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.

VL - 30 SN - 0218-3390 UR - https://doi.org/10.1142/S0218339022500085 IS - 01 JO - J. Biol. Syst. ER - TY - JOUR T1 - A comparison of reduced-order modeling approaches using artificial neural networks for PDEs with bifurcating solutions JF - ETNA - Electronic Transactions on Numerical Analysis Y1 - 2022 A1 - Martin W. Hess A1 - Annalisa Quaini A1 - Gianluigi Rozza VL - 56 ER - TY - ABST T1 - Data-Driven Enhanced Model Reduction for Bifurcating Models in Computational Fluid Dynamics Y1 - 2022 A1 - Martin W. Hess A1 - Annalisa Quaini A1 - Gianluigi Rozza ER - TY - ABST T1 - A Data-Driven Surrogate Modeling Approach for Time-Dependent Incompressible Navier-Stokes Equations with Dynamic Mode Decomposition and Manifold Interpolation Y1 - 2022 A1 - Martin W. Hess A1 - Annalisa Quaini A1 - Gianluigi Rozza ER - TY - JOUR T1 - Driving bifurcating parametrized nonlinear PDEs by optimal control strategies: application to Navier–Stokes equations with model order reduction JF - ESAIM: M2AN Y1 - 2022 A1 - Federico Pichi A1 - Maria Strazzullo A1 - F. Ballarin A1 - Gianluigi Rozza VL - 56 UR - https://doi.org/10.1051/m2an/2022044 IS - 4 ER - TY - JOUR T1 - Mathematical modelling of oscillating patterns for chronic autoimmune diseases JF - Mathematical Methods in the Applied SciencesMathematical Methods in the Applied SciencesMath Meth Appl Sci Y1 - 2022 A1 - Rossella Della Marca A1 - Maria da Piedade Machado Ramos A1 - Carolina Ribeiro A1 - Ana Jacinta Soares KW - autoimmune diseases KW - cellular interactions KW - Dynamical systems KW - Hopf bifurcation KW - kinetic theory KW - mathematical biology AB -Many 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.

VL - n/a SN - 0170-4214 UR - https://doi.org/10.1002/mma.8229 IS - n/a JO - Mathematical Methods in the Applied Sciences ER - TY - JOUR T1 - Model order reduction for bifurcating phenomena in fluid-structure interaction problems JF - International Journal for Numerical Methods in FluidsInternational Journal for Numerical Methods in FluidsInt J Numer Meth Fluids Y1 - 2022 A1 - Moaad Khamlich A1 - Federico Pichi A1 - Gianluigi Rozza KW - Bifurcation theory KW - Coandă effect KW - continuum mechanics KW - fluid dynamics KW - monolithic method KW - parametrized fluid-structure interaction problem KW - Proper orthogonal decomposition KW - reduced order modeling AB -Abstract 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.

VL - n/a SN - 0271-2091 UR - https://doi.org/10.1002/fld.5118 IS - n/a JO - International Journal for Numerical Methods in Fluids ER - TY - UNPB T1 - Model Reduction Using Sparse Polynomial Interpolation for the Incompressible Navier-Stokes Equations Y1 - 2022 A1 - Martin W. Hess A1 - Gianluigi Rozza ER - TY - JOUR T1 - The Neural Network shifted-proper orthogonal decomposition: A machine learning approach for non-linear reduction of hyperbolic equations JF - Computer Methods in Applied Mechanics and Engineering Y1 - 2022 A1 - Davide Papapicco A1 - Nicola Demo A1 - Michele Girfoglio A1 - Giovanni Stabile A1 - Gianluigi Rozza KW - Advection KW - Computational complexity KW - Deep neural network KW - Deep neural networks KW - Linear subspace KW - Multiphase simulations KW - Non linear KW - Nonlinear hyperbolic equation KW - Partial differential equations KW - Phase space methods KW - Pre-processing KW - Principal component analysis KW - reduced order modeling KW - Reduced order modelling KW - Reduced-order model KW - Shifted-POD AB -Models 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.

VL - 392 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85124488633&doi=10.1016%2fj.cma.2022.114687&partnerID=40&md5=12f82dcaba04c4a7c44f8e5b20101997 ER - TY - JOUR T1 - A POD-Galerkin reduced order model for the Navier–Stokes equations in stream function-vorticity formulation Y1 - 2022 A1 - Michele Girfoglio A1 - Annalisa Quaini A1 - Gianluigi Rozza KW - Galerkin projection KW - Navier–Stokes equations KW - Proper orthogonal decomposition KW - Reduced order model KW - Stream function-vorticity formulation AB -We 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.

SN - 0045-7930 UR - https://www.sciencedirect.com/science/article/pii/S0045793022001645 JO - Computers & Fluids ER - TY - ABST T1 - Projection based semi–implicit partitioned Reduced Basis Method for non parametrized and parametrized Fluid–Structure Interaction problems Y1 - 2022 A1 - Monica Nonino A1 - Francesco Ballarin A1 - Gianluigi Rozza A1 - Yvon Maday AB -The 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.

ER - TY - ABST T1 - A Proper Orthogonal Decomposition approach for parameters reduction of Single Shot Detector networks Y1 - 2022 A1 - Laura Meneghetti A1 - Nicola Demo A1 - Gianluigi Rozza KW - Computer Vision and Pattern Recognition (cs.CV) KW - FOS: Computer and information sciences KW - FOS: Mathematics KW - Machine Learning (cs.LG) KW - Numerical Analysis (math.NA) UR - https://arxiv.org/abs/2207.13551 ER - TY - JOUR T1 - An SIR–like kinetic model tracking individuals' viral load JF - Networks and Heterogeneous Media Y1 - 2022 A1 - Rossella Della Marca A1 - Nadia Loy A1 - Andrea Tosin ER - TY - UNPB T1 - An artificial neural network approach to bifurcating phenomena in computational fluid dynamics Y1 - 2021 A1 - Federico Pichi A1 - Francesco Ballarin A1 - Gianluigi Rozza A1 - Jan S Hesthaven ER - TY - JOUR T1 - Asymptotic approach to a rotational Taylor swimming sheet JF - Comptes Rendus. Mécanique Y1 - 2021 A1 - Giovanni Corsi VL - 349 ER - TY - JOUR T1 - ATHENA: Advanced Techniques for High dimensional parameter spaces to Enhance Numerical Analysis JF - Software Impacts Y1 - 2021 A1 - Francesco Romor A1 - Marco Tezzele A1 - Gianluigi Rozza VL - 10 ER - TY - UNPB T1 - A CERTIFIED REDUCED BASIS Method FOR LINEAR PARAMETRIZED PARABOLIC OPTIMAL CONTROL PROBLEMS IN SPACE-TIME FORMULATION Y1 - 2021 A1 - Maria Strazzullo A1 - Francesco Ballarin A1 - Gianluigi Rozza ER - TY - JOUR T1 - On the comparison of LES data-driven reduced order approaches for hydroacoustic analysis JF - Computers & Fluids Y1 - 2021 A1 - Mahmoud Gadalla A1 - Marta Cianferra A1 - Marco Tezzele A1 - Giovanni Stabile A1 - Andrea Mola A1 - Gianluigi Rozza KW - Dynamic mode decomposition KW - Ffowcs Williams and Hawkings KW - Hydroacoustics KW - Large eddy simulation KW - Model reduction KW - Proper orthogonal decomposition AB -In 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.

VL - 216 UR - https://www.sciencedirect.com/science/article/pii/S0045793020303893 ER - TY - UNPB T1 - Consistency of the full and reduced order models for Evolve-Filter-Relax Regularization of Convection-Dominated, Marginally-Resolved Flows Y1 - 2021 A1 - Maria Strazzullo A1 - Michele Girfoglio A1 - Francesco Ballarin A1 - T. Iliescu A1 - Gianluigi Rozza ER - TY - UNPB T1 - A data-driven partitioned approach for the resolution of time-dependent optimal control problems with dynamic mode decomposition Y1 - 2021 A1 - Eleonora Donadini A1 - Maria Strazzullo A1 - Marco Tezzele A1 - Gianluigi Rozza ER - TY - ABST T1 - Deep Learning Approximation of Diffeomorphisms via Linear-Control Systems Y1 - 2021 A1 - Alessandro Scagliotti KW - FOS: Computer and information sciences KW - FOS: Mathematics KW - Machine Learning (cs.LG) KW - Optimization and Control (math.OC) UR - https://arxiv.org/abs/2110.12393 ER - TY - JOUR T1 - A Differential Perspective on Gradient Flows on CAT(K)-Spaces and Applications Y1 - 2021 A1 - Nicola Gigli A1 - Francesco Nobili AB -We 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.

VL - 31 SN - 1559-002X UR - https://doi.org/10.1007/s12220-021-00701-5 IS - 12 JO - The Journal of Geometric Analysis ER - TY - ABST T1 - A Dimensionality Reduction Approach for Convolutional Neural Networks Y1 - 2021 A1 - Laura Meneghetti A1 - Nicola Demo A1 - Gianluigi Rozza ER - TY - RPRT T1 - On Dini derivatives of real functions Y1 - 2021 A1 - Giuliano Klun A1 - Alessandro Fonda A1 - Andrea Sfecci ER - TY - CONF T1 - Discontinuous Galerkin Model Order Reduction of Geometrically Parametrized Stokes Equation T2 - Numerical Mathematics and Advanced Applications ENUMATH 2019 Y1 - 2021 A1 - Nirav Shah A1 - Martin W. Hess A1 - Gianluigi Rozza ED - Vermolen, Fred J. ED - Vuik, Cornelis AB -The 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.

JF - Numerical Mathematics and Advanced Applications ENUMATH 2019 PB - Springer International Publishing CY - Cham SN - 978-3-030-55874-1 ER - TY - JOUR T1 - Displacement convexity of Entropy and the distance cost Optimal Transportation JF - Annales de la Faculté des sciences de Toulouse : Mathématiques Y1 - 2021 A1 - Fabio Cavalletti A1 - Nicola Gigli A1 - Flavia Santarcangelo VL - Ser. 6, 30 UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1679/ ER - TY - JOUR T1 - A dynamic mode decomposition extension for the forecasting of parametric dynamical systems JF - arXiv preprint arXiv:2110.09155 Y1 - 2021 A1 - Francesco Andreuzzi A1 - Nicola Demo A1 - Gianluigi Rozza ER - TY - JOUR T1 - A dynamic model for viscoelasticity in domains with time-dependent cracks Y1 - 2021 A1 - Francesco Sapio AB -In this paper, we prove the existence of solutions for a class of viscoelastic dynamic systems on time-dependent cracking domains.

VL - 28 SN - 1420-9004 UR - https://doi.org/10.1007/s00030-021-00729-0 IS - 6 JO - Nonlinear Differential Equations and Applications NoDEA ER - TY - JOUR T1 - Efficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method JF - Advances in Computational Mathematics Y1 - 2021 A1 - Moreno Pintore A1 - Federico Pichi A1 - Martin W. Hess A1 - Gianluigi Rozza A1 - Claudio Canuto AB -The 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.

VL - 47 ER - TY - JOUR T1 - An efficient computational framework for naval shape design and optimization problems by means of data-driven reduced order modeling techniques JF - Bolletino dell Unione Matematica Italiana Y1 - 2021 A1 - Nicola Demo A1 - Giulio Ortali A1 - Gianluca Gustin A1 - Gianluigi Rozza A1 - Gianpiero Lavini AB -This 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.

VL - 14 ER - TY - JOUR T1 - An existence result for the fractional Kelvin–Voigt’s model on time-dependent cracked domains Y1 - 2021 A1 - Maicol Caponi A1 - Francesco Sapio AB -We 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.

SN - 1424-3202 UR - https://doi.org/10.1007/s00028-021-00713-2 JO - Journal of Evolution Equations ER - TY - UNPB T1 - AN EXTENDED PHYSICS INFORMED NEURAL NETWORK FOR PRELIMINARY ANALYSIS OF PARAMETRIC OPTIMAL CONTROL PROBLEMS Y1 - 2021 A1 - Nicola Demo A1 - Maria Strazzullo A1 - Gianluigi Rozza ER - TY - ABST T1 - A first-order condition for the independence on p of weak gradients Y1 - 2021 A1 - Nicola Gigli A1 - Francesco Nobili ER - TY - JOUR T1 - Hierarchical model reduction techniques for flow modeling in a parametrized setting JF - Multiscale Modeling and Simulation Y1 - 2021 A1 - Matteo Zancanaro A1 - F. Ballarin A1 - Simona Perotto A1 - Gianluigi Rozza AB -In 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.

VL - 19 ER - TY - JOUR T1 - Hull Shape Design Optimization with Parameter Space and Model Reductions, and Self-Learning Mesh Morphing JF - Journal of Marine Science and Engineering Y1 - 2021 A1 - Nicola Demo A1 - Marco Tezzele A1 - Andrea Mola A1 - Gianluigi Rozza AB -In 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.

VL - 9 UR - https://www.mdpi.com/2077-1312/9/2/185 ER - TY - JOUR T1 - Hybrid Neural Network Reduced Order Modelling for Turbulent Flows with Geometric Parameters JF - Fluids Y1 - 2021 A1 - Matteo Zancanaro A1 - Markus Mrosek A1 - Giovanni Stabile A1 - Carsten Othmer A1 - Gianluigi Rozza PB - MDPI AG VL - 6 UR - https://doi.org/10.3390/fluids6080296 ER - TY - JOUR T1 - Independence of synthetic curvature dimension conditions on transport distance exponent JF - Trans. Amer. Math. Soc. Y1 - 2021 A1 - Afiny Akdemir A1 - Andrew Colinet A1 - Robert McCann A1 - Fabio Cavalletti A1 - Flavia Santarcangelo VL - 374 UR - https://doi.org/10.1090/tran/8413 ER - TY - UNPB T1 - A local approach to parameter space reduction for regression and classification tasks Y1 - 2021 A1 - Francesco Romor A1 - Marco Tezzele A1 - Gianluigi Rozza JF - arXiv preprint arXiv:2107.10867 N1 - Submitted ER - TY - ABST T1 - On master test plans for the space of BV functions Y1 - 2021 A1 - Francesco Nobili A1 - Enrico Pasqualetto A1 - Timo Schultz ER - TY - JOUR T1 - A Monolithic and a Partitioned, Reduced Basis Method for Fluid–Structure Interaction Problems JF - Fluids Y1 - 2021 A1 - Monica Nonino A1 - F. Ballarin A1 - Gianluigi Rozza AB -The 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.

VL - 6 UR - https://www.mdpi.com/2311-5521/6/6/229 ER - TY - ABST T1 - Monotonicity formulas for harmonic functions in RCD(0,N) spaces Y1 - 2021 A1 - Nicola Gigli A1 - Ivan Yuri Violo AB -We 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.

ER - TY - CONF T1 - Multi-fidelity data fusion for the approximation of scalar functions with low intrinsic dimensionality through active subspaces T2 - Proceedings in Applied Mathematics & Mechanics Y1 - 2021 A1 - Francesco Romor A1 - Marco Tezzele A1 - Gianluigi Rozza JF - Proceedings in Applied Mathematics & Mechanics PB - Wiley Online Library VL - 20 ER - TY - JOUR T1 - Multi-fidelity data fusion through parameter space reduction with applications to automotive engineering JF - arXiv preprint arXiv:2110.14396 Y1 - 2021 A1 - Francesco Romor A1 - Marco Tezzele A1 - Markus Mrosek A1 - Carsten Othmer A1 - Gianluigi Rozza ER - TY - JOUR T1 - Non-intrusive data-driven ROM framework for hemodynamics problems JF - Acta Mechanica Sinica Y1 - 2021 A1 - Michele Girfoglio A1 - Leonardo Scandurra A1 - Francesco Ballarin A1 - Giuseppe Infantino A1 - Francesca Nicolò A1 - Andrea Montalto A1 - Gianluigi Rozza A1 - Roberto Scrofani A1 - Marina Comisso A1 - Francesco Musumeci VL - 37 ER - TY - JOUR T1 - Non-well-ordered lower and upper solutions for semilinear systems of PDEs JF - Communications in Contemporary MathematicsCommunications in Contemporary Mathematics Y1 - 2021 A1 - Alessandro Fonda A1 - Giuliano Klun A1 - Andrea Sfecci AB -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.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.

SN - 0219-1997 UR - https://doi.org/10.1142/S0219199721500802 JO - Commun. Contemp. Math. ER - TY - JOUR T1 - Nutations in growing plant shoots as a morphoelastic flutter instability JF - Phil. Trans. R. Soc. A Y1 - 2021 A1 - Daniele Agostinelli A1 - Giovanni Noselli A1 - Antonio DeSimone AB -Growing 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.

VL - 379 UR - https://doi.org/10.1098/rsta.2020.0116 ER - TY - JOUR T1 - Nutations in plant shoots: Endogenous and exogenous factors in the presence of mechanical deformations JF - Frontiers in Plant Science Y1 - 2021 A1 - Daniele Agostinelli A1 - Antonio DeSimone A1 - Giovanni Noselli AB -We 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.

PB - Cold Spring Harbor Laboratory VL - 12 UR - https://www.frontiersin.org/article/10.3389/fpls.2021.608005 ER - TY - ABST T1 - Parallel transport on non-collapsed $\mathsfRCD(K,N)$ spaces Y1 - 2021 A1 - Emanuele Caputo A1 - Nicola Gigli A1 - Enrico Pasqualetto AB -We 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.

VL - 18 SN - 1660-5454 UR - https://doi.org/10.1007/s00009-021-01857-8 IS - 5 JO - Mediterranean Journal of Mathematics ER - TY - JOUR T1 - A POD-Galerkin reduced order model for a LES filtering approach JF - Journal of Computational Physics Y1 - 2021 A1 - Michele Girfoglio A1 - Annalisa Quaini A1 - Gianluigi Rozza AB -We 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.

VL - 436 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85102138957&doi=10.1016%2fj.jcp.2021.110260&partnerID=40&md5=73115708267e80754f343561c26f4744 ER - TY - JOUR T1 - A POD-Galerkin reduced order model of a turbulent convective buoyant flow of sodium over a backward-facing step JF - Applied Mathematical Modelling Y1 - 2021 A1 - Kelbij Star A1 - Giovanni Stabile A1 - Gianluigi Rozza A1 - Joris Degroote AB -A 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.

VL - 89 ER - TY - JOUR T1 - Quadratic Life Span of Periodic Gravity-capillary Water Waves Y1 - 2021 A1 - Massimiliano Berti A1 - Roberto Feola A1 - Luca Franzoi AB -We 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.

VL - 3 SN - 2523-3688 UR - https://doi.org/10.1007/s42286-020-00036-8 IS - 1 JO - Water Waves ER - TY - JOUR T1 - Quasistatic Limit of a Dynamic Viscoelastic Model with Memory Y1 - 2021 A1 - Gianni Dal Maso A1 - Francesco Sapio AB -We 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.

SN - 1424-9294 UR - https://doi.org/10.1007/s00032-021-00343-w JO - Milan Journal of Mathematics ER - TY - JOUR T1 - A Reduced Order Cut Finite Element method for geometrically parametrized steady and unsteady Navier–Stokes problems JF - Computer & Mathematics With Applications Y1 - 2021 A1 - Efthymios N Karatzas A1 - Monica Nonino A1 - F. Ballarin A1 - Gianluigi Rozza KW - Cut Finite Element Method KW - Navier–Stokes equations KW - Parameter–dependent shape geometry KW - Reduced Order Models KW - Unfitted mesh AB -We 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.

SN - 0898-1221 UR - https://www.sciencedirect.com/science/article/pii/S0898122121002790 JO - Computers & Mathematics with Applications ER - TY - CONF T1 - Reduced Order Methods for Parametrized Non-linear and Time Dependent Optimal Flow Control Problems, Towards Applications in Biomedical and Environmental Sciences T2 - Numerical Mathematics and Advanced Applications ENUMATH 2019 Y1 - 2021 A1 - Maria Strazzullo A1 - Zakia Zainib A1 - F. Ballarin A1 - Gianluigi Rozza ED - Fred J Vermolen ED - Cornelis Vuik AB -We 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.

JF - Numerical Mathematics and Advanced Applications ENUMATH 2019 PB - Springer International Publishing CY - Cham SN - 978-3-030-55874-1 UR - https://www.springerprofessional.de/en/reduced-order-methods-for-parametrized-non-linear-and-time-depen/19122676 ER - TY - ABST T1 - A remark on two notions of flatness for sets in the Euclidean space Y1 - 2021 A1 - Ivan Yuri Violo AB -In 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).

ER - TY - ABST T1 - Rigidity and almost rigidity of Sobolev inequalities on compact spaces with lower Ricci curvature bounds Y1 - 2021 A1 - Francesco Nobili A1 - Ivan Yuri Violo AB -

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.ER - TY - JOUR T1 - The sharp quantitative isocapacitary inequality JF - Revista Matematica Iberoamericana Y1 - 2021 A1 - Guido De Philippis A1 - Michele Marini A1 - Ekaterina Mukoseeva KW - Fraenkel asymmetry KW - isocapacitary inequality KW - Stability estimates AB -

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

VL - 37 SN - 02132230 (ISSN) UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85104691573&doi=10.4171%2frmi%2f1259&partnerID=40&md5=5f88bc37b87a9eea7a502ea63523ff57 IS - 6 JO - Rev. Mat. Iberoam. ER - TY - JOUR T1 - The sharp quantitative isocapacitary inequality (the case of p-capacity) JF - Advances in Calculus of Variations Y1 - 2021 A1 - Ekaterina Mukoseeva KW - isocapacitary inequality KW - Stability estimates AB -We 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.

SN - 18648258 (ISSN) UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85106363307&doi=10.1515%2facv-2020-0106&partnerID=40&md5=26dbcad781b68c1d873512e272f0e7f4 JO - Adv. Calc. Var. ER - TY - JOUR T1 - A supervised learning approach involving active subspaces for an efficient genetic algorithm in high-dimensional optimization problems JF - SIAM Journal on Scientific Computing Y1 - 2021 A1 - Nicola Demo A1 - Marco Tezzele A1 - Gianluigi Rozza AB -In 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.

VL - 43 UR - https://arxiv.org/abs/2006.07282 IS - 3 ER - TY - JOUR T1 - Traveling Quasi-periodic Water Waves with Constant Vorticity Y1 - 2021 A1 - Massimiliano Berti A1 - Luca Franzoi A1 - Alberto Maspero AB -We 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.

VL - 240 SN - 1432-0673 UR - https://doi.org/10.1007/s00205-021-01607-w IS - 1 JO - Archive for Rational Mechanics and Analysis ER - TY - JOUR T1 - A vanishing-inertia analysis for finite-dimensional rate-independent systems with nonautonomous dissipation and an application to soft crawlers Y1 - 2021 A1 - Paolo Gidoni A1 - Filippo Riva AB -We 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.

VL - 60 SN - 1432-0835 UR - https://doi.org/10.1007/s00526-021-02067-6 IS - 5 JO - Calculus of Variations and Partial Differential Equations ER - TY - JOUR T1 - A weighted POD-reduction approach for parametrized PDE-constrained optimal control problems with random inputs and applications to environmental sciences JF - Computers and Mathematics with Applications Y1 - 2021 A1 - G. Carere A1 - Maria Strazzullo A1 - Francesco Ballarin A1 - Gianluigi Rozza A1 - R. Stevenson VL - 102 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85117948561&doi=10.1016%2fj.camwa.2021.10.020&partnerID=40&md5=cb57d59a6975a35315b2cf5d0e3a6001 ER - TY - JOUR T1 - Well-Ordered and Non-Well-Ordered Lower and Upper Solutions for Periodic Planar Systems JF - Advanced Nonlinear Studies Y1 - 2021 A1 - Alessandro Fonda A1 - Giuliano Klun A1 - Andrea Sfecci VL - 21 UR - https://doi.org/10.1515/ans-2021-2117 IS - 2 ER - TY - CONF T1 - Advances in reduced order methods for parametric industrial problems in computational fluid dynamics T2 - 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 Y1 - 2020 A1 - Gianluigi Rozza A1 - M.H. Malik A1 - Nicola Demo A1 - Marco Tezzele A1 - Michele Girfoglio A1 - Giovanni Stabile A1 - Andrea Mola AB -Reduced 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.

JF - 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 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075395686&partnerID=40&md5=fb0b1a3cfdfd35a104db9921bc9be675 ER - TY - JOUR T1 - On the Approximation of Quasistatic Evolutions for the Debonding of a Thin Film via Vanishing Inertia and Viscosity Y1 - 2020 A1 - Filippo Riva AB -In 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.

VL - 30 SN - 1432-1467 UR - https://doi.org/10.1007/s00332-019-09595-8 IS - 3 JO - Journal of Nonlinear Science ER - TY - CHAP T1 - Basic ideas and tools for projection-based model reduction of parametric partial differential equations T2 - Model Order Reduction, Volume 2 Snapshot-Based Methods and Algorithms Y1 - 2020 A1 - Gianluigi Rozza A1 - Martin W. Hess A1 - Giovanni Stabile A1 - Marco Tezzele A1 - F. Ballarin JF - Model Order Reduction, Volume 2 Snapshot-Based Methods and Algorithms PB - De Gruyter CY - Berlin, Boston SN - 9783110671490 UR - https://www.degruyter.com/view/book/9783110671490/10.1515/9783110671490-001.xml ER - TY - JOUR T1 - On the blow-up of GSBV functions under suitable geometric properties of the jump set JF - Advances in Calculus of Variations Y1 - 2020 A1 - Emanuele Tasso UR - https://doi.org/10.1515/acv-2019-0068 ER - TY - JOUR T1 - Certified Reduced Basis VMS-Smagorinsky model for natural convection flow in a cavity with variable height JF - Computers and Mathematics with Applications Y1 - 2020 A1 - F. Ballarin A1 - Rebollo, T.C. A1 - E.D. Ávila A1 - Marmol, M.G. A1 - Gianluigi Rozza AB -In 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.

VL - 80 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85085843368&doi=10.1016%2fj.camwa.2020.05.013&partnerID=40&md5=7c6596865ec89651319c7dd97159dd77 ER - TY - JOUR T1 - On the continuity of the trace operator in GSBV (Ω) and GSBD (Ω) JF - ESAIM: COCV Y1 - 2020 A1 - Emanuele Tasso VL - 26 UR - https://doi.org/10.1051/cocv/2019014 ER - TY - JOUR T1 - Data-driven POD-Galerkin reduced order model for turbulent flows JF - Journal of Computational Physics Y1 - 2020 A1 - Saddam Hijazi A1 - Giovanni Stabile A1 - Andrea Mola A1 - Gianluigi Rozza AB -In 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 $Re=O(10^5)$.

VL - 416 UR - https://arxiv.org/abs/1907.09909 ER - TY - JOUR T1 - A dynamic model for viscoelastic materials with prescribed growing cracks Y1 - 2020 A1 - Maicol Caponi A1 - Francesco Sapio AB -In this paper, we prove the existence of solutions for a class of viscoelastic dynamic systems on time-dependent cracked domains, with possibly degenerate viscosity coefficients. Under stronger regularity assumptions, we also show a uniqueness result. Finally, we exhibit an example where the energy-dissipation balance is not satisfied, showing there is an additional dissipation due to the crack growth.

VL - 199 SN - 1618-1891 UR - https://doi.org/10.1007/s10231-019-00921-1 IS - 4 JO - Annali di Matematica Pura ed Applicata (1923 -) ER - TY - JOUR T1 - Efficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method JF - Advances in Computational Mathematics Y1 - 2020 A1 - Moreno Pintore A1 - Federico Pichi A1 - Martin W. Hess A1 - Gianluigi Rozza A1 - Claudio Canuto AB -The 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.

UR - https://arxiv.org/abs/1912.06089 ER - TY - JOUR T1 - Efficient Geometrical parametrization for finite-volume based reduced order methods JF - International Journal for Numerical Methods in Engineering Y1 - 2020 A1 - Giovanni Stabile A1 - Matteo Zancanaro A1 - Gianluigi Rozza AB -In 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

VL - 121 UR - https://arxiv.org/abs/1901.06373 ER - TY - CONF T1 - The Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: from Laminar to Turbulent Flows T2 - Lecture Notes in Computational Science and Engineering Y1 - 2020 A1 - Saddam Hijazi A1 - Shafqat Ali A1 - Giovanni Stabile A1 - F. Ballarin A1 - Gianluigi Rozza AB -We 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.

JF - Lecture Notes in Computational Science and Engineering PB - Springer International Publishing CY - Cham SN - 978-3-030-30705-9 ER - TY - JOUR T1 - Energy-dissipation balance of a smooth moving crack Y1 - 2020 A1 - Maicol Caponi A1 - Ilaria Lucardesi A1 - Emanuele Tasso KW - Energy-dissipation balance KW - Fracture dynamics KW - Wave equation in time-dependent domains AB -In this paper we provide necessary and sufficient conditions in order to guarantee the energy-dissipation balance of a Mode III crack, growing on a prescribed smooth path. Moreover, we characterize the singularity of the displacement near the crack tip, generalizing the result in [10] valid for straight fractures.

VL - 483 SN - 0022-247X UR - https://www.sciencedirect.com/science/article/pii/S0022247X19309242 IS - 2 JO - Journal of Mathematical Analysis and Applications ER - TY - JOUR T1 - Enhancing CFD predictions in shape design problems by model and parameter space reduction JF - Advanced Modeling and Simulation in Engineering Sciences Y1 - 2020 A1 - Marco Tezzele A1 - Nicola Demo A1 - Giovanni Stabile A1 - Andrea Mola A1 - Gianluigi Rozza AB -In 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.

VL - 7 UR - https://arxiv.org/abs/2001.05237 IS - 40 ER - TY - JOUR T1 - Existence of solutions to a phase–field model of dynamic fracture with a crack–dependent dissipation Y1 - 2020 A1 - Maicol Caponi AB -We 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.

VL - 27 SN - 1420-9004 UR - https://doi.org/10.1007/s00030-020-0617-z IS - 2 JO - Nonlinear Differential Equations and Applications NoDEA ER - TY - JOUR T1 - On functions having coincident p-norms JF - Annali di Matematica Pura ed Applicata (1923 -) Y1 - 2020 A1 - Giuliano Klun AB -In 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: $\begin{aligned} \mu (\{x\in E:|f(x)|>\alpha \})=\mu (\{x\in E:|g(x)|>\alpha \})\quad \text { for all } \alpha \ge 0. \end{aligned}$

VL - 199 UR - https://doi.org/10.1007/s10231-019-00907-z ER - TY - JOUR T1 - A hybrid reduced order method for modelling turbulent heat transfer problems JF - Computers & Fluids Y1 - 2020 A1 - Sokratia Georgaka A1 - Giovanni Stabile A1 - Kelbij Star A1 - Gianluigi Rozza A1 - Michael J. Bluck AB -A parametric, hybrid reduced order model approach based on the Proper Orthogonal Decomposition with both Galerkin projection and interpolation based on Radial Basis Functions method is presented. This method is tested against a case of turbulent non-isothermal mixing in a T-junction pipe, a common ow arrangement found in nuclear reactor cooling systems. The reduced order model is derived from the 3D unsteady, incompressible Navier-Stokes equations weakly coupled with the energy equation. For high Reynolds numbers, the eddy viscosity and eddy diffusivity are incorporated into the reduced order model with a Proper Orthogonal Decomposition (nested and standard) with Interpolation (PODI), where the interpolation is performed using Radial Basis Functions. The reduced order solver, obtained using a k-ω SST URANS full order model, is tested against the full order solver in a 3D T-junction pipe with parametric velocity inlet boundary conditions.

VL - 208 UR - https://arxiv.org/abs/1906.08725 ER - TY - BOOK T1 - Kernel-based Active Subspaces with application to CFD parametric problems using Discontinuous Galerkin method Y1 - 2020 A1 - Francesco Romor A1 - Marco Tezzele A1 - Lario, Andrea A1 - Gianluigi Rozza ER - TY - JOUR T1 - MicroMotility: State of the art, recent accomplishments and perspectives on the mathematical modeling of bio-motility at microscopic scales JF - Mathematics in Engineering Y1 - 2020 A1 - Daniele Agostinelli A1 - Roberto Cerbino A1 - Del Alamo, Juan C A1 - Antonio DeSimone A1 - Stephanie Höhn A1 - Cristian Micheletti A1 - Giovanni Noselli A1 - Eran Sharon A1 - Julia Yeomans KW - active matter KW - adhesive locomotion KW - cell motility KW - cell sheet folding KW - knotted DNA KW - topological defects KW - unicellular swimmers KW - unjamming transition AB -Mathematical modeling and quantitative study of biological motility (in particular, of motility at microscopic scales) is producing new biophysical insight and is offering opportunities for new discoveries at the level of both fundamental science and technology. These range from the explanation of how complex behavior at the level of a single organism emerges from body architecture, to the understanding of collective phenomena in groups of organisms and tissues, and of how these forms of swarm intelligence can be controlled and harnessed in engineering applications, to the elucidation of processes of fundamental biological relevance at the cellular and sub-cellular level. In this paper, some of the most exciting new developments in the fields of locomotion of unicellular organisms, of soft adhesive locomotion across scales, of the study of pore translocation properties of knotted DNA, of the development of synthetic active solid sheets, of the mechanics of the unjamming transition in dense cell collectives, of the mechanics of cell sheet folding in volvocalean algae, and of the self-propulsion of topological defects in active matter are discussed. For each of these topics, we provide a brief state of the art, an example of recent achievements, and some directions for future research.

VL - 2 UR - http://dx.doi.org/10.3934/mine.2020011 ER - TY - ABST T1 - MicroROM: An Efficient and Accurate Reduced Order Method to Solve Many-Query Problems in Micro-Motility Y1 - 2020 A1 - Nicola Giuliani A1 - Martin W. Hess A1 - Antonio DeSimone A1 - Gianluigi Rozza KW - FOS: Mathematics KW - Numerical Analysis (math.NA) UR - https://arxiv.org/abs/2006.13836 ER - TY - ABST T1 - Minimality of the ball for a model of charged liquid droplets Y1 - 2020 A1 - Ekaterina Mukoseeva A1 - Giulia Vescovo ER - TY - CHAP T1 - Non-intrusive Polynomial Chaos Method Applied to Full-Order and Reduced Problems in Computational Fluid Dynamics: A Comparison and Perspectives T2 - Quantification of Uncertainty: Improving Efficiency and Technology: QUIET selected contributions Y1 - 2020 A1 - Saddam Hijazi A1 - Giovanni Stabile A1 - Andrea Mola A1 - Gianluigi Rozza AB -In 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.

JF - Quantification of Uncertainty: Improving Efficiency and Technology: QUIET selected contributions PB - Springer International Publishing CY - Cham SN - 978-3-030-48721-8 UR - https://doi.org/10.1007/978-3-030-48721-8_10 ER - TY - JOUR T1 - Periodic solutions of nearly integrable Hamiltonian systems bifurcating from infinite-dimensional tori JF - NONLINEAR ANALYSIS Y1 - 2020 A1 - Alessandro Fonda A1 - Giuliano Klun A1 - Andrea Sfecci AB -We 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.

UR - https://doi.org/10.1016/j.na.2019.111720 ER - TY - UNPB T1 - POD-Galerkin Model Order Reduction for Parametrized Nonlinear Time Dependent Optimal Flow Control: an Application to Shallow Water Equations Y1 - 2020 A1 - Maria Strazzullo A1 - F. Ballarin A1 - Gianluigi Rozza AB -In 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.

ER - TY - JOUR T1 - POD–Galerkin Model Order Reduction for Parametrized Time Dependent Linear Quadratic Optimal Control Problems in Saddle Point Formulation JF - Journal of Scientific Computing Y1 - 2020 A1 - Maria Strazzullo A1 - F. Ballarin A1 - Gianluigi Rozza AB -In 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.

VL - 83 ER - TY - JOUR T1 - POD–Galerkin reduced order methods for combined Navier–Stokes transport equations based on a hybrid FV-FE solver JF - Computers and Mathematics with Applications Y1 - 2020 A1 - S. Busto A1 - Giovanni Stabile A1 - Gianluigi Rozza A1 - M.E. Vázquez-Cendón AB -The 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.

VL - 79 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85068068567&doi=10.1016%2fj.camwa.2019.06.026&partnerID=40&md5=a8dcce1b53b8ee872d174bbc4c20caa3 ER - TY - JOUR T1 - Projection-based reduced order models for a cut finite element method in parametrized domains JF - Computers and Mathematics with Applications Y1 - 2020 A1 - Efthymios N Karatzas A1 - F. Ballarin A1 - Gianluigi Rozza AB -This 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.

VL - 79 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85070900852&doi=10.1016%2fj.camwa.2019.08.003&partnerID=40&md5=2d222ab9c7832955d155655d3c93e1b1 ER - TY - JOUR T1 - Reduced Basis Model Order Reduction for Navier-Stokes equations in domains with walls of varying curvature JF - International Journal of Computational Fluid Dynamics Y1 - 2020 A1 - Martin W. Hess A1 - Annalisa Quaini A1 - Gianluigi Rozza AB -We 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.

VL - 34 UR - https://arxiv.org/abs/1901.03708 ER - TY - JOUR T1 - Reduced basis model order reduction for Navier–Stokes equations in domains with walls of varying curvature JF - International Journal of Computational Fluid Dynamics Y1 - 2020 A1 - Martin W. Hess A1 - Annalisa Quaini A1 - Gianluigi Rozza AB -We 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.

VL - 34 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85085233294&doi=10.1080%2f10618562.2019.1645328&partnerID=40&md5=e2ed8f24c66376cdc8b5485aa400efb0 ER - TY - CONF T1 - A Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries T2 - IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22–25, 2018 Y1 - 2020 A1 - Efthymios N Karatzas A1 - Giovanni Stabile A1 - Nabib Atallah A1 - Guglielmo Scovazzi A1 - Gianluigi Rozza ED - Fehr, Jörg ED - Bernard Haasdonk AB -A 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.

JF - IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22–25, 2018 PB - Springer International Publishing UR - https://arxiv.org/abs/1807.07753 ER - TY - JOUR T1 - Reduced order isogeometric analysis approach for pdes in parametrized domains JF - Lecture Notes in Computational Science and Engineering Y1 - 2020 A1 - Fabrizio Garotta A1 - Nicola Demo A1 - Marco Tezzele A1 - Massimo Carraturo A1 - Alessandro Reali A1 - Gianluigi Rozza AB -In 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.

VL - 137 UR - 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 ER - TY - JOUR T1 - Reduced order methods for parametric optimal flow control in coronary bypass grafts, toward patient-specific data assimilation JF - International Journal for Numerical Methods in Biomedical EngineeringInternational Journal for Numerical Methods in Biomedical EngineeringInt J Numer Meth Biomed Engng Y1 - 2020 A1 - Zakia Zainib A1 - F. Ballarin A1 - Stephen E. Fremes A1 - Piero Triverio A1 - Laura Jiménez-Juan A1 - Gianluigi Rozza KW - coronary artery bypass grafts KW - data assimilation KW - flow control KW - Galerkin methods KW - hemodynamics modeling KW - Optimization KW - patient-specific simulations KW - Proper orthogonal decomposition KW - reduced order methods AB -Abstract 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.

VL - n/a SN - 2040-7939 UR - https://onlinelibrary.wiley.com/doi/10.1002/cnm.3367?af=R IS - n/a JO - International Journal for Numerical Methods in Biomedical Engineering ER - TY - JOUR T1 - A reduced order modeling technique to study bifurcating phenomena: Application to the gross-pitaevskii equation JF - SIAM Journal on Scientific Computing Y1 - 2020 A1 - Federico Pichi A1 - Annalisa Quaini A1 - Gianluigi Rozza AB -We 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.

UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85096768803&doi=10.1137%2f20M1313106&partnerID=40&md5=47d6012d10854c2f9a04b9737f870592 ER - TY - JOUR T1 - A Reduced Order technique to study bifurcating phenomena: application to the Gross-Pitaevskii equation JF - SIAM Journal on Scientific Computing Y1 - 2020 A1 - Federico Pichi A1 - Annalisa Quaini A1 - Gianluigi Rozza AB -We 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.

UR - https://arxiv.org/abs/1907.07082 ER - TY - JOUR T1 - A reduced-order shifted boundary method for parametrized incompressible Navier–Stokes equations JF - Computer Methods in Applied Mechanics and Engineering Y1 - 2020 A1 - Efthymios N Karatzas A1 - Giovanni Stabile A1 - Leo Nouveau A1 - Guglielmo Scovazzi A1 - Gianluigi Rozza AB -We 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.

VL - 370 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85087886522&doi=10.1016%2fj.cma.2020.113273&partnerID=40&md5=d864e4808190b682ecb1c8b27cda72d8 ER - TY - JOUR T1 - Special Issue on Reduced Order Models in CFD JF - International Journal of Computational Fluid Dynamics Y1 - 2020 A1 - Simona Perotto A1 - Gianluigi Rozza VL - 34 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85084258805&doi=10.1080%2f10618562.2020.1756497&partnerID=40&md5=d9316aad9ba95f244e07379318ebbcba ER - TY - JOUR T1 - A spectral element reduced basis method for navier–stokes equations with geometric variations JF - Lecture Notes in Computational Science and Engineering Y1 - 2020 A1 - Martin W. Hess A1 - Annalisa Quaini A1 - Gianluigi Rozza AB -We 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.

VL - 134 ER - TY - JOUR T1 - Stabilized reduced basis methods for parametrized steady Stokes and Navier–Stokes equations JF - Computers and Mathematics with Applications Y1 - 2020 A1 - Shafqat Ali A1 - F. Ballarin A1 - Gianluigi Rozza AB -It 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.

VL - 80 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85083340115&doi=10.1016%2fj.camwa.2020.03.019&partnerID=40&md5=7ace96eee080701acb04d8155008dd7d ER - TY - JOUR T1 - Surface tension controls the onset of gyrification in brain organoids JF - Journal of the Mechanics and Physics of Solids Y1 - 2020 A1 - Davide Riccobelli A1 - Giulia Bevilacqua KW - Buckling KW - Embryogenesis KW - Morpho-elasticity KW - Post-buckling analysis KW - Surface tension AB -Understanding the mechanics of brain embryogenesis can provide insights on pathologies related to brain development, such as lissencephaly, a genetic disease which causes a reduction of the number of cerebral sulci. Recent experiments on brain organoids have confirmed that gyrification, i.e. the formation of the folded structures of the brain, is triggered by the inhomogeneous growth of the peripheral region. However, the rheology of these cellular aggregates and the mechanics of lissencephaly are still matter of debate. In this work, we develop a mathematical model of brain organoids based on the theory of morpho-elasticity. We describe them as non-linear elastic bodies, composed of a disk surrounded by a growing layer called cortex. The external boundary is subjected to a tissue surface tension due the intercellular adhesion forces. We show that the resulting surface energy is relevant at the small length scales of brain organoids and affects the mechanics of cellular aggregates. We perform a linear stability analysis of the radially symmetric configuration and we study the post-buckling behaviour through finite element simulations. We find that the process of gyrification is triggered by the cortex growth and modulated by the competition between two length scales: the radius of the organoid and the capillary length generated by surface tension. We show that a solid model can reproduce the results of the in-vitro experiments. Furthermore, we prove that the lack of brain sulci in lissencephaly is caused by a reduction of the cell stiffness: the softening of the organoid strengthens the role of surface tension, delaying or even inhibiting the onset of a mechanical instability at the free boundary.

VL - 134 UR - http://www.sciencedirect.com/science/article/pii/S0022509619304065 ER - TY - JOUR T1 - A theoretical study on the transient morphing of linear poroelastic plates JF - Journal of Applied Mechanics Y1 - 2020 A1 - Dario Andrini A1 - Alessandro Lucantonio A1 - Giovanni Noselli AB -Based 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.

VL - 88 UR - https://doi.org/10.1115/1.4048806 ER - TY - JOUR T1 - Weak formulation of elastodynamics in domains with growing cracks Y1 - 2020 A1 - Emanuele Tasso AB -In this paper, we formulate and study the system of elastodynamics on domains with arbitrary growing cracks. This includes homogeneous Neumann conditions on the crack sets and mixed general Dirichlet–Neumann conditions on the boundary. The only assumptions on the crack sets are to be $$(n-1)$$-rectifiable with finite surface measure, and increasing in the sense of set inclusions. In particular, they might be dense; hence, the weak formulation must fall outside the usual context of Sobolev spaces and Korn’s inequality. We prove existence of a solution for both the damped and undamped systems, while in the damped case we are also able to prove uniqueness and an energy balance.

VL - 199 SN - 1618-1891 UR - https://doi.org/10.1007/s10231-019-00932-y IS - 4 JO - Annali di Matematica Pura ed Applicata (1923 -) ER - TY - JOUR T1 - Activation of a muscle as a mapping of stress–strain curves JF - Extreme Mech. Lett. Y1 - 2019 A1 - Davide Riccobelli A1 - D. Ambrosi PB - Elsevier BV VL - 28 ER - TY - JOUR T1 - Benamou–Brenier and duality formulas for the entropic cost on RCD*(K,N) spaces JF - Probability Theory and Related Fields Y1 - 2019 A1 - Nicola Gigli A1 - Luca Tamanini AB -In this paper we prove that, within the framework of $\textsf{RCD}^\star(K,N)$ spaces with $N<\infty$, the entropic cost (i.e. the minimal value of the Schrödinger problem) admits:A threefold dynamical variational representation, in the spirit of the Benamou–Brenier formula for the Wasserstein distance; A Hamilton–Jacobi–Bellman dual representation, in line with Bobkov–Gentil–Ledoux and Otto–Villani results on the duality between Hamilton–Jacobi and continuity equation for optimal transport;A Kantorovich-type duality formula, where the Hopf–Lax semigroup is replaced by a suitable `entropic' counterpart.We thus provide a complete and unifying picture of the equivalent variational representations of the Schrödinger problem as well as a perfect parallelism with the analogous formulas for the Wasserstein distance. Riemannian manifolds with Ricci curvature bounded from below are a relevant class of $\textsf{RCD}^*(K,N)$ spaces and our results are new even in this setting.

