derivative wave equations. © 2013 Société Mathématique de France.

%B Annales Scientifiques de l'Ecole Normale Superieure %V 46 %P 301-373 %G eng %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 ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %T Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations %A Cacace, S. %A Antonin Chambolle %A Antonio DeSimone %A Livio Fedeli %B ESAIM: Mathematical Modelling and Numerical Analysis %I EDP Sciences %V 47 %P 837–858 %G eng %R 10.1051/m2an/2012048 %0 Report %D 2013 %T Minimal partitions and image classification using a gradient-free perimeter approximation %A Samuel Amstutz %A Nicolas Van Goethem %A Antonio André Novotny %K Image classification, deblurring, optimal partitions, perimeter approximation %X In this paper a new mathematically-founded method for the optimal partitioning of domains, with applications to the classification of greyscale and color images, is proposed. Since optimal partition problems are in general ill-posed, some regularization strategy is required. Here we regularize by a non-standard approximation of the total interface length, which does not involve the gradient of approximate characteristic functions, in contrast to the classical Modica-Mortola approximation. Instead, it involves a system of uncoupled linear partial differential equations and nevertheless shows $\Gamma$-convergence properties in appropriate function spaces. This approach leads to an alternating algorithm that ensures a decrease of the objective function at each iteration, and which always provides a partition, even during the iterations. The efficiency of this algorithm is illustrated by various numerical examples. Among them we consider binary and multilabel minimal partition problems including supervised or automatic image classification, inpainting, texture pattern identification and deblurring. %I SISSA %G en %U http://hdl.handle.net/1963/6976 %1 6964 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Nicolas Van Goethem (vangoeth@sissa.it) on 2013-06-27T11:35:17Z No. of bitstreams: 1 Image.pdf: 1182883 bytes, checksum: 9ca6dcd03d7fd901b0d843d0062dfc74 (MD5) %0 Thesis %D 2013 %T Minimality and stability results for a class of free-discontinuity and nonlocal isoperimetric problems %A Marco Bonacini %K free-discontinuity problems %I SISSA %G en %1 7204 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Marco Bonacini (mbonacin@sissa.it) on 2013-10-23T13:11:08Z No. of bitstreams: 1 bonacini_phd_thesis.pdf: 1472871 bytes, checksum: 5866ef2786cf6ae345bb61eba76361a7 (MD5) %] Introduction Chapter 1. Preliminaries Chapter 2. The Mumford-Shah functional Chapter 3. A variational model in epitaxial films theory Chapter 4. A nonlocal isoperimetric problem Bibliography %0 Journal Article %J Communications in Mathematical Physics %D 2013 %T The Monge Problem for Distance Cost in Geodesic Spaces %A Stefano Bianchini %A Fabio Cavalletti %XWe address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish space and dLis a geodesic Borel distance which makes (X, dL) a non branching geodesic space. We show that under the assumption that geodesics are d-continuous and locally compact, we can reduce the transport problem to 1-dimensional transport problems along geodesics. We introduce two assumptions on the transport problem π which imply that the conditional probabilities of the first marginal on each geodesic are continuous or absolutely continuous w.r.t. the 1-dimensional Hausdorff distance induced by dL. It is known that this regularity is sufficient for the construction of a transport map. We study also the dynamics of transport along the geodesic, the stability of our conditions and show that in this setting dL-cyclical monotonicity is not sufficient for optimality.

%B Communications in Mathematical Physics %V 318 %P 615–673 %8 Mar %G eng %U https://doi.org/10.1007/s00220-013-1663-8 %R 10.1007/s00220-013-1663-8 %0 Journal Article %J Journal of Mathematical Analysis and Applications. Volume 399, Issue 1, 1 March 2013, Pages 333-339 %D 2013 %T Multiplicity result for a nonhomogeneous Yamabe type equation involving the Kohn Laplacian %A Ali Maalaoui %A Vittorio Martino %K CR-Yamabe %B Journal of Mathematical Analysis and Applications. Volume 399, Issue 1, 1 March 2013, Pages 333-339 %I Elsevier %G en %U http://hdl.handle.net/1963/7374 %1 7422 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-06-17T12:33:51Z No. of bitstreams: 1 Maalaoui_Martino_2013.pdf: 322172 bytes, checksum: 56ab1f8740f578e4f0eab13319fbaa20 (MD5) %R 10.1016/j.jmaa.2012.10.014 %0 Journal Article %J Oberwolfach Reports %D 2013 %T A New Quadratic Potential for Scalar Conservation Laws %A Stefano Bianchini %A Stefano Modena %B Oberwolfach Reports %V 29 %G eng %0 Journal Article %J Geometry Partial Differential Equations – proceedings, CRM Series (15), 2013. %D 2013 %T The nonlinear multidomain model: a new formal asymptotic analysis. %A Stefano Amato %A Giovanni Bellettini %A Maurizio Paolini %K bidomain model, anisotropic mean curvature, star-shaped combination %XWe study the asymptotic analysis of a singularly perturbed weakly parabolic system of m- equations of anisotropic reaction-diffusion type. Our main result formally shows that solutions to the system approximate a geometric motion of a hypersurface by anisotropic mean curvature. The anisotropy, supposed to be uniformly convex, is explicit and turns out to be the dual of the star-shaped combination of the m original anisotropies.

%B Geometry Partial Differential Equations – proceedings, CRM Series (15), 2013. %@ 8876424724 %G en %1 7259 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Stefano Amato (samato@sissa.it) on 2013-11-29T15:38:34Z No. of bitstreams: 1 bidomain_gen.pdf: 320909 bytes, checksum: a47cfa6c6dec3318d5d75f8a6a4a425b (MD5) %0 Journal Article %J Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 24 (2013), no. 3: 437–450 %D 2013 %T A note on KAM theory for quasi-linear and fully nonlinear forced KdV %A P Baldi %A Massimiliano Berti %A Riccardo Montalto %K KAM for PDEs %X We present the recent results in [3] concerning quasi-periodic solutions for quasi-linear and fully nonlinear forced perturbations of KdV equations. For Hamiltonian or reversible nonlinearities the solutions are linearly stable. The proofs are based on a combination of di erent ideas and techniques: (i) a Nash-Moser iterative scheme in Sobolev scales. (ii) A regularization procedure, which conjugates the linearized operator to a di erential operator with constant coe cients plus a bounded remainder. These transformations are obtained by changes of variables induced by di eomorphisms of the torus and pseudo-di erential operators. (iii) A reducibility KAM scheme, which completes the reduction to constant coe cients of the linearized operator, providing a sharp asymptotic expansion of the perturbed eigenvalues. %B Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 24 (2013), no. 3: 437–450 %I European Mathematical Society %G en %1 7268 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-12-09T08:16:04Z No. of bitstreams: 1 Baldi-Berti-Montalto-Lincei-Note-KAM-forced-KdV.pdf: 322654 bytes, checksum: ddae153eff7ad17e2be36cb3ba1af9bf (MD5) %R 10.4171/RLM/660 %0 Journal Article %D 2013 %T A note on non-homogeneous hyperbolic operators with low-regularity coefficients %A Ferruccio Colombini %A Francesco Fanelli %XIn this paper we obtain an energy estimate for a complete strictly hyperbolic operator with second order coefficients satisfying a log-Zygmund-continuity condition with respect to $t$, uniformly with respect to $x$, and a log-Lipschitz-continuity condition with respect to $x$, uniformly with respect to $t$.

%G eng %0 Journal Article %D 2013 %T One-dimensional swimmers in viscous fluids: dynamics, controllability, and existence of optimal controls %A Gianni Dal Maso %A Antonio DeSimone %A Marco Morandotti %XIn this paper we study a mathematical model of one-dimensional swimmers performing a planar motion while fully immersed in a viscous fluid. The swimmers are assumed to be of small size, and all inertial effects are neglected. Hydrodynamic interactions are treated in a simplified way, using the local drag approximation of resistive force theory. We prove existence and uniqueness of the solution of the equations of motion driven by shape changes of the swimmer. Moreover, we prove a controllability result showing that given any pair of initial and final states, there exists a history of shape changes such that the resulting motion takes the swimmer from the initial to the final state. We give a constructive proof, based on the composition of elementary maneuvers (straightening and its inverse, rotation, translation), each of which represents the solution of an interesting motion planning problem. Finally, we prove the existence of solutions for the optimal control problem of finding, among the histories of shape changes taking the swimmer from an initial to a final state, the one of minimal energetic cost.

%I SISSA %G en %U http://hdl.handle.net/1963/6467 %1 6412 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-02-11T12:13:39Z No. of bitstreams: 1 DM-DeS-Mor-12-v10 sissa.pdf: 606490 bytes, checksum: 45f448186465b198ec31beb54afb0edf (MD5) %0 Journal Article %J Advanced Nonlinear Studies %D 2013 %T Pairs of nodal solutions for a class of nonlinear problems with one-sided growth conditions %A Alberto Boscaggin %A Fabio Zanolin %B Advanced Nonlinear Studies %I Advanced Nonlinear Studies, Inc. %V 13 %P 13–53 %G eng %R 10.1515/ans-2013-0103 %0 Journal Article %J Advanced Nonlinear Studies %D 2013 %T Periodic bouncing solutions for nonlinear impact oscillators %A Alessandro Fonda %A Andrea Sfecci %B Advanced Nonlinear Studies %I Advanced Nonlinear Studies, Inc. %V 13 %P 179–189 %G eng %R 10.1515/ans-2013-0110 %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 Quadratic cohomology %A Andrei A. Agrachev %X We study homological invariants of smooth families of real quadratic forms as\r\na step towards a \"Lagrange multipliers rule in the large\" that intends to\r\ndescribe topology of smooth vector functions in terms of scalar Lagrange\r\nfunctions. %I SISSA %G en %1 6456 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-02-27T15:16:17Z\nNo. of bitstreams: 1\n1301.2059v1.pdf: 236951 bytes, checksum: a481b8e5391a39e5e87402873e4023f7 (MD5) %0 Journal Article %J Annales de l'Institut Henri Poincare (C) Non Linear Analysis %D 2013 %T A quasistatic evolution model for perfectly plastic plates derived by Γ-convergence %A Elisa Davoli %A Maria Giovanna Mora %K -convergence %K Perfect plasticity %K Prandtl–Reuss plasticity %K Quasistatic evolution %K Rate-independent processes %K Thin plates %XThe subject of this paper is the rigorous derivation of a quasistatic evolution model for a linearly elastic–perfectly plastic thin plate. As the thickness of the plate tends to zero, we prove via Γ-convergence techniques that solutions to the three-dimensional quasistatic evolution problem of Prandtl–Reuss elastoplasticity converge to a quasistatic evolution of a suitable reduced model. In this limiting model the admissible displacements are of Kirchhoff–Love type and the stretching and bending components of the stress are coupled through a plastic flow rule. Some equivalent formulations of the limiting problem in rate form are derived, together with some two-dimensional characterizations for suitable choices of the data.

%B Annales de l'Institut Henri Poincare (C) Non Linear Analysis %V 30 %P 615 - 660 %G eng %U http://www.sciencedirect.com/science/article/pii/S0294144912001035 %R https://doi.org/10.1016/j.anihpc.2012.11.001 %0 Journal Article %J Numerische Mathematik, 2013 %D 2013 %T Reduced basis approximation and a posteriori error estimation for Stokes flows in parametrized geometries: roles of the inf-sup stability constants %A Gianluigi Rozza %A Phuong Huynh %A Andrea Manzoni %K parametrized Stokes equations %X In this paper we review and we extend the reduced basis approximation and a posteriori error estimation for steady Stokes flows in a ffinely parametrized geometries, focusing on the role played by the Brezzi\\\'s and Babu ska\\\'s stability constants. The crucial ingredients of the methodology are a Galerkin projection onto a low-dimensional space of basis functions properly selected, an a ne parametric dependence enabling to perform competitive Off ine-Online splitting in the computational\\r\\nprocedure and a rigorous a posteriori error estimation on eld variables.\\r\\nThe combination of these three factors yields substantial computational savings which are at the basis of an e fficient model order reduction, ideally suited for real-time simulation and many-query contexts (e.g. optimization, control or parameter identi cation). In particular, in this work we focus on i) the stability of the reduced basis approximation based on the Brezzi\\\'s saddle point theory and the introduction of a supremizer operator on the pressure terms, ii) a rigorous a posteriori error estimation procedure for velocity and pressure elds based on the Babu ska\\\'s inf-sup constant (including residuals calculations), iii) the computation of a lower bound of the stability constant, and iv) di erent options for the reduced basis spaces construction. We present some illustrative results for both\\r\\ninterior and external steady Stokes flows in parametrized geometries representing two parametrized classical Poiseuille and Couette \\r\\nflows, a channel contraction and a simple flow control problem around a curved obstacle. %B Numerische Mathematik, 2013 %I Springer %G en %U http://hdl.handle.net/1963/6339 %1 6269 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2012-12-13T17:19:05Z\\nNo. of bitstreams: 1\\nStokes_HMR10_SISSA_report.pdf: 4641267 bytes, checksum: 82a163163a62d0b9deef8d5d6590f8d7 (MD5) %0 Book Section %B CEMRACS 2013 - Modelling and simulation of complex systems: stochastic and deterministic approaches %D 2013 %T Reduced Basis Approximation for the Structural-Acoustic Design based on Energy Finite Element Analysis (RB-EFEA) %A Denis Devaud %A Gianluigi Rozza %B CEMRACS 2013 - Modelling and simulation of complex systems: stochastic and deterministic approaches %V 48 %P 98-115 %G eng %R http://dx.doi.org/10.1051/proc/201448004 %0 Report %D 2013 %T A Reduced Computational and Geometrical Framework for Inverse Problems in Haemodynamics %A Toni Lassila %A Andrea Manzoni %A Alfio Quarteroni %A Gianluigi Rozza %I SISSA %G en %1 6571 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2013-04-30T14:47:07Z No. of bitstreams: 1 LMQR_inverse_problems_Haemo.pdf: 2913600 bytes, checksum: 9bff594072e6c7b4a664bdade361a1a9 (MD5) %0 Report %D 2013 %T A reduced-order strategy for solving inverse Bayesian identification problems in physiological flows %A Toni Lassila %A Andrea Manzoni %A Alfio Quarteroni %A Gianluigi Rozza %I SISSA %G en %1 6555 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2013-04-12T10:16:42Z\nNo. of bitstreams: 1\nHanoi_RQML_2012_REVISED.pdf: 1360222 bytes, checksum: 4cb9ffaaf9fd67e3eacf4d9c060d0940 (MD5) %0 Report %D 2013 %T Reduction Strategies for Shape Dependent Inverse Problems in Haemodynamics %A Toni Lassila %A Andrea Manzoni %A Gianluigi Rozza %I SISSA %G en %1 6554 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2013-04-12T09:59:54Z\nNo. of bitstreams: 1\n03910397-1.pdf: 531448 bytes, checksum: 0ec611490748bed35d10f612e8296f27 (MD5) %0 Journal Article %J Advances in Nonlinear Analysis %D 2013 %T Remarks on the Moser–Trudinger inequality %A Gabriele Mancini %A Luca Battaglia %XWe extend the Moser-Trudinger inequality to any Euclidean domain satisfying Poincaré's inequality. We find out that the same equivalence does not hold in general for conformal metrics on the unit ball, showing counterexamples. We also study the existence of extremals for the Moser-Trudinger inequalities for unbounded domains, proving it for the infinite planar strip.

%B Advances in Nonlinear Analysis %I Advances in Nonlinear Analysis %V 2 %P 389-425 %G en %U http://edoc.unibas.ch/43974/ %N 4 %1 34666 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by gmancini@sissa.it (gmancini@sissa.it) on 2015-08-07T13:45:19Z No. of bitstreams: 1 articolo1.pdf: 526978 bytes, checksum: 941a2e14ae2d0ff88b198a2e8c8c153e (MD5) %R 10.1515/anona-2013-0014 %0 Journal Article %D 2013 %T Self-adjoint extensions and stochastic completeness of the Laplace-Beltrami operator on conic and anticonic surfaces %A Ugo Boscain %A Dario Prandi %G eng %R 10.1016/j.jde.2015.10.011 %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 Thesis %D 2013 %T Some models of crack growth in brittle materials %A Simone Racca %K Quasi-static crack evolution %I SISSA %G en %1 7205 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Simone Racca (sracca@sissa.it) on 2013-10-23T13:11:13Z No. of bitstreams: 1 Racca_PhDThesis.pdf: 1710871 bytes, checksum: ea174e98f8849253e71cdefa52c6c8b8 (MD5) %] Introduction Chapter 1. Preliminaries Chapter 2. A viscosity-driven crack evolution Chapter 3.A variational model for the quasi-static growth of fractional dimensional brittle fractures Chapter 4. A model for crack growth with branching and kinking Bibliography %0 Journal Article %D 2013 %T Some open problems %A Andrei A. Agrachev %K Geometry %X We discuss some challenging open problems in the geometric control theory and sub-Riemannian geometry. %I SISSA %G en %U http://hdl.handle.net/1963/7070 %1 7064 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-09-16T09:39:55Z No. of bitstreams: 1 1304.2590v2.pdf: 169033 bytes, checksum: 43fab332ae3bb82c336a19ab7013c373 (MD5) %0 Journal Article %J Discrete Contin. Dyn. Syst. Ser. S %D 2013 %T Some remarks on the viscous approximation of crack growth %A Giuliano Lazzaroni %A Rodica Toader %K Variational models %XWe describe an existence result for quasistatic evolutions of cracks in antiplane elasticity obtained in [16] by a vanishing viscosity approach, with free (but regular enough) crack path. We underline in particular the motivations for the choice of the class of admissible cracks and of the dissipation potential. Moreover, we extend the result to a model with applied forces depending on time.

%B Discrete Contin. Dyn. Syst. Ser. S %I SISSA %V 6 %G en %U http://hdl.handle.net/1963/4206 %1 3945 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-23T10:54:36Z No. of bitstreams: 1 Lazzaroni_Toader_24_M.pdf: 225564 bytes, checksum: 4c5000d79e83902639a8efb34ba9c0c8 (MD5) %& 131-146 %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 IEEE Transactions on Automatic Control. Volume 58, Issue 1, 2013, Article number6228517, Pages 74-85 %D 2013 %T Stabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control %A Claudio Altafini %A Francesco Ticozzi %A K. Nishio %X In this paper, we investigate parametrization-free solutions of the problem of quantum pure state preparation and subspace stabilization by means of Hamiltonian control, continuous measurement, and quantum feedback, in the presence of a Markovian environment. In particular, we show that whenever suitable dissipative effects are induced either by the unmonitored environment, or by non-Hermitian measurements, there is no need for feedback, as open-loop time-invariant control is sufficient to achieve stabilization of the target set in probability. Constructive necessary and sufficient conditions on the form of the control Hamiltonian can be provided in this case. When time-invariant control is not sufficient, state stabilization can be attained by the addition of filtering-based feedback control %B IEEE Transactions on Automatic Control. Volume 58, Issue 1, 2013, Article number6228517, Pages 74-85 %G en %U http://hdl.handle.net/1963/6503 %1 6448 %2 Mathematics %4 1 %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-02-27T15:06:12Z (GMT) No. of bitstreams: 0 %R 10.1109/TAC.2012.2206713 %0 Journal Article %J Engineering Analysis with Boundary Elements, 37(1):128 – 143, 2013. %D 2013 %T A stable and adaptive semi-Lagrangian potential model for unsteady and nonlinear ship-wave interactions %A Andrea Mola %A Luca Heltai %A Antonio DeSimone %K Unsteady ship-wave interaction %XWe present an innovative numerical discretization of the equations of inviscid potential flow for the simulation of three dimensional unsteady and nonlinear water waves generated by a ship hull advancing in water. The equations of motion are written in a semi-Lagrangian framework, and the resulting integro-diff erential equations are discretized in space via an adaptive iso-parametric collocation Boundary Element Method, and in time via adaptive implicit Backward Di erentiation Formulas (BDF) with variable step and variable order. When the velocity of the advancing ship hull is non-negligible, the semi-Lagrangian formulation (also known as Arbitrary Lagrangian Eulerian formulation, or ALE) of the free surface equations contains dominant transport terms which are stabilized with a Streamwise Upwind Petrov-Galerkin (SUPG) method. The SUPG stabilization allows automatic and robust adaptation of the spatial discretization with unstructured quadrilateral grids. Preliminary results are presented where we compare our numerical model with experimental results on the case of a Wigley hull advancing in calm water with fi xed sink and trim.

%B Engineering Analysis with Boundary Elements, 37(1):128 – 143, 2013. %I SISSA %G en %U http://hdl.handle.net/1963/5669 %1 5457 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-03-16T11:19:51Z\\nNo. of bitstreams: 1\\nMolaHeltaiDeSimone-2012-aa.pdf: 1981527 bytes, checksum: 8a82da009242da0cf884e2c7f04009a6 (MD5) %0 Journal Article %J Applicable Analysis %D 2013 %T Stable determination of a body immersed in a fluid: the nonlinear stationary case %A Andrea Ballerini %XWe consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the stationary Navier–Stokes equations, from a single measurement of force and velocity on a portion of the boundary. We obtain an estimate of stability of log–log type.

%B Applicable Analysis %I Taylor & Francis %V 92 %P 460-481 %G eng %U https://doi.org/10.1080/00036811.2011.628173 %R 10.1080/00036811.2011.628173 %0 Thesis %D 2013 %T The structure and regularity of admissible BV solutions to hyperbolic conservation laws in one space dimension %A Lei Yu %X This thesis is devoted to the study of the qualitative properties of admissible BV solutions to the strictly hyperbolic conservation laws in one space dimension by using wave-front tracking approximation. This thesis consists of two parts: • SBV-like regularity of vanishing viscosity BV solutions to strict hyperbolic systems of conservation laws. • Global structure of admissible BV solutions to strict hyperbolic conservation laws. %I SISSA %G en %1 7210 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Lei Yu (yulei@sissa.it) on 2013-10-23T15:42:25Z No. of bitstreams: 1 Thesis_main.pdf: 960810 bytes, checksum: d3e2f04a4bb7cc2c30ba82507d536edc (MD5) %] Contents 0.1 HyperbolicConservationLaws. .......................... 1 0.2 SBV and SBV-like regularity ........................... 3 0.3 Global structure of BV solutions ......................... 6 0.4 Main notations ................................... 9 1 Preliminary results 11 1.1 BV and SBV functions............................... 11 1.2 Coarea formula for BV function.......................... 15 1.3 The singular conservation law........................... 16 1.3.1 The Riemann problem........................... 17 1.3.2 Front tracking algorithm.......................... 18 1.3.3 Uniform boundedness estimates on the speed of wave fronts . . . . . . 19 1.4 The Cauchy problem for systems ......................... 21 1.4.1 Solution of Riemann problem....................... 22 1.4.2 Construction of solution by wave-front tracking approximation . . . . 26 2 SBV-like regularity for strictly hyperbolic systems of conservation laws 33 2.1 Overview of the chapter .............................. 33 2.2 The scalar case ................................... 34 2.3 Notations and settings for general systems.................... 37 2.3.1 Preliminary notation............................ 37 2.3.2 Construction of solutions to the Riemann problem . . . . . . . . . . . 38 2.3.3 Cantor part of the derivative of characteristic for i-th waves . . . . . 39 2.4 Main SBV regularity argument .......................... 40 2.5 Review of wave-front tracking approximation for general system . . . . . . . . 41 2.5.1 Description of the wave-front tracking approximation . . . . . . . . . . 42 2.5.2 Jump part of i-th waves.......................... 43 2.6 Proof of Theorem2.4.1............................... 46 2.6.1 Decay estimate for positive waves..................... 46 2.6.2 Decay estimate for negative waves .................... 47 2.7 SBV regularity for the i-th component of the i-th eigenvalue . . . . . . . . . 54 i CONTENTS 3 Global structure of admissible BV solutions to the piecewise genuinely nonlinear system 57 3.1 Description of wave-front tracking approximation . . . . . . . . . . . . . . . . 62 3.2 Construction of subdiscontinuity curves ..................... 63 3.3 Proof of the main theorems ............................ 67 3.4 A counterexample on general strict hyperbolic systems . . . . . . . . . . . . . 71 4 Global structure of entropy solutions to general scalar conservation law 75 4.1 Overview ...................................... 75 4.2 Estimates on the level sets of the front tracking approximations . . . . . . . . 76 4.2.1 Bounds on the initial points of the boundary curves of level sets . . . 77 4.2.2 Bound estimates on the derivative of the boundary curves of level sets 77 4.3 Level sets in the exact solutions.......................... 78 4.4 Lagrangian representative for the entropy solution . . . . . . . . . . . . . . . 84 4.5 Pointwise structure................................. 88 %0 Journal Article %J Discrete & Continuous Dynamical Systems - A %D 2013 %T Subharmonic solutions for nonlinear second order equations in presence of lower and upper solutions %A Alberto Boscaggin %A Fabio Zanolin %K lower and upper solutions %K parameter dependent equations %K Periodic solutions %K Poincaré-Birkhoff twist theorem %K subharmonic solutions %XWe study the problem of existence and multiplicity of subharmonic solutions for a second order nonlinear ODE in presence of lower and upper solutions. We show how such additional information can be used to obtain more precise multiplicity results. Applications are given to pendulum type equations and to Ambrosetti-Prodi results for parameter dependent equations.

%B Discrete & Continuous Dynamical Systems - A %V 33 %P 89 %G eng %U http://aimsciences.org//article/id/3638a93e-4f3e-4146-a927-3e8a64e6863f %R 10.3934/dcds.2013.33.89 %0 Report %D 2013 %T On Sudakov's type decomposition of transference plans with norm costs %A Stefano Bianchini %A Sara Daneri %I SISSA %G en %U http://hdl.handle.net/1963/7206 %1 7234 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-11-08T11:08:16Z No. of bitstreams: 1 Sudakov_160813 (1).pdf: 1030337 bytes, checksum: 121734a60b7c507acb1e0ca656676a37 (MD5) %0 Journal Article %J Communications on Pure and Applied Mathematics, Volume 66, Issue 3, March 2013, Pages 332-371 %D 2013 %T A variational Analysis of the Toda System on Compact Surfaces %A Andrea Malchiodi %A David Ruiz %X In this paper we consider the Toda system of equations on a compact surface. We will give existence results by using variational methods in a non coercive case. A key tool in our analysis is a new Moser-Trudinger type inequality under suitable conditions on the center of mass and the scale of concentration of the two components u_1, u_2. %B Communications on Pure and Applied Mathematics, Volume 66, Issue 3, March 2013, Pages 332-371 %I Wiley %G en %U http://hdl.handle.net/1963/6558 %1 6489 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Andrea Malchiodi (malchiod@sissa.it) on 2013-03-14T10:26:34Z No. of bitstreams: 1 1105.3701v2.pdf: 306787 bytes, checksum: f64fe03fd72ea85831e8f8ca25e9f99e (MD5) %R 10.1002/cpa.21433 %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 Discrete Contin. Dyn. Syst. 33, nr.7 (2012): 2777-2790 %D 2012 %T Asymptotics of the s-perimeter as s →0 %A Serena Dipierro %A Alessio Figalli %A Giampiero Palatucci %A Enrico Valdinoci %XWe deal with the asymptotic behavior of the $s$-perimeter of a set $E$ inside a domain $\Omega$ as $s\searrow0$. We prove necessary and sufficient conditions for the existence of such limit, by also providing an explicit formulation in terms of the Lebesgue measure of $E$ and $\Omega$. Moreover, we construct examples of sets for which the limit does not exist.

%B Discrete Contin. Dyn. Syst. 33, nr.7 (2012): 2777-2790 %I American Institute of Mathematical Sciences %G en %1 7317 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-03-11T15:55:21Z No. of bitstreams: 1 1204.0750v2.pdf: 216883 bytes, checksum: 3ee8d497a2c0f9a211ec5327e8aa6b9a (MD5) %R 10.3934/dcds.2013.33.2777 %0 Journal Article %J Geotechnique, Volume 62, Issue 12, December 2012, Pages 1081-1094 %D 2012 %T On the behaviour of flexible retaining walls under seismic actions %A Riccardo Conti %A G.S.P. Madabhushi %A Giulia M.B. Viggiani %K Centrifuge modelling %X This paper describes an experimental investigation of the behaviour of embedded retaining walls under seismic actions. Nine centrifuge tests were carried out on reduced-scale models of pairs of retaining walls in dry sand, either cantilevered or with one level of props near the top. The experimental data indicate that, for maximum accelerations that are smaller than the critical limit equilibrium value, the retaining walls experience significant permanent displacements under increasing structural loads, whereas for larger accelerations the walls rotate under constant internal forces. The critical acceleration at which the walls start to rotate increases with increasing maximum acceleration. No significant displacements are measured if the current earthquake is less severe than earthquakes previously experienced by the wall. The increase of critical acceleration is explained in terms of redistribution of earth pressures and progressive mobilisation of the passive strength in front of the wall. The experimental data for cantilevered retaining walls indicate that the permanent displacements of the wall can be reasonably predicted adopting a Newmark-type calculation with a critical acceleration that is a fraction of the limit equilibrium value. %B Geotechnique, Volume 62, Issue 12, December 2012, Pages 1081-1094 %I ICE Publishing %G en %U http://hdl.handle.net/1963/6933 %1 6912 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-05-30T10:11:44Z No. of bitstreams: 0 %R 10.1680/geot.11.P.029 %0 Journal Article %J Mathematical Modelling and Numerical Analysis, in press, 2012-13 %D 2012 %T Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty %A Toni Lassila %A Andrea Manzoni %A Alfio Quarteroni %A Gianluigi Rozza %K shape optimization %X We review the optimal design of an arterial bypass graft following either a (i) boundary optimal control approach, or a (ii) shape optimization formulation. The main focus is quantifying and treating the uncertainty in the residual flow when the hosting artery is not completely occluded,\\r\\nfor which the worst-case in terms of recirculation e ffects is inferred to correspond to a strong ori fice flow through near-complete occlusion. A worst-case optimal control approach is applied to the steady\\r\\nNavier-Stokes equations in 2D to identify an anastomosis angle and a cu ed shape that are robust with respect to a possible range of residual \\r\\nflows. We also consider a reduced order modelling framework\\r\\nbased on reduced basis methods in order to make the robust design problem computationally feasible. The results obtained in 2D are compared with simulations in a 3D geometry but without model\\r\\nreduction or the robust framework. %B Mathematical Modelling and Numerical Analysis, in press, 2012-13 %I Cambridge University Press %G en %U http://hdl.handle.net/1963/6337 %1 6267 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2012-12-13T15:38:41Z\\nNo. of bitstreams: 1\\nLMQR_M2AN_Special_SISSAreport.pdf: 5702019 bytes, checksum: 037e51bde713582eff1ee9766b1b4559 (MD5) %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 Journal fur die Reine und Angewandte Mathematik, Issue 671, October 2012, Pages 131-198 %D 2012 %T A Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group. %A Andrea Malchiodi %A Paul Yang %A Jih-Hsin Cheng %A JennFang Hwang %X In this paper, we study the structure of the singular set for a C 1 smooth surface in the 3-dimensional Heisenberg group ℍ 1. We discover a Codazzi-like equation for the p-area element along the characteristic curves on the surface. Information obtained from this ordinary differential equation helps us to analyze the local configuration of the singular set and the characteristic curves. In particular, we can estimate the size and obtain the regularity of the singular set. We understand the global structure of the singular set through a Hopf-type index theorem. We also justify the Codazzi-like equation by proving a fundamental theorem for local surfaces in ℍ 1 %B Journal fur die Reine und Angewandte Mathematik, Issue 671, October 2012, Pages 131-198 %I SISSA %G en %U http://hdl.handle.net/1963/6556 %1 6490 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-03-25T14:33:32Z (GMT) No. of bitstreams: 0 %R 10.1515/CRELLE.2011.159 %0 Book Section %B Natural locomotion in fluids and on surfaces : swimming, flying, and sliding / editors Stephen Childress, Anette Hosoi, William W. Schultz, and Z. Jane Wang, editors, %D 2012 %T Computing optimal strokes for low reynolds number swimmers %A Antonio DeSimone %A Luca Heltai %A François Alouges %A Lefebvre-Lepot Aline %K Numerical analysis. %XWe discuss connections between low-Reynolds-number swimming and geometric control theory, and present a general algorithm for the numerical computation of energetically optimal strokes. As an illustration of our approach, we show computed motility maps and optimal strokes for two model swimmers.

%B Natural locomotion in fluids and on surfaces : swimming, flying, and sliding / editors Stephen Childress, Anette Hosoi, William W. Schultz, and Z. Jane Wang, editors, %I Springer %@ 9781461439967 %G en %U http://hdl.handle.net/1963/6445 %1 6381 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Luca Heltai (heltai@sissa.it) on 2013-02-01T17:33:50Z\\nNo. of bitstreams: 0 %R 10.1007/978-1-4614-3997-4_13 %0 Journal Article %J Communications in Contemporary Mathematics %D 2012 %T Concentration on circles for nonlinear Schrödinger–Poisson systems with unbounded potentials vanishing at infinity %A Bonheure, Denis %A Di Cosmo, Jonathan %A Mercuri, Carlo %XThe present paper is devoted to weighted nonlinear Schrödinger–Poisson systems with potentials possibly unbounded and vanishing at infinity. Using a purely variational approach, we prove the existence of solutions concentrating on a circle.

%B Communications in Contemporary Mathematics %I World Scientific %V 14 %P 1250009 %G eng %U https://doi.org/10.1142/S0219199712500095 %R 10.1142/S0219199712500095 %0 Journal Article %J Communications in Partial Differential Equations %D 2012 %T Conservation of Geometric Structures for Non-Homogeneous Inviscid Incompressible Fluids %A Francesco Fanelli %XIn this article we get a result on propagation of geometric properties for solutions of the non-homogeneous incompressible Euler system in any dimension N ≥ 2. In particular, we investigate conservation of striated and conormal regularity, which generalize the 2-D structure of vortex patches. The results we get are only local in time, even for N = 2; however, we provide an explicit lower bound for the lifespan of the solution. In the case of physical dimension N = 2 or 3, we investigate also propagation of Hölder regularity in the interior of a bounded domain.

%B Communications in Partial Differential Equations %I Taylor & Francis %V 37 %P 1553-1595 %G eng %U https://doi.org/10.1080/03605302.2012.698343 %R 10.1080/03605302.2012.698343 %0 Journal Article %D 2012 %T Convergence of equilibria of thin elastic plates under physical growth conditions for the energy density %A Maria Giovanna Mora %A Lucia Scardia %XThe asymptotic behaviour of the equilibrium configurations of a thin elastic plate is studied, as the thickness $h$ of the plate goes to zero. More precisely, it is shown that critical points of the nonlinear elastic functional $\mathcal E^h$, whose energies (per unit thickness) are bounded by $Ch^4$, converge to critical points of the $\Gamma$-limit of $h^{-4}\mathcal E^h$. This is proved under the physical assumption that the energy density $W(F)$ blows up as $\det F\to0$.

%I Elsevier %G en %U http://hdl.handle.net/1963/3466 %1 7112 %2 Mathematics %4 -1 %$ Submitted by Francesca Arici (farici@sissa.it) on 2013-09-18T08:46:46Z No. of bitstreams: 1 0901.4041v1.pdf: 233717 bytes, checksum: 3fc33c8ee52cddb0adf0a197c87d0ce8 (MD5) %R 10.1016/j.jde.2011.09.009 %0 Journal Article %J Discrete and Computational Geometry, Volume 48, Issue 4, December 2012, Pages 1025-1047 %D 2012 %T Convex pencils of real quadratic forms %A Antonio Lerario %X We study the topology of the set X of the solutions of a system of two quadratic inequalities in the real projective space RP^n (e.g. X is the intersection of two real quadrics). We give explicit formulae for its Betti numbers and for those of its double cover in the sphere S^n; we also give similar formulae for level sets of homogeneous quadratic maps to the plane. We discuss some applications of these results, especially in classical convexity theory. We prove the sharp bound b(X)\leq 2n for the total Betti number of X; we show that for odd n this bound is attained only by a singular X. In the nondegenerate case we also prove the bound on each specific Betti number b_k(X)\leq 2(k+2). %B Discrete and Computational Geometry, Volume 48, Issue 4, December 2012, Pages 1025-1047 %I Springer %G en %U http://hdl.handle.net/1963/7099 %1 7097 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-09-17T11:33:51Z No. of bitstreams: 1 1106.4678v3.pdf: 250496 bytes, checksum: 3ad88e26b8325e50857d0d9f9aabd6ad (MD5) %R 10.1007/s00454-012-9460-2 %0 Journal Article %J The European Physical Journal E, Volume 35, Issue 9, September 2012, Article number85 %D 2012 %T Crawling motility through the analysis of model locomotors: two case studies %A Antonio DeSimone %A Amabile Tatone %X We study model locomotors on a substrate, which derive their propulsive capabilities from the tangential (viscous or frictional) resistance offered by the substrate. Our aim is to develop new tools and insight for future studies of cellular motility by crawling and of collective bacterial motion. The purely viscous case (worm) is relevant for cellular motility by crawling of individual cells. We re-examine some recent results on snail locomotion in order to assess the role of finely regulated adhesion mechanisms in crawling motility. Our main conclusion is that such regulation, although well documented in several biological systems, is not indispensable to accomplish locomotion driven by internal deformations, provided that the crawler may execute sufficiently large body deformations. Thus, there is no snail theorem. Namely, the crawling analog of the scallop theorem of low Reynolds number hydrodynamics does not hold for snail-like crawlers. The frictional case is obtained by assuming that the viscous coefficient governing tangential resistance forces, which act parallel and in the direction opposite to the velocity of the point to which they are applied, depends on the normal force acting at that point. We combine these surface interactions with inertial effects in order to investigate the mechanisms governing the motility of a bristle-robot. This model locomotor is easily manufactured and has been proposed as an effective tool to replicate and study collective bacterial motility. %B The European Physical Journal E, Volume 35, Issue 9, September 2012, Article number85 %I Springer %G en %U http://hdl.handle.net/1963/7017 %1 7014 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-08-12T11:01:46Z No. of bitstreams: 0 %R 10.1140/epje/i2012-12085-x %0 Journal Article %J Nucleic Acids Research, Volume 40, Issue 15, August 2012, Pages 7132-7149 %D 2012 %T Detection of transcriptional triggers in the dynamics of microbial growth: application to the respiratory-versatile bacterium Shewanella oneidensis %A Q Beg %A Mattia Zampieri %A N Klitgord %A S Collins %A M Serres %A Daniel Segrè %A Claudio Altafini %X The capacity of microorganisms to respond to variable external conditions requires a coordination of environment-sensing mechanisms and decisionmaking regulatory circuits. Here, we seek to understand the interplay between these two processes by combining high-throughput measurement of time-dependent mRNA profiles with a novel computational approach that searches for key genetic triggers of transcriptional changes. Our approach helped us understand the regulatory strategies of a respiratorily versatile bacterium with promising bioenergy and bioremediation applications, Shewanella oneidensis, in minimal and rich media. By comparing expression profiles across these two conditions, we unveiled components of the transcriptional program that depend mainly on the growth phase. Conversely, by integrating our time-dependent data with a previously available large compendium of static perturbation responses, we identified transcriptional changes that cannot be explained solely by internal network dynamics, but are rather triggered by specific genes acting as key mediators of an environment-dependent response. These transcriptional triggers include known and novel regulators that respond to carbon, nitrogen and oxygen limitation. Our analysis suggests a sequence of physiological responses, including a coupling between nitrogen depletion and glycogen storage, partially recapitulated through dynamic flux balance analysis, and experimentally confirmed by metabolite measurements. Our approach is broadly applicable to other systems %B Nucleic Acids Research, Volume 40, Issue 15, August 2012, Pages 7132-7149 %I SISSA %G en %U http://hdl.handle.net/1963/6506 %1 6452 %2 Mathematics %4 1 %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-02-27T15:39:07Z (GMT) No. of bitstreams: 0 %R 10.1093/nar/gks467 %0 Journal Article %J Biophysical Journal. Volume 102, Issue 12, 20 June 2012, Pages 2677-2686 %D 2012 %T A dynamical feedback model for adaptation in the olfactory transduction pathway %A Giovanna De Palo %A Anna Boccaccio %A Andrew Miri %A Anna Menini %A Claudio Altafini %X Olfactory transduction exhibits two distinct types of adaptation, which we denote multipulse and step adaptation. In terms of measured transduction current, multipulse adaptation appears as a decrease in the amplitude of the second of two consecutive responses when the olfactory neuron is stimulated with two brief pulses. Step adaptation occurs in response to a sustained steplike stimulation and is characterized by a return to a steady-state current amplitude close to the prestimulus value, after a transient peak. In this article, we formulate a dynamical model of the olfactory transduction pathway, which includes the kinetics of the CNG channels, the concentration of Ca ions flowing through them, and the Ca-complexes responsible for the regulation. Based on this model, a common dynamical explanation for the two types of adaptation is suggested. We show that both forms of adaptation can be well described using different time constants for the kinetics of Ca ions (faster) and the kinetics of the feedback mechanisms (slower). The model is validated on experimental data collected in voltage-clamp conditions using different techniques and animal species. %B Biophysical Journal. Volume 102, Issue 12, 20 June 2012, Pages 2677-2686 %I Biophysical Society, Elsevier %G en %U http://hdl.handle.net/1963/7019 %1 7012 %2 Neuroscience %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-08-12T10:21:18Z No. of bitstreams: 1 1-s2.0-S0006349512005140-main.pdf: 607871 bytes, checksum: b57c678e05477bb1551bc379bc674a88 (MD5) %R 10.1016/j.bpj.2012.04.040 %0 Journal Article %J Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. Volume 86, Issue 3, 26 September 2012, Article number036116 %D 2012 %T Exploring the low-energy landscape of large-scale signed social networks %A Giuseppe Facchetti %A Giovanni Iacono %A Claudio Altafini %X Analogously to a spin glass, a large-scale signed social network is characterized by the presence of disorder, expressed in this context (and in the social network literature) by the concept of structural balance. If, as we have recently shown, the signed social networks currently available have a limited amount of true disorder (or frustration), it is also interesting to investigate how this frustration is organized, by exploring the landscape of near-optimal structural balance. What we obtain in this paper is that while one of the networks analyzed shows a unique valley of minima, and a funneled landscape that gradually and smoothly worsens as we move away from the optimum, another network shows instead several distinct valleys of optimal or near-optimal structural balance, separated by energy barriers determined by internally balanced subcommunities of users, a phenomenon similar to the replica-symmetry breaking of spin glasses. Multiple, essentially isoenergetic, arrangements of these communities are possible. Passing from one valley to another requires one to destroy the internal arrangement of these balanced subcommunities and then to reform it again. It is essentially this process of breaking the internal balance of the subcommunities which gives rise to the energy barriers. %B Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. Volume 86, Issue 3, 26 September 2012, Article number036116 %I SISSA %G en %U http://hdl.handle.net/1963/6504 %1 6451 %2 Mathematics %4 1 %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-02-27T15:27:42Z (GMT) No. of bitstreams: 0 %R 10.1103/PhysRevE.86.036116 %0 Journal Article %J Analysis and Geometry in Metric Spaces, vol. 1 (2012), pages : 42-57 %D 2012 %T A formula for Popp\'s volume in sub-Riemannian geometry %A Luca Rizzi %A Davide Barilari %K subriemannian, volume, Popp, control %X For an equiregular sub-Riemannian manifold M, Popp\'s volume is a smooth\r\nvolume which is canonically associated with the sub-Riemannian structure, and\r\nit is a natural generalization of the Riemannian one. In this paper we prove a\r\ngeneral formula for Popp\'s volume, written in terms of a frame adapted to the\r\nsub-Riemannian distribution. As a first application of this result, we prove an\r\nexplicit formula for the canonical sub-Laplacian, namely the one associated\r\nwith Popp\'s volume. Finally, we discuss sub-Riemannian isometries, and we prove\r\nthat they preserve Popp\'s volume. We also show that, under some hypotheses on\r\nthe action of the isometry group of M, Popp\'s volume is essentially the unique\r\nvolume with such a property. %B Analysis and Geometry in Metric Spaces, vol. 1 (2012), pages : 42-57 %I SISSA %G en %U http://hdl.handle.net/1963/6501 %1 6446 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Luca Rizzi (lrizzi@sissa.it) on 2013-02-27T08:20:17Z\nNo. of bitstreams: 2\n1211.2325v2.pdf: 219748 bytes, checksum: 03a6289f4ee77387ad54e210dbb84b60 (MD5)\nagms-2012-0004.pdf: 1247984 bytes, checksum: 137bd44ed6f06bbbe02ed9dae33ab42a (MD5) %R 10.2478/agms-2012-0004 %0 Report %D 2012 %T A Fully Coupled Immersed Finite Element Method for Fluid Structure Interaction via the Deal.II Library %A Luca Heltai %A Saswati Roy %A Francesco Costanzo %K Finite Element Method %K Immersed Boundary Method %K Immersed Finite Element Method %X We present the implementation of a solution scheme for fluid-structure\\r\\ninteraction problems via the finite element software library deal.II. The\\r\\nsolution scheme is an immersed finite element method in which two independent discretizations are used for the fluid and immersed deformable body. In this type of formulation the support of the equations of motion of the fluid is extended to cover the union of the solid and fluid domains. The equations of motion over the extended solution domain govern the flow of a fluid under the action of a body force field. This body force field informs the fluid of the presence of the immersed solid. The velocity field of the immersed solid is the restriction over the immersed domain of the velocity field in the extended equations of motion. The focus of this paper is to show how the determination of the motion of the immersed domain is carried out in practice. We show that our implementation is general, that is, it is not dependent on a specific choice of the finite element spaces over the immersed solid and the extended fluid domains. We present some preliminary results concerning the accuracy of the proposed method. %I SISSA %G en %U http://hdl.handle.net/1963/6255 %1 6172 %2 Mathematics %3 Functional Analysis and Applications %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Luca Heltai (heltai@sissa.it) on 2012-09-28T11:06:13Z\\nNo. of bitstreams: 1\\n1209.2811v1.pdf: 4766431 bytes, checksum: a46803f7f8daf3195359f65c9161b944 (MD5) %0 Journal Article %J Journal de Mathématiques Pures et Appliquées, Available online 12 September 2012 %D 2012 %T Gamma-convergence and H-convergence of linear elliptic operators %A Nadia Ansini %A Gianni Dal Maso %A Caterina Ida Zeppieri %K Linear elliptic operators %B Journal de Mathématiques Pures et Appliquées, Available online 12 September 2012 %I Elsevier %G en %U http://hdl.handle.net/1963/5878 %1 5746 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-05-30T13:02:32Z\\r\\nNo. of bitstreams: 1\\r\\n04M_2012_Ansini.pdf: 226441 bytes, checksum: 789582b685e552b522a3e8a896e091f8 (MD5) %R 10.1016/j.matpur.2012.09.004 %0 Journal Article %J Journal of Differential Equations %D 2012 %T A general method for the existence of periodic solutions of differential systems in the plane %A Alessandro Fonda %A Andrea Sfecci %K Nonlinear dynamics %K Periodic solutions %XWe propose a general method to prove the existence of periodic solutions for planar systems of ordinary differential equations, which can be used in many different circumstances. Applications are given to some nonresonant cases, even for systems with superlinear growth in some direction, or with a singularity. Systems “at resonance” are also considered, provided a Landesman–Lazer type of condition is assumed.