UR - https://doi.org/10.1007/s00440-019-00909-1 ER - TY - JOUR T1 - BlackNUFFT: Modular customizable black box hybrid parallelization of type 3 NUFFT in 3D JF - Computer Physics Communications Y1 - 2019 A1 - Nicola Giuliani KW - C++ KW - Extensibility KW - FFT KW - Modularity KW - MPI KW - MRI image processing KW - NUFFT type 3 KW - TBB AB -Many applications benefit from an efficient Discrete Fourier Transform (DFT) between arbitrarily spaced points. The Non Uniform Fast Fourier Transform reduces the computational cost of such operation from O(N2) to O(NlogN) exploiting gridding algorithms and a standard Fast Fourier Transform on an equi-spaced grid. The parallelization of the NUFFT of type 3 (between arbitrary points in space and frequency) still poses some challenges: we present a novel and flexible hybrid parallelization in a MPI-multithreaded environment exploiting existing HPC libraries on modern architectures. To ensure the reliability of the developed library, we exploit continuous integration strategies using Travis CI. We present performance analyses to prove the effectiveness of our implementation, possible extensions to the existing library, and an application of NUFFT type 3 to MRI image processing. Program summary Program Title: BlackNUFFT Program Files doi: http://dx.doi.org/10.17632/vxfj6x2p8x.1 Licensing provisions: LGPL Programming language: C++ External routines/libraries: deal.II , FFTW, PFFT Nature of problem: Provide a modular and extensible implementation of a parallel Non Uniform Fast Fourier Transform of type 3. Solution method: Use of hybrid shared distributed memory paradigm to achieve high level of efficiency. We exploit existing HPC library following best practices in scientific computing (as continuous integration via TravisCI) to reach higher complexities and guarantee the accuracy of the solution proposed.

VL - 235 UR - http://www.sciencedirect.com/science/article/pii/S0010465518303539 ER - TY - CONF T1 - A complete data-driven framework for the efficient solution of parametric shape design and optimisation in naval engineering problems T2 - VIII International Conference on Computational Methods in Marine Engineering Y1 - 2019 A1 - Nicola Demo A1 - Marco Tezzele A1 - Andrea Mola A1 - Gianluigi Rozza AB -In the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples of the ROM application, in the naval field, can be found in [31, 24]. Mandatory ingredient for the ROM methods is the relation between the high-fidelity solutions and the parameters. Dealing with geometrical parameters, especially in the industrial context, this relation may be unknown and not trivial (simulations over hand morphed geometries) or very complex (high number of parameters or many nested morphing techniques). To overcome these scenarios, we propose in this contribution an efficient and complete data-driven framework involving ROM techniques for shape design and optimization, extending the pipeline presented in [7]. By applying the singular value decomposition (SVD) to the points coordinates defining the hull geometry –- assuming the topology is inaltered by the deformation –-, we are able to compute the optimal space which the deformed geometries belong to, hence using the modal coefficients as the new parameters we can reconstruct the parametric formulation of the domain. Finally the output of interest is approximated using the proper orthogonal decomposition with interpolation technique. To conclude, we apply this framework to a naval shape design problem where the bulbous bow is morphed to reduce the total resistance of the ship advancing in calm water.

JF - VIII International Conference on Computational Methods in Marine Engineering UR - https://arxiv.org/abs/1905.05982 ER - TY - CONF T1 - A complete data-driven framework for the efficient solution of parametric shape design and optimisation in naval engineering problems T2 - 8th International Conference on Computational Methods in Marine Engineering, MARINE 2019 Y1 - 2019 A1 - Nicola Demo A1 - Marco Tezzele A1 - Andrea Mola A1 - Gianluigi Rozza AB -In the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples of the ROM application, in the naval field, can be found in [31, 24]. Mandatory ingredient for the ROM methods is the relation between the high-fidelity solutions and the parameters. Dealing with geometrical parameters, especially in the industrial context, this relation may be unknown and not trivial (simulations over hand morphed geometries) or very complex (high number of parameters or many nested morphing techniques). To overcome these scenarios, we propose in this contribution an efficient and complete data-driven framework involving ROM techniques for shape design and optimization, extending the pipeline presented in [7]. By applying the singular value decomposition (SVD) to the points coordinates defining the hull geometry — assuming the topology is inaltered by the deformation —, we are able to compute the optimal space which the deformed geometries belong to, hence using the modal coefficients as the new parameters we can reconstruct the parametric formulation of the domain. Finally the output of interest is approximated using the proper orthogonal decomposition with interpolation technique. To conclude, we apply this framework to a naval shape design problem where the bulbous bow is morphed to reduce the total resistance of the ship advancing in calm water.

JF - 8th International Conference on Computational Methods in Marine Engineering, MARINE 2019 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075342565&partnerID=40&md5=d76b8a1290053e7a84fb8801c0e6bb3d ER - TY - RPRT T1 - A continuous dependence result for a dynamic debonding model in dimension one Y1 - 2019 A1 - Filippo Riva AB -In this paper we address the problem of continuous dependence on initial and boundary data for a one-dimensional debonding model describing a thin ﬁlm peeled away from a substrate. The system underlying the process couples the weakly damped wave equation with a Griﬃth’s criterion which rules the evolution of the debonded region. We show that under general convergence assumptions on the data the corresponding solutions converge to the limit one with respect to diﬀerent natural topologies.

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

UR - http://www.sciencedirect.com/science/article/pii/S0723086918300975 ER - TY - CONF T1 - Efficient reduction in shape parameter space dimension for ship propeller blade design T2 - 8th International Conference on Computational Methods in Marine Engineering, MARINE 2019 Y1 - 2019 A1 - Andrea Mola A1 - Marco Tezzele A1 - Mahmoud Gadalla A1 - Valdenazzi, Federica A1 - Grassi, Davide A1 - Padovan, Roberta A1 - Gianluigi Rozza AB -In this work, we present the results of a ship propeller design optimization campaign carried out in the framework of the research project PRELICA, funded by the Friuli Venezia Giulia regional government. The main idea of this work is to operate on a multidisciplinary level to identify propeller shapes that lead to reduced tip vortex-induced pressure and increased efficiency without altering the thrust. First, a specific tool for the bottom-up construction of parameterized propeller blade geometries has been developed. The algorithm proposed operates with a user defined number of arbitrary shaped or NACA airfoil sections, and employs arbitrary degree NURBS to represent the chord, pitch, skew and rake distribution as a function of the blade radial coordinate. The control points of such curves have been modified to generate, in a fully automated way, a family of blade geometries depending on as many as 20 shape parameters. Such geometries have then been used to carry out potential flow simulations with the Boundary Element Method based software PROCAL. Given the high number of parameters considered, such a preliminary stage allowed for a fast evaluation of the performance of several hundreds of shapes. In addition, the data obtained from the potential flow simulation allowed for the application of a parameter space reduction methodology based on active subspaces (AS) property, which suggested that the main propeller performance indices are, at a first but rather accurate approximation, only depending on a single parameter which is a linear combination of all the original geometric ones. AS analysis has also been used to carry out a constrained optimization exploiting response surface method in the reduced parameter space, and a sensitivity analysis based on such surrogate model. The few selected shapes were finally used to set up high fidelity RANS simulations and select an optimal shape.

JF - 8th International Conference on Computational Methods in Marine Engineering, MARINE 2019 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075395143&partnerID=40&md5=b6aa0fcedc2f88e78c295d0f437824d0 ER - TY - JOUR T1 - An entropic interpolation proof of the HWI inequality JF - Stochastic Processes and their Applications Y1 - 2019 A1 - Ivan Gentil A1 - Christian Léonard A1 - Luigia Ripani A1 - Luca Tamanini KW - Entropic interpolations KW - Fisher information KW - Relative entropy KW - Schrödinger problem KW - Wasserstein distance AB -The HWI inequality is an “interpolation”inequality between the Entropy H, the Fisher information I and the Wasserstein distance W. We present a pathwise proof of the HWI inequality which is obtained through a zero noise limit of the Schrödinger problem. Our approach consists in making rigorous the Otto–Villani heuristics in Otto and Villani (2000) taking advantage of the entropic interpolations, which are regular both in space and time, rather than the displacement ones.

UR - http://www.sciencedirect.com/science/article/pii/S0304414918303454 ER - TY - JOUR T1 - A Finite Volume approximation of the Navier-Stokes equations with nonlinear filtering stabilization JF - Computers & Fluids Y1 - 2019 A1 - Michele Girfoglio A1 - Annalisa Quaini A1 - Gianluigi Rozza AB -We 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.

VL - 187 UR - https://arxiv.org/abs/1901.05251 ER - TY - JOUR T1 - A Finite Volume approximation of the Navier-Stokes equations with nonlinear filtering stabilization JF - Computers and Fluids Y1 - 2019 A1 - Michele Girfoglio A1 - Annalisa Quaini A1 - Gianluigi Rozza AB -We 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.

VL - 187 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85065471890&doi=10.1016%2fj.compfluid.2019.05.001&partnerID=40&md5=c982371b5b5d4b5664a676902aaa60f4 ER - TY - JOUR T1 - Isoperimetric inequality under Measure-Contraction property Y1 - 2019 A1 - Fabio Cavalletti A1 - Flavia Santarcangelo KW - Isoperimetric inequality KW - Measure-Contraction property KW - Optimal transport KW - Ricci curvature AB -We 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.

VL - 277 SN - 0022-1236 UR - https://www.sciencedirect.com/science/article/pii/S0022123619302289 IS - 9 JO - Journal of Functional Analysis ER - TY - JOUR T1 - Local well-posedness for quasi-linear NLS with large Cauchy data on the circle JF - Annales de l'Institut Henri Poincaré C, Analyse non linéaire Y1 - 2019 A1 - Roberto Feola A1 - Felice Iandoli KW - Dispersive equations KW - Energy method KW - Local wellposedness KW - NLS KW - Para-differential calculus KW - Quasi-linear PDEs AB -We prove local in time well-posedness for a large class of quasilinear Hamiltonian, or parity preserving, Schrödinger equations on the circle. After a paralinearization of the equation, we perform several paradifferential changes of coordinates in order to transform the system into a paradifferential one with symbols which, at the positive order, are constant and purely imaginary. This allows to obtain a priori energy estimates on the Sobolev norms of the solutions.

VL - 36 UR - http://www.sciencedirect.com/science/article/pii/S0294144918300428 ER - TY - JOUR T1 - A Localized Reduced-Order Modeling Approach for PDEs with Bifurcating Solutions JF - Computer Methods in Applied Mechanics and Engineering Y1 - 2019 A1 - Martin W. Hess A1 - Alla, Alessandro A1 - Annalisa Quaini A1 - Gianluigi Rozza A1 - Max Gunzburger AB -Reduced-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.

VL - 351 UR - https://arxiv.org/abs/1807.08851 ER - TY - JOUR T1 - A localized reduced-order modeling approach for PDEs with bifurcating solutions JF - Computer Methods in Applied Mechanics and Engineering Y1 - 2019 A1 - Martin W. Hess A1 - Alla, Alessandro A1 - Annalisa Quaini A1 - Gianluigi Rozza A1 - Max Gunzburger AB -Reduced-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.

VL - 351 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85064313505&doi=10.1016%2fj.cma.2019.03.050&partnerID=40&md5=8b095034b9e539995facc7ce7bafa9e9 ER - TY - JOUR T1 - A neutrally stable shell in a Stokes flow: a rotational Taylor's sheet JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering SciencesProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Y1 - 2019 A1 - Giovanni Corsi A1 - Antonio DeSimone A1 - C. Maurini A1 - S. Vidoli VL - 475 UR - https://doi.org/10.1098/rspa.2019.0178 IS - 2227 JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences ER - TY - JOUR T1 - A non-intrusive approach for the reconstruction of POD modal coefficients through active subspaces JF - Comptes Rendus - Mecanique Y1 - 2019 A1 - Nicola Demo A1 - Marco Tezzele A1 - Gianluigi Rozza AB -Reduced 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.

VL - 347 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075379471&doi=10.1016%2fj.crme.2019.11.012&partnerID=40&md5=dcb27af39dc14dc8c3a4a5f681f7d84b ER - TY - JOUR T1 - A Note About the Strong Maximum Principle on RCD Spaces JF - Canadian Mathematical Bulletin Y1 - 2019 A1 - Nicola Gigli A1 - Chiara Rigoni AB -We give a direct proof of the strong maximum principle on finite dimensional RCD spaces based on the Laplacian comparison of the squared distance.

PB - Canadian Mathematical Society VL - 62 ER - TY - JOUR T1 - Nutations in growing plant shoots: The role of elastic deformations due to gravity loading JF - Journal of the Mechanics and Physics of Solids Y1 - 2019 A1 - Daniele Agostinelli A1 - Alessandro Lucantonio A1 - Giovanni Noselli A1 - Antonio DeSimone KW - Circumnutations KW - Flutter instability KW - Gravitropism KW - Hopf bifurcation AB -The effect of elastic deformations induced by gravity loading on the active circumnutation movements of growing plant shoots is investigated. We consider first a discrete model (a gravitropic spring-pendulum system) and then a continuous rod model which is analyzed both analytically (under the assumption of small deformations) and numerically (in the large deformation regime). We find that, for a choice of material parameters consistent with values reported in the available literature on plant shoots, rods of sufficient length may exhibit lateral oscillations of increasing amplitude, which eventually converge to limit cycles. This behavior strongly suggests the occurrence of a Hopf bifurcation, just as for the gravitropic spring-pendulum system, for which this result is rigorously established. At least in this restricted set of material parameters, our analysis supports a view of Darwin’s circumnutations as a biological analogue to structural systems exhibiting flutter instabilities, i.e., spontaneous oscillations away from equilibrium configurations driven by non-conservative loads. Here, in the context of nutation movements of growing plant shoots, the energy needed to sustain oscillations is continuously supplied to the system by the internal biochemical machinery presiding the capability of plants to maintain a vertical pose.

UR - https://doi.org/10.1016/j.jmps.2019.103702 ER - TY - JOUR T1 - Parametric POD-Galerkin Model Order Reduction for Unsteady-State Heat Transfer Problems JF - Communications in Computational Physics Y1 - 2019 A1 - Sokratia Georgaka A1 - Giovanni Stabile A1 - Gianluigi Rozza A1 - Michael J. Bluck AB -A 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.

VL - 27 UR - https://arxiv.org/abs/1808.05175 ER - TY - JOUR T1 - A POD-selective inverse distance weighting method for fast parametrized shape morphing JF - International Journal for Numerical Methods in Engineering Y1 - 2019 A1 - F. Ballarin A1 - A. D'Amario A1 - Simona Perotto A1 - Gianluigi Rozza AB -Efficient 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.

VL - 117 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85056396233&doi=10.1002%2fnme.5982&partnerID=40&md5=6aabcbdc9a0da25e36575a0ebfac034f ER - TY - JOUR T1 - Point-Like Perturbed Fractional Laplacians Through Shrinking Potentials of Finite Range JF - Complex Analysis and Operator Theory Y1 - 2019 A1 - Alessandro Michelangeli A1 - Raffaele Scandone AB -We construct the rank-one, singular (point-like) perturbations of the d-dimensional fractional Laplacian in the physically meaningful norm-resolvent limit of fractional Schrödinger operators with regular potentials centred around the perturbation point and shrinking to a delta-like shape. We analyse both possible regimes, the resonance-driven and the resonance-independent limit, depending on the power of the fractional Laplacian and the spatial dimension. To this aim, we also qualify the notion of zero-energy resonance for Schrödinger operators formed by a fractional Laplacian and a regular potential.

UR - https://doi.org/10.1007/s11785-019-00927-w ER - TY - RPRT T1 - Quasi-continuous vector fields on RCD spaces Y1 - 2019 A1 - Clément Debin A1 - Nicola Gigli A1 - Enrico Pasqualetto ER - TY - JOUR T1 - A reduced basis approach for PDEs on parametrized geometries based on the shifted boundary finite element method and application to a Stokes flow JF - Computer Methods in Applied Mechanics and Engineering Y1 - 2019 A1 - Efthymios N Karatzas A1 - Giovanni Stabile A1 - Leo Nouveau A1 - Guglielmo Scovazzi A1 - Gianluigi Rozza AB -We 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.

VL - 347 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85060107322&doi=10.1016%2fj.cma.2018.12.040&partnerID=40&md5=1a3234f0cb000c91494d946428f8ebef ER - TY - JOUR T1 - Reduced Basis Approaches for Parametrized Bifurcation Problems held by Non-linear Von Kármán Equations JF - Journal of Scientific Computing Y1 - 2019 A1 - Federico Pichi A1 - Gianluigi Rozza AB -This 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.

VL - 81 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85068973907&doi=10.1007%2fs10915-019-01003-3&partnerID=40&md5=a09af83ce45183d6965cdb79d87a919b ER - TY - JOUR T1 - Reduced basis approaches for parametrized bifurcation problems held by non-linear Von Kármán equations Y1 - 2019 A1 - Federico Pichi A1 - Gianluigi Rozza AB -This 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

VL - 81 UR - https://arxiv.org/abs/1804.02014 ER - TY - JOUR T1 - A reduced order variational multiscale approach for turbulent flows JF - Advances in Computational Mathematics Y1 - 2019 A1 - Giovanni Stabile A1 - F. Ballarin A1 - G. Zuccarino A1 - Gianluigi Rozza AB -The 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.

VL - 45 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85068076665&doi=10.1007%2fs10444-019-09712-x&partnerID=40&md5=af0142e6d13bbc2e88c6f31750aef6ad ER - TY - JOUR T1 - Reducibility for a fast-driven linear Klein–Gordon equation Y1 - 2019 A1 - Luca Franzoi A1 - Alberto Maspero AB -We 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.

VL - 198 SN - 1618-1891 UR - https://doi.org/10.1007/s10231-019-00823-2 IS - 4 JO - Annali di Matematica Pura ed Applicata (1923 -) ER - TY - JOUR T1 - Reducibility of first order linear operators on tori via Moser's theorem JF - Journal of Functional Analysis Y1 - 2019 A1 - Roberto Feola A1 - Filippo Giuliani A1 - Riccardo Montalto A1 - Michela Procesi KW - Hyperbolic PDEs KW - KAM theory KW - Nash–Moser KW - Reducibility AB -In this paper we prove reducibility of a class of first order, quasi-linear, quasi-periodic time dependent PDEs on the torus∂tu+ζ⋅∂xu+a(ωt,x)⋅∂xu=0,x∈Td,ζ∈Rd,ω∈Rν. As a consequence we deduce a stability result on the associated Cauchy problem in Sobolev spaces. By the identification between first order operators and vector fields this problem can be formulated as the problem of finding a change of coordinates which conjugates a weakly perturbed constant vector field on Tν+d to a constant diophantine flow. For this purpose we generalize Moser's straightening theorem: considering smooth perturbations we prove that the corresponding straightening torus diffeomorphism is smooth, under the assumption that the perturbation is small only in some given Sobolev norm and that the initial frequency belongs to some Cantor-like set. In view of applications in KAM theory for PDEs we provide also tame estimates on the change of variables.

VL - 276 UR - http://www.sciencedirect.com/science/article/pii/S0022123618303793 ER - TY - ABST T1 - Regularity of minimizers for a model of charged droplets Y1 - 2019 A1 - Guido De Philippis A1 - Jonas Hirsch A1 - Giulia Vescovo ER - TY - JOUR T1 - On the relaxed area of the graph of discontinuous maps from the plane to the plane taking three values with no symmetry assumptions JF - Annali di Matematica Pura ed Applicata (1923 -) Y1 - 2019 A1 - Giovanni Bellettini A1 - Alaa Elshorbagy A1 - Maurizio Paolini A1 - Riccardo Scala AB -In this paper, we estimate from above the area of the graph of a singular map u taking a disk to three vectors, the vertices of a triangle, and jumping along three $\mathcal{C}^2$-embedded curves that meet transversely at only one point of the disk. We show that the singular part of the relaxed area can be estimated from above by the solution of a Plateau-type problem involving three entangled nonparametric area-minimizing surfaces. The idea is to ``fill the hole'' in the graph of the singular map with a sequence of approximating smooth two-codimensional surfaces of graph-type, by imagining three minimal surfaces, placed vertically over the jump of u, coupled together via a triple point in the target triangle. Such a construction depends on the choice of a target triple point, and on a connection passing through it, which dictate the boundary condition for the three minimal surfaces. We show that the singular part of the relaxed area of u cannot be larger than what we obtain by minimizing over all possible target triple points and all corresponding connections.

UR - https://doi.org/10.1007/s10231-019-00887-0 ER - TY - JOUR T1 - The Serre–Swan theorem for normed modules JF - Rendiconti del Circolo Matematico di Palermo Series 2 Y1 - 2019 A1 - Danka Lučić A1 - Enrico Pasqualetto VL - 68 UR - https://doi.org/10.1007/s12215-018-0366-6 ER - TY - CONF T1 - Shape optimization through proper orthogonal decomposition with interpolation and dynamic mode decomposition enhanced by active subspaces T2 - 8th International Conference on Computational Methods in Marine Engineering, MARINE 2019 Y1 - 2019 A1 - Marco Tezzele A1 - Nicola Demo A1 - Gianluigi Rozza AB -We propose a numerical pipeline for shape optimization in naval engineering involving two different non-intrusive reduced order method (ROM) techniques. Such methods are proper orthogonal decomposition with interpolation (PODI) and dynamic mode decomposition (DMD). The ROM proposed will be enhanced by active subspaces (AS) as a pre-processing tool that reduce the parameter space dimension and suggest better sampling of the input space. We will focus on geometrical parameters describing the perturbation of a reference bulbous bow through the free form deformation (FFD) technique. The ROM are based on a finite volume method (FV) to simulate the multi-phase incompressible flow around the deformed hulls. In previous works we studied the reduction of the parameter space in naval engineering through AS [38, 10] focusing on different parts of the hull. PODI and DMD have been employed for the study of fast and reliable shape optimization cycles on a bulbous bow in [9]. The novelty of this work is the simultaneous reduction of both the input parameter space and the output fields of interest. In particular AS will be trained computing the total drag resistance of a hull advancing in calm water and its gradients with respect to the input parameters. DMD will improve the performance of each simulation of the campaign using only few snapshots of the solution fields in order to predict the regime state of the system. Finally PODI will interpolate the coefficients of the POD decomposition of the output fields for a fast approximation of all the fields at new untried parameters given by the optimization algorithm. This will result in a non-intrusive data-driven numerical optimization pipeline completely independent with respect to the full order solver used and it can be easily incorporated into existing numerical pipelines, from the reference CAD to the optimal shape.

JF - 8th International Conference on Computational Methods in Marine Engineering, MARINE 2019 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075390244&partnerID=40&md5=3e1f2e9a2539d34594caff13766c94b8 ER - TY - JOUR T1 - A spectral element reduced basis method in parametric CFD JF - Lecture Notes in Computational Science and Engineering Y1 - 2019 A1 - Martin W. Hess A1 - Gianluigi Rozza AB -We consider the Navier-Stokes equations in a channel with varying Reynolds numbers. The model is discretized with high-order spectral element ansatz functions, resulting in 14,259 degrees of freedom. The steady-state snapshot 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.

VL - 126 UR - 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 ER - TY - CHAP T1 - A Spectral Element Reduced Basis Method in Parametric CFD T2 - Numerical Mathematics and Advanced Applications - ENUMATH 2017 Y1 - 2019 A1 - Martin W. Hess A1 - Gianluigi Rozza ED - Radu, Florin Adrian ED - Kumar, Kundan ED - Berre, Inga ED - Nordbotten, Jan Martin ED - Pop, Iuliu Sorin AB -We consider the Navier-Stokes equations in a channel with varying Reynolds numbers. The model is discretized with high-order spectral element ansatz functions, resulting in 14 259 degrees of freedom. The steady-state snapshot solu- tions define a reduced order space, which allows to accurately evaluate the steady- state solutions for varying Reynolds number with a reduced order model within a fixed-point iteration. In particular, we compare different aspects of implementing the reduced order model with respect to the use of a spectral element discretization. It is shown, how a multilevel static condensation in the pressure and velocity boundary degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios.

JF - Numerical Mathematics and Advanced Applications - ENUMATH 2017 PB - Springer International Publishing VL - 126 UR - https://arxiv.org/abs/1712.06432 ER - TY - RPRT T1 - On the square distance function from a manifold with boundary Y1 - 2019 A1 - Giovanni Bellettini A1 - Alaa Elshorbagy AB -We characterize arbitrary codimensional smooth manifolds $\mathcal{M}$ with boundary embedded in $\mathbb{R}^n$ using the square distance function and the signed distance function from $\mathcal{M}$ and from its boundary. The results are localized in an open set.

UR - http://cvgmt.sns.it/media/doc/paper/4260/manif_with_bound_dist.pdf ER - TY - JOUR T1 - On the topological degree of planar maps avoiding normal cones JF - TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS Y1 - 2019 A1 - Alessandro Fonda A1 - Giuliano Klun AB -The 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.

VL - 81 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85053798049&doi=10.1007%2fs10915-018-0830-7&partnerID=40&md5=5cad501b6ef1955da55868807079ee5d ER - TY - JOUR T1 - Weighted Reduced Order Methods for Parametrized Partial Differential Equations with Random Inputs JF - PoliTO Springer Series Y1 - 2019 A1 - L. Venturi A1 - D. Torlo A1 - F. Ballarin A1 - Gianluigi Rozza AB -In 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.

UR - 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 ER - TY - RPRT T1 - Zero modes and low-energy resolvent expansion for three dimensional Schrodinger operators with point interactions Y1 - 2019 A1 - Raffaele Scandone UR - https://arxiv.org/abs/1901.02449 ER - TY - JOUR T1 - Analysis of a Dynamic Peeling Test with Speed-Dependent Toughness JF - SIAM Journal on Applied Mathematics Y1 - 2018 A1 - Giuliano Lazzaroni A1 - Lorenzo Nardini AB -We analyse a one-dimensional model of dynamic debonding for a thin film, where the local toughness of the glue between the film and the substrate also depends on the debonding speed. The wave equation on the debonded region is strongly coupled with Griffith's criterion for the evolution of the debonding front. We provide an existence and uniqueness result and find explicitly the solution in some concrete examples. We study the limit of solutions as inertia tends to zero, observing phases of unstable propagation, as well as time discontinuities, even though the toughness diverges at a limiting debonding speed.

VL - 78 UR - https://doi.org/10.1137/17M1147354 ER - TY - RPRT T1 - On the Cauchy problem for the wave equation on time-dependent domains Y1 - 2018 A1 - Gianni Dal Maso A1 - Rodica Toader AB - We introduce a notion of solution to the wave equation on a suitable class of time-dependent domains and compare it with a previous de nition. We prove an existence result for the solution of the Cauchy problem and present some additional conditions which imply uniqueness. PB - SISSA UR - http://preprints.sissa.it/handle/1963/35314 U1 - 35622 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Certified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models JF - Journal of Scientific Computing Y1 - 2018 A1 - Immanuel Martini A1 - Bernard Haasdonk A1 - Gianluigi Rozza VL - 74 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85017156114&doi=10.1007%2fs10915-017-0430-y&partnerID=40&md5=023ef0bb95713f4442d1fa374c92a964 ER - TY - RPRT T1 - Characteristic boundary layers for mixed hyperbolic systems in one space dimension and applications to the Navier-Stokes and MHD equations Y1 - 2018 A1 - Stefano Bianchini A1 - Laura Spinolo AB - We provide a detailed analysis of the boundary layers for mixed hyperbolic-parabolic systems in one space dimension and small amplitude regimes. As an application of our results, we describe the solution of the so-called boundary Riemann problem recovered as the zero viscosity limit of the physical viscous approximation. In particular, we tackle the so called doubly characteristic case, which is considerably more demanding from the technical viewpoint and occurs when the boundary is characteristic for both the mixed hyperbolic-parabolic system and for the hyperbolic system obtained by neglecting the second order terms. Our analysis applies in particular to the compressible Navier-Stokes and MHD equations in Eulerian coordinates, with both positive and null conductivity. In these cases, the doubly characteristic case occurs when the velocity is close to 0. The analysis extends to non-conservative systems. PB - SISSA UR - http://preprints.sissa.it/handle/1963/35325 U1 - 35635 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Cohesive fracture with irreversibility: Quasistatic evolution for a model subject to fatigue JF - Mathematical Models and Methods in Applied Sciences Y1 - 2018 A1 - Vito Crismale A1 - Giuliano Lazzaroni A1 - Gianluca Orlando AB -In this paper we prove the existence of quasistatic evolutions for a cohesive fracture on a prescribed crack surface, in small-strain antiplane elasticity. The main feature of the model is that the density of the energy dissipated in the fracture process depends on the total variation of the amplitude of the jump. Thus, any change in the crack opening entails a loss of energy, until the crack is complete. In particular this implies a fatigue phenomenon, i.e. a complete fracture may be produced by oscillation of small jumps. The first step of the existence proof is the construction of approximate evolutions obtained by solving discrete-time incremental minimum problems. The main difficulty in the passage to the continuous-time limit is that we lack of controls on the variations of the jump of the approximate evolutions. Therefore we resort to a weak formulation where the variation of the jump is replaced by a Young measure. Eventually, after proving the existence in this weak formulation, we improve the result by showing that the Young measure is concentrated on a function and coincides with the variation of the jump of the displacement.

VL - 28 UR - https://doi.org/10.1142/S0218202518500379 ER - TY - JOUR T1 - deal2lkit: A toolkit library for high performance programming in deal.II JF - SOFTWAREX Y1 - 2018 A1 - Alberto Sartori A1 - Nicola Giuliani A1 - Mauro Bardelloni A1 - Luca Heltai VL - 7 ER - TY - RPRT T1 - Differential of metric valued Sobolev maps Y1 - 2018 A1 - Nicola Gigli A1 - Enrico Pasqualetto A1 - Elefterios Soultanis ER - TY - RPRT T1 - Dimension reduction for thin films with transversally varying prestrain: the oscillatory and the non-oscillatory case Y1 - 2018 A1 - Marta Lewicka A1 - Danka Lučić ER - TY - RPRT T1 - Existence and uniqueness of dynamic evolutions for a one dimensional debonding model with damping Y1 - 2018 A1 - Lorenzo Nardini A1 - Filippo Riva AB -In this paper we analyse a one-dimensional debonding model for a thin film peeled from a substrate when friction is taken into account. It is described by the weakly damped wave equation whose domain, the debonded region, grows according to a Griffth's criterion. Firstly we prove that the equation admits a unique solution when the evolution of the debonding front is assigned. Finally we provide an existence and uniqueness result for the coupled problem given by the wave equation together with Griffth's criterion.

UR - http://preprints.sissa.it/xmlui/handle/1963/35319 U1 - 35629 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Existence for elastodynamic Griffith fracture with a weak maximal dissipation condition Y1 - 2018 A1 - Gianni Dal Maso A1 - Cristopher J. Larsen A1 - Rodica Toader AB - We consider a model of elastodynamics with fracture evolution, based on energy-dissipation balance and a maximal dissipation condition. We prove an existence result in the case of planar elasticity with a free crack path, where the maximal dissipation condition is satisfied among suitably regular competitor cracks. UR - http://preprints.sissa.it/handle/1963/35308 U1 - 35616 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - CHAP T1 - Failure of the Chain Rule in the Non Steady Two-Dimensional Setting T2 - Current Research in Nonlinear Analysis: In Honor of Haim Brezis and Louis Nirenberg Y1 - 2018 A1 - Stefano Bianchini A1 - Paolo Bonicatto ED - Rassias, Themistocles M. JF - Current Research in Nonlinear Analysis: In Honor of Haim Brezis and Louis Nirenberg PB - Springer International Publishing CY - Cham SN - 978-3-319-89800-1 UR - https://doi.org/10.1007/978-3-319-89800-1_2 ER - TY - JOUR T1 - Finite volume POD-Galerkin stabilised reduced order methods for the parametrised incompressible Navier–Stokes equations JF - Computers and Fluids Y1 - 2018 A1 - Giovanni Stabile A1 - Gianluigi Rozza AB -In 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.

VL - 173 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85043366603&doi=10.1016%2fj.compfluid.2018.01.035&partnerID=40&md5=c15435ea3b632e55450da19ba2bb6125 ER - TY - RPRT T1 - Foldable structures made of hydrogel bilayers Y1 - 2018 A1 - Virginia Agostiniani A1 - Antonio DeSimone A1 - Alessandro Lucantonio A1 - Danka Lučić ER - TY - JOUR T1 - Fractional powers and singular perturbations of quantum differential Hamiltonians JF - Journal of Mathematical Physics Y1 - 2018 A1 - Alessandro Michelangeli A1 - Andrea Ottolini A1 - Raffaele Scandone AB -We consider the fractional powers of singular (point-like) perturbations of the Laplacian and the singular perturbations of fractional powers of the Laplacian, and we compare two such constructions focusing on their perturbative structure for resolvents and on the local singularity structure of their domains. In application to the linear and non-linear Schrödinger equations for the corresponding operators, we outline a programme of relevant questions that deserve being investigated.

VL - 59 UR - https://doi.org/10.1063/1.5033856 ER - TY - JOUR T1 - On fractional powers of singular perturbations of the Laplacian JF - Journal of Functional Analysis Y1 - 2018 A1 - Vladimir Georgiev A1 - Alessandro Michelangeli A1 - Raffaele Scandone KW - Point interactions KW - Regular and singular component of a point-interaction operator KW - Singular perturbations of the Laplacian AB -We qualify a relevant range of fractional powers of the so-called Hamiltonian of point interaction in three dimensions, namely the singular perturbation of the negative Laplacian with a contact interaction supported at the origin. In particular we provide an explicit control of the domain of such a fractional operator and of its decomposition into regular and singular parts. We also qualify the norms of the resulting singular fractional Sobolev spaces and their mutual control with the corresponding classical Sobolev norms.

VL - 275 UR - http://www.sciencedirect.com/science/article/pii/S0022123618301046 ER - TY - JOUR T1 - Global, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials JF - Zeitschrift für angewandte Mathematik und Physik Y1 - 2018 A1 - Paolo Antonelli A1 - Alessandro Michelangeli A1 - Raffaele Scandone AB -We prove the existence of weak solutions in the space of energy for a class of nonlinear Schrödinger equations in the presence of a external, rough, time-dependent magnetic potential. Under our assumptions, it is not possible to study the problem by means of usual arguments like resolvent techniques or Fourier integral operators, for example. We use a parabolic regularisation, and we solve the approximating Cauchy problem. This is achieved by obtaining suitable smoothing estimates for the dissipative evolution. The total mass and energy bounds allow to extend the solution globally in time. We then infer sufficient compactness properties in order to produce a global-in-time finite energy weak solution to our original problem.

VL - 69 UR - https://doi.org/10.1007/s00033-018-0938-5 ER - TY - JOUR T1 - Heterogeneous elastic plates with in-plane modulation of the target curvature and applications to thin gel sheets JF - ESAIM: Control, Optimisation and Calculus of Variations Y1 - 2018 A1 - Virginia Agostiniani A1 - Alessandro Lucantonio A1 - Danka Lučić PB - EDP Sciences ER - TY - RPRT T1 - Long time existence for fully nonlinear NLS with small Cauchy data on the circle Y1 - 2018 A1 - Feola Roberto A1 - Felice Iandoli ER - TY - JOUR T1 - Lp-Boundedness of Wave Operators for the Three-Dimensional Multi-Centre Point Interaction JF - Annales Henri Poincaré Y1 - 2018 A1 - Gianfausto Dell'Antonio A1 - Alessandro Michelangeli A1 - Raffaele Scandone A1 - Kenji Yajima AB -We prove that, for arbitrary centres and strengths, the wave operators for three-dimensional Schrödinger operators with multi-centre local point interactions are bounded in Lp(R3)for 1<p<3 and unbounded otherwise.

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

VL - 117 UR - http://www.sciencedirect.com/science/article/pii/S0021782418300825 ER - TY - JOUR T1 - Minimizing Movements for Mean Curvature Flow of Partitions JF - SIAM Journal on Mathematical Analysis Y1 - 2018 A1 - Giovanni Bellettini A1 - Shokhrukh Kholmatov AB -We prove the existence of a weak global in time mean curvature flow of a bounded partition of space using the method of minimizing movements. The result is extended to the case when suitable driving forces are present. We also prove some consistency results for a minimizing movement solution with smooth and viscosity solutions when the evolution starts from a partition made by a union of bounded sets at a positive distance. In addition, the motion starting from the union of convex sets at a positive distance agrees with the classical mean curvature flow and is stable with respect to the Hausdorff convergence of the initial partitions.

VL - 50 UR - https://doi.org/10.1137/17M1159294 ER - TY - RPRT T1 - Non-linear Gross-Pitaevskii dynamics of a 2D binary condensate: a numerical analysis Y1 - 2018 A1 - Alessandro Michelangeli A1 - Giuseppe Pitton AB - We present a numerical study of the two-dimensional Gross-Pitaevskii systems in a wide range of relevant regimes of population ratios and intra-species and inter-species interactions. Our numerical method is based on a Fourier collocation scheme in space combined with a fourth order integrating factor scheme in time. UR - http://preprints.sissa.it/handle/1963/35323 U1 - 35633 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - On the notion of parallel transport on RCD spaces Y1 - 2018 A1 - Nicola Gigli A1 - Enrico Pasqualetto ER - TY - JOUR T1 - A novel reduced order model for vortex induced vibrations of long flexible cylinders Y1 - 2018 A1 - Giovanni Stabile A1 - Hermann G. Matthies A1 - Claudio Borri PB - Elsevier {BV} VL - 156 UR - https://doi.org/10.1016/j.oceaneng.2018.02.064 ER - TY - JOUR T1 - Numerical study of the Kadomtsev-Petviashvili equation and dispersive shock waves JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Y1 - 2018 A1 - Tamara Grava A1 - Christian Klein A1 - Giuseppe Pitton AB -A detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev–Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For the description of dispersive shock waves, Whitham modulation equations for KP are obtained. It is shown that the modulation equations near the soliton line are hyperbolic for the KPII equation while they are elliptic for the KPI equation leading to a focusing effect and the formation of lumps. Such a behaviour is similar to the appearance of breathers for the focusing nonlinear Schrödinger equation in the semiclassical limit.

VL - 474 UR - https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2017.0458 ER - TY - JOUR T1 - Peristaltic Waves as Optimal Gaits in Metameric Bio-Inspired Robots JF - Frontiers in Robotics and AI Y1 - 2018 A1 - Daniele Agostinelli A1 - François Alouges A1 - Antonio DeSimone KW - Biomimetic robots KW - Crawling motility KW - Lumbricus terrestris KW - Metameric robots KW - Optimization KW - Peristalsis KW - Self-propulsion KW - Soft robotics AB -*Peristalsis*, i.e., a motion pattern arising from the propagation of muscle contraction and expansion waves along the body, is a common locomotion strategy for limbless animals. Mimicking peristalsis in bio-inspired robots has attracted considerable attention in the literature. It has recently been observed that maximal velocity in a metameric earthworm-like robot is achieved by actuating the segments using a “phase coordination” principle. This paper shows that, in fact, peristalsis (which requires not only phase coordination, but also that all segments oscillate at same frequency and amplitude) emerges from optimization principles. More precisely, basing our analysis on the assumption of small deformations, we show that peristaltic waves provide the optimal actuation solution in the ideal case of a periodic infinite system, and that this is approximately true, modulo edge effects, for the real, finite length system. Therefore, this paper confirms the effectiveness of mimicking peristalsis in bio-inspired robots, at least in the small-deformation regime. Further research will be required to test the effectiveness of this strategy if large deformations are allowed.

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

PB - American Mathematical Society UR - http://urania.sissa.it/xmlui/handle/1963/35264 N1 - AMS Subject Classification: 34B15, 34B18, 34C25, 34C28, 47H11. U1 - 35568 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Positive subharmonic solutions to nonlinear ODEs with indefinite weight JF - Communications in Contemporary Mathematics Y1 - 2018 A1 - Alberto Boscaggin A1 - Guglielmo Feltrin AB -We prove that the superlinear indefinite equation u″ + a(t)up = 0, where p > 1 and a(t) is a T-periodic sign-changing function satisfying the (sharp) mean value condition ∫0Ta(t)dt < 0, has positive subharmonic solutions of order k for any large integer k, thus providing a further contribution to a problem raised by Butler in its pioneering paper [Rapid oscillation, nonextendability, and the existence of periodic solutions to second order nonlinear ordinary differential equations, J. Differential Equations 22 (1976) 467–477]. The proof, which applies to a larger class of indefinite equations, combines coincidence degree theory (yielding a positive harmonic solution) with the Poincaré–Birkhoff fixed point theorem (giving subharmonic solutions oscillating around it).

VL - 20 UR - https://doi.org/10.1142/S0219199717500213 ER - TY - JOUR T1 - Predicting and Optimizing Microswimmer Performance from the Hydrodynamics of Its Components: The Relevance of Interactions JF - SOFT ROBOTICS Y1 - 2018 A1 - Nicola Giuliani A1 - Luca Heltai A1 - Antonio DeSimone VL - 5 UR - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6094362/ ER - TY - JOUR T1 - On the Quasistatic Limit of Dynamic Evolutions for a Peeling Test in Dimension One JF - Journal of Nonlinear Science Y1 - 2018 A1 - Giuliano Lazzaroni A1 - Lorenzo Nardini AB -The aim of this paper is to study the quasistatic limit of a one-dimensional model of dynamic debonding. We start from a dynamic problem that strongly couples the wave equation in a time-dependent domain with Griffith's criterion for the evolution of the domain. Passing to the limit as inertia tends to zero, we find that the limit evolution satisfies a stability condition; however, the activation rule in Griffith's (quasistatic) criterion does not hold in general, thus the limit evolution is not rate-independent.

VL - 28 UR - https://doi.org/10.1007/s00332-017-9407-0 ER - TY - RPRT T1 - On real resonances for the three-dimensional, multi-centre point interaction Y1 - 2018 A1 - Alessandro Michelangeli A1 - Raffaele Scandone ER - TY - JOUR T1 - Recognizing the flat torus among RCD*(0,N) spaces via the study of the first cohomology group JF - Calculus of Variations and Partial Differential Equations Y1 - 2018 A1 - Nicola Gigli A1 - Chiara Rigoni AB -We prove that if the dimension of the first cohomology group of a $\mathsf{RCD}^\star (0,N)$ space is $N$, then the space is a flat torus. This generalizes a classical result due to Bochner to the non-smooth setting and also provides a first example where the study of the cohomology groups in such synthetic framework leads to geometric consequences.

VL - 57 UR - https://doi.org/10.1007/s00526-018-1377-z ER - TY - JOUR T1 - Reduced Basis Approximation and A Posteriori Error Estimation: Applications to Elasticity Problems in Several Parametric Settings JF - SEMA SIMAI Springer Series Y1 - 2018 A1 - D.B.P. Huynh A1 - Federico Pichi A1 - Gianluigi Rozza AB -In 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.

VL - 15 UR - 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 ER - TY - CHAP T1 - Reduced Basis Approximation and A Posteriori Error Estimation: Applications to Elasticity Problems in Several Parametric Settings T2 - Numerical Methods for PDEs Y1 - 2018 A1 - Huynh, D. B. P. A1 - Federico Pichi A1 - Gianluigi Rozza JF - Numerical Methods for PDEs VL - 15 UR - https://link.springer.com/chapter/10.1007/978-3-319-94676-4_8 ER - TY - RPRT T1 - Reducibility for a class of weakly dispersive linear operators arising from the Degasperis Procesi equation Y1 - 2018 A1 - Roberto Feola A1 - Filippo Giuliani A1 - Michela Procesi ER - TY - JOUR T1 - Regularity estimates for scalar conservation laws in one space dimension JF - Journal of Hyperbolic Differential Equations Y1 - 2018 A1 - Elio Marconi AB -We deal with the regularizing effect that, in scalar conservation laws in one space dimension, the nonlinearity of the flux function f has on the entropy solution. More precisely, if the set w : f″(w)≠0 is dense, the regularity of the solution can be expressed in terms of BVΦ spaces, where Φ depends on the nonlinearity of f. If moreover the set w : f″(w) = 0 is finite, under the additional polynomial degeneracy condition at the inflection points, we prove that f′∘ u(t) ∈BV loc(ℝ) for every t > 0 and that this can be improved to SBVloc(ℝ) regularity except an at most countable set of singular times. Finally, we present some examples that show the sharpness of these results and counterexamples to related questions, namely regularity in the kinetic formulation and a property of the fractional BV spaces.

VL - 15 UR - https://doi.org/10.1142/S0219891618500200 ER - TY - JOUR T1 - Second order differentiation formula on RCD(K, N) spaces JF - Rendiconti Lincei-Matematica e Applicazioni Y1 - 2018 A1 - Nicola Gigli A1 - Luca Tamanini VL - 29 ER - TY - RPRT T1 - Second order differentiation formula on RCD*(K,N) spaces Y1 - 2018 A1 - Nicola Gigli A1 - Luca Tamanini ER - TY - JOUR T1 - Singular Hartree equation in fractional perturbed Sobolev spaces JF - Journal of Nonlinear Mathematical Physics Y1 - 2018 A1 - Alessandro Michelangeli A1 - Alessandro Olgiati A1 - Raffaele Scandone AB -We establish the local and global theory for the Cauchy problem of the singular Hartree equation in three dimensions, that is, the modification of the non-linear Schrödinger equation with Hartree non-linearity, where the linear part is now given by the Hamiltonian of point interaction. The latter is a singular, self-adjoint perturbation of the free Laplacian, modelling a contact interaction at a fixed point. The resulting non-linear equation is the typical effective equation for the dynamics of condensed Bose gases with fixed point-like impurities. We control the local solution theory in the perturbed Sobolev spaces of fractional order between the mass space and the operator domain. We then control the global solution theory both in the mass and in the energy space.

PB - Taylor & Francis VL - 25 UR - https://doi.org/10.1080/14029251.2018.1503423 ER - TY - JOUR T1 - Spontaneous morphing of equibiaxially pre-stretched elastic bilayers: The role of sample geometry JF - International Journal of Mechanical Sciences Y1 - 2018 A1 - Noe Caruso A1 - Aleksandar Cvetković A1 - Alessandro Lucantonio A1 - Giovanni Noselli A1 - Antonio DeSimone KW - Bifurcation KW - Elastic bilayer KW - Pre-stretch KW - Shape programming AB -An 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.

VL - 149 UR - https://www.sciencedirect.com/science/article/pii/S0020740317311761 ER - TY - CONF T1 - SRTP 2.0 - The evolution of the safe return to port concept T2 - Technology and Science for the Ships of the Future - Proceedings of NAV 2018: 19th International Conference on Ship and Maritime Research Y1 - 2018 A1 - D. Cangelosi A1 - A. Bonvicini A1 - M. Nardo A1 - Andrea Mola A1 - A. Marchese A1 - Marco Tezzele A1 - Gianluigi Rozza AB -In 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.

JF - Technology and Science for the Ships of the Future - Proceedings of NAV 2018: 19th International Conference on Ship and Maritime Research ER - TY - JOUR T1 - Stabilized weighted reduced basis methods for parametrized advection dominated problems with random inputs JF - SIAM-ASA Journal on Uncertainty Quantification Y1 - 2018 A1 - D. Torlo A1 - F. Ballarin A1 - Gianluigi Rozza AB -In 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.

VL - 6 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85058246502&doi=10.1137%2f17M1163517&partnerID=40&md5=6c54e2f0eb727cb85060e988486b8ac8 ER - TY - RPRT T1 - Stochastic homogenisation of free-discontinuity problems Y1 - 2018 A1 - Filippo Cagnetti A1 - Gianni Dal Maso A1 - Lucia Scardia A1 - Caterina Ida Zeppieri AB - In this paper we study the stochastic homogenisation of free-discontinuity functionals. Assuming stationarity for the random volume and surface integrands, we prove the existence of a homogenised random free-discontinuity functional, which is deterministic in the ergodic case. Moreover, by establishing a connection between the deterministic convergence of the functionals at any fixed realisation and the pointwise Subadditive Ergodic Theorem by Akcoglou and Krengel, we characterise the limit volume and surface integrands in terms of asymptotic cell formulas. UR - http://preprints.sissa.it/handle/1963/35309 U1 - 35617 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - Transmission conditions obtained by homogenisation Y1 - 2018 A1 - Gianni Dal Maso A1 - Giovanni Franzina A1 - Davide Zucco AB - We study the asymptotic behaviour of solutions to variational problems in perforated domains with Neumann boundary conditions. We consider perforations that in the limit concentrate on a smooth manifold. We characterise the limits of the solutions and show that they solve a variational problem with a transmission condition across the manifold. This is expressed through a measure on the manifold, vanishing on sets of capacity zero. Then, we prove that every such measure can be obtained by homogenising suitable perforations. Eventually, we provide an asymptotic formula for this measure by using some auxiliary minimum problems. UR - http://preprints.sissa.it/handle/1963/35310 U1 - 35618 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - CONF T1 - On Uniqueness of Weak Solutions to Transport Equation with Non-smooth Velocity Field T2 - Theory, Numerics and Applications of Hyperbolic Problems I Y1 - 2018 A1 - Paolo Bonicatto ED - Klingenberg, Christian ED - Westdickenberg, Michael JF - Theory, Numerics and Applications of Hyperbolic Problems I PB - Springer International Publishing CY - Cham SN - 978-3-319-91545-6 UR - https://link.springer.com/chapter/10.1007/978-3-319-91545-6_15 ER - TY - JOUR T1 - π-BEM : A flexible parallel implementation for adaptive , geometry aware , and high order boundary element methods JF - Advances in Engineering Software Y1 - 2018 A1 - Nicola Giuliani A1 - Andrea Mola A1 - Luca Heltai VL - 121 ER - TY - RPRT T1 - On the 1D wave equation in time-dependent domains and the problem of debond initiation Y1 - 2017 A1 - Giuliano Lazzaroni A1 - Lorenzo Nardini AB -Motivated by a debonding model for a thin film peeled from a substrate, we analyse the one-dimensional wave equation, in a time-dependent domain which is degenerate at the initial time. In the first part of the paper we prove existence for the wave equation when the evolution of the domain is given; in the second part of the paper, the evolution of the domain is unknown and is governed by an energy criterion coupled with the wave equation. Our existence result for such coupled problem is a contribution to the study of crack initiation in dynamic fracture.

PB - SISSA UR - http://preprints.sissa.it/handle/1963/35302 U1 - 35608 U2 - Mathematics ER - TY - RPRT T1 - Almost global existence of solutions for capillarity-gravity water waves equations with periodic spatial boundary conditions Y1 - 2017 A1 - Massimiliano Berti A1 - Jean-Marc Delort AB - The goal of this monograph is to prove that any solution of the Cauchy problem for the capillarity-gravity water waves equations, in one space dimension, with periodic, even in space, initial data of small size ϵ, is almost globally defined in time on Sobolev spaces, i.e. it exists on a time interval of length of magnitude ϵ−N for any N, as soon as the initial data are smooth enough, and the gravity-capillarity parameters are taken outside an exceptional subset of zero measure. In contrast to the many results known for these equations on the real line, with decaying Cauchy data, one cannot make use of dispersive properties of the linear flow. Instead, our method is based on a normal forms procedure, in order to eliminate those contributions to the Sobolev energy that are of lower degree of homogeneity in the solution. Since the water waves equations are a quasi-linear system, usual normal forms approaches would face the well known problem of losses of derivatives in the unbounded transformations. In this monograph, to overcome such a difficulty, after a paralinearization of the capillarity-gravity water waves equations, necessary to obtain energy estimates, and thus local existence of the solutions, we first perform several paradifferential reductions of the equations to obtain a diagonal system with constant coefficients symbols, up to smoothing remainders. Then we may start with a normal form procedure where the small divisors are compensated by the previous paradifferential regularization.The reversible structure of the water waves equations, and the fact that we look for solutions even in x, guarantees a key cancellation which prevents the growth of the Sobolev norms of the solutions. UR - http://preprints.sissa.it/handle/1963/35285 U1 - 35590 U2 - Mathematics ER - TY - JOUR T1 - An application of coincidence degree theory to cyclic feedback type systems associated with nonlinear differential operators JF - Topol. Methods Nonlinear Anal. Y1 - 2017 A1 - Guglielmo Feltrin A1 - Fabio Zanolin PB - Nicolaus Copernicus University, Juliusz P. Schauder Centre for Nonlinear Studies VL - 50 UR - https://doi.org/10.12775/TMNA.2017.038 ER - TY - JOUR T1 - On the Application of Reduced Basis Methods to Bifurcation Problems in Incompressible Fluid Dynamics JF - Journal of Scientific Computing Y1 - 2017 A1 - Giuseppe Pitton A1 - Gianluigi Rozza AB -In this paper we apply a reduced basis framework for the computation of flow bifurcation (and stability) problems in fluid dynamics. The proposed method aims at reducing the complexity and the computational time required for the construction of bifurcation and stability diagrams. The method is quite general since it can in principle be specialized to a wide class of nonlinear problems, but in this work we focus on an application in incompressible fluid dynamics at low Reynolds numbers. The validation of the reduced order model with the full order computation for a benchmark cavity flow problem is promising.

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

VL - 262 UR - http://www.sciencedirect.com/science/article/pii/S0022039616303278 ER - TY - CHAP T1 - Certified Reduced Basis Method for Affinely Parametric Isogeometric Analysis NURBS Approximation T2 - Spectral and High Order Methods for Partial Differential Equations Y1 - 2017 A1 - Denis Devaud A1 - Gianluigi Rozza AB -In this work we apply reduced basis methods for parametric PDEs to an isogeometric formulation based on

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

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

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

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

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

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

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

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

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

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

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

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

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

JF - Spectral and High Order Methods for Partial Differential Equations PB - Springer CY - Heildeberg VL - 119 SN - 978-3-319-65869-8 ER - TY - JOUR T1 - On a certified smagorinsky reduced basis turbulence model JF - SIAM Journal on Numerical Analysis Y1 - 2017 A1 - Rebollo, T.C. A1 - E.D. Ávila A1 - Marmol, M.G. A1 - F. Ballarin A1 - Gianluigi Rozza VL - 55 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85039928218&doi=10.1137%2f17M1118233&partnerID=40&md5=221d9cd2bcc74121fcef93efd9d3d76c ER - TY - JOUR T1 - Clifford Tori and the singularly perturbed Cahn–Hilliard equation JF - Journal of Differential Equations Y1 - 2017 A1 - Matteo Rizzi KW - Cahn–Hilliard equation KW - Clifford Torus KW - Lyapunov–Schmidt reduction KW - Willmore surface AB -In this paper we construct entire solutions uε to the Cahn–Hilliard equation −ε2Δ(−ε2Δu+W′(u))+W″(u)(−ε2Δu+W′(u))=ε4λε(1−uε), under the volume constraint ∫R3(1−uε)2dx=82π2cε, with cε→1 as ε→0, whose nodal set approaches the Clifford Torus, that is the Torus with radii of ratio 1/2 embedded in R3, as ε→0. It is crucial that the Clifford Torus is a Willmore hypersurface and it is non-degenerate, up to conformal transformations. The proof is based on the Lyapunov–Schmidt reduction and on careful geometric expansions of the Laplacian.

VL - 262 UR - http://www.sciencedirect.com/science/article/pii/S0022039617300530 ER - TY - JOUR T1 - Computational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: Applications to Coanda effect in cardiology JF - Journal of Computational Physics Y1 - 2017 A1 - Giuseppe Pitton A1 - Annalisa Quaini A1 - Gianluigi Rozza KW - Parametrized Navier–Stokes equations KW - Reduced basis method KW - Stability of flows KW - Symmetry breaking bifurcation AB -We focus on reducing the computational costs associated with the hydrodynamic stability of solutions of the incompressible Navier–Stokes equations for a Newtonian and viscous fluid in contraction–expansion channels. In particular, we are interested in studying steady bifurcations, occurring when non-unique stable solutions appear as physical and/or geometric control parameters are varied. The formulation of the stability problem requires solving an eigenvalue problem for a partial differential operator. An alternative to this approach is the direct simulation of the flow to characterize the asymptotic behavior of the solution. Both approaches can be extremely expensive in terms of computational time. We propose to apply Reduced Order Modeling (ROM) techniques to reduce the demanding computational costs associated with the detection of a type of steady bifurcations in fluid dynamics. The application that motivated the present study is the onset of asymmetries (i.e., symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the regurgitant mitral valve orifice shape.

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

VL - 344 UR - http://www.sciencedirect.com/science/article/pii/S002199911730356X ER - TY - JOUR T1 - Curvature terms in small time heat kernel expansion for a model class of hypoelliptic Hörmander operators JF - Nonlinear Analysis Y1 - 2017 A1 - Davide Barilari A1 - Elisa Paoli KW - Curvature KW - Hypoelliptic heat equation KW - Small time asymptotics AB -We consider the heat equation associated with a class of second order hypoelliptic Hörmander operators with constant second order term and linear drift. We completely describe the small time heat kernel expansions on the diagonal giving a geometric characterization of the coefficients in terms of the divergence of the drift field and the curvature-like invariants of the optimal control problem associated with the diffusion operator.

VL - 164 UR - http://www.sciencedirect.com/science/article/pii/S0362546X17302298 ER - TY - RPRT T1 - Derivation of a rod theory from lattice systems with interactions beyond nearest neighbours Y1 - 2017 A1 - Roberto Alicandro A1 - Giuliano Lazzaroni A1 - Mariapia Palombaro AB - We study continuum limits of discrete models for (possibly heterogeneous) nanowires. The lattice energy includes at least nearest and next-to-nearest neighbour interactions: the latter have the role of penalising changes of orientation. In the heterogeneous case, we obtain an estimate on the minimal energy spent to match different equilibria. This gives insight into the nucleation of dislocations in epitaxially grown heterostructured nanowires. UR - http://urania.sissa.it/xmlui/handle/1963/35269 U1 - 35575 U2 - Mathematics U4 - 1 ER - TY - CHAP T1 - Dispersive Estimates for Schrödinger Operators with Point Interactions in ℝ3 T2 - Advances in Quantum Mechanics: Contemporary Trends and Open Problems Y1 - 2017 A1 - Felice Iandoli A1 - Raffaele Scandone ED - Alessandro Michelangeli ED - Gianfausto Dell'Antonio AB -The study of dispersive properties of Schrödinger operators with point interactions is a fundamental tool for understanding the behavior of many body quantum systems interacting with very short range potential, whose dynamics can be approximated by non linear Schrödinger equations with singular interactions. In this work we proved that, in the case of one point interaction in $\mathbb{R}^3$, the perturbed Laplacian satisfies the same $L^p$−$L^q$ estimates of the free Laplacian in the smaller regime $q \in [2,3)$. These estimates are implied by a recent result concerning the Lpboundedness of the wave operators for the perturbed Laplacian. Our approach, however, is more direct and relatively simple, and could potentially be useful to prove optimal weighted estimates also in the regime $q \geq 3$.

JF - Advances in Quantum Mechanics: Contemporary Trends and Open Problems PB - Springer International Publishing CY - Cham SN - 978-3-319-58904-6 UR - https://doi.org/10.1007/978-3-319-58904-6_11 ER - TY - RPRT T1 - On the effect of interactions beyond nearest neighbours on non-convex lattice systems Y1 - 2017 A1 - Roberto Alicandro A1 - Giuliano Lazzaroni A1 - Mariapia Palombaro AB - We analyse the rigidity of non-convex discrete energies where at least nearest and next-to-nearest neighbour interactions are taken into account. Our purpose is to show that interactions beyond nearest neighbours have the role of penalising changes of orientation and, to some extent, they may replace the positive-determinant constraint that is usually required when only nearest neighbours are accounted for. In a discrete to continuum setting, we prove a compactness result for a family of surface-scaled energies and we give bounds on its possible Gamma-limit in terms of interfacial energies that penalise changes of orientation. UR - http://urania.sissa.it/xmlui/handle/1963/35268 U1 - 35574 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Energy release rate and quasi-static evolution via vanishing viscosity in a fracture model depending on the crack opening JF - ESAIM: Control, Optimisation and Calculus of Variations Y1 - 2017 A1 - Stefano Almi AB -In the setting of planar linearized elasticity, we study a fracture model depending on the crack opening. Assuming that the crack path is known a priori and sufficiently smooth, we prove that the energy release rate is well defined. Then, we consider the problem of quasi-static evolution for our model. Thanks to a vanishing viscosity approach, we show the existence of such an evolution satisfying a weak Griffith’s criterion.

PB - EDP Sciences VL - 23 UR - https://www.esaim-cocv.org/component/article?access=doi&doi=10.1051/cocv/2016014 ER - TY - RPRT T1 - Gamma-Convergence of Free-discontinuity problems Y1 - 2017 A1 - Filippo Cagnetti A1 - Gianni Dal Maso A1 - Lucia Scardia A1 - Caterina Ida Zeppieri AB - We study the Gamma-convergence of sequences of free-discontinuity functionals depending on vector-valued functions u which can be discontinuous across hypersurfaces whose shape and location are not known a priori. The main novelty of our result is that we work under very general assumptions on the integrands which, in particular, are not required to be periodic in the space variable. Further, we consider the case of surface integrands which are not bounded from below by the amplitude of the jump of u. We obtain three main results: compactness with respect to Gamma-convergence, representation of the Gamma-limit in an integral form and identification of its integrands, and homogenisation formulas without periodicity assumptions. In particular, the classical case of periodic homogenisation follows as a by-product of our analysis. Moreover, our result covers also the case of stochastic homogenisation, as we will show in a forthcoming paper. PB - SISSA UR - http://preprints.sissa.it/handle/1963/35276 U1 - 35583 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - On the genesis of directional friction through bristle-like mediating elements JF - ESAIM: COCV Y1 - 2017 A1 - Paolo Gidoni A1 - Antonio DeSimone AB -We propose an explanation of the genesis of directional dry friction, as emergent property of the oscillations produced in a bristle-like mediating element by the interaction with microscale fluctuations on the surface. Mathematically, we extend a convergence result by Mielke, for Prandtl–Tomlinson-like systems, considering also non-homothetic scalings of a wiggly potential. This allows us to apply the result to some simple mechanical models, that exemplify the interaction of a bristle with a surface having small fluctuations. We find that the resulting friction is the product of two factors: a geometric one, depending on the bristle angle and on the fluctuation profile, and a energetic one, proportional to the normal force exchanged between the bristle-like element and the surface. Finally, we apply our result to discuss the with the nap/against the nap asymmetry.

VL - 23 UR - https://doi.org/10.1051/cocv/2017030 ER - TY - JOUR T1 - Globally stable quasistatic evolution for strain gradient plasticity coupled with damage JF - Annali di Matematica Pura ed Applicata (1923 -) Y1 - 2017 A1 - Vito Crismale AB -We consider evolutions for a material model which couples scalar damage with strain gradient plasticity, in small strain assumptions. For strain gradient plasticity, we follow the Gurtin–Anand formulation (J Mech Phys Solids 53:1624–1649, 2005). The aim of the present model is to account for different phenomena: On the one hand, the elastic stiffness reduces and the plastic yield surface shrinks due to material's degradation, on the other hand the dislocation density affects the damage growth. The main result of this paper is the existence of a globally stable quasistatic evolution (in the so-called energetic formulation). Furthermore, we study the limit model as the strain gradient terms tend to zero. Under stronger regularity assumptions, we show that the evolutions converge to the ones for the coupled elastoplastic damage model studied in Crismale (ESAIM Control Optim Calc Var 22:883-912, 2016).

VL - 196 UR - https://doi.org/10.1007/s10231-016-0590-7 ER - TY - JOUR T1 - Homotopically invisible singular curves JF - Calculus of Variations and Partial Differential Equations Y1 - 2017 A1 - Andrei A. Agrachev A1 - Francesco Boarotto A1 - Antonio Lerario VL - 56 UR - https://doi.org/10.1007/s00526-017-1203-z ER - TY - JOUR T1 - Homotopy properties of horizontal path spaces and a theorem of Serre in subriemannian geometry JF - Communications in Analysis and Geometry Y1 - 2017 A1 - Francesco Boarotto A1 - Antonio Lerario PB - International Press of Boston VL - 25 ER - TY - JOUR T1 - The injectivity radius of Lie manifolds JF - ArXiv e-prints Y1 - 2017 A1 - Paolo Antonini A1 - Guido De Philippis A1 - Nicola Gigli KW - (58J40) KW - 53C21 KW - Mathematics - Differential Geometry AB -We prove in a direct, geometric way that for any compatible Riemannian metric on a Lie manifold the injectivity radius is positive

UR - https://arxiv.org/pdf/1707.07595.pdf ER - TY - RPRT T1 - A Lagrangian approach for scalar multi-d conservation laws Y1 - 2017 A1 - Stefano Bianchini A1 - Paolo Bonicatto A1 - Elio Marconi UR - http://preprints.sissa.it/handle/1963/35290 U1 - 35596 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Lagrangian representations for linear and nonlinear transport JF - Contemporary Mathematics. Fundamental Directions Y1 - 2017 A1 - Stefano Bianchini A1 - Paolo Bonicatto A1 - Elio Marconi AB -In this note we present a unifying approach for two classes of first order partial differential equations: we introduce the notion of Lagrangian representation in the settings of continuity equation and scalar conservation laws. This yields, on the one hand, the uniqueness of weak solutions to transport equation driven by a two dimensional BV nearly incompressible vector field. On the other hand, it is proved that the entropy dissipation measure for scalar conservation laws in one space dimension is concentrated on countably many Lipschitz curves.

PB - Peoples' Friendship University of Russia VL - 63 UR - http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=cmfd&paperid=327&option_lang=eng ER - TY - JOUR T1 - Limit of viscous dynamic processes in delamination as the viscosity and inertia vanish JF - ESAIM: COCV Y1 - 2017 A1 - Riccardo Scala AB -We introduce a model of dynamic evolution of a delaminated visco-elastic body with viscous adhesive. We prove the existence of solutions of the corresponding system of PDEs and then study the behavior of such solutions when the data of the problem vary slowly. We prove that a rescaled version of the dynamic evolutions converge to a “local” quasistatic evolution, which is an evolution satisfying an energy inequality and a momentum balance at all times. In the one-dimensional case we give a more detailed description of the limit evolution and we show that it behaves in a very similar way to the limit of the solutions of the dynamic model in [T. Roubicek, SIAM J. Math. Anal. 45 (2013) 101–126], where no viscosity in the adhesive is taken into account.

VL - 23 UR - https://doi.org/10.1051/cocv/2016006 ER - TY - JOUR T1 - Linear Hyperbolic Systems in Domains with Growing Cracks Y1 - 2017 A1 - Maicol Caponi AB -We 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.

VL - 85 SN - 1424-9294 UR - https://doi.org/10.1007/s00032-017-0268-7 IS - 1 JO - Milan Journal of Mathematics ER - TY - RPRT T1 - Linearisation of multiwell energies Y1 - 2017 A1 - Roberto Alicandro A1 - Gianni Dal Maso A1 - Giuliano Lazzaroni A1 - Mariapia Palombaro AB - Linear elasticity can be rigorously derived from finite elasticity under the assumption of small loadings in terms of Gamma-convergence. This was first done in the case of one-well energies with super-quadratic growth and later generalised to different settings, in particular to the case of multi-well energies where the distance between the wells is very small (comparable to the size of the load). In this paper we study the case when the distance between the wells is independent of the size of the load. In this context linear elasticity can be derived by adding to the multi-well energy a singular higher order term which penalises jumps from one well to another. The size of the singular term has to satisfy certain scaling assumptions whose optimality is shown in most of the cases. Finally, the derivation of linear elasticty from a two-well discrete model is provided, showing that the role of the singular perturbation term is played in this setting by interactions beyond nearest neighbours. UR - http://preprints.sissa.it/handle/1963/35288 U1 - 35594 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Lower semicontinuity of a class of integral functionals on the space of functions of bounded deformation JF - Advances in Calculus of Variations Y1 - 2017 A1 - Gianni Dal Maso A1 - Gianluca Orlando A1 - Rodica Toader AB -We study the lower semicontinuity of some free discontinuity functionals with linear growth defined on the space of functions with bounded deformation. The volume term is convex and depends only on the Euclidean norm of the symmetrized gradient. We introduce a suitable class of surface terms, which make the functional lower semicontinuous with respect to $L^1$ convergence.

PB - De Gruyter VL - 10 ER - TY - JOUR T1 - A lower semicontinuity result for a free discontinuity functional with a boundary term JF - Journal de Mathématiques Pures et Appliquées Y1 - 2017 A1 - Stefano Almi A1 - Gianni Dal Maso A1 - Rodica Toader AB -We study the lower semicontinuity in $GSBV^{p}(\Omega;\mathbb{R}^{m})$ of a free discontinuity functional $\mathcal{F}(u)$ that can be written as the sum of a crack term, depending only on the jump set $S_{u}$, and of a boundary term, depending on the trace of $u$ on $\partial\Omega$. We give sufficient conditions on the integrands for the lower semicontinuity of $\mathcal{F}$. Moreover, we prove a relaxation result, which shows that, if these conditions are not satisfied, the lower semicontinuous envelope of $\mathcal{F}$ can be represented by the sum of two integrals on $S_{u}$ and $\partial\Omega$, respectively.

VL - 108 UR - http://hdl.handle.net/20.500.11767/15979 IS - 6 U1 - 34731 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Minimizers of anisotropic perimeters with cylindrical norms JF - Communications on Pure & Applied Analysis Y1 - 2017 A1 - Giovanni Bellettini A1 - Matteo Novaga A1 - Shokhrukh Kholmatov KW - anisotropic Bernstein problem; KW - minimal cones KW - Non parametric minimal surfaces KW - Sets of finite perimeter AB -We study various regularity properties of minimizers of the Φ–perimeter, where Φ is a norm. Under suitable assumptions on Φ and on the dimension of the ambient space, we prove that the boundary of a cartesian minimizer is locally a Lipschitz graph out of a closed singular set of small Hausdorff dimension. Moreover, we show the following anisotropic Bernstein-type result: any entire cartesian minimizer is the subgraph of a monotone function depending only on one variable.

VL - 16 UR - http://aimsciences.org//article/id/47054f15-00c7-40b7-9da1-4c0b1d0a103d ER - TY - JOUR T1 - Multiple positive solutions of a sturm-liouville boundary value problem with conflicting nonlinearities JF - Communications on Pure & Applied Analysis Y1 - 2017 A1 - Guglielmo Feltrin KW - Leray-Schauder topological degree; KW - positive solutions KW - Sturm-Liouville boundary conditions KW - Superlinear indefinite problems AB -We study the second order nonlinear differential equation

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

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

VL - 16 UR - http://aimsciences.org//article/id/1163b042-0c64-4597-b25c-3494b268e5a1 ER - TY - JOUR T1 - Multiplicity of positive periodic solutions in the superlinear indefinite case via coincidence degree JF - Journal of Differential Equations Y1 - 2017 A1 - Guglielmo Feltrin A1 - Fabio Zanolin KW - Coincidence degree KW - Multiplicity results KW - Neumann boundary value problems KW - Positive periodic solutions KW - subharmonic solutions KW - Superlinear indefinite problems AB -We study the periodic boundary value problem associated with the second order nonlinear differential equationu″+cu′+(a+(t)−μa−(t))g(u)=0, where g(u) has superlinear growth at zero and at infinity, a(t) is a periodic sign-changing weight, c∈R and μ>0 is a real parameter. Our model includes (for c=0) the so-called nonlinear Hill's equation. We prove the existence of 2m−1 positive solutions when a(t) has m positive humps separated by m negative ones (in a periodicity interval) and μ is sufficiently large, thus giving a complete solution to a problem raised by G.J. Butler in 1976. The proof is based on Mawhin's coincidence degree defined in open (possibly unbounded) sets and applies also to Neumann boundary conditions. Our method also provides a topological approach to detect subharmonic solutions.

VL - 262 UR - http://www.sciencedirect.com/science/article/pii/S0022039617300219 ER - TY - JOUR T1 - A note on a fixed point theorem on topological cylinders JF - Ann. Mat. Pura Appl. Y1 - 2017 A1 - Guglielmo Feltrin AB -We present a fixed point theorem on topological cylinders in normed linear spaces for maps satisfying a property of stretching a space along paths. This result is a generalization of a similar theorem obtained by D. Papini and F. Zanolin. In view of the main result, we discuss the existence of fixed points for maps defined on different types of domains and we propose alternative proofs for classical fixed point theorems, as Brouwer, Schauder and Krasnosel’skii ones.

PB - Springer Verlag UR - http://urania.sissa.it/xmlui/handle/1963/35263 N1 - AMS Subject Classification: 47H10, 37C25, 47H11, 54H25. U1 - 35567 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - A Note on the Convergence of Singularly Perturbed Second Order Potential-Type Equations JF - Journal of Dynamics and Differential Equations Y1 - 2017 A1 - Lorenzo Nardini VL - 29 UR - https://doi.org/10.1007/s10884-015-9461-y ER - TY - JOUR T1 - Numerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts JF - Biomechanics and Modeling in Mechanobiology Y1 - 2017 A1 - F. Ballarin A1 - Elena Faggiano A1 - Andrea Manzoni A1 - Alfio Quarteroni A1 - Gianluigi Rozza A1 - Sonia Ippolito A1 - Roberto Scrofani VL - 16 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85015065851&doi=10.1007%2fs10237-017-0893-7&partnerID=40&md5=c388f20bd5de14187bad9ed7d9affbd0 ER - TY - JOUR T1 - POD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder JF - Communications in Applied and Industrial Mathematics Y1 - 2017 A1 - Giovanni Stabile A1 - Saddam Hijazi A1 - Andrea Mola A1 - Stefano Lorenzi A1 - Gianluigi Rozza AB -Vortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. In this work a Reduced Order Model (ROM) of the incompressible flow around a circular cylinder, built performing a Galerkin projection of the governing equations onto a lower dimensional space is presented. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pressure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) for this purpose the projection of the Governing equations (momentum equation and Poisson equation for pressure) is performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework are presented. The accuracy of the reduced order model is assessed against full order results.

VL - 8 ER - TY - JOUR T1 - Quasi-periodic solutions for quasi-linear generalized KdV equations JF - Journal of Differential Equations Y1 - 2017 A1 - Filippo Giuliani KW - KAM for PDE's KW - KdV KW - Nash–Moser theory KW - Quasi-linear PDE's KW - Quasi-periodic solutions AB -We prove the existence of Cantor families of small amplitude, linearly stable, quasi-periodic solutions of quasi-linear autonomous Hamiltonian generalized KdV equations. We consider the most general quasi-linear quadratic nonlinearity. The proof is based on an iterative Nash–Moser algorithm. To initialize this scheme, we need to perform a bifurcation analysis taking into account the strongly perturbative effects of the nonlinearity near the origin. In particular, we implement a weak version of the Birkhoff normal form method. The inversion of the linearized operators at each step of the iteration is achieved by pseudo-differential techniques, linear Birkhoff normal form algorithms and a linear KAM reducibility scheme.

VL - 262 UR - http://www.sciencedirect.com/science/article/pii/S0022039617300487 ER - TY - JOUR T1 - Quasistatic crack growth based on viscous approximation: a model with branching and kinking JF - Nonlinear Differential Equations and Applications NoDEA Y1 - 2017 A1 - Vito Crismale A1 - Giuliano Lazzaroni AB -Employing the technique of vanishing viscosity and time rescaling, we show the existence of quasistatic evolutions of cracks in brittle materials in the setting of antiplane shear. The crack path is not prescribed a priori and is chosen in an admissible class of piecewise regular sets that allows for branching and kinking.

VL - 24 UR - https://doi.org/10.1007/s00030-016-0426-6 ER - TY - JOUR T1 - Reduced Basis Methods for Uncertainty Quantification JF - SIAM/ASA Journal on Uncertainty Quantification Y1 - 2017 A1 - Peng Chen A1 - Alfio Quarteroni A1 - Gianluigi Rozza AB -In this work we review a reduced basis method for the solution of uncertainty quantification problems. Based on the basic setting of an elliptic partial differential equation with random input, we introduce the key ingredients of the reduced basis method, including proper orthogonal decomposition and greedy algorithms for the construction of the reduced basis functions, a priori and a posteriori error estimates for the reduced basis approximations, as well as its computational advantages and weaknesses in comparison with a stochastic collocation method [I. Babuška, F. Nobile, and R. Tempone, *SIAM Rev.*, 52 (2010), pp. 317--355]. We demonstrate its computational efficiency and accuracy for a benchmark problem with parameters ranging from a few to a few hundred dimensions. Generalizations to more complex models and applications to uncertainty quantification problems in risk prediction, evaluation of statistical moments, Bayesian inversion, and optimal control under uncertainty are also presented to illustrate how to use the reduced basis method in practice. Further challenges, advancements, and research opportunities are outlined.

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

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

JF - Model Reduction of Parametrized Systems PB - Springer International Publishing ER - TY - RPRT T1 - Regularity estimates for scalar conservation laws in one space dimension Y1 - 2017 A1 - Elio Marconi AB - In this paper we deal with the regularizing effect that, in a scalar conservation laws in one space dimension, the nonlinearity of the flux function ƒ has on the entropy solution. More precisely, if the set ⟨w : ƒ " (w) ≠ 0⟩ is dense, the regularity of the solution can be expressed in terms of BV Ф spaces, where Ф depends on the nonlinearity of ƒ. If moreover the set ⟨w : ƒ " (w) = 0⟩ is finite, under the additional polynomial degeneracy condition at the inflection points, we prove that ƒ' 0 u(t) ∈ BVloc (R) for every t > 0 and that this can be improved to SBVloc (R) regularity except an at most countable set of singular times. Finally we present some examples that shows the sharpness of these results and counterexamples to related questions, namely regularity in the kinetic formulation and a property of the fractional BV spaces. UR - http://preprints.sissa.it/handle/1963/35291 U1 - 35597 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Second order differentiation formula on compact RCD*(K,N) spaces Y1 - 2017 A1 - Nicola Gigli A1 - Luca Tamanini ER - TY - JOUR T1 - Small Time Asymptotics on the Diagonal for Hörmander's Type Hypoelliptic Operators JF - Journal of Dynamical and Control Systems Y1 - 2017 A1 - Elisa Paoli AB -We compute the small time asymptotics of the fundamental solution of Hörmander's type hypoelliptic operators with drift, on the diagonal at a point x0. We show that the order of the asymptotics depends on the controllability of an associated control problem and of its approximating system. If the control problem of the approximating system is controllable at x0, then so is also the original control problem, and in this case we show that the fundamental solution blows up as t−N/2\$\backslashphantom {\backslashdot {i}\backslash!}t^{-\backslashmathcal {N}/2}\$, where N\$\backslashphantom {\backslashdot {i}\backslash!}\backslashmathcal {N}\$is a number determined by the Lie algebra at x0 of the fields, that define the hypoelliptic operator.

VL - 23 UR - https://doi.org/10.1007/s10883-016-9321-z ER - TY - JOUR T1 - Stasis domains and slip surfaces in the locomotion of a bio-inspired two-segment crawler JF - Meccanica Y1 - 2017 A1 - Paolo Gidoni A1 - Antonio DeSimone AB -We formulate and solve the locomotion problem for a bio-inspired crawler consisting of two active elastic segments (i.e., capable of changing their rest lengths), resting on three supports providing directional frictional interactions. The problem consists in finding the motion produced by a given, slow actuation history. By focusing on the tensions in the elastic segments, we show that the evolution laws for the system are entirely analogous to the flow rules of elasto-plasticity. In particular, sliding of the supports and hence motion cannot occur when the tensions are in the interior of certain convex regions (stasis domains), while support sliding (and hence motion) can only take place when the tensions are on the boundary of such regions (slip surfaces). We solve the locomotion problem explicitly in a few interesting examples. In particular, we show that, for a suitable range of the friction parameters, specific choices of the actuation strategy can lead to net displacements also in the direction of higher friction.

VL - 52 UR - https://doi.org/10.1007/s11012-016-0408-0 ER - TY - RPRT T1 - Time quasi-periodic gravity water waves in finite depth Y1 - 2017 A1 - P Baldi A1 - Massimiliano Berti A1 - Emanuele Haus A1 - Riccardo Montalto AB - We prove the existence and the linear stability of Cantor families of small amplitude time quasi-periodic standing water wave solutions - namely periodic and even in the space variable x - of a bi-dimensional ocean with finite depth under the action of pure gravity. Such a result holds for all the values of the depth parameter in a Borel set of asymptotically full measure. This is a small divisor problem. The main difficulties are the quasi-linear nature of the gravity water waves equations and the fact that the linear frequencies grow just in a sublinear way at infinity. We overcome these problems by first reducing the linearized operators obtained at each approximate quasi-periodic solution along the Nash-Moser iteration to constant coefficients up to smoothing operators, using pseudo-differential changes of variables that are quasi-periodic in time. Then we apply a KAM reducibility scheme which requires very weak Melnikov non-resonance conditions (losing derivatives both in time and space), which we are able to verify for most values of the depth parameter using degenerate KAM theory arguments. UR - http://preprints.sissa.it/handle/1963/35296 U1 - 35602 U2 - Mathematics ER - TY - RPRT T1 - A uniqueness result for the decomposition of vector fields in Rd Y1 - 2017 A1 - Stefano Bianchini A1 - Paolo Bonicatto AB -Given a vector field $\rho (1,\b) \in L^1_\loc(\R^+\times \R^{d},\R^{d+1})$ such that $\dive_{t,x} (\rho (1,\b))$ is a measure, we consider the problem of uniqueness of the representation $\eta$ of $\rho (1,\b) \mathcal L^{d+1}$ as a superposition of characteristics $\gamma : (t^-_\gamma,t^+_\gamma) \to \R^d$, $\dot \gamma (t)= \b(t,\gamma(t))$. We give conditions in terms of a local structure of the representation $\eta$ on suitable sets in order to prove that there is a partition of $\R^{d+1}$ into disjoint trajectories $\wp_\a$, $\a \in \A$, such that the PDE \begin{equation*} \dive_{t,x} \big( u \rho (1,\b) \big) \in \mathcal M(\R^{d+1}), \qquad u \in L^\infty(\R^+\times \R^{d}), \end{equation*} can be disintegrated into a family of ODEs along $\wp_\a$ with measure r.h.s.. The decomposition $\wp_\a$ is essentially unique. We finally show that $\b \in L^1_t(\BV_x)_\loc$ satisfies this local structural assumption and this yields, in particular, the renormalization property for nearly incompressible $\BV$ vector fields.

PB - SISSA UR - http://preprints.sissa.it/handle/1963/35274 U1 - 35581 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Wet and Dry Transom Stern Treatment for Unsteady and Nonlinear Potential Flow Model for Naval Hydrodynamics Simulations JF - Journal of Ship Research Y1 - 2017 A1 - Andrea Mola A1 - Luca Heltai A1 - Antonio DeSimone AB -We present a model for the fast evaluation of the total drag of ship hulls operating in both wet and dry transom stern conditions, in calm or wavy water, based on the combination of an unsteady semi-Lagrangian potential flow formulation with fully nonlinear free-surface treatment, experimental correlations, and simplified viscous drag modeling. The implementation is entirely based on open source libraries. The spatial discretization is solved using a streamline upwind Petrov‐Galerkin stabilization of an iso-parametric, collocation based, boundary element method, implemented using the open source library deal.II. The resulting nonlinear differential-algebraic system is integrated in time using implicit backward differentiation formulas, implemented in the open source library SUNDIALS. The Open CASCADE library is used to interface the model directly with computer-aided design data structures. The model accounts automatically for hulls with a transom stern, both in wet and dry regimes, by using a specific treatment of the free-surface nodes on the stern edge that automatically detects when the hull advances at low speeds. In this case, the transom stern is partially immersed, and a pressure patch is applied on the water surface detaching from the transom stern, to recover the gravity effect of the recirculating water on the underlying irrotational flow domain. The parameters of the model used to impose the pressure patch are approximated from experimental relations found in the literature. The test cases considered are those of the U.S. Navy Combatant DTMB-5415 and the National Physical Laboratory hull. Comparisons with experimental data on quasi-steady test cases for both water elevation and total hull drag are presented and discussed. The quality of the results obtained on quasi-steady simulations suggests that this model can represent a promising alternative to current unsteady solvers for simulations with Froude numbers below 0.35.

VL - 61 ER - TY - CONF T1 - Advances in geometrical parametrization and reduced order models and methods for computational fluid dynamics problems in applied sciences and engineering: overview and perspectives T2 - Proceedings of the ECCOMAS Congress 2016, VII European Conference on Computational Methods in Applied Sciences and Engineering, Y1 - 2016 A1 - Filippo Salmoiraghi A1 - F. Ballarin A1 - Giovanni Corsi A1 - Andrea Mola A1 - Marco Tezzele A1 - Gianluigi Rozza ED - Papadrakakis, M. ED - Papadopoulos, V. ED - Stefanou, G. ED - Plevris, V. AB -Several problems in applied sciences and engineering require reduction techniques in order to allow computational tools to be employed in the daily practice, especially in iterative procedures such as optimization or sensitivity analysis. Reduced order methods need to face increasingly complex problems in computational mechanics, especially into a multiphysics setting. Several issues should be faced: stability of the approximation, efficient treatment of nonlinearities, uniqueness or possible bifurcations of the state solutions, proper coupling between fields, as well as offline-online computing, computational savings and certification of errors as measure of accuracy. Moreover, efficient geometrical parametrization techniques should be devised to efficiently face shape optimization problems, as well as shape reconstruction and shape assimilation problems. A related aspect deals with the management of parametrized interfaces in multiphysics problems, such as fluid-structure interaction problems, and also a domain decomposition based approach for complex parametrized networks. We present some illustrative industrial and biomedical problems as examples of recent advances on methodological developments.

JF - Proceedings of the ECCOMAS Congress 2016, VII European Conference on Computational Methods in Applied Sciences and Engineering, PB - ECCOMAS CY - Crete, Greece U1 - 35466 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - On the area of the graph of a piecewise smooth map from the plane to the plane with a curve discontinuity JF - ESAIM: COCV Y1 - 2016 A1 - Giovanni Bellettini A1 - Lucia Tealdi A1 - Maurizio Paolini KW - Area functional AB -In this paper we provide an estimate from above for the value of the relaxed area functional for a map defined on a bounded domain of the plane with values in the plane and discontinuous on a regular simple curve with two endpoints. We show that, under suitable assumptions, the relaxed area does not exceed the area of the regular part of the map, with the addition of a singular term measuring the area of a disk type solution of the Plateau's problem spanning the two traces of the map on the jump. The result is valid also when the area minimizing surface has self intersections. A key element in our argument is to show the existence of what we call a semicartesian parametrization of this surface, namely a conformal parametrization defined on a suitable parameter space, which is the identity in the first component. To prove our result, various tools of parametric minimal surface theory are used, as well as some result from Morse theory.

VL - 22 UR - https://www.esaim-cocv.org/articles/cocv/abs/2016/01/cocv140065/cocv140065.html IS - 1 U1 - 7257 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - RPRT T1 - Behaviour of the reference measure on RCD spaces under charts Y1 - 2016 A1 - Nicola Gigli A1 - Enrico Pasqualetto ER - TY - JOUR T1 - On the concentration of entropy for scalar conservation laws JF - Discrete & Continuous Dynamical Systems - S Y1 - 2016 A1 - Stefano Bianchini A1 - Elio Marconi KW - concentration KW - Conservation laws KW - entropy solutions KW - Lagrangian representation KW - shocks AB -We prove that the entropy for an $L^∞$-solution to a scalar conservation laws with continuous initial data is concentrated on a countably $1$-rectifiable set. To prove this result we introduce the notion of Lagrangian representation of the solution and give regularity estimates on the solution.

VL - 9 UR - http://aimsciences.org//article/id/ce4eb91e-9553-4e8d-8c4c-868f07a315ae ER - TY - JOUR T1 - Confinement of dislocations inside a crystal with a prescribed external strain Y1 - 2016 A1 - Ilaria Lucardesi A1 - Marco Morandotti A1 - Riccardo Scala A1 - Davide Zucco AB - We study screw dislocations in an isotropic crystal undergoing antiplane shear. In the framework of linear elasticity, by fixing a suitable boundary condition for the strain (prescribed non-vanishing boundary integral), we manage to confine the dislocations inside the material. More precisely, in the presence of an external strain with circulation equal to n times the lattice spacing, it is energetically convenient to have n distinct dislocations lying inside the crystal. The novelty of introducing a Dirichlet boundary condition for the tangential strain is crucial to the confinement: it is well known that, if Neumann boundary conditions are imposed, the dislocations tend to migrate to the boundary. The results are achieved using PDE techniques and Ƭ-convergence theory, in the framework of the so-called core radius approach. UR - http://urania.sissa.it/xmlui/handle/1963/35247 N1 - Preprint SISSA 20/2016/MATE U1 - 35558 U2 - Mathematics ER - TY - JOUR T1 - Conformal Equivalence of 3D Contact Structures on Lie Groups JF - Journal of Dynamical and Control Systems Y1 - 2016 A1 - Francesco Boarotto AB -In this paper, a conformal classification of three dimensional left-invariant sub-Riemannian contact structures is carried out; in particular, we will prove the following dichotomy: either a structure is locally conformal to the Heisenberg group $mathbbH^3$ or its conformal classification coincides with the metric one. If a structure is locally conformally flat, then its conformal group is locally isomorphic to $SU(2,1)$.

VL - 22 UR - https://doi.org/10.1007/s10883-015-9273-8 ER - TY - JOUR T1 - Critical points of a perturbed Otha-Kawasaki functional JF - arXiv preprint arXiv:1601.07093 Y1 - 2016 A1 - Matteo Rizzi ER - TY - JOUR T1 - Currents and dislocations at the continuum scale JF - Methods and Applications of Analysis Y1 - 2016 A1 - Riccardo Scala A1 - Nicolas Van Goethem AB -A striking geometric property of elastic bodies with dislocations is that the deformation tensor cannot be written as the gradient of a one-to-one immersion, its curl being nonzero and equal to the density of the dislocations, a measure concentrated in the dislocation lines. In this work, we discuss the mathematical properties of such constrained deformations and study a variational problem in finite-strain elasticity, where Cartesian maps allow us to consider deformations in $L^p$ with $1\leq p<2$, as required for dislocation-induced strain singularities. Firstly, we address the problem of mathematical modeling of dislocations. It is a key purpose of the paper to build a framework where dislocations are described in terms of integral 1-currents and to extract from this theoretical setting a series of notions having a mechanical meaning in the theory of dislocations. In particular, the paper aims at classifying integral 1-currents, with modeling purposes. In the second part of the paper, two variational problems are solved for two classes of dislocations, at the mesoscopic and at the continuum scale. By continuum it is here meant that a countable family of dislocations is considered, allowing for branching and cluster formation, with possible complex geometric patterns. Therefore, modeling assumptions of the defect part of the energy must also be provided, and discussed.