%B Journal of Differential Equations %V 252 %P 1369 - 1391 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022039611003196 %R https://doi.org/10.1016/j.jde.2011.08.005 %0 Book Section %B Springer, Indam Series, Vol. 4, 2012 %D 2012 %T Generalized reduced basis methods and n-width estimates for the approximation of the solution manifold of parametric PDEs %A Toni Lassila %A Andrea Manzoni %A Alfio Quarteroni %A Gianluigi Rozza %K solution manifold %X The set of solutions of a parameter-dependent linear partial di fferential equation with smooth coe fficients typically forms a compact manifold in a Hilbert space. In this paper we review the generalized reduced basis method as a fast computational tool for the uniform approximation of the solution manifold. We focus on operators showing an affi ne parametric dependence, expressed as a linear combination of parameter-independent operators through some smooth, parameter-dependent scalar functions. In the case that the parameter-dependent operator has a dominant term in its affi ne expansion, one can prove the existence of exponentially convergent uniform approximation spaces for the entire solution manifold. These spaces can be constructed without any assumptions on the parametric regularity of the manifold \\r\\nonly spatial regularity of the solutions is required. The exponential convergence rate is then inherited by the generalized reduced basis method. We provide a numerical example related to parametrized elliptic\\r\\nequations con rming the predicted convergence rates. %B Springer, Indam Series, Vol. 4, 2012 %I Springer %G en %U http://hdl.handle.net/1963/6340 %1 6270 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2012-12-13T17:47:45Z\\nNo. of bitstreams: 1\\nqlmr-bumi_FINAL_SISSAreport.pdf: 377397 bytes, checksum: ecaf5713afa6a6f68992f6331631aff4 (MD5) %0 Journal Article %J Calculus of Variations and Partial Differential Equations. Volume 43, Issue 3-4, March 2012, Pages 355-388 %D 2012 %T On the Hausdorff volume in sub-Riemannian geometry %A Andrei A. Agrachev %A Davide Barilari %A Ugo Boscain %X For a regular sub-Riemannian manifold we study the Radon-Nikodym derivative\r\nof the spherical Hausdorff measure with respect to a smooth volume. We prove\r\nthat this is the volume of the unit ball in the nilpotent approximation and it\r\nis always a continuous function. We then prove that up to dimension 4 it is\r\nsmooth, while starting from dimension 5, in corank 1 case, it is C^3 (and C^4\r\non every smooth curve) but in general not C^5. These results answer to a\r\nquestion addressed by Montgomery about the relation between two intrinsic\r\nvolumes that can be defined in a sub-Riemannian manifold, namely the Popp and\r\nthe Hausdorff volume. If the nilpotent approximation depends on the point (that\r\nmay happen starting from dimension 5), then they are not proportional, in\r\ngeneral. %B Calculus of Variations and Partial Differential Equations. Volume 43, Issue 3-4, March 2012, Pages 355-388 %I SISSA %G en %U http://hdl.handle.net/1963/6454 %1 6399 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-02-05T13:55:36Z\r\nNo. of bitstreams: 1\r\n1005.0540v3.pdf: 352986 bytes, checksum: 7d3e71cad3c7ff917dc8769ba4cd96c5 (MD5) %R 10.1007/s00526-011-0414-y %0 Journal Article %J Nanoscale. 2012 Mar; 4(5):1734-41 %D 2012 %T Hybridization in nanostructured DNA monolayers probed by AFM: theory versus experiment %A Alessandro Bosco %A Fouzia Bano %A Pietro Parisse %A Loredana Casalis %A Antonio DeSimone %A Cristian Micheletti %X Nanografted monolayers (NAMs) of DNA show novel physico-chemical properties that make them ideally suited for advanced biosensing applications. In comparison with alternative solid-phase techniques for diagnostic DNA detection, NAMs have the advantage of combining a small size with a high homogeneity of the DNA surface coverage. These two properties favour the extreme miniaturization and ultrasensitivity in high-throughput biosensing devices. The systematic use of NAMs for quantitative DNA (and protein) detection has so far suffered from the lack of a control on key fabrication parameters, such as the ss- or ds-DNA surface coverage. Here we report on a combined experimental-computational study that allows us to estimate the surface density of the grafted DNA by analyzing the sample mechanical response, that is the DNA patch height vs. applied tip load curves. It is shown that the same analysis scheme can be used to detect the occurrence of hybridization with complementary strands in solution and estimate its efficiency. Thanks to these quantitative relationships it is possible to use a single AFM-based setup to: (i) fabricate a DNA NAM, (ii) control the DNA surface coverage, and (iii) characterize its level of hybridization helping the design of NAMs with pre-determined fabrication parameters. %B Nanoscale. 2012 Mar; 4(5):1734-41 %I Royal Society of Chemistry %G en %1 6998 %2 Physics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-08-08T07:48:55Z No. of bitstreams: 0 %R 10.1039/c2nr11662f %0 Report %D 2012 %T Introduction to Riemannian and sub-Riemannian geometry %A Andrei A. Agrachev %A Davide Barilari %A Ugo Boscain %I SISSA %G en %U http://hdl.handle.net/1963/5877 %1 5747 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-05-30T13:23:26Z\r\nNo. of bitstreams: 1\r\n09M_2012_Barilari.pdf: 1146702 bytes, checksum: 28492a78df0fdf2435dd0606fdfc78f5 (MD5) %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire %D 2012 %T Linear elasticity obtained from finite elasticity by Gamma-convergence under weak coerciveness conditions %A Virginia Agostiniani %A Gianni Dal Maso %A Antonio DeSimone %K Nonlinear elasticity %XThe energy functional of linear elasticity is obtained as G-limit of suitable rescalings of the energies of finite elasticity...

%B Ann. Inst. H. Poincare Anal. Non Lineaire %I Gauthier-Villars;Elsevier %V 29 %P 715-735 %G en %U http://hdl.handle.net/1963/4267 %1 3996 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-26T15:11:45Z\\r\\nNo. of bitstreams: 1\\r\\nAgostiniani_DalMaso_30_M.pdf: 407057 bytes, checksum: 2009d1218f7735191a1c768a73b400a3 (MD5) %R 10.1016/j.anihpc.2012.04.001 %0 Conference Proceedings %B Materials Research Society Symposium Proceedings. Volume 1403, 2012, Pages 125-130 %D 2012 %T Mathematical and numerical modeling of liquid crystal elastomer phase transition and deformation %A Mariarita De Luca %A Antonio DeSimone %K Artificial muscle %X Liquid crystal (in particular, nematic) elastomers consist of cross-linked flexible polymer chains with embedded stiff rod molecules that allow them to behave as a rubber and a liquid crystal. Nematic elastomers are characterized by a phase transition from isotropic to nematic past a temperature threshold. They behave as rubber at high temperature and show nematic behavior below the temperature threshold. Such transition is reversible. While in the nematic phase, the rod molecules are aligned along the direction of the "nematic director". This molecular rearrangement induces a stretch in the polymer chains and hence macroscopic spontaneous deformations. The coupling between nematic order parameter and deformation gives rise to interesting phenomena with a potential for new interesting applications. In the biological field, the ability to considerably change their length makes them very promising as artificial muscles actuators. Their tunable optical properties make them suitable, for example, as lenses for new imaging systems. We present a mathematical model able to describe the behavior of nematic elastomers and numerical simulations reproducing such peculiar behavior. We use a geometrically linear version of the Warner and Terentjev model [1] and consider cooling experiments and stretching experiments in the direction perpendicular to the one of the director at cross-linking. %B Materials Research Society Symposium Proceedings. Volume 1403, 2012, Pages 125-130 %I Cambridge University Press %@ 9781605113807 %G en %U http://hdl.handle.net/1963/7020 %1 7011 %2 Physics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-08-12T10:02:18Z No. of bitstreams: 0 %R 10.1557/opl.2012.249 %0 Journal Article %J IEEE Transactions on Automatic Control. Volume 57, Issue 8, 2012, Article number6189035, Pages 1898-1917 %D 2012 %T Modeling and control of quantum systems: An introduction %A Claudio Altafini %A Francesco Ticozzi %X The scope of this work is to provide a self-contained introduction to a selection of basic theoretical aspects in the modeling and control of quantum mechanical systems, as well as a brief survey on the main approaches to control synthesis. While part of the existing theory, especially in the open-loop setting, stems directly from classical control theory (most notably geometric control and optimal control), a number of tools specifically tailored for quantum systems have been developed since the 1980s, in order to take into account their distinctive features: the probabilistic nature of atomic-scale physical systems, the effect of dissipation and the irreversible character of the measurements have all proved to be critical in feedback-design problems. The relevant dynamical models for both closed and open quantum systems are presented, along with the main results on their controllability and stability. A brief review of several currently available control design methods is meant to provide the interested reader with a roadmap for further studies %B IEEE Transactions on Automatic Control. Volume 57, Issue 8, 2012, Article number6189035, Pages 1898-1917 %I Institute of Electrical and Electronics Engineers %G en %U http://hdl.handle.net/1963/6505 %1 6449 %2 Mathematics %4 1 %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-02-27T15:32:35Z (GMT) No. of bitstreams: 0 %R 10.1109/TAC.2012.2195830 %0 Journal Article %J Calculus of Variations and Partial Differential Equations %D 2012 %T The Monge problem in Wiener space %A Fabio Cavalletti %XWe address the Monge problem in the abstract Wiener space and we give an existence result provided both marginal measures are absolutely continuous with respect to the infinite dimensional Gaussian measure γ.

%B Calculus of Variations and Partial Differential Equations %V 45 %P 101–124 %8 Sep %G eng %U https://doi.org/10.1007/s00526-011-0452-5 %R 10.1007/s00526-011-0452-5 %0 Journal Article %J Math. Models Methods Appl. Sci. 22, 1150016 (2012) %D 2012 %T Nonlinear thin-walled beams with a rectangular cross-section-Part I %A Lorenzo Freddi %A Maria Giovanna Mora %A Roberto Paroni %X Our aim is to rigorously derive a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section, starting from three-dimensional nonlinear elasticity. The different limit models are distinguished by the different scaling of the elastic energy and of the ratio between the sides of the cross-section. In this paper we report the first part of our results. %B Math. Models Methods Appl. Sci. 22, 1150016 (2012) %I World Scientific %G en_US %U http://hdl.handle.net/1963/4104 %1 300 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-11-17T08:45:48Z\\r\\nNo. of bitstreams: 1\\r\\nFreddi_79M.pdf: 331698 bytes, checksum: 3b0d6e3d51984a8e8222753a57064ee9 (MD5) %R 10.1142/S0218202511500163 %0 Journal Article %J Nonlinear Analysis: Theory, Methods & Applications %D 2012 %T A nonresonance condition for radial solutions of a nonlinear Neumann elliptic problem %A Andrea Sfecci %K Neumann problem %K Nonresonance %K Radial solutions %K Time-map %XWe prove an existence result for radial solutions of a Neumann elliptic problem whose nonlinearity asymptotically lies between the first two eigenvalues. To this aim, we introduce an alternative nonresonance condition with respect to the second eigenvalue which, in the scalar case, generalizes the classical one, in the spirit of Fonda et al. (1991) [2]. Our approach also applies for nonlinearities which do not necessarily satisfy a subcritical growth assumption.

%B Nonlinear Analysis: Theory, Methods & Applications %V 75 %P 6191 - 6202 %G eng %U http://www.sciencedirect.com/science/article/pii/S0362546X12002659 %R https://doi.org/10.1016/j.na.2012.06.023 %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 Acta Geotechnica, Volume 7, Issue 3, September 2012, Pages 219-237 %D 2012 %T Numerical modelling of installation effects for diaphragm walls in sand %A Riccardo Conti %A Luca de Sanctis %A Giulia M.B. Viggiani %K Constitutive relations %X The scopes of this work are to study the mechanisms of load transfer and the deformations of the ground during slurry trenching and concreting in dry sand and to evaluate their effects on service structural loads, wall deflections and ground displacements behind the wall caused by subsequent excavation. A series of three-dimensional finite element analyses was carried out modelling the installation of diaphragm walls consisting of panels of different length. The soil was modelled as either linearly elastic-perfectly plastic or incrementally non-linear (hypoplastic) with elastic strain range. Plane strain analyses of diaphragm walls of identical cross section were also carried out in which wall installation was either modelled or the wall was wished in place (WIP). The analyses predict ground movements consistent with the experimental observations both in magnitude and trend. The results also show that the maximum horizontal wall deflections and structural loads reduce with increasing panel aspect ratio towards a minimum which is about twice the value computed for WIP analyses. Panel aspect ratios should be larger than about three to take advantage of the three-dimensional effects. The pattern and magnitude of surface vertical displacements obtained from linearly elastic-perfectly plastic analyses, no matter whether three- or two-dimensional, are unrealistic. %B Acta Geotechnica, Volume 7, Issue 3, September 2012, Pages 219-237 %I Springer %G en %U http://hdl.handle.net/1963/6934 %1 6916 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-05-30T10:23:32Z No. of bitstreams: 0 %R 10.1007/s11440-011-0157-0 %0 Journal Article %J International Journal of Non-Linear mechanics %D 2012 %T Ogden-type energies for nematic elastomers %A Virginia Agostiniani %A Antonio DeSimone %K Nonlinear elasticity %XOgden-type extensions of the free-energy densities currently used to model the mechanical behavior of nematic elastomers are proposed and analyzed. Based on a multiplicative decomposition of the deformation gradient into an elastic and a spontaneous or remanent part, they provide a suitable framework to study the stiffening response at high imposed stretches. Geometrically linear versions of the models (Taylor expansions at order two) are provided and discussed. These small strain theories provide a clear illustration of the geometric structure of the underlying energy landscape (the energy grows quadratically with the distance from a non-convex set of spontaneous strains or energy wells). The comparison between small strain and finite deformation theories may also be useful in the opposite direction, inspiring finite deformation generalizations of small strain theories currently used in the mechanics of active and phase-transforming materials. The energy well structure makes the free-energy densities non-convex. Explicit quasi-convex envelopes are provided, and applied to compute the stiffening response of a specimen tested in plane strain extension experiments (pure shear).

%B International Journal of Non-Linear mechanics %I Elsevier %V 47 %P 402-412 %G en %N 2 %1 6971 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-07-15T14:33:38Z No. of bitstreams: 0 %R 10.1016/j.ijnonlinmec.2011.10.001 %0 Journal Article %J Advanced Nonlinear Studies %D 2012 %T One-signed harmonic solutions and sign-changing subharmonic solutions to scalar second order differential equations %A Alberto Boscaggin %B Advanced Nonlinear Studies %I Advanced Nonlinear Studies, Inc. %V 12 %P 445–463 %G eng %R 10.1515/ans-2012-0302 %0 Journal Article %J SIAM Journal on Mathematical Analysis %D 2012 %T Optimal Transport with Branching Distance Costs and the Obstacle Problem %A Fabio Cavalletti %B SIAM Journal on Mathematical Analysis %V 44 %P 454-482 %G eng %U https://doi.org/10.1137/100801433 %R 10.1137/100801433 %0 Journal Article %J Journal of Differential Equations %D 2012 %T Pairs of positive periodic solutions of second order nonlinear equations with indefinite weight %A Alberto Boscaggin %A Fabio Zanolin %K Critical points %K Necessary conditions %K Pairs of positive solutions %K Periodic solutions %XWe study the problem of the existence and multiplicity of positive periodic solutions to the scalar ODEu″+λa(t)g(u)=0,λ>0, where g(x) is a positive function on R+, superlinear at zero and sublinear at infinity, and a(t) is a T-periodic and sign indefinite weight with negative mean value. We first show the nonexistence of solutions for some classes of nonlinearities g(x) when λ is small. Then, using critical point theory, we prove the existence of at least two positive T-periodic solutions for λ large. Some examples are also provided.

%B Journal of Differential Equations %V 252 %P 2900 - 2921 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022039611003895 %R https://doi.org/10.1016/j.jde.2011.09.011 %0 Journal Article %J Differential Integral Equations %D 2012 %T Periodic solutions of a system of coupled oscillators with one-sided superlinear retraction forces %A Alessandro Fonda %A Andrea Sfecci %B Differential Integral Equations %I Khayyam Publishing, Inc. %V 25 %P 993–1010 %8 11 %G eng %U https://projecteuclid.org:443/euclid.die/1356012248 %0 Journal Article %J Portugaliae Mathematica %D 2012 %T Periodic solutions to superlinear planar Hamiltonian systems %A Alberto Boscaggin %XWe prove the existence of infinitely many periodic (harmonic and subharmonic) solutions to planar Hamiltonian systems satisfying a suitable superlinearity condition at infinity. The proof relies on the Poincare-Birkhoff fixed point theorem.

%B Portugaliae Mathematica %I European Mathematical Society Publishing House %V 69 %P 127–141 %G eng %0 Journal Article %J Journal of Differential Equations %D 2012 %T Positive periodic solutions of second order nonlinear equations with indefinite weight: Multiplicity results and complex dynamics %A Alberto Boscaggin %A Fabio Zanolin %K Complex dynamics %K Poincaré map %K Positive periodic solutions %K Subharmonics %XWe prove the existence of a pair of positive T-periodic solutions as well as the existence of positive subharmonic solutions of any order and the presence of chaotic-like dynamics for the scalar second order ODEu″+aλ,μ(t)g(u)=0, where g(x) is a positive function on R+, superlinear at zero and sublinear at infinity, and aλ,μ(t) is a T-periodic and sign indefinite weight of the form λa+(t)−μa−(t), with λ,μ>0 and large.

%B Journal of Differential Equations %V 252 %P 2922 - 2950 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022039611003883 %R https://doi.org/10.1016/j.jde.2011.09.010 %0 Journal Article %J BMC Systems Biology. 29 August 2012, Page 115 %D 2012 %T Predicting and characterizing selective multiple drug treatments for metabolic diseases and cancer. %A Giuseppe Facchetti %A Claudio Altafini %A Mattia Zampieri %X Background: In the field of drug discovery, assessing the potential of multidrug therapies is a difficult task because of the combinatorial complexity (both theoretical and experimental) and because of the requirements on the selectivity of the therapy. To cope with this problem, we have developed a novel method for the systematic in silico investigation of synergistic effects of currently available drugs on genome-scale metabolic networks. The algorithm finds the optimal combination of drugs which guarantees the inhibition of an objective function, while minimizing the side effect on the overall network. Results: Two different applications are considered: finding drug synergisms for human metabolic diseases (like diabetes, obesity and hypertension) and finding antitumoral drug combinations with minimal side effect on the normal human metabolism.The results we obtain are consistent with some of the available therapeutic indications and predict some new multiple drug treatments.A cluster analysis on all possible interactions among the currently available drugs indicates a limited variety on the metabolic targets for the approved drugs. Conclusion: The in silico prediction of drug synergism can represent an important tool for the repurposing of drug in a realistic perspective which considers also the selectivty of the therapy. Moreover, for a more profitable exploitation of drug-drug interactions, also drugs which show a too low efficacy but which have a non-common mechanism of action, can be reconsider as potential ingredients of new multicompound therapeutic indications.Needless to say the clues provided by a computational study like ours need in any case to be thoroughly evaluated experimentally. %B BMC Systems Biology. 29 August 2012, Page 115 %I BioMed Central %G en %U http://hdl.handle.net/1963/6515 %1 6450 %2 Mathematics %4 1 %$ Submitted by Claudio Altafini (altafini@sissa.it) on 2013-02-27T13:12:49Z\nNo. of bitstreams: 0 %R doi:10.1186/1752-0509-6-115 %0 Journal Article %J Calculus of variations and partial differential equations 44 (2012) 495-541 %D 2012 %T Quasistatic evolution for Cam-Clay plasticity: properties of the viscosity solution %A Gianni Dal Maso %A Antonio DeSimone %A Francesco Solombrino %XCam-Clay plasticity is a well established model for the description of the mechanics of fine grained soils. As solutions can develop discontinuities in time, a weak notion of solution, in terms of a rescaled time s , has been proposed in [8] to give a meaning to this discontinuous evolution. In this paper we first prove that this rescaled evolution satisfies the flow-rule for the rate of plastic strain, in a suitable measure-theoretical sense. In the second part of the paper we consider the behavior of the evolution in terms of the original time variable t . We prove that the unrescaled solution satisfies an energy-dissipation balance and an evolution law for the internal variable, which can be expressed in terms of integrals depending only on the original time. Both these integral identities contain terms concentrated on the jump times, whose size can only be determined by looking at the rescaled formulation.

%B Calculus of variations and partial differential equations 44 (2012) 495-541 %I Springer %G en_US %U http://hdl.handle.net/1963/3900 %1 809 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-07-26T09:17:50Z\\r\\nNo. of bitstreams: 1\\r\\nSolombrino_46M.pdf: 382911 bytes, checksum: dd118cc7f80d4cb1902713eb18747ac6 (MD5) %R 10.1007/s00526-011-0443-6 %0 Journal Article %J SIAM Journal on Mathematical Analysis 44, nr. 1 (2012) 245-292 %D 2012 %T Quasistatic evolution in non-associative plasticity - the cap models %A Jean-Francois Babadjian %A Gilles A. Francfort %A Maria Giovanna Mora %K Elasto-plasticity %X Non-associative elasto-plasticity is the working model of plasticity for soil and rocks mechanics. Yet, it is usually viewed as non-variational. In this work, we prove a contrario the existence of a variational evolution for such a model under a natural capping assumption on the hydrostatic stresses and a less natural mollification of the stress admissibility constraint. The obtained elasto-plastic evolution is expressed for times that are conveniently rescaled. %B SIAM Journal on Mathematical Analysis 44, nr. 1 (2012) 245-292 %I SIAM %G en %U http://hdl.handle.net/1963/4139 %1 3879 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-15T12:13:15Z No. of bitstreams: 1 Bab-Fra-Mora_05M.pdf: 420336 bytes, checksum: cf8a2e6bd6c333fb5b6b130ae22de0a7 (MD5) %R 10.1137/110823511 %0 Conference Proceedings %B European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012) J. Eberhardsteiner et.al. (eds.), Vienna, Austria, 10-14 sept. 2012 %D 2012 %T Reduction strategies for PDE-constrained oprimization problems in Haemodynamics %A Gianluigi Rozza %A Andrea Manzoni %A Federico Negri %K inverse problems %X Solving optimal control problems for many different scenarios obtained by varying a set of parameters in the state system is a computationally extensive task. In this paper we present a new reduced framework for the formulation, the analysis and the numerical solution of parametrized PDE-constrained optimization problems. This framework is based on a suitable saddle-point formulation of the optimal control problem and exploits the reduced basis method for the rapid and reliable solution of parametrized PDEs, leading to a relevant computational reduction with respect to traditional discretization techniques such as the finite element method. This allows a very efficient evaluation of state solutions and cost functionals, leading to an effective solution of repeated optimal control problems, even on domains of variable shape, for which a further (geometrical) reduction is pursued, relying on flexible shape parametrization techniques. This setting is applied to the solution of two problems arising from haemodynamics, dealing with both data reconstruction and data assimilation over domains of variable shape,\\r\\nwhich can be recast in a common PDE-constrained optimization formulation. %B European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012) J. Eberhardsteiner et.al. (eds.), Vienna, Austria, 10-14 sept. 2012 %G en %U http://hdl.handle.net/1963/6338 %1 6268 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2012-12-13T16:30:48Z\\r\\nNo. of bitstreams: 1\\r\\npaper_ECCOMAS2012_AM_SISSAreport.pdf: 4599005 bytes, checksum: 014a5a01276f25177386ad374a5917c8 (MD5) %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 %J Proceedings of the National Academy of Sciences of the United States of America. Volume 109, Issue 44, 30 October 2012, Pages 17874-17879 %D 2012 %T Reverse engineering the euglenoid movement %A Marino Arroyo %A Luca Heltai %A Daniel Millán %A Antonio DeSimone %K microswimmers %X Euglenids exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large-amplitude highly concerted deformations of the entire body (euglenoid movement or metaboly). A plastic cell envelope called pellicle mediates these deformations. Unlike ciliary or flagellar motility, the biophysics of this mode is not well understood, including its efficiency and molecular machinery. We quantitatively examine video recordings of four euglenids executing such motions with statistical learning methods. This analysis reveals strokes of high uniformity in shape and pace. We then interpret the observations in the light of a theory for the pellicle kinematics, providing a precise understanding of the link between local actuation by pellicle shear and shape control. We systematically understand common observations, such as the helical conformations of the pellicle, and identify previously unnoticed features of metaboly. While two of our euglenids execute their stroke at constant body volume, the other two exhibit deviations of about 20% from their average volume, challenging current models of low Reynolds number locomotion. We find that the active pellicle shear deformations causing shape changes can reach 340%, and estimate the velocity of the molecular motors. Moreover, we find that metaboly accomplishes locomotion at hydrodynamic efficiencies comparable to those of ciliates and flagellates. Our results suggest new quantitative experiments, provide insight into the evolutionary history of euglenids, and suggest that the pellicle may serve as a model for engineered active surfaces with applications in microfluidics. %B Proceedings of the National Academy of Sciences of the United States of America. Volume 109, Issue 44, 30 October 2012, Pages 17874-17879 %G en %U http://hdl.handle.net/1963/6444 %1 6380 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Luca Heltai (heltai@sissa.it) on 2013-02-01T17:29:31Z\\nNo. of bitstreams: 0 %R 10.1073/pnas.1213977109 %0 Journal Article %J Systems and Control Letters. Volume 61, Issue 2, February 2012, Pages 347-353 %D 2012 %T On robust Lie-algebraic stability conditions for switched linear systems %A Andrei A. Agrachev %A Yurij Baryshnikov %A Daniel Liberzon %X This paper presents new sufficient conditions for exponential stability of switched linear systems under arbitrary switching, which involve the commutators (Lie brackets) among the given matrices generating the switched system. The main novelty feature of these stability criteria is that, unlike their earlier counterparts, they are robust with respect to small perturbations of the system parameters. %B Systems and Control Letters. Volume 61, Issue 2, February 2012, Pages 347-353 %G en %U http://hdl.handle.net/1963/6455 %1 6400 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-02-05T14:15:25Z\\nNo. of bitstreams: 0 %R 10.1016/j.sysconle.2011.11.016 %0 Journal Article %J Communications in Mathematical Physics 313 (2012) 1-33 %D 2012 %T SBV regularity for genuinely nonlinear, strictly hyperbolic systems of conservation laws in one space dimension %A Stefano Bianchini %A Laura Caravenna %B Communications in Mathematical Physics 313 (2012) 1-33 %I Springer %G en_US %U http://hdl.handle.net/1963/4091 %1 313 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-10-19T09:31:49Z\\r\\nNo. of bitstreams: 1\\r\\nBianchini_Caravenna_71M_2010.pdf: 591519 bytes, checksum: 388c1d8be60af95097574c718b4708b2 (MD5) %R 10.1007/s00220-012-1480-5 %0 Journal Article %J Siam Journal on Mathematical Analysis %D 2012 %T SBV regularity for Hamilton-Jacobi equations with Hamiltonian depending on (t,x) %A Stefano Bianchini %A Daniela Tonon %B Siam Journal on Mathematical Analysis %I SISSA %V 44 %P 2179-2203 %G en %U http://hdl.handle.net/20.500.11767/14066 %N 3 %1 3890 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-20T13:28:47Z\r\nNo. of bitstreams: 1\r\nBianchini_Tonon_13M.pdf: 249849 bytes, checksum: 461aecb2ce41d2bff011ba0062ed1cfb (MD5) %R 10.1137/110827272 %0 Journal Article %J Acta Mathematica Scientia, Volume 32, Issue 1, January 2012, Pages 380-388 %D 2012 %T SBV regularity of genuinely nonlinear hyperbolic systems of conservation laws in one space dimension %A Stefano Bianchini %K Hyperbolic systems %X The problem of the presence of Cantor part in the derivative of a solution to a hyperbolic system of conservation laws is considered. An overview of the techniques involved in the proof is given, and a collection of related problems concludes the paper. Key words hyperbolic systems; conservation laws; SBV; regularity %B Acta Mathematica Scientia, Volume 32, Issue 1, January 2012, Pages 380-388 %I Elsevier %G en %U http://hdl.handle.net/1963/6535 %1 6510 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-03-21T08:22:40Z\nNo. of bitstreams: 0 %R 10.1016/S0252-9602(12)60024-1 %0 Journal Article %J Rend. Istit. Mat. Univ. Trieste %D 2012 %T SBV-like regularity for general hyperbolic systems of conservation laws in one space dimension %A Stefano Bianchini %A Lei Yu %B Rend. Istit. Mat. Univ. Trieste %V 44 %P 439–472 %G eng %0 Journal Article %J Journal of Mathematical Analysis and Applications %D 2012 %T SBV-like regularity for Hamilton-Jacobi equations with a convex Hamiltonian %A Stefano Bianchini %A Daniela Tonon %B Journal of Mathematical Analysis and Applications %I SISSA %V 391 %P 190-208 %G en %U http://hdl.handle.net/20.500.11767/13909 %N 1 %1 4352 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-10-07T11:24:37Z\\r\\nNo. of bitstreams: 1\\r\\n45M_Tonon_Bianchini.pdf: 179519 bytes, checksum: c157fc19ae52c2fb8bcd2ca28815d26e (MD5) %R 10.1016/j.jmaa.2012.02.017 %0 Journal Article %J Discrete & Continuous Dynamical Systems - A %D 2012 %T Second order approximations of quasistatic evolution problems in finite dimension %A Virginia Agostiniani %K discrete approximations %K perturbation methods %K saddle-node bifurcation %K Singular perturbations %K vanishing viscosity %XIn this paper, we study the limit, as ε goes to zero, of a particular solution of the equation $\epsilon^2A\ddot u^ε(t)+εB\dot u^ε(t)+\nabla_xf(t,u^ε(t))=0$, where $f(t,x)$ is a potential satisfying suitable coerciveness conditions. The limit $u(t)$ of $u^ε(t)$ is piece-wise continuous and verifies $\nabla_xf(t,u(t))=0$. Moreover, certain jump conditions characterize the behaviour of $u(t)$ at the discontinuity times. The same limit behaviour is obtained by considering a different approximation scheme based on time discretization and on the solutions of suitable autonomous systems.

%B Discrete & Continuous Dynamical Systems - A %V 32 %P 1125 %G eng %U http://aimsciences.org//article/id/560b82d9-f289-498a-a619-a4b132aaf9f8 %R 10.3934/dcds.2012.32.1125 %0 Journal Article %J Journal of Biological Dynamics %D 2012 %T Self-propelled micro-swimmers in a Brinkman fluid %A Marco Morandotti %XWe prove an existence, uniqueness, and regularity result for the motion of a self-propelled micro-swimmer in a particulate viscous medium, modelled as a Brinkman fluid. A suitable functional setting is introduced to solve the Brinkman system for the velocity field and the pressure of the fluid by variational techniques. The equations of motion are written by imposing a self-propulsion constraint, thus allowing the viscous forces and torques to be the only ones acting on the swimmer. From an infinite-dimensional control on the shape of the swimmer, a system of six ordinary differential equations for the spatial position and the orientation of the swimmer is obtained. This is dealt with standard techniques for ordinary differential equations, once the coefficients are proved to be measurable and bounded. The main result turns out to extend an analogous result previously obtained for the Stokes system.

%B Journal of Biological Dynamics %I Taylor & Francis %V 6 %P 88-103 %G eng %U https://doi.org/10.1080/17513758.2011.611260 %R 10.1080/17513758.2011.611260 %0 Journal Article %J International Journal Numerical Methods Biomedical Engineering %D 2012 %T Simulation-based uncertainty quantification of human arterial network hemodynamics %A Peng Chen %A Alfio Quarteroni %A Gianluigi Rozza %K uncertainty quantification, mathematical modelling of the cardiovascular system, fluid-structure interaction %X This work aims at identifying and quantifying uncertainties from various sources in human cardiovascular\r\nsystem based on stochastic simulation of a one dimensional arterial network. A general analysis of\r\ndifferent uncertainties and probability characterization with log-normal distribution of these uncertainties\r\nis introduced. Deriving from a deterministic one dimensional fluid structure interaction model, we establish\r\nthe stochastic model as a coupled hyperbolic system incorporated with parametric uncertainties to describe\r\nthe blood flow and pressure wave propagation in the arterial network. By applying a stochastic collocation\r\nmethod with sparse grid technique, we study systemically the statistics and sensitivity of the solution with\r\nrespect to many different uncertainties in a relatively complete arterial network with potential physiological\r\nand pathological implications for the first time. %B International Journal Numerical Methods Biomedical Engineering %I Wiley %G en %1 6467 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2013-03-07T12:33:02Z\nNo. of bitstreams: 1\nreport.pdf: 1605405 bytes, checksum: bb12cf074ce32a80567a0cde0c0861db (MD5) %0 Journal Article %J Riv. Mat. Univ. Parma %D 2012 %T Some applications of the SBV Regularity Theorem for entropy solutions of 1D scalar conservation laws to ConvectionTheory and sticky particles %A Daniela Tonon %XWe show how it is possible to apply the SBV Regularity Theorem for entropy solutions of one-dimensional scalar conservation laws, proved by Ambrosio and De Lellis, to Convection Theory and sticky particles. In the multi-dimensional case we present a counterexample which prevent us from using the same approach.

%B Riv. Mat. Univ. Parma %V 3 %P 163–175 %G eng %U https://hal.archives-ouvertes.fr/hal-00918409 %0 Conference Paper %B 17th Int. Conf. Ships Shipp. Res. %D 2012 %T A stable semi-lagrangian potential method for the simulation of ship interaction with unsteady and nonlinear waves %A Andrea Mola %A Luca Heltai %A Antonio DeSimone %B 17th Int. Conf. Ships Shipp. Res. %G eng %0 Journal Article %J Journal of Dynamical and Control Systems. Volume 18, Issue 1, January 2012, Pages 21-44 %D 2012 %T Sub-Riemannian structures on 3D Lie groups %A Andrei A. Agrachev %A Davide Barilari %XWe give a complete classification of left-invariant sub-Riemannian structures on three dimensional Lie groups in terms of the basic differential invariants. As a corollary we explicitly find a sub-Riemannian isometry between the nonisomorphic Lie groups $SL(2)$ and $A^+(\mathbb{R})\times S^1$, where $A^+(\mathbb{R})$ denotes the group of orientation preserving affine maps on the real line.

%B Journal of Dynamical and Control Systems. Volume 18, Issue 1, January 2012, Pages 21-44 %I SISSA %G en %U http://hdl.handle.net/1963/6453 %1 6397 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-02-05T13:48:29Z\r\nNo. of bitstreams: 1\r\n1007.4970v2.pdf: 453953 bytes, checksum: 4330325299743bad4afe9f1ac7121e21 (MD5) %R 10.1007/s10883-012-9133-8 %0 Journal Article %J Proceedings of the London Mathematical Society, Volume 105, Issue 3, September 2012, Pages 622-660 %D 2012 %T Systems of Quadratic Inequalities %A Andrei A. Agrachev %A Antonio Lerario %X We present a spectral sequence which efficiently computes Betti numbers of a closed semi-algebraic subset of RP^n defined by a system of quadratic inequalities and the image of the homology homomorphism induced by the inclusion of this subset in RP^n. We do not restrict ourselves to the term E_2 of the spectral sequence and give a simple explicit formula for the differential d_2. %B Proceedings of the London Mathematical Society, Volume 105, Issue 3, September 2012, Pages 622-660 %I SISSA %G en %U http://hdl.handle.net/1963/7072 %1 7066 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-09-16T10:02:51Z No. of bitstreams: 1 1012.5731v2.pdf: 367584 bytes, checksum: 136c7bc2abeeb2a239c15689929eae30 (MD5) %R DOI: 10.1112/plms/pds010 %0 Report %D 2012 %T Topological sensitivity analysis for high order elliptic operators %A Samuel Amstutz %A Antonio André Novotny %A Nicolas Van Goethem %K Topological derivative, Elliptic operators, Polarization tensor %X The topological derivative is defined as the first term of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of a singular domain perturbation. It has applications in many different fields such as shape and topology optimization, inverse problems, image processing and mechanical modeling including synthesis and/or optimal design of microstructures, fracture mechanics sensitivity analysis and damage evolution modeling. The topological derivative has been fully developed for a wide range of second order differential operators. In this paper we deal with the topological asymptotic expansion of a class of shape functionals associated with elliptic differential operators of order 2m, m>=1. The general structure of the polarization tensor is derived and the concept of degenerate polarization tensor is introduced. We provide full mathematical justifications for the derived formulas, including precise estimates of remainders. %I SISSA %G en %U http://hdl.handle.net/1963/6343 %1 6272 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Nicolas Van Goethem (vangoeth@sissa.it) on 2012-12-14T17:45:48Z No. of bitstreams: 1 Degenerate_sub.pdf: 479352 bytes, checksum: eefab8b4e64b0ef0c7d7f0e16d529008 (MD5) %0 Journal Article %J Computer Methods in Applied Mechanics and Engineering. Volume 229-232, 1 July 2012, Pages 110-127 %D 2012 %T Variational implementation of immersed finite element methods %A Luca Heltai %A Francesco Costanzo %K Turbulent flow %XDirac-delta distributions are often crucial components of the solid-fluid coupling operators in immersed solution methods for fluid-structure interaction (FSI) problems. This is certainly so for methods like the Immersed Boundary Method (IBM) or the Immersed Finite Element Method (IFEM), where Dirac-delta distributions are approximated via smooth functions. By contrast, a truly variational formulation of immersed methods does not require the use of Dirac-delta distributions, either formally or practically. This has been shown in the Finite Element Immersed Boundary Method (FEIBM), where the variational structure of the problem is exploited to avoid Dirac-delta distributions at both the continuous and the discrete level. In this paper, we generalize the FEIBM to the case where an incompressible Newtonian fluid interacts with a general hyperelastic solid. Specifically, we allow (i) the mass density to be different in the solid and the fluid, (ii) the solid to be either viscoelastic of differential type or purely elastic, and (iii) the solid to be and either compressible or incompressible. At the continuous level, our variational formulation combines the natural stability estimates of the fluid and elasticity problems. In immersed methods, such stability estimates do not transfer to the discrete level automatically due to the non- matching nature of the finite dimensional spaces involved in the discretization. After presenting our general mathematical framework for the solution of FSI problems, we focus in detail on the construction of natural interpolation operators between the fluid and the solid discrete spaces, which guarantee semi-discrete stability estimates and strong consistency of our spatial discretization.

%B Computer Methods in Applied Mechanics and Engineering. Volume 229-232, 1 July 2012, Pages 110-127 %I Elsevier %G en %U http://hdl.handle.net/1963/6462 %1 6389 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Lucio Lubiana (lubiana@sissa.it) on 2013-02-04T16:21:56Z\\nNo. of bitstreams: 0 %R 10.1016/j.cma.2012.04.001 %0 Journal Article %J Advances in Calculus of Variations 5 (2012) 433-483 %D 2012 %T A Viscosity-driven crack evolution %A Simone Racca %XWe present a model of crack growth in brittle materials which couples dissipative effects on the crack tip and viscous effects. We consider the 2 -dimensional antiplane case with pre-assigned crack path, and firstly prove an existence result for a rate-dependent evolution problem by means of time-discretization. The next goal is to describe the rate-independent evolution as limit of the rate-dependent ones when the dissipative and viscous effects vanish. The rate-independent evolution satisfies a Griffith’s criterion for the crack growth, but, in general, it does not fulfil a global minimality condition; its fracture set may exhibit jump discontinuities with respect to time. Under suitable regularity assumptions, the quasi-static crack growth is described by solving a finite-dimensional problem.

%B Advances in Calculus of Variations 5 (2012) 433-483 %I SISSA %G en %U http://hdl.handle.net/1963/5130 %1 4944 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-11-29T07:47:42Z\\r\\nNo. of bitstreams: 1\\r\\n63M_Racca.pdf: 473110 bytes, checksum: f4d49c3f7e2b984e9694fbd66a806447 (MD5) %R 10.1515/acv-2011-0012 %0 Journal Article %J Journal of Functional Analysis 262 (2012) 409-450 %D 2012 %T Weighted barycentric sets and singular Liouville equations on compact surfaces %A Alessandro Carlotto %A Andrea Malchiodi %X Given a closed two dimensional manifold, we prove a general existence result\\r\\nfor a class of elliptic PDEs with exponential nonlinearities and negative Dirac\\r\\ndeltas on the right-hand side, extending a theory recently obtained for the\\r\\nregular case. This is done by global methods: since the associated Euler\\r\\nfunctional is in general unbounded from below, we need to define a new model\\r\\nspace, generalizing the so-called space of formal barycenters and\\r\\ncharacterizing (up to homotopy equivalence) its very low sublevels. As a\\r\\nresult, the analytic problem is reduced to a topological one concerning the\\r\\ncontractibility of this model space. To this aim, we prove a new functional\\r\\ninequality in the spirit of [16] and then we employ a min-max scheme based on a cone-style construction, jointly with the blow-up analysis given in [5] (after\\r\\n[6] and [8]). This study is motivated by abelian Chern- Simons theory in\\r\\nself-dual regime, or from the problem of prescribing the Gaussian curvature in\\r\\npresence of conical singularities (hence generalizing a problem raised by\\r\\nKazdan and Warner in [26]). %B Journal of Functional Analysis 262 (2012) 409-450 %I Elsevier %G en %U http://hdl.handle.net/1963/5218 %1 5040 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-01-10T11:49:50Z\\nNo. of bitstreams: 1\\n1105.2363v2.pdf: 793763 bytes, checksum: 4996db876d03946c03fa0d4766801974 (MD5) %R 10.1016/j.jfa.2011.09.012 %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 %D 2011 %T Bishop and Laplacian Comparison Theorems on Three Dimensional Contact Subriemannian Manifolds with Symmetry %A Andrei A. Agrachev %A Paul Lee %X We prove a Bishop volume comparison theorem and a Laplacian comparison\r\ntheorem for three dimensional contact subriemannian manifolds with symmetry. %I SISSA %G en %U http://hdl.handle.net/1963/6508 %1 6455 %2 Mathematics %4 1 %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-02-27T15:12:11Z\nNo. of bitstreams: 1\n1105.2206v1.pdf: 252509 bytes, checksum: c5f4299fedd5f685c7b283c5a4ea995d (MD5) %0 Journal Article %J Comptes Rendus Mathematique 349 (2011) 161-166 %D 2011 %T A class of existence results for the singular Liouville equation %A Alessandro Carlotto %A Andrea Malchiodi %X We consider a class of elliptic PDEs on closed surfaces with exponential nonlinearities and Dirac deltas on the right-hand side. The study arises from abelian Chern–Simons theory in self-dual regime, or from the problem of prescribing the Gaussian curvature in presence of conical singularities. A general existence result is proved using global variational methods: the analytic problem is reduced to a topological problem concerning the contractibility of a model space, the so-called space of formal barycenters, characterizing the very low sublevels of a suitable functional. %B Comptes Rendus Mathematique 349 (2011) 161-166 %I Elsevier %G en %U http://hdl.handle.net/1963/5793 %1 5648 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-05-07T07:37:16Z\\nNo. of bitstreams: 0 %R 10.1016/j.crma.2010.12.016 %0 Journal Article %J Rev. Mat. Iberoamericana %D 2011 %T Cluster solutions for the Schrödinger-Poisson-Slater problem around a local minimum of the potential %A David Ruiz %A Giusi Vaira %B Rev. Mat. Iberoamericana %I Real Sociedad Matemática Española %V 27 %P 253–271 %8 01 %G eng %U https://projecteuclid.org:443/euclid.rmi/1296828834 %0 Report %D 2011 %T Compactness by maximality %A Sandro Zagatti %X We derive a compactness property in the Sobolev space $W^{1,1}(\O)$ in order to study the Dirichlet problem for the eikonal equation \begin{displaymath} \begin{cases} \ha |\n u(x)|^2 - a(x) = 0 & \ \textrm{in} \ \O\cr u(x)=\varphi(x) & \ \textrm{on} \ \partial \O, \end{cases} \end{displaymath} without continuity assumptions on the map $a$. %G en %U http://preprints.sissa.it/handle/1963/35317 %1 35626 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-05-24T07:53:14Z No. of bitstreams: 0 %0 Journal Article %J Annales de l'I.H.P. Analyse non linéaire %D 2011 %T Concentration of solutions for a singularly perturbed Neumann problem in non-smooth domains %A Serena Dipierro %B Annales de l'I.H.P. Analyse non linéaire %I Elsevier %V 28 %P 107-126 %G eng %U http://www.numdam.org/item/AIHPC_2011__28_1_107_0 %R 10.1016/j.anihpc.2010.11.003 %0 Journal Article %J Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1219-1231 %D 2011 %T Crack growth with non-interpenetration : a simplified proof for the pure Neumann problem %A Gianni Dal Maso %A Giuliano Lazzaroni %X We present a recent existence result concerning the quasi-static evolution of cracks in hyperelastic brittle materials, in the frame-work of finite elasticity with non-interpenetration. In particular, here we consider the problem where no Dirichlet conditions are imposed, the boundary is traction-free, and the body is subject only to time-dependent volume forces. This allows us to present the main ideas of the proof in a simpler way, avoiding some of the technicalities needed in the general case, studied in. %B Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1219-1231 %I American Institute of Mathematical Sciences %G en_US %U http://hdl.handle.net/1963/3801 %1 526 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-11-27T10:24:55Z\\r\\nNo. of bitstreams: 1\\r\\nDM-Laz-proc-pre.pdf: 195002 bytes, checksum: 44e408b134f19e4d31e77b3e0762cd73 (MD5) %R 10.3934/dcds.2011.31.1219 %0 Report %D 2011 %T Critical points of the Moser-Trudinger functional %A Francesca De Marchis %A Andrea Malchiodi %A Luca Martinazzi %K Moser-Trudinger inequality %I SISSA %G en %U http://hdl.handle.net/1963/4592 %1 4353 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-10-07T11:40:39Z\\nNo. of bitstreams: 1\\n46M_Malchiodi.pdf: 234581 bytes, checksum: 365098bf21692bfa547056b200acb4c6 (MD5) %0 Journal Article %J PNAS 108 (2011) 13978 %D 2011 %T Cytoskeletal actin networks in motile cells are critically self-organized systems synchronized by mechanical interactions %A Luca Cardamone %A Alessandro Laio %A Rajesh Shahapure %A Antonio DeSimone %B PNAS 108 (2011) 13978 %I National Academy of Sciences %G en %U http://hdl.handle.net/1963/4358 %1 4066 %2 Physics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-28T06:31:24Z\\nNo. of bitstreams: 0 %R 10.1073/pnas.1100549108 %0 Journal Article %J Communications on Pure and Applied Analysis %D 2011 %T A Decomposition Theorem for BV functions %A Stefano Bianchini %A Daniela Tonon %B Communications on Pure and Applied Analysis %I American Institute of Mathematical Sciences %V 10 %P 1549-1566 %G en_US %U http://hdl.handle.net/20.500.11767/14599 %N 6 %1 693 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-04-07T15:11:02Z\\r\\nNo. of bitstreams: 1\\r\\narticoloBV-preprint.pdf: 278021 bytes, checksum: db1d8f4c30a60313b69e105977010165 (MD5) %R 10.3934/cpaa.2011.10.1549 %0 Thesis %D 2011 %T Dimensional Reduction and Approximation of Measures and Weakly Differentiable Homeomorphisms %A Sara Daneri %X This thesis is devoted to the study of two different problems: the properties of the disintegration of the Lebesgue measure on the faces of a convex function and the existence of smooth approximations of bi-Lipschitz orientation-preserving homeomorphisms in the plane. %I SISSA %G en %U http://hdl.handle.net/1963/5348 %1 5178 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-02-02T16:17:40Z\\nNo. of bitstreams: 1\\nTesiPhDDaneriFinal.pdf: 1042283 bytes, checksum: be3ac0827af99c78eafc9395b4670544 (MD5) %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 Journal of Differential Equations %D 2011 %T Embedding theorems and existence results for nonlinear Schrödinger–Poisson systems with unbounded and vanishing potentials %A Bonheure, Denis %A Mercuri, Carlo %XMotivated by existence results for positive solutions of non-autonomous nonlinear Schrödinger–Poisson systems with potentials possibly unbounded or vanishing at infinity, we prove embedding theorems for weighted Sobolev spaces. We both consider a general framework and spaces of radially symmetric functions when assuming radial symmetry of the potentials.