PB - International Press of Boston VL - 23 ER - TY - RPRT T1 - Equivalence of two different notions of tangent bundle on rectifiable metric measure spaces Y1 - 2016 A1 - Nicola Gigli A1 - Enrico Pasqualetto ER - TY - RPRT T1 - Eulerian, Lagrangian and Broad continuous solutions to a balance law with non convex flux II Y1 - 2016 A1 - Giovanni Alberti A1 - Stefano Bianchini A1 - Laura Caravenna UR - http://urania.sissa.it/xmlui/handle/1963/35197 U1 - 35494 U2 - Mathematics ER - TY - JOUR T1 - Eulerian, Lagrangian and Broad continuous solutions to a balance law with non-convex flux I JF - Journal of Differential Equations, vol. 261, issue 8 (2016): 4298-4337 Y1 - 2016 A1 - Giovanni Alberti A1 - Stefano Bianchini A1 - Laura Caravenna PB - Elsevier UR - http://urania.sissa.it/xmlui/handle/1963/35207 U1 - 35507 U2 - Mathematics ER - TY - JOUR T1 - Existence and non-existence results for the SU(3) singular Toda system on compact surfaces JF - Journal of Functional Analysis Y1 - 2016 A1 - Luca Battaglia A1 - Andrea Malchiodi KW - Liouville-type equations KW - Min–max solutions KW - Non-existence results KW - Toda system AB -We consider the SU(3) singular Toda system on a compact surface (Σ,g)−Δu1=2ρ1(h1eu1∫Σh1eu1dVg−1)−ρ2(h2eu2∫Σh2eu2dVg−1)−4π∑m=1Mα1m(δpm−1)−Δu2=2ρ2(h2eu2∫Σh2eu2dVg−1)−ρ1(h1eu1∫Σh1eu1dVg−1)−4π∑m=1Mα2m(δpm−1), where hi are smooth positive functions on Σ, ρi∈R+, pm∈Σ and αim>−1. We give both existence and non-existence results under some conditions on the parameters ρi and αim. Existence results are obtained using variational methods, which involve a geometric inequality of new type; non-existence results are obtained using blow-up analysis and localized Pohožaev-type identities."

VL - 270 UR - http://www.sciencedirect.com/science/article/pii/S0022123615004942 ER - TY - JOUR T1 - Existence and uniqueness of dynamic evolutions for a peeling test in dimension one JF - Journal of Differential Equations Y1 - 2016 A1 - Gianni Dal Maso A1 - Giuliano Lazzaroni A1 - Lorenzo Nardini KW - Dynamic debonding KW - Dynamic energy release rate KW - Dynamic fracture KW - Griffith's criterion KW - Maximum dissipation principle KW - Wave equation in time-dependent domains AB -In this paper we present a one-dimensional model of a dynamic peeling test for a thin film, where the wave equation is coupled with a Griffith criterion for the propagation of the debonding front. Our main results provide existence and uniqueness for the solution to this coupled problem under different assumptions on the data.

VL - 261 UR - http://www.sciencedirect.com/science/article/pii/S0022039616301772 ER - TY - RPRT T1 - A fast virtual surgery platform for many scenarios haemodynamics of patient-specific coronary artery bypass grafts Y1 - 2016 A1 - F. Ballarin A1 - Elena Faggiano A1 - Andrea Manzoni A1 - Gianluigi Rozza A1 - Alfio Quarteroni A1 - Sonia Ippolito A1 - Roberto Scrofani A1 - Carlo Antona AB - A fast computational framework is devised to the study of several configurations of patient-specific coronary artery bypass grafts. This is especially useful to perform a sensitivity analysis of the haemodynamics for different flow conditions occurring in native coronary arteries and bypass grafts, the investigation of the progression of the coronary artery disease and the choice of the most appropriate surgical procedure. A complete pipeline, from the acquisition of patientspecific medical images to fast parametrized computational simulations, is proposed. Complex surgical configurations employed in the clinical practice, such as Y-grafts and sequential grafts, are studied. A virtual surgery platform based on model reduction of unsteady Navier Stokes equations for blood dynamics is proposed to carry out sensitivity analyses in a very rapid and reliable way. A specialized geometrical parametrization is employed to compare the effect of stenosis and anastomosis variation on the outcome of the surgery in several relevant cases. PB - Submitted UR - http://urania.sissa.it/xmlui/handle/1963/35240 U1 - 35545 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - Fracture models for elasto-plastic materials as limits of gradient damage models coupled with plasticity: the antiplane case JF - Calculus of Variations and Partial Differential Equations Y1 - 2016 A1 - Gianni Dal Maso A1 - Gianluca Orlando A1 - Rodica Toader AB -We study the asymptotic behavior of a variational model for damaged elasto-plastic materials in the case of antiplane shear. The energy functionals we consider depend on a small parameter $\varepsilon$, which forces damage concentration on regions of codimension one. We determine the $\Gamma$-limit as $\varepsilon$ tends to zero and show that it contains an energy term involving the crack opening.

VL - 55 UR - https://doi.org/10.1007/s00526-016-0981-z ER - TY - JOUR T1 - Generalizing the Poincaré–Miranda theorem: the avoiding cones condition JF - Annali di Matematica Pura ed Applicata (1923 -) Y1 - 2016 A1 - Alessandro Fonda A1 - Paolo Gidoni AB -After proposing a variant of the Poincaré–Bohl theorem, we extend the Poincaré–Miranda theorem in several directions, by introducing an avoiding cones condition. We are thus able to deal with functions defined on various types of convex domains, and situations where the topological degree may be different from \$\$\backslashpm \$\$±1. An illustrative application is provided for the study of functionals having degenerate multi-saddle points.

VL - 195 UR - https://doi.org/10.1007/s10231-015-0519-6 ER - TY - JOUR T1 - Globally stable quasistatic evolution for a coupled elastoplastic–damage model JF - ESAIM: Control, Optimisation and Calculus of Variations Y1 - 2016 A1 - Vito Crismale AB -We show the existence of globally stable quasistatic evolutions for a rate-independent material model with elastoplasticity and incomplete damage, in small strain assumptions. The main feature of our model is that the scalar internal variable which describes the damage affects both the elastic tensor and the plastic yield surface. It is also possible to require that the history of plastic strain up to the current state influences the future evolution of damage.

PB - EDP Sciences VL - 22 UR - https://www.esaim-cocv.org/articles/cocv/abs/2016/03/cocv150037/cocv150037.html ER - TY - THES T1 - Integrability of continuous bundles and applications to dynamical systems Y1 - 2016 A1 - Khadim Mbacke War AB - In this dissertation we study the problem of integrability of bundles with low regularities. PB - SISSA U1 - 35529 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - Isogeometric analysis-based reduced order modelling for incompressible linear viscous flows in parametrized shapes Y1 - 2016 A1 - Filippo Salmoiraghi A1 - F. Ballarin A1 - Luca Heltai A1 - Gianluigi Rozza AB - In this work we provide a combination of isogeometric analysis with reduced order modelling techniques, based on proper orthogonal decomposition, to guarantee computational reduction for the numerical model, and with free-form deformation, for versatile geometrical parametrization. We apply it to computational fluid dynamics problems considering a Stokes flow model. The proposed reduced order model combines efficient shape deformation and accurate and stable velocity and pressure approximation for incompressible viscous flows, computed with a reduced order method. Efficient offine-online computational decomposition is guaranteed in view of repetitive calculations for parametric design and optimization problems. Numerical test cases show the efficiency and accuracy of the proposed reduced order model. PB - Springer, AMOS Advanced Modelling and Simulation in Engineering Sciences UR - http://urania.sissa.it/xmlui/handle/1963/35199 U1 - 35493 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - RPRT T1 - Large KAM tori for perturbations of the dNLS equation Y1 - 2016 A1 - Massimiliano Berti A1 - Thomas Kappeler A1 - Riccardo Montalto AB - We prove that small, semi-linear Hamiltonian perturbations of the defocusing nonlinear Schr\"odinger (dNLS) equation on the circle have an abundance of invariant tori of any size and (finite) dimension which support quasi-periodic solutions. When compared with previous results the novelty consists in considering perturbations which do not satisfy any symmetry condition (they may depend on x in an arbitrary way) and need not be analytic. The main difficulty is posed by pairs of almost resonant dNLS frequencies. The proof is based on the integrability of the dNLS equation, in particular the fact that the nonlinear part of the Birkhoff coordinates is one smoothing. We implement a Newton-Nash-Moser iteration scheme to construct the invariant tori. The key point is the reduction of linearized operators, coming up in the iteration scheme, to 2×2 block diagonal ones with constant coefficients together with sharp asymptotic estimates of their eigenvalues. UR - http://preprints.sissa.it/handle/1963/35284 U1 - 35589 U2 - Mathematics ER - TY - RPRT T1 - A model for the quasistatic growth of cracks with fractional dimension Y1 - 2016 A1 - Gianni Dal Maso A1 - Marco Morandotti AB - We study a variational model for the quasistatic growth of cracks with fractional dimension in brittle materials. We give a minimal set of properties of the collection of admissible cracks which ensure the existence of a quasistatic evolution. Both the antiplane and the planar cases are treated. UR - http://urania.sissa.it/xmlui/handle/1963/35175 U1 - 35459 U2 - Mathematics ER - TY - CHAP T1 - Model Order Reduction: a survey T2 - Wiley Encyclopedia of Computational Mechanics, 2016 Y1 - 2016 A1 - Francisco Chinesta A1 - Antonio Huerta A1 - Gianluigi Rozza A1 - Karen Willcox JF - Wiley Encyclopedia of Computational Mechanics, 2016 PB - Wiley UR - http://urania.sissa.it/xmlui/handle/1963/35194 U1 - 35470 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - Moser–Trudinger inequalities for singular Liouville systems JF - Mathematische Zeitschrift Y1 - 2016 A1 - Luca Battaglia AB -In this paper we prove a Moser–Trudinger inequality for the Euler–Lagrange functional of general singular Liouville systems on a compact surface. We characterize the values of the parameters which yield coercivity for the functional, hence the existence of energy-minimizing solutions for the system, and we give necessary conditions for boundedness from below. We also provide a sharp inequality under assuming the coefficients of the system to be non-positive outside the diagonal. The proofs use a concentration-compactness alternative, Pohožaev-type identities and blow-up analysis.

VL - 282 UR - https://doi.org/10.1007/s00209-015-1584-7 ER - TY - JOUR T1 - Motion planning and motility maps for flagellar microswimmers JF - The European Physical Journal E Y1 - 2016 A1 - Giancarlo Cicconofri A1 - Antonio DeSimone AB -We study two microswimmers consisting of a spherical rigid head and a passive elastic tail. In the first one the tail is clamped to the head, and the system oscillates under the action of an external torque. In the second one, head and tail are connected by a joint allowing the angle between them to vary periodically, as a result of an oscillating internal torque. Previous studies on these models were restricted to sinusoidal actuations, showing that the swimmers can propel while moving on average along a straight line, in the direction given by the symmetry axis around which beating takes place. We extend these results to motions produced by generic (non-sinusoidal) periodic actuations within the regime of small compliance of the tail. We find that modulation in the velocity of actuation can provide a mechanism to select different directions of motion. With velocity-modulated inputs, the externally actuated swimmer can translate laterally with respect to the symmetry axis of beating, while the internally actuated one is able to move along curved trajectories. The governing equations are analysed with an asymptotic perturbation scheme, providing explicit formulas, whose results are expressed through motility maps. Asymptotic approximations are further validated by numerical simulations.

VL - 39 UR - https://doi.org/10.1140/epje/i2016-16072-y ER - TY - JOUR T1 - A multi-physics reduced order model for the analysis of Lead Fast Reactor single channel JF - Annals of Nuclear Energy, 87, 2 (2016): pp. 198-208 Y1 - 2016 A1 - Alberto Sartori A1 - Antonio Cammi A1 - Lelio Luzzi A1 - Gianluigi Rozza AB - In this work, a Reduced Basis method, with basis functions sampled by a Proper Orthogonal Decomposition technique, has been employed to develop a reduced order model of a multi-physics parametrized Lead-cooled Fast Reactor single-channel. Being the first time that a reduced order model is developed in this context, the work focused on a methodological approach and the coupling between the neutronics and the heat transfer, where the thermal feedbacks on neutronics are explicitly taken into account, in time-invariant settings. In order to address the potential of such approach, two different kinds of varying parameters have been considered, namely one related to a geometric quantity (i.e., the inner radius of the fuel pellet) and one related to a physical quantity (i.e., the inlet lead velocity). The capabilities of the presented reduced order model (ROM) have been tested and compared with a high-fidelity finite element model (upon which the ROM has been constructed) on different aspects. In particular, the comparison focused on the system reactivity prediction (with and without thermal feedbacks on neutronics), the neutron flux and temperature field reconstruction, and on the computational time. The outcomes provided by the reduced order model are in good agreement with the high-fidelity finite element ones, and a computational speed-up of at least three orders of magnitude is achieved as well. PB - Elsevier VL - 87 UR - http://urania.sissa.it/xmlui/handle/1963/35191 U1 - 35471 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - New existence results for the mean field equation on compact surfaces via degree theory JF - Rend. Sem. Mat. Univ. Padova Y1 - 2016 A1 - Aleks Jevnikar VL - 136 ER - TY - RPRT T1 - Non-linear Schrödinger system for the dynamics of a binary condensate: theory and 2D numerics Y1 - 2016 A1 - Alessandro Michelangeli A1 - Giuseppe Pitton AB - We present a comprehensive discussion of the mathematical framework for binary Bose-Einstein condensates and for the rigorous derivation of their effective dynamics, governed by a system of coupled non-linear Gross-Pitaevskii equations. We also develop in the 2D case a systematic numerical study of the Gross-Pitaevskii systems in a wide range of relevant regimes of population ratios and intra-species and inter-species interactions. Our numerical method is based on a Fourier collocation scheme in space combined with a fourth order integrating factor scheme in time. UR - http://urania.sissa.it/xmlui/handle/1963/35266 U1 - 35572 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - A note on a multiplicity result for the mean field equation on compact surfaces JF - Advanced Nonlinear Studies Y1 - 2016 A1 - Aleks Jevnikar PB - De Gruyter VL - 16 ER - TY - JOUR T1 - Pairs of positive periodic solutions of nonlinear ODEs with indefinite weight: a topological degree approach for the super-sublinear case JF - Proc. Roy. Soc. Edinburgh Sect. A 146 (2016), 449–474. Y1 - 2016 A1 - Alberto Boscaggin A1 - Guglielmo Feltrin A1 - Fabio Zanolin AB -We study the periodic and Neumann boundary value problems associated with the second order nonlinear differential equation u''+cu'+λa(t)g(u)=0, where g:[0,+∞[→[0,+∞[ is a sublinear function at infinity having superlinear growth at zero. We prove the existence of two positive solutions when ∫a(t)dt 0 is sufficiently large. Our approach is based on Mawhin's coincidence degree theory and index computations.

PB - Cambridge University Press UR - http://urania.sissa.it/xmlui/handle/1963/35262 N1 - AMS Subject Classification: Primary 34B18; 34C25; Secondary 34B15; 47H11; U1 - 35566 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Periodic perturbations of Hamiltonian systems JF - Advances in Nonlinear Analysis Y1 - 2016 A1 - Alessandro Fonda A1 - Maurizio Garrione A1 - Paolo Gidoni AB -We prove existence and multiplicity results for periodic solutions of Hamiltonian systems, by the use of a higher dimensional version of the Poincaré–Birkhoff fixed point theorem. The first part of the paper deals with periodic perturbations of a completely integrable system, while in the second part we focus on some suitable global conditions, so to deal with weakly coupled systems.

PB - De Gruyter VL - 5 ER - TY - JOUR T1 - POD-Galerkin Method for Finite Volume Approximation of Navier-Stokes and RANS Equations Y1 - 2016 A1 - Stefano Lorenzi A1 - Antonio Cammi A1 - Lelio Luzzi A1 - Gianluigi Rozza AB - Numerical simulation of fluid flows requires important computational efforts but it is essential in engineering applications. Reduced Order Model (ROM) can be employed whenever fast simulations are required, or in general, whenever a trade-off between computational cost and solution accuracy is a preeminent issue as in process optimization and control. In this work, the efforts have been put to develop a ROM for Computational Fluid Dynamics (CFD) application based on Finite Volume approximation, starting from the results available in turbulent Reynold-Averaged Navier Stokes simulations in order to enlarge the application field of Proper Orthogonal Decomposition – Reduced Order Model (POD – ROM) technique to more industrial fields. The approach is tested in the classic benchmark of the numerical simulation of the 2D lid-driven cavity. In particular, two simulations at Re = 103 and Re = 105 have been considered in order to assess both a laminar and turbulent case. Some quantities have been compared with the Full Order Model in order to assess the performance of the proposed ROM procedure i.e., the kinetic energy of the system and the reconstructed quantities of interest (velocity, pressure and turbulent viscosity). In addition, for the laminar case, the comparison between the ROM steady-state solution and the data available in literature has been presented. The results have turned out to be very satisfactory both for the accuracy and the computational times. As a major outcome, the approach turns out not to be affected by the energy blow up issue characterizing the results obtained by classic turbulent POD-Galerkin methods. PB - Computer Methods in Applied Mechanics and Engineering, Elsevier U1 - 35502 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - POD–Galerkin monolithic reduced order models for parametrized fluid-structure interaction problems JF - International Journal Numerical Methods for Fluids Y1 - 2016 A1 - F. Ballarin A1 - Gianluigi Rozza AB - In this paper we propose a monolithic approach for reduced order modelling of parametrized fluid-structure interaction problems based on a proper orthogonal decomposition (POD)–Galerkin method. Parameters of the problem are related to constitutive properties of the fluid or structural problem, or to geometrical parameters related to the domain configuration at the initial time. We provide a detailed description of the parametrized formulation of the multiphysics problem in its components, together with some insights on how to obtain an offline-online efficient computational procedure through the approximation of parametrized nonlinear tensors. Then, we present the monolithic POD–Galerkin method for the online computation of the global structural displacement, fluid velocity and pressure of the coupled problem. Finally, we show some numerical results to highlight the capabilities of the proposed reduced order method and its computational performances PB - Wiley U1 - 35465 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - THES T1 - Positive solutions to indefinite problems: a topological approach Y1 - 2016 A1 - Guglielmo Feltrin KW - positive solutions AB - The present Ph.D. thesis is devoted to the study of positive solutions to indefinite problems. In particular, we deal with the second order nonlinear differential equation u'' + a(t) g(u) = 0, where g : [0,+∞[→[0,+∞[ is a continuous nonlinearity and a : [0,T]→R is a Lebesgue integrable sign-changing weight. We analyze the Dirichlet, Neumann and periodic boundary value problems on [0,T] associated with the equation and we provide existence, nonexistence and multiplicity results for positive solutions. In the first part of the manuscript, we investigate nonlinearities g(u) with a superlinear growth at zero and at infinity (including the classical superlinear case g(u)=u^p, with p>1). In particular, we prove that there exist 2^m-1 positive solutions when a(t) has m positive humps separated by negative ones and the negative part of a(t) is sufficiently large. Then, for the Dirichlet problem, we solve a conjecture by Gómez‐Reñasco and López‐Gómez (JDE, 2000) and, for the periodic problem, we give a complete answer to a question raised by Butler (JDE, 1976). In the second part, we study the super-sublinear case (i.e. g(u) is superlinear at zero and sublinear at infinity). If a(t) has m positive humps separated by negative ones, we obtain the existence of 3^m-1 positive solutions of the boundary value problems associated with the parameter-dependent equation u'' + λ a(t) g(u) = 0, when both λ>0 and the negative part of a(t) are sufficiently large. We propose a new approach based on topological degree theory for locally compact operators on open possibly unbounded sets, which applies for Dirichlet, Neumann and periodic boundary conditions. As a byproduct of our method, we obtain infinitely many subharmonic solutions and globally defined positive solutions with complex behavior, and we deal with chaotic dynamics. Moreover, we study positive radially symmetric solutions to the Dirichlet and Neumann problems associated with elliptic PDEs on annular domains. Furthermore, this innovative technique has the potential and the generality needed to deal with indefinite problems with more general differential operators. Indeed, our approach apply also for the non-Hamiltonian equation u'' + cu' + a(t) g(u) = 0. Meanwhile, more general operators in the one-dimensional case and problems involving PDEs will be subjects of future investigations. PB - SISSA N1 - The research work described in this Ph.D. thesis has produced 10 papers. U1 - 35528 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - A quadratic interaction estimate for conservation laws: motivations, techniques and open problems JF - Bulletin of the Brazilian Mathematical Society, New Series Y1 - 2016 A1 - Stefano Modena AB -In a series of joint works with S. Bianchini [3, 4, 5], we proved a quadratic interaction estimate for general systems of conservation laws. Aim of this paper is to present the results obtained in the three cited articles [3, 4, 5], discussing how they are related with the general theory of hyperbolic conservation laws. To this purpose, first we explain why this quadratic estimate is interesting, then we give a brief overview of the techniques we used to prove it and finally we present some related open problems.

VL - 47 UR - https://doi.org/10.1007/s00574-016-0171-9 ER - TY - JOUR T1 - Quadratic interaction estimate for hyperbolic conservation laws, an overview JF - Contemporary Mathematics. Fundamental Directions Y1 - 2016 A1 - Stefano Modena PB - Peoples' Friendship University of Russia VL - 59 ER - TY - THES T1 - Qualitative properties and construction of solutions to some semilinear elliptic PDEs Y1 - 2016 A1 - Matteo Rizzi KW - moving planes method, maximum principle, Lyapunov-Schmidt reduction, Willmore surfaces, Otha-Kawasaki functional AB - This thesis is devoted to the study of elliptic equations. On the one hand, we study some qualitative properties, such as symmetry of solutions, on the other hand we explicitly construct some solutions vanishing near some fixed manifold. The main techniques are the moving planes method, in order to investigate the qualitative properties and the Lyapunov-Schmidt reduction. PB - SISSA U1 - 35500 U5 - MAT/05 ER - TY - RPRT T1 - Quasi-static hydraulic crack growth driven by Darcy's law Y1 - 2016 A1 - Stefano Almi AB -In the framework of rate independent processes, we present a variational model of quasi-static crack growth in hydraulic fracture. We first introduce the energy functional and study the equilibrium conditions of an unbounded linearly elastic body subject to a remote strain ε ∈ R and with a sufficiently regular crack Γ filled by a volume V of incompressible fluid. In particular, we are able to find the pressure p of the fluid inside the crack as a function of Γ, V , and ε. Then, we study the problem of quasi-static evolution for our model, imposing that the fluid volume V and the fluid pressure p are related by Darcy’s law. We show the existence of such an evolution, and we prove that it satisfies a weak notion of the so-called Griffith’s criterion.

UR - http://urania.sissa.it/xmlui/handle/1963/35198 U1 - 35492 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - A Reduced Basis Approach for Modeling the Movement of Nuclear Reactor Control Rods JF - NERS-14-1062; ASME J of Nuclear Rad Sci, 2, 2 (2016) 021019 Y1 - 2016 A1 - Alberto Sartori A1 - Antonio Cammi A1 - Lelio Luzzi A1 - Gianluigi Rozza AB - This work presents a reduced order model (ROM) aimed at simulating nuclear reactor control rods movement and featuring fast-running prediction of reactivity and neutron flux distribution as well. In particular, the reduced basis (RB) method (built upon a high-fidelity finite element (FE) approximation) has been employed. The neutronics has been modeled according to a parametrized stationary version of the multigroup neutron diffusion equation, which can be formulated as a generalized eigenvalue problem. Within the RB framework, the centroidal Voronoi tessellation is employed as a sampling technique due to the possibility of a hierarchical parameter space exploration, without relying on a “classical” a posteriori error estimation, and saving an important amount of computational time in the offline phase. Here, the proposed ROM is capable of correctly predicting, with respect to the high-fidelity FE approximation, both the reactivity and neutron flux shape. In this way, a computational speedup of at least three orders of magnitude is achieved. If a higher precision is required, the number of employed basis functions (BFs) must be increased. PB - ASME VL - 2 UR - http://urania.sissa.it/xmlui/handle/1963/35192 IS - 2 N1 - 8 pages U1 - 35473 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries JF - Computers and Mathematics with Applications Y1 - 2016 A1 - Laura Iapichino A1 - Alfio Quarteroni A1 - Gianluigi Rozza AB - The aim of this work is to solve parametrized partial differential equations in computational domains represented by networks of repetitive geometries by combining reduced basis and domain decomposition techniques. The main idea behind this approach is to compute once, locally and for few reference shapes, some representative finite element solutions for different values of the parameters and with a set of different suitable boundary conditions on the boundaries: these functions will represent the basis of a reduced space where the global solution is sought for. The continuity of the latter is assured by a classical domain decomposition approach. Test results on Poisson problem show the flexibility of the proposed method in which accuracy and computational time may be tuned by varying the number of reduced basis functions employed, or the set of boundary conditions used for defining locally the basis functions. The proposed approach simplifies the pre-computation of the reduced basis space by splitting the global problem into smaller local subproblems. Thanks to this feature, it allows dealing with arbitrarily complex network and features more flexibility than a classical global reduced basis approximation where the topology of the geometry is fixed. PB - Elsevier VL - 71 IS - 1 U1 - 35187 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - Renormalization for Autonomous Nearly Incompressible BV Vector Fields in Two Dimensions JF - SIAM Journal on Mathematical Analysis Y1 - 2016 A1 - Stefano Bianchini A1 - Paolo Bonicatto A1 - N.A. Gusev AB -Given a bounded autonomous vector field $b \colon \mathbb{R}^d \to \mathbb{R}^d$, we study the uniqueness of bounded solutions to the initial value problem for the related transport equation \begin{equation*} \partial_t u + b \cdot \nabla u= 0. \end{equation*} We are interested in the case where $b$ is of class BV and it is nearly incompressible. Assuming that the ambient space has dimension $d=2$, we prove uniqueness of weak solutions to the transport equation. The starting point of the present work is the result which has been obtained in [7] (where the steady case is treated). Our proof is based on splitting the equation onto a suitable partition of the plane: this technique was introduced in [3], using the results on the structure of level sets of Lipschitz maps obtained in [1]. Furthermore, in order to construct the partition, we use Ambrosio's superposition principle [4].

VL - 48 UR - https://doi.org/10.1137/15M1007380 ER - TY - RPRT T1 - Second-order structured deformations Y1 - 2016 A1 - Ana Cristina Barroso A1 - Jose Matias A1 - Marco Morandotti A1 - David R. Owen PB - SISSA U1 - 35497 U2 - Mathematics U4 - 1 ER - TY - CONF T1 - Ship Sinkage and Trim Predictions Based on a CAD Interfaced Fully Nonlinear Potential Model T2 - The 26th International Ocean and Polar Engineering Conference Y1 - 2016 A1 - Andrea Mola A1 - Luca Heltai A1 - Antonio DeSimone A1 - Massimiliano Berti JF - The 26th International Ocean and Polar Engineering Conference PB - International Society of Offshore and Polar Engineers VL - 3 ER - TY - THES T1 - Some results on quasistatic evolution problems for unidirectional processes Y1 - 2016 A1 - Vito Crismale PB - SISSA U1 - 35522 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - THES T1 - Some results on the mathematical analysis of crack problems with forces applied on the fracture lips Y1 - 2016 A1 - Stefano Almi KW - Fracture mechanics AB - This thesis is devoted to the study of some models of fracture growth in elastic materials, characterized by the presence of forces acting on the crack lips. Working in the general framework of rate-independent processes, we first discuss a variational formulation of the problem of quasi-static crack evolution in hydraulic fracture. Then, we investigate the crack growth process in a cohesive fracture model, showing the existence of an evolution satisfying a weak Griffith's criterion. Finally, in the last chapter of this work we investigate, in the static case, the interaction between the energy spent in order to create a new fracture and the energy spent by the applied surface forces. This leads us to study the lower semicontinuity properties of a free discontinuity functional F(u) that can be written as the sum of a crack term, depending on the jump set of u, and of a boundary term, depending on the trace of u. PB - SISSA U1 - 35503 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Spectral analysis and the Aharonov-Bohm effect on certain almost-Riemannian manifolds JF - Communications in Partial Differential Equations Y1 - 2016 A1 - Ugo Boscain A1 - Dario Prandi A1 - M. Seri AB -We study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. This operator contains first order diverging terms caused by the divergence of the volume. We get explicit descriptions of the spectrum and the eigenfunctions. In particular in both cases we get a Weyl's law with leading term Elog E. We then study the drastic effect of Aharonov-Bohm magnetic potentials on the spectral properties. Other generalized Riemannian structures including conic and anti-conic type manifolds are also studied. In this case, the Aharonov-Bohm magnetic potential may affect the self-adjointness of the Laplace-Beltrami operator.

PB - Taylor & Francis VL - 41 UR - https://doi.org/10.1080/03605302.2015.1095766 ER - TY - RPRT T1 - On the structure of $L^\infty$-entropy solutions to scalar conservation laws in one-space dimension Y1 - 2016 A1 - Stefano Bianchini A1 - Elio Marconi AB -We prove that if $u$ is the entropy solution to a scalar conservation law in one space dimension, then the entropy dissipation is a measure concentrated on countably many Lipschitz curves. This result is a consequence of a detailed analysis of the structure of the characteristics. In particular the characteristic curves are segments outside a countably 1-rectifiable set and the left and right traces of the solution exist in a $C^0$-sense up to the degeneracy due to the segments where $f''=0$. We prove also that the initial data is taken in a suitably strong sense and we give some counterexamples which show that these results are sharp.

PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/35209 U1 - 35508 U2 - Mathematics U5 - MAT/05 ER - TY - JOUR T1 - Symmetry properties of some solutions to some semilinear elliptic equations JF - Annali della Scuola Normale Superiore di Pisa. Classe di scienze Y1 - 2016 A1 - Farina, Alberto A1 - Andrea Malchiodi A1 - Matteo Rizzi PB - Classe di Scienze VL - 16 ER - TY - THES T1 - Two explorations in Dynamical Systems and Mechanics Y1 - 2016 A1 - Paolo Gidoni KW - Poincaré-Birkhoff Theorem AB - This thesis contains the work done by Paolo Gidoni during the doctorate programme in Matematical Analysis at SISSA, under the supervision of A. Fonda and A. DeSimone. The thesis is composed of two parts: "Avoiding cones conditions and higher dimensional twist" and "Directional friction in bio-inspired locomotion". PB - SISSA U1 - 35527 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Viscous approximation of quasistatic evolutions for a coupled elastoplastic-damage model JF - Calculus of Variations and Partial Differential Equations Y1 - 2016 A1 - Vito Crismale A1 - Giuliano Lazzaroni AB -Employing the technique of vanishing viscosity and time rescaling, we show the existence of quasistatic evolutions for elastoplastic materials with incomplete damage affecting both the elastic tensor and the plastic yield surface, in a softening framework and in small strain assumptions.

VL - 55 UR - https://doi.org/10.1007/s00526-015-0947-6 ER - TY - JOUR T1 - Volume geodesic distortion and Ricci curvature for Hamiltonian dynamics JF - arXiv preprint arXiv:1602.08745 Y1 - 2016 A1 - Andrei A. Agrachev A1 - Davide Barilari A1 - Elisa Paoli ER - TY - JOUR T1 - Young towers for product systems JF - Discrete & Continuous Dynamical Systems - A Y1 - 2016 A1 - Stefano Luzzatto A1 - Marks Ruziboev AB -We show that the direct product of maps with Young towers admits a Young tower whose return times decay at a rate which is bounded above by the slowest of the rates of decay of the return times of the component maps. An application of this result, together with other results in the literature, yields various statistical properties for the direct product of various classes of systems, including Lorenz-like maps, multimodal maps, piecewise $C^2$ interval maps with critical points and singularities, Hénon maps and partially hyperbolic systems.

VL - 36 UR - http://aimsciences.org//article/id/18d4526e-470d-467e-967a-a0345ad4c642 ER - TY - JOUR T1 - Anisotropic mean curvature on facets and relations with capillarity Y1 - 2015 A1 - Stefano Amato A1 - Lucia Tealdi A1 - Giovanni Bellettini AB -We discuss the relations between the anisotropic calibrability of a facet F of a solid crystal E, and the capillary problem on a capillary tube with base F. When F is parallel to a facet of the Wulff shape, calibrability is equivalent to show the existence of an anisotropic subunitary vector field in $F, with suitable normal trace on the boundary of the facet, and with constant divergence equal to the anisotropic mean curvature of F. When the Wulff shape is a cylynder, assuming E convex at F, and F (strictly) calibrable, such a vector field is obtained by solving the capillary problem on F in absence of gravity and with zero contact angle. We show some examples of facets for which it is possible, even without the strict calibrability assumption, to build one of these vector fields. The construction provides, at least for convex facets of class C^{1,1}, the solution of the total variation flow starting at 1_F.

PB - de Gruyter UR - http://urania.sissa.it/xmlui/handle/1963/34481 U1 - 34663 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Benchmarking the Immersed Finite Element Method for Fluid-Structure Interaction Problems JF - Computers and Mathematics with Applications 69 (2015) 1167–1188 Y1 - 2015 A1 - Roy Saswati A1 - Luca Heltai A1 - Francesco Costanzo AB - We present an implementation of a fully variational formulation of an immersed methods for fluid-structure interaction problems based on the finite element method. While typical implementation of immersed methods are characterized by the use of approximate Dirac delta distributions, fully variational formulations of the method do not require the use of said distributions. In our implementation the immersed solid is general in the sense that it is not required to have the same mass density and the same viscous response as the surrounding fluid. We assume that the immersed solid can be either viscoelastic of differential type or hyperelastic. Here we focus on the validation of the method via various benchmarks for fluid-structure interaction numerical schemes. This is the first time that the interaction of purely elastic compressible solids and an incompressible fluid is approached via an immersed method allowing a direct comparison with established benchmarks. U1 - 34633 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - RPRT T1 - A bridging mechanism in the homogenisation of brittle composites with soft inclusions Y1 - 2015 A1 - Marco Barchiesi A1 - Giuliano Lazzaroni A1 - Caterina Ida Zeppieri AB - We provide a homogenisation result for the energy-functional associated with a purely brittle composite whose microstructure is characterised by soft periodic inclusions embedded in a stiffer matrix. We show that the two constituents as above can be suitably arranged on a microscopic scale ε to obtain, in the limit as ε tends to zero, a homogeneous macroscopic energy-functional explicitly depending on the opening of the crack. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7492 U1 - 7621 ER - TY - BOOK T1 - Certified Reduced Basis Methods for Parametrized Partial Differential Equations T2 - Springer Briefs in Mathematics Y1 - 2015 A1 - Jan S Hesthaven A1 - Gianluigi Rozza A1 - Benjamin Stamm KW - a posteriori error bounds KW - empirical interpolation KW - parametrized partial differential equations KW - reduced basis methods, greedy algorithms AB -This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.

JF - Springer Briefs in Mathematics PB - Springer CY - Switzerland SN - 978-3-319-22469-5 ER - TY - JOUR T1 - A compatible-incompatible decomposition of symmetric tensors in Lp with application to elasticity JF - Mathematical Methods in the Applied Sciences Y1 - 2015 A1 - Maggiani, Giovanni Battista A1 - Riccardo Scala A1 - Nicolas Van Goethem KW - 35J58 KW - 35Q74 KW - compatibility conditions KW - elasticity KW - Korn inequality KW - strain decomposition KW - subclass74B05 AB -In this paper, we prove the Saint-Venant compatibility conditions in $L^p$ for $p\in(1,∞)$, in a simply connected domain of any space dimension. As a consequence, alternative, simple, and direct proofs of some classical Korn inequalities in Lp are provided. We also use the Helmholtz decomposition in $L^p$ to show that every symmetric tensor in a smooth domain can be decomposed in a compatible part, which is the symmetric part of a displacement gradient, and in an incompatible part, which is the incompatibility of a certain divergence-free tensor. Moreover, under a suitable Dirichlet boundary condition, this Beltrami-type decomposition is proved to be unique. This decomposition result has several applications, one of which being in dislocation models, where the incompatibility part is related to the dislocation density and where $1 < p < 2$. This justifies the need to generalize and prove these rather classical results in the Hilbertian case ($p = 2$), to the full range $p\in(1,∞)$. Copyright © 2015 John Wiley & Sons, Ltd.

VL - 38 UR - https://onlinelibrary.wiley.com/doi/abs/10.1002/mma.3450 ER - TY - JOUR T1 - Complexity of Control-Affine Motion Planning JF - SIAM Journal on Control and Optimization Y1 - 2015 A1 - Jean, F. A1 - Dario Prandi AB -In this paper we study the complexity of the motion planning problem for control-affine systems. Such complexities are already defined and rather well understood in the particular case of nonholonomic (or sub-Riemannian) systems. Our aim is to generalize these notions and results to systems with a drift. Accordingly, we present various definitions of complexity, as functions of the curve that is approximated, and of the precision of the approximation. Due to the lack of time-rescaling invariance of these systems, we consider geometric and parametrized curves separately. Then, we give some asymptotic estimates for these quantities. As a byproduct, we are able to treat the long time local controllability problem, giving quantitative estimates on the cost of stabilizing the system near a nonequilibrium point of the drift.

VL - 53 UR - https://doi.org/10.1137/130950793 ER - TY - JOUR T1 - Constrained BV functions on double coverings for Plateau's type problems JF - Adv. Calc. Var. Y1 - 2015 A1 - Stefano Amato A1 - Giovanni Bellettini A1 - Maurizio Paolini AB -We link Brakke's "soap films" covering construction with the theory of finite perimeter sets, in order to study Plateau's problem without fixing a priori the topology of the solution. The minimization is set up in the class of $BV$ functions defined on a double covering space of the complement of an $(n − 2)$-dimensional smooth compact manifold $S$ without boundary. The main novelty of our approach stands in the presence of a suitable constraint on the fibers, which couples together the covering sheets. The model allows to avoid all issues concerning the presence of the boundary $S$. The constraint is lifted in a natural way to Sobolev spaces, allowing also an approach based on $Γ$-convergence theory.

U1 - 7597 ER - TY - JOUR T1 - Convergence rate of the Glimm scheme JF - Bulletin of the Institute of Mathematics of Academia Sinica (New Series) Y1 - 2015 A1 - Stefano Modena A1 - Stefano Bianchini ER - TY - RPRT T1 - Convex combinations of low eigenvalues, Fraenkel asymmetries and attainable sets Y1 - 2015 A1 - Dario Mazzoleni A1 - Davide Zucco AB - We consider the problem of minimizing convex combinations of the first two eigenvalues of the Dirichlet-Laplacian among open set of $R^N$ of fixed measure. We show that, by purely elementary arguments, based on the minimality condition, it is possible to obtain informations on the geometry of the minimizers of convex combinations: we study, in particular, when these minimizers are no longer convex, and the optimality of balls. As an application of our results we study the boundary of the attainable set for the Dirichlet spectrum. Our techniques involve symmetry results à la Serrin, explicit constants in quantitative inequalities, as well as a purely geometrical problem: the minimization of the Fraenkel 2-asymmetry among convex sets of fixed measure. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/35140 U1 - 35378 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Deal2lkit: a Toolkit Library for High Performance Programming in deal.II Y1 - 2015 A1 - Alberto Sartori A1 - Nicola Giuliani A1 - Mauro Bardelloni A1 - Luca Heltai AB - We present version 1.0.0 of the deal2lkit (deal.II ToolKit) library. deal2lkit is a collection of modules and classes for the general purpose finite element library deal.II. Its principal aim is to provide a high level interface, controlled via parameter files, for those steps that are common in all finite element programs: mesh generation, selection of the finite element type, application of boundary conditions and many others. Each module can be used as a building block independently on the others, and can be integrated in existing finite element codes based on deal.II, drastically reducing the size of programs, rendering their use automatically parametrised, and reducing the overall time-to-market of finite element programming. Moreover, deal2lkit features interfaces with the SUNDIALS (SUite of Nonlinear and DIfferential/ALgebraic equation Solvers) and ASSIMP (Open Asset Import Library) libraries. Some examples are provided which show the aim and scopes of deal2lkit. The deal2lkit library is released under the GNU Lesser General Public License (LGPL) and can be retrieved from the deal2lkit repository https://github.com/mathLab/deal2lkit. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/35006 U1 - 35235 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - The deal.II Library, Version 8.2 JF - Archive of Numerical Software, vol. 3, n. 100, (2015), pages : 1-8 Y1 - 2015 A1 - Wolfgang Bangerth A1 - Timo Heister A1 - Luca Heltai A1 - G. Kanschat A1 - Martin Kronbichler A1 - Matthias Maier A1 - Bruno Turcksin A1 - T. D. Young AB - This paper provides an overview of the new features of the finite element library deal.II version 8.2 UR - http://urania.sissa.it/xmlui/handle/1963/34464 U1 - 34637 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - Decay of correlations for invertible maps with non-Hölder observables JF - Dynamical Systems Y1 - 2015 A1 - Marks Ruziboev AB -An invertible dynamical system with some hyperbolic structure is considered. Upper estimates for the correlations of continuous observables are given in terms of modulus of continuity. The result is applied to certain Hénon maps and Solenoid maps with intermittency.

PB - Taylor & Francis VL - 30 UR - https://doi.org/10.1080/14689367.2015.1046816 ER - TY - RPRT T1 - Dynamics of screw dislocations: a generalised minimising-movements scheme approach Y1 - 2015 A1 - Giovanni A. Bonaschi A1 - Patrick Van Meurs A1 - Marco Morandotti AB - The gradient flow structure of the model introduced in [CG99] for the dynamics of screw dislocations is investigated by means of a generalised minimising-movements scheme approach. The assumption of a finite number of available glide directions, together with the "maximal dissipation criterion" that governs the equations of motion, results into solving a differential inclusion rather than an ODE. This paper addresses how the model in [CG99] is connected to a time-discrete evolution scheme which explicitly confines dislocations to move each time step along a single glide direction. It is proved that the time-continuous model in [CG99] is the limit of these time-discrete minimising-movement schemes when the time step converges to 0. The study presented here is a first step towards a generalization of the setting in [AGS08, Chap. 2 and 3] that allows for dissipations which cannot be described by a metric. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/34495 U1 - 34692 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Existence and multiplicity result for the singular Toda system JF - Journal of Mathematical Analysis and Applications Y1 - 2015 A1 - Luca Battaglia KW - Existence result KW - Liouville-type equations KW - Multiplicity result KW - PDEs on compact surfaces KW - Toda system AB -We consider the Toda system on a compact surface (Σ,g)−Δu1=2ρ1(h1eu1∫Σh1eu1dVg−1)−ρ2(h2eu2∫Σh2eu2dVg−1)−4π∑j=1Jα1j(δpj−1),−Δu2=2ρ2(h2eu2∫Σh2eu2dVg−1)−ρ1(h1eu1∫Σh1eu1dVg−1)−4π∑j=1Jα2j(δpj−1), where hi are smooth positive functions, ρi are positive real parameters, pj are given points on Σ and αij are numbers greater than −1. We give existence and multiplicity results, using variational and Morse-theoretical methods. It is the first existence result when some of the αij's are allowed to be negative."

VL - 424 UR - http://www.sciencedirect.com/science/article/pii/S0022247X14010191 ER - TY - RPRT T1 - Existence for constrained dynamic Griffith fracture with a weak maximal dissipation condition Y1 - 2015 A1 - Gianni Dal Maso A1 - Cristopher J. Larsen A1 - Rodica Toader AB - There are very few existence results for fracture evolution, outside of globally minimizing quasi-static evolutions. Dynamic evolutions are particularly problematic, due to the difficulty of showing energy balance, as well as of showing that solutions obey a maximal dissipation condition, or some similar condition that prevents stationary cracks from always being solutions. Here we introduce a new weak maximal dissipation condition and show that it is compatible with cracks constrained to grow smoothly on a smooth curve. In particular, we show existence of dynamic fracture evolutions satisfying this maximal dissipation condition, subject to the above smoothness constraints, and exhibit explicit examples to show that this maximal dissipation principle can indeed rule out stationary cracks as solutions. UR - http://urania.sissa.it/xmlui/handle/1963/35045 U1 - 35277 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Existence of positive solutions in the superlinear case via coincidence degree: the Neumann and the periodic boundary value problems JF - Adv. Differential Equations 20 (2015), 937–982. Y1 - 2015 A1 - Guglielmo Feltrin A1 - Fabio Zanolin AB -We prove the existence of positive periodic solutions for the second order nonlinear equation u'' + a(x) g(u) = 0, where g(u) has superlinear growth at zero and at infinity. The weight function a(x) is allowed to change its sign. Necessary and sufficient conditions for the existence of nontrivial solutions are obtained. The proof is based on Mawhin's coincidence degree and applies also to Neumann boundary conditions. Applications are given to the search of positive solutions for a nonlinear PDE in annular domains and for a periodic problem associated to a non-Hamiltonian equation.

PB - Khayyam Publishing UR - http://projecteuclid.org/euclid.ade/1435064518 N1 - AMS Subject Classification: 34B18, 34B15, 34C25, 47H11. U1 - 35388 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Existence of positive solutions of a superlinear boundary value problem with indefinite weight JF - Conference Publications Y1 - 2015 A1 - Guglielmo Feltrin KW - boundary value problem KW - indefinite weight KW - Positive solution; existence result. KW - superlinear equation AB -We deal with the existence of positive solutions for a two-point boundary value problem associated with the nonlinear second order equation $u''+a(x)g(u)=0$. The weight $a(x)$ is allowed to change sign. We assume that the function $g\colon\mathopen[0,+∞\mathclose[\to\mathbb{R}$ is continuous, $g(0)=0$ and satisfies suitable growth conditions, including the superlinear case $g(s)=s^p$, with $p>1$. In particular we suppose that $g(s)/s$ is large near infinity, but we do not require that $g(s)$ is non-negative in a neighborhood of zero. Using a topological approach based on the Leray-Schauder degree we obtain a result of existence of at least a positive solution that improves previous existence theorems.

VL - 2015 UR - http://aimsciences.org//article/id/b3c1c765-e8f5-416e-8130-05cc48478026 ER - TY - RPRT T1 - Explicit formulas for relaxed disarrangement densities arising from structured deformations Y1 - 2015 A1 - Ana Cristina Barroso A1 - Jose Matias A1 - Marco Morandotti A1 - David R. Owen AB - Structured deformations provide a multiscale geometry that captures the contributions at the macrolevel of both smooth geometrical changes and non-smooth geometrical changes (disarrangements) at submacroscopic levels. For each (first-order) structured deformation (g,G) of a continuous body, the tensor field G is known to be a measure of deformations without disarrangements, and M:=∇g−G is known to be a measure of deformations due to disarrangements. The tensor fields G and M together deliver not only standard notions of plastic deformation, but M and its curl deliver the Burgers vector field associated with closed curves in the body and the dislocation density field used in describing geometrical changes in bodies with defects. Recently, Owen and Paroni [13] evaluated explicitly some relaxed energy densities arising in Choksi and Fonseca’s energetics of structured deformations [4] and thereby showed: (1) (trM)+ , the positive part of trM, is a volume density of disarrangements due to submacroscopic separations, (2) (trM)−, the negative part of trM, is a volume density of disarrangements due to submacroscopic switches and interpenetrations, and (3) trM, the absolute value of trM, is a volume density of all three of these non-tangential disarrangements: separations, switches, and interpenetrations. The main contribution of the present research is to show that a different approach to the energetics of structured deformations, that due to Ba\'{i}a, Matias, and Santos [1], confirms the roles of (trM)+, (trM)−, and trM established by Owen and Paroni. In doing so, we give an alternative, shorter proof of Owen and Paroni’s results, and we establish additional explicit formulas for other measures of disarrangements. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/34492 U1 - 34687 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Fast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization Y1 - 2015 A1 - F. Ballarin A1 - Elena Faggiano A1 - Sonia Ippolito A1 - Andrea Manzoni A1 - Alfio Quarteroni A1 - Gianluigi Rozza A1 - Roberto Scrofani AB - In this work a reduced-order computational framework for the study of haemodynamics in three-dimensional patient-specific configurations of coronary artery bypass grafts dealing with a wide range of scenarios is proposed. We combine several efficient algorithms to face at the same time both the geometrical complexity involved in the description of the vascular network and the huge computational cost entailed by time dependent patient-specific flow simulations. Medical imaging procedures allow to reconstruct patient-specific configurations from clinical data. A centerlines-based parametrization is proposed to efficiently handle geometrical variations. POD–Galerkin reduced-order models are employed to cut down large computational costs. This computational framework allows to characterize blood flows for different physical and geometrical variations relevant in the clinical practice, such as stenosis factors and anastomosis variations, in a rapid and reliable way. Several numerical results are discussed, highlighting the computational performance of the proposed framework, as well as its capability to perform sensitivity analysis studies, so far out of reach. UR - http://urania.sissa.it/xmlui/handle/1963/34623 U1 - 34824 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - FEM SUPG stabilisation of mixed isoparametric BEMs: application to linearised free surface flows JF - Engineering Analysis with Boundary Elements 59 (2015), pp. 8-22 Y1 - 2015 A1 - Nicola Giuliani A1 - Andrea Mola A1 - Luca Heltai A1 - L. Formaggia AB -In finite element formulations, transport dominated problems are often stabilised through the Streamline-Upwind-Petrov–Galerkin (SUPG) method. Its application is straightforward when the problem at hand is solved using Galerkin methods. Applications of boundary integral formulations often resort to collocation techniques which are computationally more tractable. In this framework, the Galerkin method and the stabilisation may still be used to successfully apply boundary conditions and resolve instabilities that are frequently observed in transport dominated problems. We apply this technique to an adaptive collocation boundary element method for the solution of stationary potential flows, where we solve a mixed Poisson problem in boundary integral form, with the addition of linearised free surface boundary conditions. We use a mixed boundary element formulation to allow for different finite dimensional spaces describing the flow potential and its normal derivative, and we validate our method simulating the flow around both a submerged body and a surface piercing body. The coupling of mixed surface finite elements and strongly consistent stabilisation techniques with boundary elements opens up the possibility to use non conformal unstructured grids with local refinement, without introducing the inconsistencies of other stabilisation techniques based on up-winding and finite difference schemes.

UR - http://urania.sissa.it/xmlui/handle/1963/34466 U1 - 34640 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - A general existence result for the Toda system on compact surfaces JF - Advances in Mathematics Y1 - 2015 A1 - Luca Battaglia A1 - Aleks Jevnikar A1 - Andrea Malchiodi A1 - David Ruiz KW - Geometric PDEs KW - Min–max schemes KW - Variational methods AB -In this paper we consider the following Toda system of equations on a compact surface:−Δu1=2ρ1(h1eu1∫Σh1eu1dVg−1)−ρ2(h2eu2∫Σh2eu2dVg−1)−Δu1=−4π∑j=1mα1,j(δpj−1),−Δu2=2ρ2(h2eu2∫Σh2eu2dVg−1)−ρ1(h1eu1∫Σh1eu1dVg−1)−Δu2=−4π∑j=1mα2,j(δpj−1), which is motivated by the study of models in non-abelian Chern–Simons theory. Here h1,h2 are smooth positive functions, ρ1,ρ2 two positive parameters, pi points of the surface and α1,i,α2,j non-negative numbers. We prove a general existence result using variational methods. The same analysis applies to the following mean field equation−Δu=ρ1(heu∫ΣheudVg−1)−ρ2(he−u∫Σhe−udVg−1), which arises in fluid dynamics."

VL - 285 UR - http://www.sciencedirect.com/science/article/pii/S0001870815003072 ER - TY - JOUR T1 - Geodesics and horizontal-path spaces in Carnot groups JF - Geometry & Topology Y1 - 2015 A1 - Andrei A. Agrachev A1 - Alessandro Gentile A1 - Antonio Lerario AB -We study properties of the space of horizontal paths joining the origin with a vertical point on a generic two-step Carnot group. The energy is a Morse-Bott functional on paths and its critical points (sub-Riemannian geodesics) appear in families (compact critical manifolds) with controlled topology. We study the asymptotic of the number of critical manifolds as the energy grows. The topology of the horizontal-path space is also investigated, and we find asymptotic results for the total Betti number of the sublevels of the energy as it goes to infinity. We interpret these results as local invariants of the sub-Riemannian structure.

PB - Mathematical Sciences Publishers VL - 19 ER - TY - THES T1 - Gibbs-Markov-Young Structures and Decay of Correlations Y1 - 2015 A1 - Marks Ruziboev KW - Decay of Correlations, GMY-towers AB - In this work we study mixing properties of discrete dynamical systems and related to them geometric structure. In the first chapter we show that the direct product of maps with Young towers admits a Young tower whose return times decay at a rate which is bounded above by the slowest of the rates of decay of the return times of the component maps. An application of this result, together with other results in the literature, yields various statistical properties for the direct product of various classes of systems, including Lorenz-like maps, multimodal maps, piecewise $C^2$ interval maps with critical points and singularities, H\'enon maps and partially hyperbolic systems. The second chapter is dedicated to the problem of decay of correlations for continuous observables. First we show that if the underlying system admits Young tower then the rate of decay of correlations for continuous observables can be estimated in terms of modulus of continuity and the decay rate of tail of Young tower. In the rest of the second chapter we study the relations between the rates of decay of correlations for smooth observables and continuous observables. We show that if the rates of decay of correlations is known for $C^r,$ observables ($r\ge 1$) then it is possible to obtain decay of correlations for continuous observables in terms of modulus of continuity. PB - SISSA U1 - 34677 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - Homogenization problems in the Calculus of Variations: an overview Y1 - 2015 A1 - Jose Matias A1 - Marco Morandotti AB - In this note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundamental theoretical tools, both classical and modern. We conclude by mentioning some open problems. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/34455 N1 - DEDICATED TO PROF. ORLANDO LOPES U1 - 34598 U2 - Mathematics U4 - 1 ER - TY - THES T1 - Interaction functionals, Glimm approximations and Lagrangian structure of BV solutions for Hyperbolic Systems of Conservations Laws Y1 - 2015 A1 - Stefano Modena KW - Hyperbolic conservation laws AB - This thesis is a contribution to the mathematical theory of Hyperbolic Conservation Laws. Three are the main results which we collect in this work. The first and the second result (denoted in the thesis by Theorem A and Theorem B respectively) deal with the following problem. The most comprehensive result about existence, uniqueness and stability of the solution to the Cauchy problem \begin{equation}\tag{$\mathcal C$} \label{E:abstract} \begin{cases} u_t + F(u)_x = 0, \\u(0, x) = \bar u(x), \end{cases} \end{equation} where $F: \R^N \to \R^N$ is strictly hyperbolic, $u = u(t,x) \in \R^N$, $t \geq 0$, $x \in \R$, $\TV(\bar u) \ll 1$, can be found in [Bianchini, Bressan 2005], where the well-posedness of \eqref{E:abstract} is proved by means of vanishing viscosity approximations. After the paper [Bianchini, Bressan 2005], however, it seemed worthwhile to develop a \emph{purely hyperbolic} theory (based, as in the genuinely nonlinear case, on Glimm or wavefront tracking approximations, and not on vanishing viscosity parabolic approximations) to prove existence, uniqueness and stability results. The reason of this interest can be mainly found in the fact that hyperbolic approximate solutions are much easier to study and to visualize than parabolic ones. Theorems A and B in this thesis are a contribution to this line of research. In particular, Theorem A proves an estimate on the change of the speed of the wavefronts present in a Glimm approximate solution when two of them interact; Theorem B proves the convergence of the Glimm approximate solutions to the weak admissible solution of \eqref{E:abstract} and provides also an estimate on the rate of convergence. Both theorems are proved in the most general setting when no assumption on $F$ is made except the strict hyperbolicity. The third result of the thesis, denoted by Theorem C, deals with the Lagrangian structure of the solution to \eqref{E:abstract}. The notion of Lagrangian flow is a well-established concept in the theory of the transport equation and in the study of some particular system of conservation laws, like the Euler equation. However, as far as we know, the general system of conservations laws \eqref{E:abstract} has never been studied from a Lagrangian point of view. This is exactly the subject of Theorem C, where a Lagrangian representation for the solution to the system \eqref{E:abstract} is explicitly constructed. The main reasons which led us to look for a Lagrangian representation of the solution of \eqref{E:abstract} are two: on one side, this Lagrangian representation provides the continuous counterpart in the exact solution of \eqref{E:abstract} to the well established theory of wavefront approximations; on the other side, it can lead to a deeper understanding of the behavior of the solutions in the general setting, when the characteristic field are not genuinely nonlinear or linearly degenerate. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/34542 U1 - 34739 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Liquid crystal elastomer strips as soft crawlers JF - Journal of the Mechanics and Physics of Solids Y1 - 2015 A1 - Antonio DeSimone A1 - Paolo Gidoni A1 - Giovanni Noselli KW - Crawling motility KW - Directional surfaces KW - Frictional interactions KW - Liquid crystal elastomers KW - Soft biomimetic robots AB -In this paper, we speculate on a possible application of Liquid Crystal Elastomers to the field of soft robotics. In particular, we study a concept for limbless locomotion that is amenable to miniaturisation. For this purpose, we formulate and solve the evolution equations for a strip of nematic elastomer, subject to directional frictional interactions with a flat solid substrate, and cyclically actuated by a spatially uniform, time-periodic stimulus (e.g., temperature change). The presence of frictional forces that are sensitive to the direction of sliding transforms reciprocal, ‘breathing-like’ deformations into directed forward motion. We derive formulas quantifying this motion in the case of distributed friction, by solving a differential inclusion for the displacement field. The simpler case of concentrated frictional interactions at the two ends of the strip is also solved, in order to provide a benchmark to compare the continuously distributed case with a finite-dimensional benchmark. We also provide explicit formulas for the axial force along the crawler body.

VL - 84 UR - http://www.sciencedirect.com/science/article/pii/S0022509615300430 ER - TY - THES T1 - Mathematical Models of Locomotion: Legged Crawling, Snake-like Motility, and Flagellar Swimming Y1 - 2015 A1 - Giancarlo Cicconofri KW - Motility PB - SISSA U1 - 34743 U2 - Mathematics U4 - 1 U5 - FIS/02 ER - TY - JOUR T1 - Motility of a model bristle-bot: A theoretical analysis JF - International Journal of Non-Linear Mechanics Y1 - 2015 A1 - Giancarlo Cicconofri A1 - Antonio DeSimone KW - Bristle-robots KW - Crawling motility KW - Frictional interactions AB -Bristle-bots are legged robots that can be easily made out of a toothbrush head and a small vibrating engine. Despite their simple appearance, the mechanism enabling them to propel themselves by exploiting friction with the substrate is far from trivial. Numerical experiments on a model bristle-bot have been able to reproduce such a mechanism revealing, in addition, the ability to switch direction of motion by varying the vibration frequency. This paper provides a detailed account of these phenomena through a fully analytical treatment of the model. The equations of motion are solved through an expansion in terms of a properly chosen small parameter. The convergence of the expansion is rigorously proven. In addition, the analysis delivers formulas for the average velocity of the robot and for the frequency at which the direction switch takes place. A quantitative description of the mechanism for the friction modulation underlying the motility of the bristle-bot is also provided.

VL - 76 UR - http://www.sciencedirect.com/science/article/pii/S0020746215000025 ER - TY - JOUR T1 - Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations JF - Numerische Mathematik, (2015), 36 p. Article in Press Y1 - 2015 A1 - Gianluigi Rozza A1 - Peng Chen A1 - Alfio Quarteroni AB - In this paper we develop and analyze a multilevel weighted reduced basis method for solving stochastic optimal control problems constrained by Stokes equations. We prove the analytic regularity of the optimal solution in the probability space under certain assumptions on the random input data. The finite element method and the stochastic collocation method are employed for the numerical approximation of the problem in the deterministic space and the probability space, respectively, resulting in many large-scale optimality systems to solve. In order to reduce the unaffordable computational effort, we propose a reduced basis method using a multilevel greedy algorithm in combination with isotropic and anisotropic sparse-grid techniques. A weighted a posteriori error bound highlights the contribution stemming from each method. Numerical tests on stochastic dimensions ranging from 10 to 100 demonstrate that our method is very efficient, especially for solving high-dimensional and large-scale optimization problems. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34491 U1 - 34680 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - Multiple positive solutions for a superlinear problem: a topological approach JF - J. Differential Equations 259 (2015), 925–963. Y1 - 2015 A1 - Guglielmo Feltrin A1 - Fabio Zanolin AB -We study the multiplicity of positive solutions for a two-point boundary value problem associated to the nonlinear second order equation u''+f(x,u)=0. We allow x ↦ f(x,s) to change its sign in order to cover the case of scalar equations with indefinite weight. Roughly speaking, our main assumptions require that f(x,s)/s is below λ_1 as s→0^+ and above λ_1 as s→+∞. In particular, we can deal with the situation in which f(x,s) has a superlinear growth at zero and at infinity. We propose a new approach based on the topological degree which provides the multiplicity of solutions. Applications are given for u'' + a(x) g(u) = 0, where we prove the existence of 2^n-1 positive solutions when a(x) has n positive humps and a^-(x) is sufficiently large.

PB - Elsevier UR - http://urania.sissa.it/xmlui/handle/1963/35147 N1 - Work presented at the "Special Session 21" of the "10th AIMS Conference on Dynamical Systems, Differential Equations and Applications" (Madrid, July 7-11, 2014). U1 - 35387 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - A note on compactness properties of the singular Toda system JF - Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Y1 - 2015 A1 - Luca Battaglia A1 - Gabriele Mancini AB -In this note, we consider blow-up for solutions of the SU(3) Toda system on compact surfaces. In particular, we give a complete proof of a compactness result stated by Jost, Lin and Wang and we extend it to the case of singular systems. This is a necessary tool to find solutions through variational methods.

VL - 26 U1 - 34669 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Onofri-Type Inequalities for Singular Liouville Equations Y1 - 2015 A1 - Gabriele Mancini AB -We study the blow-up behavior of minimizing sequences for the singular Moser–Trudinger functional on compact surfaces. Assuming non-existence of minimum points, we give an estimate for the infimum value of the functional. This result can be applied to give sharp Onofri-type inequalities on the sphere in the presence of at most two singularities.

PB - Springer US U1 - 34668 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - A permanence theorem for local dynamical systems JF - Nonlinear Analysis: Theory, Methods & Applications Y1 - 2015 A1 - Alessandro Fonda A1 - Paolo Gidoni KW - Lotka–Volterra KW - permanence KW - Predator–prey KW - Uniform persistence AB -We provide a necessary and sufficient condition for permanence related to a local dynamical system on a suitable topological space. We then present an illustrative application to a Lotka–Volterra predator–prey model with intraspecific competition.

VL - 121 UR - http://www.sciencedirect.com/science/article/pii/S0362546X14003332 N1 - Nonlinear Partial Differential Equations, in honor of Enzo Mitidieri for his 60th birthday ER - TY - JOUR T1 - The phototransduction machinery in the rod outer segment has a strong efficacy gradient Y1 - 2015 A1 - Monica Mazzolini A1 - Giuseppe Facchetti A1 - L. Andolfi A1 - R. Proietti Zaccaria A1 - S. Tuccio A1 - J. Treud A1 - Claudio Altafini A1 - Enzo M. Di Fabrizio A1 - Marco Lazzarino A1 - G. Rapp A1 - Vincent Torre PB - National Academy of Sciences UR - http://urania.sissa.it/xmlui/handle/1963/35157 N1 - Open Access article U1 - 35382 U2 - Neuroscience ER - TY - JOUR T1 - Quadratic Interaction Functional for General Systems of Conservation Laws JF - Communications in Mathematical Physics Y1 - 2015 A1 - Stefano Bianchini A1 - Stefano Modena AB -For the Glimm scheme approximation to the solution of the system of conservation laws in one space dimension with initial data u 0 with small total variation, we prove a quadratic (w.r.t. Tot. Var. ( u 0)) interaction estimate, which has been used in the literature for stability and convergence results. No assumptions on the structure of the flux f are made (apart from smoothness), and this estimate is the natural extension of the Glimm type interaction estimate for genuinely nonlinear systems. More precisely, we obtain the following results: a new analysis of the interaction estimates of simple waves;

VL - 338 ER - TY - JOUR T1 - Reduced basis approximation and a-posteriori error estimation for the coupled Stokes-Darcy system JF - Advances in Computational Mathematics Y1 - 2015 A1 - Immanuel Martini A1 - Gianluigi Rozza A1 - Bernard Haasdonk KW - Domain decomposition KW - Error estimation KW - Non-coercive problem KW - Porous medium equation KW - Reduced basis method KW - Stokes flow AB -The coupling of a free flow with a flow through porous media has many potential applications in several fields related with computational science and engineering, such as blood flows, environmental problems or food technologies. We present a reduced basis method for such coupled problems. The reduced basis method is a model order reduction method applied in the context of parametrized systems. Our approach is based on a heterogeneous domain decomposition formulation, namely the Stokes-Darcy problem. Thanks to an offline/online-decomposition, computational times can be drastically reduced. At the same time the induced error can be bounded by fast evaluable a-posteriori error bounds. In the offline-phase the proposed algorithms make use of the decomposed problem structure. Rigorous a-posteriori error bounds are developed, indicating the accuracy of certain lifting operators used in the offline-phase as well as the accuracy of the reduced coupled system. Also, a strategy separately bounding pressure and velocity errors is extended. Numerical experiments dealing with groundwater flow scenarios demonstrate the efficiency of the approach as well as the limitations regarding a-posteriori error estimation.

VL - special issue for MoRePaS 2012 IS - in press ER - TY - JOUR T1 - Reduced basis approximation of parametrized optimal flow control problems for the Stokes equations JF - Computers and Mathematics with Applications Y1 - 2015 A1 - Federico Negri A1 - Andrea Manzoni A1 - Gianluigi Rozza AB -This paper extends the reduced basis method for the solution of parametrized optimal control problems presented in Negri et al. (2013) to the case of noncoercive (elliptic) equations, such as the Stokes equations. We discuss both the theoretical properties-with particular emphasis on the stability of the resulting double nested saddle-point problems and on aggregated error estimates-and the computational aspects of the method. Then, we apply it to solve a benchmark vorticity minimization problem for a parametrized bluff body immersed in a two or a three-dimensional flow through boundary control, demonstrating the effectivity of the methodology.

VL - 69 ER - TY - JOUR T1 - Reduced Basis Isogeometric Methods (RB-IGA) for the real-time simulation of potential flows about parametrized NACA airfoils JF - Comput Methods Appl Mech Eng. 2015;284:1147–1180 Y1 - 2015 A1 - Andrea Manzoni A1 - Filippo Salmoiraghi A1 - Luca Heltai AB - We present a Reduced Basis (RB) method based on Isogeometric Analysis (IGA) for the rapid and reliable evaluation of PDE systems characterized by complex geometrical features. At the current state of the art, this is the first case of coupling between RB and IGA methods. The construction of the RB method relies on an Isogeometric Boundary Element Method (IGA-BEM) as the high-fidelity technique, allowing a direct interface with Computer Aided Design (CAD) tools. A suitable Empirical Interpolation Method (EIM) ensures an efficient offline/online decomposition between the construction and the evaluation of the RB method. We consider the real-time simulation of potential flows past airfoils, parametrized with respect to the angle of attack and the NACA number identifying their shape, and we provide a validation of our methodology with respect to experimental data and reference numerical codes, showing in both cases a very good agreement.We present a Reduced Basis (RB) method based on Isogeometric Analysis (IGA) for the rapid and reliable evaluation of PDE systems characterized by complex geometrical features. At the current state of the art, this is the first case of coupling between RB and IGA methods. The construction of the RB method relies on an Isogeometric Boundary Element Method (IGA-BEM) as the high-fidelity technique, allowing a direct interface with Computer Aided Design (CAD) tools. A suitable Empirical Interpolation Method (EIM) ensures an efficient offline/online decomposition between the construction and the evaluation of the RB method. We consider the real-time simulation of potential flows past airfoils, parametrized with respect to the angle of attack and the NACA number identifying their shape, and we provide a validation of our methodology with respect to experimental data and reference numerical codes, showing in both cases a very good agreement. U1 - 34587 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - THES T1 - The relaxed area of maps from the plane to the plane with a line discontinuity, and the role of semicartesian surfaces. Y1 - 2015 A1 - Lucia Tealdi KW - Area functional AB - In this thesis we study the relaxation of the area functional w.r.t. the L^1 topology of a map from a bounded planar domain with values in the plane and jumping on a segment. We estimate from above the singular contribution of this functional due to the presence of the jump in terms of the infimum of the area among a suitable family of surfaces that we call semicartesian surfaces. In our analysis, we also introduce a different notion of area, namely the relaxation of the area w.r.t. a convergence stronger than the L^1 convergence, whose singular contribution is completely characterized in terms of suitable semicartesian area minimizing problems. We propose also some examples of maps for which the two notions of relaxation are different: these examples underline the highly non-local behaviour of the L^1-relaxation, and justify the introduction of the other functional. Some result about the existence of a semicartesian area-minimizing surface is also provided. PB - SISSA U1 - 34732 U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - Results on the minimization of the Dirichlet functional among semicartesian parametrizations Y1 - 2015 A1 - Lucia Tealdi A1 - Giovanni Bellettini A1 - Maurizio Paolini AB -We start to investigate the existence of conformal minimizers for the Dirichlet functional in the setting of the so-called semicartesian parametrizations, adapting to this context some techniques used in solving the classical Plateau's problem. The final goal is to find area minimizing semicartesian parametrizations spanning a Jordan curve obtained as union of two graphs; this problem appeared in the study of the relaxed area functional for maps from the plane to the plane jumping on a line.

UR - http://urania.sissa.it/xmlui/handle/1963/34488 N1 - The article is compsed of 18 pages and is recorded in PDF format U1 - 34671 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - Rigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires Y1 - 2015 A1 - Giuliano Lazzaroni A1 - Mariapia Palombaro A1 - Anja Schlomerkemper AB - In the context of nanowire heterostructures we perform a discrete to continuum limit of the corresponding free energy by means of Γ-convergence techniques. Nearest neighbours are identified by employing the notions of Voronoi diagrams and Delaunay triangulations. The scaling of the nanowire is done in such a way that we perform not only a continuum limit but a dimension reduction simultaneously. The main part of the proof is a discrete geometric rigidity result that we announced in an earlier work and show here in detail for a variety of three-dimensional lattices. We perform the passage from discrete to continuum twice: once for a system that compensates a lattice mismatch between two parts of the heterogeneous nanowire without defects and once for a system that creates dislocations. It turns out that we can verify the experimentally observed fact that the nanowires show dislocations when the radius of the specimen is large PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7494 U1 - 7623 ER - TY - RPRT T1 - Semicartesian surfaces and the relaxed area of maps from the plane to the plane with a line discontinuity Y1 - 2015 A1 - Lucia Tealdi A1 - Giovanni Bellettini A1 - Maurizio Paolini AB -We address the problem of estimating the area of the graph of a map u, defined on a bounded planar domain O and taking values in the plane, jumping on a segment J, either compactly contained in O or having both the end points on the boundary of O. We define the relaxation of the area functional w.r.t. a sort of uniform convergence, and we characterize it in terms of the infimum of the area among those surfaces in the space spanning the graphs of the traces of u on the two side of J and having what we have called a semicartesian structure. We exhibit examples showing that the relaxed area functional w.r.t the L^1 convergence may depend also on the values of u far from J, and on the relative position of J w.r.t. the boundary of O; these examples confirm the non-local behaviour of the L^1 relaxed area functional, and justify the interest in studying the relaxation w.r.t. a stronger convergence. We prove also that the L^1 relaxed area functional in non-subadditive for a rather class of maps.

UR - http://urania.sissa.it/xmlui/handle/1963/34483 N1 - The preprint is compsed of 37 pages and is recorded in PDF format U1 - 34670 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - THES T1 - Sharp Inequalities and Blow-up Analysis for Singular Moser-Trudinger Embeddings. Y1 - 2015 A1 - Gabriele Mancini KW - Moser-Trudinger AB - We investigate existence of solutions for a singular Liouville equation on S^2 and prove sharp Onofri-type inequalities for a Moser-Trudinger functional in the presence of singular potentials. As a consequence we obtain existence of extremal functions for the Moser-Trudinger embedding on compact surfaces with conical singularities. Finally we study the blow-up behavior for sequences of solutions Liouville-type systems and prove a compactness condition which plays an important role in the variational analysis of Toda systems. PB - SISSA U1 - 34738 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - Singular Liouville Equations on S^2: Sharp Inequalities and Existence Results Y1 - 2015 A1 - Gabriele Mancini AB -We prove a sharp Onofri-type inequality and non-existence of extremals for a Moser-Tudinger functional on S^2 in the presence of potentials having positive order singularities. We also investigate the existence of critical points and give some sufficient conditions under symmetry or nondegeneracy assumptions.

UR - http://urania.sissa.it/xmlui/handle/1963/34489 U1 - 34672 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - THES T1 - Some results on anisotropic mean curvature and other phase-transition problems Y1 - 2015 A1 - Stefano Amato KW - Anisotropic mean curvature AB - The present thesis is divided into three parts. In the first part, we analyze a suitable regularization — which we call nonlinear multidomain model — of the motion of a hypersurface under smooth anisotropic mean curvature flow. The second part of the thesis deals with crystalline mean curvature of facets of a solid set of R^3 . Finally, in the third part we study a phase-transition model for Plateau’s type problems based on the theory of coverings and of BV functions. PB - SISSA U1 - 34733 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Stable regular critical points of the Mumford-Shah functional are local minimizers JF - Annales de l'Institut Henri Poincare (C) Non Linear Analysis Y1 - 2015 A1 - Marco Bonacini A1 - Massimiliano Morini KW - Mumford-Shah functional AB -In this paper it is shown that any regular critical point of the Mumford–Shah functional, with positive definite second variation, is an isolated local minimizer with respect to competitors which are sufficiently close in the $L^1$

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

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

VL - 471 UR - https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2015.0054 ER - TY - JOUR T1 - Supremizer stabilization of POD-Galerkin approximation of parametrized Navier-Stokes equations Y1 - 2015 A1 - F. Ballarin A1 - Andrea Manzoni A1 - Alfio Quarteroni A1 - Gianluigi Rozza AB - In this work, we present a stable proper orthogonal decomposition–Galerkin approximation for parametrized steady incompressible Navier–Stokes equations with low Reynolds number. PB - Wiley UR - http://urania.sissa.it/xmlui/handle/1963/34701 U1 - 34915 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - Three-sphere low-Reynolds-number swimmer with a passive elastic arm Y1 - 2015 A1 - Alessandro Montino A1 - Antonio DeSimone AB - One of the simplest model swimmers at low Reynolds number is the three-sphere swimmer by Najafi and Golestanian. It consists of three spheres connected by two rods which change their lengths periodically in non-reciprocal fashion. Here we investigate a variant of this model in which one rod is periodically actuated while the other is replaced by an elastic spring. We show that the competition between the elastic restoring force and the hydrodynamic drag produces a delay in the response of the passive elastic arm with respect to the active one. This leads to non-reciprocal shape changes and self-propulsion. After formulating the equations of motion, we study their solutions qualitatively and numerically. The leading-order term of the solution is computed analytically. We then address questions of optimization with respect to both actuation frequency and swimmer's geometry. Our results can provide valuable conceptual guidance in the engineering of robotic microswimmers. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34530 U1 - 34735 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - A topological join construction and the Toda system on compact surfaces of arbitrary genus JF - Analysis & PDE Y1 - 2015 A1 - Aleks Jevnikar A1 - Kallel, Sadok A1 - Andrea Malchiodi PB - Mathematical Sciences Publishers VL - 8 ER - TY - THES T1 - Variational aspects of Liouville equations and systems Y1 - 2015 A1 - Aleks Jevnikar KW - Toda system PB - SISSA N1 - The PHD thesis is composed of 112 pages and is recorded in PDF format U1 - 34676 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - THES T1 - Variational aspects of singular Liouville systems Y1 - 2015 A1 - Luca Battaglia KW - Variational methods, Liouville systems, Moser-Trudinger inequalities, min-max methods AB - I studied singular Liouville systems on compact surfaces from a variational point of view. I gave sufficient and necessary conditions for the existence of globally minimizing solutions, then I found min-max solutions for some particular systems. Finally, I also gave some non-existence results. PB - SISSA U1 - 34737 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - THES T1 - Volume variation and heat kernel for affine control problems Y1 - 2015 A1 - Elisa Paoli KW - Heat kernel asymptotics AB - In this thesis we study two main problems. The first one is the small-time heat kernel expansion on the diagonal for second order hypoelliptic opeartors. We consider operators that can depend on a drift field and that satisfy only the weak Hörmander condition. In a first work we use perturbation techniques to determine the exact order of decay of the heat kernel, that depends on the Lie algebra generated by the fields involved in the hypoelliptic operator. We generalize in particular some results already obtained in the sub-Riemannian setting. In a second work we consider a model class of hypoelliptic operators and we characterize geometrically all the coefficients in the on-the diagonal asymptotics at the equilibrium points of the drift field. The class of operators that we consider contains the linear hypoelliptic operators with constant second order part on the Euclidean space. We describe the coefficients in terms only of the divergence of the drift field and of curvature-like invariants, related to the minimal cost of geodesics of the associated optimal control problem. In the second part of the thesis we consider the variation of a smooth volume along a geodesic. The structure of the manifold is induced by a quadratic Hamiltonian and the geodesic in described as the projection of the Hamiltonian flow. We find an expansion similar to the classical Riemannian one. It depends on the curvature operator associated to the Hamiltonian, on the symbol of the geodesic and on a new metric-measure invariant determined by the symbol of the geodesic and by the given volume. PB - SISSA U1 - 35290 U2 - Mathematics U4 - -1 U5 - MAT/05 ER - TY - RPRT T1 - The wave equation on domains with cracks growing on a prescribed path: existence, uniqueness, and continuous dependence on the data Y1 - 2015 A1 - Gianni Dal Maso A1 - Ilaria Lucardesi AB - Given a bounded open set $\Omega \subset \mathbb R^d$ with Lipschitz boundary and an increasing family $\Gamma_t$, $t\in [0,T]$, of closed subsets of $\Omega$, we analyze the scalar wave equation $\ddot{u} - div (A \nabla u) = f$ in the time varying cracked domains $\Omega\setminus\Gamma_t$. Here we assume that the sets $\Gamma_t$ are contained into a prescribed $(d-1)$-manifold of class $C^2$. Our approach relies on a change of variables: recasting the problem on the reference configuration $\Omega\setminus \Gamma_0$, we are led to consider a hyperbolic problem of the form $\ddot{v} - div (B\nabla v) + a \cdot \nabla v - 2 b \cdot \nabla \dot{v} = g$ in $\Omega \setminus \Gamma_0$. Under suitable assumptions on the regularity of the change of variables that transforms $\Omega\setminus \Gamma_t$ into $\Omega\setminus \Gamma_0$, we prove existence and uniqueness of weak solutions for both formulations. Moreover, we provide an energy equality, which gives, as a by-product, the continuous dependence of the solutions with respect to the cracks. UR - http://urania.sissa.it/xmlui/handle/1963/34629 U1 - 34832 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - An Abstract Nash–Moser Theorem and Quasi-Periodic Solutions for NLW and NLS on Compact Lie Groups and Homogeneous Manifolds Y1 - 2014 A1 - Massimiliano Berti A1 - Livia Corsi A1 - Michela Procesi AB - We prove an abstract implicit function theorem with parameters for smooth operators defined on scales of sequence spaces, modeled for the search of quasi-periodic solutions of PDEs. The tame estimates required for the inverse linearised operators at each step of the iterative scheme are deduced via a multiscale inductive argument. The Cantor-like set of parameters where the solution exists is defined in a non inductive way. This formulation completely decouples the iterative scheme from the measure theoretical analysis of the parameters where the small divisors non-resonance conditions are verified. As an application, we deduce the existence of quasi-periodic solutions for forced NLW and NLS equations on any compact Lie group or manifold which is homogeneous with respect to a compact Lie group, extending previous results valid only for tori. A basic tool of harmonic analysis is the highest weight theory for the irreducible representations of compact Lie groups. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34651 U1 - 34858 U2 - Mathematics ER - TY - JOUR T1 - Achieving unanimous opinions in signed social networks Y1 - 2014 A1 - Claudio Altafini A1 - Gabriele Lini AB - Being able to predict the outcome of an opinion forming process is an important problem in social network theory. However, even for linear dynamics, this becomes a difficult task as soon as non-cooperative interactions are taken into account. Such interactions are naturally modeled as negative weights on the adjacency matrix of the social network. In this paper we show how the Perron-Frobenius theorem can be used for this task also beyond its standard formulation for cooperative systems. In particular we show how it is possible to associate the achievement of unanimous opinions with the existence of invariant cones properly contained in the positive orthant. These cases correspond to signed adjacency matrices having the eventual positivity property, i.e., such that in sufficiently high powers all negative entries have disappeared. More generally, we show how for social networks the achievement of a, possibily non-unanimous, opinion can be associated to the existence of an invariant cone fully contained in one of the orthants of n. PB - Institute of Electrical and Electronics Engineers Inc. UR - http://urania.sissa.it/xmlui/handle/1963/34935 U1 - 35137 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Buckling dynamics of a solvent-stimulated stretched elastomeric sheet Y1 - 2014 A1 - Alessandro Lucantonio A1 - Matthieu Roché A1 - Paola Nardinocchi A1 - Howard A. Stone AB - When stretched uniaxially, a thin elastic sheet may exhibit buckling. The occurrence of buckling depends on the geometrical properties of the sheet and the magnitude of the applied strain. Here we show that an elastomeric sheet initially stable under uniaxial stretching can destabilize when exposed to a solvent that swells the elastomer. We demonstrate experimentally and computationally that the features of the buckling pattern depend on the magnitude of stretching, and this observation offers a new way for controlling the shape of a swollen homogeneous thin sheet. PB - Royal Society of Chemistry UR - http://urania.sissa.it/xmlui/handle/1963/34967 U1 - 35197 U2 - Physics U4 - 1 ER - TY - JOUR T1 - Comparison between reduced basis and stochastic collocation methods for elliptic problems Y1 - 2014 A1 - Peng Chen A1 - Alfio Quarteroni A1 - Gianluigi Rozza AB - The stochastic collocation method (Babuška et al. in SIAM J Numer Anal 45(3):1005-1034, 2007; Nobile et al. in SIAM J Numer Anal 46(5):2411-2442, 2008a; SIAM J Numer Anal 46(5):2309-2345, 2008b; Xiu and Hesthaven in SIAM J Sci Comput 27(3):1118-1139, 2005) has recently been applied to stochastic problems that can be transformed into parametric systems. Meanwhile, the reduced basis method (Maday et al. in Comptes Rendus Mathematique 335(3):289-294, 2002; Patera and Rozza in Reduced basis approximation and a posteriori error estimation for parametrized partial differential equations Version 1.0. Copyright MIT, http://augustine.mit.edu, 2007; Rozza et al. in Arch Comput Methods Eng 15(3):229-275, 2008), primarily developed for solving parametric systems, has been recently used to deal with stochastic problems (Boyaval et al. in Comput Methods Appl Mech Eng 198(41-44):3187-3206, 2009; Arch Comput Methods Eng 17:435-454, 2010). In this work, we aim at comparing the performance of the two methods when applied to the solution of linear stochastic elliptic problems. Two important comparison criteria are considered: (1), convergence results of the approximation error; (2), computational costs for both offline construction and online evaluation. Numerical experiments are performed for problems from low dimensions O (1) to moderate dimensions O (10) and to high dimensions O (100). The main result stemming from our comparison is that the reduced basis method converges better in theory and faster in practice than the stochastic collocation method for smooth problems, and is more suitable for large scale and high dimensional stochastic problems when considering computational costs. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34727 U1 - 34916 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Conformal invariants from nodal sets. I. negative eigenvalues and curvature prescription Y1 - 2014 A1 - Rod R. Gover A1 - Yaiza Canzani A1 - Dmitry Jakobson A1 - Raphaël Ponge A1 - Andrea Malchiodi AB - In this paper, we study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators; more specifically, the Graham, Jenne, Mason, and Sparling (GJMS) operators, which include the Yamabe and Paneitz operators. We give several applications to curvature prescription problems. We establish a version in conformal geometry of Courant's Nodal Domain Theorem. We also show that on any manifold of dimension n≥3, there exist many metrics for which our invariants are nontrivial. We prove that the Yamabe operator can have an arbitrarily large number of negative eigenvalues on any manifold of dimension n≥3. We obtain similar results for some higher order GJMS operators on some Einstein and Heisenberg manifolds. We describe the invariants arising from the Yamabe and Paneitz operators associated to left-invariant metrics on Heisenberg manifolds. Finally, in Appendix, the second named author and Andrea Malchiodi study the Q-curvature prescription problems for noncritical Q-curvatures. PB - Oxford University Press UR - http://urania.sissa.it/xmlui/handle/1963/35128 U1 - 35366 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - A correction and an extension of Stampacchia's work on the geometric BVP Y1 - 2014 A1 - Giovanni Vidossich AB - G. Stampacchia introduced the geometric boundary value problem for ODEs in his doctoral thesis and published four papers related to it. Here we point out that the proof of his last theorem on the subject is incorrect and we provide a substitute for it as well as a generalizations of some of his earlier results. PB - Advanced Nonlinear Studies UR - http://urania.sissa.it/xmlui/handle/1963/35023 U1 - 35263 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Crawling on directional surfaces JF - International Journal of Non-Linear Mechanics Y1 - 2014 A1 - Paolo Gidoni A1 - Giovanni Noselli A1 - Antonio DeSimone KW - Bio-mimetic micro-robots KW - Cell migration KW - Crawling motility KW - Directional surfaces KW - Self-propulsion AB -In this paper we study crawling locomotion based on directional frictional interactions, namely, frictional forces that are sensitive to the sign of the sliding velocity. Surface interactions of this type are common in biology, where they arise from the presence of inclined hairs or scales at the crawler/substrate interface, leading to low resistance when sliding ‘along the grain’, and high resistance when sliding ‘against the grain’. This asymmetry can be exploited for locomotion, in a way analogous to what is done in cross-country skiing (classic style, diagonal stride). We focus on a model system, namely, a continuous one-dimensional crawler and provide a detailed study of the motion resulting from several strategies of shape change. In particular, we provide explicit formulae for the displacements attainable with reciprocal extensions and contractions (breathing), or through the propagation of extension or contraction waves. We believe that our results will prove particularly helpful for the study of biological crawling motility and for the design of bio-mimetic crawling robots.

VL - 61 UR - http://www.sciencedirect.com/science/article/pii/S0020746214000213 ER - TY - JOUR T1 - Critical points of the Moser-Trudinger functional on a disk Y1 - 2014 A1 - Andrea Malchiodi A1 - Luca Martinazzi AB - On the 2-dimensional unit disk $B_1$ we study the Moser-Trudinger functional $$E(u)=\int_{B_1}(e^{u^2}-1)dx, u\in H^1_0(B_1)$$ and its restrictions to $M_\Lambda:=\{u \in H^1_0(B_1):\|u\|^2_{H^1_0}=\Lambda\}$ for $\Lambda>0$. We prove that if a sequence $u_k$ of positive critical points of $E|_{M_{\Lambda_k}}$ (for some $\Lambda_k>0$) blows up as $k\to\infty$, then $\Lambda_k\to 4\pi$, and $u_k\to 0$ weakly in $H^1_0(B_1)$ and strongly in $C^1_{\loc}(\bar B_1\setminus\{0\})$. Using this we also prove that when $\Lambda$ is large enough, then $E|_{M_\Lambda}$ has no positive critical point, complementing previous existence results by Carleson-Chang, M. Struwe and Lamm-Robert-Struwe. PB - European Mathematical Society UR - http://hdl.handle.net/1963/6560 N1 - 16 pages U1 - 6487 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Curvature-adapted remeshing of CAD surfaces JF - Procedia Engineering Y1 - 2014 A1 - Franco Dassi A1 - Andrea Mola A1 - Hang Si AB -A common representation of surfaces with complicated topology and geometry is through composite parametric surfaces as is the case for most CAD modelers. A challenging problem is how to generate a mesh of such a surface that well approximates the geometry of the surface, preserves its topology and important geometric features, and contains nicely shaped elements. In this work, we present an optimization-based surface remeshing method that is able to satisfy many of these requirements simultaneously. This method is inspired by the recent work of Lévy and Bonneel (Proc. 21th International Meshing Roundtable, October 2012), which embeds a smooth surface into a high-dimensional space and remesh it uniformly in that embedding space. Our method works directly in the 3d spaces and uses an embedding space in R6 to evaluate mesh size and mesh quality. It generates a curvatureadapted anisotropic surface mesh that well represents the geometry of the surface with a low number of elements. We illustrate our approach through various examples.

PB - Elsevier VL - 82 UR - https://doi.org/10.1016/j.proeng.2014.10.388 N1 - This is an open access article under the CC BY-NC-ND license U1 - 35220 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - The decomposition of optimal transportation problems with convex cost Y1 - 2014 A1 - Stefano Bianchini A1 - Mauro Bardelloni PB - SISSA UR - http://hdl.handle.net/1963/7433 U1 - 7527 ER - TY - THES T1 - The decomposition of optimal transportation problems with convex cost Y1 - 2014 A1 - Mauro Bardelloni KW - Optimal Transportation PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7475 U1 - 7570 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - A density result for GSBD and its application to the approximation of brittle fracture energies Y1 - 2014 A1 - Flaviana Iurlano AB -We present an approximation result for functions u: Ω → ℝ^n belonging to the space GSBD(Ω) ∩ L2(Ω, ℝn) with e(u) square integrable and Hn-1(Ju) finite. The approximating functions uk are piecewise continuous functions such that uk → u in (Formula Presented). As an application, we provide the extension to the vector-valued case of the Γ-convergence result in GSBV(Ω) proved by Ambrosio and Tortorelli (Commun Pure Appl Math 43:999-1036, 1990; Boll. Un. Mat. Ital. B (7) 6:105-123, 1992).

PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34647 U1 - 34851 U2 - Mathematics ER - TY - JOUR T1 - Discrete one-dimensional crawlers on viscous substrates: achievable net displacements and their energy cost Y1 - 2014 A1 - Giovanni Noselli A1 - Amabile Tatone A1 - Antonio DeSimone KW - Cell migration AB - We study model one-dimensional crawlers, namely, model mechanical systems that can achieve self-propulsion by controlled shape changes of their body (extension or contraction of portions of the body), thanks to frictional interactions with a rigid substrate. We evaluate the achievable net displacement and the related energetic cost for self-propulsion by discrete crawlers (i.e., whose body is made of a discrete number of contractile or extensile segments) moving on substrates with either a Newtonian (linear) or a Bingham-type (stick-slip) rheology. Our analysis is aimed at constructing the basic building blocks towards an integrative, multi-scale description of crawling cell motility. PB - Elsevier UR - http://urania.sissa.it/xmlui/handle/1963/34449 U1 - 34591 U2 - Mathematics ER - TY - RPRT T1 - Dislocations at the continuum scale: functional setting and variational properties Y1 - 2014 A1 - Riccardo Scala A1 - Nicolas Van Goethem UR - http://cvgmt.sns.it/paper/2294/ ER - TY - JOUR T1 - Editorial Y1 - 2014 A1 - Ciro Ciliberto A1 - Gianni Dal Maso A1 - Pasquale Vetro PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34712 U1 - 34926 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - An effective model for nematic liquid crystal composites with ferromagnetic inclusions Y1 - 2014 A1 - Maria Carme Calderer A1 - Antonio DeSimone A1 - Dmitry Golovaty A1 - Alexander Panchenko AB - Molecules of a nematic liquid crystal respond to an applied magnetic field by reorienting themselves in the direction of the field. Since the dielectric anisotropy of a nematic is small, it takes relatively large fields to elicit a significant liquid crystal response. The interaction may be enhanced in colloidal suspensions of ferromagnetic particles in a liquid crystalline matrix- ferronematics-as proposed by Brochard and de Gennes in 1970. The ability of these particles to align with the field and simultaneously cause reorientation of the nematic molecules greatly increases the magnetic response of the mixture. Essentially the particles provide an easy axis of magnetization that interacts with the liquid crystal via surface anchoring. We derive an expression for the effective energy of ferronematic in the dilute limit, that is, when the number of particles tends to infinity while their total volume fraction tends to zero. The total energy of the mixture is assumed to be the sum of the bulk elastic liquid crystal contribution, the anchoring energy of the liquid crystal on the surfaces of the particles, and the magnetic energy of interaction between the particles and the applied magnetic field. The homogenized limiting ferronematic energy is obtained rigorously using a variational approach. It generalizes formal expressions previously reported in the physical literature. PB - Society for Industrial and Applied Mathematics Publications UR - http://urania.sissa.it/xmlui/handle/1963/34940 U1 - 35194 U2 - Physics U4 - 1 ER - TY - RPRT T1 - An efficient computational framework for reduced basis approximation and a posteriori error estimation of parametrized Navier-Stokes flows Y1 - 2014 A1 - Andrea Manzoni KW - Reduced Basis Method, parametrized Navier-Stokes equations, steady incompressible fluids, a posteriori error estimation, approximation stability AB - We present the current Reduced Basis framework for the efficient numerical approximation of parametrized steady Navier-Stokes equations. We have extended the existing setting developed in the last decade (see e.g. [Deparis, Veroy & Patera, Quarteroni & Rozza] to more general affine and nonaffine parametrizations (such as volume-based techniques), to a simultaneous velocity-pressure error estimates and to a fully decoupled Offline/Online procedure in order to speedup the solution of the reduced-order problem. This is particularly suitable for real-time and many-query contexts, which are both part of our final goal. Furthermore, we present an efficient numerical implementation for treating nonlinear advection terms in a convenient way. A residual-based a posteriori error estimation with respect to a truth, full-order Finite Element approximation is provided for joint pressure/velocity errors, according to the Brezzi-Rappaz-Raviart stability theory. To do this, we take advantage of an extension of the Successive Constraint Method for the estimation of stability factors and of a suitable fixed-point algorithm for the approximation of Sobolev embedding constants. Finally, we present some numerical test cases, in order to show both the approximation properties and the computational efficiency of the derived framework. U1 - 7291 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - Existence and uniqueness of the gradient flow of the Entropy in the space of probability measures Y1 - 2014 A1 - Stefano Bianchini A1 - Alexander Dabrowski AB - After a brief introduction on gradient flows in metric spaces and on geodesically convex functionals, we give an account of the proof (following the outline of [3, 7]) of the existence and uniqueness of the gradient flow of the Entropy in the space of Borel probability measures over a compact geodesic metric space with Ricci curvature bounded from below. PB - EUT Edizioni Universita di Trieste UR - http://urania.sissa.it/xmlui/handle/1963/34693 N1 - This paper resumes the main part of the Bachelor thesis of the second author, discussed in 2013 at the University of Trieste. U1 - 34907 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Existence of immersed spheres minimizing curvature functionals in non-compact 3-manifolds JF - Annales de l'Institut Henri Poincare (C) Non Linear Analysis Y1 - 2014 A1 - Andrea Mondino A1 - Johannes Schygulla KW - Direct methods in the calculus of variations KW - General Relativity KW - Geometric measure theory KW - second fundamental form KW - Willmore functional AB -We study curvature functionals for immersed 2-spheres in non-compact, three-dimensional Riemannian manifold $(M,h)$ without boundary. First, under the assumption that $(M,h)$ is the euclidean 3-space endowed with a semi-perturbed metric with perturbation small in $C^1$ norm and of compact support, we prove that if there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})>0$ then there exists a smooth embedding $ f:\mathbb{S}^2 \hookrightarrow M$ minimizing the Willmore functional $\frac{1}{4}\int |H|^2$, where $H$ is the mean curvature. Second, assuming that $(M,h)$ is of bounded geometry (i.e. bounded sectional curvature and strictly positive injectivity radius) and asymptotically euclidean or hyperbolic we prove that if there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})>6$ then there exists a smooth immersion $f:\mathbb{S}^2\hookrightarrow M$ minimizing the functional $\int (\frac{1}{2}|A|^2+1)$, where $A$ is the second fundamental form. Finally, adding the bound $K^M \leq 2$ to the last assumptions, we obtain a smooth minimizer $f:\mathbb{S}^2 \hookrightarrow M$ for the functional $\int \frac{1}{4}(|H|^2+1)$. The assumptions of the last two theorems are satisfied in a large class of 3-manifolds arising as spacelike timeslices solutions of the Einstein vacuum equation in case of null or negative cosmological constant.

VL - 31 UR - http://www.sciencedirect.com/science/article/pii/S0294144913000851 ER - TY - JOUR T1 - Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds JF - Mathematische Annalen Y1 - 2014 A1 - Kuwert, Ernst A1 - Andrea Mondino A1 - Johannes Schygulla AB -We study curvature functionals for immersed 2-spheres in a compact, three-dimensional Riemannian manifold $M$. Under the assumption that the sectional curvature $K^M$ is strictly positive, we prove the existence of a smooth immersion $f:{\mathbb{S}}^2 \rightarrow M$ minimizing the $L^2$ integral of the second fundamental form. Assuming instead that $K^M \leq 2 $ and that there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})>6$, we obtain a smooth minimizer $f:{\mathbb{S}}^2 \rightarrow M$ for the functional $\int \frac{1}{4}|H|^2+1$, where $H$ is the mean curvature.

VL - 359 UR - https://doi.org/10.1007/s00208-013-1005-3 ER - TY - JOUR T1 - Existence of integral m-varifolds minimizing $\int |A|^p $ and $\int |H|^p$ , p>m, in Riemannian manifolds JF - Calculus of Variations and Partial Differential Equations Y1 - 2014 A1 - Andrea Mondino AB -We prove existence of integral rectifiable $m$-dimensional varifolds minimizing functionals of the type $\int |H|^p$ and $\int |A|^p$ in a given Riemannian $n$-dimensional manifold $(N,g)$, $2 \leq m<n$ and $p>m$ under suitable assumptions on $N$ (in the end of the paper we give many examples of such ambient manifolds). To this aim we introduce the following new tools: some monotonicity formulas for varifolds in ${\mathbb{R }^S}$ involving $\int |H|^p$to avoid degeneracy of the minimizer, and a sort of isoperimetric inequality to bound the mass in terms of the mentioned functionals.

VL - 49 UR - https://doi.org/10.1007/s00526-012-0588-y ER - TY - Generic T1 - A fully nonlinear potential model for ship hydrodynamics directly interfaced with CAD data structures T2 - Proceedings of the 24th International Ocean and Polar Engineering Conference, Busan, 2014 Y1 - 2014 A1 - Andrea Mola A1 - Luca Heltai A1 - Antonio DeSimone KW - ship hydrodynamics AB - We present a model for ship hydrodynamics simulations currently under development at SISSA. The model employs potential flow theory and fully nonlinear free surface boundary conditions. The spatial discretization of the equations is performed by means of a collocation BEM. This gives rise to a Differential Algbraic Equations (DAE) system, solved using an implicit BDF scheme to time advance the solution. The model has been implemented into a C++ software able to automatically generate the computational grids from the CAD geometry of the hull. Numerical results on Kriso KCS and KVLCC2 hulls are presented and discussed. JF - Proceedings of the 24th International Ocean and Polar Engineering Conference, Busan, 2014 PB - SISSA U1 - 7357 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - CHAP T1 - Fundamentals of Reduced Basis Method for problems governed by parametrized PDEs and applications T2 - Separated representations and PGD-based model reduction : fundamentals and applications Y1 - 2014 A1 - Gianluigi Rozza KW - reduced basis method, linear elasticity, heat transfer, error bounds, parametrized PDEs AB -In this chapter we consider Reduced Basis (RB) approximations of parametrized Partial Differential Equations (PDEs). The the idea behind RB is to decouple the generation and projection stages (Offline/Online computational procedures) of the approximation process in order to solve parametrized PDEs in a fast, inexpensive and reliable way. The RB method, especially applied to 3D problems, allows great computational savings with respect to the classical Galerkin Finite Element (FE) Method. The standard FE method is typically ill suited to (i) iterative contexts like optimization, sensitivity analysis and many-queries in general, and (ii) real time evaluation. We consider for simplicity coercive PDEs. We discuss all the steps to set up a RB approximation, either from an analytical and a numerical point of view. Then we present an application of the RB method to a steady thermal conductivity problem in heat transfer with emphasis on geometrical and physical parameters.

JF - Separated representations and PGD-based model reduction : fundamentals and applications T3 - CISM International Centre for Mechanical Sciences PB - Springer CY - Wien VL - 554 ER - TY - THES T1 - Geometry and analysis of control-affine systems: motion planning, heat and Schrödinger evolution Y1 - 2014 A1 - Dario Prandi KW - control theory AB - This thesis is dedicated to two problems arising from geometric control theory, regarding control-affine systems $\dot q= f_0(q)+\sum_{j=1}^m u_j f_j(q)$, where $f_0$ is called the drift. In the first part we extend the concept of complexity of non-admissible trajectories, well understood for sub-Riemannian systems, to this more general case, and find asymptotic estimates. In order to do this, we also prove a result in the same spirit as the Ball-Box theorem for sub-Riemannian systems, in the context of control-affine systems equipped with the L1 cost. Then, in the second part of the thesis, we consider a family of 2-dimensional driftless control systems. For these, we study how the set where the control vector fields become collinear affects the diffusion dynamics. More precisely, we study whether solutions to the heat and Schrödinger equations associated with this Laplace-Beltrami operator are able to cross this singularity, and how its the presence affects the spectral properties of the operator, in particular under a magnetic Aharonov–Bohm-type perturbation. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7474 U1 - 7576 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Global Structure of Admissible BV Solutions to Piecewise Genuinely Nonlinear, Strictly Hyperbolic Conservation Laws in One Space Dimension Y1 - 2014 A1 - Stefano Bianchini A1 - Lei Yu AB -The paper describes the qualitative structure of an admissible BV solution to a strictly hyperbolic system of conservation laws whose characteristic families are piecewise genuinely nonlinear. More precisely, we prove that there are a countable set of points Θ and a countable family of Lipschitz curves T{script} such that outside T{script} ∪ Θ the solution is continuous, and for all points in T{script}{set minus}Θ the solution has left and right limit. This extends the corresponding structural result in [7] for genuinely nonlinear systems. An application of this result is the stability of the wave structure of solution w.r.t. -convergence. The proof is based on the introduction of subdiscontinuities of a shock, whose behavior is qualitatively analogous to the discontinuities of the solution to genuinely nonlinear systems.

PB - Taylor & Francis UR - http://urania.sissa.it/xmlui/handle/1963/34694 U1 - 34908 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Hölder equivalence of the value function for control-affine systems JF - ESAIM: Control, Optimisation and Calculus of Variations Y1 - 2014 A1 - Dario Prandi PB - EDP Sciences VL - 20 ER - TY - RPRT T1 - Homogenization of functional with linear growth in the context of A-quasiconvexity Y1 - 2014 A1 - Jose Matias A1 - Marco Morandotti A1 - Pedro M. Santos AB - This work deals with the homogenization of functionals with linear growth in the context of A-quasiconvexity. A representation theorem is proved, where the new integrand function is obtained by solving a cell problem where the coupling between homogenization and the A-free condition plays a crucial role. This result extends some previous work to the linear case, thus allowing for concentration effects. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7436 U1 - 7528 ER - TY - JOUR T1 - Homology computation for a class of contact structures on T3 Y1 - 2014 A1 - Ali Maalaoui A1 - Vittorio Martino AB - We consider a family of tight contact forms on the three-dimensional torus and we compute the relative Contact Homology by using the variational theory of critical points at infinity. We will also show local stability. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34649 U1 - 34856 U2 - Mathematics ER - TY - THES T1 - KAM for quasi-linear and fully nonlinear perturbations of Airy and KdV equations Y1 - 2014 A1 - Riccardo Montalto PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7476 U1 - 7571 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - KAM for quasi-linear KdV JF - C. R. Math. Acad. Sci. Paris Y1 - 2014 A1 - P Baldi A1 - Massimiliano Berti A1 - Riccardo Montalto AB -We prove the existence and stability of Cantor families of quasi-periodic, small-amplitude solutions of quasi-linear autonomous Hamiltonian perturbations of KdV.

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

PB - Springer VL - 212 UR - http://urania.sissa.it/xmlui/handle/1963/34646 IS - 3 U1 - 34850 U2 - Mathematics ER - TY - JOUR T1 - Laplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length Y1 - 2014 A1 - Gianni Dal Maso A1 - Gianluca Orlando A1 - Rodica Toader KW - cracked domains, energy release rate, higher order derivatives, asymptotic expansion of solutions AB -We consider the weak solution of the Laplace equation in a planar domain with a straight crack, prescribing a homogeneous Neumann condition on the crack and a nonhomogeneous Dirichlet condition on the rest of the boundary. For every k we express the k-th derivative of the energy with respect to the crack length in terms of a finite number of coefficients of the asymptotic expansion of the solution near the crack tip and of a finite number of other parameters, which only depend on the shape of the domain.

PB - SISSA UR - http://hdl.handle.net/1963/7271 U1 - 7316 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - CHAP T1 - Lecture notes on gradient flows and optimal transport Y1 - 2014 A1 - Sara Daneri A1 - Giuseppe Savarè AB - We present a short overview on the strongest variational formulation for gradient flows of geodesically λ-convex functionals in metric spaces, with applications to diffusion equations in Wasserstein spaces of probability measures. These notes are based on a series of lectures given by the second author for the Summer School "Optimal transportation: Theory and applications" in Grenoble during the week of June 22-26, 2009. PB - Cambridge University Press UR - http://urania.sissa.it/xmlui/handle/1963/35093 N1 - Book title: Optimal transportation U1 - 35348 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Legendre duality on hypersurfaces in Kähler manifolds Y1 - 2014 A1 - Vittorio Martino AB - We give a sufficient condition on real strictly Levi-convex hypersurfaces M, embedded in four-dimensional Kähler manifolds V , such that Legendre duality can be performed. We consider the contact form onM whose kernel is the restriction of the holomorphic tangent space of V and show that if there exists a Legendrian Killing vector field v, then the dual form β(̇) := d(v, ̇) is a contact form on M with the same orientation than theta. PB - Walter de Gruyter and Co. UR - http://urania.sissa.it/xmlui/handle/1963/34777 U1 - 34998 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Linearized plastic plate models as Γ-limits of 3D finite elastoplasticity JF - ESAIM: Control, Optimisation and Calculus of Variations Y1 - 2014 A1 - Elisa Davoli AB -The subject of this paper is the rigorous derivation of reduced models for a thin plate by means of $\Gamma$-convergence, in the framework of finite plasticity. Denoting by $\epsilon$ the thickness of the plate, we analyse the case where the scaling factor of the elasto-plastic energy per unit volume is of order $\epsilon^{2 \alpha -2}$, with $\alpha \geq 3$. According to the value of $\alpha$, partially or fully linearized models are deduced, which correspond, in the absence of plastic deformation, to the Von Kármán plate theory and the linearized plate theory.

PB - EDP Sciences VL - 20 ER - TY - JOUR T1 - Lipschitz continuous viscosity solutions for a class of fully nonlinear equations on lie groups Y1 - 2014 A1 - Vittorio Martino A1 - Annamaria Montanari AB - In this paper, we prove existence and uniqueness of Lipschitz continuous viscosity solutions for Dirichlet problems involving a class a fully non-linear operators on Lie groups. In particular, we consider the elementary symmetric functions of the eigenvalues of the Hessian built with left-invariant vector fields. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34699 U1 - 34910 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Local and global minimality results for a nonlocal isoperimetric problem on R^N JF - SIAM Journal on Mathematical Analysis Y1 - 2014 A1 - Marco Bonacini A1 - Riccardo Cristoferi KW - Nonlocal isoperimetric problem AB -We consider a nonlocal isoperimetric problem defined in the whole space R^N, whose nonlocal part is given by a Riesz potential with exponent $\alpha\in(0, N-1)$. We show that critical configurations with positive second variation are local minimizers and satisfy a quantitative inequality with respect to the L^1-norm. This criterion provides the existence of a (explicitly determined) critical threshold determining the interval of volumes for which the ball is a local minimizer, and allows to address several global minimality issues.

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

PB - SISSA U1 - 7301 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - On the Lp-differentiability of certain classes of functions Y1 - 2014 A1 - Giovanni Alberti A1 - Stefano Bianchini A1 - Gianluca Crippa AB - We prove the Lp-differentiability at almost every point for convolution products on ℝd of the form K*μ, where μ is bounded measure and K is a homogeneous kernel of degree 1-d. From this result we derive the Lp-differentiability for vector fields on R d whose curl and divergence are measures, and also for vector fields with bounded deformation. PB - European Mathematical Society UR - http://urania.sissa.it/xmlui/handle/1963/34695 U1 - 34909 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Maximal generalized solution of eikonal equation Y1 - 2014 A1 - Sandro Zagatti AB - We study the Dirichlet problem for the eikonal equation: 1/2 |∇u(x)|^2-a(x)=0 in Ω u(x)=(x) on Ω, without continuity assumptions on the map a(.). We find a class of maps a(.) contained in the space L∞(Ω) for which the problem admits a (maximal) generalized solution, providing a generalization of the notion of viscosity solution. PB - Elsevier UR - http://urania.sissa.it/xmlui/handle/1963/34642 U1 - 34846 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - A model for crack growth with branching and kinking JF - Asymptotic Analysis Y1 - 2014 A1 - Simone Racca KW - quasistatic crack evolution, branching, kinking, Griffith\\\'s criterion AB -We study an evolution model for fractured elastic materials in the 2-dimensional case, for which the crack path is not assumed to be known a priori. We introduce some general assumptions on the structure of the fracture sets suitable to remove the restrictions on the regularity of the crack sets and to allow for kinking and branching to develop. In addition we define the front of the fracture and its velocity. By means of a time-discretization approach, we prove the existence of a continuous-time evolution that satisfies an energy inequality and a stability criterion. The energy balance also takes into account the energy dissipated at the front of the fracture. The stability criterion is stated in the framework of Griffith's theory, in terms of the energy release rate, when the crack grows at least at one point of its front.

PB - SISSA VL - 89 UR - https://content.iospress.com/articles/asymptotic-analysis/asy1233 IS - 1-2 U1 - 6293 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Model Order Reduction in Fluid Dynamics: Challenges and Perspectives Y1 - 2014 A1 - Toni Lassila A1 - Andrea Manzoni A1 - Alfio Quarteroni A1 - Gianluigi Rozza AB - This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities - which are mainly related either to nonlinear convection terms and/or some geometric variability - that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration. We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of inf-sup stability, certification through error estimation, computational issues and-in the unsteady case - long-time stability of the reduced model. Moreover, we provide an extensive list of literature references. PB - Springer U1 - 34923 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - A Moser-Trudinger inequality for the singular Toda system JF - Bull. Inst. Math. Acad. Sin. Y1 - 2014 A1 - Luca Battaglia A1 - Andrea Malchiodi VL - 9 ER - TY - JOUR T1 - New results on Gamma-limits of integral functionals Y1 - 2014 A1 - Nadia Ansini A1 - Gianni Dal Maso A1 - Caterina Ida Zeppieri KW - Gamma-convergence PB - Elsevier UR - http://hdl.handle.net/1963/5880 U1 - 5745 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Nonsingular Isogeometric Boundary Element Method for Stokes Flows in 3D Y1 - 2014 A1 - Luca Heltai A1 - Marino Arroyo A1 - Antonio DeSimone KW - Isogeometric Analysis AB - Isogeometric analysis (IGA) is emerging as a technology bridging Computer Aided Geometric Design (CAGD), most commonly based on Non-Uniform Rational B-Splines (NURBS) surfaces, and engineering analysis. In finite element and boundary element isogeometric methods (FE-IGA and IGA-BEM), the NURBS basis functions that de- scribe the geometry define also the approximation spaces. In the FE-IGA approach, the surfaces generated by the CAGD tools need to be extended to volumetric descriptions, a major open problem in 3D. This additional passage can be avoided in principle when the partial differential equations to be solved admit a formulation in terms of bound- ary integral equations, leading to Boundary Element Isogeometric Analysis (IGA-BEM). The main advantages of such an approach are given by the dimensionality reduction of the problem (from volumetric-based to surface-based), by the fact that the interface with CAGD tools is direct, and by the possibility to treat exterior problems, where the computational domain is infinite. By contrast, these methods produce system matrices which are full, and require the integration of singular kernels. In this paper we address the second point and propose a nonsingular formulation of IGA-BEM for 3D Stokes flows, whose convergence is carefully tested numerically. Standard Gaussian quadrature rules suffice to integrate the boundary integral equations, and carefully chosen known exact solutions of the interior Stokes problem are used to correct the resulting matrices, extending the work by Klaseboer et al. [27] to IGA-BEM. PB - Elsevier UR - http://hdl.handle.net/1963/6326 U1 - 6250 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - On a quadratic functional for scalar conservation laws JF - Journal of Hyperbolic Differential Equations Y1 - 2014 A1 - Stefano Bianchini A1 - Stefano Modena AB -We prove a quadratic interaction estimate for approximate solutions to scalar conservation laws obtained by the wavefront tracking approximation or the Glimm scheme. This quadratic estimate has been used in the literature to prove the convergence rate of the Glimm scheme.

PB - World Scientific Publishing VL - 11 UR - http://arxiv.org/abs/1311.2929 IS - 2 U1 - 34903 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Quadratic interaction functional for systems of conservation laws: a case study JF - Bulletin of the Institute of Mathematics of Academia Sinica (New Series) Y1 - 2014 A1 - Stefano Bianchini A1 - Stefano Modena VL - 9 UR - https://w3.math.sinica.edu.tw/bulletin_ns/20143/2014308.pdf ER - TY - JOUR T1 - Quasi-static crack growth in hydraulic fracture JF - Nonlinear Analysis Y1 - 2014 A1 - Stefano Almi A1 - Gianni Dal Maso A1 - Rodica Toader AB -We present a variational model for the quasi-static crack growth in hydraulic fracture in the framework of the energy formulation of rate-independent processes. The cracks are assumed to lie on a prescribed plane and to satisfy a very weak regularity assumption.

PB - Elsevier VL - 109 UR - http://hdl.handle.net/20.500.11767/17350 IS - Nov U1 - 34741 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Quasistatic Evolution in Perfect Plasticity as Limit of Dynamic Processes JF - Journal of Dynamics and Differential Equations Y1 - 2014 A1 - Gianni Dal Maso A1 - Riccardo Scala AB -We introduce a model of dynamic visco-elasto-plastic evolution in the linearly elastic regime and prove an existence and uniqueness result. Then we study the limit of (a rescaled version of) the solutions when the data vary slowly. We prove that they converge, up to a subsequence, to a quasistatic evolution in perfect plasticity.

VL - 26 UR - https://doi.org/10.1007/s10884-014-9409-7 ER - TY - JOUR T1 - Quasistatic evolution models for thin plates arising as low energy Γ-limits of finite plasticity JF - Mathematical Models and Methods in Applied Sciences Y1 - 2014 A1 - Elisa Davoli AB -In this paper we deduce by $\Gamma$-convergence some partially and fully linearized quasistatic evolution models for thin plates, in the framework of finite plasticity. Denoting by $\epsilon$ the thickness of the plate, we study the case where the scaling factor of the elasto-plastic energy is of order $\epsilon^{2 \alpha -2}$, with $\alpha\geq 3$. These scalings of the energy lead, in the absence of plastic dissipation, to the Von Kármán and linearized Von Kármán functionals for thin plates. We show that solutions to the three-dimensional quasistatic evolution problems converge, as the thickness of the plate tends to zero, to a quasistatic evolution associated to a suitable reduced model depending on $\alpha$.

VL - 24 UR - https://doi.org/10.1142/S021820251450016X ER - TY - RPRT T1 - Rate-independent damage in thermo-viscoelastic materials with inertia Y1 - 2014 A1 - Giuliano Lazzaroni A1 - Riccarda Rossi A1 - Marita Thomas A1 - Rodica Toader AB - We present a model for rate-independent, unidirectional, partial damage in visco-elastic materials with inertia and thermal effects. The damage process is modeled by means of an internal variable, governed by a rate-independent flow rule. The heat equation and the momentum balance for the displacements are coupled in a highly nonlinear way. Our assumptions on the corresponding energy functional also comprise the case of the Ambrosio-Tortorelli phase-field model (without passage to the brittle limit). We discuss a suitable weak formulation and prove an existence theorem obtained with the aid of a (partially) decoupled time-discrete scheme and variational convergence methods. We also carry out the asymptotic analysis for vanishing viscosity and inertia and obtain a fully rate-independent limit model for displacements and damage, which is Independent of temperature. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7444 U1 - 7542 ER - TY - CONF T1 - Reduced basis method for the Stokes equations in decomposable domains using greedy optimization T2 - ECMI 2014 proceedings Y1 - 2014 A1 - Laura Iapichino A1 - Alfio Quarteroni A1 - Gianluigi Rozza A1 - Volkwein, Stefan JF - ECMI 2014 proceedings ER - TY - BOOK T1 - Reduced Order Methods for Modeling and Computational Reduction T2 - MS&A Y1 - 2014 A1 - Alfio Quarteroni A1 - Gianluigi Rozza KW - reduced order methods, MOR, ROM, POD, RB, greedy, CFD, Numerical Analysis AB -This monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics.

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

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

JF - MS&A PB - Springer CY - Milano VL - 9 ER - TY - CHAP T1 - Reduction on characteristics for continuous of a scalar balance law T2 - AIMS Series on Applied Mathematics, vol. 8 (2014): 399 - 406 Y1 - 2014 A1 - Giovanni Alberti A1 - Stefano Bianchini A1 - Laura Caravenna KW - Method of characteristics JF - AIMS Series on Applied Mathematics, vol. 8 (2014): 399 - 406 PB - SISSA UR - http://hdl.handle.net/1963/6562 U1 - 6516 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - A robotic crawler exploiting directional frictional interactions: experiments, numerics, and derivation of a reduced model JF - Proceedings of the Royal Society A 470, 20140333 (2014) Y1 - 2014 A1 - Giovanni Noselli A1 - Antonio DeSimone AB - We present experimental and numerical results for a model crawler which is able to extract net positional changes from reciprocal shape changes, i.e. ‘breathing-like’ deformations, thanks to directional, frictional interactions with a textured solid substrate, mediated by flexible inclined feet. We also present a simple reduced model that captures the essential features of the kinematics and energetics of the gait, and compare its predictions with the results from experiments and from numerical simulations. PB - Royal Society Publishing U1 - 34594 U2 - Mathematics ER - TY - JOUR T1 - SBV Regularity of Systems of Conservation Laws and Hamilton–Jacobi Equations Y1 - 2014 A1 - Stefano Bianchini AB - We review the SBV regularity for solutions to hyperbolic systems of conservation laws and Hamilton-Jacobi equations. We give an overview of the techniques involved in the proof, and a collection of related problems concludes the paper. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34691 U1 - 34904 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Second Order Asymptotic Development for the Anisotropic Cahn-Hilliard Functional Y1 - 2014 A1 - Gianni Dal Maso A1 - Irene Fonseca A1 - Giovanni Leoni KW - Gamma-convergence, Cahn-Hilliard functional, phase transitions AB - The asymptotic behavior of an anisotropic Cahn-Hilliard functional with prescribed mass and Dirichlet boundary condition is studied when the parameter $\varepsilon$ that determines the width of the transition layers tends to zero. The double-well potential is assumed to be even and equal to $|s-1|^\beta$ near $s=1$, with $1<\beta<2$. The first order term in the asymptotic development by $\Gamma$-convergence is well-known, and is related to a suitable anisotropic perimeter of the interface. Here it is shown that, under these assumptions, the second order term is zero, which gives an estimate on the rate of convergence of the minimum values. PB - SISSA UR - http://hdl.handle.net/1963/7390 N1 - This article is composed if 33 pages and recorded in PDF format U1 - 7439 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Shape control of active surfaces inspired by the movement of euglenids Y1 - 2014 A1 - Marino Arroyo A1 - Antonio DeSimone AB - We examine a novel mechanism for active surface morphing inspired by the cell body deformations of euglenids. Actuation is accomplished through in-plane simple shear along prescribed slip lines decorating the surface. Under general non-uniform actuation, such local deformation produces Gaussian curvature, and therefore leads to shape changes. Geometrically, a deformation that realizes the prescribed local shear is an isometric embedding. We explore the possibilities and limitations of this bio-inspired shape morphing mechanism, by first characterizing isometric embeddings under axisymmetry, understanding the limits of embeddability, and studying in detail the accessibility of surfaces of zero and constant curvature. Modeling mechanically the active surface as a non-Euclidean plate (NEP), we further examine the mechanism beyond the geometric singularities arising from embeddability, where mechanics and buckling play a decisive role. We also propose a non-axisymmetric actuation strategy to accomplish large amplitude bending and twisting motions of elongated cylindrical surfaces. Besides helping understand how euglenids delicately control their shape, our results may provide the background to engineer soft machines. PB - Elsevier UR - http://urania.sissa.it/xmlui/handle/1963/35118 U1 - 35375 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Shape Optimization by Free-Form Deformation: Existence Results and Numerical Solution for Stokes Flows Y1 - 2014 A1 - F. Ballarin A1 - Andrea Manzoni A1 - Gianluigi Rozza A1 - Sandro Salsa AB - Shape optimization problems governed by PDEs result from many applications in computational fluid dynamics. These problems usually entail very large computational costs and require also a suitable approach for representing and deforming efficiently the shape of the underlying geometry, as well as for computing the shape gradient of the cost functional to be minimized. Several approaches based on the displacement of a set of control points have been developed in the last decades, such as the so-called free-form deformations. In this paper we present a new theoretical result which allows to recast free-form deformations into the general class of perturbation of identity maps, and to guarantee the compactness of the set of admissible shapes. Moreover, we address both a general optimization framework based on the continuous shape gradient and a numerical procedure for solving efficiently three-dimensional optimal design problems. This framework is applied to the optimal design of immersed bodies in Stokes flows, for which we consider the numerical solution of a benchmark case study from literature. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34698 U1 - 34914 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Smooth approximation of bi-Lipschitz orientation-preserving homeomorphisms JF - Annales de l'Institut Henri Poincare (C) Non Linear Analysis Y1 - 2014 A1 - Sara Daneri A1 - Aldo Pratelli AB -

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

VL - 31 UR - http://www.sciencedirect.com/science/article/pii/S0294144913000711 ER - TY - RPRT T1 - Some remarks on a model for rate-independent damage in thermo-visco-elastodynamics Y1 - 2014 A1 - Giuliano Lazzaroni A1 - Riccarda Rossi A1 - Marita Thomas A1 - Rodica Toader AB - This note deals with the analysis of a model for partial damage, where the rateindependent, unidirectional flow rule for the damage variable is coupled with the rate-dependent heat equation, and with the momentum balance featuring inertia and viscosity according to Kelvin-Voigt rheology. The results presented here combine the approach from Roubicek [1] with the methods from Lazzaroni/Rossi/Thomas/Toader [2] and extend the analysis to the setting of inhomogeneous time-dependent Dirichlet data. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7463 U1 - 7566 ER - TY - JOUR T1 - Some remarks on the seismic behaviour of embedded cantilevered retaining walls Y1 - 2014 A1 - Riccardo Conti A1 - F. Burali D'Arezzo A1 - Giulia M.B. Viggiani AB - This paper is a numerical investigation of the physical phenomena that control the dynamic behaviour of embedded cantilevered retaining walls. Recent experimental observations obtained from centrifuge tests have shown that embedded cantilevered retaining walls experience permanent displacements even before the acceleration reaches its critical value, corresponding to full mobilisation of the soil strength. The motivation for this work stems from the need to incorporate these observations in simplified design procedures. A parametric study was carried out on a pair of embedded cantilevered walls in dry sand, subjected to real earthquakes scaled at different values of the maximum acceleration. The results of these analyses indicate that, for the geotechnical design of the wall, the equivalent acceleration to be used in pseudo-static calculations can be related to the maximum displacement that the structure can sustain, and can be larger than the maximum acceleration expected at the site. For the structural design of the wall, it is suggested that the maximum bending moments of the wall can be computed using a realistic distribution of contact stress and a conservative value of the pseudo-static acceleration, taking into account two-dimensional amplification effects near the walls. PB - Thomas Telford UR - http://urania.sissa.it/xmlui/handle/1963/35073 U1 - 35308 U2 - Physics U4 - 2 ER - TY - JOUR T1 - Spontaneous division and motility in active nematic droplets Y1 - 2014 A1 - Luca Giomi A1 - Antonio DeSimone AB - We investigate the mechanics of an active droplet endowed with internal nematic order and surrounded by an isotropic Newtonian fluid. Using numerical simulations we demonstrate that, due to the interplay between the active stresses and the defective geometry of the nematic director, this system exhibits two of the fundamental functions of living cells: spontaneous division and motility, by means of self-generated hydrodynamic flows. These behaviors can be selectively activated by controlling a single physical parameter, namely, an active variant of the capillary number. PB - American Physical Society UR - http://urania.sissa.it/xmlui/handle/1963/34902 U1 - 35107 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Stability of equilibrium configurations for elastic films in two and three dimensions JF - Advances in Calculus of Variations Y1 - 2014 A1 - Marco Bonacini KW - Epitaxially strained elastic films AB -We establish a local minimality sufficiency criterion, based on the strict positivity of the second variation, in the context of a variational model for the epitaxial growth of elastic films. Our result holds also in the three-dimensional case and for a general class of nonlinear elastic energies. Applications to the study of the local minimality of flat morphologies are also shown.

PB - SISSA VL - 8 UR - https://www.degruyter.com/view/j/acv.2015.8.issue-2/acv-2013-0018/acv-2013-0018.xml IS - 2 U1 - 6997 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Stabilized reduced basis method for parametrized advection-diffusion PDEs JF - Computer Methods in Applied Mechanics and Engineering Y1 - 2014 A1 - Pacciarini, P. A1 - Gianluigi Rozza AB -In this work, we propose viable and efficient strategies for the stabilization of the reduced basis approximation of an advection dominated problem. In particular, we investigate the combination of a classic stabilization method (SUPG) with the Offline-Online structure of the RB method. We explain why the stabilization is needed in both stages and we identify, analytically and numerically, which are the drawbacks of a stabilization performed only during the construction of the reduced basis (i.e. only in the Offline stage). We carry out numerical tests to assess the performances of the ``double'' stabilization both in steady and unsteady problems, also related to heat transfer phenomena.

VL - 274 ER - TY - CONF T1 - Stabilized reduced basis method for parametrized scalar advection-diffusion problems at higher Péclet number: Roles of the boundary layers and inner fronts T2 - 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014 Y1 - 2014 A1 - Pacciarini, P. A1 - Gianluigi Rozza AB -Advection-dominated problems, which arise in many engineering situations, often require a fast and reliable approximation of the solution given some parameters as inputs. In this work we want to investigate the coupling of the reduced basis method - which guarantees rapidity and reliability - with some classical stabilization techiques to deal with the advection-dominated condition. We provide a numerical extension of the results presented in [1], focusing in particular on problems with curved boundary layers and inner fronts whose direction depends on the parameter.

JF - 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014 UR - https://infoscience.epfl.ch/record/203327/files/ECCOMAS_PP_GR.pdf ER - TY - RPRT T1 - Steady nearly incompressible vector elds in 2D: chain rule and renormalization Y1 - 2014 A1 - Stefano Bianchini A1 - N.A. Gusev PB - SISSA U1 - 7464 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - Structure of entropy solutions to general scalar conservation laws in one space dimension JF - Journal of Mathematical Analysis and Applications Y1 - 2014 A1 - Stefano Bianchini A1 - Lei Yu PB - SISSA VL - 428 UR - https://www.sciencedirect.com/science/article/pii/S0022247X15002218 IS - 1 U1 - 7305 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - Swelling dynamics of a thin elastomeric sheet under uniaxial pre-stretch Y1 - 2014 A1 - Alessandro Lucantonio A1 - Paola Nardinocchi A1 - Howard A. Stone AB - It has been demonstrated experimentally that pre-stretch affects the swelling of an elastomeric membrane when it is exposed to a solvent. We study theoretically the one-dimensional swelling of a pre-stretched thin elastomeric sheet, bonded to an impermeable rigid substrate, to quantify the influence of pre-stretch. We show that the solvent uptake increases when pre-stretch increases, both at equilibrium and during the swelling transient, where it exhibits two different scaling regimes. The coupling between the solvent uptake and pre-stretch may be practically exploited to design soft actuators where the swelling-induced deformations can be controlled by varying the pre-stretch. PB - American Institute of Physics UR - http://urania.sissa.it/xmlui/handle/1963/35113 U1 - 35370 U2 - Physics U4 - 1 ER - TY - JOUR T1 - Swelling-induced and controlled curving in layered gel beams Y1 - 2014 A1 - Alessandro Lucantonio A1 - Paola Nardinocchi A1 - Matteo Pezzulla AB - We describe swelling-driven curving in originally straight and non-homogeneous beams. We present and verify a structural model of swollen beams, based on a new point of view adopted to describe swelling-induced deformation processes in bilayered gel beams, that is based on the split of the swelling-induced deformation of the beam at equilibrium into two components, both depending on the elastic properties of the gel. The method allows us to: (i) determine beam stretching and curving, once assigned the characteristics of the solvent bath and of the non-homogeneous beam, and (ii) estimate the characteristics of non-homogeneous flat gel beams in such a way as to obtain, under free-swelling conditions, three-dimensional shapes. The study was pursued by means of analytical, semi-analytical and numerical tools; excellent agreement of the outcomes of the different techniques was found, thus confirming the strength of the method. PB - Royal Society of London UR - http://urania.sissa.it/xmlui/handle/1963/34987 U1 - 35229 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - The topology of a subspace of the Legendrian curves on a closed contact 3-manifold Y1 - 2014 A1 - Ali Maalaoui A1 - Vittorio Martino AB - In this paper we study a subspace of the space of Legendrian loops and we show that the injection of this space into the full loop space is an S 1-equivariant homotopy equivalence. This space can be also seen as the space of zero Maslov index Legendrian loops and it shows up as a suitable space of variations in contact form geometry. PB - Advanced Nonlinear Studies UR - http://urania.sissa.it/xmlui/handle/1963/35016 U1 - 35262 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - A uniqueness result for the continuity equation in two dimensions: dedicated to constantine dafermos on the occasion of his 70th birthday Y1 - 2014 A1 - Giovanni Alberti A1 - Stefano Bianchini A1 - Gianluca Crippa AB - We characterize the autonomous, divergence-free vector fields b on the plane such that the Cauchy problem for the continuity equation ∂tu +div(bu) = 0 admits a unique bounded solution (in the weak sense) for every bounded initial datum; the characterization is given in terms of a property of Sard type for the potential f associated to b. As a corollary we obtain uniqueness under the assumption that the curl of b is a measure. This result can be extended to certain nonautonomous vector fields b with bounded divergence. PB - European Mathematical Society; Springer Verlag UR - http://urania.sissa.it/xmlui/handle/1963/34692 U1 - 34906 U2 - Mathematics U4 - 1 ER - TY - THES T1 - A variational approach to statics and dynamics of elasto-plastic systems Y1 - 2014 A1 - Riccardo Scala KW - delamination AB - We prove some existence results for dynamic evolutions in elasto-plasticity and delamination. We study the limit as the data vary very slowly and prove convergence results to quasistatic evolutions. We model dislocations by mean of currents, we introduce the space of deformations in the presence of dislocations and study the graphs of these maps. We prove existence results for minimum problems. We study the properties of minimizers. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7471 U1 - 7583 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - A variational model for the quasi-static growth of fractional dimensional brittle fractures Y1 - 2014 A1 - Simone Racca A1 - Rodica Toader KW - Variational models AB -We propose a variational model for the irreversible quasi-static evolution of brittle fractures having fractional Hausdorff dimension in the setting of two-dimensional antiplane and plane elasticity. The evolution along such irregular crack paths can be obtained as $\Gamma$-limit of evolutions along one-dimensional cracks when the fracture toughness tends to zero.

PB - European Mathematical Society UR - http://hdl.handle.net/1963/6983 U1 - 6973 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - A weighted empirical interpolation method: A priori convergence analysis and applications Y1 - 2014 A1 - Peng Chen A1 - Alfio Quarteroni A1 - Gianluigi Rozza AB - We extend the classical empirical interpolation method [M. Barrault, Y. Maday, N.C. Nguyen and A.T. Patera, An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations. Compt. Rend. Math. Anal. Num. 339 (2004) 667-672] to a weighted empirical interpolation method in order to approximate nonlinear parametric functions with weighted parameters, e.g. random variables obeying various probability distributions. A priori convergence analysis is provided for the proposed method and the error bound by Kolmogorov N-width is improved from the recent work [Y. Maday, N.C. Nguyen, A.T. Patera and G.S.H. Pau, A general, multipurpose interpolation procedure: the magic points. Commun. Pure Appl. Anal. 8 (2009) 383-404]. We apply our method to geometric Brownian motion, exponential Karhunen-Loève expansion and reduced basis approximation of non-affine stochastic elliptic equations. We demonstrate its improved accuracy and efficiency over the empirical interpolation method, as well as sparse grid stochastic collocation method. PB - EDP Sciences UR - http://urania.sissa.it/xmlui/handle/1963/35021 U1 - 35253 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - Where best to place a Dirichlet condition in an anisotropic membrane? Y1 - 2014 A1 - Paolo Tilli A1 - Davide Zucco AB - We study a shape optimization problem for the first eigenvalue of an elliptic operator in divergence form, with non constant coefficients, over a fixed domain $\Omega$. Dirichlet conditions are imposed along $\partial\Omega$ and, in addition, along a set $\Sigma$ of prescribed length ($1$-dimensional Hausdorff measure). We look for the best shape and position for the supplementary Dirichlet region $\Sigma$ in order to maximize the first eigenvalue. We characterize the limit distribution of the optimal sets, as their prescribed length tends to infinity, via $\Gamma$-convergence. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7481 U1 - 7592 ER - TY - RPRT T1 - Ambrosio-Tortorelli approximation of cohesive fracture models in linearized elasticity Y1 - 2013 A1 - Matteo Focardi A1 - Flaviana Iurlano KW - Functions of bounded deformation AB -We provide an approximation result in the sense of $\Gamma$-convergence for cohesive fracture energies of the form \[ \int_\Omega \mathscr{Q}_1(e(u))\,dx+a\,\mathcal{H}^{n-1}(J_u)+b\,\int_{J_u}\mathscr{Q}_0^{1/2}([u]\odot\nu_u)\,d\mathcal{H}^{n-1}, \] where $\Omega\subset{\mathbb R}^n$ is a bounded open set with Lipschitz boundary, $\mathscr{Q}_0$ and $\mathscr{Q}_1$ are coercive quadratic forms on ${\mathbb M}^{n\times n}_{sym}$, $a,\,b$ are positive constants, and $u$ runs in the space of fields $SBD^2(\Omega)$ , i.e., it's a special field with bounded deformation such that its symmetric gradient $e(u)$ is square integrable, and its jump set $J_u$ has finite $(n-1)$-Hausdorff measure in ${\mathbb R}^n$. The approximation is performed by means of Ambrosio-Tortorelli type elliptic regularizations, the prototype example being \[ \int_\Omega\Big(v|e(u)|^2+\frac{(1-v)^2}{\varepsilon}+{\gamma\,\varepsilon}|\nabla v|^2\Big)\,dx, \] where $(u,v)\in H^1(\Omega,{\mathbb R}^n){\times} H^1(\Omega)$, $\varepsilon\leq v\leq 1$ and $\gamma>0$.