%B Journal of Differential Equations %I Elsevier %V 251 %P 1056–1085 %G eng %U https://doi.org/10.1016/j.jde.2011.04.010 %R 10.1016/j.jde.2011.04.010 %0 Journal Article %J Journal de Mathematiques Pures et Appliquees 95 (2011) 565-584 %D 2011 %T Energy release rate and stress intensity factor in antiplane elasticity %A Giuliano Lazzaroni %A Rodica Toader %X In the setting of antiplane linearized elasticity, we show the existence of the stress intensity factor and its relation with the energy release rate when the crack path is a C1,1 curve. Finally, we show that the energy release rate is continuous with respect to the Hausdorff convergence in a class of admissible cracks. %B Journal de Mathematiques Pures et Appliquees 95 (2011) 565-584 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3780 %1 546 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-11-17T11:50:32Z\\r\\nNo. of bitstreams: 2\\r\\nLazzaroni_67M_2009.pdf: 259616 bytes, checksum: 3c3adef52607bc6238c11a84904a9fb9 (MD5)\\r\\nLazzaroni_67M_2009: 259616 bytes, checksum: 3c3adef52607bc6238c11a84904a9fb9 (MD5) %R 10.1016/j.matpur.2011.01.001 %0 Journal Article %J Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1017-1021 %D 2011 %T Ennio De Giorgi and Γ-convergence %A Gianni Dal Maso %X Γ-convergence was introduced by Ennio De Giorgi in a series of papers published between 1975 and 1983. In the same years he developed many applications of this tool to a great variety of asymptotic problems in the calculus of variations and in the theory of partial differential equations. %B Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1017-1021 %I American Institute of Mathematical Sciences %G en %U http://hdl.handle.net/1963/5308 %1 5138 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-01-31T12:04:34Z\\nNo. of bitstreams: 0 %R 10.3934/dcds.2011.31.1017 %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 SIAM J. Math. Anal. %D 2011 %T An Existence and Uniqueness Result for the Motion of Self-Propelled Microswimmers %A Gianni Dal Maso %A Antonio DeSimone %A Marco Morandotti %XWe present an analytical framework to study the motion of micro-swimmers in a viscous fluid. Our main result is that, under very mild regularity assumptions, the change of shape determines uniquely the motion of the swimmer. We assume that the Reynolds number is very small, so that the velocity field of the surrounding, infinite fluid is governed by the Stokes system and all inertial effects can be neglected. Moreover, we enforce the self propulsion constraint (no external forces and torques). Therefore, Newton\\\'s equations of motion reduce to the vanishing of the viscous drag force and torque acting on the body. By exploiting an integral representation of viscous force and torque, the equations of motion can be reduced to a system of six ordinary differential equations. Variational techniques are used to prove the boundedness and measurability of its coefficients, so that classical results on ordinary differential equations can be invoked to prove existence and uniqueness of the solution.

%B SIAM J. Math. Anal. %I Society for Industrial and Applied Mathematics %V 43 %P 1345-1368 %G en_US %U http://hdl.handle.net/1963/3894 %1 815 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-07-23T11:44:06Z\\r\\nNo. of bitstreams: 1\\r\\nMorandotti_44M.pdf: 217358 bytes, checksum: 4c362016bb2220e7a97805254b7fb870 (MD5) %R 10.1137/10080083X %0 Journal Article %J Rend. Lincei Mat. Appl. 22 (2011) 387-408 %D 2011 %T Existence for wave equations on domains with arbitrary growing cracks %A Gianni Dal Maso %A Cristopher J. Larsen %K Wave equation %X In this paper we formulate and study scalar wave equations on domains with arbitrary growing cracks. This includes a zero Neumann condition on the crack sets, and the only assumptions on these sets are that they have bounded surface measure and are growing in the sense of set inclusion. In particular, they may be dense, so the weak formulations must fall outside of the usual weak formulations using Sobolev spaces. We study both damped and undamped equations, showing existence and, for the damped equation, uniqueness and energy conservation. %B Rend. Lincei Mat. Appl. 22 (2011) 387-408 %I European Mathematical Society %G en %U http://hdl.handle.net/1963/4284 %1 4015 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-27T09:09:30Z\\r\\nNo. of bitstreams: 1\\r\\nDM-Lar_32_M.pdf: 223891 bytes, checksum: 7c6c66b6d21936b33ed0c21574928e24 (MD5) %R 10.4171/RLM/606 %0 Journal Article %J Advances in Calculus of Variations., to appear. %D 2011 %T Fracture and plastic models as Gamma-limits of damage models under different regimes %A Flaviana Iurlano %XWe consider a variational model for damaged elastic materials. This model depends on three small parameters, which are related to the cost of the damage, to the width of the damaged regions, and to the minimum elasticity constant attained in the damaged regions. As these parameters tend to zero, our models Gamma-converge to a model for brittle fracture, for fracture with a cohesive zone, or for perfect plasticity, depending on the asymptotic ratios of the three parameters.

%B Advances in Calculus of Variations., to appear. %I Walter de Gruyter %G en %U http://hdl.handle.net/1963/5069 %1 4883 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-11-15T11:55:02Z\\r\\nNo. of bitstreams: 1\\r\\nIurlano_59M_2011.pdf: 387080 bytes, checksum: e5aab40ae643ec056bf0adc92bcaa7c8 (MD5) %R 10.1515/acv-2011-0011 %0 Journal Article %J Continuum. Mech. Therm. %D 2011 %T Gamma-convergence of energies for nematic elastomers in the small strain limit %A Virginia Agostiniani %A Antonio DeSimone %K Liquid crystals %XWe study two variational models recently proposed in the literature to describe the mechanical behaviour of nematic elastomers either in the fully nonlinear regime or in the framework of a geometrically linear theory. We show that, in the small strain limit, the energy functional of the first one I\\\"-converges to the relaxation of the second one, a functional for which an explicit representation formula is available.

%B Continuum. Mech. Therm. %I Springer %V 23 %G en %U http://hdl.handle.net/1963/4141 %1 3882 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-15T13:10:38Z\\nNo. of bitstreams: 1\\nAgost_DeSim07M.pdf: 348761 bytes, checksum: b9b69eb7da7ca6962e4a46e904646a6b (MD5) %& 257 %R 10.1007/s00161-011-0180-2 %0 Journal Article %J J. Eur. Math. Soc. (JEMS), to appear %D 2011 %T Generalised functions of bounded deformation %A Gianni Dal Maso %K free discontinuity problems, special functions of bounded deformation, jump set, rec- tifiability, slicing, approximate differentiability %XWe introduce the space GBD of generalized functions of bounded deformation and study the structure properties of these functions: the rectifiability and the slicing properties of their jump sets, and the existence of their approximate symmetric gradients. We conclude by proving a compactness results for GBD, which leads to a compactness result for the space GSBD of generalized special functions of bounded deformation. The latter is connected to the existence of solutions to a weak formulation of some variational problems arising in fracture mechanics in the framework of linearized elasticity.

%B J. Eur. Math. Soc. (JEMS), to appear %I SISSA %G en %U http://hdl.handle.net/1963/6374 %1 6309 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-10T18:54:48Z\\nNo. of bitstreams: 1\\nDM-11.pdf: 413971 bytes, checksum: eca2a953ba1b97755da281bca4e099e4 (MD5) %0 Journal Article %D 2011 %T Generalized Ricci Curvature Bounds for Three Dimensional Contact Subriemannian manifolds %A Andrei A. Agrachev %A Paul Lee %I SISSA %G en %U http://hdl.handle.net/1963/6507 %1 6454 %2 Mathematics %4 1 %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-02-27T15:07:16Z\nNo. of bitstreams: 2\n0903.2550v3.pdf: 413981 bytes, checksum: 6f08d5002703670b5985e13d642ef755 (MD5)\n0903.2550v3.pdf: 413981 bytes, checksum: 6f08d5002703670b5985e13d642ef755 (MD5) %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 Thesis %D 2011 %T Homology invariants of quadratic maps %A Antonio Lerario %X Given a real projective algebraic set X we could hope that the equations describing it can give some information on its topology, e.g. on the number of its connected components. Unfortunately in the general case this hope is too vague and there is no direct way to extract such information from the algebraic description of X: Even the problem to decide whether X is empty or not is far from an easy visualization and requires some complicated algebraic machinery. A fi rst step observation is that as long as we are interested only in the topology of X, we can replace, using some Veronese embedding, the original ambient space with a much bigger RPn and assume that X is cut by quadratic equations. The price for this is the increase of the number of equations de ning our set; the advantage is that quadratic polynomials are easier to handle and our hope becomes more concrete... %I SISSA %G en %U http://hdl.handle.net/1963/6245 %1 6145 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-09-14T09:24:43Z\\nNo. of bitstreams: 1\\nPhd_Thesis_Lerario_Antonio.pdf: 937331 bytes, checksum: f34eea56b610434e63b6f3dd1dded09c (MD5) %] 1 Basic theory. 2 Nondegeneracy conditions. 3 Spectral sequences. 4 Complex theory. 5 Applications and examples %0 Journal Article %J Nonlinear Analysis: Theory, Methods & Applications %D 2011 %T Infinitely many positive solutions for a Schrödinger–Poisson system %A Pietro d’Avenia %A Alessio Pomponio %A Giusi Vaira %K Non-autonomous Schrödinger–Poisson system %K Perturbation method %XWe are interested in the existence of infinitely many positive solutions of the Schrödinger–Poisson system −Δu+u+V(|x|)ϕu=|u|p−1u,x∈R3,−Δϕ=V(|x|)u2,x∈R3, where V(|x|) is a positive bounded function, 1<p<5 and V(r

%B Nonlinear Analysis: Theory, Methods & Applications %V 74 %P 5705 - 5721 %G eng %U http://www.sciencedirect.com/science/article/pii/S0362546X11003518 %R https://doi.org/10.1016/j.na.2011.05.057 %0 Journal Article %J Journal of Convex Analysis 18 (2011) 1141-1170 %D 2011 %T An Integro-Extremization Approach for Non Coercive and Evolution Hamilton-Jacobi Equations %A Sandro Zagatti %X We devote the \\\\textit{integro-extremization} method to the study of the Dirichlet problem for homogeneous Hamilton-Jacobi equations \\\\begin{displaymath} \\\\begin{cases} F(Du)=0 & \\\\quad \\\\textrm{in} \\\\quad\\\\O\\\\cr u(x)=\\\\varphi(x) & \\\\quad \\\\textrm{for} \\\\quad x\\\\in \\\\partial \\\\O, \\\\end{cases} \\\\end{displaymath} with a particular interest for non coercive hamiltonians $F$, and to the Cauchy-Dirichlet problem for the corresponding homogeneous time-dependent equations \\\\begin{displaymath} \\\\begin{cases} \\\\frac{\\\\partial u}{\\\\partial t}+ F(\\\\nabla u)=0 & \\\\quad \\\\textrm{in} \\\\quad ]0,T[\\\\times \\\\O\\\\cr u(0,x)=\\\\eta(x) & \\\\quad \\\\textrm{for} \\\\quad x\\\\in\\\\O \\\\cr u(t,x)=\\\\psi(x) & \\\\quad \\\\textrm{for} \\\\quad (t,x)\\\\in[0,T]\\\\times \\\\partial \\\\O. \\\\end{cases} \\\\end{displaymath} We prove existence and some qualitative results for viscosity and almost everywhere solutions, under suitably convexity conditions on the hamiltonian $F$, on the domain $\\\\O$ and on the boundary datum, without any growth assumptions on $F$. %B Journal of Convex Analysis 18 (2011) 1141-1170 %I Heldermann Verlag %G en %U http://hdl.handle.net/1963/5538 %1 5375 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-02-23T14:37:59Z\\nNo. of bitstreams: 0 %0 Journal Article %J Journal of Differential Equations 250 (2011) 1788-1827 %D 2011 %T Invariant manifolds for a singular ordinary differential equation %A Stefano Bianchini %A Laura Spinolo %B Journal of Differential Equations 250 (2011) 1788-1827 %I Elsevier %G en_US %U http://hdl.handle.net/1963/2554 %1 1565 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-01-15T10:35:53Z\\r\\nNo. of bitstreams: 1\\r\\nSissa0408M.pdf: 296248 bytes, checksum: 7563bf5d03a78a0e2c2c606a9b609827 (MD5) %R 10.1016/j.jde.2010.11.010 %0 Thesis %D 2011 %T Invariants, volumes and heat kernels in sub-Riemannian geometry %A Davide Barilari %K Sub-Riemannian geometry %X Sub-Riemannian geometry can be seen as a generalization of Riemannian geometry under non-holonomic constraints. From the theoretical point of view, sub-Riemannian geometry is the geometry underlying the theory of hypoelliptic operators (see [32, 57, 70, 92] and references therein) and many problems of geometric measure theory (see for instance [18, 79]). In applications it appears in the study of many mechanical problems (robotics, cars with trailers, etc.) and recently in modern elds of research such as mathematical models of human behaviour, quantum control or motion of self-propulsed micro-organism (see for instance [15, 29, 34])\\r\\nVery recently, it appeared in the eld of cognitive neuroscience to model the\\r\\nfunctional architecture of the area V1 of the primary visual cortex, as proposed by Petitot in [87, 86], and then by Citti and Sarti in [51]. In this context, the sub-Riemannian heat equation has been used as basis to new applications in image reconstruction (see [35]). %I SISSA %G en %U http://hdl.handle.net/1963/6124 %1 6005 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-08-08T07:49:33Z\\nNo. of bitstreams: 1\\nPhD_Thesis_Barilari.pdf: 924464 bytes, checksum: dd34c4627062993f1d72d4c7eff914e6 (MD5) %0 Journal Article %J Communication in Partial Differential Equations 36 (2011) 2062-2102 %D 2011 %T Large Time Existence for Thin Vibrating Plates %A Helmut Abels %A Maria Giovanna Mora %A Stefan Müller %X We construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence of strong solutions for large\\r\\ntimes under appropriate scaling of the initial values such that the limit system as h --> 0 is either the nonlinear von Karman plate equation or the linear fourth order Germain-Lagrange equation. In the case of the\\r\\nlinear Germain-Lagrange equation we even obtain a convergence rate of the three-dimensional solution to the solution of the two-dimensional linear plate equation. %B Communication in Partial Differential Equations 36 (2011) 2062-2102 %I Taylor & Francis %G en_US %U http://hdl.handle.net/1963/3755 %1 562 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-09-15T09:12:35Z\\r\\nNo. of bitstreams: 1\\r\\nLongTimeExistence.pdf: 331066 bytes, checksum: eba3dcbc86ddcd7b92e10fddca5964c4 (MD5) %R 10.1080/03605302.2011.618209 %0 Journal Article %J Archive for Rational Mechanics and Analysis 200 (2011) 1023-1050 %D 2011 %T The matching property of infinitesimal isometries on elliptic surfaces and elasticity on thin shells %A Marta Lewicka %A Maria Giovanna Mora %A Mohammad Reza Pakzad %X Using the notion of Γ-convergence, we discuss the limiting behavior of the three-dimensional nonlinear elastic energy for thin elliptic shells, as their thickness h converges to zero, under the assumption that the elastic energy of deformations scales like h β with 2 < β < 4. We establish that, for the given scaling regime, the limiting theory reduces to linear pure bending. Two major ingredients of the proofs are the density of smooth infinitesimal isometries in the space of W 2,2 first order infinitesimal isometries, and a result on matching smooth infinitesimal isometries with exact isometric immersions on smooth elliptic surfaces. %B Archive for Rational Mechanics and Analysis 200 (2011) 1023-1050 %I Springer %G en_US %U http://hdl.handle.net/1963/3392 %1 940 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-12-05T19:03:58Z\\r\\nNo. of bitstreams: 1\\r\\nlemopa_convex4.pdf: 284015 bytes, checksum: 201392cdf06b00dfe1026dba836582b8 (MD5) %R 10.1007/s00205-010-0387-6 %0 Journal Article %J Continuum Mechanics and Thermodynamics %D 2011 %T Metastable equilibria of capillary drops on solid surfaces: a phase field approach %A Livio Fedeli %A Turco, Alessandro %A Antonio DeSimone %XWe discuss a phase field model for the numerical simulation of metastable equilibria of capillary drops resting on rough solid surfaces and for the description of contact angle hysteresis phenomena in wetting. The model is able to reproduce observed transitions of drops on micropillars from Cassie–Baxter to Wenzel states. When supplemented with a dissipation potential which describes energy losses due to frictional forces resisting the motion of the contact line, the model can describe metastable states such as drops in equilibrium on vertical glass plates. The reliability of the model is assessed by a detailed comparison of its predictions with experimental data on the maximal size of water drops that can stick on vertical glass plates which have undergone different surface treatments.

%B Continuum Mechanics and Thermodynamics %V 23 %P 453–471 %8 Sep %G eng %U https://doi.org/10.1007/s00161-011-0189-6 %R 10.1007/s00161-011-0189-6 %0 Journal Article %J {MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES} %D 2011 %T A MODEL FOR CRACK PROPAGATION BASED ON VISCOUS APPROXIMATION %A Giuliano Lazzaroni %A Rodica Toader %K Brittle fracture %K Crack propagation %K energy derivative %K energy release rate %K free-discontinuity problems %K Griffith's criterion %K local minimizers %K stress intensity factor} %K vanishing viscosity %K {Variational models %X{In the setting of antiplane linearized elasticity, we show the existence of quasistatic evolutions of cracks in brittle materials by using a vanishing viscosity approach, thus taking into account local minimization. The main feature of our model is that the path followed by the crack need not be prescribed a priori: indeed, it is found as the limit (in the sense of Hausdorff convergence) of curves obtained by an incremental procedure. The result is based on a continuity property for the energy release rate in a suitable class of admissible cracks.}

%B {MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES} %I {WORLD SCIENTIFIC PUBL CO PTE LTD} %C {5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE} %V {21} %P {2019-2047} %8 {OCT} %G eng %9 {Article} %R {10.1142/S0218202511005647} %0 Conference Paper %B Nonlinear Conservation Laws and Applications %D 2011 %T The Monge Problem in Geodesic Spaces %A Stefano Bianchini %A Fabio Cavalletti %E Alberto Bressan %E Chen, Gui-Qiang G. %E Marta Lewicka %E Wang, Dehua %XWe address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish non branching geodesic space. We show that we can reduce the transport problem to 1-dimensional transport problems along geodesics. We introduce an assumption on the transport problem π which implies that the conditional probabilities of the first marginal on each geodesic are continuous. It is known that this regularity is sufficient for the construction of an optimal transport map.

%B Nonlinear Conservation Laws and Applications %I Springer US %C Boston, MA %P 217–233 %@ 978-1-4419-9554-4 %G eng %0 Journal Article %J Boll. Unione Mat. Ital.(9) %D 2011 %T Multiplicity of solutions for a mean field equation on compact surfaces %A Francesca De Marchis %XWe consider a scalar field equation on compact surfaces which has variational structure. When the surface is a torus and a physical parameter ρ belongs to $(8\pi, 4\pi^2 )$ we show under some extra assumptions that, as conjectured in [9], the functional admits at least three saddle points other than a local minimum.

%B Boll. Unione Mat. Ital.(9) %V 4 %P 245–257 %G eng %0 Journal Article %J Geometric and Functional Analysis 21 (2011) 1196-1217 %D 2011 %T New improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces %A Andrea Malchiodi %A David Ruiz %X We consider a singular Liouville equation on a compact surface, arising from the study of Chern-Simons vortices in a self dual regime. Using new improved versions of the Moser-Trudinger inequalities (whose main feature is to be scaling invariant) and a variational scheme, we prove new existence results. %B Geometric and Functional Analysis 21 (2011) 1196-1217 %I Springer %G en_US %U http://hdl.handle.net/1963/4099 %1 305 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-11-10T10:27:54Z\\r\\nNo. of bitstreams: 1\\r\\nMalchiodi-Ruiz-74M.pdf: 192985 bytes, checksum: 61acb10ab3cde055824228920d16987a (MD5) %R 10.1007/s00039-011-0134-7 %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 Report %D 2011 %T Nonlinear thin-walled beams with a rectangular cross-section - Part II %A Lorenzo Freddi %A Maria Giovanna Mora %A Roberto Paroni %K Thin-walled cross-section beams %X In this paper we report the second part of our results concerning the rigorous derivation of a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section.. %I SISSA %G en %U http://hdl.handle.net/1963/4169 %1 3891 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-20T13:52:25Z\\nNo. of bitstreams: 1\\nFreddi_Mora_14_M.pdf: 427788 bytes, checksum: e3682dceada2647cc7dee99102979180 (MD5) %0 Journal Article %J Duke Mathematical Journal %D 2011 %T Nonlinear wave and Schrödinger equations on compact Lie groups and homogeneous spaces %A Massimiliano Berti %A Michela Procesi %X We develop linear and nonlinear harmonic analysis on compact Lie groups and homogeneous spaces relevant for the theory of evolutionary Hamiltonian PDEs. A basic tool is the theory of the highest weight for irreducible representations of compact Lie groups. This theory provides an accurate description of the eigenvalues of the Laplace-Beltrami operator as well as the multiplication rules of its eigenfunctions. As an application, we prove the existence of Cantor families of small amplitude time-periodic solutions for wave and Schr¨odinger equations with differentiable nonlinearities. We apply an abstract Nash-Moser implicit function theorem to overcome the small divisors problem produced by the degenerate eigenvalues of the Laplace operator. We provide a new algebraic framework to prove the key tame estimates for the inverse linearized operators on Banach scales of Sobolev functions. %B Duke Mathematical Journal %V 159 %8 2011 %G eng %N 3 %& 479 %R 10.1215/00127094-1433403 %0 Journal Article %J Journal of Mathematical Analysis and Applications %D 2011 %T A note on a superlinear indefinite Neumann problem with multiple positive solutions %A Alberto Boscaggin %K Indefinite weight %K Nonlinear boundary value problems %K positive solutions %K Shooting method %XWe prove the existence of three positive solutions for the Neumann problem associated to u″+a(t)uγ+1=0, assuming that a(t) has two positive humps and ∫0Ta−(t)dt is large enough. Actually, the result holds true for a more general class of superlinear nonlinearities.

%B Journal of Mathematical Analysis and Applications %V 377 %P 259 - 268 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022247X10008796 %R https://doi.org/10.1016/j.jmaa.2010.10.042 %0 Journal Article %J Mathematical Models and Methods in Applied Sciences 21 (2011) 361-387 %D 2011 %T Numerical Strategies for Stroke Optimization of Axisymmetric Microswimmers %A François Alouges %A Antonio DeSimone %A Luca Heltai %K Optimal swimming %X We propose a computational method to solve optimal swimming problems, based on the boundary integral formulation of the hydrodynamic interaction between swimmer and surrounding fluid and direct constrained minimization of the energy consumed by the swimmer. We apply our method to axisymmetric model examples. We consider a classical model swimmer (the three-sphere swimmer of Golestanian et al.) as well as a novel axisymmetric swimmer inspired by the observation of biological micro-organisms. %B Mathematical Models and Methods in Applied Sciences 21 (2011) 361-387 %I World Scientific %G en_US %U http://hdl.handle.net/1963/3657 %1 648 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-06-23T17:30:51Z\\r\\nNo. of bitstreams: 1\\r\\nSissa33_2009M.pdf: 708341 bytes, checksum: 6134bd52f083488620fb5bb24bcf9b93 (MD5) %R 10.1142/S0218202511005088 %0 Journal Article %J Rendiconti Lincei - Matematica e Applicazioni 22 (2011) 3-15 %D 2011 %T Osservazioni sui teoremi di inversione globale %A Antonio Ambrosetti %X Some global inversion theorems with applications to semilinear elliptic equation are discussed. %B Rendiconti Lincei - Matematica e Applicazioni 22 (2011) 3-15 %I European Mathematical Society %G en_US %U http://hdl.handle.net/1963/4068 %1 334 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-09-20T10:54:19Z\\r\\nNo. of bitstreams: 1\\r\\nAmbrosetti_64M_2010.pdf: 208213 bytes, checksum: 21e1562f4cbcd9ceb8c1b8c8afe9e442 (MD5) %R 10.4171/RLM/584 %0 Report %D 2011 %T A planar bi-Lipschitz extension Theorem %A Sara Daneri %A Aldo Pratelli %G eng %U http://arxiv.org/abs/1110.6124 %0 Journal Article %J Proceedings of the American Mathematical Society 139 (2011) 4445-4459 %D 2011 %T Planar loops with prescribed curvature: existence, multiplicity and uniqueness results %A Roberta Musina %K Plane curves %B Proceedings of the American Mathematical Society 139 (2011) 4445-4459 %I American Mathematical Society %G en_US %U http://hdl.handle.net/1963/3842 %1 867 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-02-08T14:32:58Z\\r\\nNo. of bitstreams: 1\\r\\nMusina_loops.pdf: 273296 bytes, checksum: f8e3d605bca8421d5c606f9e490c911b (MD5) %R 10.1090/S0002-9939-2011-10915-8 %0 Journal Article %J Mathematische Zeitschrift 268 (2011) 371-407 %D 2011 %T A proof of Sudakov theorem with strictly convex norms %A Laura Caravenna %X We establish a solution to the Monge problem in Rn, with an asymmetric, strictly convex norm cost function, when the initial measure is absolutely continuous. We focus on the strategy, based on disintegration of measures, initially proposed by Sudakov. As known, there is a gap to fill. The missing step is completed when the unit ball is strictly convex, but not necessarily differentiable nor uniformly convex. The key disintegration is achieved following a similar proof for a variational problem. %B Mathematische Zeitschrift 268 (2011) 371-407 %I Springer %G en_US %U http://hdl.handle.net/1963/2967 %1 1733 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-24T10:14:57Z\\r\\nNo. of bitstreams: 1\\r\\nsudStrConv.pdf: 432852 bytes, checksum: 0c4df310f125711293cef790005abc33 (MD5) %R 10.1007/s00209-010-0677-6 %0 Journal Article %J Journal of the Mechanics and Physics of Solids 59 (2011) 787-803 %D 2011 %T Quasiconvex envelopes of energies for nematic elastomers in the small strain regime and applications %A Pierluigi Cesana %A Antonio DeSimone %X We provide some explicit formulas for the quasiconvex envelope of energy densities for nematic elastomers in the small strain regime and plane strain conditions. We then demonstrate their use as a powerful tool for the interpretation of mechanical experiments. %B Journal of the Mechanics and Physics of Solids 59 (2011) 787-803 %G en_US %U http://hdl.handle.net/1963/4065 %1 337 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-09-15T10:43:52Z\\r\\nNo. of bitstreams: 1\\r\\nCesana_DeSimone_62M.pdf: 1146834 bytes, checksum: 514b1b282763c0351f234702f96e73f4 (MD5) %0 Journal Article %J ESAIM: COCV 17 (2011) 1-27 %D 2011 %T Quasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a Young measures approach %A Filippo Cagnetti %A Rodica Toader %X A new approach to irreversible quasistatic fracture growth is given, by means of Young measures. The study concerns a cohesive zone model with prescribed crack path, when the material gives different responses to loading and unloading phases. In the particular situation of constant unloading response, the result contained in [6] is recovered. In this case, the convergence of the discrete time approximations is improved. %B ESAIM: COCV 17 (2011) 1-27 %I Cambridge University Press / EDP Sciences %G en_US %U http://hdl.handle.net/1963/2355 %1 1662 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-11-07T13:38:16Z\\r\\nNo. of bitstreams: 1\\r\\nQuasCrack.pdf: 298737 bytes, checksum: 127034af65efce0ab97317eccb47e76c (MD5) %R 10.1051/cocv/2009037 %0 Journal Article %J {ANNALI DI MATEMATICA PURA ED APPLICATA} %D 2011 %T Quasistatic crack growth in finite elasticity with Lipschitz data %A Giuliano Lazzaroni %K Brittle fracture %K Crack propagation %K Energy minimization %K Finite elasticity %K free-discontinuity problems %K Griffith's criterion %K Non-interpenetration} %K Polyconvexity %K Quasistatic evolution %K Rate-independent processes %K {Variational models %X{We extend the recent existence result of Dal Maso and Lazzaroni (Ann Inst H Poincare Anal Non Lineaire 27:257-290, 2010) for quasistatic evolutions of cracks in finite elasticity, allowing for boundary conditions and external forces with discontinuous first derivatives.}

%B {ANNALI DI MATEMATICA PURA ED APPLICATA} %I {SPRINGER HEIDELBERG} %C {TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY} %V {190} %P {165-194} %8 {JAN} %G eng %9 {Article} %R {10.1007/s10231-010-0145-2} %0 Journal Article %J Calculus of Variations and Partial Differential Equations 40 (2011) 125-181 %D 2011 %T Quasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling %A Gianni Dal Maso %A Antonio DeSimone %A Francesco Solombrino %K Cam-Clay plasticity %XCam-Clay nonassociative plasticity exhibits both hardening and softening behaviour, depending on the loading. For many initial data the classical formulation of the quasistatic evolution problem has no smooth solution. We propose here a notion of generalized solution, based on a viscoplastic approximation. To study the limit of the viscoplastic evolutions we rescale time, in such a way that the plastic strain is uniformly Lipschitz with respect to the rescaled time. The limit of these rescaled solutions, as the viscosity parameter tends to zero, is characterized through an energy-dissipation balance, that can be written in a natural way using the rescaled time. As shown in [4] and [6], the proposed solution may be discontinuous with respect to the original time. Our formulation allows to compute the amount of viscous dissipation occurring instantaneously at each discontinuity time.

%B Calculus of Variations and Partial Differential Equations 40 (2011) 125-181 %I Springer %G en_US %U http://hdl.handle.net/1963/3670 %1 635 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-07-20T08:26:03Z\\r\\nNo. of bitstreams: 1\\r\\nDM-DeS-Sol-36_2009_preprint.pdf: 421582 bytes, checksum: 011806364200378d6deec80b88978550 (MD5) %R 10.1007/s00526-010-0336-0 %0 Journal Article %J Arch. Rational Mech. Anal. 202 (2011) 295-348 %D 2011 %T Quasistatic evolution of sessile drops and contact angle hysteresis %A Giovanni Alberti %A Antonio DeSimone %X We consider the classical model of capillarity coupled with a rate-independent dissipation mechanism due to frictional forces acting on the contact line, and prove the existence of quasistatic evolutions with prescribed initial configuration. We also discuss in detail some explicit solutions to show that the model does account for contact angle hysteresis, and to compare its predictions with experimental observations. %B Arch. Rational Mech. Anal. 202 (2011) 295-348 %I Springer %G en %U http://hdl.handle.net/1963/4912 %1 4693 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-25T09:46:50Z\\nNo. of bitstreams: 1\\ngads2.pdf: 620848 bytes, checksum: f5fef67c4e88cd294016f704c59394bd (MD5) %R 10.1007/s00205-011-0427-x %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 Arch. Rational Mech. Anal. 200 (2011) 1003-1021 %D 2011 %T SBV regularity for Hamilton-Jacobi equations in R^n %A Stefano Bianchini %A Camillo De Lellis %A Roger Robyr %XIn this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$ \partial_t u + H(D_{x} u)=0 \qquad \textrm{in}\quad \Omega\subset \mathbb{R}\times \mathbb{R}^{n} . $$ In particular, under the assumption that the Hamiltonian $H\in C^2(\mathbb{R}^n)$ is uniformly convex, we prove that $D_{x}u$ and $\partial_t u$ belong to the class $SBV_{loc}(\Omega)$.

%B Arch. Rational Mech. Anal. 200 (2011) 1003-1021 %I Springer %G en %U http://hdl.handle.net/1963/4911 %1 4695 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-25T10:18:41Z\\nNo. of bitstreams: 1\\n1002.4087v1.pdf: 272486 bytes, checksum: 551dab603b0252ec9c22800b33360d02 (MD5) %R 10.1007/s00205-010-0381-z %0 Journal Article %J Indiana Univ. Math. J. 60 (2011) 367-409 %D 2011 %T Singular perturbation models in phase transitions for second order materials %A Milena Chermisi %A Gianni Dal Maso %A Irene Fonseca %A Giovanni Leoni %X A variational model proposed in the physics literature to describe the onset of pattern formation in two-component bilayer membranes and amphiphilic monolayers leads to the analysis of a Ginzburg-Landau type energy with a negative term depending on the first derivative of the phase function. Scaling arguments motivate the study of the family of second order singular perturbed energies Fe having a negative term depending on the first derivative of the phase function. Here, the asymptotic behavior of {Fe} is studied using G-convergence techniques. In particular, compactness results and an integral representation of the limit energy are obtained. %B Indiana Univ. Math. J. 60 (2011) 367-409 %I Indiana University %G en_US %U http://hdl.handle.net/1963/3858 %1 851 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-04-27T10:47:12Z\\r\\nNo. of bitstreams: 1\\r\\nCheDMaFonLeo_2010.pdf: 350746 bytes, checksum: b384a4d0b82dd9713e1849ad3ef6a2be (MD5) %R 10.1512/iumj.2011.60.4346 %0 Journal Article %J Functional Analysis and its Applications, Volume 45, Issue 4, December 2011, Pages 241-251 %D 2011 %T On the Space of Symmetric Operators with Multiple Ground States %A Andrei A. Agrachev %K Multiple eigenvalue %X We study homological structure of the filtrations of the spaces of self-adjoint operators by the multiplicity of the ground state. We consider only operators acting in a finite dimensional complex or real Hilbert space but infinite dimensional generalizations are easily guessed. %B Functional Analysis and its Applications, Volume 45, Issue 4, December 2011, Pages 241-251 %I SISSA %G en %U http://hdl.handle.net/1963/7069 %1 6392 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-09-16T09:28:52Z No. of bitstreams: 1 1107.3010v2.pdf: 187825 bytes, checksum: 3e6e04aeadc87e130c87ada77fe862a1 (MD5) %R DOI: 10.1007/s10688-011-0026-5 %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 Report %D 2011 %T Structure of level sets and Sard-type properties of Lipschitz maps %A Giovanni Alberti %A Stefano Bianchini %A Gianluca Crippa %I SISSA %G en %U http://hdl.handle.net/1963/4657 %1 4424 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-10-10T12:07:33Z\\nNo. of bitstreams: 1\\nAlberti_Bianchini_Crippa_51_M.pdf: 361735 bytes, checksum: b3f27bce1ab515dca94a6ad93d822160 (MD5) %0 Journal Article %J Advanced Nonlinear Studies %D 2011 %T Subharmonic solutions of planar Hamiltonian systems: a rotation number approach %A Alberto Boscaggin %B Advanced Nonlinear Studies %I Advanced Nonlinear Studies, Inc. %V 11 %P 77–103 %G eng %R 10.1515/ans-2011-0104 %0 Journal Article %J Le Matematiche %D 2011 %T Subharmonic solutions of planar Hamiltonian systems via the Poincaré́-Birkhoff theorem %A Alberto Boscaggin %XWe revisit some recent results obtained in [1] about the existence of subharmonic solutions for a class of (nonautonomous) planar Hamiltonian systems, and we compare them with the existing literature. New applications to undamped second order equations are discussed, as well.

%B Le Matematiche %V 66 %P 115–122 %G eng %0 Journal Article %J Int Math Res Notices (2011) 2011 (24): 5625-5643 %D 2011 %T Supercritical conformal metrics on surfaces with conical singularities %A Mauro Bardelloni %A Francesca De Marchis %A Andrea Malchiodi %XWe study the problem of prescribing the Gaussian curvature on surfaces with conical singularities in supercritical regimes. Using a Morse-theoretical approach we prove a general existence theorem on surfaces with positive genus, with a generic multiplicity result.

%B Int Math Res Notices (2011) 2011 (24): 5625-5643 %I Oxford University Press %G en_US %U http://hdl.handle.net/1963/4095 %1 309 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-10-26T07:12:29Z\\r\\nNo. of bitstreams: 1\\r\\nBarDemMal-56M.pdf: 317906 bytes, checksum: 6b2dc3222c15d6690b75440300fa4aed (MD5) %R 10.1093/imrn/rnq285 %0 Report %D 2011 %T Thin-walled beams with a cross-section of arbitrary geometry: derivation of linear theories starting from 3D nonlinear elasticity %A Elisa Davoli %XThe subject of this paper is the rigorous derivation of lower dimensional models for a nonlinearly elastic thin-walled beam whose cross-section is given by a thin tubular neighbourhood of a smooth curve. Denoting by h and δ_h, respectively, the diameter and the thickness of the cross-section, we analyse the case where the scaling factor of the elastic energy is of order ε_h^2, with ε_h/δ_h^2 \rightarrow l \in [0, +\infty). Different linearized models are deduced according to the relative order of magnitude of δ_h with respect to h.

%G eng %0 Journal Article %J Calculus of Variations and Partial Differential Equations 41 (2011) 241-259 %D 2011 %T The time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity %A Helmut Abels %A Maria Giovanna Mora %A Stefan Müller %X The asymptotic behaviour of the solutions of three-dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness $h$ of the plate tends to zero. Under appropriate scalings of the applied force and of the initial values in terms of $h$, it is shown that three-dimensional solutions of the nonlinear elastodynamic equation converge to solutions of the time-dependent von K\\\\\\\'arm\\\\\\\'an plate equation. %B Calculus of Variations and Partial Differential Equations 41 (2011) 241-259 %I Springer %G en_US %U http://hdl.handle.net/1963/3835 %1 492 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-01-26T16:49:12Z\\r\\nNo. of bitstreams: 1\\r\\n0912.4135v1.pdf: 217528 bytes, checksum: 4ee557860670b3d876174b2e053958e4 (MD5) %R 10.1007/s00526-010-0360-0 %0 Journal Article %J Nonlinear Analysis: Theory, Methods & Applications %D 2011 %T Uniqueness and nondegeneracy of the ground state for a quasilinear Schrödinger equation with a small parameter %A Alessandro Selvitella %K Bifurcation theory %K Nonlinear Schrödinger equations %K Stationary solutions %XWe study least energy solutions of a quasilinear Schrödinger equation with a small parameter. We prove that the ground state is nondegenerate and unique up to translations and phase shifts using bifurcation theory.

%B Nonlinear Analysis: Theory, Methods & Applications %V 74 %P 1731 - 1737 %G eng %U http://www.sciencedirect.com/science/article/pii/S0362546X10007613 %R https://doi.org/10.1016/j.na.2010.10.045 %0 Report %D 2011 %T A uniqueness result for the continuity equation in two dimensions %A Giovanni Alberti %A Stefano Bianchini %A Gianluca Crippa %I SISSA %G en %U http://hdl.handle.net/1963/4663 %1 4425 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-10-10T12:10:26Z\\nNo. of bitstreams: 1\\nAlberti_Bianchini_Crippa_52M.pdf: 318780 bytes, checksum: 556a1d21b44c58d90201b25b2c104744 (MD5) %0 Journal Article %J Journal de Mathématiques Pures et Appliquées %D 2011 %T The well-posedness issue for the density-dependent Euler equations in endpoint Besov spaces %A Raphaël Danchin %A Francesco Fanelli %K Blow-up criterion %K Critical regularity %K Incompressible Euler equations %K Lifespan %K Nonhomogeneous inviscid fluids %XThis work is the continuation of the recent paper (Danchin, 2010) [9] devoted to the density-dependent incompressible Euler equations. Here we concentrate on the well-posedness issue in Besov spaces of type B∞,rs embedded in the set of Lipschitz continuous functions, a functional framework which contains the particular case of Hölder spaces C1,α and of the endpoint Besov space B∞,11. For such data and under the non-vacuum assumption, we establish the local well-posedness and a continuation criterion in the spirit of that of Beale, Kato and Majda (1984) [2]. In the last part of the paper, we give lower bounds for the lifespan of a solution. In dimension two, we point out that the lifespan tends to infinity when the initial density tends to be a constant. This is, to our knowledge, the first result of this kind for the density-dependent incompressible Euler equations. Résumé Ce travail complète lʼarticle récent (Danchin, 2010) [9] consacré au système dʼEuler incompressible à densité variable. Lorsque lʼétat initial ne comporte pas de vide, on montre ici que le système est bien posé dans tous les espaces de Besov B∞,rs inclus dans lʼensemble des fonctions lipschitziennes. Ce cadre fonctionnel contient en particulier les espaces de Hölder C1,α et lʼespace de Besov limite B∞,11. On établit également un critère de prolongement dans lʼesprit de celui de Beale, Kato et Majda (1984) [2] pour le cas homogène. Dans la dernière partie de lʼarticle, on donne des minorations pour le temps de vie des solutions du système. En dimension deux, on montre que ce temps de vie tend vers lʼinfini lorsque la densité tend à être homogène. À notre connaissance, il sʼagit du premier résultat de ce type pour le système dʼEuler incompressible à densité variable.

%B Journal de Mathématiques Pures et Appliquées %V 96 %P 253 - 278 %G eng %U http://www.sciencedirect.com/science/article/pii/S0021782411000511 %R https://doi.org/10.1016/j.matpur.2011.04.005 %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 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 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 Calculus of Variations and Partial Differential Equations. Volume 39, Issue 1, 2010, Pages 213-232 %D 2010 %T Continuity of optimal control costs and its application to weak KAM theory %A Andrei A. Agrachev %A Paul Lee %X We prove continuity of certain cost functions arising from optimal control of\\r\\naffine control systems. We give sharp sufficient conditions for this\\r\\ncontinuity. As an application, we prove a version of weak KAM theorem and\\r\\nconsider the Aubry-Mather problems corresponding to these systems. %B Calculus of Variations and Partial Differential Equations. Volume 39, Issue 1, 2010, Pages 213-232 %I SISSA %G en %U http://hdl.handle.net/1963/6459 %1 6405 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-02-05T14:56:31Z\\nNo. of bitstreams: 1\\n0909.3826v2.pdf: 264638 bytes, checksum: 5f13730dcb51f57d19a692ea1d6c48c6 (MD5) %R 10.1007/s00526-010-0308-4 %0 Report %D 2010 %T Convergence of equilibria of thin elastic rods under physical growth conditions for the energy density %A Elisa Davoli %A Maria Giovanna Mora %X The subject of this paper is the study of the asymptotic behaviour of the equilibrium configurations of a nonlinearly elastic thin rod, as the diameter of the cross-section tends to zero. Convergence results are established assuming physical growth conditions for the elastic energy density and suitable scalings of the applied loads, that correspond at the limit to different rod models: the constrained linear theory, the analogous of von Kármán plate theory for rods, and the linear theory. %G en_US %U http://hdl.handle.net/1963/4086 %1 317 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-10-05T08:49:01Z\\nNo. of bitstreams: 1\\nDavoli-Mora_67M_2010.pdf: 243056 bytes, checksum: 8542ff47b9dc1ae7275fe95bc296a870 (MD5) %0 Journal Article %J J. Funct. Anal. 258 (2010) 3604-3661 %D 2010 %T The disintegration of the Lebesgue measure on the faces of a convex function %A Laura Caravenna %A Sara Daneri %XWe consider the disintegration of the Lebesgue measure on the graph of a convex function f:\\\\Rn-> \\\\R w.r.t. the partition into its faces, which are convex sets and therefore have a well defined linear dimension, and we prove that each conditional measure is equivalent to the k-dimensional Hausdorff measure of the k-dimensional face on which it is concentrated. The remarkable fact is that a priori the directions of the faces are just Borel and no Lipschitz regularity is known. Notwithstanding that, we also prove that a Green-Gauss formula for these directions holds on special sets.

%B J. Funct. Anal. 258 (2010) 3604-3661 %G en_US %U http://hdl.handle.net/1963/3622 %1 682 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-04-24T15:53:31Z\\nNo. of bitstreams: 1\\ndisconvCaravDaneri.pdf: 759110 bytes, checksum: e22e069339fc07c3bde1855b76e61d1e (MD5) %R 10.1016/j.jfa.2010.01.024 %0 Journal Article %J Journal of Dynamical and Control Systems. Volume 16, Issue 2, April 2010, Pages :149-162 %D 2010 %T Dynamics control by a time-varying feedback %A Andrei A. Agrachev %A Marco Caponigro %K Discrete-time dynamics %X We consider a smooth bracket generating control-affine system in R^d and show that any orientation preserving diffeomorphism of R^d can be approximated, in the very strong sense, by a diffeomorphism included in the flow generated by a time-varying feedback control which is polynomial with respect to the state variables and trigonometric-polynomial with respect to the time variable. %B Journal of Dynamical and Control Systems. Volume 16, Issue 2, April 2010, Pages :149-162 %I SISSA %G en %U http://hdl.handle.net/1963/6461 %1 6407 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-02-06T09:37:23Z (GMT) No. of bitstreams: 0 %R 10.1007/s10883-010-9087-7 %0 Journal Article %J SIAM J. Math. Anal. 42 (2010) 1179-1217 %D 2010 %T Estimates on path functionals over Wasserstein Spaces %A Stefano Bianchini %A Alessio Brancolini %X In this paper we consider the class a functionals (introduced in [Brancolini, Buttazzo, and Santambrogio, J. Eur. Math. Soc. (JEMS), 8 (2006), pp. 415-434] $\\\\mathcal{G}_{r,p}$ defined on Lipschitz curves $\\\\gamma$ valued in the $p$-Wasserstein space. The problem considered is the following: given a measure $\\\\mu$, give conditions in order to assure the existence of a curve $\\\\gamma$ such that $\\\\gamma(0)=\\\\mu$, $\\\\gamma(1)=\\\\delta_{x_0}$, and $\\\\mathcal{G}_{r,p}(\\\\gamma)<+\\\\infty$. To this end, new estimates on $\\\\mathcal{G}_{r,p}(\\\\mu)$ are given, and a notion of dimension of a measure (called path dimension) is introduced: the path dimension specifies the values of the parameters $(r,p)$ for which the answer to the previous reachability problem is positive. Finally, we compare the path dimension with other known dimensions. %B SIAM J. Math. Anal. 42 (2010) 1179-1217 %G en_US %U http://hdl.handle.net/1963/3583 %1 717 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-03-09T09:05:25Z\\nNo. of bitstreams: 1\\nestimates_path_functionals.prerint.pdf: 356623 bytes, checksum: 6bc99a8752ef3aae9d1b91d05e8a2f8e (MD5) %R 10.1137/100782693 %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 Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 1291-1331 %D 2010 %T Exact reconstruction of damaged color images using a total variation model %A Irene Fonseca %A Giovanni Leoni %A Francesco Maggi %A Massimiliano Morini %X In this paper the reconstruction of damaged piecewice constant color images is studied using a RGB total variation based model for colorization/inpainting. In particular, it is shown that when color is known in a uniformly distributed region, then reconstruction is possible with maximal fidelity. %B Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 1291-1331 %I Elsevier %G en_US %U http://hdl.handle.net/1963/4039 %1 363 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-09-06T09:54:56Z\\nNo. of bitstreams: 1\\nflmm.pdf: 434739 bytes, checksum: f315d8807349e077c524fe14a1619a56 (MD5) %R 10.1016/j.anihpc.2010.06.004 %0 Journal Article %J Proc. Steklov Inst. Math. 270 (2010) 43-56 %D 2010 %T Existence of planar curves minimizing length and curvature %A Ugo Boscain %A Grégoire Charlot %A Francesco Rossi %X In this paper we consider the problem of reconstructing a curve that is partially hidden or corrupted by minimizing the functional $\\\\int \\\\sqrt{1+K_\\\\gamma^2} ds$, depending both on length and curvature $K$. We fix starting and ending points as well as initial and final directions.\\nFor this functional we discuss the problem of existence of minimizers on various functional spaces. We find non-existence of minimizers in cases in which initial and final directions are considered with orientation. In this case, minimizing sequences of trajectories can converge to curves with angles.\\nWe instead prove existence of minimizers for the \\\"time-reparameterized\\\" functional $$\\\\int \\\\| \\\\dot\\\\gamma(t) \\\\|\\\\sqrt{1+K_\\\\ga^2} dt$$ for all boundary conditions if initial and final directions are considered regardless to orientation. In this case, minimizers can present cusps (at most two) but not angles. %B Proc. Steklov Inst. Math. 270 (2010) 43-56 %I Springer %G en_US %U http://hdl.handle.net/1963/4107 %1 297 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-12-06T13:30:01Z\\nNo. of bitstreams: 1\\n0906.5290v2.pdf: 305594 bytes, checksum: 3966f5a798b69743ce88a29bf73edc47 (MD5) %R 10.1134/S0081543810030041 %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 Journal of Functional Analysis %D 2010 %T Generic multiplicity for a scalar field equation on compact surfaces %A Francesca De Marchis %K Generic multiplicity %K Geometric PDE's %K Morse inequalities %K Scalar field equations %XWe prove generic multiplicity of solutions for a scalar field equation on compact surfaces via Morse inequalities. In particular our result improves significantly the multiplicity estimate which can be deduced from the degree-counting formula in Chen and Lin (2003) [12]. Related results are derived for the prescribed Q-curvature equation.