PB - SISSA UR - http://hdl.handle.net/1963/6615 U1 - 6573 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Analytical validation of a continuum model for epitaxial growth with elasticity on vicinal surfaces Y1 - 2013 A1 - Gianni Dal Maso A1 - Irene Fonseca A1 - Giovanni Leoni KW - singular nonlinear parabolic equations, Hilbert transform, thin films AB - In this paper it is shown existence of weak solutions of a variational inequality derived from the continuum model introduced by Xiang [7, formula (3.62)] (see also the work of Xiang and E [8] and Xu and Xiang [9]) to describe the self-organization of terraces and steps driven by misfit elasticity between a film and a substrate in heteroepitaxial growth. This model is obtained as a continuum limit of discrete theories of Duport, Politi, and Villain [3] and Tersoff, Phang, Zhang, and Lagally[6]. PB - Springer UR - http://hdl.handle.net/1963/7245 U1 - 7284 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - THES T1 - An Approximation Result for Generalised Functions of Bounded Deformation and Applications to Damage Problems Y1 - 2013 A1 - Flaviana Iurlano KW - Functions of bounded deformation PB - SISSA U1 - 7203 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Asymptotics of the first Laplace eigenvalue with Dirichlet regions of prescribed length Y1 - 2013 A1 - Paolo Tilli A1 - Davide Zucco AB - We consider the problem of maximizing the first eigenvalue of the $p$-Laplacian (possibly with nonconstant coefficients) over a fixed domain $\Omega$, with Dirichlet conditions along $\partial\Omega$ and along a supplementary set $\Sigma$, which is the unknown of the optimization problem. The set $\Sigma$, which plays the role of a supplementary stiffening rib for a membrane $\Omega$, is a compact connected set (e.g., a curve or a connected system of curves) that can be placed anywhere in $\overline{\Omega}$ and is subject to the constraint of an upper bound $L$ to its total length (one-dimensional Hausdorff measure). This upper bound prevents $\Sigma$ from spreading throughout $\Omega$ and makes the problem well-posed. We investigate the behavior of optimal sets $\Sigma_L$ as $L\to\infty$ via $\Gamma$-convergence, and we explicitly construct certain asymptotically optimal configurations. We also study the behavior as $p\to\infty$ with $L$ fixed, finding connections with maximum-distance problems related to the principal frequency of the $\infty$-Laplacian. PB - Society for Industrial and Applied Mathematics UR - http://urania.sissa.it/xmlui/handle/1963/35141 U1 - 35379 U2 - Physics U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - Attainment results for nematic elastomers Y1 - 2013 A1 - Virginia Agostiniani A1 - Gianni Dal Maso A1 - Antonio DeSimone AB - We consider a class of non-quasiconvex frame indifferent energy densities which includes Ogden-type energy densities for nematic elastomers. For the corresponding geometrically linear problem we provide an explicit minimizer of the energy functional satisfying a nontrivial boundary condition. Other attainment results, both for the nonlinear and the linearized model, are obtained by using the theory of convex integration introduced by Mueller and Sverak in the context of crystalline solids. PB - SISSA UR - http://hdl.handle.net/1963/7174 U1 - 7201 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - A combination between the reduced basis method and the ANOVA expansion: On the computation of sensitivity indices JF - Comptes Rendus Mathematique. Volume 351, Issue 15-16, August 2013, Pages 593-598 Y1 - 2013 A1 - Denis Devaud A1 - Andrea Manzoni A1 - Gianluigi Rozza KW - Partial differential equations AB -We consider a method to efficiently evaluate in a real-time context an output based on the numerical solution of a partial differential equation depending on a large number of parameters. We state a result allowing to improve the computational performance of a three-step RB-ANOVA-RB method. This is a combination of the reduced basis (RB) method and the analysis of variations (ANOVA) expansion, aiming at compressing the parameter space without affecting the accuracy of the output. The idea of this method is to compute a first (coarse) RB approximation of the output of interest involving all the parameter components, but with a large tolerance on the a posteriori error estimate; then, we evaluate the ANOVA expansion of the output and freeze the least important parameter components; finally, considering a restricted model involving just the retained parameter components, we compute a second (fine) RB approximation with a smaller tolerance on the a posteriori error estimate. The fine RB approximation entails lower computational costs than the coarse one, because of the reduction of parameter dimensionality. Our result provides a criterion to avoid the computation of those terms in the ANOVA expansion that are related to the interaction between parameters in the bilinear form, thus making the RB-ANOVA-RB procedure computationally more feasible.

PB - Elsevier UR - http://hdl.handle.net/1963/7389 U1 - 7434 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Common dynamical features of sensory adaptation in photoreceptors and olfactory sensory neurons. JF - Nature. Scientific Reports 3, Article number: 1251, Published : 13 February 2013 Y1 - 2013 A1 - Giovanna De Palo A1 - Giuseppe Facchetti A1 - Monica Mazzolini A1 - Anna Menini A1 - Vincent Torre A1 - Claudio Altafini AB -Sensory systems adapt, i.e., they adjust their sensitivity to external stimuli according to the ambient level. In this paper we show that single cell electrophysiological responses of vertebrate olfactory receptors and of photoreceptors to different input protocols exhibit several common features related to adaptation, and that these features can be used to investigate the dynamical structure of the feedback regulation responsible for the adaptation. In particular, we point out that two different forms of adaptation can be observed, in response to steps and to pairs of pulses. These two forms of adaptation appear to be in a dynamical trade-off: the more adaptation to a step is close to perfect, the slower is the recovery in adaptation to pulse pairs and viceversa. Neither of the two forms is explained by the dynamical models currently used to describe adaptation, such as the integral feedback model.

PB - SISSA U1 - 6453 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Concentration of solutions for a singularly perturbed mixed problem in non-smooth domains JF - Journal of Differential Equations Y1 - 2013 A1 - Serena Dipierro KW - Finite-dimensional reductions KW - Local inversion KW - Singularly perturbed elliptic problems AB -We consider a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^n$ whose boundary has an $(n−2)$-dimensional singularity. Assuming $1<p<\frac{n+2}{n−2}$, we prove that, under suitable geometric conditions on the boundary of the domain, there exist solutions which approach the intersection of the Neumann and the Dirichlet parts as the singular perturbation parameter tends to zero.

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

VL - 23 UR - https://doi.org/10.1007/s12220-011-9263-3 ER - TY - JOUR T1 - Connected Sum Construction for σk-Yamabe Metrics JF - Journal of Geometric Analysis 23, nr.2 (2013), pages 812-854 Y1 - 2013 A1 - Giovanni Catino A1 - Lorenzo Mazzieri AB - In this paper we produce families of Riemannian metrics with positive constant $\sigma_k$-curvature equal to $2^{-k} {n \choose k}$ by performing the connected sum of two given compact {\em non degenerate} $n$--dimensional solutions $(M_1,g_1)$ and $(M_2,g_2)$ of the (positive) $\sigma_k$-Yamabe problem, provided $2 \leq 2k < n$. The problem is equivalent to solve a second order fully nonlinear elliptic equation. PB - Springer UR - http://hdl.handle.net/1963/6441 N1 - This article has not yet been published. U1 - 6366 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - Crawlers in viscous environments: linear vs nonlinear rheology JF - International Journal of Non-Linear Mechanics 56, 142-147 (2013) Y1 - 2013 A1 - Antonio DeSimone A1 - Federica Guarnieri A1 - Giovanni Noselli A1 - Amabile Tatone AB - We study model self-propelled crawlers which derive their propulsive capabilities from the tangential resistance to motion offered by the environment. Two types of relationships between tangential forces and slip velocities are considered: a linear, Newtonian one and a nonlinear one of Bingham-type. Different behaviors result from the two different rheologies. These differences and their implications in terms of motility performance are discussed. Our aim is to develop new tools and insight for future studies of cell motility by crawling. PB - Elsevier U1 - 34590 U2 - Mathematics ER - TY - RPRT T1 - The curvature: a variational approach Y1 - 2013 A1 - Andrei A. Agrachev A1 - Davide Barilari A1 - Luca Rizzi KW - Crurvature, subriemannian metric, optimal control problem AB - The curvature discussed in this paper is a rather far going generalization of the Riemannian sectional curvature. We define it for a wide class of optimal control problems: a unified framework including geometric structures such as Riemannian, sub-Riemannian, Finsler and sub-Finsler structures; a special attention is paid to the sub-Riemannian (or Carnot-Caratheodory) metric spaces. Our construction of the curvature is direct and naive, and it is similar to the original approach of Riemann. Surprisingly, it works in a very general setting and, in particular, for all sub-Riemannian spaces. PB - SISSA UR - http://hdl.handle.net/1963/7226 N1 - 88 pages, 10 figures, (v2) minor typos corrected, (v3) added sections on Finsler manifolds, slow growth distributions, Heisenberg group U1 - 7260 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - RPRT T1 - The deal.II Library, Version 8.1 Y1 - 2013 A1 - Wolfgang Bangerth A1 - Timo Heister A1 - Luca Heltai A1 - G. Kanschat A1 - Martin Kronbichler A1 - Matthias Maier A1 - Bruno Turcksin A1 - T. D. Young AB - This paper provides an overview of the new features of the finite element library deal.II version 8.0. PB - SISSA UR - http://hdl.handle.net/1963/7236 N1 - 5 pages U1 - 7272 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - RPRT T1 - Defect annihilation and proliferation in active nematics Y1 - 2013 A1 - Luca Giomi A1 - Mark J. Bowick A1 - Xu Ma A1 - M. Cristina Marchetti AB - Liquid crystals inevitably possess topological defect excitations generated\r\nthrough boundary conditions, applied fields or in quenches to the ordered\r\nphase. In equilibrium pairs of defects coarsen and annihilate as the uniform\r\nground state is approached. Here we show that defects in active liquid crystals\r\nexhibit profoundly different behavior, depending on the degree of activity and\r\nits contractile or extensile character. While contractile systems enhance the\r\nannihilation dynamics of passive systems, extensile systems act to drive\r\ndefects apart so that they swarm around in the manner of topologically\r\nwell-characterized self-propelled particles. We develop a simple analytical\r\nmodel for the defect dynamics which reproduces the key features of both the\r\nnumerical solutions and recent experiments on microtuble-kinesin assemblies. PB - SISSA UR - http://hdl.handle.net/1963/6566 N1 - 5 pages, 4 figures U1 - 6517 U2 - Mathematics U4 - 2 U5 - FIS/02 FISICA TEORICA, MODELLI E METODI MATEMATICI ER - TY - RPRT T1 - Dislocation dynamics in crystals: a macroscopic theory in a fractional Laplace setting Y1 - 2013 A1 - Serena Dipierro A1 - Giampiero Palatucci A1 - Enrico Valdinoci KW - nonlocal Allen-Cahn equation AB - We consider an evolution equation arising in the Peierls-Nabarro model for crystal dislocation. We study the evolution of such dislocation function and show that, at a macroscopic scale, the dislocations have the tendency to concentrate at single points of the crystal, where the size of the slip coincides with the natural periodicity of the medium. These dislocation points evolve according to the external stress and an interior repulsive potential. PB - SISSA UR - http://hdl.handle.net/1963/7124 U1 - 7124 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Early phase of plasticity-related gene regulation and SRF dependent transcription in the hippocampus JF - PloS one. Volume 8, Issue 7, July 2013 : e68078 Y1 - 2013 A1 - Giovanni Iacono A1 - Claudio Altafini A1 - Vincent Torre AB - Hippocampal organotypic cultures are a highly reliable in vitro model for studying neuroplasticity: in this paper, we analyze the early phase of the transcriptional response induced by a 20 µM gabazine treatment (GabT), a GABA-Ar antagonist, by using Affymetrix oligonucleotide microarray, RT-PCR based time-course and chromatin-immuno-precipitation. The transcriptome profiling revealed that the pool of genes up-regulated by GabT, besides being strongly related to the regulation of growth and synaptic transmission, is also endowed with neuro-protective and pro-survival properties. By using RT-PCR, we quantified a time-course of the transient expression for 33 of the highest up-regulated genes, with an average sampling rate of 10 minutes and covering the time interval [10:90] minutes. The cluster analysis of the time-course disclosed the existence of three different dynamical patterns, one of which proved, in a statistical analysis based on results from previous works, to be significantly related with SRF-dependent regulation (p-value<0.05). The chromatin immunoprecipitation (chip) assay confirmed the rich presence of working CArG boxes in the genes belonging to the latter dynamical pattern and therefore validated the statistical analysis. Furthermore, an in silico analysis of the promoters revealed the presence of additional conserved CArG boxes upstream of the genes Nr4a1 and Rgs2. The chip assay confirmed a significant SRF signal in the Nr4a1 CArG box but not in the Rgs2 CArG box. PB - Public Library of Science UR - http://hdl.handle.net/1963/7287 N1 - The article is composed of 15 pages U1 - 7332 U2 - Neuroscience U4 - -1 ER - TY - JOUR T1 - Epitaxially strained elastic films: the case of anisotropic surface energies JF - ESAIM Control. Optim. Calc. Var. 19 (2013) 167-189 Y1 - 2013 A1 - Marco Bonacini AB -In the context of a variational model for the epitaxial growth of strained elastic films, we study the effects of the presence of anisotropic surface energies in the determination of equilibrium configurations. We show that the threshold effect that describes the stability of flat morphologies in the isotropic case remains valid for weak anisotropies, but is no longer present in the case of highly anisotropic surface energies, where we show that the flat configuration is always a local minimizer of the total energy. The main tool used to obtain these results is a minimality criterion based on the positivity of the second variation.

PB - EDP Sciences UR - http://hdl.handle.net/1963/4268 U1 - 3999 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Existence and symmetry results for a Schrodinger type problem involving the fractional Laplacian JF - Le Matematiche (Catania), Vol. 68 (2013), no. 1: 201-216 Y1 - 2013 A1 - Serena Dipierro A1 - Giampiero Palatucci A1 - Enrico Valdinoci AB -This paper deals with the following class of nonlocal Schr\"odinger equations $$ \displaystyle (-\Delta)^s u + u = |u|^{p-1}u \ \ \text{in} \ \mathbb{R}^N, \quad \text{for} \ s\in (0,1). $$ We prove existence and symmetry results for the solutions $u$ in the fractional Sobolev space $H^s(\mathbb{R}^N)$. Our results are in clear accordance with those for the classical local counterpart, that is when $s=1$.

PB - University of Catania U1 - 7318 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - An existence result for the mean-field equation on compact surfaces in a doubly supercritical regime JF - Proceedings of the Royal Society of Edinburgh: Section A Mathematics Y1 - 2013 A1 - Aleks Jevnikar PB - Royal Society of Edinburgh Scotland Foundation VL - 143 ER - TY - JOUR T1 - Fields of bounded deformation for mesoscopic dislocations Y1 - 2013 A1 - Nicolas Van Goethem AB - In this paper we discuss the consequences of the distributional approach to dislocations in terms of the mathematical properties\\r\\nof the auxiliary model fields such as displacement and displacement gradient which are obtained directly from \\r\\nthe main model field here considered as the linear strain. We show that these fields cannot be introduced rigourously without \\r\\nthe introduction of gauge fields, or equivalently, without cuts in the Riemann foliation associated to the dislocated crystal.\\r\\nIn a second step we show that the space of bounded deformations follows from the distributional approach in a natural way and \\r\\ndiscuss the reasons why it is adequate to model dislocations. The case of dislocation clusters is also addressed, as it represents an important issue in industrial crystal growth while from a mathematical point of view, peculiar phenomena might appear at the set of accumulation points. \\r\\nThe elastic-plastic decomposition of the strain within this approach is also given a precise meaning. PB - SISSA UR - http://hdl.handle.net/1963/6378 U1 - 6311 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Fracture models as Gamma-limits of damage models JF - Communications on Pure and Applied Analysis 12 (2013) 1657-1686 Y1 - 2013 A1 - Gianni Dal Maso A1 - Flaviana Iurlano AB -We analyze the asymptotic behavior of a variational model for damaged elastic materials. This model depends on two small parameters, which govern the width of the damaged regions and the minimum elasticity constant attained in the damaged regions. When these parameters tend to zero, we find that the corresponding functionals Gamma-converge to a functional related to fracture mechanics. The corresponding problem is brittle or cohesive, depending on the asymptotic ratio of the two parameters.

PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/4225 U1 - 3952 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Generalized Sturm-Liouville boundary conditions for first order differential systems in the plane JF - Topol. Methods Nonlinear Anal. Y1 - 2013 A1 - Alessandro Fonda A1 - Maurizio Garrione AB -We study asymptotically positively homogeneous first order systems in the plane, with boundary conditions which are positively homogeneous, as well. Defining a generalized concept of Fučík spectrum which extends the usual one for the scalar second order equation, we prove existence and multiplicity of solutions. In this way, on one hand we extend to the plane some known results for scalar second order equations (with Dirichlet, Neumann or Sturm-Liouville boundary conditions), while, on the other hand, we investigate some other kinds of boundary value problems, where the boundary points are chosen on a polygonal line, or in a cone. Our proofs rely on the shooting method.

PB - Nicolaus Copernicus University, Juliusz P. Schauder Centre for Nonlinear Studies VL - 42 UR - https://projecteuclid.org:443/euclid.tmna/1461248981 ER - TY - JOUR T1 - An improved geometric inequality via vanishing moments, with applications to singular Liouville equations JF - Communications in Mathematical Physics 322, nr.2 (2013): 415-452 Y1 - 2013 A1 - Mauro Bardelloni A1 - Andrea Malchiodi PB - SISSA UR - http://hdl.handle.net/1963/6561 U1 - 6486 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - KAM theory for the Hamiltonian derivative wave equation JF - Annales Scientifiques de l'Ecole Normale Superieure Y1 - 2013 A1 - Massimiliano Berti A1 - Luca Biasco A1 - Michela Procesi AB -We prove an infinite dimensional KAM theorem which implies the existence of Can- tor families of small-amplitude, reducible, elliptic, analytic, invariant tori of Hamiltonian derivative wave equations. © 2013 Société Mathématique de France.

VL - 46 N1 - cited By (since 1996)4 ER - TY - JOUR T1 - Lipschitz Classification of Almost-Riemannian Distances on Compact Oriented Surfaces JF - Journal of Geometric Analysis Y1 - 2013 A1 - Ugo Boscain A1 - Grégoire Charlot A1 - Roberta Ghezzi A1 - Mario Sigalotti AB -Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We consider the Carnot–Carathéodory distance canonically associated with an almost-Riemannian structure and study the problem of Lipschitz equivalence between two such distances on the same compact oriented surface. We analyze the generic case, allowing in particular for the presence of tangency points, i.e., points where two generators of the distribution and their Lie bracket are linearly dependent. The main result of the paper provides a characterization of the Lipschitz equivalence class of an almost-Riemannian distance in terms of a labeled graph associated with it.

VL - 23 UR - https://doi.org/10.1007/s12220-011-9262-4 ER - TY - JOUR T1 - Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations JF - ESAIM: Mathematical Modelling and Numerical Analysis Y1 - 2013 A1 - Cacace, S. A1 - Antonin Chambolle A1 - Antonio DeSimone A1 - Livio Fedeli PB - EDP Sciences VL - 47 ER - TY - RPRT T1 - Minimal partitions and image classification using a gradient-free perimeter approximation Y1 - 2013 A1 - Samuel Amstutz A1 - Nicolas Van Goethem A1 - Antonio André Novotny KW - Image classification, deblurring, optimal partitions, perimeter approximation AB - In this paper a new mathematically-founded method for the optimal partitioning of domains, with applications to the classification of greyscale and color images, is proposed. Since optimal partition problems are in general ill-posed, some regularization strategy is required. Here we regularize by a non-standard approximation of the total interface length, which does not involve the gradient of approximate characteristic functions, in contrast to the classical Modica-Mortola approximation. Instead, it involves a system of uncoupled linear partial differential equations and nevertheless shows $\Gamma$-convergence properties in appropriate function spaces. This approach leads to an alternating algorithm that ensures a decrease of the objective function at each iteration, and which always provides a partition, even during the iterations. The efficiency of this algorithm is illustrated by various numerical examples. Among them we consider binary and multilabel minimal partition problems including supervised or automatic image classification, inpainting, texture pattern identification and deblurring. PB - SISSA UR - http://hdl.handle.net/1963/6976 U1 - 6964 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - THES T1 - Minimality and stability results for a class of free-discontinuity and nonlocal isoperimetric problems Y1 - 2013 A1 - Marco Bonacini KW - free-discontinuity problems PB - SISSA U1 - 7204 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - The Monge Problem for Distance Cost in Geodesic Spaces JF - Communications in Mathematical Physics Y1 - 2013 A1 - Stefano Bianchini A1 - Fabio Cavalletti AB -We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish space and dLis a geodesic Borel distance which makes (X, dL) a non branching geodesic space. We show that under the assumption that geodesics are d-continuous and locally compact, we can reduce the transport problem to 1-dimensional transport problems along geodesics. We introduce two assumptions on the transport problem π which imply that the conditional probabilities of the first marginal on each geodesic are continuous or absolutely continuous w.r.t. the 1-dimensional Hausdorff distance induced by dL. It is known that this regularity is sufficient for the construction of a transport map. We study also the dynamics of transport along the geodesic, the stability of our conditions and show that in this setting dL-cyclical monotonicity is not sufficient for optimality.

VL - 318 UR - https://doi.org/10.1007/s00220-013-1663-8 ER - TY - JOUR T1 - Multiplicity result for a nonhomogeneous Yamabe type equation involving the Kohn Laplacian JF - Journal of Mathematical Analysis and Applications. Volume 399, Issue 1, 1 March 2013, Pages 333-339 Y1 - 2013 A1 - Ali Maalaoui A1 - Vittorio Martino KW - CR-Yamabe PB - Elsevier UR - http://hdl.handle.net/1963/7374 N1 - The article is composed of 13 pages and is recorded in PDF format U1 - 7422 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - A New Quadratic Potential for Scalar Conservation Laws JF - Oberwolfach Reports Y1 - 2013 A1 - Stefano Bianchini A1 - Stefano Modena VL - 29 ER - TY - JOUR T1 - The nonlinear multidomain model: a new formal asymptotic analysis. JF - Geometry Partial Differential Equations – proceedings, CRM Series (15), 2013. Y1 - 2013 A1 - Stefano Amato A1 - Giovanni Bellettini A1 - Maurizio Paolini KW - bidomain model, anisotropic mean curvature, star-shaped combination AB -We study the asymptotic analysis of a singularly perturbed weakly parabolic system of m- equations of anisotropic reaction-diffusion type. Our main result formally shows that solutions to the system approximate a geometric motion of a hypersurface by anisotropic mean curvature. The anisotropy, supposed to be uniformly convex, is explicit and turns out to be the dual of the star-shaped combination of the m original anisotropies.

SN - 8876424724 U1 - 7259 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - A note on KAM theory for quasi-linear and fully nonlinear forced KdV JF - Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 24 (2013), no. 3: 437–450 Y1 - 2013 A1 - P Baldi A1 - Massimiliano Berti A1 - Riccardo Montalto KW - KAM for PDEs AB - We present the recent results in [3] concerning quasi-periodic solutions for quasi-linear and fully nonlinear forced perturbations of KdV equations. For Hamiltonian or reversible nonlinearities the solutions are linearly stable. The proofs are based on a combination of di erent ideas and techniques: (i) a Nash-Moser iterative scheme in Sobolev scales. (ii) A regularization procedure, which conjugates the linearized operator to a di erential operator with constant coe cients plus a bounded remainder. These transformations are obtained by changes of variables induced by di eomorphisms of the torus and pseudo-di erential operators. (iii) A reducibility KAM scheme, which completes the reduction to constant coe cients of the linearized operator, providing a sharp asymptotic expansion of the perturbed eigenvalues. PB - European Mathematical Society U1 - 7268 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - A note on non-homogeneous hyperbolic operators with low-regularity coefficients Y1 - 2013 A1 - Ferruccio Colombini A1 - Francesco Fanelli AB -In this paper we obtain an energy estimate for a complete strictly hyperbolic operator with second order coefficients satisfying a log-Zygmund-continuity condition with respect to $t$, uniformly with respect to $x$, and a log-Lipschitz-continuity condition with respect to $x$, uniformly with respect to $t$.

ER - TY - JOUR T1 - One-dimensional swimmers in viscous fluids: dynamics, controllability, and existence of optimal controls Y1 - 2013 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Marco Morandotti AB -In this paper we study a mathematical model of one-dimensional swimmers performing a planar motion while fully immersed in a viscous fluid. The swimmers are assumed to be of small size, and all inertial effects are neglected. Hydrodynamic interactions are treated in a simplified way, using the local drag approximation of resistive force theory. We prove existence and uniqueness of the solution of the equations of motion driven by shape changes of the swimmer. Moreover, we prove a controllability result showing that given any pair of initial and final states, there exists a history of shape changes such that the resulting motion takes the swimmer from the initial to the final state. We give a constructive proof, based on the composition of elementary maneuvers (straightening and its inverse, rotation, translation), each of which represents the solution of an interesting motion planning problem. Finally, we prove the existence of solutions for the optimal control problem of finding, among the histories of shape changes taking the swimmer from an initial to a final state, the one of minimal energetic cost.

PB - SISSA UR - http://hdl.handle.net/1963/6467 U1 - 6412 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Pairs of nodal solutions for a class of nonlinear problems with one-sided growth conditions JF - Advanced Nonlinear Studies Y1 - 2013 A1 - Alberto Boscaggin A1 - Fabio Zanolin PB - Advanced Nonlinear Studies, Inc. VL - 13 ER - TY - JOUR T1 - Periodic bouncing solutions for nonlinear impact oscillators JF - Advanced Nonlinear Studies Y1 - 2013 A1 - Alessandro Fonda A1 - Andrea Sfecci PB - Advanced Nonlinear Studies, Inc. VL - 13 ER - TY - JOUR T1 - Planar Hamiltonian systems at resonance: the Ahmad–Lazer–Paul condition JF - Nonlinear Differential Equations and Applications NoDEA Y1 - 2013 A1 - Alberto Boscaggin A1 - Maurizio Garrione AB -We consider the planar Hamiltonian system\$\$Ju^{\backslashprime} = \backslashnabla F(u) + \backslashnabla_u R(t,u), \backslashquad t \backslashin [0,T], \backslash,u \backslashin \backslashmathbb{R}^2,\$\$with F(u) positive and positively 2-homogeneous and \$\${\backslashnabla_{u}R(t, u)}\$\$sublinear in u. By means of an Ahmad-Lazer-Paul type condition, we prove the existence of a T-periodic solution when the system is at resonance. The proof exploits a symplectic change of coordinates which transforms the problem into a perturbation of a linear one. The relationship with the Landesman–Lazer condition is analyzed, as well.

VL - 20 UR - https://doi.org/10.1007/s00030-012-0181-2 ER - TY - JOUR T1 - Quadratic cohomology Y1 - 2013 A1 - Andrei A. Agrachev AB - We study homological invariants of smooth families of real quadratic forms as\r\na step towards a \"Lagrange multipliers rule in the large\" that intends to\r\ndescribe topology of smooth vector functions in terms of scalar Lagrange\r\nfunctions. PB - SISSA N1 - 24 pages U1 - 6456 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - A quasistatic evolution model for perfectly plastic plates derived by Γ-convergence JF - Annales de l'Institut Henri Poincare (C) Non Linear Analysis Y1 - 2013 A1 - Elisa Davoli A1 - Maria Giovanna Mora KW - -convergence KW - Perfect plasticity KW - Prandtl–Reuss plasticity KW - Quasistatic evolution KW - Rate-independent processes KW - Thin plates AB -The subject of this paper is the rigorous derivation of a quasistatic evolution model for a linearly elastic–perfectly plastic thin plate. As the thickness of the plate tends to zero, we prove via Γ-convergence techniques that solutions to the three-dimensional quasistatic evolution problem of Prandtl–Reuss elastoplasticity converge to a quasistatic evolution of a suitable reduced model. In this limiting model the admissible displacements are of Kirchhoff–Love type and the stretching and bending components of the stress are coupled through a plastic flow rule. Some equivalent formulations of the limiting problem in rate form are derived, together with some two-dimensional characterizations for suitable choices of the data.

VL - 30 UR - http://www.sciencedirect.com/science/article/pii/S0294144912001035 ER - TY - JOUR T1 - Reduced basis approximation and a posteriori error estimation for Stokes flows in parametrized geometries: roles of the inf-sup stability constants JF - Numerische Mathematik, 2013 Y1 - 2013 A1 - Gianluigi Rozza A1 - Phuong Huynh A1 - Andrea Manzoni KW - parametrized Stokes equations AB - In this paper we review and we extend the reduced basis approximation and a posteriori error estimation for steady Stokes flows in a ffinely parametrized geometries, focusing on the role played by the Brezzi\\\'s and Babu ska\\\'s stability constants. The crucial ingredients of the methodology are a Galerkin projection onto a low-dimensional space of basis functions properly selected, an a ne parametric dependence enabling to perform competitive Off ine-Online splitting in the computational\\r\\nprocedure and a rigorous a posteriori error estimation on eld variables.\\r\\nThe combination of these three factors yields substantial computational savings which are at the basis of an e fficient model order reduction, ideally suited for real-time simulation and many-query contexts (e.g. optimization, control or parameter identi cation). In particular, in this work we focus on i) the stability of the reduced basis approximation based on the Brezzi\\\'s saddle point theory and the introduction of a supremizer operator on the pressure terms, ii) a rigorous a posteriori error estimation procedure for velocity and pressure elds based on the Babu ska\\\'s inf-sup constant (including residuals calculations), iii) the computation of a lower bound of the stability constant, and iv) di erent options for the reduced basis spaces construction. We present some illustrative results for both\\r\\ninterior and external steady Stokes flows in parametrized geometries representing two parametrized classical Poiseuille and Couette \\r\\nflows, a channel contraction and a simple flow control problem around a curved obstacle. PB - Springer UR - http://hdl.handle.net/1963/6339 U1 - 6269 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - CHAP T1 - Reduced Basis Approximation for the Structural-Acoustic Design based on Energy Finite Element Analysis (RB-EFEA) T2 - CEMRACS 2013 - Modelling and simulation of complex systems: stochastic and deterministic approaches Y1 - 2013 A1 - Denis Devaud A1 - Gianluigi Rozza JF - CEMRACS 2013 - Modelling and simulation of complex systems: stochastic and deterministic approaches VL - 48 ER - TY - RPRT T1 - A Reduced Computational and Geometrical Framework for Inverse Problems in Haemodynamics Y1 - 2013 A1 - Toni Lassila A1 - Andrea Manzoni A1 - Alfio Quarteroni A1 - Gianluigi Rozza PB - SISSA U1 - 6571 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - RPRT T1 - A reduced-order strategy for solving inverse Bayesian identification problems in physiological flows Y1 - 2013 A1 - Toni Lassila A1 - Andrea Manzoni A1 - Alfio Quarteroni A1 - Gianluigi Rozza PB - SISSA U1 - 6555 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - RPRT T1 - Reduction Strategies for Shape Dependent Inverse Problems in Haemodynamics Y1 - 2013 A1 - Toni Lassila A1 - Andrea Manzoni A1 - Gianluigi Rozza PB - SISSA U1 - 6554 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - Remarks on the Moser–Trudinger inequality JF - Advances in Nonlinear Analysis Y1 - 2013 A1 - Gabriele Mancini A1 - Luca Battaglia AB -We extend the Moser-Trudinger inequality to any Euclidean domain satisfying Poincaré's inequality. We find out that the same equivalence does not hold in general for conformal metrics on the unit ball, showing counterexamples. We also study the existence of extremals for the Moser-Trudinger inequalities for unbounded domains, proving it for the infinite planar strip.

PB - Advances in Nonlinear Analysis VL - 2 UR - http://edoc.unibas.ch/43974/ IS - 4 N1 - The article is composed of 32 pages inad recorded in PDF format U1 - 34666 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Self-adjoint extensions and stochastic completeness of the Laplace-Beltrami operator on conic and anticonic surfaces Y1 - 2013 A1 - Ugo Boscain A1 - Dario Prandi ER - TY - JOUR T1 - Softly Constrained Films Y1 - 2013 A1 - Luca Giomi AB - The shape of materials is often subject to a number of geometric constraints\r\nthat limit the size of the system or fix the structure of its boundary. In soft\r\nand biological materials, however, these constraints are not always hard, but\r\nare due to other physical mechanisms that affect the overall force balance. A\r\ncapillary film spanning a flexible piece of wire or a cell anchored to a\r\ncompliant substrate by mean of adhesive contacts are examples of these softly\r\nconstrained systems in the macroscopic and microscopic world. In this article I\r\nreview some of the important mathematical and physical developments that\r\ncontributed to our understanding of shape formation in softly constrained films\r\nand their recent application to the mechanics of adherent cells. PB - SISSA UR - http://hdl.handle.net/1963/6563 N1 - Review article, 21 pages, 16 figures, submitted to Soft Matter U1 - 6518 U2 - Mathematics U4 - 2 U5 - FIS/02 FISICA TEORICA, MODELLI E METODI MATEMATICI ER - TY - THES T1 - Some models of crack growth in brittle materials Y1 - 2013 A1 - Simone Racca KW - Quasi-static crack evolution PB - SISSA U1 - 7205 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Some open problems Y1 - 2013 A1 - Andrei A. Agrachev KW - Geometry AB - We discuss some challenging open problems in the geometric control theory and sub-Riemannian geometry. PB - SISSA UR - http://hdl.handle.net/1963/7070 U1 - 7064 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Some remarks on the viscous approximation of crack growth JF - Discrete Contin. Dyn. Syst. Ser. S Y1 - 2013 A1 - Giuliano Lazzaroni A1 - Rodica Toader KW - Variational models AB -We describe an existence result for quasistatic evolutions of cracks in antiplane elasticity obtained in [16] by a vanishing viscosity approach, with free (but regular enough) crack path. We underline in particular the motivations for the choice of the class of admissible cracks and of the dissipation potential. Moreover, we extend the result to a model with applied forces depending on time.

PB - SISSA VL - 6 UR - http://hdl.handle.net/1963/4206 U1 - 3945 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - RPRT T1 - The splitting theorem in non-smooth context Y1 - 2013 A1 - Nicola Gigli AB - We prove that an infinitesimally Hilbertian $CD(0,N)$ space containing a line splits as the product of $R$ and an infinitesimally Hilbertian $CD(0,N −1)$ space. By ‘infinitesimally Hilbertian’ we mean that the Sobolev space $W^{1,2}(X,d,m)$, which in general is a Banach space, is an Hilbert space. When coupled with a curvature-dimension bound, this condition is known to be stable with respect to measured Gromov-Hausdorff convergence. UR - http://preprints.sissa.it/handle/1963/35306 U1 - 35613 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Stabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control JF - IEEE Transactions on Automatic Control. Volume 58, Issue 1, 2013, Article number6228517, Pages 74-85 Y1 - 2013 A1 - Claudio Altafini A1 - Francesco Ticozzi A1 - K. Nishio AB - In this paper, we investigate parametrization-free solutions of the problem of quantum pure state preparation and subspace stabilization by means of Hamiltonian control, continuous measurement, and quantum feedback, in the presence of a Markovian environment. In particular, we show that whenever suitable dissipative effects are induced either by the unmonitored environment, or by non-Hermitian measurements, there is no need for feedback, as open-loop time-invariant control is sufficient to achieve stabilization of the target set in probability. Constructive necessary and sufficient conditions on the form of the control Hamiltonian can be provided in this case. When time-invariant control is not sufficient, state stabilization can be attained by the addition of filtering-based feedback control UR - http://hdl.handle.net/1963/6503 U1 - 6448 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - A stable and adaptive semi-Lagrangian potential model for unsteady and nonlinear ship-wave interactions JF - Engineering Analysis with Boundary Elements, 37(1):128 – 143, 2013. Y1 - 2013 A1 - Andrea Mola A1 - Luca Heltai A1 - Antonio DeSimone KW - Unsteady ship-wave interaction AB -We present an innovative numerical discretization of the equations of inviscid potential flow for the simulation of three dimensional unsteady and nonlinear water waves generated by a ship hull advancing in water. The equations of motion are written in a semi-Lagrangian framework, and the resulting integro-diff erential equations are discretized in space via an adaptive iso-parametric collocation Boundary Element Method, and in time via adaptive implicit Backward Di erentiation Formulas (BDF) with variable step and variable order. When the velocity of the advancing ship hull is non-negligible, the semi-Lagrangian formulation (also known as Arbitrary Lagrangian Eulerian formulation, or ALE) of the free surface equations contains dominant transport terms which are stabilized with a Streamwise Upwind Petrov-Galerkin (SUPG) method. The SUPG stabilization allows automatic and robust adaptation of the spatial discretization with unstructured quadrilateral grids. Preliminary results are presented where we compare our numerical model with experimental results on the case of a Wigley hull advancing in calm water with fi xed sink and trim.

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

PB - Taylor & Francis VL - 92 UR - https://doi.org/10.1080/00036811.2011.628173 ER - TY - THES T1 - The structure and regularity of admissible BV solutions to hyperbolic conservation laws in one space dimension Y1 - 2013 A1 - Lei Yu AB - This thesis is devoted to the study of the qualitative properties of admissible BV solutions to the strictly hyperbolic conservation laws in one space dimension by using wave-front tracking approximation. This thesis consists of two parts: • SBV-like regularity of vanishing viscosity BV solutions to strict hyperbolic systems of conservation laws. • Global structure of admissible BV solutions to strict hyperbolic conservation laws. PB - SISSA U1 - 7210 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Subharmonic solutions for nonlinear second order equations in presence of lower and upper solutions JF - Discrete & Continuous Dynamical Systems - A Y1 - 2013 A1 - Alberto Boscaggin A1 - Fabio Zanolin KW - lower and upper solutions KW - parameter dependent equations KW - Periodic solutions KW - Poincaré-Birkhoff twist theorem KW - subharmonic solutions AB -We study the problem of existence and multiplicity of subharmonic solutions for a second order nonlinear ODE in presence of lower and upper solutions. We show how such additional information can be used to obtain more precise multiplicity results. Applications are given to pendulum type equations and to Ambrosetti-Prodi results for parameter dependent equations.

VL - 33 UR - http://aimsciences.org//article/id/3638a93e-4f3e-4146-a927-3e8a64e6863f ER - TY - RPRT T1 - On Sudakov's type decomposition of transference plans with norm costs Y1 - 2013 A1 - Stefano Bianchini A1 - Sara Daneri PB - SISSA UR - http://hdl.handle.net/1963/7206 U1 - 7234 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - A variational Analysis of the Toda System on Compact Surfaces JF - Communications on Pure and Applied Mathematics, Volume 66, Issue 3, March 2013, Pages 332-371 Y1 - 2013 A1 - Andrea Malchiodi A1 - David Ruiz AB - In this paper we consider the Toda system of equations on a compact surface. We will give existence results by using variational methods in a non coercive case. A key tool in our analysis is a new Moser-Trudinger type inequality under suitable conditions on the center of mass and the scale of concentration of the two components u_1, u_2. PB - Wiley UR - http://hdl.handle.net/1963/6558 N1 - pre-peer version, to appear in Comm. Pure Applied Math U1 - 6489 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - On 2-step, corank 2 nilpotent sub-Riemannian metrics JF - SIAM J. Control Optim., 50 (2012) 559–582 Y1 - 2012 A1 - Davide Barilari A1 - Ugo Boscain A1 - Jean-Paul Gauthier AB - In this paper we study the nilpotent 2-step, corank 2 sub-Riemannian metrics\\r\\nthat are nilpotent approximations of general sub-Riemannian metrics. We exhibit optimal syntheses for these problems. It turns out that in general the cut time is not equal to the first conjugate time but has a simple explicit expression. As a byproduct of this study we get some smoothness properties of the spherical Hausdorff measure in the case of a generic 6 dimensional, 2-step corank 2 sub-Riemannian metric. PB - Society for Industrial and Applied Mathematics UR - http://hdl.handle.net/1963/6065 U1 - 5950 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Asymptotics of the s-perimeter as s →0 JF - Discrete Contin. Dyn. Syst. 33, nr.7 (2012): 2777-2790 Y1 - 2012 A1 - Serena Dipierro A1 - Alessio Figalli A1 - Giampiero Palatucci A1 - Enrico Valdinoci AB -We deal with the asymptotic behavior of the $s$-perimeter of a set $E$ inside a domain $\Omega$ as $s\searrow0$. We prove necessary and sufficient conditions for the existence of such limit, by also providing an explicit formulation in terms of the Lebesgue measure of $E$ and $\Omega$. Moreover, we construct examples of sets for which the limit does not exist.

PB - American Institute of Mathematical Sciences U1 - 7317 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - On the behaviour of flexible retaining walls under seismic actions JF - Geotechnique, Volume 62, Issue 12, December 2012, Pages 1081-1094 Y1 - 2012 A1 - Riccardo Conti A1 - G.S.P. Madabhushi A1 - Giulia M.B. Viggiani KW - Centrifuge modelling AB - This paper describes an experimental investigation of the behaviour of embedded retaining walls under seismic actions. Nine centrifuge tests were carried out on reduced-scale models of pairs of retaining walls in dry sand, either cantilevered or with one level of props near the top. The experimental data indicate that, for maximum accelerations that are smaller than the critical limit equilibrium value, the retaining walls experience significant permanent displacements under increasing structural loads, whereas for larger accelerations the walls rotate under constant internal forces. The critical acceleration at which the walls start to rotate increases with increasing maximum acceleration. No significant displacements are measured if the current earthquake is less severe than earthquakes previously experienced by the wall. The increase of critical acceleration is explained in terms of redistribution of earth pressures and progressive mobilisation of the passive strength in front of the wall. The experimental data for cantilevered retaining walls indicate that the permanent displacements of the wall can be reasonably predicted adopting a Newmark-type calculation with a critical acceleration that is a fraction of the limit equilibrium value. PB - ICE Publishing UR - http://hdl.handle.net/1963/6933 U1 - 6912 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty JF - Mathematical Modelling and Numerical Analysis, in press, 2012-13 Y1 - 2012 A1 - Toni Lassila A1 - Andrea Manzoni A1 - Alfio Quarteroni A1 - Gianluigi Rozza KW - shape optimization AB - We review the optimal design of an arterial bypass graft following either a (i) boundary optimal control approach, or a (ii) shape optimization formulation. The main focus is quantifying and treating the uncertainty in the residual flow when the hosting artery is not completely occluded,\\r\\nfor which the worst-case in terms of recirculation e ffects is inferred to correspond to a strong ori fice flow through near-complete occlusion. A worst-case optimal control approach is applied to the steady\\r\\nNavier-Stokes equations in 2D to identify an anastomosis angle and a cu ed shape that are robust with respect to a possible range of residual \\r\\nflows. We also consider a reduced order modelling framework\\r\\nbased on reduced basis methods in order to make the robust design problem computationally feasible. The results obtained in 2D are compared with simulations in a 3D geometry but without model\\r\\nreduction or the robust framework. PB - Cambridge University Press UR - http://hdl.handle.net/1963/6337 U1 - 6267 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - On a class of vector fields with discontinuity of divide-by-zero type and its applications JF - Journal of dynamical and control systems Y1 - 2012 A1 - Roberta Ghezzi A1 - Alexey O. Remizov AB -We study phase portraits and singular points of vector fields of a special type, that is, vector fields whose components are fractions with a common denominator vanishing on a smooth regular hypersurface in the phase space. We assume also some additional conditions, which are fulfilled, for instance, if the vector field is divergence-free. This problem is motivated by a large number of applications. In this paper, we consider three of them in the framework of differential geometry: singularities of geodesic flows in various singular metrics on surfaces.

PB - Springer VL - 18 IS - 1 U1 - 7038 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - A Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group. JF - Journal fur die Reine und Angewandte Mathematik, Issue 671, October 2012, Pages 131-198 Y1 - 2012 A1 - Andrea Malchiodi A1 - Paul Yang A1 - Jih-Hsin Cheng A1 - JennFang Hwang AB - In this paper, we study the structure of the singular set for a C 1 smooth surface in the 3-dimensional Heisenberg group ℍ 1. We discover a Codazzi-like equation for the p-area element along the characteristic curves on the surface. Information obtained from this ordinary differential equation helps us to analyze the local configuration of the singular set and the characteristic curves. In particular, we can estimate the size and obtain the regularity of the singular set. We understand the global structure of the singular set through a Hopf-type index theorem. We also justify the Codazzi-like equation by proving a fundamental theorem for local surfaces in ℍ 1 PB - SISSA UR - http://hdl.handle.net/1963/6556 U1 - 6490 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - CHAP T1 - Computing optimal strokes for low reynolds number swimmers T2 - Natural locomotion in fluids and on surfaces : swimming, flying, and sliding / editors Stephen Childress, Anette Hosoi, William W. Schultz, and Z. Jane Wang, editors, Y1 - 2012 A1 - Antonio DeSimone A1 - Luca Heltai A1 - François Alouges A1 - Lefebvre-Lepot Aline KW - Numerical analysis. AB -We discuss connections between low-Reynolds-number swimming and geometric control theory, and present a general algorithm for the numerical computation of energetically optimal strokes. As an illustration of our approach, we show computed motility maps and optimal strokes for two model swimmers.

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

PB - World Scientific VL - 14 UR - https://doi.org/10.1142/S0219199712500095 ER - TY - JOUR T1 - Conservation of Geometric Structures for Non-Homogeneous Inviscid Incompressible Fluids JF - Communications in Partial Differential Equations Y1 - 2012 A1 - Francesco Fanelli AB -In this article we get a result on propagation of geometric properties for solutions of the non-homogeneous incompressible Euler system in any dimension N ≥ 2. In particular, we investigate conservation of striated and conormal regularity, which generalize the 2-D structure of vortex patches. The results we get are only local in time, even for N = 2; however, we provide an explicit lower bound for the lifespan of the solution. In the case of physical dimension N = 2 or 3, we investigate also propagation of Hölder regularity in the interior of a bounded domain.

PB - Taylor & Francis VL - 37 UR - https://doi.org/10.1080/03605302.2012.698343 ER - TY - JOUR T1 - Convergence of equilibria of thin elastic plates under physical growth conditions for the energy density Y1 - 2012 A1 - Maria Giovanna Mora A1 - Lucia Scardia AB -The asymptotic behaviour of the equilibrium configurations of a thin elastic plate is studied, as the thickness $h$ of the plate goes to zero. More precisely, it is shown that critical points of the nonlinear elastic functional $\mathcal E^h$, whose energies (per unit thickness) are bounded by $Ch^4$, converge to critical points of the $\Gamma$-limit of $h^{-4}\mathcal E^h$. This is proved under the physical assumption that the energy density $W(F)$ blows up as $\det F\to0$.