%B Journal of Functional Analysis %V 259 %P 2165 - 2192 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022123610002697 %R https://doi.org/10.1016/j.jfa.2010.07.003 %0 Journal Article %J Discrete & Continuous Dynamical Systems-A %D 2010 %T A global compactness result for the p-Laplacian involving critical nonlinearities %A Mercuri, Carlo %A Willem, Michel %XWe prove a representation theorem for Palais-Smale sequences involving the p-Laplacian and critical nonlinearities. Applications are given to a critical problem.

%B Discrete & Continuous Dynamical Systems-A %V 28 %P 469–493 %G eng %U http://www.aimsciences.org/journals/displayArticles.jsp?paperID=5097 %R 10.3934/dcds.2010.28.469 %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 %X

Many-body states whose wave-function admits a representation in terms of a uniform binary-tree tensor decomposition are shown to obey to power-law two-body correlations functions. Any such state can be associated with the ground state of a translational invariant Hamiltonian which, depending on the dimension of the systems sites, involve at most couplings between third-neighboring sites. A detailed analysis of their spectra shows that they admit an exponentially large ground space.

%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 Adv. Calc. Var. 3 (2010) 345-370 %D 2010 %T Homogenization of fiber reinforced brittle material: the intermediate case %A Gianni Dal Maso %A Caterina Ida Zeppieri %X We derive a cohesive fracture model by homogenizing a periodic composite material whose microstructure is characterized by the presence of brittle inclusions in a reticulated unbreakable elastic structure. %B Adv. Calc. Var. 3 (2010) 345-370 %I Walter de Gruyter %G en_US %U http://hdl.handle.net/1963/3607 %1 694 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-04-02T10:43:00Z\\r\\nNo. of bitstreams: 1\\r\\nDM-Zep.pdf: 294507 bytes, checksum: 5ba95ca12abb15953a564aeedf353087 (MD5) %R 10.1515/ACV.2010.011 %0 Journal Article %J Russian Mathematical Surveys. Volume 65, Issue 5, 2010, Pages: 977-978 %D 2010 %T Invariant Lagrange submanifolds of dissipative systems %A Andrei A. Agrachev %X We study solutions of modified Hamilton-Jacobi equations H(du/dq,q) + cu(q) =\\r\\n0, q \\\\in M, on a compact manifold M . %B Russian Mathematical Surveys. Volume 65, Issue 5, 2010, Pages: 977-978 %I SISSA %G en %U http://hdl.handle.net/1963/6457 %1 6403 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-02-05T14:35:25Z\\nNo. of bitstreams: 1\\n0912.2248v2.pdf: 74166 bytes, checksum: 6c6c803e56c96e455631b40eb7ef91b5 (MD5) %R 10.1070/RM2010v065n05ABEH004707 %0 Thesis %B Università degli Studi di Trieste and SISSA %D 2010 %T New approximation results for free discontinuity problems %A Flaviana Iurlano %B Università degli Studi di Trieste and SISSA %G eng %9 Master's thesis %0 Journal Article %J Adv. Calc. Var. 3 (2010) 287-319 %D 2010 %T Nonlocal character of the reduced theory of thin films with higher order perturbations %A Gianni Dal Maso %A Irene Fonseca %A Giovanni Leoni %B Adv. Calc. Var. 3 (2010) 287-319 %G en_US %U http://hdl.handle.net/1963/3754 %1 563 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-09-15T09:06:42Z\\nNo. of bitstreams: 1\\nDM-Fon-Leo.pdf: 288658 bytes, checksum: 7815e9376b53eb044b2fb2b57cd49b53 (MD5) %R 10.1515/ACV.2010.012, /July/2010 %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 On the number of positive solutions of some semilinear elliptic problems %A Antonio Ambrosetti %G en_US %U http://hdl.handle.net/1963/4083 %1 320 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-10-04T09:32:44Z\\nNo. of bitstreams: 1\\nAmbrosetti_66M_2010.pdf: 141739 bytes, checksum: c56d5c17199fdefcd3d62c0b2da958a1 (MD5) %0 Journal Article %J Comptes Rendus Mathematique 348 (2010) 613-618 %D 2010 %T On optimality of c-cyclically monotone transference plans %A Stefano Bianchini %A Laura Caravenna %X Abstract. This note deals with the equivalence between the optimality of a transport plan for the Monge-Kantorovich problem and the condition of c-cyclical monotonicity, as an outcome of the construction in [7]. We emphasize the measurability assumption on the hidden structure of linear preorder, applied also to extremality and uniqueness problems. Resume. Dans la presente note nous decrivons brievement la construction introduite dans [7] a propos de l\\\'equivalence entre l\\\'optimalite d\\\'un plan de transport pour le probleme de Monge-Kantorovich et la condition de monotonie c-cyclique ainsi que d\\\'autres sujets que cela nous amene a aborder. Nous souhaitons mettre en evidence l\\\'hypothese de mesurabilite sur la structure sous-jacente de pre-ordre lineaire. %B Comptes Rendus Mathematique 348 (2010) 613-618 %I Elsevier %G en_US %U http://hdl.handle.net/1963/4023 %1 379 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-09-02T09:13:11Z\\nNo. of bitstreams: 1\\ncmonoNoteCRM.pdf: 154086 bytes, checksum: f2efc74ccfedd2e335ff99ff279b5cfd (MD5) %R 10.1016/j.crma.2010.03.022 %0 Report %D 2010 %T Optimally swimming Stokesian Robots %A François Alouges %A Antonio DeSimone %A Luca Heltai %A Aline Lefebvre %A Benoit Merlet %X We study self propelled stokesian robots composed of assemblies of balls, in dimen-\\nsions 2 and 3, and prove that they are able to control their position and orientation. This is a result of controllability, and its proof relies on applying Chow\\\'s theorem in an analytic framework, similarly to what has been done in [3] for an axisymmetric system swimming along the axis of symmetry. However, we simplify drastically\\nthe analyticity result given in [3] and apply it to a situation where more complex swimmers move either in a plane or in three-dimensional space, hence experiencing also rotations. We then focus our attention on energetically optimal strokes, which we are able to compute numerically. Some examples of computed optimal strokes are discussed in detail. %G en_US %U http://hdl.handle.net/1963/3929 %1 472 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-07-29T11:02:56Z\\nNo. of bitstreams: 1\\nHeltai_54M_2010.pdf: 993075 bytes, checksum: 77225380bab031438ac940e694ea0e6c (MD5) %0 Conference Paper %B IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials %D 2010 %T A Phase Field Approach to Wetting and Contact Angle Hysteresis Phenomena %A Antonio DeSimone %A Livio Fedeli %A Turco, Alessandro %E Hackl, Klaus %XWe discuss a phase field model for the numerical simulation of contact angle hysteresis phenomena in wetting. The performance of the model is assessed by comparing its predictions with experimental data on the critical size of drops that can stick on a vertical glass plate.

%B IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials %I Springer Netherlands %C Dordrecht %P 51–63 %@ 978-90-481-9195-6 %G eng %0 Journal Article %J Nonlinearity. vol. 23, (2010), page 2501-2507 %D 2010 %T Poles of Integrale Tritronquee and Anharmonic Oscillators. Asymptotic localization from WKB analysis %A Davide Masoero %XPoles of integrale tritronquee are in bijection with cubic oscillators that admit the simultaneous solutions of two quantization conditions. We show that the poles lie near the solutions of a pair of Bohr-Sommerfeld quantization conditions (the Bohr-Sommerfeld-Boutroux system): the distance between a pole and the corresponding solution of the Bohr-Sommerfeld-Boutroux system vanishes asymptotically.

%B Nonlinearity. vol. 23, (2010), page 2501-2507 %G en_US %U http://hdl.handle.net/1963/3841 %1 486 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-02-05T13:17:03Z No. of bitstreams: 1 1002.1042v1.pdf: 166705 bytes, checksum: eebb138b8560474f3bc975c18b76da51 (MD5) %R 10.1088/0951-7715/23/10/008 %0 Journal Article %J Journal of Differential Equations %D 2010 %T Positive solutions for some non-autonomous Schrödinger–Poisson systems %A Giovanna Cerami %A Giusi Vaira %B Journal of Differential Equations %I Academic Press %V 248 %P 521–543 %G eng %0 Journal Article %J ESAIM COCV 16 (2010) 275-297 %D 2010 %T Projective Reeds-Shepp car on $S^2$ with quadratic cost %A Ugo Boscain %A Francesco Rossi %X Fix two points $x,\\\\bar{x}\\\\in S^2$ and two directions (without orientation) $\\\\eta,\\\\bar\\\\eta$ of the velocities in these points. In this paper we are interested to the problem of minimizing the cost $$ J[\\\\gamma]=\\\\int_0^T g_{\\\\gamma(t)}(\\\\dot\\\\gamma(t),\\\\dot\\\\gamma(t))+\\nK^2_{\\\\gamma(t)}g_{\\\\gamma(t)}(\\\\dot\\\\gamma(t),\\\\dot\\\\gamma(t)) ~dt$$ along all smooth curves starting from $x$ with direction $\\\\eta$ and ending in $\\\\bar{x}$ with direction $\\\\bar\\\\eta$. Here $g$ is the standard Riemannian metric on $S^2$ and $K_\\\\gamma$ is the corresponding geodesic curvature.\\nThe interest of this problem comes from mechanics and geometry of vision. It can be formulated as a sub-Riemannian problem on the lens space L(4,1).\\nWe compute the global solution for this problem: an interesting feature is that some optimal geodesics present cusps. The cut locus is a stratification with non trivial topology. %B ESAIM COCV 16 (2010) 275-297 %G en_US %U http://hdl.handle.net/1963/2668 %1 1429 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-06-11T11:22:54Z\\nNo. of bitstreams: 1\\n0805.4800v1.pdf: 610220 bytes, checksum: b0fa81a60fc43e6da6a4682e91b4d21e (MD5) %R 10.1051/cocv:2008075 %0 Journal Article %J Arch. Ration. Mech. Anal. 196 (2010) 867-906 %D 2010 %T Quasistatic crack growth in elasto-plastic materials: the two-dimensional case %A Gianni Dal Maso %A Rodica Toader %X We study a variational model for the quasistatic evolution of elasto-plastic materials with cracks in the case of planar small strain associative elasto-plasticity. %B Arch. Ration. Mech. Anal. 196 (2010) 867-906 %G en_US %U http://hdl.handle.net/1963/2964 %1 1736 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-23T17:17:34Z\\nNo. of bitstreams: 1\\nDM-Toa-07-preprint.pdf: 320979 bytes, checksum: e4f2a1856f9bd91d63fc45557cbd6a16 (MD5) %R 10.1007/s00205-009-0258-1 %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 257-290 %D 2010 %T Quasistatic crack growth in finite elasticity with non-interpenetration %A Gianni Dal Maso %A Giuliano Lazzaroni %XWe present a variational model to study the quasistatic growth of brittle cracks in hyperelastic materials, in the framework of finite elasticity, taking\\ninto account the non-interpenetration condition.

%B Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 257-290 %G en_US %U http://hdl.handle.net/1963/3397 %1 935 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-12-15T09:16:46Z\\nNo. of bitstreams: 1\\nDM-Laz-08pre.pdf: 360778 bytes, checksum: 14a35b4647fde0ea0931df8ae6cbfb73 (MD5) %R 10.1016/j.anihpc.2009.09.006 %0 Journal Article %J Netw. Heterog. Media 5 (2010) 97-132 %D 2010 %T Quasistatic evolution for Cam-Clay plasticity: the spatially homogeneous case %A Gianni Dal Maso %A Francesco Solombrino %K Cam-Clay plasticity %XWe study the spatially uniform case of the problem of quasistatic evolution in small strain nonassociative elastoplasticity (Cam-Clay model). Through the introdution of a viscous approximation, the problem reduces to determine the limit behavior of the solutions of a singularly perturbed system of ODE\\\'s in a finite dimensional Banach space. Depending on the sign of two explicit scalar indicators, we see that the limit dynamics presents, under quite generic assumptions, the alternation of three possible regimes: the elastic regime, when the limit equation is just the equation of linearized elasticity, the slow dynamics, when the strain evolves smoothly on the yield surface and plastic flow is produced, and the fast dynamics, which may happen only in the softening regime, where\\nviscous solutions exhibit a jump across a heteroclinic orbit of an auxiliary system.

%B Netw. Heterog. Media 5 (2010) 97-132 %G en_US %U http://hdl.handle.net/1963/3671 %1 634 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-07-20T08:35:17Z\\nNo. of bitstreams: 1\\nDM-Sol2-39_2009_preprint.pdf: 345995 bytes, checksum: 073ce622e3320be1f56a1cc9f8904fae (MD5) %R 10.3934/nhm.2010.5.97 %0 Journal Article %J Discrete & Continuous Dynamical Systems - A %D 2010 %T Quasistatic evolution for plasticity with softening: The spatially homogeneous case %A Francesco Solombrino %K plasticity with softening %K rate independent processes %XThe spatially uniform case of the problem of quasistatic evolution in small strain associative elastoplasticity with softening is studied. Through the introdution of a viscous approximation, the problem reduces to determine the limit behaviour of the solutions of a singularly perturbed system of ODE's in a finite dimensional Banach space. We see that the limit dynamics presents, for a generic choice of the initial data, the alternation of three possible regimes (elastic regime, slow dynamics, fast dynamics), which is determined by the sign of two scalar indicators, whose explicit expression is given.

%B Discrete & Continuous Dynamical Systems - A %V 27 %P 1189 %G eng %U http://aimsciences.org//article/id/4c2301d8-f553-493e-b672-b4f76a3ede2f %R 10.3934/dcds.2010.27.1189 %0 Report %D 2010 %T The role of membrane viscosity in the dynamics of fluid membranes %A Marino Arroyo %A Antonio DeSimone %A Luca Heltai %X Fluid membranes made out of lipid bilayers are the fundamental separation structure in eukaryotic cells. Many physiological processes rely on dramatic shape and topological changes (e.g. fusion, fission) of fluid membrane systems. Fluidity is key to the versatility and constant reorganization of lipid bilayers. Here, we study the role of the membrane intrinsic viscosity, arising from the friction of the lipid molecules as they rearrange to accommodate shape changes, in the dynamics of morphological changes of fluid vesicles. In particular, we analyze the competition between the membrane viscosity and the viscosity of the bulk fluid surrounding the vesicle as the dominant dissipative mechanism. We consider the relaxation dynamics of fluid vesicles put in an out-of-equilibrium state, but conclusions can be drawn regarding the kinetics or power consumption in regulated shape changes in the cell. On the basis of numerical calculations, we find that the dynamics arising from the membrane viscosity are qualitatively different from the dynamics arising from the bulk viscosity. When these two dissipation mechanisms are put in competition, we find that for small vesicles the membrane dissipation dominates, with a relaxation time that scales as the size of the vesicle to the power 2. For large vesicles, the bulk dissipation dominates, and the exponent in the relaxation time vs. size relation is 3. %G en_US %U http://hdl.handle.net/1963/3930 %1 471 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-07-29T11:13:35Z\\nNo. of bitstreams: 1\\nArroyo_55M.pdf: 4419667 bytes, checksum: ca8a9c175a457ad33996d46a08e85e44 (MD5) %0 Journal Article %J Adv. Differential Equations %D 2010 %T Semiclassical evolution of two rotating solitons for the Nonlinear Schrödinger Equation with electric potential %A Alessandro Selvitella %B Adv. Differential Equations %I Khayyam Publishing, Inc. %V 15 %P 315–348 %8 03 %G eng %U https://projecteuclid.org:443/euclid.ade/1355854752 %0 Report %D 2010 %T Sharp nonexistence results for a linear elliptic inequality involving Hardy and Leray potentials %A Mouhamed Moustapha Fall %A Roberta Musina %X In this paper we deal with nonnegative distributional supersolutions for a class of linear\\nelliptic equations involving inverse-square potentials and logarithmic weights. We prove sharp nonexistence results. %G en_US %U http://hdl.handle.net/1963/3869 %1 840 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-05-28T10:38:12Z\\nNo. of bitstreams: 1\\nFall_Musina_2010.pdf: 232933 bytes, checksum: cfcad2e3f6d3120912888f823d290d5c (MD5) %0 Journal Article %J Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. IX (2010) 253-295 %D 2010 %T Shell theories arising as low energy Gamma-limit of 3d nonlinear elasticity %A Marta Lewicka %A Maria Giovanna Mora %A Mohammad Reza Pakzad %X We discuss the limiting behavior (using the notion of gamma-limit) of the 3d nonlinear elasticity for thin shells around an arbitrary smooth 2d surface. In particular, under the assumption that the elastic energy of deformations scales like h4, h being the thickness of a shell, we derive a limiting theory which is a generalization of the von Karman theory for plates. %B Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. IX (2010) 253-295 %G en_US %U http://hdl.handle.net/1963/2601 %1 1521 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-03-11T11:36:01Z\\nNo. of bitstreams: 1\\nLewMorPak08.pdf: 342797 bytes, checksum: 4293029876d53186e1ecce89c98e5c0c (MD5) %R 10.2422/2036-2145.2010.2.02 %0 Journal Article %J Inverse Problems %D 2010 %T Stable determination of an immersed body in a stationary Stokes fluid %A Andrea Ballerini %XWe consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the Stokes equations, from a single measurement of force and velocity on a portion of the boundary. We obtain an estimate of the stability of log–log type.

%B Inverse Problems %I IOP Publishing %V 26 %P 125015 %8 nov %G eng %U https://doi.org/10.1088%2F0266-5611%2F26%2F12%2F125015 %R 10.1088/0266-5611/26/12/125015 %0 Journal Article %J Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology %D 2010 %T A three-dimensional model for the dynamics and hydrodynamics of rowing boats %A L. Formaggia %A Andrea Mola %A N Parolini %A M Pischiutta %XThis paper proposes a new model describing the dynamics of a rowing boat for general three-dimensional motions. The complex interaction between the different components of the rowers–-oars–-boat system is analysed and reduced to a set of ordinary differential equations governing the rigid motion along the six degrees of freedom. To treat the unstable nature of the physical problem, a rather simple (but effective) control model is included, which mimics the main active control techniques adopted by the rowers during their action.

%B Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology %V 224 %P 51-61 %G eng %U https://doi.org/10.1243/17543371jset46 %R 10.1243/17543371jset46 %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 Proceedings of the Steklov Institute of Mathematics. Volume 268, Issue 1, 2010, Pages 17-31 %D 2010 %T Well-posed infinite horizon variational problems on a compact manifold %A Andrei A. Agrachev %X We give an effective sufficient condition for a variational problem with infinite horizon on a compact Riemannian manifold M to admit a smooth optimal synthesis, i. e., a smooth dynamical system on M whose positive semi-trajectories are solutions to the problem. To realize the synthesis, we construct an invariant Lagrangian submanifold (well-projected to M) of the flow of extremals in the cotangent bundle T*M. The construction uses the curvature of the flow in the cotangent bundle and some ideas of hyperbolic dynamics %B Proceedings of the Steklov Institute of Mathematics. Volume 268, Issue 1, 2010, Pages 17-31 %I SISSA %G en %U http://hdl.handle.net/1963/6458 %1 6404 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-02-05T14:50:56Z\\nNo. of bitstreams: 1\\ndiscount.pdf: 256111 bytes, checksum: 78c64c5edffbe71a9201c6023252b87d (MD5) %R 10.1134/S0081543810010037 %0 Book Section %B Encyclopedia of Complexity and Systems Science / Robert A. Meyers (ed.). - Springer, 2009, 548-554 %D 2009 %T Biological Fluid Dynamics, Non-linear Partial Differential Equations %A Antonio DeSimone %A François Alouges %A Aline Lefebvre %B Encyclopedia of Complexity and Systems Science / Robert A. Meyers (ed.). - Springer, 2009, 548-554 %G en_US %U http://hdl.handle.net/1963/2630 %1 1493 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-04-16T08:35:02Z\\nNo. of bitstreams: 1\\nEncyclopedia_SISSA_Preprint.pdf: 157119 bytes, checksum: 6db74c2f0a9ba80b7b1e5375bd550c0c (MD5) %0 Journal Article %J Arch. Ration. Mech. Anal. 191 (2009) 1-96 %D 2009 %T The boundary Riemann solver coming from the real vanishing viscosity approximation %A Stefano Bianchini %A Laura Spinolo %X We study the limit of the hyperbolic-parabolic approximation $$ \\\\begin{array}{lll} v_t + \\\\tilde{A} ( v, \\\\, \\\\varepsilon v_x ) v_x = \\\\varepsilon \\\\tilde{B}(v ) v_{xx} \\\\qquad v \\\\in R^N\\\\\\\\ \\\\tilde \\\\beta (v (t, \\\\, 0)) = \\\\bar g \\\\\\\\ v (0, \\\\, x) = \\\\bar v_0. \\\\\\\\ \\\\end{array} \\\\right. $$\\nThe function $\\\\tilde \\\\beta$ is defined in such a way to guarantee that the initial boundary value problem is well posed even if $\\\\tilde \\\\beta$ is not invertible.\\nThe data $\\\\bar g$ and $\\\\bar v_0$ are constant. When $\\\\tilde B$ is invertible, the previous problem takes the simpler form $$ \\\\left\\\\{ \\\\begin{array}{lll} v_t + \\\\tilde{A} \\\\big( v, \\\\, \\\\varepsilon v_x \\\\big) v_x = \\\\varepsilon \\\\tilde{B}(v ) v_{xx} \\\\qquad v \\\\in \\\\mathbb{R}^N\\\\\\\\ v (t, \\\\, 0) \\\\equiv \\\\bar v_b \\\\\\\\ v (0, \\\\, x) \\\\equiv \\\\bar{v}_0. \\\\\\\\ \\\\end{array} \\\\right. $$\\nAgain, the data $\\\\bar v_b$ and $\\\\bar v_0$ are constant. The conservative case is included in the previous formulations. It is assumed convergence of the v, smallness of the total variation and other technical hypotheses and it is provided a complete characterization of the limit. The most interesting points are the following two. First, the boundary characteristic case is considered, i.e. one eigenvalue of $\\\\tilde A$ can be 0.\\n Second, as pointed out before we take into account the possibility that $\\\\tilde B$ is not invertible. To deal with this case, we take as hypotheses conditions that were introduced by Kawashima and Shizuta relying on physically meaningful examples. We also introduce a new condition of block linear degeneracy. We prove that, if it is not satisfied, then pathological behaviours may occur. %B Arch. Ration. Mech. Anal. 191 (2009) 1-96 %G en_US %U http://hdl.handle.net/1963/1831 %1 2385 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-06-08T11:20:08Z\\nNo. of bitstreams: 1\\nmath.AP-0605575.pdf: 716141 bytes, checksum: 7686c7f41f7b1f82a595f668049640f2 (MD5) %R 10.1007/s00205-008-0177-6 %0 Report %D 2009 %T Bubbles with prescribed mean curvature: the variational approach %A Paolo Caldiroli %A Roberta Musina %G en_US %U http://hdl.handle.net/1963/3659 %1 646 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-07-08T13:03:07Z\\nNo. of bitstreams: 1\\nSISSA 35-2009-M.pdf: 294313 bytes, checksum: cf6b1d87612220dc9238502f59175615 (MD5) %0 Journal Article %J Rend. Istit. Mat. Univ. Trieste 41 (2009) 35-41 %D 2009 %T A connection between viscous profiles and singular ODEs %A Stefano Bianchini %A Laura Spinolo %B Rend. Istit. Mat. Univ. Trieste 41 (2009) 35-41 %G en_US %U http://hdl.handle.net/1963/2555 %1 1564 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-01-15T10:38:45Z\\nNo. of bitstreams: 1\\nSissa0508M.pdf: 107079 bytes, checksum: 5af029f1d9bcd4f14be2d8774cfa251e (MD5) %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire 26 (2009) 329-349 %D 2009 %T Controllability of the discrete-spectrum Schrodinger equation driven by an external field %A Thomas Chambrion %A Paolo Mason %A Mario Sigalotti %A Ugo Boscain %X We prove approximate controllability of the bilinear Schrodinger equation in the case in which the uncontrolled Hamiltonian has discrete nonresonant\\nspectrum. The results that are obtained apply both to bounded or unbounded domains and to the case in which the control potential is bounded or unbounded. The method relies on finite-dimensional techniques applied to the\\nGalerkin approximations and permits, in addition, to get some controllability properties for the density matrix. Two examples are presented: the harmonic oscillator and the 3D well of potential controlled by suitable potentials. %B Ann. Inst. H. Poincare Anal. Non Lineaire 26 (2009) 329-349 %G en_US %U http://hdl.handle.net/1963/2547 %1 1572 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-01-10T13:32:19Z\\nNo. of bitstreams: 1\\n2008-ttinger.pdf: 270196 bytes, checksum: e706dbae08d996576cefe55f53d7284e (MD5) %R 10.1016/j.anihpc.2008.05.001 %0 Journal Article %J Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009) 2503-2509 %D 2009 %T Controllability on the group of diffeomorphisms %A Andrei A. Agrachev %A Marco Caponigro %X Given a compact manifold M, we prove that any bracket generating family of vector fields on M, which is invariant under multiplication by smooth functions, generates the connected component of identity of the group of diffeomorphisms of M. %B Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009) 2503-2509 %G en_US %U http://hdl.handle.net/1963/3396 %1 936 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-12-11T12:06:43Z\\nNo. of bitstreams: 1\\nAgrachev_Caponigro.pdf: 145136 bytes, checksum: 90eebd9912f15c33d1d93f5108ab93aa (MD5) %R 10.1016/j.anihpc.2009.07.003 %0 Journal Article %J Discrete Contin. Dyn. Syst. 23 (2009) 29-48 %D 2009 %T On the convergence of viscous approximations after shock interactions %A Alberto Bressan %A Carlotta Donadello %X We consider a piecewise smooth solution to a scalar conservation law, with possibly interacting shocks. We show that, after the interactions have taken place, vanishing viscosity approximations can still be represented by a regular expansion on smooth regions and by a singular perturbation expansion near the shocks, in terms of powers of the viscosity coefficient. %B Discrete Contin. Dyn. Syst. 23 (2009) 29-48 %I American Institute of Mathematical Sciences %G en_US %U http://hdl.handle.net/1963/3412 %1 923 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-09T12:23:11Z\\nNo. of bitstreams: 1\\n019.pdf: 273198 bytes, checksum: 4513df79a27da75ea57c4374c83b0cf6 (MD5) %R 10.3934/dcds.2009.23.29 %0 Journal Article %J Differential Geom. Appl. 27 (2009) 723-742 %D 2009 %T Differential geometry of curves in Lagrange Grassmannians with given Young diagram %A Igor Zelenko %A Li Chengbo %X Curves in Lagrange Grassmannians appear naturally in the intrinsic study of geometric structures on manifolds. By a smooth geometric structure on a manifold we mean any submanifold of its tangent bundle, transversal to the fibers. One can consider the time-optimal problem naturally associate with a geometric structure. The Pontryagin extremals of this optimal problem are integral curves of certain Hamiltonian system in the cotangent bundle. The dynamics of the fibers of the cotangent bundle w.r.t. this system along an extremal is described by certain curve in a Lagrange Grassmannian, called Jacobi curve of the extremal. Any symplectic invariant of the Jacobi curves produces the invariant of the original geometric structure. The basic characteristic of a curve in a Lagrange Grassmannian is its Young diagram. The number of boxes in its kth column is equal to the rank of the kth derivative of the curve (which is an appropriately defined linear mapping) at a generic point. We will describe the construction of the complete system of symplectic invariants for parameterized curves in a Lagrange Grassmannian with given Young diagram. It allows to develop in a unified way local differential geometry of very wide classes of geometric structures on manifolds, including both classical geometric structures such as Riemannian and Finslerian structures and less classical ones such as sub-Riemannian and sub-Finslerian structures, defined on nonholonomic distributions. %B Differential Geom. Appl. 27 (2009) 723-742 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3819 %1 508 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-01-18T16:06:20Z\\nNo. of bitstreams: 1\\n0708.1100v1.pdf: 330722 bytes, checksum: 31be09831ca0758a658e2fc9fe6a900f (MD5) %R 10.1016/j.difgeo.2009.07.002 %0 Journal Article %J Netw. Heterog. Media 4 (2009) 667-708 %D 2009 %T Discrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers %A Marco Cicalese %A Antonio DeSimone %A Caterina Ida Zeppieri %X In the framework of linear elasticity, we study the limit of a class of discrete free energies modeling strain-alignment-coupled systems by a rigorous coarse-graining procedure, as the number of molecules diverges. We focus on three paradigmatic examples: magnetostrictive solids, ferroelectric crystals and nematic elastomers, obtaining in the limit three continuum models consistent with those commonly employed in the current literature. We also derive the correspondent macroscopic energies in the presence of displacement boundary conditions and of various kinds of applied external fields. %B Netw. Heterog. Media 4 (2009) 667-708 %I American Institute of Mathematical Sciences %G en_US %U http://hdl.handle.net/1963/3788 %1 538 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-11-25T10:31:11Z\\nNo. of bitstreams: 1\\nCDSZ08.pdf: 390765 bytes, checksum: 2b3fcd3668352c286200e0a3b7e12c1a (MD5) %R 10.3934/nhm.2009.4.667 %0 Thesis %D 2009 %T The Disintegration Theorem and Applications to Optimal Mass Transportation %A Laura Caravenna %I SISSA %G en %U http://hdl.handle.net/1963/5900 %1 5750 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-06-08T09:44:06Z\\nNo. of bitstreams: 1\\nPhDThesisCaravenna.pdf: 1700326 bytes, checksum: 9638dd5ad25fc3e1fb91399b1b12c293 (MD5) %0 Journal Article %J Nonlinear Anal. 70 (2009) 3002-3007 %D 2009 %T Existence of extremals for the Maz\\\'ya and for the Caffarelli-Kohn-Nirenberg inequalities %A Roberta Musina %X This paper deals with some Sobolev-type inequalities with weights that were proved by Maz\\\'ya in 1980 and by Caffarelli-Kohn-Nirenberg in 1984. %B Nonlinear Anal. 70 (2009) 3002-3007 %G en_US %U http://hdl.handle.net/1963/2739 %1 1961 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-08-27T08:18:23Z\\nNo. of bitstreams: 1\\nMusinaCortona2.pdf: 220927 bytes, checksum: aeec20cde67e9e00bc1109988f192159 (MD5) %R 10.1016/j.na.2008.12.024 %0 Report %D 2009 %T An existence result for the Monge problem in R^n with norm cost %A Laura Caravenna %G en_US %U http://hdl.handle.net/1963/3647 %1 657 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-06-10T13:31:00Z\\nNo. of bitstreams: 1\\nMonge.sel.pdf: 1037029 bytes, checksum: 3f852fb5f7d74223ddee50818368c3f5 (MD5) %0 Journal Article %J Bull. Inst. Math. Acad. Sin. (N.S.) 4 (2009) 353-458 %D 2009 %T On the extremality, uniqueness and optimality of transference plans %A Stefano Bianchini %A Laura Caravenna %X We consider the following standard problems appearing in optimal mass transportation theory: when a transference plan is extremal; when a transference plan is the unique transference plan concentrated on a set A,; when a transference plan is optimal. %B Bull. Inst. Math. Acad. Sin. (N.S.) 4 (2009) 353-458 %G en_US %U http://hdl.handle.net/1963/3692 %1 613 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-07-24T11:10:18Z\\nNo. of bitstreams: 1\\n46M2009.pdf: 485239 bytes, checksum: ebe15dc163dd6bdffcbe875730432b12 (MD5) %0 Journal Article %J Nonlinear Analysis: Theory, Methods & Applications %D 2009 %T Foliations of small tubes in Riemannian manifolds by capillary minimal discs %A Fall, Mouhamed Moustapha %A Mercuri, Carlo %XLetting be an embedded curve in a Riemannian manifold , we prove the existence of minimal disc-type surfaces centered at inside the surface of revolution of around , having small radius, and intersecting it with constant angles. In particular we obtain that small tubular neighborhoods can be foliated by minimal discs.

%B Nonlinear Analysis: Theory, Methods & Applications %I Elsevier %V 70 %P 4422–4440 %G eng %U https://doi.org/10.1016/j.na.2008.10.024 %R 10.1016/j.na.2008.10.024 %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 SIAM J. Math. Anal. 40 (2009) 2351-2391 %D 2009 %T A higher order model for image restoration: the one dimensional case %A Gianni Dal Maso %A Irene Fonseca %A Giovanni Leoni %A Massimiliano Morini %X The higher order total variation-based model for image restoration proposed by Chan, Marquina, and Mulet in [6] is analyzed in one dimension. A suitable functional framework in which the minimization problem is well posed is being proposed and it is proved analytically that the\\nhigher order regularizing term prevents the occurrence of the staircase effect. The generalized version of the model considered here includes, as particular cases, some curvature dependent functionals. %B SIAM J. Math. Anal. 40 (2009) 2351-2391 %G en_US %U http://hdl.handle.net/1963/3174 %1 1127 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-23T07:52:52Z\\nNo. of bitstreams: 1\\nDM-Fon-Leo-Mor-08-preprint.pdf: 336946 bytes, checksum: 32db893a2b928f559b6744296e1d4f2c (MD5) %R 10.1137/070697823 %0 Journal Article %J SIAM J. Math. Anal. 41 (2009) 1874-1889 %D 2009 %T Homogenization of fiber reinforced brittle materials: the extremal cases %A Marco Barchiesi %A Gianni Dal Maso %X We analyze the behavior of a fragile material reinforced by a reticulated elastic unbreakable structure in the case of antiplane shear. The microscopic geometry of this material is described by means of two small parameters: the period $\\\\varepsilon$ of the grid and the ratio $\\\\delta$ between the thickness of the fibers and the period $\\\\varepsilon$. We show that the asymptotic behavior as $\\\\varepsilon\\\\to0^+$ and $\\\\delta\\\\to0^+$ depends dramatically on the relative size of these parameters. Indeed, in the two cases considered, i.e., $\\\\varepsilon\\\\ll\\\\delta$ and $\\\\varepsilon\\\\gg\\\\delta$, we obtain two different limit models: a perfectly elastic model and an elastic model with macroscopic cracks, respectively. %B SIAM J. Math. Anal. 41 (2009) 1874-1889 %I SIAM %G en_US %U http://hdl.handle.net/1963/2705 %1 1396 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-08-13T12:57:01Z\\nNo. of bitstreams: 1\\nmicrofibre.pdf: 236545 bytes, checksum: 53ef9ce789d27bba7dcac550930f306b (MD5) %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 Report %D 2009 %T Jacobi Equations and Comparison Theorems for Corank 1 Sub-Riemannian structures with symmetries %A Li Chengbo %A Igor Zelenko %X The Jacobi curve of an extremal of optimal control problem is a curve in a Lagrangian Grassmannian defined up to a symplectic transformation and containing all information about the solutions of the Jacobi equations along this extremal. In our previous works we constructed the canonical\\nbundle of moving frames and the complete system of symplectic invariants, called curvature maps, for\\nparametrized curves in Lagrange Grassmannians satisfying very general assumptions. The structural\\nequation for a canonical moving frame of the Jacobi curve of an extremal can be interpreted as the\\nnormal form for the Jacobi equation along this extremal and the curvature maps can be seen as the\\n\\\"coefficients\\\"of this normal form. In the case of a Riemannian metric there is only one curvature map and it is naturally related to the Riemannian sectional curvature. In the present paper we study the curvature maps for a sub-Riemannian structure on a corank 1 distribution having an additional transversal infinitesimal symmetry. After the factorization by the integral foliation of this symmetry, such sub-Riemannian structure can be reduced to a Riemannian manifold equipped with a closed 2-form(a magnetic field). We obtain explicit expressions for the curvature maps of the original sub-Riemannian structure in terms of the curvature tensor of this Riemannian manifold and the magnetic field. We also estimate the number of conjugate points along the sub-Riemannian extremals in terms of the bounds for the curvature tensor of this Riemannian manifold and the magnetic field in the case of an uniform magnetic field. The language developed for the calculation of the curvature maps can be applied to more general sub-Riemannian structures with symmetries, including sub-Riemmannian structures appearing naturally in Yang-Mills fields. %G en_US %U http://hdl.handle.net/1963/3736 %1 581 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-09-08T13:36:18Z\\nNo. of bitstreams: 1\\njacompfin.pdf: 329060 bytes, checksum: 48bb88c074e19b86902a553f2055ddea (MD5) %0 Journal Article %J Differential and Integral Equations %D 2009 %T Minimal disc-type surfaces embedded in a perturbed cylinder %A Fall, Mouhamed Moustapha %A Mercuri, Carlo %XIn the present note we deal with small perturbations of an infinite cylinder in the 3D euclidian space. We find minimal disc-type surfaces embedded in the cylinder and intersecting its boundary perpendicularly. The existence and localization of those minimal discs is a consequence of a non-degeneracy condition for the critical points of a functional related to the oscillations of the cylinder from the flat configuration.

%B Differential and Integral Equations %I Khayyam Publishing, Inc. %V 22 %P 1115–1124 %G eng %U https://projecteuclid.org/euclid.die/1356019407 %0 Journal Article %J C. R. Math. 347 (2009) 211-216 %D 2009 %T A nonlinear theory for shells with slowly varying thickness %A Marta Lewicka %A Maria Giovanna Mora %A Mohammad Reza Pakzad %X We study the Γ-limit of 3d nonlinear elasticity for shells of small, variable thickness, around an arbitrary smooth 2d surface. %B C. R. Math. 347 (2009) 211-216 %G en_US %U http://hdl.handle.net/1963/2632 %1 1491 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-04-17T10:05:31Z\\nNo. of bitstreams: 1\\nLew-Mor-Pak-08.pdf: 159399 bytes, checksum: a9f5009829a4633482d74870c6fd22b6 (MD5) %R 10.1016/j.crma.2008.12.017 %0 Journal Article %J J. Funct. Anal. 256 (2009) 2741-2745 %D 2009 %T A note on the paper \\\"Optimizing improved Hardy inequalities\\\" by S. Filippas and A. Tertikas %A Roberta Musina %B J. Funct. Anal. 256 (2009) 2741-2745 %G en_US %U http://hdl.handle.net/1963/2698 %1 1402 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-07-25T14:46:48Z\\nNo. of bitstreams: 1\\nMusina_FiTe.pdf: 141073 bytes, checksum: 84d3efccc14d223256f9971f03942f4e (MD5) %R 10.1016/j.jfa.2008.08.009 %0 Journal Article %J Trans. Amer. Math. Soc. 361 (2009) 6019-6047 %D 2009 %T Optimal transportation under nonholonomic constraints %A Andrei A. Agrachev %A Paul Lee %X We study the Monge\\\'s optimal transportation problem where the cost is given by optimal control cost. We prove the existence and uniqueness of optimal map under certain regularity conditions on the Lagrangian, absolute continuity of the measures and most importantly the absent of sharp abnormal minimizers. In particular, this result is applicable in the case of subriemannian manifolds with a 2-generating distribution and cost given by d2, where d is the subriemannian distance. Also, we discuss some properties of the optimal plan when abnormal minimizers are present. Finally, we consider some examples of displacement interpolation in the case of Grushin plane. %B Trans. Amer. Math. Soc. 361 (2009) 6019-6047 %G en_US %U http://hdl.handle.net/1963/2176 %1 2068 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-04T08:42:08Z\\nNo. of bitstreams: 1\\ntransportpre.pdf: 448316 bytes, checksum: 815a3d8cd33b8f3ea07264062b59ec46 (MD5) %R 10.1090/S0002-9947-09-04813-2 %0 Journal Article %J Math. Models Methods Appl. Sci. 19 (2009) 1643-1711 %D 2009 %T Quasistatic evolution for Cam-Clay plasticity: examples of spatially homogeneous solutions %A Gianni Dal Maso %A Antonio DeSimone %X We study a quasistatic evolution problem for Cam-Clay plasticity under a special loading program which leads to spatially homogeneous solutions. Under some initial conditions, the solutions exhibit a softening behaviour and time discontinuities.\\nThe behavior of the solutions at the jump times is studied by a viscous approximation. %B Math. Models Methods Appl. Sci. 19 (2009) 1643-1711 %G en_US %U http://hdl.handle.net/1963/3395 %1 937 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-12-10T11:56:05Z\\nNo. of bitstreams: 1\\nDal_Maso-DeSimone.pdf: 1160572 bytes, checksum: fd49c80a369183f1941b0fcf3cd65341 (MD5) %R 10.1142/S0218202509003942 %0 Journal Article %J J. Convex Anal. %D 2009 %T Quasistatic evolution problems for nonhomogeneous elastic plastic materials %A Francesco Solombrino %XThe paper studies the quasistatic evolution for elastoplastic materials when the yield surface depends on the position in the reference configuration. The main results are obtained when the yield surface is continuous with respect to the space variable. The case of piecewise constant dependence is also considered. The evolution is studied in the framework of the variational formulation for rate independent problems developed by Mielke. The results are proved by adapting the arguments introduced for a constant yield surface, using some properties of convex valued semicontinuous multifunctions. A strong formulation of the problem is also obtained, which includes a pointwise version of the plastic flow rule. Some examples are considered, which show that strain concentration may occur as a consequence of a nonconstant yield surface.

%B J. Convex Anal. %V 16 %P 89–119 %G eng %0 Journal Article %J Phys. Rev. E 79 (2009) 031915 %D 2009 %T Relaxation dynamics of fluid membranes %A Marino Arroyo %A Antonio DeSimone %X We study the effect of membrane viscosity in the dynamics of liquid membranes-possibly with free or internal boundaries-driven by conservative forces (curvature elasticity and line tension) and dragged by the bulk dissipation of the ambient fluid and the friction occurring when the amphiphilic molecules move relative to each other. To this end, we formulate a continuum model which includes a form of the governing equations for a two-dimensional viscous fluid moving on a curved, time-evolving surface. The effect of membrane viscosity has received very limited attention in previous continuum studies of the dynamics of fluid membranes, although recent coarse-grained discrete simulations suggest its importance. By applying our model to the study of vesiculation and membrane fusion in a simplified geometry, we conclude that membrane viscosity plays a dominant role in the relaxation dynamics of fluid membranes of sizes comparable to those found in eukaryotic cells, and is not negligible in many large synthetic systems of current interest. %B Phys. Rev. E 79 (2009) 031915 %I American Physical Society %G en_US %U http://hdl.handle.net/1963/3618 %1 686 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-04-22T08:29:29Z\\nNo. of bitstreams: 1\\nmembrane_dynamics_PRE_2.pdf: 1000677 bytes, checksum: e7ab0f6e2046800e154d399808ea314c (MD5) %R 10.1103/PhysRevE.79.031915 %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 Mathematical Models and Methods in Applied Sciences %D 2009 %T Solutions of the Schrödinger–Poisson problem concentrating on spheres, part I: necessary conditions %A Ianni, Isabella %A Giusi Vaira %XIn this paper we study a coupled nonlinear Schrödinger–Poisson problem with radial functions. This system has been introduced as a model describing standing waves for the nonlinear Schrödinger equations in the presence of the electrostatic field. We provide necessary conditions for concentration on sphere for the solutions of this kind of problem extending the results already known.

%B Mathematical Models and Methods in Applied Sciences %V 19 %P 707-720 %G eng %U https://doi.org/10.1142/S0218202509003589 %R 10.1142/S0218202509003589 %0 Journal Article %J Adv. Math. 221 (2009) 1843-1909 %D 2009 %T Some new entire solutions of semilinear elliptic equations on Rn %A Andrea Malchiodi %B Adv. Math. 221 (2009) 1843-1909 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3645 %1 659 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-06-08T15:11:59Z\\nNo. of bitstreams: 1\\nentire.pdf: 478191 bytes, checksum: 1b7ea59917a621bf7b2793f7228fade6 (MD5) %R 10.1016/j.aim.2009.03.012 %0 Journal Article %J Math. Models Methods Appl. Sci. 19 (2009) 601-630 %D 2009 %T Strain-order coupling in nematic elastomers: equilibrium configurations %A Pierluigi Cesana %A Antonio DeSimone %X We consider models that describe liquid crystal elastomers either in a biaxial or in a uniaxial phase and in the framework of Frank\\\'s director theory. We prove existence of static equilibrium solutions in the presence of frustrations due to electro-mechanical boundary conditions and to applied loads and fields. We find explicit solutions arising in connection with special boundary conditions and the corresponding phase diagrams, leading to significant implications on possible experimental observations. %B Math. Models Methods Appl. Sci. 19 (2009) 601-630 %G en_US %U http://hdl.handle.net/1963/2700 %1 1400 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-07-25T15:04:59Z\\nNo. of bitstreams: 1\\nprprCdS.pdf: 504721 bytes, checksum: 2ef9aff006dbc9353a50a122cb98d381 (MD5) %0 Report %D 2009 %T Stratos: a code for 3D free surface flows with floating constraints %A Antonio DeSimone %A B. Bianchi %A Luca Heltai %X This report presents a brief discussion of the theoretical aspects and practical implementation of STRATOS . STRATOS is a 3D code for the simulation\\nof hydrodynamic flows for incompressible fluids, in the presence of a free surface, capable of simulating the interaction between the free surface and a\\nfloating object via Lagrange multipliers...... %G en_US %U http://hdl.handle.net/1963/3701 %1 604 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-07-30T14:37:01Z\\nNo. of bitstreams: 1\\nBianchiDeSimoneHeltai.pdf: 899803 bytes, checksum: aff44eb1a39c6fd4acd4b3cb285e2d64 (MD5) %0 Report %D 2009 %T Tools for the Solution of PDEs Defined on Curved Manifolds with deal.II %A Antonio DeSimone %A Luca Heltai %A Cataldo Manigrasso %X The deal.II finite element library was originally designed to solve partial differential equations defined on one, two or three space dimensions, mostly\\nvia the Finite Element Method. In its versions prior to version 6.2, the user could not solve problems defined on curved manifolds embedded in two or\\nthree spacial dimensions. This infrastructure is needed if one wants to solve, for example, Boundary Integral Equations. %G en_US %U http://hdl.handle.net/1963/3700 %1 605 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-07-30T14:20:01Z\\nNo. of bitstreams: 1\\nDeSimoneHeltaiManigrasso.pdf: 915137 bytes, checksum: c3144348b6aab67a5f547060049c7847 (MD5) %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 Trans. Amer. Math. Soc. 361 (2009) 41-59 %D 2009 %T On viscosity solutions of Hamilton-Jacobi equations %A Sandro Zagatti %X We consider the Dirichlet problem for Hamilton-Jacobi equations and prove existence, uniqueness and continuous dependence on boundary data of Lipschitz continuous maximal viscosity solutions. %B Trans. Amer. Math. Soc. 361 (2009) 41-59 %I American Mathematical Society %G en_US %U http://hdl.handle.net/1963/3420 %1 915 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-12T11:15:26Z\\nNo. of bitstreams: 1\\nvisco1.pdf: 200249 bytes, checksum: d80a45752b5394539504d0029276b1dc (MD5) %R 10.1090/S0002-9947-08-04557-1 %0 Journal Article %J Journal of Differential Equations %D 2008 %T Asymptotic evolution for the semiclassical nonlinear Schrödinger equation in presence of electric and magnetic fields %A Alessandro Selvitella %XIn this paper we study the semiclassical limit for the solutions of a subcritical focusing NLS with electric and magnetic potentials. We consider in particular the Cauchy problem for initial data close to solitons and show that, when the Planck constant goes to zero, the motion shadows that of a classical particle. Several works were devoted to the case of standing waves: differently from these we show that, in the dynamic version, the Lorentz force appears crucially.

%B Journal of Differential Equations %V 245 %P 2566 - 2584 %G eng %U http://www.sciencedirect.com/science/article/pii/S002203960800243X %R https://doi.org/10.1016/j.jde.2008.05.012 %0 Journal Article %J Front. Math. China 3 (2008) 239-252 %D 2008 %T Concentrating solutions of some singularly perturbed elliptic equations %A Andrea Malchiodi %X We study singularly perturbed elliptic equations arising from models in physics or biology, and investigate the asymptotic behavior of some special solutions. We also discuss some connections with problems arising in differential geometry. %B Front. Math. China 3 (2008) 239-252 %G en_US %U http://hdl.handle.net/1963/2657 %1 1466 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-05-12T13:25:45Z\\nNo. of bitstreams: 1\\nprocmalchiodi.pdf: 183157 bytes, checksum: 5d6ee64d87eb139b09968558c74ab0f5 (MD5) %R 10.1007/s11464-008-0015-z %0 Journal Article %J Advanced nonlinear studies %D 2008 %T On concentration of positive bound states for the Schrödinger-Poisson problem with potentials %A Ianni, Isabella %A Giusi Vaira %XWe study the existence of semiclassical states for a nonlinear Schrödinger-Poisson system that concentrate near critical points of the external potential and of the density charge function. We use a perturbation scheme in a variational setting, extending the results in [1]. We also discuss necessary conditions for concentration.

%B Advanced nonlinear studies %I Advanced Nonlinear Studies, Inc. %V 8 %P 573–595 %G eng %R 10.1515/ans-2008-0305. %0 Journal Article %J Proc. Roy. Soc. Edinburgh Sect. A 138 (2008) 873-896 %D 2008 %T Convergence of equilibria of three-dimensional thin elastic beams %A Maria Giovanna Mora %A Stefan Müller %X A convergence result is proved for the equilibrium configurations of a three-dimensional thin elastic beam, as the diameter $h$ of the cross-section tends to zero. More precisely, we show that stationary points of the nonlinear elastic functional $E^h$, whose energies (per unit cross-section) are bounded by $Ch^2$, converge to stationary points of the $\\\\varGamma$-limit of $E^h/h^2$. This corresponds to a nonlinear one-dimensional model for inextensible rods, describing bending and torsion effects. The proof is based on the rigidity estimate for low-energy deformations by Friesecke, James and Müller and on a compensated compactness argument in a singular geometry. In addition, possible concentration effects of the strain are controlled by a careful truncation argument. %B Proc. Roy. Soc. Edinburgh Sect. A 138 (2008) 873-896 %G en_US %U http://hdl.handle.net/1963/1896 %1 2339 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-11-24T10:09:06Z\\nNo. of bitstreams: 1\\n69M-2006.pdf: 3633291 bytes, checksum: b5dba64c671bbcd8b87e52ce24963341 (MD5) %R 10.1017/S0308210506001120 %0 Journal Article %J Boll. Unione Mat. Ital. (9) 1 (2008) 497-505 %D 2008 %T Decomposition results for functions with bounded variation %A Gianni Dal Maso %A Rodica Toader %B Boll. Unione Mat. Ital. (9) 1 (2008) 497-505 %I Unione Matematica Italiana %G en_US %U http://hdl.handle.net/1963/3535 %1 729 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-23T10:23:36Z\\nNo. of bitstreams: 1\\nDM-Toa.pdf: 186814 bytes, checksum: bbc754f60013f0d8fd61b90a278ac837 (MD5) %0 Journal Article %J Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 19 (2008) 65-72 %D 2008 %T Entire solutions of autonomous equations on Rn with nontrivial asymptotics %A Andrea Malchiodi %X We prove existence of a new type of solutions for the semilinear equation $- \\\\D u + u = u^p$ on $\\\\R^n$, with $1 < p < \\\\frac{n+2}{n-2}$. These solutions are positive, bounded, decay exponentially to zero away from three half-lines with a common origin, and at infinity are asymptotically periodic. %B Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 19 (2008) 65-72 %G en_US %U http://hdl.handle.net/1963/2640 %1 1483 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-04-30T08:06:29Z\\nNo. of bitstreams: 1\\ngluingnote.pdf: 178833 bytes, checksum: eca0da57985e983d19aac5964c9a1e55 (MD5) %0 Journal Article %J J. Hyperbolic Differ. Equ. 5 (2008) 643-662 %D 2008 %T An entropy based Glimm-type functional %A Laura Caravenna %B J. Hyperbolic Differ. Equ. 5 (2008) 643-662 %I World Scientific %G en_US %U http://hdl.handle.net/1963/4051 %1 351 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-09-09T11:15:30Z\\nNo. of bitstreams: 1\\nglimm.potential.pdf: 405855 bytes, checksum: e2a5f3fed36ffe727c6d43240482aa6d (MD5) %R 10.1142/S0219891608001635 %0 Journal Article %J SIAM J. Math. Anal. 40 (2008) 1104-1122 %D 2008 %T Eulerian calculus for the displacement convexity in the Wasserstein distance %A Sara Daneri %A Giuseppe Savarè %X In this paper we give a new proof of the (strong) displacement convexity of a class of integral functionals defined on a compact Riemannian manifold satisfying a lower Ricci curvature bound. Our approach does not rely on existence and regularity results for optimal transport maps on Riemannian manifolds, but it is based on the Eulerian point of view recently introduced by Otto and Westdickenberg [SIAM J. Math. Anal., 37 (2005), pp. 1227-1255] and on the metric characterization of the gradient flows generated by the functionals in the Wasserstein space. %B SIAM J. Math. Anal. 40 (2008) 1104-1122 %I SIAM %G en_US %U http://hdl.handle.net/1963/3413 %1 922 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-09T12:32:55Z\\nNo. of bitstreams: 1\\n0801.2455v1.pdf: 504916 bytes, checksum: 7ccfac515ef559e376c7e7d213bd4091 (MD5) %R 10.1137/08071346X %0 Journal Article %J Ann. of Math. 168 (2008) 813-858 %D 2008 %T Existence of conformal metrics with constant $Q$-curvature %A Zindine Djadli %A Andrea Malchiodi %X Given a compact four dimensional manifold, we prove existence of conformal metrics with constant $Q$-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure. Since the corresponding Euler functional is in general unbounded from above and from below, we employ topological methods and minimax schemes, jointly with a compactness result by the second author. %B Ann. of Math. 168 (2008) 813-858 %G en_US %U http://hdl.handle.net/1963/2308 %1 1708 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-29T14:05:55Z\\nNo. of bitstreams: 1\\nDjadliMalchiodiFinal.pdf: 342979 bytes, checksum: fc2b0b8e4e01a5327ed8e01dc1bae6c5 (MD5) %0 Journal Article %J SIAM J. Math. Anal. 40 (2008) 382-412 %D 2008 %T Forced Vibrations of a Nonhomogeneous String %A P Baldi %A Massimiliano Berti %X We prove existence of vibrations of a nonhomogeneous string under a nonlinear time periodic forcing term in the case in which the forcing frequency avoids resonances with the vibration modes of the string (nonresonant case). The proof relies on a Lyapunov-Schmidt reduction and a Nash-Moser iteration scheme. %B SIAM J. Math. Anal. 40 (2008) 382-412 %G en_US %U http://hdl.handle.net/1963/2643 %1 1480 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-05-07T08:29:52Z\\nNo. of bitstreams: 1\\nBaldiBerti06-1.pdf: 277037 bytes, checksum: 6abb75a412da123c87879c25714e41b2 (MD5) %R 10.1137/060665038 %0 Journal Article %J Phys. Rev. B 77 (2008) 245105 %D 2008 %T Fulde-Ferrell-Larkin-Ovchinnikov pairing in one-dimensional optical lattices %A Matteo Rizzi %A Marco Polini %A Miguel A. Cazalilla %A M.R. Bakhtiari %A Mario P. Tosi %A Rosario Fazio %XSpin-polarized attractive Fermi gases in one-dimensional (1D) optical lattices are expected to be remarkably good candidates for the observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We model these systems with an attractive Hubbard model with population imbalance. By means of the density-matrix renormalization-group method we compute the pairing correlations as well as the static spin and charge structure factors in the whole range from weak to strong coupling. We demonstrate that pairing correlations exhibit quasi-long range order and oscillations at the wave number expected from FFLO theory. However, we also show by numerically computing the mixed spin-charge static structure factor that charge and spin degrees of freedom appear to be coupled already for small imbalance. We discuss the consequences of this coupling for the observation of the FFLO phase, as well as for the stabilization of the quasi-long range order into long-range order by coupling many identical 1D systems, as in quasi-1D optical lattices.

%B Phys. Rev. B 77 (2008) 245105 %G en_US %U http://hdl.handle.net/1963/2694 %1 1406 %2 Physics %3 Condensed Matter Theory %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-07-14T09:46:14Z\\nNo. of bitstreams: 1\\n0712.3364v1.pdf: 305409 bytes, checksum: 13081c375909264afc4c0282b9de9f68 (MD5) %R 10.1103/PhysRevB.77.245105 %0 Journal Article %J Discrete Contin. Dyn. Syst. 20 (2008) 801-822 %D 2008 %T A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds %A Andrei A. Agrachev %A Ugo Boscain %A Mario Sigalotti %X We consider a generalization of Riemannian geometry that naturally arises in the framework of control theory. Let $X$ and $Y$ be two smooth vector fields on a two-dimensional manifold $M$. If $X$ and $Y$ are everywhere linearly independent, then they define a classical Riemannian metric on $M$ (the metric for which they are orthonormal) and they give to $M$ the structure of metric space. If $X$ and $Y$ become linearly dependent somewhere on $M$, then the corresponding Riemannian metric has singularities, but under generic conditions the metric structure is still well defined. Metric structures that can be defined locally in this way are called almost-Riemannian structures. They are special cases of rank-varying sub-Riemannian structures, which are naturally defined in terms of submodules of the space of smooth vector fields on $M$. Almost-Riemannian structures show interesting phenomena, in particular for what concerns the relation between curvature, presence of conjugate points, and topology of the manifold. The main result of the paper is a generalization to almost-Riemannian structures of the Gauss-Bonnet formula. %B Discrete Contin. Dyn. Syst. 20 (2008) 801-822 %G en_US %U http://hdl.handle.net/1963/1869 %1 2353 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-10-11T07:14:06Z\\nNo. of bitstreams: 1\\nmath.oc0609566.pdf: 920147 bytes, checksum: c6f020bc9676ee3966b64f4135e4ce52 (MD5) %R 10.3934/dcds.2008.20.801 %0 Journal Article %J Netw. Heterog. Media 3 (2008) 567-614 %D 2008 %T Globally stable quasistatic evolution in plasticity with softening %A Gianni Dal Maso %A Antonio DeSimone %A Maria Giovanna Mora %A Massimiliano Morini %X We study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is characterized by the following properties: global stability at each time and energy balance on each\\ntime interval. An example developed in detail compares the solutions obtained by this method with the ones provided by a vanishing viscosity approximation, and shows that only the latter capture a decreasing branch in the stress-strain response. %B Netw. Heterog. Media 3 (2008) 567-614 %G en_US %U http://hdl.handle.net/1963/1965 %1 2228 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-05-15T11:03:21Z\\nNo. of bitstreams: 1\\nDM-DeS-Mor-Mor-05-3-final.pdf: 395475 bytes, checksum: 5789494df44986207d416d5d1ea15d22 (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 SIAM J. Control Optim. 47 (2008) 1851-1878 %D 2008 %T Invariant Carnot-Caratheodory metrics on S3, SO(3), SL(2) and Lens Spaces %A Ugo Boscain %A Francesco Rossi %X In this paper we study the invariant Carnot-Caratheodory metrics on SU(2) \\\' S3,\\nSO(3) and SL(2) induced by their Cartan decomposition. Beside computing explicitly geodesics and conjugate loci, we compute the cut loci (globally) and we give the expression of the Carnot-Caratheodory distance as the inverse of an elementary function. We then prove that the metric\\ngiven on SU(2) projects on the so called Lens Spaces L(p; q). Also for Lens Spaces, we compute\\nthe cut loci (globally). %B SIAM J. Control Optim. 47 (2008) 1851-1878 %G en_US %U http://hdl.handle.net/1963/2144 %1 2099 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-27T08:46:25Z\\nNo. of bitstreams: 1\\nBoscain-Rossi-2007.pdf: 587872 bytes, checksum: 6b4998700cd692ddbd99e14289405bdf (MD5) %R 10.1137/070703727 %0 Report %D 2008 %T Invariant Manifolds for Viscous Profiles of a Class of Mixed Hyperbolic-Parabolic Systems %A Stefano Bianchini %A Laura Spinolo %G en_US %U http://hdl.handle.net/1963/3400 %1 932 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-12-15T12:03:08Z\\nNo. of bitstreams: 1\\nBianchini_Spinolo.pdf: 146920 bytes, checksum: 27283c16ae26e782e9f0d17c1fbb29d4 (MD5) %0 Journal Article %J SIAM J. Control Optim. 47 (2008) 111-143 %D 2008 %T Limit Time Optimal Syntheses for a control-affine system on S² %A Paolo Mason %A Rebecca Salmoni %A Ugo Boscain %A Yacine Chitour %X For $\\\\alpha \\\\in ]0,\\\\pi/2[$, let $(\\\\Sigma)_\\\\alpha$ be the control system $\\\\dot{x}=(F+uG)x$, where $x$ belongs to the two-dimensional unit sphere $S^2$, $u\\\\in [-1,1]$, and $F,G$ are $3\\\\times3$ skew-symmetric matrices generating rotations with perpendicular axes and of respective norms $\\\\cos(\\\\alpha)$ and $\\\\sin(\\\\alpha)$. In this paper, we study the time optimal synthesis (TOS) from the north pole $(0,0,1)^T$ associated to $(\\\\Sigma)_\\\\alpha$, as the parameter $\\\\alpha$ tends to zero; this problem is motivated by specific issues in the control of quantum systems. We first prove that the TOS is characterized by a \\\"two-snakes\\\" configuration on the whole $S^2$, except for a neighborhood $U_\\\\alpha$ of the south pole $(0,0,-1)^T$ of diameter at most ${\\\\cal O}(\\\\alpha)$. We next show that, inside $U_\\\\alpha$, the TOS depends on the relationship between $r(\\\\alpha):=\\\\pi/2\\\\alpha-[\\\\pi/2\\\\alpha]$ and $\\\\alpha$. More precisely, we characterize three main relationships by considering sequences $(\\\\alpha_k)_{k\\\\geq 0}$ satisfying (a) $r(\\\\alpha_k)=\\\\bar{r}$, (b) $r(\\\\alpha_k)=C\\\\alpha_k$, and (c) $r(\\\\alpha_k)=0$, where $\\\\bar{r}\\\\in (0,1)$ and $C>0$. In each case, we describe the TOS and provide, after a suitable rescaling, the limiting behavior, as $\\\\alpha$ tends to zero, of the corresponding TOS inside $U_\\\\alpha$. %B SIAM J. Control Optim. 47 (2008) 111-143 %G en_US %U http://hdl.handle.net/1963/1862 %1 2360 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-09-28T11:24:18Z\\nNo. of bitstreams: 1\\n48-M.pdf: 5823285 bytes, checksum: 7f66cf9d280da78b56a423c415d9078c (MD5) %R 10.1137/060675988 %0 Journal Article %J Discrete Contin. Dyn. Syst. 21 (2008) 625-641 %D 2008 %T Minimization of non quasiconvex functionals by integro-extremization method %A Sandro Zagatti %B Discrete Contin. Dyn. Syst. 21 (2008) 625-641 %G en_US %U http://hdl.handle.net/1963/2761 %1 1939 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-08-29T10:49:03Z\\nNo. of bitstreams: 1\\ndcdsprep.pdf: 193173 bytes, checksum: dc350ec75ad4fad83ec12ee96aaddabe (MD5) %R 10.3934/dcds.2008.21.625 %0 Journal Article %J Calc. Var. Partial Differential Equations 31 (2008) 511-519 %D 2008 %T Minimizers of non convex scalar functionals and viscosity solutions of Hamilton-Jacobi equations %A Sandro Zagatti %B Calc. Var. Partial Differential Equations 31 (2008) 511-519 %G en_US %U http://hdl.handle.net/1963/2760 %1 1940 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-08-29T10:38:03Z\\nNo. of bitstreams: 1\\nxugrad1.pdf: 129424 bytes, checksum: e067ce39ac2059a9ee78b46fc06884c3 (MD5) %R 10.1007/s00526-007-0124-7 %0 Journal Article %J Adv. Differential Equations 13 (2008) 1109-1129 %D 2008 %T Morse theory and a scalar field equation on compact surfaces %A Andrea Malchiodi %B Adv. Differential Equations 13 (2008) 1109-1129 %I Khayyam Publishing %G en_US %U http://hdl.handle.net/1963/3531 %1 733 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-20T09:55:31Z\\nNo. of bitstreams: 1\\nMalchiodi07.pdf: 259636 bytes, checksum: f8380ae02625bce2ba51c6bf7dcb737d (MD5) %0 Journal Article %J Commun. Contemp. Math. 10 (2008) 391-404 %D 2008 %T Multiple bound states for the Schroedinger-Poisson problem %A Antonio Ambrosetti %A David Ruiz %B Commun. Contemp. Math. 10 (2008) 391-404 %G en_US %U http://hdl.handle.net/1963/2679 %1 1421 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-07-01T12:26:30Z\\nNo. of bitstreams: 1\\nAmbrosettiRuiz06.pdf: 226363 bytes, checksum: 59048d8662e1823466ba8f56a48d2808 (MD5) %R 10.1142/S021919970800282X %0 Report %D 2008 %T A note on the differentiability of Lipschitz functions and the chain rule in Sobolev spaces %A Massimiliano Morini %G en_US %U http://hdl.handle.net/1963/2654 %1 1469 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-05-12T11:42:20Z\\nNo. of bitstreams: 1\\nchainmor.pdf: 232603 bytes, checksum: 2798c276d92d0d30c48523748c30a163 (MD5) %0 Journal Article %J J. Nonlinear Sci. 18 (2008) 277-302 %D 2008 %T Optimal Strokes for Low Reynolds Number Swimmers: An Example %A François Alouges %A Antonio DeSimone %A Aline Lefebvre %X Swimming, i.e., being able to advance in the absence of external forces by performing cyclic shape changes, is particularly demanding at low Reynolds numbers. This is the regime of interest for micro-organisms and micro- or nano-robots. We focus in this paper on a simple yet representative example: the three-sphere swimmer of Najafi and Golestanian (Phys. Rev. E, 69, 062901-062904, 2004). For this system, we show how to cast the problem of swimming in the language of control theory, prove global controllability (which implies that the three-sphere swimmer can indeed swim), and propose a numerical algorithm to compute optimal strokes (which turn out to be suitably defined sub-Riemannian geodesics). %B J. Nonlinear Sci. 18 (2008) 277-302 %I Springer %G en_US %U http://hdl.handle.net/1963/4006 %1 396 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-08-26T10:49:24Z\\nNo. of bitstreams: 1\\nADL2008a.pdf: 273047 bytes, checksum: 36ba2c2914fff62c05124f1ac1453733 (MD5) %R 10.1007/s00332-007-9013-7 %0 Journal Article %J Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl %D 2008 %T Positive solutions of nonlinear Schrödinger-Poisson systems with radial potentials vanishing at infinity %A Mercuri, Carlo %XWe deal with a weighted nonlinear Schr¨odinger-Poisson system, allowing the potentials to vanish at infinity.

%B Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl %I Citeseer %V 19 %P 211–227 %G eng %U http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.510.3635&rep=rep1&type=pdf %R 10.1.1.510.3635 %0 Journal Article %J Math. Models Methods Appl. Sci. 18 (2008) 1-20 %D 2008 %T Relaxation of some transversally isotropic energies and applications to smectic A elastomers %A James Adams %A Sergio Conti %A Antonio DeSimone %A Georg Dolzmann %B Math. Models Methods Appl. Sci. 18 (2008) 1-20 %G en_US %U http://hdl.handle.net/1963/1912 %1 2325 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-02-02T14:15:25Z\\nNo. of bitstreams: 1\\nsma_Preprint_SISSA.pdf: 271875 bytes, checksum: eb0cf2c367021718506356a73bda219a (MD5) %R 10.1142/S0218202508002693 %0 Journal Article %J Calc. Var. Partial Differential Equations 33 (2008) 37-74 %D 2008 %T A second order minimality condition for the Mumford-Shah functional %A Filippo Cagnetti %A Maria Giovanna Mora %A Massimiliano Morini %X A new necessary minimality condition for the Mumford-Shah functional is derived by means of second order variations. It is expressed in terms of a sign condition for a nonlocal quadratic form on $H^1_0(\\\\Gamma)$, $\\\\Gamma$ being a submanifold of the regular part of the discontinuity set of the critical point. Two equivalent formulations are provided: one in terms of the first eigenvalue of a suitable compact operator, the other involving a sort of nonlocal capacity of $\\\\Gamma$. A sufficient condition for minimality is also deduced. Finally, an explicit example is discussed, where a complete characterization of the domains where the second variation is nonnegative can be given. %B Calc. Var. Partial Differential Equations 33 (2008) 37-74 %G en_US %U http://hdl.handle.net/1963/1955 %1 2318 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-03-02T12:54:00Z\\nNo. of bitstreams: 1\\nCMM.pdf: 358759 bytes, checksum: c414c0080a17971ecba1251a5890b94f (MD5) %R 10.1007/s00526-007-0152-3 %0 Journal Article %J J. Funct. Anal. 254 (2008) 2816-2845 %D 2008 %T Solitons of linearly coupled systems of semilinear non-autonomous equations on Rn %A Antonio Ambrosetti %A Giovanna Cerami %A David Ruiz %X Using concentration compactness type arguments, we prove some results about the existence of positive ground and bound state of linearly coupled systems of nonlinear Schrödinger equations. %B J. Funct. Anal. 254 (2008) 2816-2845 %G en_US %U http://hdl.handle.net/1963/2175 %1 2069 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-04T08:29:15Z\\nNo. of bitstreams: 1\\nambceruiz.pdf: 305881 bytes, checksum: f00a4a8078e5c5d78d4309cceb317906 (MD5) %R 10.1016/j.jfa.2007.11.013 %0 Journal Article %J Commun. Pure Appl. Anal. 7 (2008) 1-21 %D 2008 %T Stability of planar switched systems: the nondiagonalizable case %A Ugo Boscain %A Moussa Balde %B Commun. Pure Appl. Anal. 7 (2008) 1-21 %G en_US %U http://hdl.handle.net/1963/1857 %1 2361 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-09-28T09:15:19Z\\nNo. of bitstreams: 1\\n44-M.pdf: 3158552 bytes, checksum: c4fee14d81a9fcf026efd4448da88c75 (MD5) %R 10.3934/cpaa.2008.7.1 %0 Journal Article %J Discrete Contin. Dyn. Syst. 21 (2008) 277-294 %D 2008 %T Topological methods for an elliptic equation with exponential nonlinearities %A Andrea Malchiodi %X We consider a class of variational equations with exponential nonlinearities on compact surfaces. From considerations involving the Moser-Trudinger inequality, we characterize some sublevels of the Euler-Lagrange functional in terms of the topology of the surface and of the data of the equation. This is used together with a min-max argument to obtain existence results. %B Discrete Contin. Dyn. Syst. 21 (2008) 277-294 %G en_US %U http://hdl.handle.net/1963/2594 %1 1528 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-02-26T11:51:21Z\\nNo. of bitstreams: 1\\nnotemalchiodi.pdf: 260737 bytes, checksum: eddd4d053e3aa35b1cd0562f82bd0e7e (MD5) %R 10.3934/dcds.2008.21.277 %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire 25 (2008) 609-631 %D 2008 %T Transition layer for the heterogeneous Allen-Cahn equation %A Fethi Mahmoudi %A Andrea Malchiodi %A Juncheng Wei %X We consider the equation $\\\\e^{2}\\\\Delta u=(u-a(x))(u^2-1)$ in $\\\\Omega$, $\\\\frac{\\\\partial u}{\\\\partial \\\\nu} =0$ on $\\\\partial \\\\Omega$, where $\\\\Omega$ is a smooth and bounded domain in $\\\\R^n$, $\\\\nu$ the outer unit normal to $\\\\pa\\\\Omega$, and $a$ a smooth function satisfying $-10} and {a<0}. Assuming $\\\\nabla a \\\\neq 0$ on $K$ and $a\\\\ne 0$ on $\\\\partial \\\\Omega$, we show that there exists a sequence $\\\\e_j \\\\to 0$ such that the above equation has a solution $u_{\\\\e_j}$ which converges uniformly to $\\\\pm 1$ on the compact sets of $\\\\O_{\\\\pm}$ as $j \\\\to + \\\\infty$. %B Ann. Inst. H. Poincare Anal. Non Lineaire 25 (2008) 609-631 %G en_US %U http://hdl.handle.net/1963/2656 %1 1467 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-05-12T13:00:33Z\\nNo. of bitstreams: 1\\n0702878v1.pdf: 345060 bytes, checksum: a1e9182e6448c835b1c66b4f226b0b8d (MD5) %R 10.1016/j.anihpc.2007.03.008 %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 Arch. Ration. Mech. Anal. 189 (2008) 469-544 %D 2008 %T A vanishing viscosity approach to quasistatic evolution in plasticity with softening %A Gianni Dal Maso %A Antonio DeSimone %A Maria Giovanna Mora %A Massimiliano Morini %X We deal with quasistatic evolution problems in plasticity with softening, in the framework of small strain associative elastoplasticity. The presence of a nonconvex term due to the softening phenomenon requires a nontrivial extension of the variational framework for rate-independent problems to the case of a nonconvex energy functional. We argue that, in this case, the use of global minimizers in the corresponding incremental problems is not justified from the mechanical point of view. Thus, we analize a different selection criterion for the solutions of the quasistatic evolution problem, based on a viscous approximation. This leads to a generalized formulation in terms of Young measures, developed in the first part of the paper. In the second part we apply our approach to some concrete examples. %B Arch. Ration. Mech. Anal. 189 (2008) 469-544 %G en_US %U http://hdl.handle.net/1963/1844 %1 2373 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-07-21T11:03:58Z\\nNo. of bitstreams: 1\\nmath.AP-0606718.pdf: 563956 bytes, checksum: 80e8ac8a9120c15b452698af3abc77d1 (MD5) %R 10.1007/s00205-008-0117-5 %0 Journal Article %J Comm. Pure Appl. Math. 60 (2007) 1559-1622 %D 2007 %T Asymptotic behaviour of smooth solutions for partially dissipative hyperbolic systems with a convex entropy %A Stefano Bianchini %A Bernard Hanouzet %A Roberto Natalini %X We study the asymptotic time behavior of global smooth solutions to general entropy dissipative hyperbolic systems of balance law in m space dimensions, under the Shizuta-Kawashima condition. %B Comm. Pure Appl. Math. 60 (2007) 1559-1622 %G en_US %U http://hdl.handle.net/1963/1780 %1 2764 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-30T10:33:17Z\\nNo. of bitstreams: 1\\n83M.pdf: 393359 bytes, checksum: f3f7b61564332b98b8706af95942dd69 (MD5) %R 10.1002/cpa.20195 %0 Journal Article %J Arch. Ration. Mech. Anal. 183 (2007) 163-185 %D 2007 %T Asymptotic variational wave equations %A Alberto Bressan %A Zhang Ping %A Zheng Yuxi %X We investigate the equation $(u_t + (f(u))_x)_x = f\\\'\\\'(u) (u_x)^2/2$ where $f(u)$ is a given smooth function. Typically $f(u)= u^2/2$ or $u^3/3$. This equation models unidirectional and weakly nonlinear waves for the variational wave equation $u_{tt} - c(u) (c(u)u_x)_x =0$ which models some liquid crystals with a natural sinusoidal $c$. The equation itself is also the Euler-Lagrange equation of a variational problem. Two natural classes of solutions can be associated with this equation. A conservative solution will preserve its energy in time, while a dissipative weak solution loses energy at the time when singularities appear. Conservative solutions are globally defined, forward and backward in time, and preserve interesting geometric features, such as the Hamiltonian structure. On the other hand, dissipative solutions appear to be more natural from the physical point of view.\\nWe establish the well-posedness of the Cauchy problem within the class of conservative solutions, for initial data having finite energy and assuming that the flux function $f$ has Lipschitz continuous second-order derivative. In the case where $f$ is convex, the Cauchy problem is well-posed also within the class of dissipative solutions. However, when $f$ is not convex, we show that the dissipative solutions do not depend continuously on the initial data. %B Arch. Ration. Mech. Anal. 183 (2007) 163-185 %G en_US %U http://hdl.handle.net/1963/2182 %1 2062 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-05T07:08:27Z\\nNo. of bitstreams: 1\\n0502124v1.pdf: 205978 bytes, checksum: a1efb4667d7315509947b4d7a4999bd1 (MD5) %R 10.1007/s00205-006-0014-8 %0 Journal Article %J J. Fixed Point Theory Appl. 1 (2007) 305-336 %D 2007 %T Boundary interface for the Allen-Cahn equation %A Andrea Malchiodi %A Juncheng Wei %B J. Fixed Point Theory Appl. 1 (2007) 305-336 %G en_US %U http://hdl.handle.net/1963/2027 %1 2169 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-03T11:10:26Z\\nNo. of bitstreams: 1\\nMalchiodiWei07.pdf: 379788 bytes, checksum: 4c87f76e7db9858a9acfeca0a8ec75c1 (MD5) %R 10.1007/s11784-007-0016-7 %0 Journal Article %J Pacific Journal of Mathematics 229 (2007), No. 2, 447–468 %D 2007 %T Boundary-clustered interfaces for the Allen–Cahn equation %A Andrea Malchiodi %A Wei-Ming Ni %A Juncheng Wei %B Pacific Journal of Mathematics 229 (2007), No. 2, 447–468 %I Mathematical Sciences Publishers %G en %U http://hdl.handle.net/1963/5089 %1 4905 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-11-17T13:19:29Z\\nNo. of bitstreams: 1\\nmnw-pjm-final.pdf: 287316 bytes, checksum: 2a18e3af66be7b9b793a528138cf493a (MD5) %0 Report %D 2007 %T BV instability for the Lax-Friedrichs scheme %A Paolo Baiti %A Alberto Bressan %A Helge Kristian Jenssen %X It is proved that discrete shock profiles (DSPs) for the Lax-Friedrichs scheme for a system of conservation laws do not necessarily depend continuously in BV on their speed. We construct examples of $2 \\\\times 2$-systems for which there are sequences of DSPs with speeds converging to a rational number. Due to a resonance phenomenon, the difference between the limiting DSP and any DSP in the sequence will contain an order-one amount of variation. %G en_US %U http://hdl.handle.net/1963/2335 %1 1681 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-11-05T09:55:21Z\\nNo. of bitstreams: 1\\n0502043v1.pdf: 257155 bytes, checksum: 5055aa260394ac1339fa775b656f3b15 (MD5) %0 Journal Article %J Adv. Math. 209 (2007) 460-525 %D 2007 %T Concentration on minimal submanifolds for a singularly perturbed Neumann problem %A Fethi Mahmoudi %A Andrea Malchiodi %X We consider the equation $- \\\\e^2 \\\\D u + u= u^p$ in $\\\\Omega \\\\subseteq \\\\R^N$, where $\\\\Omega$ is open, smooth and bounded, and we prove concentration of solutions along $k$-dimensional minimal submanifolds of $\\\\partial \\\\O$, for $N \\\\geq 3$ and for $k \\\\in \\\\{1, ..., N-2\\\\}$. We impose Neumann boundary conditions, assuming $13 or with two inputs for n=4 and n=5, up to state-feedback transformations, preserving the affine structure. First using the Poincare series of moduli numbers we introduce the intrinsic numbers of functional moduli of each prescribed number of variables on which a classification problem depends. In order to classify affine systems with scalar input we associate with such a system the canonical frame by normalizing some structural functions in a commutative relation of the vector fields, which define our control system. Then, using this canonical frame, we introduce the canonical coordinates and find a complete system of state-feedback invariants of the system. It also gives automatically the micro-local (i.e. local in state-input space) classification of the generic non-affine n-dimensional control system with scalar input for n>2. Further we show how the problem of feedback-equivalence of affine systems with two-dimensional input in state space of dimensions 4 and 5 can be reduced to the same problem for affine systems with scalar input. In order to make this reduction we distinguish the subsystem of our control system, consisting of the directions of all extremals in dimension 4 and all abnormal extremals in dimension 5 of the time optimal problem, defined by the original control system. In each classification problem under consideration we find the intrinsic numbers of functional moduli of each prescribed number of variables according to its Poincare series. %B SIAM J. Control Optim. 46 (2007) 1431-1460 %G en_US %U http://hdl.handle.net/1963/2186 %1 2058 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-05T09:10:03Z\\nNo. of bitstreams: 1\\n0502031v2.pdf: 352804 bytes, checksum: 261d7075283ef8321d485a773ab50353 (MD5) %R 10.1137/050623711 %0 Journal Article %J Ann. Inst. Henri Poincare-Prob. Stat. 43 (2007) 399-415 %D 2007 %T On finite-dimensional projections of distributions for solutions of randomly forced PDE\\\'s %A Andrei A. Agrachev %A Sergei Kuksin %A Andrey Sarychev %A Armen Shirikyan %X The paper is devoted to studying the image of probability measures on a Hilbert space under finite-dimensional analytic maps. We establish sufficient conditions under which the image of a measure has a density with respect to the Lebesgue measure and continuously depends on the map. The results obtained are applied to the 2D Navier-Stokes equations perturbed by various random forces of low dimension. %B Ann. Inst. Henri Poincare-Prob. Stat. 43 (2007) 399-415 %G en_US %U http://hdl.handle.net/1963/2012 %1 2184 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-08-31T09:21:55Z\\nNo. of bitstreams: 1\\nmathAP0603295v1.pdf: 316127 bytes, checksum: 6686ad78dcb2dbc5efb64a959b30750c (MD5) %R 10.1016/j.anihpb.2006.06.001 %0 Journal Article %J Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 333-342 %D 2007 %T Gaussian estimates for hypoelliptic operators via optimal control %A Ugo Boscain %A Sergio Polidoro %X We obtain Gaussian lower bounds for the fundamental solution of a class of hypoelliptic equations, by using repeatedly an invariant Harnack inequality. Our main result is given in terms of the value function of a suitable optimal control problem. %B Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 333-342 %G en_US %U http://hdl.handle.net/1963/1994 %1 2202 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-08-09T13:14:42Z\\nNo. of bitstreams: 1\\n45-2007M.pdf: 181670 bytes, checksum: 6f262dccd2b3004cfd0b0b711bd011b2 (MD5) %R 10.4171/RLM/499 %0 Report %D 2007 %T High-order angles in almost-Riemannian geometry %A Ugo Boscain %A Mario Sigalotti %X Let X and Y be two smooth vector fields on a two-dimensional manifold M. If X and Y are everywhere linearly independent, then they define a Riemannian metric on M (the metric for which they are orthonormal) and they give to M the structure of metric space. If X and Y become linearly dependent somewhere on M, then the corresponding Riemannian metric has singularities, but under generic conditions the metric structure is still well defined. Metric structures that can be defined locally in this way are called almost-Riemannian structures. The main result of the paper is a generalization to almost-Riemannian structures of the Gauss-Bonnet formula for domains with piecewise-C2 boundary. The main feature of such formula is the presence of terms that play the role of high-order angles at the intersection points with the set of singularities. %G en_US %U http://hdl.handle.net/1963/1995 %1 2201 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-08-24T12:00:46Z\\nNo. of bitstreams: 1\\nhigh-order.pdf: 168685 bytes, checksum: 11d6f55bf9b07b4da01dae3f3deb969a (MD5) %0 Journal Article %J Phys. Rev. Lett. 98 (2007) 030404 %D 2007 %T Luther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas %A Gao Xianlong %A Matteo Rizzi %A Marco Polini %A Rosario Fazio %A Mario P. Tosi %A Vivaldo L. Jr. Campo %A Klaus Capelle %X

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

%B Phys. Rev. Lett. 98 (2007) 030404 %G en_US %U http://hdl.handle.net/1963/2056 %1 2140 %2 Physics %3 Condensed Matter Theory %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-06T11:46:28Z\\nNo. of bitstreams: 1\\ncond-mat0609346v1.pdf: 218755 bytes, checksum: 06a409d540e05ece03bbac85198ee19c (MD5) %R 10.1103/PhysRevLett.98.030404 %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 Report %D 2007 %T Multi-bump solitons to linearly coupled systems of nonlinear Schrödinger equations %A Antonio Ambrosetti %A Eduardo Colorado %A David Ruiz %B Calc. Var. Partial Differential Equations 30 (2007) 85-112 %G en_US %U http://hdl.handle.net/1963/1835 %1 2381 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-06-13T09:30:35Z\\nNo. of bitstreams: 1\\n29M-2006.pdf: 394371 bytes, checksum: de96976aa35a5289ec5ab93a664b9be5 (MD5) %R 10.1007/s00526-006-0079-0 %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire 24 (2007) 279-310 %D 2007 %T Nearly time optimal stabilizing patchy feedbacks %A Fabio Ancona %A Alberto Bressan %X We consider the time optimal stabilization problem for a nonlinear control system $\\\\dot x=f(x,u)$. Let $\\\\tau(y)$ be the minimum time needed to steer the system from the state $y\\\\in\\\\R^n$ to the origin, and call $\\\\A(T)$ the set of initial states that can be steered to the origin in time $\\\\tau(y)\\\\leq T$. Given any $\\\\ve>0$, in this paper we construct a patchy feedback $u=U(x)$ such that every solution of $\\\\dot x=f(x, U(x))$, $x(0)=y\\\\in \\\\A(T)$ reaches an $\\\\ve$-neighborhood of the origin within time $\\\\tau(y)+\\\\ve$. %B Ann. Inst. H. Poincare Anal. Non Lineaire 24 (2007) 279-310 %G en_US %U http://hdl.handle.net/1963/2185 %1 2059 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-05T08:22:02Z\\nNo. of bitstreams: 1\\n0512531v1.pdf: 428805 bytes, checksum: 8eae0ca68a7339938991d987a677d6f9 (MD5) %R 10.1016/j.anihpc.2006.03.010 %0 Journal Article %J J. Eur. Math. Soc. (JEMS) 9 (2007) 219-252 %D 2007 %T Necessary and sufficient conditions for the chainrule in W1,1loc(RN;Rd) and BVloc(RN;Rd) %A Giovanni Leoni %A Massimiliano Morini %XIn this paper we prove necessary and sufficient conditions for the validity of the classical chain rule in Sobolev spaces and in the space of functions of bounded variation.

%B J. Eur. Math. Soc. (JEMS) 9 (2007) 219-252 %G en_US %U http://hdl.handle.net/1963/2037 %1 2159 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-03T16:39:37Z\\nNo. of bitstreams: 1\\n05-CNA-001.pdf: 331793 bytes, checksum: b6fd9f7cf79aacffa4d60dda74d183a6 (MD5) %R 10.4171/JEMS/78 %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 Journal Article %J NoDEA 13 (2007) 713-734 %D 2007 %T On a notion of unilateral slope for the Mumford-Shah functional %A Gianni Dal Maso %A Rodica Toader %X In this paper we introduce a notion of unilateral slope for the Mumford-Shah functional, and provide an explicit formula in the case of smooth cracks. We show that the slope is not lower semicontinuous and study the corresponding relaxed functional. %B NoDEA 13 (2007) 713-734 %G en_US %U http://hdl.handle.net/1963/2059 %1 2137 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-06T14:02:51Z\\nNo. of bitstreams: 1\\n0410525v1.pdf: 214576 bytes, checksum: 3722f413401cdb51f778a8c15eeebe71 (MD5) %R 10.1007/s00030-006-4054-4 %0 Journal Article %J C. R. Math. 345 (2007) 647-652 %D 2007 %T Parametrized curves in Lagrange Grassmannians %A Igor Zelenko %A Li Chengbo %B C. R. Math. 345 (2007) 647-652 %G en_US %U http://hdl.handle.net/1963/2560 %1 1559 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-01-17T13:49:21Z\\nNo. of bitstreams: 1\\n0708.1100v1.pdf: 336234 bytes, checksum: d04e21a2139ddd8622a28c31cd370eed (MD5) %R 10.1016/j.crma.2007.10.034 %0 Report %D 2007 %T Perturbation techniques applied to the real vanishing viscosity approximation of an initial boundary value problem %A Stefano Bianchini %I SISSA %G en %U http://preprints.sissa.it/handle/1963/35315 %1 35623 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-05-22T11:26:14Z No. of bitstreams: 1 boundarysingular.pdf: 312896 bytes, checksum: 59e29e4c3042b208b70e76cde63fbf32 (MD5) %0 Report %D 2007 %T Quasistatic crack growth for a cohesive zone model with prescribed crack path %A Gianni Dal Maso %A Chiara Zanini %X In this paper we study the quasistatic crack growth for a cohesive zone model. We assume that the crack path is prescribed and we study the time evolution of the crack in the framework of the variational theory of rate-independent processes. %B Proc. Roy. Soc. Edinburgh Sect. A 137 (2007) 253-279 %G en_US %U http://hdl.handle.net/1963/1686 %1 2447 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2005-06-20T12:05:32Z\\nNo. of bitstreams: 1\\nDM-Zan-04.pdf: 312529 bytes, checksum: 2373a684663d7901c85daad77c7aa8b6 (MD5) %R 10.1017/S030821050500079X %0 Journal Article %J Milan J. Math. 75 (2007) 117-134 %D 2007 %T Quasistatic evolution problems for pressure-sensitive plastic materials %A Gianni Dal Maso %A Alexey Demyanov %A Antonio DeSimone %X We study quasistatic evolution problems for pressure-sensitive plastic materials in the context of small strain associative perfect plasticity. %B Milan J. Math. 75 (2007) 117-134 %G en_US %U http://hdl.handle.net/1963/1962 %1 2231 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-05-15T10:32:12Z\\nNo. of bitstreams: 1\\nSissa27_2007M.pdf: 223083 bytes, checksum: a4cdbb7a1018403355c560749680e47a (MD5) %R 10.1007/s00032-007-0071-y %0 Journal Article %J Atti .Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 209-219 %D 2007 %T On the regularity of weak solutions to H-systems %A Roberta Musina %X Abstract. In this paper we prove that every weak solution to the H-surface equation is locally bounded, provided the prescibed mean curvatore H is asymptotic to a constant at infinity (with a suitable decay rate). No smoothness ssumptions are required on H. We consider also the Dirichlet problem.... %B Atti .Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 209-219 %G en_US %U http://hdl.handle.net/1963/1753 %1 2791 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-20T11:28:05Z\\nNo. of bitstreams: 1\\n36M.pdf: 150157 bytes, checksum: 61fa8ec27fb7c35396978c1aa4dd26fd (MD5) %0 Report %D 2007 %T Soft elasticity and microstructure in smectic C elastomers %A Antonio DeSimone %A James Adams %A Sergio Conti %X Smectic C elastomers are layered materials exhibiting a solid-like elastic response along the layer normal and a rubbery one in the plane. The set of strains minimizing the elastic energy contains a one-parameter family of simple stretches associated with an internal degree of freedom, coming from the in-plane component of the director. We investigate soft elasticity and the corresponding microstructure by determining the quasiconvex hull of the set , and use this to propose experimental tests that should make the predicted soft response observable. %B Contin. Mech. Thermodyn. 18 (2007) 319-334 %G en_US %U http://hdl.handle.net/1963/1811 %1 2403 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-04-12T09:42:24Z\\nNo. of bitstreams: 1\\nsissa05M-06.pdf: 394760 bytes, checksum: 95c4183d6cb1210bf2a689ae083a3cb7 (MD5) %R 10.1007/s00161-006-0031-8 %0 Journal Article %J J. Math. Anal. Appl. 335 (2007) 1143-1160 %D 2007 %T Solutions of vectorial Hamilton-Jacobi equations and minimizers of nonquasiconvex functionals %A Sandro Zagatti %X We provide a unified approach to prove existence results for the Dirichlet problem for Hamilton-Jacobi equations and for the minimum problem for nonquasiconvex functionals of the Calculus of Variations with affine boundary data. The idea relies on the definition of integro-extremal solutions introduced in the study of nonconvex scalar variational problem. %B J. Math. Anal. Appl. 335 (2007) 1143-1160 %G en_US %U http://hdl.handle.net/1963/2763 %1 1937 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-08-29T11:05:58Z\\nNo. of bitstreams: 1\\nhjcvjmaa2.pdf: 158429 bytes, checksum: 712208cb11d8543ac2f9f5f01956dcfe (MD5) %R 10.1016/j.jmaa.2007.02.034 %0 Report %D 2007 %T Solutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part II: proof of the existence result %A Fethi Mahmoudi %A Andrea Malchiodi %X We prove existence of a special class of solutions to the (elliptic) Nonlinear Schroedinger Equation $- \\\\epsilon^2 \\\\Delta \\\\psi + V(x) \\\\psi = |\\\\psi|^{p-1} \\\\psi$ on a manifold or in the Euclidean space. Here V represents the potential, p is an exponent greater than 1 and $\\\\epsilon$ a small parameter corresponding to the Planck constant. As $\\\\epsilon$ tends to zero (namely in the semiclassical limit) we prove existence of complex-valued solutions which concentrate along closed curves, and whose phase in highly oscillatory. Physically, these solutions carry quantum-mechanical momentum along the limit curves. In the first part of this work we identified the limit set and constructed approximate solutions, while here we give the complete proof of our main existence result. %G en_US %U http://hdl.handle.net/1963/2111 %1 2578 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-17T08:58:17Z\\nNo. of bitstreams: 1\\n0708.0104v1.pdf: 663755 bytes, checksum: bbc4a382b0338288fa6ce9002872d955 (MD5) %0 Report %D 2007 %T Solutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part I: study of the limit set and approximate solutions %A Fethi Mahmoudi %A Andrea Malchiodi %A Marcelo Montenegro %X We prove existence of a special class of solutions to the (elliptic) Nonlinear Schroeodinger Equation $- \\\\epsilon^2 \\\\Delta \\\\psi + V(x) \\\\psi = |\\\\psi|^{p-1} \\\\psi$, on a manifold or in the Euclidean space. Here V represents the potential, p an exponent greater than 1 and $\\\\epsilon$ a small parameter corresponding to the Planck constant. As $\\\\epsilon$ tends to zero (namely in the semiclassical limit) we prove existence of complex-valued solutions which concentrate along closed curves, and whose phase is highly oscillatory. Physically, these solutions carry quantum-mechanical momentum along the limit curves. In this first part we provide the characterization of the limit set, with natural stationarity and non-degeneracy conditions. We then construct an approximate solution up to order $\\\\epsilon^2$, showing that these conditions appear naturally in a Taylor expansion of the equation in powers of $\\\\epsilon$. Based on these, an existence result will be proved in the second part. %G en_US %U http://hdl.handle.net/1963/2112 %1 2577 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-17T09:14:27Z\\nNo. of bitstreams: 1\\n0708.0125v1.pdf: 498331 bytes, checksum: 95036be8fb1f07136be4d6bdc1aab642 (MD5) %0 Journal Article %J Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 391-412 %D 2007 %T Some existence results for the Toda system on closed surfaces %A Andrea Malchiodi %A Cheikh Birahim Ndiaye %X Given a compact closed surface $\\\\Sig$, we consider the {\\\\em generalized Toda} system of equations on $\\\\Sig$: $- \\\\D u_i = \\\\sum_{j=1}^2 \\\\rho_j a_{ij} \\\\left( \\\\frac{h_j e^{u_j}}{\\\\int_\\\\Sig h_j e^{u_j} dV_g} - 1 \\\\right)$ for $i = 1, 2$, where $\\\\rho_1, \\\\rho_2$ are real parameters and $h_1, h_2$ are smooth positive functions. Exploiting the variational structure of the problem and using a new minimax scheme we prove existence of solutions for generic values of $\\\\rho_1$ and for $\\\\rho_2 < 4 \\\\pi$. %B Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 391-412 %G en_US %U http://hdl.handle.net/1963/1775 %1 2769 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-29T08:29:06Z\\nNo. of bitstreams: 1\\n75M.pdf: 258110 bytes, checksum: 18821ff73b71e5079c15c32f59961ad9 (MD5) %R 10.4171/RLM/504 %0 Journal Article %J NoDEA Nonlinear Differential Equations Appl. 14 (2007) 569-592 %D 2007 %T Stability of front tracking solutions to the initial and boundary value problem for systems of conservation laws %A Andrea Marson %A Carlotta Donadello %B NoDEA Nonlinear Differential Equations Appl. 14 (2007) 569-592 %G en_US %U http://hdl.handle.net/1963/1769 %1 2775 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-28T10:29:02Z\\nNo. of bitstreams: 1\\n68M.pdf: 209186 bytes, checksum: 79dcb94eb1405cbadb411592b2cffe66 (MD5) %R 10.1007/s00030-007-5010-7 %0 Report %D 2007 %T Standing waves of some coupled Nonlinear Schrödinger Equations %A Antonio Ambrosetti %A Eduardo Colorado %X We deal with a class of systems of NLS equations, proving the existence of bound and ground states provided the coupling parameter is small, respectively, large. %B J. Lond. Math. Soc. 75 (2007) 67-82 %G en_US %U http://hdl.handle.net/1963/1821 %1 2393 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-04-18T14:55:22Z\\nNo. of bitstreams: 1\\nsissa,2_2006_M.pdf: 431407 bytes, checksum: 0e294e77a4423c4b41ce178df2187dd3 (MD5) %R 10.1112/jlms/jdl020 %0 Journal Article %J Arch. Rational Mech. Anal. 183 (2007) 411-456 %D 2007 %T Surfactants in Foam Stability: A Phase-Field Model %A Irene Fonseca %A Massimiliano Morini %A Valeriy Slastikov %X The role of surfactants in stabilizing the formation of bubbles in foams is studied using a phase-field model. The analysis is centered on a van der Walls-Cahn-Hilliard-type energy with an added term accounting for the interplay between the presence of a surfactant density and the creation of interfaces. In particular, it is concluded that the surfactant segregates to the interfaces, and that the prescriptionof the distribution of surfactant will dictate the locus of interfaces, what is in agreement with experimentation. %B Arch. Rational Mech. Anal. 183 (2007) 411-456 %G en_US %U http://hdl.handle.net/1963/2035 %1 2161 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-03T15:51:40Z\\nNo. of bitstreams: 1\\n05-CNA-012.pdf: 414998 bytes, checksum: 3c44841388edba53080d531beadad798 (MD5) %R 10.1007/s00205-006-0012-x %0 Journal Article %J 46th IEEE Conference on Decision and Control (2007) 5389 - 5394 %D 2007 %T Time optimal swing-up of the planar pendulum %A Mireille E. Broucke %A Paolo Mason %A Benedetto Piccoli %X This paper presents qualitative and numerical results on the global structure of the time optimal trajectories of the planar pendulum on a cart. %B 46th IEEE Conference on Decision and Control (2007) 5389 - 5394 %G en_US %U http://hdl.handle.net/1963/1867 %1 2355 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-10-11T06:54:22Z\\nNo. of bitstreams: 1\\n50-2006M.pdf: 688756 bytes, checksum: d32f46138cc2e7400dfec38315fdb24a (MD5) %R 10.1109/CDC.2007.4434688 %0 Report %D 2007 %T Time-dependent systems of generalized Young measures %A Gianni Dal Maso %A Antonio DeSimone %A Maria Giovanna Mora %A Massimiliano Morini %X In this paper some new tools for the study of evolution problems in the framework of Young measures are introduced. A suitable notion of time-dependent system of generalized Young measures is defined, which allows to extend the classical notions of total variation and absolute continuity with respect to time, as well as the notion of time derivative. The main results are a Helly type theorem for sequences of systems of generalized Young measures and a theorem about the existence of the time derivative for systems with bounded variation with respect to time. %B Netw. Heterog. Media 2 (2007) 1-36 %G en_US %U http://hdl.handle.net/1963/1795 %1 2749 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-04-04T13:16:42Z\\nNo. of bitstreams: 1\\n98M-2005.pdf: 339547 bytes, checksum: 695874ce74733dc0020a7e357f04cb1b (MD5) %0 Journal Article %J J. Convex Anal. 14 (2007) 705-727 %D 2007 %T Uniqueness and continuous dependence on boundary data for integro-extremal minimizers of the functional of the gradient %A Sandro Zagatti %X We study some qualitative properties of the integro-extremal minimizers of the functional of the gradient defined on Sobolev spaces with Dirichlet boundary conditions. We discuss their use in the non-convex case via viscosity methods and give conditions under which they are unique and depend continuously on boundary data. %B J. Convex Anal. 14 (2007) 705-727 %G en_US %U http://hdl.handle.net/1963/2762 %1 1938 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-08-29T10:56:35Z\\nNo. of bitstreams: 1\\nwpca3.pdf: 193462 bytes, checksum: 05e86c2307278ebd530e02f2baf5072e (MD5) %0 Journal Article %J J. Hyperbolic Differ. Equ. 4 (2007) 771-795 %D 2007 %T Viscosity solutions of Hamilton-Jacobi equations with discontinuous coefficients %A Giuseppe Maria Coclite %A Nils Henrik Risebro %X We consider Hamilton--Jacobi equations, where the Hamiltonian depends discontinuously on both the spatial and temporal location. Our main results are the existence and well--posedness of a viscosity solution to the Cauchy problem. We define a viscosity solution by treating the discontinuities in the coefficients analogously to \\\"internal boundaries\\\". By defining an appropriate penalization function, we prove that viscosity solutions are unique. The existence of viscosity solutions is established by showing that a sequence of front tracking approximations is compact in $L^\\\\infty$, and that the limits are viscosity solutions. %B J. Hyperbolic Differ. Equ. 4 (2007) 771-795 %I World Scientific %G en_US %U http://hdl.handle.net/1963/2907 %1 1793 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T10:55:33Z\\nNo. of bitstreams: 1\\nmath.AP0303288.pdf: 286583 bytes, checksum: ec274415af1f87dc1406bdc76cab8159 (MD5) %R 10.1142/S0219891607001355 %0 Journal Article %J Calc. Var. Partial Differential Equations 27 (2006) 233-253 %D 2006 %T 2-d stability of the Néel wall %A Antonio DeSimone %A Hans Knuepfer %A Felix Otto %X We are interested in thin-film samples in micromagnetism, where the magnetization m is a 2-d unit-length vector field. More precisely we are interested in transition layers which connect two opposite magnetizations, so called Néel walls. %B Calc. Var. Partial Differential Equations 27 (2006) 233-253 %G en_US %U http://hdl.handle.net/1963/2194 %1 2050 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-10T12:14:45Z\\nNo. of bitstreams: 1\\nstability.pdf: 226255 bytes, checksum: dec90ada941ac865d9451848ca2faa5f (MD5) %R 10.1007/s00526-006-0019-z %0 Journal Article %J Phys. Rev. B 73 (2006) 100502(R) %D 2006 %T 4e-condensation in a fully frustrated Josephson junction diamond chain %A Matteo Rizzi %A Vittorio Cataudella %A Rosario Fazio %XFully frustrated one-dimensional diamond Josephson chains have been shown [B. Dou\\\\c{c}ot and J. Vidal, Phys. Rev. Lett. {\\\\bf 88}, 227005 (2002)] to posses a remarkable property: The superfluid phase occurs through the condensation of pairs of Cooper pairs. By means of Monte Carlo simulations we analyze quantitatively the Insulator to $4e$-Superfluid transition. We determine the location of the critical point and discuss the behaviour of the phase-phase correlators. For comparison we also present the case of a diamond chain at zero and 1/3 frustration where the standard $2e$-condensation is observed.

%B Phys. Rev. B 73 (2006) 100502(R) %G en_US %U http://hdl.handle.net/1963/2400 %1 2297 %2 Physics %3 Condensed Matter Theory %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-11-13T08:27:31Z\\nNo. of bitstreams: 1\\n0511423v1.pdf: 197406 bytes, checksum: 754c3576bbb6a549f4dac12eeb8fc92d (MD5) %R 10.1103/PhysRevB.73.100502 %0 Report %D 2006 %T An artificial viscosity approach to quasistatic crack growth %A Rodica Toader %A Chiara Zanini %X We introduce a new model of irreversible quasistatic crack growth in which the evolution of cracks is the limit of a suitably modified $\\\\epsilon$-gradient flow of the energy functional, as the \\\"viscosity\\\" parameter $\\\\epsilon$ tends to zero. %G en_US %U http://hdl.handle.net/1963/1850 %1 2367 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-07-26T10:13:38Z\\nNo. of bitstreams: 1\\nmath.AP-0607596.pdf: 297980 bytes, checksum: 7a13d5d5fe36a4577923b3ccd0b0acaf (MD5) %0 Journal Article %J SIAM J. Math. Anal. 37 (2006) 83-102 %D 2006 %T A Birkhoff-Lewis-Type Theorem for Some Hamiltonian PDEs %A Dario Bambusi %A Massimiliano Berti %X In this paper we give an extension of the Birkhoff--Lewis theorem to some semilinear PDEs. Accordingly we prove existence of infinitely many periodic orbits with large period accumulating at the origin. Such periodic orbits bifurcate from resonant finite dimensional invariant tori of the fourth order normal form of the system. Besides standard nonresonance and nondegeneracy assumptions, our main result is obtained assuming a regularizing property of the nonlinearity. We apply our main theorem to a semilinear beam equation and to a nonlinear Schr\\\\\\\"odinger equation with smoothing nonlinearity. %B SIAM J. Math. Anal. 37 (2006) 83-102 %G en_US %U http://hdl.handle.net/1963/2159 %1 2085 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-02T09:24:09Z\\nNo. of bitstreams: 1\\n0310182v1.pdf: 221749 bytes, checksum: 1ca47fecc44576d771b14ead5f53db0e (MD5) %R 10.1137/S0036141003436107 %0 Journal Article %J C. R. Acad. Sci. Paris, Ser. I 342 (2006) 453-458 %D 2006 %T Bound and ground states of coupled nonlinear Schrödinger equations %A Antonio Ambrosetti %A Eduardo Colorado %X We prove existence of bound and ground states of some systems of coupled nonlinear Schrodinger equations. %B C. R. Acad. Sci. Paris, Ser. I 342 (2006) 453-458 %G en_US %U http://hdl.handle.net/1963/2149 %1 2094 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-28T10:05:04Z\\nNo. of bitstreams: 1\\nAmbrosettiColorado05.pdf: 205538 bytes, checksum: 7ada83c882cd1488c72316a917a79c87 (MD5) %R 10.1016/j.crma.2006.01.024 %0 Journal Article %J J. Anal. Math. 98 (2006) 317-348 %D 2006 %T Bound states of Nonlinear Schroedinger Equations with Potentials Vanishing at Infinity %A Antonio Ambrosetti %A Andrea Malchiodi %A David Ruiz %B J. Anal. Math. 98 (2006) 317-348 %G en_US %U http://hdl.handle.net/1963/1756 %1 2788 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-21T12:13:53Z\\nNo. of bitstreams: 1\\n18M-2005.pdf: 300610 bytes, checksum: cf46904521c6dfea82ac4f4516bc9fe0 (MD5) %R 10.1007/BF02790279 %0 Journal Article %J Self-Similar Solutions of Nonlinear PDE / Ed. Piotr Biler and Grzegorz Karch. - Banach Center Publ. 74 (2006) 13-31 %D 2006 %T On Bressan\\\'s conjecture on mixing properties of vector fields %A Stefano Bianchini %B Self-Similar Solutions of Nonlinear PDE / Ed. Piotr Biler and Grzegorz Karch. - Banach Center Publ. 74 (2006) 13-31 %G en_US %U http://hdl.handle.net/1963/1806 %1 2408 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-04-06T13:44:58Z\\nNo. of bitstreams: 1\\n70M.pdf: 252974 bytes, checksum: 6abff10ab36790484305a3078d9cbfd7 (MD5) %0 Report %D 2006 %T A Canonical Frame for Nonholonomic Rank Two Distributions of Maximal Class %A Boris Doubrov %A Igor Zelenko %X In 1910 E. Cartan constructed the canonical frame and found the most symmetric case for maximally nonholonomic rank 2 distributions in R5. We solve the analogous problems for rank 2 distributions in Rn for arbitrary n > 5. Our method is a kind of symplectification of the problem and it is completely different from the Cartan method of equivalence. %B C. R. Math. Acad. Sci. Paris 342 (2006) 589-594 %G en_US %U http://hdl.handle.net/1963/1712 %1 2439 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-01-18T10:08:04Z\\nNo. of bitstreams: 1\\nmath.DG0504319.pdf: 158321 bytes, checksum: 4a76e9fa42a9ea4440d0fcd628df9c34 (MD5) %R 10.1016/j.crma.2006.02.010 %0 Journal Article %J Duke Math. J. 134 (2006) 359-419 %D 2006 %T Cantor families of periodic solutions for completely resonant nonlinear wave equations %A Massimiliano Berti %A Philippe Bolle %X We prove the existence of small amplitude, $2\\\\pi \\\\slash \\\\om$-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions, for any frequency $ \\\\om $ belonging to a Cantor-like set of positive measure and for a new set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem. In spite of the complete resonance of the equation we show that we can still reduce the problem to a {\\\\it finite} dimensional bifurcation equation. Moreover, a new simple approach for the inversion of the linearized operators required by the Nash-Moser scheme is developed. It allows to deal also with nonlinearities which are not odd and with finite spatial regularity. %B Duke Math. J. 134 (2006) 359-419 %G en_US %U http://hdl.handle.net/1963/2161 %1 2083 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-02T09:53:35Z\\nNo. of bitstreams: 1\\n0410618v1.pdf: 427752 bytes, checksum: 08750b5fadd830fbe76aa48d54824f17 (MD5) %R 10.1215/S0012-7094-06-13424-5 %0 Journal Article %J J. Math. Sci. 135 (2006) 3109-3124 %D 2006 %T Classification of stable time-optimal controls on 2-manifolds %A Ugo Boscain %A Igor Nikolaev %A Benedetto Piccoli %B J. Math. Sci. 135 (2006) 3109-3124 %G en_US %U http://hdl.handle.net/1963/2196 %1 2048 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-11T07:48:50Z\\nNo. of bitstreams: 1\\nboscain-paper.pdf: 322031 bytes, checksum: 560c6fdce3f93d196d1cc9d9c4115edb (MD5) %R 10.1007/s10958-006-0148-0 %0 Journal Article %J SIAM J. Control Optim. 45 (2006) 226-245 %D 2006 %T Common Polynomial Lyapunov Functions for Linear Switched Systems %A Paolo Mason %A Ugo Boscain %A Yacine Chitour %X In this paper, we consider linear switched systems $\\\\dot x(t)=A_{u(t)} x(t)$, $x\\\\in\\\\R^n$, $u\\\\in U$, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching ({\\\\bf UAS} for short). We first prove that, given a {\\\\bf UAS} system, it is always possible to build a common polynomial Lyapunov function. Then our main result is that the degree of that common polynomial Lyapunov function is not uniformly bounded over all the {\\\\bf UAS} systems. This result answers a question raised by Dayawansa and Martin. A generalization to a class of piecewise-polynomial Lyapunov functions is given. %B SIAM J. Control Optim. 45 (2006) 226-245 %G en_US %U http://hdl.handle.net/1963/2181 %1 2063 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-04T14:36:21Z\\nNo. of bitstreams: 1\\n0403209v2.pdf: 244831 bytes, checksum: 1762d79876f9eb915a68dbc25d9a3a21 (MD5) %R 10.1137/040613147 %0 Journal Article %J J. Reine Angew. Math. 594 (2006) 137-174 %D 2006 %T Compactness of solutions to some geometric fourth-order equations %A Andrea Malchiodi %X We prove compactness of solutions to some fourth order equations with exponential nonlinearities on four manifolds. The proof is based on a refined bubbling analysis, for which the main estimates are given in integral form. Our result is used in a subsequent paper to find critical points (via minimax arguments) of some geometric functional, which give rise to conformal metrics of constant $Q$-curvature. As a byproduct of our method, we also obtain compactness of such metrics. %B J. Reine Angew. Math. 594 (2006) 137-174 %G en_US %U http://hdl.handle.net/1963/2126 %1 2117 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-18T08:13:05Z\\nNo. of bitstreams: 1\\n0410140v2.pdf: 335757 bytes, checksum: 30341fcdac6b4d8f187b4bab1191c993 (MD5) %R 10.1515/CRELLE.2006.038 %0 Journal Article %J Atti Accad. Naz Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 17 (2006) 279-290 %D 2006 %T Concentration at manifolds of arbitrary dimension for a singularly perturbed Neumann problem %A Fethi Mahmoudi %A Andrea Malchiodi %X We consider the equation $- \\\\e^2 \\\\D u + u = u^p$ in $\\\\O \\\\subseteq \\\\R^N$, where $\\\\O$ is open, smooth and bounded, and we prove concentration of solutions along $k$-dimensional minimal submanifolds of $\\\\pa \\\\O$, for $N \\\\geq 3$ and for $k \\\\in \\\\{1, \\\\dots, N-2\\\\}$. We impose Neumann boundary conditions, assuming $1<\\\\frac{N-k+2}{N-k-2}$ and $\\\\e \\\\to 0^+$. This result settles in full generality a phenomenon previously considered only in the particular case $N = 3$ and $k = 1$. %B Atti Accad. Naz Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 17 (2006) 279-290 %G en_US %U http://hdl.handle.net/1963/2170 %1 2074 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-03T12:23:19Z\\nNo. of bitstreams: 1\\nMahmoudiMalchiodi06.pdf: 624613 bytes, checksum: 030160de63323a3b0c3864b8f5102b0b (MD5) %0 Journal Article %J Comm. Math. Phys. 266 (2006) 471-497 %D 2006 %T Conservative Solutions to a Nonlinear Variational Wave Equation %A Alberto Bressan %A Zheng Yuxi %X We establish the existence of a conservative weak solution to the Cauchy problem for the nonlinear variational wave equation $u_{tt} - c(u)(c(u)u_x)_x=0$, for initial data of finite energy. Here $c(\\\\cdot)$ is any smooth function with uniformly positive bounded values. %B Comm. Math. Phys. 266 (2006) 471-497 %G en_US %U http://hdl.handle.net/1963/2184 %1 2060 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-05T08:06:00Z\\nNo. of bitstreams: 1\\n0502058v1.pdf: 265359 bytes, checksum: 77983b4834210b17aa4c758dbf189d4a (MD5) %R 10.1007/s00220-006-0047-8 %0 Journal Article %J Arch. Ration. Mech. Anal. 181 (2006) 1-42 %D 2006 %T The Dirichlet problem for H-systems with small boundary data: blowup phenomena and nonexistence results %A Paolo Caldiroli %A Roberta Musina %B Arch. Ration. Mech. Anal. 181 (2006) 1-42 %G en_US %U http://hdl.handle.net/1963/2252 %1 1995 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-18T07:32:51Z\\nNo. of bitstreams: 1\\nCaldiroliMusina04.pdf: 395788 bytes, checksum: f37ad36b2fc2eb85d6430053a575ed8c (MD5) %R 10.1007/s00205-005-0398-x %0 Journal Article %J ESAIM Control Optim. Calc. Var. 12 (2006) 409-441 %D 2006 %T An estimation of the controllability time for single-input systems on compact Lie Groups %A Andrei A. Agrachev %A Thomas Chambrion %X Geometric control theory and Riemannian techniques are used to describe the reachable set at time t of left invariant single-input control systems on semi-simple compact Lie groups and to estimate the minimal time needed to reach any point from identity. This method provides an effective way to give an upper and a lower bound for the minimal time needed to transfer a controlled quantum system with a drift from a given initial position to a given final position. The bounds include diameters of the flag manifolds; the latter are also explicitly computed in the paper. %B ESAIM Control Optim. Calc. Var. 12 (2006) 409-441 %G en_US %U http://hdl.handle.net/1963/2135 %1 2108 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-24T13:09:42Z\\nNo. of bitstreams: 1\\ncocv0452.pdf: 441157 bytes, checksum: 7c8ead7c835051e17567fe9bb8a60fbe (MD5) %R 10.1051/cocv:2006007 %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 Journal Article %J Ann. Inst. H. Poincaré Anal. Non Linéaire 23 (2006) 439-474 %D 2006 %T Forced vibrations of wave equations with non-monotone nonlinearities %A Massimiliano Berti %A Luca Biasco %X We prove existence and regularity of periodic in time solutions of completely resonant nonlinear forced wave equations with Dirichlet boundary conditions for a large class of non-monotone forcing terms. Our approach is based on a variational Lyapunov-Schmidt reduction. It turns out that the infinite dimensional bifurcation equation exhibits an intrinsic lack of compactness. We solve it via a minimization argument and a-priori estimate methods inspired to regularity theory of Rabinowitz. %B Ann. Inst. H. Poincaré Anal. Non Linéaire 23 (2006) 439-474 %G en_US %U http://hdl.handle.net/1963/2160 %1 2084 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-02T09:35:53Z\\nNo. of bitstreams: 1\\n0410619v1.pdf: 401724 bytes, checksum: 1aeb5616e38d96fffc8efa0b0e6cdc14 (MD5) %R 10.1016/j.anihpc.2005.05.004 %0 Journal Article %J J. Dyn. Control Syst. 12 (2006) 247-276 %D 2006 %T Fundamental form and Cartan tensor of (2,5)-distributions coincide %A Igor Zelenko %X In our previous paper for generic rank 2 vector distributions on n-dimensional manifold (n greater or equal to 5) we constructed a special differential invariant, the fundamental form. In the case n=5 this differential invariant has the same algebraic nature, as the covariant binary biquadratic form, constructed by E.Cartan in 1910, using his ``reduction- prolongation\\\'\\\' procedure (we call this form Cartan\\\'s tensor). In the present paper we prove that our fundamental form coincides (up to constant factor -35) with Cartan\\\'s tensor. This result explains geometric reason for existence of Cartan\\\'s tensor (originally this tensor was obtained by very sophisticated algebraic manipulations) and gives the true analogs of this tensor in Riemannian geometry. In addition, as a part of the proof, we obtain a new useful formula for Cartan\\\'s tensor in terms of structural functions of any frame naturally adapted to the distribution. %B J. Dyn. Control Syst. 12 (2006) 247-276 %G en_US %U http://hdl.handle.net/1963/2187 %1 2057 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-05T10:55:36Z\\nNo. of bitstreams: 1\\n0402195v2.pdf: 284986 bytes, checksum: dae1f8053a160dbaf2913b802569c21a (MD5) %R 10.1007/s10450-006-0383-1 %0 Journal Article %J J. Math. Sci. 135 (2006) 3168-3194 %D 2006 %T On geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on distributions of corank 1 %A Igor Zelenko %X The present paper is devoted to the problem of (local) geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on generic corank 1 distributions. Using Pontryagin Maximum Principle, we treat Riemannian and sub-Riemannian cases in an unified way and obtain some algebraic necessary conditions for the geodesic equivalence of (sub-)Riemannian metrics. In this way first we obtain a new elementary proof of classical Levi-Civita\\\'s Theorem about the classification of all Riemannian geodesically equivalent metrics in a neighborhood of so-called regular (stable) point w.r.t. these metrics. Secondly we prove that sub-Riemannian metrics on contact distributions are geodesically equivalent iff they are constantly proportional. Then we describe all geodesically equivalent sub-Riemannian metrics on quasi-contact distributions. Finally we make the classification of all pairs of geodesically equivalent Riemannian metrics on a surface, which proportional in an isolated point. This is the simplest case, which was not covered by Levi-Civita\\\'s Theorem. %B J. Math. Sci. 135 (2006) 3168-3194 %G en_US %U http://hdl.handle.net/1963/2205 %1 2039 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-11T13:59:27Z\\nNo. of bitstreams: 1\\n0406111v1.pdf: 375215 bytes, checksum: cc4213e75a28857f98f01a294abff5e0 (MD5) %R 10.1007/s10958-006-0151-5 %0 Report %D 2006 %T Glimm interaction functional for BGK schemes %A Stefano Bianchini %G en_US %U http://hdl.handle.net/1963/1770 %1 2774 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-28T10:37:13Z\\nNo. of bitstreams: 1\\n69M.pdf: 213784 bytes, checksum: 597991852480bdc1aed7ed05ecc610c5 (MD5) %0 Report %D 2006 %T Infinite Horizon Noncooperative Differential Games %A Alberto Bressan %A Fabio Simone Priuli %X For a non-cooperative differential game, the value functions of the various players satisfy a system of Hamilton-Jacobi equations. In the present paper, we consider a class of infinite-horizon games with nonlinear costs exponentially discounted in time. By the analysis of the value\\nfunctions, we establish the existence of Nash equilibrium solutions in feedback form and provide results and counterexamples on their uniqueness and stability. %B J. Differential Equations 227 (2006) 230-257 %G en_US %U http://hdl.handle.net/1963/1720 %1 2431 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-01-24T09:08:57Z\\nNo. of bitstreams: 1\\nmath.AP0505212.pdf: 267217 bytes, checksum: 4c2f5eb11250fa9b31d9b46983c201e0 (MD5) %R 10.1016/j.jde.2006.01.005 %0 Journal Article %J Comm. Pure Appl. Math. 59 (2006) 1604-1638 %D 2006 %T An instability of the Godunov scheme %A Alberto Bressan %A Helge Kristian Jenssen %A Paolo Baiti %X We construct a solution to a $2\\\\times 2$ strictly hyperbolic system of conservation laws, showing that the Godunov scheme \\\\cite{Godunov59} can produce an arbitrarily large amount of oscillations. This happens when the speed of a shock is close to rational, inducing a resonance with the grid. Differently from the Glimm scheme or the vanishing viscosity method, for systems of conservation laws our counterexample indicates that no a priori BV bounds or $L^1$ stability estimates can in general be valid for finite difference schemes. %B Comm. Pure Appl. Math. 59 (2006) 1604-1638 %G en_US %U http://hdl.handle.net/1963/2183 %1 2061 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-05T07:52:50Z\\nNo. of bitstreams: 1\\n0502125v1.pdf: 337578 bytes, checksum: 41193faac363c00e9f80d6c05c0b098c (MD5) %R 10.1002/cpa.20141 %0 Journal Article %J Adv. Differential Equations 11 (2006) 931-960 %D 2006 %T On Palais-Smale sequences for H-systems: some examples %A Paolo Caldiroli %A Roberta Musina %X We exhibit a series of examples of Palais-Smale sequences for the Dirichlet problem associated to the mean curvature equation with null boundary condition, and we show that in the case of nonconstant mean curvature functions different kinds of blow up phenomena appear and Palais-Smale sequences may have quite wild behaviour. %B Adv. Differential Equations 11 (2006) 931-960 %G en_US %U http://hdl.handle.net/1963/2157 %1 2087 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-02T07:36:26Z\\nNo. of bitstreams: 1\\n32M.pdf: 296654 bytes, checksum: 7052b4b72f783376708b6bc60c882375 (MD5) %0 Journal Article %J J. Differential Geom. 73 (2006) 1-44 %D 2006 %T Q-curvature flow on S^4 %A Andrea Malchiodi %A Michael Struwe %B J. Differential Geom. 73 (2006) 1-44 %G en_US %U http://hdl.handle.net/1963/2193 %1 2051 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-10T11:52:21Z\\nNo. of bitstreams: 1\\nQ-curv-Nov-05.pdf: 298052 bytes, checksum: 2916315e6ffcef99b7748745e768d831 (MD5) %0 Journal Article %J Comm. Partial Differential Equations 31 (2006) 959 - 985 %D 2006 %T Quasi-periodic solutions of completely resonant forced wave equations %A Massimiliano Berti %A Michela Procesi %X We prove existence of quasi-periodic solutions with two frequencies of completely resonant, periodically forced nonlinear wave equations with periodic spatial boundary conditions. We consider both the cases the forcing frequency is: (Case A) a rational number and (Case B) an irrational number. %B Comm. Partial Differential Equations 31 (2006) 959 - 985 %G en_US %U http://hdl.handle.net/1963/2234 %1 2010 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-16T07:48:45Z\\nNo. of bitstreams: 1\\n0504406v1.pdf: 330239 bytes, checksum: 5dbf59bdd590a6876ea206f70cf0ecc9 (MD5) %R 10.1080/03605300500358129 %0 Journal Article %J Arch. Ration. Mech. Anal. 180 (2006) 237-291 %D 2006 %T Quasistatic evolution problems for linearly elastic-perfectly plastic materials %A Gianni Dal Maso %A Antonio DeSimone %A Maria Giovanna Mora %X The problem of quasistatic evolution in small strain associative elastoplasticity is studied in the framework of the variational theory for rate-independent processes. Existence of solutions is proved through the use of incremental variational problems in spaces of functions with bounded deformation. This provides a new approximation result for the solutions of the quasistatic evolution problem, which are shown to be absolutely continuous in time. Four equivalent formulations of the problem in rate form are derived. A strong formulation of the flow rule is obtained by introducing a precise definition of the stress on the singular set of the plastic strain. %B Arch. Ration. Mech. Anal. 180 (2006) 237-291 %G en_US %U http://hdl.handle.net/1963/2129 %1 2114 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-18T10:14:12Z\\nNo. of bitstreams: 1\\n0412212v1.pdf: 419970 bytes, checksum: fa4e3c2a5db22bfa28aa4f682cb55da4 (MD5) %R 10.1007/s00205-005-0407-0 %0 Journal Article %J Proc. Roy. Soc. Edinburgh Sect. A 136 (2006) 889-907 %D 2006 %T Radial solutions concentrating on spheres of nonlinear Schrödinger equations with vanishing potentials %A Antonio Ambrosetti %A David Ruiz %X We prove the existence of radial solutions of 1.2) concentrating at a sphere for potentials which might be zero and might decay to zero at\\r\\ninfinity. The proofs use a perturbation technique in a variational setting, through a Lyapunov-Schmidt reduction. %B Proc. Roy. Soc. Edinburgh Sect. A 136 (2006) 889-907 %G en_US %U http://hdl.handle.net/1963/1755 %1 2789 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-20T13:11:31Z\\r\\nNo. of bitstreams: 1\\r\\n38M.pdf: 251285 bytes, checksum: e0773652a2fcb13cab0758778b6ea906 (MD5) %R 10.1017/S0308210500004789 %0 Book Section %B The science of hysteresis / eds. Giorgio Bertotti, Isaak D. Mayergoyz. - Amsterdam: Elsevier, 2006. Vol.2, 269-381. %D 2006 %T Recent analytical developments in micromagnetics %A Antonio DeSimone %A Robert V. Kohn %A Stefan Müller %A Felix Otto %B The science of hysteresis / eds. Giorgio Bertotti, Isaak D. Mayergoyz. - Amsterdam: Elsevier, 2006. Vol.2, 269-381. %@ 978-0-12-480874-4 %G en_US %U http://hdl.handle.net/1963/2230 %1 2014 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-15T15:16:57Z\\nNo. of bitstreams: 1\\nDKMO.pdf: 1644450 bytes, checksum: 4c1079e4854e372d31af9a285f87f400 (MD5) %0 Report %D 2006 %T Stability of planar nonlinear switched systems %A Ugo Boscain %A Grégoire Charlot %A Mario Sigalotti %X We consider the time-dependent nonlinear system ˙ q(t) = u(t)X(q(t)) + (1 − u(t))Y (q(t)), where q ∈ R2, X and Y are two smooth vector fields, globally asymptotically stable at the origin and u : [0,∞) → {0, 1} is an arbitrary measurable function. Analysing the topology of the set where X and Y are parallel, we give some sufficient and some necessary conditions for global asymptotic stability, uniform with respect to u(.). Such conditions can be verified without any integration or construction of a Lyapunov function, and they are robust under small perturbations of the vector fields. %B Discrete Contin. Dyn. Syst. 15 (2006) 415-432 %G en_US %U http://hdl.handle.net/1963/1710 %1 2441 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-01-18T08:35:31Z\\nNo. of bitstreams: 1\\nmath.OC0502361.pdf: 322404 bytes, checksum: e56f0d709d97e2e300e3cb9d4a629a1b (MD5) %0 Report %D 2006 %T Time Minimal Trajectories for a Spin 1/2 Particle in a Magnetic field %A Ugo Boscain %A Paolo Mason %X In this paper we consider the minimum time population transfer problem for the z-component\\nof the spin of a (spin 1/2) particle driven by a magnetic field, controlled along the x axis, with bounded amplitude. On the Bloch sphere (i.e. after a suitable Hopf projection), this problem can be attacked with techniques of optimal syntheses on 2-D manifolds. Let (-E,E) be the two energy levels, and |omega (t)| ≤ M the bound on the field amplitude. For each couple of values E and M, we determine the time optimal synthesis starting from the level -E and we provide the explicit expression of the time optimal trajectories steering the state one to the state two, in terms of a parameter that can be computed solving numerically a suitable equation. For M/E << 1, every time optimal trajectory is bang-bang and in particular the corresponding control is periodic with frequency of the order of the resonance frequency wR = 2E. On the other side, for M/E > 1, the time optimal trajectory steering the state one to the state two is bang-bang with exactly one switching. Fixed E we also prove that for M → ∞ the time needed to reach the state two tends to zero. In the case M/E > 1 there are time optimal trajectories containing a singular arc. Finally we compare these results with some known results of Khaneja, Brockett and Glaser and with those obtained by controlling the magnetic field both on the x and y directions (or with one external field, but in the rotating wave approximation). As byproduct we prove that the qualitative shape of the time optimal synthesis presents different patterns, that cyclically alternate as M/E → 0, giving a partial proof of a conjecture formulated in a previous paper. %B Journal of Mathematical Physics 47, 062101 (2006) %G en_US %U http://hdl.handle.net/1963/1734 %1 2418 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-02-03T08:14:36Z\\nNo. of bitstreams: 1\\nquant-ph0512074.pdf: 550597 bytes, checksum: 588a3483219fa1360d5f71c131e2488e (MD5) %R 10.1063/1.2203236 %0 Journal Article %J Differential Geom. Appl. 24 (2006) 235-259 %D 2006 %T On variational approach to differential invariants of rank two distributions %A Igor Zelenko %X n the present paper we construct differential invariants for generic rank 2 vector distributions on n-dimensional manifold. In the case n=5 (the first case containing functional parameters) E. Cartan found in 1910 the covariant fourth-order tensor invariant for such distributions, using his \\\"reduction-prolongation\\\" procedure. After Cartan\\\'s work the following questions remained open: first the geometric reason for existence of Cartan\\\'s tensor was not clear; secondly it was not clear how to generalize this tensor to other classes of distributions; finally there were no explicit formulas for computation of Cartan\\\'s tensor. Our paper is the first in the series of papers, where we develop an alternative approach, which gives the answers to the questions mentioned above. It is based on the investigation of dynamics of the field of so-called abnormal extremals (singular curves) of rank 2 distribution and on the general theory of unparametrized curves in the Lagrange Grassmannian, developed in our previous works with A. Agrachev . In this way we construct the fundamental form and the projective Ricci curvature of rank 2 vector distributions for arbitrary n greater than 4.\\nFor n=5 we give an explicit method for computation of these invariants and demonstrate it on several examples. In our next paper we show that in the case n=5 our fundamental form coincides with Cartan\\\'s tensor. %B Differential Geom. Appl. 24 (2006) 235-259 %G en_US %U http://hdl.handle.net/1963/2188 %1 2056 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-05T11:38:23Z\\nNo. of bitstreams: 1\\n0402171v2.pdf: 447361 bytes, checksum: e7f578202115704506587340079a39d3 (MD5) %R 10.1016/j.difgeo.2005.09.004 %0 Report %D 2006 %T Variational problems in fracture mechanics %A Gianni Dal Maso %X We present some recent existence results for the variational model of crack growth in brittle materials proposed by Francfort and Marigo in 1998. These results, obtained in collaboration with Francfort and Toader, cover the case of arbitrary space dimension with a general quasiconvex bulk energy and with prescribed boundary deformations and applied loads. %G en_US %U http://hdl.handle.net/1963/1816 %1 2398 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-04-18T12:50:25Z\\nNo. of bitstreams: 1\\nmath.AP0602614.pdf: 122115 bytes, checksum: 8a582db939c08c52510bcc1c7da7c563 (MD5) %0 Journal Article %J Comm. Anal. Geom. 13 (2005) 187-252 %D 2005 %T Asymptotic Morse theory for the equation $\\\\Delta v=2v\\\\sb x\\\\wedge v\\\\sb y$ %A Sagun Chanillo %A Andrea Malchiodi %X Given a smooth bounded domain ${\\\\O}\\\\subseteq \\\\R^2$, we consider the equation $\\\\D v = 2 v_x \\\\wedge v_y$ in $\\\\O$, where $v: {\\\\O}\\\\to \\\\R^3$. We prescribe Dirichlet boundary datum, and consider the case in which this datum converges to zero. An asymptotic study of the corresponding Euler functional is performed, analyzing multiple-bubbling phenomena. This allows us to settle a particular case of a question raised by H. Brezis and J.M. Coron. %B Comm. Anal. Geom. 13 (2005) 187-252 %I International Press %G en_US %U http://hdl.handle.net/1963/3533 %1 731 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-20T10:28:24Z\\nNo. of bitstreams: 1\\n0205106v1.pdf: 508637 bytes, checksum: 9894eb1ef04ac61cd02aebdee04ff5fa (MD5) %0 Journal Article %J SIAM J. Control Optim. 43 (2005) 2166-2190 %D 2005 %T On the attainable set for Temple class systems with boundary controls %A Fabio Ancona %A Giuseppe Maria Coclite %X Consider the initial-boundary value problem for a strictly hyperbolic, genuinely nonlinear, Temple class system of conservation laws % $$ u_t+f(u)_x=0, \\\\qquad u(0,x)=\\\\ov u(x), \\\\qquad {{array}{ll} &u(t,a)=\\\\widetilde u_a(t), \\\\noalign{\\\\smallskip} &u(t,b)=\\\\widetilde u_b(t), {array}. \\\\eqno(1) $$ on the domain $\\\\Omega =\\\\{(t,x)\\\\in\\\\R^2 : t\\\\geq 0, a \\\\le x\\\\leq b\\\\}.$ We study the mixed problem (1) from the point of view of control theory, taking the initial data $\\\\bar u$ fixed, and regarding the boundary data $\\\\widetilde u_a, \\\\widetilde u_b$ as control functions that vary in prescribed sets $\\\\U_a, \\\\U_b$, of $\\\\li$ boundary controls. In particular, we consider the family of configurations $$ \\\\A(T) \\\\doteq \\\\big\\\\{u(T,\\\\cdot); ~ u {\\\\rm is a sol. to} (1), \\\\quad \\\\widetilde u_a\\\\in \\\\U_a, \\\\widetilde u_b \\\\in \\\\U_b \\\\big\\\\} $$ that can be attained by the system at a given time $T>0$, and we give a description of the attainable set $\\\\A(T)$ in terms of suitable Oleinik-type conditions. We also establish closure and compactness of the set $\\\\A(T)$ in the $lu$ topology. %B SIAM J. Control Optim. 43 (2005) 2166-2190 %I SISSA Library %G en %U http://hdl.handle.net/1963/1581 %1 2537 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:51Z (GMT). No. of bitstreams: 1\\nmath.AP0205167.pdf: 356214 bytes, checksum: 05474bd7744107031887816262b561b3 (MD5)\\n Previous issue date: 2002 %R 10.1137/S0363012902407776 %0 Journal Article %J Discrete Contin. Dyn. Syst. 13 (2005) 1-12 %D 2005 %T On the Blow-up for a Discrete Boltzmann Equation in the Plane %A Alberto Bressan %A Massimo Fonte %X We study the possibility of finite-time blow-up for a two dimensional Broadwell model. In a set of rescaled variables, we prove that no self-similar blow-up solution exists, and derive some a priori bounds on the blow-up rate. In the final section, a possible blow-up scenario is discussed. %B Discrete Contin. Dyn. Syst. 13 (2005) 1-12 %G en_US %U http://hdl.handle.net/1963/2244 %1 2000 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-17T09:31:05Z\\nNo. of bitstreams: 1\\n0403047v2.pdf: 116770 bytes, checksum: a7432c5b660f4e4672c952003dd0210f (MD5) %0 Book Section %B Differential geometry and its applications, 367-382, Matfyzpress, Prague, 2005 %D 2005 %T Complete systems of invariants for rank 1 curves in Lagrange Grassmannians %A Igor Zelenko %X Curves in Lagrange Grassmannians naturally appear when one studies intrinsically \\\"the Jacobi equations for extremals\\\", associated with control systems and geometric structures. In this way one reduces the problem of construction of the curvature-type invariants for these objects to the much more concrete problem of finding of invariants of curves in Lagrange Grassmannians w.r.t. the action of the linear Symplectic group. In the present paper we develop a new approach to differential geometry of so-called rank 1 curves in Lagrange Grassmannian, i.e., the curves with velocities being rank one linear mappings (under the standard identification of the tangent space to a point of the Lagrange Grassmannian with an appropriate space of linear mappings). The curves of this class are associated with \\\"the Jacobi equations for extremals\\\", corresponding to control systems with scalar control and to rank 2 vector distributions. In particular, we construct the tuple of m principal invariants, where m is equal to half of dimension of the ambient linear symplectic space, such that for a given tuple of arbitrary m smooth functions there exists the unique, up to a symplectic transformation, rank 1 curve having this tuple, as the tuple of the principal invariants. This approach extends and essentially simplifies some results of our previous paper (J. Dynamical and Control Systems, 8, 2002, No. 1, 93-140), where only the uniqueness part was proved and in rather cumbersome way. It is based on the construction of the new canonical moving frame with the most simple structural equation. %B Differential geometry and its applications, 367-382, Matfyzpress, Prague, 2005 %G en_US %U http://hdl.handle.net/1963/2310 %1 1706 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-29T14:39:11Z\\nNo. of bitstreams: 1\\n0411190v1.pdf: 227302 bytes, checksum: f4c17631a146df10f7ea9facaa0949b2 (MD5) %0 Journal Article %J Geometric and Functional Analysis 15 (6) 1162-1222 (2005) %D 2005 %T Concentration at curves for a singularly perturbed Neumann problem in three-dimensional domains %A Andrea Malchiodi %X We prove new concentration phenomena for the equation −ɛ2 Δu + u = up in a smooth bounded domain R3 and with Neumann boundary conditions. Here p > 1 and ɛ > 0 is small. We show that concentration of solutions occurs at some geodesics of ∂Ω when ɛ → 0. %B Geometric and Functional Analysis 15 (6) 1162-1222 (2005) %I Springer %G en %U http://hdl.handle.net/1963/4866 %1 4645 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-20T13:51:52Z\\nNo. of bitstreams: 1\\nMalchiodi03.pdf: 521628 bytes, checksum: 3aa8a237bad84b04bdd17669f210e057 (MD5) %R 10.1007/s00039-005-0542-7 %0 Journal Article %J SIAM J. Math. Anal. 36 (2005) 1293-1309 %D 2005 %T Conservation laws with time dependent discontinuous coefficients %A Giuseppe Maria Coclite %A Nils Henrik Risebro %X We consider scalar conservation laws where the flux function depends discontinuously on both the spatial and temporal location. Our main results are the existence and well-posedness of an entropy solution to the Cauchy problem. The existence is established by showing that a sequence of front tracking approximations is compact in L1, and that the limits are entropy solutions. Then, using the definition of an entropy solution taken form [11], we show that the solution operator is L1 contractive. These results generalize the corresponding results from [16] and [11]. %B SIAM J. Math. Anal. 36 (2005) 1293-1309 %I SISSA Library %G en %U http://hdl.handle.net/1963/1666 %1 2452 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:06:09Z (GMT). No. of bitstreams: 1\\n96_02.pdf: 3363466 bytes, checksum: 5ed39a522bb68737585e74668afafc5a (MD5)\\n Previous issue date: 2002 %R 10.1137/S0036141002420005 %0 Journal Article %J J. Dyn. Control Syst. 11 (2005) 297-327 %D 2005 %T On curvatures and focal points of distributions of dynamical Lagrangian distributions and their reductions by first integrals %A Andrei A. Agrachev %A Natalia N. Chtcherbakova %A Igor Zelenko %X Pairs (Hamiltonian system, Lagrangian distribution), called dynamical Lagrangian distributions, appear naturally in Differential Geometry, Calculus of Variations and Rational Mechanics. The basic differential invariants of a dynamical Lagrangian distribution w.r.t. the action of the group of symplectomorphisms of the ambient symplectic manifold are the curvature operator and the curvature form. These invariants can be seen as generalizations of the classical curvature tensor in Riemannian Geometry. In particular, in terms of these invariants one can localize the focal points along extremals of the corresponding variational problems. In the present paper we study the behavior of the curvature operator, the curvature form and the focal points of a dynamical Lagrangian distribution after its reduction by arbitrary first integrals in involution. The interesting phenomenon is that the curvature form of so-called monotone increasing Lagrangian dynamical distributions, which appear naturally in mechanical systems, does not decrease after reduction. It also turns out that the set of focal points to the given point w.r.t. the monotone increasing dynamical Lagrangian distribution and the corresponding set of focal points w.r.t. its reduction by one integral are alternating sets on the corresponding integral curve of the Hamiltonian system of the considered dynamical distributions. Moreover, the first focal point corresponding to the reduced Lagrangian distribution comes before any focal point related to the original dynamical distribution. We illustrate our results on the classical $N$-body problem. %B J. Dyn. Control Syst. 11 (2005) 297-327 %G en_US %U http://hdl.handle.net/1963/2254 %1 1993 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-18T08:53:27Z\\nNo. of bitstreams: 1\\n0409152v1.pdf: 335893 bytes, checksum: bf4dfeb39ad05ff60c2c2cc745fa0fc1 (MD5) %R 10.1007/s10883-005-6581-4 %0 Journal Article %J C. R. Acad. Sci. Paris, Ser. I 340 (2005) 341-346. %D 2005 %T A fourth order uniformization theorem on some four manifolds with large total Q-curvature %A Zindine Djadli %A Andrea Malchiodi %X Given a four-dimensional manifold (M,g), we study the existence of a conformal metric for which the Q-curvature, associated to a conformally invariant fourth-order operator (the Paneitz operator), is constant. Using a topological argument, we obtain a new result in cases which were still open. %B C. R. Acad. Sci. Paris, Ser. I 340 (2005) 341-346. %I Elsevier %G en %U http://hdl.handle.net/1963/4868 %1 4649 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-20T14:43:43Z\\nNo. of bitstreams: 1\\nexistencep81.pdf: 151457 bytes, checksum: 024bd42cba2f35fe4c206a1ef0f9a125 (MD5) %R 10.1016/j.crma.2005.01.013 %0 Journal Article %J SIAM J. Math. Anal. 37 (2005) 996-1026 %D 2005 %T Global solutions of the Hunter-Saxton equation %A Alberto Bressan %A Adrian Constantin %X We construct a continuous semigroup of weak, dissipative solutions to a nonlinear partial differential equations modeling nematic liquid crystals. A new distance functional, determined by a problem of optimal transportation, yields sharp estimates on the continuity of solutions with respect to the initial data. %B SIAM J. Math. Anal. 37 (2005) 996-1026 %G en_US %U http://hdl.handle.net/1963/2256 %1 1991 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-18T10:16:52Z\\nNo. of bitstreams: 1\\n0502059v1.pdf: 276204 bytes, checksum: ba0bfd37b8aa3a5ef2c0ef7358081cf9 (MD5) %R 10.1137/050623036 %0 Journal Article %J J. Eur. Math. Soc. 7 (2005) 117-144 %D 2005 %T Ground states of nonlinear Schroedinger equations with potentials vanishing at infinity %A Antonio Ambrosetti %A Veronica Felli %A Andrea Malchiodi %X We deal with a class on nonlinear Schr\\\\\\\"odinger equations \\\\eqref{eq:1} with potentials $V(x)\\\\sim |x|^{-\\\\a}$, $0<\\\\a<2$, and $K(x)\\\\sim |x|^{-\\\\b}$, $\\\\b>0$. Working in weighted Sobolev spaces, the existence of ground states $v_{\\\\e}$ belonging to $W^{1,2}(\\\\Rn)$ is proved under the assumption that $p$ satisfies \\\\eqref{eq:p}. Furthermore, it is shown that $v_{\\\\e}$ are {\\\\em spikes} concentrating at a minimum of ${\\\\cal A}=V^{\\\\theta}K^{-2/(p-1)}$, where $\\\\theta= (p+1)/(p-1)-1/2$. %B J. Eur. Math. Soc. 7 (2005) 117-144 %G en_US %U http://hdl.handle.net/1963/2352 %1 1664 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-11-07T08:16:53Z\\nNo. of bitstreams: 1\\nGround states.pdf: 901500 bytes, checksum: 741c3d55677b872a40e8e3ff2df2a5d2 (MD5) %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 Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (5), 4 (2005) 129-177. %D 2005 %T Minimal surfaces in pseudohermitian geometry %A Jih-Hsin Cheng %A JennFang Hwang %A Andrea Malchiodi %A Paul Yang %X We consider surfaces immersed in three-dimensional pseudohermitian manifolds. We define the notion of (p-)mean curvature and of the associated (p-)minimal surfaces, extending some concepts previously given for the (flat) Heisenberg group. We interpret the p-mean curvature not only as the tangential sublaplacian of a defining function, but also as the curvature of a characteristic curve, and as a quantity in terms of calibration geometry. As a differential equation, the p-minimal surface equation is degenerate (hyperbolic and elliptic). To analyze the singular set, we formulate some {\em extension} theorems, which describe how the characteristic curves meet the singular set. This allows us to classify the entire solutions to this equation and to solve a Bernstein-type problem (for graphs over the $xy$-plane) in the Heisenberg group $H_1$. In $H_{1}$, identified with the Euclidean space $R^{3}$, the p-minimal surfaces are classical ruled surfaces with the rulings generated by Legendrian lines. We also prove a uniqueness theorem for the Dirichlet problem under a condition on the size of the singular set in two dimensions, and generalize to higher dimensions without any size control condition. We also show that there are no closed, connected, $C^{2}$ smoothly immersed constant p-mean curvature or p-minimal surfaces of genus greater than one in the standard $S^{3}.$ This fact continues to hold when $S^{3}$ is replaced by a general spherical pseudohermitian 3-manifold. %B Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (5), 4 (2005) 129-177. %I Scuola Normale Superiore %G en %U http://hdl.handle.net/1963/4579 %1 4347 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-07T09:39:45Z No. of bitstreams: 1 math_0401136v3.pdf: 476553 bytes, checksum: 85c9b54a1f7e6c159e8fbc2486849a53 (MD5) %R 10.2422/2036-2145.2005.1.05 %0 Journal Article %J SIAM J. Math. Anal. 37 (2005) 982-995 %D 2005 %T On the Minimum Problem for Nonconvex Scalar Functionals %A Sandro Zagatti %X We study the minimum problem for scalar nonconvex functionals defined on Sobolev maps satisfying a Dirichlet boundary condition and refine well-known existence results under standard regularity assumptions. %B SIAM J. Math. Anal. 37 (2005) 982-995 %G en_US %U http://hdl.handle.net/1963/2764 %1 1936 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-08-29T11:16:58Z\\nNo. of bitstreams: 1\\ngrad3.pdf: 146157 bytes, checksum: 596c11c76c56b834876568a2157e2202 (MD5) %R 10.1137/040612506 %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire 22 (2005) 143-163 %D 2005 %T Multiple clustered layer solutions for semilinear Neumann problems on a ball %A Andrea Malchiodi %A Wei-Ming Ni %A Juncheng Wei %B Ann. Inst. H. Poincare Anal. Non Lineaire 22 (2005) 143-163 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3532 %1 732 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-20T10:15:49Z\\nNo. of bitstreams: 1\\nMalchiodiNiWei04.pdf: 340366 bytes, checksum: a0bb6df9ca59c557fdacb5e7142ecf3d (MD5) %R 10.1016/j.anihpc.2004.05.003 %0 Journal Article %J Discrete Contin. Dyn. Syst. Ser. B 5 (2005) 957-990 %D 2005 %T Nonisotropic 3-level quantum systems: complete solutions for minimum time and minimum energy %A Ugo Boscain %A Thomas Chambrion %A Grégoire Charlot %X We apply techniques of subriemannian geometry on Lie groups and of optimal synthesis on 2-D manifolds to the population transfer problem in a three-level quantum system driven by two laser pulses, of arbitrary shape and frequency. In the rotating wave approximation, we consider a nonisotropic model i.e. a model in which the two coupling constants of the lasers are different. The aim is to induce transitions from the first to the third level, minimizing 1) the time of the transition (with bounded laser amplitudes),\\n2) the energy of lasers (with fixed final time). After reducing the problem to real variables, for the purpose 1) we develop a theory of time optimal syntheses for distributional problem on 2-D-manifolds, while for the purpose 2) we use techniques of subriemannian geometry on 3-D Lie groups. The complete optimal syntheses are computed. %B Discrete Contin. Dyn. Syst. Ser. B 5 (2005) 957-990 %G en_US %U http://hdl.handle.net/1963/2259 %1 1988 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-18T11:55:27Z\\nNo. of bitstreams: 1\\n0409022v2.pdf: 578605 bytes, checksum: db7298996e781c3a8546c3d01ee28384 (MD5) %0 Report %D 2005 %T Nonlinear Schrödinger Equations with vanishing and decaying potentials %A Antonio Ambrosetti %A Wang Zhi-Qiang %B Differential Integral Equations 18 (2005), no. 12, 1321-1332 %G en_US %U http://hdl.handle.net/1963/1760 %1 2784 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-22T09:32:48Z\\nNo. of bitstreams: 1\\n52M-2005.pdf: 2540023 bytes, checksum: a022763e63174283e8e626a5c191eb2a (MD5) %0 Report %D 2005 %T An Optimal Transportation Metric for Solutions of the Camassa-Holm Equation %A Alberto Bressan %A Massimo Fonte %X In this paper we construct a global, continuous flow of solutions to the Camassa-Holm equation on the entire space H1. Our solutions are conservative, in the sense that the total energy int[(u2 + u2x) dx] remains a.e. constant in time. Our new approach is based on a distance functional J(u, v), defined in terms of an optimal transportation problem, which satisfies d dtJ(u(t), v(t)) ≤ κ · J(u(t), v(t)) for every couple of solutions. Using this new distance functional, we can construct arbitrary solutions as the uniform limit of multi-peakon solutions, and prove a general uniqueness result. %B Methods Appl. Anal. 12 (2005) 191-219 %G en_US %U http://hdl.handle.net/1963/1719 %1 2432 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-01-24T09:03:54Z\\nNo. of bitstreams: 1\\nmath.AP0504450.pdf: 261370 bytes, checksum: 75945d031343a82836b46ab9705ed6de (MD5) %0 Journal Article %J Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 16 (2005), no. 2, 117-124 %D 2005 %T Periodic solutions of nonlinear wave equations with non-monotone forcing terms %A Massimiliano Berti %A Luca Biasco %B Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 16 (2005), no. 2, 117-124 %I Accademia Nazionale dei Lincei %G en %U http://hdl.handle.net/1963/4581 %1 4349 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-07T10:23:29Z\\nNo. of bitstreams: 1\\nBertiBiasco04-1.pdf: 267180 bytes, checksum: 2e0e4b98f4985c1e79dc4c03fb30618e (MD5) %0 Journal Article %J Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 16 (2005), no. 2, 109-116 %D 2005 %T Quasi-periodic oscillations for wave equations under periodic forcing %A Massimiliano Berti %A Michela Procesi %B Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 16 (2005), no. 2, 109-116 %I Accademia Nazionale dei Lincei %G en %U http://hdl.handle.net/1963/4583 %1 4350 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-07T10:27:05Z\\nNo. of bitstreams: 1\\nBertiProcesi05-1.pdf: 211758 bytes, checksum: b6c3ae059191cddb5c025aee61a23799 (MD5) %0 Journal Article %J Arch. Ration. Mech. Anal. 176 (2005) 165-225 %D 2005 %T Quasistatic Crack Growth in Nonlinear Elasticity %A Gianni Dal Maso %A Gilles A. Francfort %A Rodica Toader %X In this paper, we prove a new existence result for a variational model of crack growth in brittle materials proposed in [15]. We consider the case of $n$-dimensional finite elasticity, for an arbitrary $n\\\\ge1$, with a quasiconvex bulk energy and with prescribed boundary deformations and applied loads, both depending on time. %B Arch. Ration. Mech. Anal. 176 (2005) 165-225 %G en_US %U http://hdl.handle.net/1963/2293 %1 1723 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-24T09:12:09Z\\nNo. of bitstreams: 1\\n0401196v1.pdf: 664295 bytes, checksum: cb1000c44e6ae356984e24b55ee97117 (MD5) %R 10.1007/s00205-004-0351-4 %0 Journal Article %J Journal of Mathematical Sciences 126 (2005) 1561-1573 %D 2005 %T Regularity properties of optimal trajectories of single-input control systems in dimension three %A Mario Sigalotti %X Let q=f(q)+ug(q) be a smooth control system on a three-dimensional manifold. Given a point q 0 of the manifold at which the iterated Lie brackets of f and g satisfy some prescribed independence condition, we analyze the structure of a control function u(t) corresponding to a time-optimal trajectory lying in a neighborhood of q 0. The control turns out to be the concatenation of some bang-bang and some singular arcs. More general optimality criteria than time-optimality are considered. The paper is a step toward to the analysis of generic single-input systems affine in the control in dimension 3. The main techniques used are second-order optimality conditions and, in particular, the index of the second variation of the switching times for bang-bang trajectories. %B Journal of Mathematical Sciences 126 (2005) 1561-1573 %I Springer %G en %U http://hdl.handle.net/1963/4794 %1 4564 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-17T08:06:19Z\\nNo. of bitstreams: 1\\nsuz.pdf: 199707 bytes, checksum: 1d18998eb7281177da4a442135d9b77d (MD5) %R 10.1007/s10958-005-0044-z %0 Journal Article %J Comput. Methods Appl. Mech. Engrg. 194 (2005) 2534-2549 %D 2005 %T Self-similar folding patterns and energy scaling in compressed elastic sheets %A Sergio Conti %A Antonio DeSimone %A Stefan Müller %X Thin elastic sheets under isotropic compression, such as for example blisters formed by thin films which debonded from the substrate, can exhibit remarkably complex folding patterns. We discuss the scaling of the elastic energy with respect to the film thickness, and show that in certain regimes the optimal energy scaling can be reached\\nby self-similar folding patterns that refine towards the boundary, in agreement with experimental observations. We then extend the analysis\\nto anisotropic compression, and discuss a simplified scalar model which suggests the presence of a transition between a regime where\\nthe deformation is governed by global properties of the domain and another one where the direction of maximal compression dominates and the scale of the folds is mainly determined by the distance to the boundary in the direction of the folds themselves. %B Comput. Methods Appl. Mech. Engrg. 194 (2005) 2534-2549 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3000 %1 1333 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-01T10:37:14Z\\nNo. of bitstreams: 1\\npreprint2004_3.pdf: 907333 bytes, checksum: 2b22c209b91ba2ddacc1a1c14a9054a2 (MD5) %R 10.1016/j.cma.2004.07.044 %0 Book Section %B Contrôle non linéaire et applications: Cours donnés à l\\\'école d\\\'été du Cimpa de l\\\'Université de Tlemcen / Sari Tewfit [ed.]. - Paris: Hermann, 2005 %D 2005 %T A short introduction to optimal control %A Ugo Boscain %A Benedetto Piccoli %B Contrôle non linéaire et applications: Cours donnés à l\\\'école d\\\'été du Cimpa de l\\\'Université de Tlemcen / Sari Tewfit [ed.]. - Paris: Hermann, 2005 %@ 2 7056 6511 0 %G en_US %U http://hdl.handle.net/1963/2257 %1 1990 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-18T11:30:24Z\\nNo. of bitstreams: 1\\nNotes-OptCont.pdf: 442775 bytes, checksum: 196e4d9cc52950dd18cf17feb0e89808 (MD5) %0 Generic %D 2005 %T Solutions of Neumann problems in domains with cracks and applications to fracture mechanics %A Gianni Dal Maso %G en_US %U http://hdl.handle.net/1963/1684 %1 79 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2005-05-20T07:18:38Z\\nNo. of bitstreams: 1\\nmath.AP0105132.pdf: 225826 bytes, checksum: d7308b70020a416522235ed54b404379 (MD5) %0 Journal Article %J J. Math. Anal. Appl. 308 (2005) 221-239 %D 2005 %T Stability of solutions of quasilinear parabolic equations %A Giuseppe Maria Coclite %A Helge Holden %X We bound the difference between solutions $u$ and $v$ of $u_t = a\\\\Delta u+\\\\Div_x f+h$ and $v_t = b\\\\Delta v+\\\\Div_x g+k$ with initial data $\\\\phi$ and $ \\\\psi$, respectively, by $\\\\Vert u(t,\\\\cdot)-v(t,\\\\cdot)\\\\Vert_{L^p(E)}\\\\le A_E(t)\\\\Vert \\\\phi-\\\\psi\\\\Vert_{L^\\\\infty(\\\\R^n)}^{2\\\\rho_p}+ B(t)(\\\\Vert a-b\\\\Vert_{\\\\infty}+ \\\\Vert \\\\nabla_x\\\\cdot f-\\\\nabla_x\\\\cdot g\\\\Vert_{\\\\infty}+ \\\\Vert f_u-g_u\\\\Vert_{\\\\infty} + \\\\Vert h-k\\\\Vert_{\\\\infty})^{\\\\rho_p} \\\\abs{E}^{\\\\eta_p}$. Here all functions $a$, $f$, and $h$ are smooth and bounded, and may depend on $u$, $x\\\\in\\\\R^n$, and $t$. The functions $a$ and $h$ may in addition depend on $\\\\nabla u$. Identical assumptions hold for the functions that determine the solutions $v$. Furthermore, $E\\\\subset\\\\R^n$ is assumed to be a bounded set, and $\\\\rho_p$ and $\\\\eta_p$ are fractions that depend on $n$ and $p$. The diffusion coefficients $a$ and $b$ are assumed to be strictly positive and the initial data are smooth. %B J. Math. Anal. Appl. 308 (2005) 221-239 %I Elsevier %G en_US %U http://hdl.handle.net/1963/2892 %1 1808 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-10T12:48:15Z\\nNo. of bitstreams: 1\\n0306160v1.pdf: 240791 bytes, checksum: 4654ca0f7a1735bc7ee6666d37a2d57a (MD5) %R 10.1016/j.jmaa.2005.01.026 %0 Journal Article %J Int. J. Numer. Anal. Met. 29 (2005) 73-101 %D 2005 %T Stress-dilatancy based modelling of granular materials and extensions to soils with crushable grains %A Antonio DeSimone %A Claudio Tamagnini %X Stress-dilatancy relations have played a crucial role in the understanding of the mechanical behaviour of soils and in the development of realistic constitutive models for their response. Recent investigations on the mechanical behaviour of materials with crushable grains have called into question the validity of classical relations such as those used in critical state soil mechanics.\\nIn this paper, a method to construct thermodynamically consistent (isotropic, three-invariant) elasto-plastic models based on a given stress-dilatancy relation is discussed. Extensions to cover the case of granular materials with crushable grains are also presented, based on the interpretation of some classical model parameters (e.g. the stress ratio at critical state) as internal variables that evolve according to suitable hardening laws. %B Int. J. Numer. Anal. Met. 29 (2005) 73-101 %G en_US %U http://hdl.handle.net/1963/2165 %1 2079 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-02T12:02:04Z\\nNo. of bitstreams: 1\\nDeSimoneTamagnini_2005.pdf: 1179767 bytes, checksum: 23b892b2314ea8e2199cc2b2449386b0 (MD5) %R 10.1002/nag.405 %0 Report %D 2005 %T Time minimal trajectories for two-level quantum systems with drift %A Ugo Boscain %A Paolo Mason %X On a two-level quantum system driven by an external field, we consider the population transfer problem from the first to the second level, minimizing the time of transfer, with bounded field amplitude. On the Bloch sphere (i.e. after a suitable Hopf projection), this problem can be attacked with techniques of optimal syntheses on 2-D manifolds. %B Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC \\\'05. 44th IEEE Conference on %G en_US %U http://hdl.handle.net/1963/1688 %1 2445 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2005-06-20T12:25:55Z\\nNo. of bitstreams: 1\\nquant-ph0502151.pdf: 136766 bytes, checksum: d23bf76326e4a9a09555f4ead6edc808 (MD5) %0 Journal Article %J SIAM J. Control Optim. 44 (2005) 111-139 %D 2005 %T Time Optimal Synthesis for Left-Invariant Control Systems on SO(3) %A Ugo Boscain %A Yacine Chitour %X Consider the control system given by $\\\\dot x=x(f+ug)$, where $x\\\\in SO(3)$, $|u|\\\\leq 1$ and $f,g\\\\in so(3)$ define two perpendicular left-invariant vector fields normalized so that $\\\\|f\\\\|=\\\\cos(\\\\al)$ and $\\\\|g\\\\|=\\\\sin(\\\\al)$, $\\\\al\\\\in ]0,\\\\pi/4[$. In this paper, we provide an upper bound and a lower bound for $N(\\\\alpha)$, the maximum number of switchings for time-optimal trajectories. More precisely, we show that $N_S(\\\\al)\\\\leq N(\\\\al)\\\\leq N_S(\\\\al)+4$, where $N_S(\\\\al)$ is a suitable integer function of $\\\\al$ which for $\\\\al\\\\to 0$ is of order $\\\\pi/(4\\\\alpha).$ The result is obtained by studying the time optimal synthesis of a projected control problem on $R P^2$, where the projection is defined by an appropriate Hopf fibration. Finally, we study the projected control problem on the unit sphere $S^2$. It exhibits interesting features which will be partly rigorously derived and partially described by numerical simulations. %B SIAM J. Control Optim. 44 (2005) 111-139 %G en_US %U http://hdl.handle.net/1963/2258 %1 1989 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-18T11:43:01Z\\nNo. of bitstreams: 1\\n0502483v1.pdf: 429552 bytes, checksum: 9f72f53d7031cdc7ccb2aca8b8ec16de (MD5) %R 10.1137/S0363012904441532 %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 Journal Article %J Ann. of Math. 161 (2005) 223-342 %D 2005 %T Vanishing viscosity solutions of nonlinear hyperbolic systems %A Stefano Bianchini %A Alberto Bressan %X We consider the Cauchy problem for a strictly hyperbolic, $n\\\\times n$ system in one space dimension: $u_t+A(u)u_x=0$, assuming that the initial data has small total variation.\\nWe show that the solutions of the viscous approximations $u_t+A(u)u_x=\\\\ve u_{xx}$ are defined globally in time and satisfy uniform BV estimates, independent of $\\\\ve$. Moreover, they depend continuously on the initial data in the $\\\\L^1$ distance, with a Lipschitz constant independent of $t,\\\\ve$. Letting $\\\\ve\\\\to 0$, these viscous solutions converge to a unique limit, depending Lipschitz continuously on the initial data. In the conservative case where $A=Df$ is the Jacobian of some flux function $f:\\\\R^n\\\\mapsto\\\\R^n$, the vanishing viscosity limits are precisely the unique entropy weak solutions to the system of conservation laws $u_t+f(u)_x=0$. %B Ann. of Math. 161 (2005) 223-342 %I Annals of Mathematics %G en_US %U http://hdl.handle.net/1963/3074 %1 1259 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-10T10:46:16Z\\nNo. of bitstreams: 1\\n0111321v1.pdf: 746310 bytes, checksum: f3b7c9e76e33050e9f367ba2c57e2161 (MD5) %0 Journal Article %J Proc. R. Soc. Lon. Ser. A 461 (2005) 79-97 %D 2005 %T Wetting of rough surfaces: a homogenization approach %A Antonio DeSimone %A Giovanni Alberti %X The contact angle of a drop in equilibrium on a solid is strongly affected by the roughness of the surface on which it rests. We study the roughness-induced enhancement of the hydrophobic or hydrophilic properties of a solid surface through homogenization theory. By relying on a variational formulation of the problem, we show that the macroscopic contact angle is associated with the solution of two cell problems, giving the minimal energy per unit macroscopic area for a transition layer between the rough solid surface and a liquid or vapor phase. Our results are valid for both chemically heterogeneous and homogeneous surfaces. In the latter case, a very transparent structure emerges from the variational\\napproach: the classical laws of Wenzel and Cassie-Baxter give bounds for the optimal energy, and configurations of minimal energy are those leading to the smallest macroscopic contact angle in the hydrophobic case, to the largest one in the hydrophilic case. %B Proc. R. Soc. Lon. Ser. A 461 (2005) 79-97 %G en_US %U http://hdl.handle.net/1963/2253 %1 1994 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-18T07:46:26Z\\nNo. of bitstreams: 1\\n75-04.pdf: 370259 bytes, checksum: 3ac1bc80248a4e54ff5294b7baffa66f (MD5) %R 10.1098/rspa.2004.1364 %0 Journal Article %J Ann. Inst. H. Poincaré. Anal. Non Linéaire 21 (2004), (4), p. 445-486. %D 2004 %T Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains %A Gianni Dal Maso %A Francois Murat %X We consider a sequence of Dirichlet problems in varying domains (or, more generally, of relaxed Dirichlet problems involving measures in M_0) for second order linear elliptic operators in divergence form with varying matrices of coefficients. When the matrices H-converge to a matrix A^0, we prove that there exist a subsequence and a measure mu^0 in M_0 such that the limit problem is the relaxed Dirichlet problem corresponding to A^0 and mu^0. We also prove a corrector result which provides an explicit approximation of the solutions in the H^1-norm, and which is obtained by multiplying the corrector for the H-converging matrices by some special test function which depends both on the varying matrices and on the varying domains. %B Ann. Inst. H. Poincaré. Anal. Non Linéaire 21 (2004), (4), p. 445-486. %I SISSA Library %G en %U http://hdl.handle.net/1963/1611 %1 2507 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:17Z (GMT). No. of bitstreams: 1\\r\\nmath.AP0205225.pdf: 404809 bytes, checksum: 472524cb28afed2e55fcf0a7c46e7598 (MD5)\\r\\n Previous issue date: 2002 %0 Journal Article %J Boll. Unione Mat. Ital. Sez. B 7 (2004) 519-528 %D 2004 %T Bifurcation of free vibrations for completely resonant wave equations %A Massimiliano Berti %A Philippe Bolle %X We prove existence of small amplitude, 2 pi/omega -periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for any frequency omega belonging to a Cantor-like set of positive measure and for a generic set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem. %B Boll. Unione Mat. Ital. Sez. B 7 (2004) 519-528 %G en_US %U http://hdl.handle.net/1963/2245 %1 1999 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-17T09:55:20Z\\nNo. of bitstreams: 1\\n0409052v1.pdf: 145050 bytes, checksum: 68913e2c100ffa7488447933554c30e7 (MD5) %0 Journal Article %J Int. J. Numer. Meth. Fluids %D 2004 %T Calculation of impulsively started incompressible viscous flows %A Marra, Andrea %A Andrea Mola %A Quartapelle, Luigi %A Riviello, Luca %B Int. J. Numer. Meth. Fluids %V 46 %P 877–902 %G eng %0 Journal Article %J Computer methods in applied mechanics and engineering , 193 (2004) 5129-5141 %D 2004 %T Coarse-grained models of materials with non-convex free-energy: two case studies %A Antonio DeSimone %X Bridging across length scales is one of the fundamental challenges in the computational modelling of material systems whose mechanical response is driven by rough energy landscapes. The typical feature of such systems is that of exhibiting fine scale microstructures. Two case studies, namely, nematic elastomers and ferromagnetic shape memory alloys, are presented to illustrate the use of modern techniques from (non-convex) calculus of variations in developing coarse-grained models of microstructure-driven material response. %B Computer methods in applied mechanics and engineering , 193 (2004) 5129-5141 %I Elsevier %G en %U http://hdl.handle.net/1963/4884 %1 4664 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-24T06:59:37Z\\nNo. of bitstreams: 0 %R 10.1016/j.cma.2003.12.064 %0 Journal Article %J Comm. Pure Appl. Math. 57 (2004) 1075-1109 %D 2004 %T On the convergence rate of vanishing viscosity approximations %A Alberto Bressan %A Tong Yang %X Given a strictly hyperbolic, genuinely nonlinear system of conservation laws, we prove the a priori bound $\\\\big\\\\|u(t,\\\\cdot)-u^\\\\ve(t,\\\\cdot)\\\\big\\\\|_{\\\\L^1}= \\\\O(1)(1+t)\\\\cdot \\\\sqrt\\\\ve|\\\\ln\\\\ve|$ on the distance between an exact BV solution $u$ and a viscous approximation $u^\\\\ve$, letting the viscosity coefficient $\\\\ve\\\\to 0$. In the proof, starting from $u$ we construct an approximation of the viscous solution $u^\\\\ve$ by taking a mollification $u*\\\\phi_{\\\\strut \\\\sqrt\\\\ve}$ and inserting viscous shock profiles at the locations of finitely many large shocks, for each fixed $\\\\ve$. Error estimates are then obtained by introducing new Lyapunov functionals which control shock interactions, interactions between waves of different families and by using sharp decay estimates for positive nonlinear waves. %B Comm. Pure Appl. Math. 57 (2004) 1075-1109 %I Wiley %G en_US %U http://hdl.handle.net/1963/2915 %1 1785 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T13:30:25Z\\nNo. of bitstreams: 1\\nmath.AP0307141.pdf: 265243 bytes, checksum: 795adebd067228364ac1240add5f7b02 (MD5) %R 10.1002/cpa.20030 %0 Journal Article %J M2AN Math. Model. Numer. Anal. 38 (2004) 235-248 %D 2004 %T Energetics and switching of quasi-uniform states in small ferromagnetic particles %A François Alouges %A Sergio Conti %A Antonio DeSimone %A Ivo Pokern %X We present a numerical algorithm to solve the micromagnetic equations based on tangential-plane minimization for the magnetization update and a homothethic-layer decomposition of outer space for the computation of the demagnetization field. As a first application, detailed results on the flower-vortex transition in the cube of Micromagnetic Standard Problem number 3 are obtained, which confirm, with a different method, those already present in the literature, and validate our method and code. We then turn to switching of small cubic or almost-cubic particles, in the single-domain limit. Our data show systematic deviations from the Stoner-Wohlfarth model due to the non-ellipsoidal shape of the particle, and in particular a non-monotone dependence on the particle size. %B M2AN Math. Model. Numer. Anal. 38 (2004) 235-248 %I EDP Sciences %G en_US %U http://hdl.handle.net/1963/2999 %1 1334 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-01T10:25:50Z\\nNo. of bitstreams: 1\\npreprint2003_88.pdf: 297354 bytes, checksum: d907d5a9d74d0a3dcb244e26ff2af68a (MD5) %R 10.1051/m2an:2004011 %0 Journal Article %J Rev. Mat. Iberoamericana 20 (2004) 611-626 %D 2004 %T Existence of H-bubbles in a perturbative setting %A Paolo Caldiroli %A Roberta Musina %X Given a $C^{1}$ function $H: \\\\mathbb{R}^3 \\\\to \\\\mathbb{R}$, we look for $H$-bubbles, i.e., surfaces in $\\\\mathbb{R}^3$ parametrized by the sphere $\\\\mathbb{S}^2$ with mean curvature $H$ at every regular point. Here we study the case $H(u)=H_{0}(u)+\\\\epsilon H_{1}(u)$ where $H_{0}$ is some \\\"good\\\" curvature (for which there exist $H_{0}$-bubbles with minimal energy, uniformly bounded in $L^{\\\\infty}$), $\\\\epsilon$ is the smallness parameter, and $H_{1}$ is {\\\\em any} $C^{1}$ function. %B Rev. Mat. Iberoamericana 20 (2004) 611-626 %I SISSA Library %G en %U http://hdl.handle.net/1963/1606 %1 2512 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:13Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002 %0 Journal Article %J Duke Math. J. 122 (2004), no. 3, 457--484 %D 2004 %T H-bubbles in a perturbative setting: the finite-dimensional reduction\\\'s method %A Paolo Caldiroli %A Roberta Musina %X Given a regular function $H\\\\colon\\\\mathbb{R}^{3}\\\\to\\\\mathbb{R}$, we look for $H$-bubbles, that is, regular surfaces in $\\\\mathbb{R}^{3}$ parametrized on the sphere $\\\\mathbb{S}+^{2}$ with mean curvature $H$ at every point. Here we study the case of $H(u)=H_{0}+\\\\varepsilon H_{1}(u)=:H_{\\\\varepsilon}(u)$, where $H_{0}$ is a nonzero constant, $\\\\varepsilon$ is the smallness parameter, and $H_{1}$ is any $C^{2}$-function. We prove that if $\\\\bar p\\\\in\\\\mathbb{R}^{3}$ is a ``good\\\'\\\' stationary point for the Melnikov-type function $\\\\Gamma(p)=-\\\\int_{|q-p|<|H_{0}|^{-1}}H_{1}(q)\\\\,dq$, then for $|\\\\varepsilon|$ small there exists an $H_{\\\\varepsilon}$-bubble $\\\\omega^{\\\\varepsilon}$ that converges to a sphere of radius $|H_{0}|^{-1}$ centered at $\\\\bar p$, as $\\\\varepsilon\\\\to 0$. %B Duke Math. J. 122 (2004), no. 3, 457--484 %I SISSA Library %G en %U http://hdl.handle.net/1963/1607 %1 2511 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:13Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002 %R 10.1215/S0012-7094-04-12232-8 %0 Journal Article %J Arch. Ration. Mech. Anal. 171 (2004) 55-81 %D 2004 %T Higher order quasiconvexity reduces to quasiconvexity %A Gianni Dal Maso %A Irene Fonseca %A Giovanni Leoni %A Massimiliano Morini %X In this paper it is shown that higher order quasiconvex functions suitable in the variational treatment of problems involving second derivatives may be extended to the space of all matrices as classical quasiconvex functions. Precisely, it is proved that a smooth strictly 2-quasiconvex function with p-growth at infinity, p>1, is the restriction to symmetric matrices of a 1-quasiconvex function with the same growth. As a consequence, lower semicontinuity results for second-order variational problems are deduced as corollaries of well-known first order theorems. %B Arch. Ration. Mech. Anal. 171 (2004) 55-81 %I Springer %G en_US %U http://hdl.handle.net/1963/2911 %1 1789 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T12:36:19Z\\nNo. of bitstreams: 1\\nmath.AP0305138.pdf: 272082 bytes, checksum: 245f93702444ac3eb1de7c86c1f83551 (MD5) %R 10.1007/s00205-003-0278-1 %0 Conference Proceedings %B 43rd IEEE Conference on Decision and Control, 2004, 2786 - 2791 Vol.3 %D 2004 %T On the minimal degree of a common Lyapunov function for planar switched systems %A Paolo Mason %A Ugo Boscain %A Yacine Chitour %X In this paper, we consider linear switched systems x(t) = Au(t)x(t), x ε Rn, u ε U, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching (UAS for short). We first prove that, given a UAS system, it is always possible to build a polynomial common Lyapunov function. Then our main result is that the degree of that the common polynomial Lyapunov function is not uniformly bounded over all the UAS systems. This result answers a question raised by Dayawansa and Martin. %B 43rd IEEE Conference on Decision and Control, 2004, 2786 - 2791 Vol.3 %I IEEE %G en %U http://hdl.handle.net/1963/4834 %1 4611 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-19T07:47:35Z\\nNo. of bitstreams: 0 %R 10.1109/CDC.2004.1428884 %0 Journal Article %J Duke Math. J. 124 (2004) 105-143 %D 2004 %T Multidimensional boundary layers for a singularly perturbed Neumann problem %A Andrea Malchiodi %A Marcelo Montenegro %B Duke Math. J. 124 (2004) 105-143 %I Duke University Press %G en_US %U http://hdl.handle.net/1963/2960 %1 1740 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-22T08:57:55Z\\nNo. of bitstreams: 1\\nMalchiodiMontenegro03.pdf: 414971 bytes, checksum: a647d87b29bbf0808629d5647dfd1dad (MD5) %R 10.1215/S0012-7094-04-12414-5 %0 Journal Article %J Nonlinear Anal. 56 (2004) 1011-1046 %D 2004 %T Multiplicity of periodic solutions of nonlinear wave equations %A Massimiliano Berti %A Philippe Bolle %B Nonlinear Anal. 56 (2004) 1011-1046 %I Elsevier %G en_US %U http://hdl.handle.net/1963/2974 %1 1359 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-29T12:46:01Z\\nNo. of bitstreams: 1\\nBertiBolle04.pdf: 387346 bytes, checksum: 6374d2229ca34f3936e690a01f4b4eab (MD5) %R 10.1016/j.na.2003.11.001 %0 Journal Article %J Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 3 (2004) 87-138 %D 2004 %T Periodic orbits close to elliptic tori and applications to the three-body problem %A Massimiliano Berti %A Luca Biasco %A Enrico Valdinoci %X We prove, under suitable non-resonance and non-degeneracy ``twist\\\'\\\' conditions, a Birkhoff-Lewis type result showing the existence of infinitely many periodic solutions, with larger and larger minimal period, accumulating onto elliptic invariant tori (of Hamiltonian systems). We prove the applicability of this result to the spatial planetary three-body problem in the small eccentricity-inclination regime. Furthermore, we find other periodic orbits under some restrictions on the period and the masses of the ``planets\\\'\\\'. The proofs are based on averaging theory, KAM theory and variational methods. (Supported by M.U.R.S.T. Variational Methods and Nonlinear Differential Equations.) %B Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 3 (2004) 87-138 %I Scuola Normale Superiore di Pisa %G en_US %U http://hdl.handle.net/1963/2985 %1 1348 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-30T09:03:01Z\\nNo. of bitstreams: 1\\n0304103v1.pdf: 482533 bytes, checksum: 5da7f32109202edb44f004885b665b48 (MD5) %0 Journal Article %J Quad. Mat. Dip. Mat. Seconda Univ. Napoli 14 (2004) 245-266 %D 2004 %T Quasi-static evolution in brittle fracture: the case of bounded solutions %A Gianni Dal Maso %A Gilles A. Francfort %A Rodica Toader %X The main steps of the proof of the existence result for the quasi-static evolution of cracks in brittle materials, obtained in [7] in the vector case and for a general quasiconvex elastic energy, are presented here under the simplifying assumption that the minimizing sequences involved in the problem are uniformly bounded in $L^\\\\infty$. %B Quad. Mat. Dip. Mat. Seconda Univ. Napoli 14 (2004) 245-266 %G en_US %U http://hdl.handle.net/1963/2229 %1 2015 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-15T15:04:28Z\\r\\nNo. of bitstreams: 1\\r\\n0401198v1.pdf: 166634 bytes, checksum: c21fba2b1fbbaec4fe14c56595b0664e (MD5) %0 Journal Article %J ESAIM COCV 10 (2004) 593-614 %D 2004 %T Resonance of minimizers for n-level quantum systems with an arbitrary cost %A Ugo Boscain %A Grégoire Charlot %X We consider an optimal control problem describing a laser-induced population transfer on a $n$-level quantum system.\\nFor a convex cost depending only on the moduli of controls (i.e. the lasers intensities), we prove that there always exists a minimizer in resonance. This permits to justify some strategies used in experimental physics. It is also quite important because it permits to reduce remarkably the complexity of the problem (and extend some of our previous results for $n=2$ and $n=3$): instead of looking for minimizers on the sphere $S^{2n-1}\\\\subset\\\\C^n$ one is reduced to look just for minimizers on the sphere $S^{n-1}\\\\subset \\\\R^n$. Moreover, for the reduced problem, we investigate on the question of existence of strict abnormal minimizer. %B ESAIM COCV 10 (2004) 593-614 %I EDP Sciences %G en_US %U http://hdl.handle.net/1963/2910 %1 1790 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T12:22:45Z\\nNo. of bitstreams: 1\\n0308103v2.pdf: 290972 bytes, checksum: 2195a0a0002da9f91cbc9fff24262981 (MD5) %R 10.1051/cocv:2004022 %0 Journal Article %J J. Anal. Math. 94 (2004) 265-291 %D 2004 %T The role of the spectrum of the Laplace operator on \\\\S2 in the H-bubble problem %A Roberta Musina %B J. Anal. Math. 94 (2004) 265-291 %I Hebrew University Magnes Press %G en_US %U http://hdl.handle.net/1963/2894 %1 1806 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T08:25:18Z\\nNo. of bitstreams: 1\\n30-03.pdf: 329914 bytes, checksum: 3895c2d75f9be226052e7d4797d7cd9c (MD5) %R 10.1007/BF02789050 %0 Journal Article %J Internat. J. Game Theory 32 (2004) 561-593 %D 2004 %T Semi-cooperative strategies for differential games %A Alberto Bressan %A Wen Shen %X The paper is concerned with a non-cooperative differential game for two players. We first consider Nash equilibrium solutions in feedback form. In this case, we show that the Cauchy problem for the value functions is generically ill-posed. Looking at vanishing viscosity approximations, one can construct special solutions in the form of chattering controls, but these also appear to be unstable. In the second part of the paper we propose an alternative \\\"semi-cooperative\\\" pair of strategies for the two players, seeking a Pareto optimum instead of a Nash equilibrium. In this case, we prove that the corresponding Hamiltonian system for the value functions is always weakly hyperbolic. %B Internat. J. Game Theory 32 (2004) 561-593 %I Springer %G en_US %U http://hdl.handle.net/1963/2893 %1 1807 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T08:11:56Z\\nNo. of bitstreams: 1\\n069.pdf: 389569 bytes, checksum: 3cea0d9a5adfd0be673a7d69218e238a (MD5) %R 10.1007/s001820400180 %0 Journal Article %J SIAM J. Math. Anal. 36 (2004) 659-677 %D 2004 %T A sharp decay estimate for positive nonlinear waves %A Alberto Bressan %A Tong Yang %X We consider a strictly hyperbolic, genuinely nonlinear system of conservation laws in one space dimension. A sharp decay estimate is proved for the positive waves in an entropy weak solution. The result is stated in terms of a partial ordering among positive measures, using symmetric rearrangements and a comparison with a solution of Burgers\\\' equation with impulsive sources. %B SIAM J. Math. Anal. 36 (2004) 659-677 %I SIAM %G en_US %U http://hdl.handle.net/1963/2916 %1 1784 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T13:37:38Z\\nNo. of bitstreams: 1\\nmath.AP0307140.pdf: 167236 bytes, checksum: 9e7a6fecd3de67843ca5c73f13bd841d (MD5) %R 10.1137/S0036141003427774 %0 Journal Article %J Indiana Univ. Math. J. 53 (2004) 297-392 %D 2004 %T Singularity perturbed elliptic equations with symmetry: existence of solutions concetrating on spheres, Part II %A Antonio Ambrosetti %A Andrea Malchiodi %A Wei-Ming Ni %B Indiana Univ. Math. J. 53 (2004) 297-392 %I Indiana University Mathematics Journal %G en %U http://hdl.handle.net/1963/1663 %1 2455 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:06:06Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002 %R 10.1512/iumj.2004.53.2400 %0 Journal Article %J SIAM J. Control Optim. 43 (2004) 194-215 %D 2004 %T Small BV solutions of hyperbolic noncooperative differential games %A Alberto Bressan %A Wen Shen %X The paper is concerned with an n-persons differential game in one space dimension. We state conditions for which the system of Hamilton-Jacobi equations for the value functions is strictly hyperbolic. In the positive case, we show that the weak solution of a corresponding system of conservation laws determines an n-tuple of feedback strategies. These yield a Nash equilibrium solution to the non-cooperative differential game. %B SIAM J. Control Optim. 43 (2004) 194-215 %I SIAM %G en_US %U http://hdl.handle.net/1963/2917 %1 1783 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T13:46:04Z\\nNo. of bitstreams: 1\\n021.pdf: 296267 bytes, checksum: 16f3c148f2a00551188fee22ac90f666 (MD5) %R 10.1137/S0363012903425581 %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 C. R. Acad. Sci. Paris, Ser. I 338 (2004) 775-780 %D 2004 %T Solutions concentrating at curves for some singularly perturbed elliptic problems %A Andrea Malchiodi %B C. R. Acad. Sci. Paris, Ser. I 338 (2004) 775-780 %I Elsevier %G en %U http://hdl.handle.net/1963/4869 %1 4647 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-20T14:23:50Z\\nNo. of bitstreams: 0 %R 10.1016/j.crma.2004.03.023 %0 Journal Article %J Bollettino dell\\\'Unione Matematica Italiana Serie 8 7-B (2004), p. 647-661 %D 2004 %T Soluzioni periodiche di PDEs Hamiltoniane %A Massimiliano Berti %B Bollettino dell\\\'Unione Matematica Italiana Serie 8 7-B (2004), p. 647-661 %I Unione Matematica Italiana %G en %U http://hdl.handle.net/1963/4582 %1 4351 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-07T10:33:48Z\\nNo. of bitstreams: 1\\nberti2004.pdf: 249023 bytes, checksum: bab6b2d956c1de46de694dfca3bc4cec (MD5) %0 Journal Article %J Rend. Mat. Acc. Lincei, s. 9, v. 15 (2004) 3-4, pp. 225 - 233 %D 2004 %T Some remarks on multidimensional systems of conservation laws %A Alberto Bressan %X This note is concerned with the Cauchy problem for hyperbolic systems of conservation\\nlaws in several space dimensions. We first discuss an example of ill-posedness, for a special system\\nhaving a radial symmetry property. Some conjectures are formulated, on the compactness of the set of\\nflow maps generated by vector fields with bounded variation. %B Rend. Mat. Acc. Lincei, s. 9, v. 15 (2004) 3-4, pp. 225 - 233 %I Accademia Nazionale dei Lincei %G en_US %U http://hdl.handle.net/1963/3642 %1 662 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-05-21T10:01:16Z\\nNo. of bitstreams: 1\\nM2004-34-21.pdf: 187400 bytes, checksum: 045bd5d68458b90865a3a4c132a90163 (MD5) %0 Journal Article %J ESAIM COCV 10 (2004) 168-200 %D 2004 %T Stability rates for patchy vector fields %A Fabio Ancona %A Alberto Bressan %X This paper is concerned with the stability of the set of trajectories of a patchy vector field, in the presence of impulsive perturbations. Patchy vector fields are discontinuous, piecewise smooth vector fields that were introduced in Ancona and Bressan (1999) to study feedback stabilization problems. For patchy vector fields in the plane, with polygonal patches in generic position, we show that the distance between a perturbed trajectory and an unperturbed one is of the same order of magnitude as the impulsive forcing term. %B ESAIM COCV 10 (2004) 168-200 %I EDP Sciences %G en_US %U http://hdl.handle.net/1963/2959 %1 1741 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-22T08:49:39Z\\nNo. of bitstreams: 1\\n0111109v1.pdf: 336899 bytes, checksum: 851fc204f3e9f254b9122e0bd1f8894f (MD5) %R 10.1051/cocv:2004003 %0 Journal Article %J Mem. Amer. Math. Soc. 169 (2004), no. 801, x+170 pp. %D 2004 %T Well-posedness for general 2x2 systems of conservation laws %A Fabio Ancona %A Andrea Marson %B Mem. Amer. Math. Soc. 169 (2004), no. 801, x+170 pp. %I SISSA Library %G en %U http://hdl.handle.net/1963/1241 %1 2702 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:11Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %0 Journal Article %J Applied Math.Optim. 48 (2003), no.1, p.39-66 %D 2003 %T Autonomous integral functionals with discontinous nonconvex integrands: Lipschitz regularity of mimimizers, DuBois-Reymond necessary conditions and Hamilton-Jacobi equations %A Gianni Dal Maso %A Helene Frankowska %B Applied Math.Optim. 48 (2003), no.1, p.39-66 %I SISSA Library %G en %U http://hdl.handle.net/1963/1625 %1 2493 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:30Z (GMT). No. of bitstreams: 1\\r\\nmath.AP0207230.pdf: 302400 bytes, checksum: e660ec855386e1a29edd2e20f7abc796 (MD5)\\r\\n Previous issue date: 2002 %R 10.1007/s00245-003-0768-4 %0 Journal Article %J Calc. Var. Partial Differential Equations 16 (2003) 299-333 %D 2003 %T The calibration method for the Mumford-Shah functional and free-discontinuity problems %A Giovanni Alberti %A Guy Bouchitte %A Gianni Dal Maso %X We present a minimality criterion for the Mumford-Shah functional, and more generally for non convex variational integrals on SBV which couple a surface and a bulk term. This method provides short and easy proofs for several minimality results. %B Calc. Var. Partial Differential Equations 16 (2003) 299-333 %I Springer %G en_US %U http://hdl.handle.net/1963/3051 %1 1282 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-09T15:00:19Z\\nNo. of bitstreams: 1\\n0105013v1.pdf: 428802 bytes, checksum: de75d15134f2a74b36b0d71355e04835 (MD5) %R 10.1007/s005260100152 %0 Thesis %D 2003 %T Control Problems for Systems of Conservation Laws %A Giuseppe Maria Coclite %K Asymptotic Stabilization %I SISSA %G en %U http://hdl.handle.net/1963/5325 %1 5154 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Gerardina Cargnelutti (gerry@sissa.it) on 2012-02-01T11:55:57Z\\nNo. of bitstreams: 1\\nPhD_Coclite_Giuseppe_Maria.pdf: 6164510 bytes, checksum: 461d3d4a88e73be06d19b21a85ab149a (MD5) %0 Journal Article %J J. Math. Pures Appl. 82 (2003) 613-664 %D 2003 %T Drift in phase space: a new variational mechanism with optimal diffusion time %A Massimiliano Berti %A Luca Biasco %A Philippe Bolle %X We consider non-isochronous, nearly integrable, a-priori unstable Hamiltonian systems with a (trigonometric polynomial) $O(\\\\mu)$-perturbation which does not preserve the unperturbed tori. We prove the existence of Arnold diffusion with diffusion time $ T_d = O((1/ \\\\mu) \\\\log (1/ \\\\mu))$ by a variational method which does not require the existence of ``transition chains of tori\\\'\\\' provided by KAM theory. We also prove that our estimate of the diffusion time $T_d $ is optimal as a consequence of a general stability result derived from classical perturbation theory. %B J. Math. Pures Appl. 82 (2003) 613-664 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3020 %1 1313 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-02T15:07:59Z\\nNo. of bitstreams: 1\\n0205307v1.pdf: 505505 bytes, checksum: 2dab01ff574df56912b2fe8d3c56108a (MD5) %R 10.1016/S0021-7824(03)00032-1 %0 Journal Article %J Numer. Math., 2003, 95, 653 %D 2003 %T A finite element approximation of the Griffith\\\'s model in fracture mechanics %A Matteo Negri %X The Griffith model for the mechanics of fractures in brittle materials is consider in the weak formulation of SBD spaces. We suggest an approximation, in the sense of Gamma-convergence, by a sequence of discrete functionals defined on finite elements spaces over structured and adaptive triangulations. The quasi-static evolution for boundary value problems is also taken into account and some numerical results are shown. %B Numer. Math., 2003, 95, 653 %I SISSA Library %G en %U http://hdl.handle.net/1963/1548 %1 2570 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:58Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1007/s00211-003-0456-y %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 %D 2003 %T An ill posed Cauchy problem for a hyperbolic system in two space dimensions %A Alberto Bressan %X The theory of weak solutions for nonlinear conservation laws is now well developed in the case of scalar equations [3] and for one-dimensional hyperbolic systems [1, 2]. For systems in several space dimensions, however, even the global existence of solutions to the Cauchy problem remains a challenging open question. In this note we construct a conterexample showing that, even for a simple class of hyperbolic systems, in two space dimensions the Cauchy problem can be ill posed. %I Università di Padova %G en_US %U http://hdl.handle.net/1963/2913 %1 1787 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T13:18:40Z\\nNo. of bitstreams: 1\\nmath.AP0302227.pdf: 126071 bytes, checksum: 3536c415c6e375bb55591a913ced63c2 (MD5) %0 Journal Article %J J.Math.Anal.Appl. 284 (2003) no.1, 49 %D 2003 %T An interior estimate for a nonlinear parabolic equation %A Giuseppe Maria Coclite %B J.Math.Anal.Appl. 284 (2003) no.1, 49 %I SISSA Library %G en %U http://hdl.handle.net/1963/1622 %1 2496 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:27Z (GMT). No. of bitstreams: 1\\nmath.AP0207193.pdf: 123937 bytes, checksum: e3147ae778a391681315f33680cefa66 (MD5)\\n Previous issue date: 2002 %R 10.1016/S0022-247X(03)00157-4 %0 Journal Article %J Rend. Sem. Mat. Univ. Padova 110 (2003) 97-102 %D 2003 %T A lemma and a conjecture on the cost of rearrangements %A Alberto Bressan %X Consider a stack of books, containing both white and black books. Suppose that we want to sort them out, putting the white books on the right, and the black books on the left (fig.~1). This will be done by a finite sequence of elementary transpositions. In other words, if we have a stack of all black books of length $a$ followed by a stack of all white books of length $b$, we are allowed to reverse their order at the cost of $a+b$. We are interested in a lower bound on the total cost of the rearrangement. %B Rend. Sem. Mat. Univ. Padova 110 (2003) 97-102 %I Università di Padova %G en_US %U http://hdl.handle.net/1963/2914 %1 1786 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T13:23:07Z\\nNo. of bitstreams: 1\\nmath.AP0302228.pdf: 114252 bytes, checksum: 85213b6876996792213f6032c6fe2035 (MD5) %0 Journal Article %J SIAM J. Control Optim. 42 (2003) 513-531 %D 2003 %T On the local structure of optimal trajectories in R3 %A Andrei A. Agrachev %A Mario Sigalotti %X We analyze the structure of a control function u(t) corresponding to an optimal trajectory for the system $\\\\dot q =f(q)+u\\\\, g(q)$ in a three-dimensional manifold, near a point where some nondegeneracy conditions are satisfied. The kind of optimality which is studied includes time-optimality. The control turns out to be the concatenation of some bang and some singular arcs. Studying the index of the second variation of the switching times, the number of such arcs is bounded by four. %B SIAM J. Control Optim. 42 (2003) 513-531 %I SISSA Library %G en %U http://hdl.handle.net/1963/1612 %1 2506 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:18Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002 %R 10.1137/S0363012902409246 %0 Journal Article %J Commun. Pure Appl. Ana., 2003, 2, 51-64 %D 2003 %T A note on singular limits to hyperbolic systems of conservation laws %A Stefano Bianchini %X In this note we consider two different singular limits to hyperbolic system of conservation laws, namely the standard backward schemes for non linear semigroups and the semidiscrete scheme. \\nUnder the assumption that the rarefaction curve of the corresponding hyperbolic system are straight lines, we prove the stability of the solution and the convergence to the perturbed system to the unique solution of the limit system for initial data with small total variation. %B Commun. Pure Appl. Ana., 2003, 2, 51-64 %I SISSA Library %G en %U http://hdl.handle.net/1963/1542 %1 2621 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:52Z (GMT). No. of bitstreams: 1\\nmath.AP0009012.pdf: 134454 bytes, checksum: 922fd2c2a00dd9dd36fc10453824437c (MD5)\\n Previous issue date: 2000 %0 Journal Article %J Rend. Mat. Appl. 23 (2003) 189-201 %D 2003 %T A note on the integral representation of functionals in the space SBD(O) %A Francois Ebobisse %A Rodica Toader %X In this paper we study the integral representation in the space SBD(O) of special functions with bounded deformation of some L^1-norm lower semicontinuous functionals invariant with respect to rigid motions. %B Rend. Mat. Appl. 23 (2003) 189-201 %I Rendiconti di Matematica %G en_US %U http://hdl.handle.net/1963/3064 %1 1269 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-10T08:08:06Z\\nNo. of bitstreams: 1\\n0104264v1.pdf: 157593 bytes, checksum: 8afd09d4c0f34e5fa55e357804395f3d (MD5) %0 Journal Article %J Comm.Math.Phys. 243 (2003) no.2, 315 %D 2003 %T Periodic solutions of nonlinear wave equations with general nonlinearities %A Massimiliano Berti %A Philippe Bolle %B Comm.Math.Phys. 243 (2003) no.2, 315 %I SISSA Library %G en %U http://hdl.handle.net/1963/1648 %1 2470 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:51Z (GMT). No. of bitstreams: 1\\nmath.AP0211310.pdf: 363476 bytes, checksum: 15bbb8f96ff0c106ea4dc1343e19afa4 (MD5)\\n Previous issue date: 2002 %R 10.1007/s00220-003-0972-8 %0 Journal Article %J Discrete Contin.Dyn.Syst. 9 (2003), no.1, 55-68 %D 2003 %T Positive solutions to a class of quasilinear elliptic equations on R %A Antonio Ambrosetti %A Wang Zhi-Qiang %X We discuss the existence of positive solutions of perturbation to a class of quasilinear elliptic equations on R. %B Discrete Contin.Dyn.Syst. 9 (2003), no.1, 55-68 %I American Institute of Mathematical Sciences %G en %U http://hdl.handle.net/1963/1628 %1 2490 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:32Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002 %R 10.3934/dcds.2003.9.55 %0 Journal Article %J J. Geom. Anal. 13 (2003) 255-289 %D 2003 %T Prescribing scalar and boundary mean curvature on the three dimensional half sphere %A Zindine Djadli %A Andrea Malchiodi %A Mohameden Ould Ahmedou %X We consider the problem of prescribing the scalar curvature and the boundary mean curvature of the standard half three sphere, by deforming conformally its standard metric. Using blow up analysis techniques and minimax arguments, we prove some existence and compactness results. %B J. Geom. Anal. 13 (2003) 255-289 %I Springer %G en_US %U http://hdl.handle.net/1963/3086 %1 1247 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-13T14:32:25Z\\nNo. of bitstreams: 1\\n0211227v1.pdf: 359886 bytes, checksum: e4e0c1b0979d1cb348e41f2351b74254 (MD5) %R 10.1007/BF02930697 %0 Journal Article %J SIAM J. Math. Anal. 35 (2003) 759-805 %D 2003 %T Sequences of Singularly Perturbed Functionals Generating Free-Discontinuity Problems %A Massimiliano Morini %X We prove that a wide class of singularly perturbed functionals generates as $\\\\Gamma$-limit a functional related to a free-discontinuity problem. Several applications of the result are shown. %B SIAM J. Math. Anal. 35 (2003) 759-805 %I SIAM %G en_US %U http://hdl.handle.net/1963/3071 %1 1262 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-10T10:24:32Z\\nNo. of bitstreams: 1\\nsingper.pdf: 523839 bytes, checksum: 9d1bcc064d165e9b964422c8acd396bb (MD5) %R 10.1137/S0036141001395388 %0 Thesis %D 2003 %T Single-Input Control Affine Systems: Local Regularity of Optimal Trajectories and a Geometric Controllability Problem %A Mario Sigalotti %I SISSA %G en %U http://hdl.handle.net/1963/5342 %1 5170 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Gerardina Cargnelutti (gerry@sissa.it) on 2012-02-02T12:08:29Z\\nNo. of bitstreams: 1\\nPhD_Sigalotti_Mario.pdf: 8050196 bytes, checksum: e113b00d1c0f5b37484c26f023914baa (MD5) %0 Journal Article %J Comm. Math. Phys. 235 (2003) no.3, 427-466 %D 2003 %T Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres, Part I %A Antonio Ambrosetti %A Andrea Malchiodi %A Wei-Ming Ni %B Comm. Math. Phys. 235 (2003) no.3, 427-466 %I Springer %G en %U http://hdl.handle.net/1963/1633 %1 2485 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:37Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002 %R 10.1007/s00220-003-0811-y %0 Journal Article %J SIAM J.Control Optim. 41 (2003),no.2, 607 %D 2003 %T Some results on the boundary control of systems of conservation laws %A Alberto Bressan %A Fabio Ancona %A Giuseppe Maria Coclite %B SIAM J.Control Optim. 41 (2003),no.2, 607 %I SISSA Library %G en %U http://hdl.handle.net/1963/1615 %1 2503 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:20Z (GMT). No. of bitstreams: 1\\nmath.AP0205246.pdf: 155904 bytes, checksum: 294663b00a9e6b6ae91096fd628a942a (MD5)\\n Previous issue date: 2002 %R 10.1137/S0363012901392529 %0 Journal Article %J J.Math. Pures Appl. (9) 82 (2003) no.5 , 503 %D 2003 %T A stability result for nonlinear Neumann problems under boundary variations %A Gianni Dal Maso %A Francois Ebobisse %A Marcello Ponsiglione %X In this paper we study, in dimension two, the stability of the solutions of some nonlinear elliptic equations with Neumann boundary conditions, under perturbations of the domains in the Hausdorff complementary topology. %B J.Math. Pures Appl. (9) 82 (2003) no.5 , 503 %I SISSA Library %G en %U http://hdl.handle.net/1963/1618 %1 2500 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:23Z (GMT). No. of bitstreams: 1\\nmath.AP0206215.pdf: 329673 bytes, checksum: 40d537fd197fbaec56be0729d3a72ee3 (MD5)\\n Previous issue date: 2002 %R 10.1016/S0021-7824(03)00014-X %0 Journal Article %J J. Differ. Equations, 2002, 180, 395 %D 2002 %T Admissible Riemann solvers for genuinely nonlinear P-systems of mixed type %A Jean-Marc Mercier %A Benedetto Piccoli %B J. Differ. Equations, 2002, 180, 395 %I SISSA Library %G en %U http://hdl.handle.net/1963/1491 %1 2672 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:09Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1006/jdeq.2001.4066 %0 Journal Article %J Pr. Inst. Mat. Nats. Akad. Nauk Ukr. Mat. Zastos., 43, Part 1, 2, Natsīonal. Akad. Nauk Ukraïni, Īnst. Mat., Kiev, 2002 %D 2002 %T Arnold diffusion: a functional analysis approach %A Massimiliano Berti %X We present, in the context of nearly integrable Hamiltonian systems, a functional analysis approach to study the “splitting of the whiskers” and the “shadowing problem” developed in collaboration with P. Bolle in the recent papers [1] and [2] . This method is applied to the problem of Arnold diffusion for nearly integrable partially isochronous systems improving known results. %B Pr. Inst. Mat. Nats. Akad. Nauk Ukr. Mat. Zastos., 43, Part 1, 2, Natsīonal. Akad. Nauk Ukraïni, Īnst. Mat., Kiev, 2002 %I Natsīonal. Akad. Nauk Ukraïni %G en %1 7269 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-12-09T08:37:48Z No. of bitstreams: 1 Berti712-719.pdf: 135161 bytes, checksum: 75afb14b28171db9cab374b3ccbbc265 (MD5) %0 Journal Article %J SIAM J. Control Optim. 41 (2002) 607-622 %D 2002 %T On the Boundary Control of Systems of Conservation Laws %A Alberto Bressan %A Giuseppe Maria Coclite %X The paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand, we give an example showing that exact controllability in finite time cannot be achieved, in general. %B SIAM J. Control Optim. 41 (2002) 607-622 %I SIAM %G en_US %U http://hdl.handle.net/1963/3070 %1 1263 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-10T10:05:11Z\\nNo. of bitstreams: 1\\n0108224v1.pdf: 198822 bytes, checksum: b08b507c4b17c8b48aaa3aafdc4d7360 (MD5) %R 10.1137/S0363012901392529 %0 Journal Article %J J. Convex Anal. 9 (2002) 1-29 %D 2002 %T The Calibration Method for Free-Discontinuity Problems on Vector-Valued Maps %A Maria Giovanna Mora %X The calibration method is a classical minimality criterion, which has been recently adapted to functionals with free discontinuities by Alberti, Bouchitté, Dal Maso. In this paper we present a further generalization of this theory to functionals defined on vector-valued maps. %B J. Convex Anal. 9 (2002) 1-29 %I Heldermann Verlag %G en_US %U http://hdl.handle.net/1963/3049 %1 1284 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-09T14:39:36Z\\nNo. of bitstreams: 1\\nvcal_method.pdf: 345795 bytes, checksum: 8f1703daddffd1c18d837fccf4dfc9bf (MD5) %0 Journal Article %J Commun. Pure Appl. Anal. 1 (2002) 161-190 %D 2002 %T A center manifold technique for tracing viscous waves %A Stefano Bianchini %A Alberto Bressan %X In this paper we introduce a new technique for tracing viscous travelling profiles. To illustrate the method, we consider a special 2 x 2 hyperbolic system of conservation laws with viscosity, and show that any solution can be locally decomposed as the sum of 2 viscous travelling profiles. This yields the global existence, stability and uniform BV bounds for every solution with suitably small BV data. %B Commun. Pure Appl. Anal. 1 (2002) 161-190 %I American Institute of Mathematical Sciences %G en_US %U http://hdl.handle.net/1963/3075 %1 1258 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-10T10:55:34Z\\nNo. of bitstreams: 1\\npreprint2001_53.pdf: 444727 bytes, checksum: 26cee63284464e4850e1e6426216fe70 (MD5) %0 Journal Article %J Nonlinear Anal. 48 (2002) 481-504 %D 2002 %T Chaotic dynamics for perturbations of infinite-dimensional Hamiltonian systems %A Massimiliano Berti %A Carlo Carminati %B Nonlinear Anal. 48 (2002) 481-504 %I Elsevier %G en %U http://hdl.handle.net/1963/1279 %1 3176 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:42Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %R 10.1016/S0362-546X(00)00200-5 %0 Journal Article %J Interfaces Free Bound. 7 (2002) 345-370 %D 2002 %T Curvature theory of boundary phases: the two-dimensional case %A Andrea Braides %A Andrea Malchiodi %X We describe the behaviour of minimum problems involving non-convex surface integrals in 2D, singularly perturbed by a curvature term. We show that their limit is described by functionals which take into account energies concentrated on vertices of polygons. Non-locality and non-compactness effects are highlighted. %B Interfaces Free Bound. 7 (2002) 345-370 %I European Mathematical Society %G en_US %U http://hdl.handle.net/1963/3537 %1 1164 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-23T15:34:33Z\\nNo. of bitstreams: 1\\n2001BM.pdf: 361945 bytes, checksum: eb748fdc7f69d6fef497ebaf68f155a6 (MD5) %0 Journal Article %J Commun. Contemp. Math. 4 (2002) 177-209 %D 2002 %T Existence of minimal H-bubbles %A Paolo Caldiroli %A Roberta Musina %B Commun. Contemp. Math. 4 (2002) 177-209 %I SISSA Library %G en %U http://hdl.handle.net/1963/1525 %1 2638 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:37Z (GMT). No. of bitstreams: 1\\nmath.AP0006157.pdf: 242337 bytes, checksum: ad4f345871a0c7fb33e9c4bc361ce4d8 (MD5)\\n Previous issue date: 2000 %R 10.1142/S021919970200066X %0 Journal Article %J Discrete Contin. Dyn. Syst. 8 (2002) 795-811 %D 2002 %T Fast Arnold diffusion in systems with three time scales %A Massimiliano Berti %A Philippe Bolle %X We consider the problem of Arnold Diffusion for nearly integrable partially isochronous Hamiltonian systems with three time scales. By means of a careful shadowing analysis, based on a variational technique, we prove that, along special directions, Arnold diffusion takes place with fast (polynomial) speed, even though the \\\"splitting determinant\\\" is exponentially small. %B Discrete Contin. Dyn. Syst. 8 (2002) 795-811 %I American Institute of Mathematical Sciences %G en_US %U http://hdl.handle.net/1963/3058 %1 1275 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-09T16:26:36Z\\nNo. of bitstreams: 1\\n0103065v1.pdf: 229503 bytes, checksum: eb476d4f1629873c6d0688c3a4a9dc61 (MD5) %0 Journal Article %J SIAM J. Control Optim. 41 (2002) 1455-1476 %D 2002 %T Flow Stability of Patchy Vector Fields and Robust Feedback Stabilization %A Fabio Ancona %A Alberto Bressan %X The paper is concerned with patchy vector fields, a class of discontinuous, piecewise smooth vector fields that were introduced in AB to study feedback stabilization problems. We prove the stability of the corresponding solution set w.r.t. a wide class of impulsive perturbations. These results yield the robusteness of patchy feedback controls in the presence of measurement errors and external disturbances. %B SIAM J. Control Optim. 41 (2002) 1455-1476 %I SIAM %G en_US %U http://hdl.handle.net/1963/3073 %1 1260 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-10T10:37:20Z\\nNo. of bitstreams: 1\\n0111107v1.pdf: 227962 bytes, checksum: 76bf14ce144f1803bb403d8781e00a0d (MD5) %R 10.1137/S0363012901391676 %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire 19 (2002) 395-450 %D 2002 %T A functional analysis approach to Arnold diffusion %A Massimiliano Berti %A Philippe Bolle %X We discuss in the context of nearly integrable Hamiltonian systems a functional analysis approach to the \\\"splitting of separatrices\\\" and to the \\\"shadowing problem\\\". As an application we apply our method to the problem of Arnold Diffusion for nearly integrable partially isochronous systems improving known results. %B Ann. Inst. H. Poincare Anal. Non Lineaire 19 (2002) 395-450 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3151 %1 1182 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-20T14:35:29Z\\nNo. of bitstreams: 1\\nArnold_diffusion.pdf: 397794 bytes, checksum: 16e32aa6198ef17e8f55e7292307ee09 (MD5) %R 10.1016/S0294-1449(01)00084-1 %0 Journal Article %J J. Dynam. Control Systems 8 (2002) 93-140 %D 2002 %T Geometry of Jacobi Curves I %A Andrei A. Agrachev %A Igor Zelenko %X Jacobi curves are deep generalizations of the spaces of \\\"Jacobi fields\\\" along Riemannian geodesics. Actually, Jacobi curves are curves in the Lagrange Grassmannians. In our paper we develop differential geometry of these curves which provides basic feedback or gauge invariants for a wide class of smooth control systems and geometric structures. Two principal invariants are the generalized Ricci curvature, which is an invariant of the parametrized curve in the Lagrange Grassmannian endowing the curve with a natural projective structure, and a fundamental form, which is a fourth-order differential on the curve. The so-called rank 1 curves are studied in more detail. Jacobi curves of this class are associated with systems with scalar controls and with rank 2 vector distributions.\\nIn the forthcoming second part of the paper we will present the comparison theorems (i.e., the estimates for the conjugate points in terms of our invariants( for rank 1 curves an introduce an important class of \\\"flat curves\\\". %B J. Dynam. Control Systems 8 (2002) 93-140 %I Springer %G en_US %U http://hdl.handle.net/1963/3110 %1 1223 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-15T09:36:40Z\\nNo. of bitstreams: 1\\nJacobicurves.pdf: 365662 bytes, checksum: 23c0d55e84f95c2c8f386ea136ef18d0 (MD5) %R 10.1023/A:1013904801414 %0 Journal Article %J J. Dynam. Control Systems 8 (2002), no. 2, 167--215 %D 2002 %T Geometry of Jacobi curves II %A Andrei A. Agrachev %A Igor Zelenko %B J. Dynam. Control Systems 8 (2002), no. 2, 167--215 %I SISSA Library %G en %U http://hdl.handle.net/1963/1589 %1 2529 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:58Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002 %R 10.1023/A:1015317426164 %0 Journal Article %J Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 1 (2002) 603-648 %D 2002 %T Global calibrations for the non-homogeneous Mumford-Shah functional %A Massimiliano Morini %X Using a calibration method we prove that, if $\\\\Gamma\\\\subset \\\\Omega$ is a closed regular hypersurface and if the function $g$ is discontinuous along $\\\\Gamma$ and regular outside, then the function $u_{\\\\beta}$ which solves $$ \\\\begin{cases} \\\\Delta u_{\\\\beta}=\\\\beta(u_{\\\\beta}-g)& \\\\text{in $\\\\Omega\\\\setminus\\\\Gamma$} \\\\partial_{\\\\nu} u_{\\\\beta}=0 & \\\\text{on $\\\\partial\\\\Omega\\\\cup\\\\Gamma$} \\\\end{cases} $$ is in turn discontinuous along $\\\\Gamma$ and it is the unique absolute minimizer of the non-homogeneous Mumford-Shah functional $$ \\\\int_{\\\\Omega\\\\setminus S_u}|\\\\nabla u|^2 dx +{\\\\cal H}^{n-1}(S_u)+\\\\beta\\\\int_{\\\\Omega\\\\setminus S_u}(u-g)^2 dx, $$ over $SBV(\\\\Omega)$, for $\\\\beta$ large enough. Applications of the result to the study of the gradient flow by the method of minimizing movements are shown. %B Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 1 (2002) 603-648 %I Scuola Normale Superiore di Pisa %G en_US %U http://hdl.handle.net/1963/3089 %1 1244 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-13T15:10:43Z\\nNo. of bitstreams: 1\\n0105141v1.pdf: 402689 bytes, checksum: 50ca626f4a7fc3ff76a466c506ca755b (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 Set-Valued Anal. 10 (2002), p.165-183 %D 2002 %T Linearized elasticity as gamma-limit of finite elasticity %A Gianni Dal Maso %A Matteo Negri %A Danilo Percivale %B Set-Valued Anal. 10 (2002), p.165-183 %I Springer %G en_US %U http://hdl.handle.net/1963/3052 %1 1281 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-09T15:20:52Z\\r\\nNo. of bitstreams: 1\\r\\nDM-Neg-Per-01.pdf: 199909 bytes, checksum: ddd0bf6c6890234f6d9c820fd6ab7f47 (MD5) %R 10.1023/A:1016577431636 %0 Journal Article %J Commun. Contemp. Math. 4 (2002) 297-326 %D 2002 %T Local calibrations for minimizers of the Mumford-Shah functional with a triple junction %A Maria Giovanna Mora %X We prove that, if u is a function satisfying all Euler conditions for the Mumford-Shah functional and the discontinuity set of u is given by three line segments meeting at the origin with equal angles, then there exists a neighbourhood U of the origin such that u is a minimizer of the Mumford-Shah functional on U with respect to its own boundary conditions on the boundary of U. The proof is obtained by using the calibration method. %B Commun. Contemp. Math. 4 (2002) 297-326 %I World Scientific %G en_US %U http://hdl.handle.net/1963/3050 %1 1283 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-09T14:49:33Z\\nNo. of bitstreams: 1\\n0105057v2.pdf: 321835 bytes, checksum: e085f082e744017d9dfa6a7372760af2 (MD5) %R 10.1142/S0219199702000646 %0 Journal Article %J Nonlinear Anal. 51 (2002) 649-662 %D 2002 %T On a Lyapunov functional relating shortening curves and viscous conservation laws %A Stefano Bianchini %A Alberto Bressan %X We study a nonlinear functional which controls the area swept by a curve moving in the plane in the direction of curvature. In turn, this yields a priori estimates on solutions to a class of parabolic equations and of scalar viscous conservation laws. A further application provides an estimate on the \\\"change of shape\\\" of a BV solution to a scalar conservation law. %B Nonlinear Anal. 51 (2002) 649-662 %I Elsevier %G en %U http://hdl.handle.net/1963/1337 %1 3118 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:56:28Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %R 10.1016/S0362-546X(01)00848-3 %0 Journal Article %J Math. Models Methods Appl. Sci., 12 (2002), no. 12, 1773 %D 2002 %T A model for the quasi-static growth of a brittle fracture: existence and approximation results %A Gianni Dal Maso %A Rodica Toader %X We study a variant of the variational model for the quasi-static growth of brittle fractures proposed by Francfort and Marigo.9 The main feature of our model is that, in the discrete-time formulation, in each step we do not consider absolute minimizers of the energy, but, in a sense, we look for local minimizers which are sufficiently close to the approximate solution obtained in the previous step. This is done by introducing in the variational problem an additional term which penalizes the L2-distance between the approximate solutions at two consecutive times. We study the continuous-time version of this model, obtained by passing to the limit as the time step tends to zero, and show that it satisfies (for almost every time) some minimality conditions which are slightly different from those considered in Refs. 9 and 8, but are still enough to prove (under suitable regularity assumptions on the crack path) that the classical Griffith\\\'s criterion holds at the crack tips. We also prove that, if no initial crack is present and if the data of the problem are sufficiently smooth, no crack will develop in this model, provided the penalization term is large enough. %B Math. Models Methods Appl. Sci., 12 (2002), no. 12, 1773 %I SISSA Library %G en %U http://hdl.handle.net/1963/1571 %1 2547 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:18Z (GMT). No. of bitstreams: 1\\nmath.AP0101089.pdf: 313965 bytes, checksum: 0373da7254cb4d172659dd2402174562 (MD5)\\n Previous issue date: 2000 %R 10.1142/S0218202502002331 %0 Journal Article %J Math.Models Methods Appl. Sci., 12 (2002) , p.1773-1800. %D 2002 %T A model for the quasi-static growth of brittle fractures based on local minimization %A Gianni Dal Maso %A Rodica Toader %X We study a variant of the variational model for the quasi-static growth of brittle fractures proposed by Francfort and Marigo.9 The main feature of our model is that, in the discrete-time formulation, in each step we do not consider absolute minimizers of the energy, but, in a sense, we look for local minimizers which are sufficiently close to the approximate solution obtained in the previous step. This is done by introducing in the variational problem an additional term which penalizes the L2-distance between the approximate solutions at two consecutive times. We study the continuous-time version of this model, obtained by passing to the limit as the time step tends to zero, and show that it satisfies (for almost every time) some minimality conditions which are slightly different from those considered in Refs. 9 and 8, but are still enough to prove (under suitable regularity assumptions on the crack path) that the classical Griffith\\\'s criterion holds at the crack tips. We also prove that, if no initial crack is present and if the data of the problem are sufficiently smooth, no crack will develop in this model, provided the penalization term is large enough. %B Math.Models Methods Appl. Sci., 12 (2002) , p.1773-1800. %I SISSA Library %G en %U http://hdl.handle.net/1963/1621 %1 2497 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:26Z (GMT). No. of bitstreams: 1\\r\\nmath.AP0207002.pdf: 268810 bytes, checksum: 00401d0491ec9d938b05dcdb884832b7 (MD5)\\r\\n Previous issue date: 2002 %R 10.1142/S0218202502002331 %0 Journal Article %J Arch. Ration. Mech. Anal. 162 (2002) 101-135 %D 2002 %T A Model for the Quasi-Static Growth of Brittle Fractures: Existence and Approximation Results %A Gianni Dal Maso %A Rodica Toader %X We give a precise mathematical formulation of a variational model for the irreversible quasi-static evolution of brittle fractures proposed by G.A. Francfort and J.-J. Marigo, and based on Griffith\\\'s theory of crack growth. In the two-dimensional case we prove an existence result for the quasi-static evolution and show that the total energy is an absolutely continuous function of time, although we can not exclude that the bulk energy and the surface energy may present some jump discontinuities. This existence result is proved by a time discretization process, where at each step a global energy minimization is performed, with the constraint that the new crack contains all cracks formed at the previous time steps. This procedure provides an effective way to approximate the continuous time evolution. %B Arch. Ration. Mech. Anal. 162 (2002) 101-135 %I Springer %G en_US %U http://hdl.handle.net/1963/3056 %1 1277 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-09T16:01:33Z\\nNo. of bitstreams: 1\\n0103221v1.pdf: 340988 bytes, checksum: 433e8545f072a326fc7a6d80a9e7a401 (MD5) %R 10.1007/s002050100187 %0 Journal Article %J Ann. Pol. Math. 79 (2002) 21-30 %D 2002 %T A multiplicity result for the Schrodinger-Maxwell equations with negative potential %A Giuseppe Maria Coclite %X We prove the existence of a sequence of radial solutions with negative energy of the Schrödinger-Maxwell equations under the action of a negative potential. %B Ann. Pol. Math. 79 (2002) 21-30 %I IMPAN %G en_US %U http://hdl.handle.net/1963/3053 %1 1280 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-09T15:31:03Z\\nNo. of bitstreams: 1\\n0109017v1.pdf: 119291 bytes, checksum: 3cab63ccaba611cce6115aa21acc9fbf (MD5) %0 Journal Article %J Proceedings of the National Academy of Sciences of the United States of America. 2002 Nov; 99(24):15252-6 %D 2002 %T Multiplicity results for the Yamabe problem on Sn %A Antonio Ambrosetti %X We discuss some results related to the existence of multiple solutions for the Yamabe problem. %B Proceedings of the National Academy of Sciences of the United States of America. 2002 Nov; 99(24):15252-6 %I National Academy of Sciences %G en %U http://hdl.handle.net/1963/5885 %1 5757 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Marta Maurutto (maurutto@sissa.it) on 2012-06-09T13:56:14Z\\nNo. of bitstreams: 0 %R 10.1073/pnas.222494199 %0 Journal Article %D 2002 %T An optimal fast-diffusion variational method for non isochronous system %A Luca Biasco %A Massimiliano Berti %A Philippe Bolle %I SISSA Library %G en %U http://hdl.handle.net/1963/1579 %1 2539 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:50Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002 %0 Journal Article %J Atti.Accad.Naz.Lincei Cl.Sci.Fis.Mat.Natur.Rend.Lincei (9) Mat.Appl.13(2002),no.2,77-84 %D 2002 %T Optimal stability and instability results for a class of nearly integrable Hamiltonian systems %A Massimiliano Berti %A Luca Biasco %A Philippe Bolle %B Atti.Accad.Naz.Lincei Cl.Sci.Fis.Mat.Natur.Rend.Lincei (9) Mat.Appl.13(2002),no.2,77-84 %I SISSA Library %G en %U http://hdl.handle.net/1963/1596 %1 2522 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:04Z (GMT). No. of bitstreams: 1\\nmath.DS0203188.pdf: 131832 bytes, checksum: 468589170f7f79086f08c3a5902e94d7 (MD5)\\n Previous issue date: 2002 %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 Ann. Sc. Norm. Super. Pisa Cl. Sci., 2002, 1, 387 %D 2002 %T Prescribing a fourth oder conformal invariant on the standard sphere - Part II: blow up analysis and applications %A Zindine Djadli %A Andrea Malchiodi %A Mohameden Ould Ahmedou %B Ann. Sc. Norm. Super. Pisa Cl. Sci., 2002, 1, 387 %I SISSA Library %G en %U http://hdl.handle.net/1963/1540 %1 2623 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:51Z (GMT). No. of bitstreams: 1\\nmath.AP0104091.pdf: 438502 bytes, checksum: 97c6b7ab20d77a3a40904db3f08928d1 (MD5)\\n Previous issue date: 2000 %0 Journal Article %J Commun. Contemp. Math., 2002, 4, 375 %D 2002 %T Prescribing a fourth oder conformal invariant on the standard sphere - Part I: a perturbation result %A Zindine Djadli %A Mohameden Ould Ahmedou %A Andrea Malchiodi %B Commun. Contemp. Math., 2002, 4, 375 %I SISSA Library %G en %U http://hdl.handle.net/1963/1539 %1 2624 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:50Z (GMT). No. of bitstreams: 1\\nmath.AP0101101.pdf: 273679 bytes, checksum: 772598ac956e1f555f866f6330ec1fd6 (MD5)\\n Previous issue date: 2000 %R 10.1142/S0219199702000695 %0 Journal Article %J IEEE Trans. Automat. Contr. 47 (2002) 546-563 %D 2002 %T On the reachability of quantized control systems %A Antonio Bicchi %A Alessia Marigo %A Benedetto Piccoli %X In this paper, we study control systems whose input sets are quantized, i.e., finite or regularly distributed on a mesh. We specifically focus on problems relating to the structure of the reachable set of such systems, which may turn out to be either dense or discrete. We report results on the reachable set of linear quantized systems, and on a particular but interesting class of nonlinear systems, i.e., nonholonomic chained-form systems. For such systems, we provide a complete characterization of the reachable set, and, in case the set is discrete, a computable method to completely and succinctly describe its structure. Implications and open problems in the analysis and synthesis of quantized control systems are addressed. %B IEEE Trans. Automat. Contr. 47 (2002) 546-563 %I SISSA Library %G en %U http://hdl.handle.net/1963/1501 %1 2662 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:18Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1109/9.995034 %0 Journal Article %J Calc. Var. Partial Differential Equations 14 (2002), no. 4, 429-445 %D 2002 %T The scalar curvature problem on $S\\\\sp n$: an approach via Morse theory %A Andrea Malchiodi %B Calc. Var. Partial Differential Equations 14 (2002), no. 4, 429-445 %I Springer %G en %U http://hdl.handle.net/1963/1331 %1 3124 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:56:24Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %R 10.1007/s005260100110 %0 Journal Article %J Comm. Partial Differential Equations 27 (2002), no. 5-6, 847-876 %D 2002 %T Singular elliptic problems with critical growth %A Paolo Caldiroli %A Andrea Malchiodi %B Comm. Partial Differential Equations 27 (2002), no. 5-6, 847-876 %I Dekker %G en %U http://hdl.handle.net/1963/1268 %1 3187 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:34Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %R 10.1081/PDE-120004887 %0 Journal Article %J C.R.Math.Acad.Sci. Paris 335 (2002),no.2,145-150 %D 2002 %T Solutions concentrating on spheres to symmetric singularly perturbed problems %A Antonio Ambrosetti %A Andrea Malchiodi %A Wei-Ming Ni %X We discuss some existence results concerning problems (NLS) and (N), proving the existence of radial solutions concentrating on a sphere. %B C.R.Math.Acad.Sci. Paris 335 (2002),no.2,145-150 %I SISSA Library %G en %U http://hdl.handle.net/1963/1594 %1 2524 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:03Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 2002 %R 10.1016/S1631-073X(02)02414-7 %0 Journal Article %J SIAM J. Control Optim. 41 (2002), no. 1, 89-112 %D 2002 %T Stability of planar switched systems: the linear single input case %A Ugo Boscain %X We study the stability of the origin for the dynamical system $\\\\dot x(t)=u(t)Ax(t)+(1-u(t))Bx(t),$ where A and B are two 2 × 2 real matrices with eigenvalues having strictly negative real part, $x\\\\in {\\\\mbox{{\\\\bf R}}}^2$, and $u(.):[0,\\\\infty[\\\\to[0,1]$ is a completely random measurable function. More precisely, we find a (coordinates invariant) necessary and sufficient condition on A and B for the origin to be asymptotically stable for each function u(.). The result is obtained without looking for a common Lyapunov function but studying the locus in which the two vector fields Ax and Bx are collinear. There are only three relevant parameters: the first depends only on the eigenvalues of A, the second depends only on the eigenvalues of B, and the third contains the interrelation among the two systems, and it is the cross ratio of the four eigenvectors of A and B in the projective line CP1. In the space of these parameters, the shape and the convexity of the region in which there is stability are studied. %B SIAM J. Control Optim. 41 (2002), no. 1, 89-112 %I SIAM %G en %U http://hdl.handle.net/1963/1529 %1 2634 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:40Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1137/S0363012900382837 %0 Journal Article %J P. Am. Math. Soc., 2002, 130, 1961 %D 2002 %T On the Stability of the Standard Riemann Semigroup %A Stefano Bianchini %A Rinaldo M. Colombo %B P. Am. Math. Soc., 2002, 130, 1961 %I SISSA Library %G en %U http://hdl.handle.net/1963/1528 %1 2635 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:40Z (GMT). No. of bitstreams: 1\\nmath.AP0007055.pdf: 195640 bytes, checksum: 3708c7f60ae79e0790175863c0290b0e (MD5)\\n Previous issue date: 2000 %0 Journal Article %J Math. Ann., 2002, 322, 667 %D 2002 %T On the Yamabe problem and the scalar curvature problems under boundary conditions %A Antonio Ambrosetti %A Li YanYan %A Andrea Malchiodi %B Math. Ann., 2002, 322, 667 %I SISSA Library %G en %U http://hdl.handle.net/1963/1510 %1 2653 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:24Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1007/s002080100267 %0 Journal Article %J Asymptotic Anal., 2001, 25, 149-181 %D 2001 %T Adiabatic limits of closed orbits for some Newtonian systems in R-n %A Andrea Malchiodi %X We deal with a Newtonian system like x\\\'\\\' + V\\\'(x) = 0. We suppose that V: \\\\R^n \\\\to \\\\R possesses an (n-1)-dimensional compact manifold M of critical points, and we prove the existence of arbitrarity slow periodic orbits. When the period tends to infinity these orbits, rescaled in time, converge to some closed geodesics on M. %B Asymptotic Anal., 2001, 25, 149-181 %I SISSA Library %G en %U http://hdl.handle.net/1963/1511 %1 2652 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:25Z (GMT). No. of bitstreams: 1\\nmath.DS0006229.pdf: 332070 bytes, checksum: 05767d978ee641c261858a4e235cfeb3 (MD5)\\n Previous issue date: 2000 %0 Journal Article %J Discrete Cont. Dyn. Syst. 7 (2001) 449-476 %D 2001 %T A case study in vanishing viscosity %A Stefano Bianchini %A Alberto Bressan %B Discrete Cont. Dyn. Syst. 7 (2001) 449-476 %I American Institute of Mathematical Sciences %G en_US %U http://hdl.handle.net/1963/3091 %1 1242 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-14T08:16:28Z\\nNo. of bitstreams: 1\\ncasestudy.pdf: 289769 bytes, checksum: d1ec5d9048e85bd7ebbd1e3de3259336 (MD5) %0 Journal Article %J Math. Control Signals Systems 14 (2001) 173-193 %D 2001 %T Controllability for discrete systems with a finite control set %A Yacine Chitour %A Benedetto Piccoli %B Math. Control Signals Systems 14 (2001) 173-193 %I Springer %G en_US %U http://hdl.handle.net/1963/3114 %1 1219 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-15T10:33:44Z\\nNo. of bitstreams: 1\\ncontrollability.pdf: 247896 bytes, checksum: 6f94f9b27348f59bb506c1e79beba6e1 (MD5) %R 10.1007/PL00009881 %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 Adv. Differential Equations 6 (2001), no. 3, 303-326 %D 2001 %T Existence and nonexistence results for a class of nonlinear, singular Sturm-Liouville equations %A Paolo Caldiroli %A Roberta Musina %B Adv. Differential Equations 6 (2001), no. 3, 303-326 %I SISSA Library %G en %U http://hdl.handle.net/1963/1319 %1 3136 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:56:13Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %0 Journal Article %J J. Dynam. Control Systems, 2001, 7, 209 %D 2001 %T Extremal synthesis for generic planar systems %A Ugo Boscain %A Benedetto Piccoli %B J. Dynam. Control Systems, 2001, 7, 209 %I SISSA Library %G en %U http://hdl.handle.net/1963/1503 %1 2660 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:19Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1023/A:1013003204923 %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 Thesis %D 2001 %T Free-discontinuity problems: calibration and approximation of solutions %A Massimiliano Morini %K Calibration of solutions %I SISSA %G en %U http://hdl.handle.net/1963/5398 %1 5223 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-02-08T08:33:00Z\\nNo. of bitstreams: 1\\nPhD_Morini_Massimiliano.pdf: 12298275 bytes, checksum: 4f513b32d38e8cca2297cce0ee09cfc6 (MD5) %0 Journal Article %J Acta Appl. Math., 2001, 65, 207-215 %D 2001 %T Gamma-limit of periodic obstacles %A Gianni Dal Maso %A Paola Trebeschi %X We compute the Gamma-limit of a sequence obstacle functionals in the case of periodic obstacles. %B Acta Appl. Math., 2001, 65, 207-215 %I SISSA Library %G en %U http://hdl.handle.net/1963/1495 %1 2668 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:12Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1023/A:1010668530972 %0 Journal Article %J Ann. Inst. H. Poincare\\\' Anal. Non Lineaire 18 (2001), no. 1, 19-42 %D 2001 %T A Glimm type functional for a special Jin-Xin relaxation model %A Stefano Bianchini %B Ann. Inst. H. Poincare\\\' Anal. Non Lineaire 18 (2001), no. 1, 19-42 %I Elsevier %G en %U http://hdl.handle.net/1963/1355 %1 3100 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:56:44Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %R 10.1016/S0294-1449(00)00124-4 %0 Journal Article %J Arch. Ration. Mech. An., 2001, 156, 89 %D 2001 %T Global continuous Riemann solver for nonlinear elasticity %A Jean-Marc Mercier %A Benedetto Piccoli %B Arch. Ration. Mech. An., 2001, 156, 89 %I SISSA Library %G en %U http://hdl.handle.net/1963/1493 %1 2670 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:11Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1007/s002050100118 %0 Journal Article %J Ann. I. H. Poincare - An., 2001, 18, 403 %D 2001 %T Local calibrations for minimizers of the Mumford-Shah functional with a regular discontinuity set %A Maria Giovanna Mora %A Massimiliano Morini %B Ann. I. H. Poincare - An., 2001, 18, 403 %I SISSA Library %G en %U http://hdl.handle.net/1963/1479 %1 2684 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:02:59Z (GMT). No. of bitstreams: 1\\nmath.FA0006032.pdf: 333515 bytes, checksum: 2bace45bae580c519969228abb3d4db7 (MD5)\\n Previous issue date: 2000 %R 10.1016/S0294-1449(01)00075-0 %0 Journal Article %J Adv. Math. Sci. Appl. 11 (2001) 721-751 %D 2001 %T A monotonicity approach to nonlinear Dirichlet problems in perforated domains %A Gianni Dal Maso %A Igor V. Skrypnik %X We study the asymptotic behaviour of solutions to Dirichlet problems in perforated domains for nonlinear elliptic equations associated with monotone operators. The main difference with respect to the previous papers on this subject is that no uniformity is assumed in the monotonicity condition. Under a very general hypothesis on the holes of the domains, we construct a limit equation, which is satisfied by the weak limits of the solutions. The additional term in the limit problem depends only on the local behaviour of the holes, which can be expressed in terms of suitable nonlinear capacities associated with the monotone operator. %B Adv. Math. Sci. Appl. 11 (2001) 721-751 %I SISSA Library %G en %U http://hdl.handle.net/1963/1555 %1 2563 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:04Z (GMT). No. of bitstreams: 1\\nmath.AP0010232.pdf: 246554 bytes, checksum: 691b6fb5c795a48324b128ced5a3cc44 (MD5)\\n Previous issue date: 2000 %0 Journal Article %J J. Dynam. Control Systems 7 (2001), no. 3, 385--423 %D 2001 %T Morse properties for the minimum time function on 2-D manifolds %A Ugo Boscain %A Benedetto Piccoli %B J. Dynam. Control Systems 7 (2001), no. 3, 385--423 %I SISSA Library %G en %U http://hdl.handle.net/1963/1541 %1 2622 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:51Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1023/A:1013190914234 %0 Journal Article %J Nonlinear Anal. 43 (2001) 159-172 %D 2001 %T Multiple positive solutions of some elliptic equations in \\\\bold R\\\\sp N %A Andrea Malchiodi %B Nonlinear Anal. 43 (2001) 159-172 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3094 %1 1239 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-14T10:05:40Z\\nNo. of bitstreams: 1\\nMalchiodixx.pdf: 223149 bytes, checksum: 40e292ff9c4d2277feb12d4615559618 (MD5) %R 10.1016/S0362-546X(99)00186-8 %0 Journal Article %J Arch. Ration. Mech. An., 2001, 159, 253 %D 2001 %T Multiplicity results for some nonlinear Schrodinger equations with potentials %A Antonio Ambrosetti %A Andrea Malchiodi %A Simone Secchi %B Arch. Ration. Mech. An., 2001, 159, 253 %I SISSA Library %G en %U http://hdl.handle.net/1963/1564 %1 2554 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:12Z (GMT). No. of bitstreams: 1\\nmath.AP0011195.pdf: 190473 bytes, checksum: a234c5a09c7dc021355fabc212c8ccb4 (MD5)\\n Previous issue date: 2000 %R 10.1007/s002050100152 %0 Journal Article %J J. Funct. Anal. 180 (2001) 210-241 %D 2001 %T Non-compactness and multiplicity results for the Yamabe problem on Sn %A Massimiliano Berti %A Andrea Malchiodi %B J. Funct. Anal. 180 (2001) 210-241 %I Elsevier %G en %U http://hdl.handle.net/1963/1345 %1 3110 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:56:35Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %R 10.1006/jfan.2000.3699 %0 Thesis %D 2001 %T Numerical Methods for Free-Discontinuity Problems Based on Approximations by Γ-Convergence %A Matteo Negri %K Mumford-Shah functional %I SISSA %G en %U http://hdl.handle.net/1963/5399 %1 5226 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-02-08T08:42:37Z\\nNo. of bitstreams: 1\\nPhD_Negri_Matteo.pdf: 9815789 bytes, checksum: 517224e4dfc63645a4ba399a34d9cb8f (MD5) %0 Journal Article %J Calcolo, 2001, 38, 67 %D 2001 %T Numerical minimization of the Mumford-Shah functional %A Matteo Negri %A Maurizio Paolini %B Calcolo, 2001, 38, 67 %I SISSA Library %G en %U http://hdl.handle.net/1963/1461 %1 3079 %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 %R 10.1007/s100920170004 %0 Book Section %B Nonlinear equations : methods, models and applications (Bergamo, 2001) / Daniela Lupo, Carlo D. Pagani, Bernhard Ruf, editors. - Basel : Birkhäuser, 2003. - (Progress in nonlinear differential equations and their applications; 54). - p. 61-77 %D 2001 %T S^2 type parametric surfaces with prescribed mean curvature and minimal energy %A Paolo Caldiroli %A Roberta Musina %B Nonlinear equations : methods, models and applications (Bergamo, 2001) / Daniela Lupo, Carlo D. Pagani, Bernhard Ruf, editors. - Basel : Birkhäuser, 2003. - (Progress in nonlinear differential equations and their applications; 54). - p. 61-77 %I Birkhauser %G en %U http://hdl.handle.net/1963/1605 %1 2513 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:12Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002 %0 Journal Article %J Proc. Roy. Soc. Edinburgh Sect. A 131 (2001) 909-925 %D 2001 %T On the spreading of characteristics for non-convex conservation laws %A Helge Kristian Jenssen %A Carlo Sinestrari %X We study the spreading of characteristics for a class of one-dimensional scalar conservation laws for which the flux function has one point of inflection. It is well known that in the convex case the characteristic speed satisfies a one-sided Lipschitz estimate. Using Dafermos\\\' theory of generalized characteristics, we show that the characteristic speed in the non-convex case satisfies an Hölder estimate. In addition, we give a one-sided Lipschitz estimate with an error term given by the decrease of the total variation of the solution. %B Proc. Roy. Soc. Edinburgh Sect. A 131 (2001) 909-925 %I Cambridge University Press %G en_US %U http://hdl.handle.net/1963/3265 %1 1436 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-11-10T13:53:07Z\\nNo. of bitstreams: 1\\nJS2.pdf: 302742 bytes, checksum: 563821a822c34aef0ca1b4c55065827c (MD5) %R 10.1017/S0308210500001189 %0 Journal Article %J Siam J. Math. Anal., 2001, 33, 959 %D 2001 %T Stability of L-infinity solutions for hyperbolic systems with coinciding shocks and rarefactions %A Stefano Bianchini %X We consider a hyperbolic system of conservation laws u_t + f(u)_x = 0 and u(0,\\\\cdot) = u_0, where each characteristic field is either linearly degenerate or genuinely nonlinear. Under the assumption of coinciding shock and rarefaction curves and the existence of a set of Riemann coordinates $w$, we prove that there exists a semigroup of solutions $u(t) = \\\\mathcal{S}_t u_0$, defined on initial data $u_0 \\\\in L^\\\\infty$. The semigroup $\\\\mathcal{S}$ is continuous w.r.t. time and the initial data $u_0$ in the $L^1_{\\\\text{loc}}$ topology. Moreover $\\\\mathcal{S}$ is unique and its trajectories are obtained as limits of wave front tracking approximations. %B Siam J. Math. Anal., 2001, 33, 959 %I SISSA Library %G en %U http://hdl.handle.net/1963/1523 %1 2640 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:35Z (GMT). No. of bitstreams: 1\\nmath.AP0006094.pdf: 295215 bytes, checksum: 756406a074bc2e1702b76422489572cc (MD5)\\n Previous issue date: 2000 %R 10.1137/S0036141000377900 %0 Journal Article %J Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 4 (2001), no. 3, 609-633. %D 2001 %T Stationary states for a two-dimensional singular Schrodinger equation %A Paolo Caldiroli %A Roberta Musina %B Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 4 (2001), no. 3, 609-633. %I SISSA Library %G en %U http://hdl.handle.net/1963/1249 %1 3206 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:18Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %0 Journal Article %J Ann. I. H. Poincare - An., 2001, 18, 359 %D 2001 %T On the subanalyticity of Carnot-Caratheodory distances %