PB - Elsevier UR - http://hdl.handle.net/1963/3466 N1 - 21 pages U1 - 7112 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - Convex pencils of real quadratic forms JF - Discrete and Computational Geometry, Volume 48, Issue 4, December 2012, Pages 1025-1047 Y1 - 2012 A1 - Antonio Lerario AB - We study the topology of the set X of the solutions of a system of two quadratic inequalities in the real projective space RP^n (e.g. X is the intersection of two real quadrics). We give explicit formulae for its Betti numbers and for those of its double cover in the sphere S^n; we also give similar formulae for level sets of homogeneous quadratic maps to the plane. We discuss some applications of these results, especially in classical convexity theory. We prove the sharp bound b(X)\leq 2n for the total Betti number of X; we show that for odd n this bound is attained only by a singular X. In the nondegenerate case we also prove the bound on each specific Betti number b_k(X)\leq 2(k+2). PB - Springer UR - http://hdl.handle.net/1963/7099 N1 - Updated version to be published in DCG ; was published in : Discrete and Computational Geometry, Volume 48, Issue 4, December 2012, Pages 1025-1047 U1 - 7097 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Crawling motility through the analysis of model locomotors: two case studies JF - The European Physical Journal E, Volume 35, Issue 9, September 2012, Article number85 Y1 - 2012 A1 - Antonio DeSimone A1 - Amabile Tatone AB - We study model locomotors on a substrate, which derive their propulsive capabilities from the tangential (viscous or frictional) resistance offered by the substrate. Our aim is to develop new tools and insight for future studies of cellular motility by crawling and of collective bacterial motion. The purely viscous case (worm) is relevant for cellular motility by crawling of individual cells. We re-examine some recent results on snail locomotion in order to assess the role of finely regulated adhesion mechanisms in crawling motility. Our main conclusion is that such regulation, although well documented in several biological systems, is not indispensable to accomplish locomotion driven by internal deformations, provided that the crawler may execute sufficiently large body deformations. Thus, there is no snail theorem. Namely, the crawling analog of the scallop theorem of low Reynolds number hydrodynamics does not hold for snail-like crawlers. The frictional case is obtained by assuming that the viscous coefficient governing tangential resistance forces, which act parallel and in the direction opposite to the velocity of the point to which they are applied, depends on the normal force acting at that point. We combine these surface interactions with inertial effects in order to investigate the mechanisms governing the motility of a bristle-robot. This model locomotor is easily manufactured and has been proposed as an effective tool to replicate and study collective bacterial motility. PB - Springer UR - http://hdl.handle.net/1963/7017 U1 - 7014 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Detection of transcriptional triggers in the dynamics of microbial growth: application to the respiratory-versatile bacterium Shewanella oneidensis JF - Nucleic Acids Research, Volume 40, Issue 15, August 2012, Pages 7132-7149 Y1 - 2012 A1 - Q Beg A1 - Mattia Zampieri A1 - N Klitgord A1 - S Collins A1 - M Serres A1 - Daniel Segrè A1 - Claudio Altafini AB - The capacity of microorganisms to respond to variable external conditions requires a coordination of environment-sensing mechanisms and decisionmaking regulatory circuits. Here, we seek to understand the interplay between these two processes by combining high-throughput measurement of time-dependent mRNA profiles with a novel computational approach that searches for key genetic triggers of transcriptional changes. Our approach helped us understand the regulatory strategies of a respiratorily versatile bacterium with promising bioenergy and bioremediation applications, Shewanella oneidensis, in minimal and rich media. By comparing expression profiles across these two conditions, we unveiled components of the transcriptional program that depend mainly on the growth phase. Conversely, by integrating our time-dependent data with a previously available large compendium of static perturbation responses, we identified transcriptional changes that cannot be explained solely by internal network dynamics, but are rather triggered by specific genes acting as key mediators of an environment-dependent response. These transcriptional triggers include known and novel regulators that respond to carbon, nitrogen and oxygen limitation. Our analysis suggests a sequence of physiological responses, including a coupling between nitrogen depletion and glycogen storage, partially recapitulated through dynamic flux balance analysis, and experimentally confirmed by metabolite measurements. Our approach is broadly applicable to other systems PB - SISSA UR - http://hdl.handle.net/1963/6506 U1 - 6452 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - A dynamical feedback model for adaptation in the olfactory transduction pathway JF - Biophysical Journal. Volume 102, Issue 12, 20 June 2012, Pages 2677-2686 Y1 - 2012 A1 - Giovanna De Palo A1 - Anna Boccaccio A1 - Andrew Miri A1 - Anna Menini A1 - Claudio Altafini AB - Olfactory transduction exhibits two distinct types of adaptation, which we denote multipulse and step adaptation. In terms of measured transduction current, multipulse adaptation appears as a decrease in the amplitude of the second of two consecutive responses when the olfactory neuron is stimulated with two brief pulses. Step adaptation occurs in response to a sustained steplike stimulation and is characterized by a return to a steady-state current amplitude close to the prestimulus value, after a transient peak. In this article, we formulate a dynamical model of the olfactory transduction pathway, which includes the kinetics of the CNG channels, the concentration of Ca ions flowing through them, and the Ca-complexes responsible for the regulation. Based on this model, a common dynamical explanation for the two types of adaptation is suggested. We show that both forms of adaptation can be well described using different time constants for the kinetics of Ca ions (faster) and the kinetics of the feedback mechanisms (slower). The model is validated on experimental data collected in voltage-clamp conditions using different techniques and animal species. PB - Biophysical Society, Elsevier UR - http://hdl.handle.net/1963/7019 U1 - 7012 U2 - Neuroscience U4 - -1 ER - TY - JOUR T1 - Exploring the low-energy landscape of large-scale signed social networks JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. Volume 86, Issue 3, 26 September 2012, Article number036116 Y1 - 2012 A1 - Giuseppe Facchetti A1 - Giovanni Iacono A1 - Claudio Altafini AB - Analogously to a spin glass, a large-scale signed social network is characterized by the presence of disorder, expressed in this context (and in the social network literature) by the concept of structural balance. If, as we have recently shown, the signed social networks currently available have a limited amount of true disorder (or frustration), it is also interesting to investigate how this frustration is organized, by exploring the landscape of near-optimal structural balance. What we obtain in this paper is that while one of the networks analyzed shows a unique valley of minima, and a funneled landscape that gradually and smoothly worsens as we move away from the optimum, another network shows instead several distinct valleys of optimal or near-optimal structural balance, separated by energy barriers determined by internally balanced subcommunities of users, a phenomenon similar to the replica-symmetry breaking of spin glasses. Multiple, essentially isoenergetic, arrangements of these communities are possible. Passing from one valley to another requires one to destroy the internal arrangement of these balanced subcommunities and then to reform it again. It is essentially this process of breaking the internal balance of the subcommunities which gives rise to the energy barriers. PB - SISSA UR - http://hdl.handle.net/1963/6504 U1 - 6451 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - A formula for Popp\'s volume in sub-Riemannian geometry JF - Analysis and Geometry in Metric Spaces, vol. 1 (2012), pages : 42-57 Y1 - 2012 A1 - Luca Rizzi A1 - Davide Barilari KW - subriemannian, volume, Popp, control AB - For an equiregular sub-Riemannian manifold M, Popp\'s volume is a smooth\r\nvolume which is canonically associated with the sub-Riemannian structure, and\r\nit is a natural generalization of the Riemannian one. In this paper we prove a\r\ngeneral formula for Popp\'s volume, written in terms of a frame adapted to the\r\nsub-Riemannian distribution. As a first application of this result, we prove an\r\nexplicit formula for the canonical sub-Laplacian, namely the one associated\r\nwith Popp\'s volume. Finally, we discuss sub-Riemannian isometries, and we prove\r\nthat they preserve Popp\'s volume. We also show that, under some hypotheses on\r\nthe action of the isometry group of M, Popp\'s volume is essentially the unique\r\nvolume with such a property. PB - SISSA UR - http://hdl.handle.net/1963/6501 N1 - 16 pages, minor revisions U1 - 6446 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - RPRT T1 - A Fully Coupled Immersed Finite Element Method for Fluid Structure Interaction via the Deal.II Library Y1 - 2012 A1 - Luca Heltai A1 - Saswati Roy A1 - Francesco Costanzo KW - Finite Element Method KW - Immersed Boundary Method KW - Immersed Finite Element Method AB - We present the implementation of a solution scheme for fluid-structure\\r\\ninteraction problems via the finite element software library deal.II. The\\r\\nsolution scheme is an immersed finite element method in which two independent discretizations are used for the fluid and immersed deformable body. In this type of formulation the support of the equations of motion of the fluid is extended to cover the union of the solid and fluid domains. The equations of motion over the extended solution domain govern the flow of a fluid under the action of a body force field. This body force field informs the fluid of the presence of the immersed solid. The velocity field of the immersed solid is the restriction over the immersed domain of the velocity field in the extended equations of motion. The focus of this paper is to show how the determination of the motion of the immersed domain is carried out in practice. We show that our implementation is general, that is, it is not dependent on a specific choice of the finite element spaces over the immersed solid and the extended fluid domains. We present some preliminary results concerning the accuracy of the proposed method. PB - SISSA UR - http://hdl.handle.net/1963/6255 N1 - 28 pages, 9 figures U1 - 6172 U2 - Mathematics U3 - Functional Analysis and Applications U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - Gamma-convergence and H-convergence of linear elliptic operators JF - Journal de Mathématiques Pures et Appliquées, Available online 12 September 2012 Y1 - 2012 A1 - Nadia Ansini A1 - Gianni Dal Maso A1 - Caterina Ida Zeppieri KW - Linear elliptic operators PB - Elsevier UR - http://hdl.handle.net/1963/5878 U1 - 5746 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - A general method for the existence of periodic solutions of differential systems in the plane JF - Journal of Differential Equations Y1 - 2012 A1 - Alessandro Fonda A1 - Andrea Sfecci KW - Nonlinear dynamics KW - Periodic solutions AB -We propose a general method to prove the existence of periodic solutions for planar systems of ordinary differential equations, which can be used in many different circumstances. Applications are given to some nonresonant cases, even for systems with superlinear growth in some direction, or with a singularity. Systems “at resonance” are also considered, provided a Landesman–Lazer type of condition is assumed.

VL - 252 UR - http://www.sciencedirect.com/science/article/pii/S0022039611003196 ER - TY - CHAP T1 - Generalized reduced basis methods and n-width estimates for the approximation of the solution manifold of parametric PDEs T2 - Springer, Indam Series, Vol. 4, 2012 Y1 - 2012 A1 - Toni Lassila A1 - Andrea Manzoni A1 - Alfio Quarteroni A1 - Gianluigi Rozza KW - solution manifold AB - The set of solutions of a parameter-dependent linear partial di fferential equation with smooth coe fficients typically forms a compact manifold in a Hilbert space. In this paper we review the generalized reduced basis method as a fast computational tool for the uniform approximation of the solution manifold. We focus on operators showing an affi ne parametric dependence, expressed as a linear combination of parameter-independent operators through some smooth, parameter-dependent scalar functions. In the case that the parameter-dependent operator has a dominant term in its affi ne expansion, one can prove the existence of exponentially convergent uniform approximation spaces for the entire solution manifold. These spaces can be constructed without any assumptions on the parametric regularity of the manifold \\r\\nonly spatial regularity of the solutions is required. The exponential convergence rate is then inherited by the generalized reduced basis method. We provide a numerical example related to parametrized elliptic\\r\\nequations con rming the predicted convergence rates. JF - Springer, Indam Series, Vol. 4, 2012 PB - Springer UR - http://hdl.handle.net/1963/6340 U1 - 6270 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - On the Hausdorff volume in sub-Riemannian geometry JF - Calculus of Variations and Partial Differential Equations. Volume 43, Issue 3-4, March 2012, Pages 355-388 Y1 - 2012 A1 - Andrei A. Agrachev A1 - Davide Barilari A1 - Ugo Boscain AB - For a regular sub-Riemannian manifold we study the Radon-Nikodym derivative\r\nof the spherical Hausdorff measure with respect to a smooth volume. We prove\r\nthat this is the volume of the unit ball in the nilpotent approximation and it\r\nis always a continuous function. We then prove that up to dimension 4 it is\r\nsmooth, while starting from dimension 5, in corank 1 case, it is C^3 (and C^4\r\non every smooth curve) but in general not C^5. These results answer to a\r\nquestion addressed by Montgomery about the relation between two intrinsic\r\nvolumes that can be defined in a sub-Riemannian manifold, namely the Popp and\r\nthe Hausdorff volume. If the nilpotent approximation depends on the point (that\r\nmay happen starting from dimension 5), then they are not proportional, in\r\ngeneral. PB - SISSA UR - http://hdl.handle.net/1963/6454 U1 - 6399 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Hybridization in nanostructured DNA monolayers probed by AFM: theory versus experiment JF - Nanoscale. 2012 Mar; 4(5):1734-41 Y1 - 2012 A1 - Alessandro Bosco A1 - Fouzia Bano A1 - Pietro Parisse A1 - Loredana Casalis A1 - Antonio DeSimone A1 - Cristian Micheletti AB - Nanografted monolayers (NAMs) of DNA show novel physico-chemical properties that make them ideally suited for advanced biosensing applications. In comparison with alternative solid-phase techniques for diagnostic DNA detection, NAMs have the advantage of combining a small size with a high homogeneity of the DNA surface coverage. These two properties favour the extreme miniaturization and ultrasensitivity in high-throughput biosensing devices. The systematic use of NAMs for quantitative DNA (and protein) detection has so far suffered from the lack of a control on key fabrication parameters, such as the ss- or ds-DNA surface coverage. Here we report on a combined experimental-computational study that allows us to estimate the surface density of the grafted DNA by analyzing the sample mechanical response, that is the DNA patch height vs. applied tip load curves. It is shown that the same analysis scheme can be used to detect the occurrence of hybridization with complementary strands in solution and estimate its efficiency. Thanks to these quantitative relationships it is possible to use a single AFM-based setup to: (i) fabricate a DNA NAM, (ii) control the DNA surface coverage, and (iii) characterize its level of hybridization helping the design of NAMs with pre-determined fabrication parameters. PB - Royal Society of Chemistry U1 - 6998 U2 - Physics U4 - -1 ER - TY - RPRT T1 - Introduction to Riemannian and sub-Riemannian geometry Y1 - 2012 A1 - Andrei A. Agrachev A1 - Davide Barilari A1 - Ugo Boscain PB - SISSA UR - http://hdl.handle.net/1963/5877 U1 - 5747 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Linear elasticity obtained from finite elasticity by Gamma-convergence under weak coerciveness conditions JF - Ann. Inst. H. Poincare Anal. Non Lineaire Y1 - 2012 A1 - Virginia Agostiniani A1 - Gianni Dal Maso A1 - Antonio DeSimone KW - Nonlinear elasticity AB -The energy functional of linear elasticity is obtained as G-limit of suitable rescalings of the energies of finite elasticity...

PB - Gauthier-Villars;Elsevier VL - 29 UR - http://hdl.handle.net/1963/4267 U1 - 3996 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - Generic T1 - Mathematical and numerical modeling of liquid crystal elastomer phase transition and deformation T2 - Materials Research Society Symposium Proceedings. Volume 1403, 2012, Pages 125-130 Y1 - 2012 A1 - Mariarita De Luca A1 - Antonio DeSimone KW - Artificial muscle AB - Liquid crystal (in particular, nematic) elastomers consist of cross-linked flexible polymer chains with embedded stiff rod molecules that allow them to behave as a rubber and a liquid crystal. Nematic elastomers are characterized by a phase transition from isotropic to nematic past a temperature threshold. They behave as rubber at high temperature and show nematic behavior below the temperature threshold. Such transition is reversible. While in the nematic phase, the rod molecules are aligned along the direction of the "nematic director". This molecular rearrangement induces a stretch in the polymer chains and hence macroscopic spontaneous deformations. The coupling between nematic order parameter and deformation gives rise to interesting phenomena with a potential for new interesting applications. In the biological field, the ability to considerably change their length makes them very promising as artificial muscles actuators. Their tunable optical properties make them suitable, for example, as lenses for new imaging systems. We present a mathematical model able to describe the behavior of nematic elastomers and numerical simulations reproducing such peculiar behavior. We use a geometrically linear version of the Warner and Terentjev model [1] and consider cooling experiments and stretching experiments in the direction perpendicular to the one of the director at cross-linking. JF - Materials Research Society Symposium Proceedings. Volume 1403, 2012, Pages 125-130 PB - Cambridge University Press SN - 9781605113807 UR - http://hdl.handle.net/1963/7020 U1 - 7011 U2 - Physics U4 - 1 ER - TY - JOUR T1 - Modeling and control of quantum systems: An introduction JF - IEEE Transactions on Automatic Control. Volume 57, Issue 8, 2012, Article number6189035, Pages 1898-1917 Y1 - 2012 A1 - Claudio Altafini A1 - Francesco Ticozzi AB - The scope of this work is to provide a self-contained introduction to a selection of basic theoretical aspects in the modeling and control of quantum mechanical systems, as well as a brief survey on the main approaches to control synthesis. While part of the existing theory, especially in the open-loop setting, stems directly from classical control theory (most notably geometric control and optimal control), a number of tools specifically tailored for quantum systems have been developed since the 1980s, in order to take into account their distinctive features: the probabilistic nature of atomic-scale physical systems, the effect of dissipation and the irreversible character of the measurements have all proved to be critical in feedback-design problems. The relevant dynamical models for both closed and open quantum systems are presented, along with the main results on their controllability and stability. A brief review of several currently available control design methods is meant to provide the interested reader with a roadmap for further studies PB - Institute of Electrical and Electronics Engineers UR - http://hdl.handle.net/1963/6505 U1 - 6449 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - The Monge problem in Wiener space JF - Calculus of Variations and Partial Differential Equations Y1 - 2012 A1 - Fabio Cavalletti AB -We address the Monge problem in the abstract Wiener space and we give an existence result provided both marginal measures are absolutely continuous with respect to the infinite dimensional Gaussian measure γ.

VL - 45 UR - https://doi.org/10.1007/s00526-011-0452-5 ER - TY - JOUR T1 - Nonlinear thin-walled beams with a rectangular cross-section-Part I JF - Math. Models Methods Appl. Sci. 22, 1150016 (2012) Y1 - 2012 A1 - Lorenzo Freddi A1 - Maria Giovanna Mora A1 - Roberto Paroni AB - Our aim is to rigorously derive a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section, starting from three-dimensional nonlinear elasticity. The different limit models are distinguished by the different scaling of the elastic energy and of the ratio between the sides of the cross-section. In this paper we report the first part of our results. PB - World Scientific UR - http://hdl.handle.net/1963/4104 U1 - 300 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A nonresonance condition for radial solutions of a nonlinear Neumann elliptic problem JF - Nonlinear Analysis: Theory, Methods & Applications Y1 - 2012 A1 - Andrea Sfecci KW - Neumann problem KW - Nonresonance KW - Radial solutions KW - Time-map AB -We prove an existence result for radial solutions of a Neumann elliptic problem whose nonlinearity asymptotically lies between the first two eigenvalues. To this aim, we introduce an alternative nonresonance condition with respect to the second eigenvalue which, in the scalar case, generalizes the classical one, in the spirit of Fonda et al. (1991) [2]. Our approach also applies for nonlinearities which do not necessarily satisfy a subcritical growth assumption.

VL - 75 UR - http://www.sciencedirect.com/science/article/pii/S0362546X12002659 ER - TY - JOUR T1 - Non-uniqueness results for critical metrics of regularized determinants in four dimensions JF - Communications in Mathematical Physics, Volume 315, Issue 1, September 2012, Pages 1-37 Y1 - 2012 A1 - Matthew Gursky A1 - Andrea Malchiodi AB - The regularized determinant of the Paneitz operator arises in quantum gravity (see Connes 1994, IV.4.$\gamma$). An explicit formula for the relative determinant of two conformally related metrics was computed by Branson in Branson (1996). A similar formula holds for Cheeger's half-torsion, which plays a role in self-dual field theory (see Juhl, 2009), and is defined in terms of regularized determinants of the Hodge laplacian on $p$-forms ($p < n/2$). In this article we show that the corresponding actions are unbounded (above and below) on any conformal four-manifold. We also show that the conformal class of the round sphere admits a second solution which is not given by the pull-back of the round metric by a conformal map, thus violating uniqueness up to gauge equivalence. These results differ from the properties of the determinant of the conformal Laplacian established in Chang and Yang (1995), Branson, Chang, and Yang (1992), and Gursky (1997). We also study entire solutions of the Euler-Lagrange equation of $\log \det P$ and the half-torsion $\tau_h$ on $\mathbb{R}^4 \setminus {0}$, and show the existence of two families of periodic solutions. One of these families includes Delaunay-type solutions. PB - Springer UR - http://hdl.handle.net/1963/6559 N1 - 35 pages, title changed, added determinant of half-torsion, references added. Comm. Math. Phys., to appear U1 - 6488 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Numerical modelling of installation effects for diaphragm walls in sand JF - Acta Geotechnica, Volume 7, Issue 3, September 2012, Pages 219-237 Y1 - 2012 A1 - Riccardo Conti A1 - Luca de Sanctis A1 - Giulia M.B. Viggiani KW - Constitutive relations AB - The scopes of this work are to study the mechanisms of load transfer and the deformations of the ground during slurry trenching and concreting in dry sand and to evaluate their effects on service structural loads, wall deflections and ground displacements behind the wall caused by subsequent excavation. A series of three-dimensional finite element analyses was carried out modelling the installation of diaphragm walls consisting of panels of different length. The soil was modelled as either linearly elastic-perfectly plastic or incrementally non-linear (hypoplastic) with elastic strain range. Plane strain analyses of diaphragm walls of identical cross section were also carried out in which wall installation was either modelled or the wall was wished in place (WIP). The analyses predict ground movements consistent with the experimental observations both in magnitude and trend. The results also show that the maximum horizontal wall deflections and structural loads reduce with increasing panel aspect ratio towards a minimum which is about twice the value computed for WIP analyses. Panel aspect ratios should be larger than about three to take advantage of the three-dimensional effects. The pattern and magnitude of surface vertical displacements obtained from linearly elastic-perfectly plastic analyses, no matter whether three- or two-dimensional, are unrealistic. PB - Springer UR - http://hdl.handle.net/1963/6934 U1 - 6916 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - Ogden-type energies for nematic elastomers JF - International Journal of Non-Linear mechanics Y1 - 2012 A1 - Virginia Agostiniani A1 - Antonio DeSimone KW - Nonlinear elasticity AB -Ogden-type extensions of the free-energy densities currently used to model the mechanical behavior of nematic elastomers are proposed and analyzed. Based on a multiplicative decomposition of the deformation gradient into an elastic and a spontaneous or remanent part, they provide a suitable framework to study the stiffening response at high imposed stretches. Geometrically linear versions of the models (Taylor expansions at order two) are provided and discussed. These small strain theories provide a clear illustration of the geometric structure of the underlying energy landscape (the energy grows quadratically with the distance from a non-convex set of spontaneous strains or energy wells). The comparison between small strain and finite deformation theories may also be useful in the opposite direction, inspiring finite deformation generalizations of small strain theories currently used in the mechanics of active and phase-transforming materials. The energy well structure makes the free-energy densities non-convex. Explicit quasi-convex envelopes are provided, and applied to compute the stiffening response of a specimen tested in plane strain extension experiments (pure shear).

PB - Elsevier VL - 47 IS - 2 U1 - 6971 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - One-signed harmonic solutions and sign-changing subharmonic solutions to scalar second order differential equations JF - Advanced Nonlinear Studies Y1 - 2012 A1 - Alberto Boscaggin PB - Advanced Nonlinear Studies, Inc. VL - 12 ER - TY - JOUR T1 - Optimal Transport with Branching Distance Costs and the Obstacle Problem JF - SIAM Journal on Mathematical Analysis Y1 - 2012 A1 - Fabio Cavalletti VL - 44 UR - https://doi.org/10.1137/100801433 ER - TY - JOUR T1 - Pairs of positive periodic solutions of second order nonlinear equations with indefinite weight JF - Journal of Differential Equations Y1 - 2012 A1 - Alberto Boscaggin A1 - Fabio Zanolin KW - Critical points KW - Necessary conditions KW - Pairs of positive solutions KW - Periodic solutions AB -We study the problem of the existence and multiplicity of positive periodic solutions to the scalar ODEu″+λa(t)g(u)=0,λ>0, where g(x) is a positive function on R+, superlinear at zero and sublinear at infinity, and a(t) is a T-periodic and sign indefinite weight with negative mean value. We first show the nonexistence of solutions for some classes of nonlinearities g(x) when λ is small. Then, using critical point theory, we prove the existence of at least two positive T-periodic solutions for λ large. Some examples are also provided.

VL - 252 UR - http://www.sciencedirect.com/science/article/pii/S0022039611003895 ER - TY - JOUR T1 - Periodic solutions of a system of coupled oscillators with one-sided superlinear retraction forces JF - Differential Integral Equations Y1 - 2012 A1 - Alessandro Fonda A1 - Andrea Sfecci PB - Khayyam Publishing, Inc. VL - 25 UR - https://projecteuclid.org:443/euclid.die/1356012248 ER - TY - JOUR T1 - Periodic solutions to superlinear planar Hamiltonian systems JF - Portugaliae Mathematica Y1 - 2012 A1 - Alberto Boscaggin AB -We prove the existence of infinitely many periodic (harmonic and subharmonic) solutions to planar Hamiltonian systems satisfying a suitable superlinearity condition at infinity. The proof relies on the Poincare-Birkhoff fixed point theorem.

PB - European Mathematical Society Publishing House VL - 69 ER - TY - JOUR T1 - Positive periodic solutions of second order nonlinear equations with indefinite weight: Multiplicity results and complex dynamics JF - Journal of Differential Equations Y1 - 2012 A1 - Alberto Boscaggin A1 - Fabio Zanolin KW - Complex dynamics KW - Poincaré map KW - Positive periodic solutions KW - Subharmonics AB -We prove the existence of a pair of positive T-periodic solutions as well as the existence of positive subharmonic solutions of any order and the presence of chaotic-like dynamics for the scalar second order ODEu″+aλ,μ(t)g(u)=0, where g(x) is a positive function on R+, superlinear at zero and sublinear at infinity, and aλ,μ(t) is a T-periodic and sign indefinite weight of the form λa+(t)−μa−(t), with λ,μ>0 and large.

VL - 252 UR - http://www.sciencedirect.com/science/article/pii/S0022039611003883 ER - TY - JOUR T1 - Predicting and characterizing selective multiple drug treatments for metabolic diseases and cancer. JF - BMC Systems Biology. 29 August 2012, Page 115 Y1 - 2012 A1 - Giuseppe Facchetti A1 - Claudio Altafini A1 - Mattia Zampieri AB - Background: In the field of drug discovery, assessing the potential of multidrug therapies is a difficult task because of the combinatorial complexity (both theoretical and experimental) and because of the requirements on the selectivity of the therapy. To cope with this problem, we have developed a novel method for the systematic in silico investigation of synergistic effects of currently available drugs on genome-scale metabolic networks. The algorithm finds the optimal combination of drugs which guarantees the inhibition of an objective function, while minimizing the side effect on the overall network. Results: Two different applications are considered: finding drug synergisms for human metabolic diseases (like diabetes, obesity and hypertension) and finding antitumoral drug combinations with minimal side effect on the normal human metabolism.The results we obtain are consistent with some of the available therapeutic indications and predict some new multiple drug treatments.A cluster analysis on all possible interactions among the currently available drugs indicates a limited variety on the metabolic targets for the approved drugs. Conclusion: The in silico prediction of drug synergism can represent an important tool for the repurposing of drug in a realistic perspective which considers also the selectivty of the therapy. Moreover, for a more profitable exploitation of drug-drug interactions, also drugs which show a too low efficacy but which have a non-common mechanism of action, can be reconsider as potential ingredients of new multicompound therapeutic indications.Needless to say the clues provided by a computational study like ours need in any case to be thoroughly evaluated experimentally. PB - BioMed Central UR - http://hdl.handle.net/1963/6515 U1 - 6450 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Quasistatic evolution for Cam-Clay plasticity: properties of the viscosity solution JF - Calculus of variations and partial differential equations 44 (2012) 495-541 Y1 - 2012 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Francesco Solombrino AB -Cam-Clay plasticity is a well established model for the description of the mechanics of fine grained soils. As solutions can develop discontinuities in time, a weak notion of solution, in terms of a rescaled time s , has been proposed in [8] to give a meaning to this discontinuous evolution. In this paper we first prove that this rescaled evolution satisfies the flow-rule for the rate of plastic strain, in a suitable measure-theoretical sense. In the second part of the paper we consider the behavior of the evolution in terms of the original time variable t . We prove that the unrescaled solution satisfies an energy-dissipation balance and an evolution law for the internal variable, which can be expressed in terms of integrals depending only on the original time. Both these integral identities contain terms concentrated on the jump times, whose size can only be determined by looking at the rescaled formulation.

PB - Springer UR - http://hdl.handle.net/1963/3900 U1 - 809 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic evolution in non-associative plasticity - the cap models JF - SIAM Journal on Mathematical Analysis 44, nr. 1 (2012) 245-292 Y1 - 2012 A1 - Jean-Francois Babadjian A1 - Gilles A. Francfort A1 - Maria Giovanna Mora KW - Elasto-plasticity AB - Non-associative elasto-plasticity is the working model of plasticity for soil and rocks mechanics. Yet, it is usually viewed as non-variational. In this work, we prove a contrario the existence of a variational evolution for such a model under a natural capping assumption on the hydrostatic stresses and a less natural mollification of the stress admissibility constraint. The obtained elasto-plastic evolution is expressed for times that are conveniently rescaled. PB - SIAM UR - http://hdl.handle.net/1963/4139 U1 - 3879 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - Generic T1 - Reduction strategies for PDE-constrained oprimization problems in Haemodynamics T2 - European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012) J. Eberhardsteiner et.al. (eds.), Vienna, Austria, 10-14 sept. 2012 Y1 - 2012 A1 - Gianluigi Rozza A1 - Andrea Manzoni A1 - Federico Negri KW - inverse problems AB - Solving optimal control problems for many different scenarios obtained by varying a set of parameters in the state system is a computationally extensive task. In this paper we present a new reduced framework for the formulation, the analysis and the numerical solution of parametrized PDE-constrained optimization problems. This framework is based on a suitable saddle-point formulation of the optimal control problem and exploits the reduced basis method for the rapid and reliable solution of parametrized PDEs, leading to a relevant computational reduction with respect to traditional discretization techniques such as the finite element method. This allows a very efficient evaluation of state solutions and cost functionals, leading to an effective solution of repeated optimal control problems, even on domains of variable shape, for which a further (geometrical) reduction is pursued, relying on flexible shape parametrization techniques. This setting is applied to the solution of two problems arising from haemodynamics, dealing with both data reconstruction and data assimilation over domains of variable shape,\\r\\nwhich can be recast in a common PDE-constrained optimization formulation. JF - European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012) J. Eberhardsteiner et.al. (eds.), Vienna, Austria, 10-14 sept. 2012 UR - http://hdl.handle.net/1963/6338 U1 - 6268 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - Resonance at the first eigenvalue for first-order systems in the plane: vanishing Hamiltonians and the Landesman-Lazer condition JF - Differential Integral Equations Y1 - 2012 A1 - Maurizio Garrione PB - Khayyam Publishing, Inc. VL - 25 UR - https://projecteuclid.org:443/euclid.die/1356012676 ER - TY - JOUR T1 - Reverse engineering the euglenoid movement JF - Proceedings of the National Academy of Sciences of the United States of America. Volume 109, Issue 44, 30 October 2012, Pages 17874-17879 Y1 - 2012 A1 - Marino Arroyo A1 - Luca Heltai A1 - Daniel Millán A1 - Antonio DeSimone KW - microswimmers AB - Euglenids exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large-amplitude highly concerted deformations of the entire body (euglenoid movement or metaboly). A plastic cell envelope called pellicle mediates these deformations. Unlike ciliary or flagellar motility, the biophysics of this mode is not well understood, including its efficiency and molecular machinery. We quantitatively examine video recordings of four euglenids executing such motions with statistical learning methods. This analysis reveals strokes of high uniformity in shape and pace. We then interpret the observations in the light of a theory for the pellicle kinematics, providing a precise understanding of the link between local actuation by pellicle shear and shape control. We systematically understand common observations, such as the helical conformations of the pellicle, and identify previously unnoticed features of metaboly. While two of our euglenids execute their stroke at constant body volume, the other two exhibit deviations of about 20% from their average volume, challenging current models of low Reynolds number locomotion. We find that the active pellicle shear deformations causing shape changes can reach 340%, and estimate the velocity of the molecular motors. Moreover, we find that metaboly accomplishes locomotion at hydrodynamic efficiencies comparable to those of ciliates and flagellates. Our results suggest new quantitative experiments, provide insight into the evolutionary history of euglenids, and suggest that the pellicle may serve as a model for engineered active surfaces with applications in microfluidics. UR - http://hdl.handle.net/1963/6444 U1 - 6380 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - On robust Lie-algebraic stability conditions for switched linear systems JF - Systems and Control Letters. Volume 61, Issue 2, February 2012, Pages 347-353 Y1 - 2012 A1 - Andrei A. Agrachev A1 - Yurij Baryshnikov A1 - Daniel Liberzon AB - This paper presents new sufficient conditions for exponential stability of switched linear systems under arbitrary switching, which involve the commutators (Lie brackets) among the given matrices generating the switched system. The main novelty feature of these stability criteria is that, unlike their earlier counterparts, they are robust with respect to small perturbations of the system parameters. UR - http://hdl.handle.net/1963/6455 U1 - 6400 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - SBV regularity for genuinely nonlinear, strictly hyperbolic systems of conservation laws in one space dimension JF - Communications in Mathematical Physics 313 (2012) 1-33 Y1 - 2012 A1 - Stefano Bianchini A1 - Laura Caravenna PB - Springer UR - http://hdl.handle.net/1963/4091 U1 - 313 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - SBV regularity for Hamilton-Jacobi equations with Hamiltonian depending on (t,x) JF - Siam Journal on Mathematical Analysis Y1 - 2012 A1 - Stefano Bianchini A1 - Daniela Tonon PB - SISSA VL - 44 UR - http://hdl.handle.net/20.500.11767/14066 IS - 3 U1 - 3890 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - SBV regularity of genuinely nonlinear hyperbolic systems of conservation laws in one space dimension JF - Acta Mathematica Scientia, Volume 32, Issue 1, January 2012, Pages 380-388 Y1 - 2012 A1 - Stefano Bianchini KW - Hyperbolic systems AB - The problem of the presence of Cantor part in the derivative of a solution to a hyperbolic system of conservation laws is considered. An overview of the techniques involved in the proof is given, and a collection of related problems concludes the paper. Key words hyperbolic systems; conservation laws; SBV; regularity PB - Elsevier UR - http://hdl.handle.net/1963/6535 U1 - 6510 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - SBV-like regularity for general hyperbolic systems of conservation laws in one space dimension JF - Rend. Istit. Mat. Univ. Trieste Y1 - 2012 A1 - Stefano Bianchini A1 - Lei Yu VL - 44 ER - TY - JOUR T1 - SBV-like regularity for Hamilton-Jacobi equations with a convex Hamiltonian JF - Journal of Mathematical Analysis and Applications Y1 - 2012 A1 - Stefano Bianchini A1 - Daniela Tonon PB - SISSA VL - 391 UR - http://hdl.handle.net/20.500.11767/13909 IS - 1 U1 - 4352 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Second order approximations of quasistatic evolution problems in finite dimension JF - Discrete & Continuous Dynamical Systems - A Y1 - 2012 A1 - Virginia Agostiniani KW - discrete approximations KW - perturbation methods KW - saddle-node bifurcation KW - Singular perturbations KW - vanishing viscosity AB -In this paper, we study the limit, as ε goes to zero, of a particular solution of the equation $\epsilon^2A\ddot u^ε(t)+εB\dot u^ε(t)+\nabla_xf(t,u^ε(t))=0$, where $f(t,x)$ is a potential satisfying suitable coerciveness conditions. The limit $u(t)$ of $u^ε(t)$ is piece-wise continuous and verifies $\nabla_xf(t,u(t))=0$. Moreover, certain jump conditions characterize the behaviour of $u(t)$ at the discontinuity times. The same limit behaviour is obtained by considering a different approximation scheme based on time discretization and on the solutions of suitable autonomous systems.

VL - 32 UR - http://aimsciences.org//article/id/560b82d9-f289-498a-a619-a4b132aaf9f8 ER - TY - JOUR T1 - Self-propelled micro-swimmers in a Brinkman fluid JF - Journal of Biological Dynamics Y1 - 2012 A1 - Marco Morandotti AB -We prove an existence, uniqueness, and regularity result for the motion of a self-propelled micro-swimmer in a particulate viscous medium, modelled as a Brinkman fluid. A suitable functional setting is introduced to solve the Brinkman system for the velocity field and the pressure of the fluid by variational techniques. The equations of motion are written by imposing a self-propulsion constraint, thus allowing the viscous forces and torques to be the only ones acting on the swimmer. From an infinite-dimensional control on the shape of the swimmer, a system of six ordinary differential equations for the spatial position and the orientation of the swimmer is obtained. This is dealt with standard techniques for ordinary differential equations, once the coefficients are proved to be measurable and bounded. The main result turns out to extend an analogous result previously obtained for the Stokes system.

PB - Taylor & Francis VL - 6 UR - https://doi.org/10.1080/17513758.2011.611260 N1 - PMID: 22873677 ER - TY - JOUR T1 - Simulation-based uncertainty quantification of human arterial network hemodynamics JF - International Journal Numerical Methods Biomedical Engineering Y1 - 2012 A1 - Peng Chen A1 - Alfio Quarteroni A1 - Gianluigi Rozza KW - uncertainty quantification, mathematical modelling of the cardiovascular system, fluid-structure interaction AB - This work aims at identifying and quantifying uncertainties from various sources in human cardiovascular\r\nsystem based on stochastic simulation of a one dimensional arterial network. A general analysis of\r\ndifferent uncertainties and probability characterization with log-normal distribution of these uncertainties\r\nis introduced. Deriving from a deterministic one dimensional fluid structure interaction model, we establish\r\nthe stochastic model as a coupled hyperbolic system incorporated with parametric uncertainties to describe\r\nthe blood flow and pressure wave propagation in the arterial network. By applying a stochastic collocation\r\nmethod with sparse grid technique, we study systemically the statistics and sensitivity of the solution with\r\nrespect to many different uncertainties in a relatively complete arterial network with potential physiological\r\nand pathological implications for the first time. PB - Wiley U1 - 6467 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - Some applications of the SBV Regularity Theorem for entropy solutions of 1D scalar conservation laws to ConvectionTheory and sticky particles JF - Riv. Mat. Univ. Parma Y1 - 2012 A1 - Daniela Tonon AB -We show how it is possible to apply the SBV Regularity Theorem for entropy solutions of one-dimensional scalar conservation laws, proved by Ambrosio and De Lellis, to Convection Theory and sticky particles. In the multi-dimensional case we present a counterexample which prevent us from using the same approach.

VL - 3 UR - https://hal.archives-ouvertes.fr/hal-00918409 ER - TY - CONF T1 - A stable semi-lagrangian potential method for the simulation of ship interaction with unsteady and nonlinear waves T2 - 17th Int. Conf. Ships Shipp. Res. Y1 - 2012 A1 - Andrea Mola A1 - Luca Heltai A1 - Antonio DeSimone JF - 17th Int. Conf. Ships Shipp. Res. ER - TY - JOUR T1 - Sub-Riemannian structures on 3D Lie groups JF - Journal of Dynamical and Control Systems. Volume 18, Issue 1, January 2012, Pages 21-44 Y1 - 2012 A1 - Andrei A. Agrachev A1 - Davide Barilari AB -We give a complete classification of left-invariant sub-Riemannian structures on three dimensional Lie groups in terms of the basic differential invariants. As a corollary we explicitly find a sub-Riemannian isometry between the nonisomorphic Lie groups $SL(2)$ and $A^+(\mathbb{R})\times S^1$, where $A^+(\mathbb{R})$ denotes the group of orientation preserving affine maps on the real line.

PB - SISSA UR - http://hdl.handle.net/1963/6453 U1 - 6397 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Systems of Quadratic Inequalities JF - Proceedings of the London Mathematical Society, Volume 105, Issue 3, September 2012, Pages 622-660 Y1 - 2012 A1 - Andrei A. Agrachev A1 - Antonio Lerario AB - We present a spectral sequence which efficiently computes Betti numbers of a closed semi-algebraic subset of RP^n defined by a system of quadratic inequalities and the image of the homology homomorphism induced by the inclusion of this subset in RP^n. We do not restrict ourselves to the term E_2 of the spectral sequence and give a simple explicit formula for the differential d_2. PB - SISSA UR - http://hdl.handle.net/1963/7072 U1 - 7066 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - RPRT T1 - Topological sensitivity analysis for high order elliptic operators Y1 - 2012 A1 - Samuel Amstutz A1 - Antonio André Novotny A1 - Nicolas Van Goethem KW - Topological derivative, Elliptic operators, Polarization tensor AB - The topological derivative is defined as the first term of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of a singular domain perturbation. It has applications in many different fields such as shape and topology optimization, inverse problems, image processing and mechanical modeling including synthesis and/or optimal design of microstructures, fracture mechanics sensitivity analysis and damage evolution modeling. The topological derivative has been fully developed for a wide range of second order differential operators. In this paper we deal with the topological asymptotic expansion of a class of shape functionals associated with elliptic differential operators of order 2m, m>=1. The general structure of the polarization tensor is derived and the concept of degenerate polarization tensor is introduced. We provide full mathematical justifications for the derived formulas, including precise estimates of remainders. PB - SISSA UR - http://hdl.handle.net/1963/6343 U1 - 6272 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Variational implementation of immersed finite element methods JF - Computer Methods in Applied Mechanics and Engineering. Volume 229-232, 1 July 2012, Pages 110-127 Y1 - 2012 A1 - Luca Heltai A1 - Francesco Costanzo KW - Turbulent flow AB -Dirac-delta distributions are often crucial components of the solid-fluid coupling operators in immersed solution methods for fluid-structure interaction (FSI) problems. This is certainly so for methods like the Immersed Boundary Method (IBM) or the Immersed Finite Element Method (IFEM), where Dirac-delta distributions are approximated via smooth functions. By contrast, a truly variational formulation of immersed methods does not require the use of Dirac-delta distributions, either formally or practically. This has been shown in the Finite Element Immersed Boundary Method (FEIBM), where the variational structure of the problem is exploited to avoid Dirac-delta distributions at both the continuous and the discrete level. In this paper, we generalize the FEIBM to the case where an incompressible Newtonian fluid interacts with a general hyperelastic solid. Specifically, we allow (i) the mass density to be different in the solid and the fluid, (ii) the solid to be either viscoelastic of differential type or purely elastic, and (iii) the solid to be and either compressible or incompressible. At the continuous level, our variational formulation combines the natural stability estimates of the fluid and elasticity problems. In immersed methods, such stability estimates do not transfer to the discrete level automatically due to the non- matching nature of the finite dimensional spaces involved in the discretization. After presenting our general mathematical framework for the solution of FSI problems, we focus in detail on the construction of natural interpolation operators between the fluid and the solid discrete spaces, which guarantee semi-discrete stability estimates and strong consistency of our spatial discretization.

PB - Elsevier UR - http://hdl.handle.net/1963/6462 N1 - 42 pages, 5 figures, Revision 1 U1 - 6389 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - A Viscosity-driven crack evolution JF - Advances in Calculus of Variations 5 (2012) 433-483 Y1 - 2012 A1 - Simone Racca AB -We present a model of crack growth in brittle materials which couples dissipative effects on the crack tip and viscous effects. We consider the 2 -dimensional antiplane case with pre-assigned crack path, and firstly prove an existence result for a rate-dependent evolution problem by means of time-discretization. The next goal is to describe the rate-independent evolution as limit of the rate-dependent ones when the dissipative and viscous effects vanish. The rate-independent evolution satisfies a Griffith’s criterion for the crack growth, but, in general, it does not fulfil a global minimality condition; its fracture set may exhibit jump discontinuities with respect to time. Under suitable regularity assumptions, the quasi-static crack growth is described by solving a finite-dimensional problem.

PB - SISSA UR - http://hdl.handle.net/1963/5130 U1 - 4944 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Weighted barycentric sets and singular Liouville equations on compact surfaces JF - Journal of Functional Analysis 262 (2012) 409-450 Y1 - 2012 A1 - Alessandro Carlotto A1 - Andrea Malchiodi AB - Given a closed two dimensional manifold, we prove a general existence result\\r\\nfor a class of elliptic PDEs with exponential nonlinearities and negative Dirac\\r\\ndeltas on the right-hand side, extending a theory recently obtained for the\\r\\nregular case. This is done by global methods: since the associated Euler\\r\\nfunctional is in general unbounded from below, we need to define a new model\\r\\nspace, generalizing the so-called space of formal barycenters and\\r\\ncharacterizing (up to homotopy equivalence) its very low sublevels. As a\\r\\nresult, the analytic problem is reduced to a topological one concerning the\\r\\ncontractibility of this model space. To this aim, we prove a new functional\\r\\ninequality in the spirit of [16] and then we employ a min-max scheme based on a cone-style construction, jointly with the blow-up analysis given in [5] (after\\r\\n[6] and [8]). This study is motivated by abelian Chern- Simons theory in\\r\\nself-dual regime, or from the problem of prescribing the Gaussian curvature in\\r\\npresence of conical singularities (hence generalizing a problem raised by\\r\\nKazdan and Warner in [26]). PB - Elsevier UR - http://hdl.handle.net/1963/5218 U1 - 5040 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Axial symmetry of some steady state solutions to nonlinear Schrödinger equations JF - Proc. Amer. Math. Soc. 139 (2011), 1023-1032 Y1 - 2011 A1 - Changfeng Gui A1 - Andrea Malchiodi A1 - Haoyuan Xu A1 - Paul Yang KW - Nonlinear Schrödinger equation AB - In this note, we show the axial symmetry of steady state solutions of nonlinear Schrodinger equations when the exponent of the nonlinearity is between the critical Sobolev exponent of n dimensional space and n - 1 dimensional space. PB - American Mathematical Society UR - http://hdl.handle.net/1963/4100 U1 - 304 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Bishop and Laplacian Comparison Theorems on Three Dimensional Contact Subriemannian Manifolds with Symmetry Y1 - 2011 A1 - Andrei A. Agrachev A1 - Paul Lee AB - We prove a Bishop volume comparison theorem and a Laplacian comparison\r\ntheorem for three dimensional contact subriemannian manifolds with symmetry. PB - SISSA UR - http://hdl.handle.net/1963/6508 N1 - 25 pages U1 - 6455 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - A class of existence results for the singular Liouville equation JF - Comptes Rendus Mathematique 349 (2011) 161-166 Y1 - 2011 A1 - Alessandro Carlotto A1 - Andrea Malchiodi AB - We consider a class of elliptic PDEs on closed surfaces with exponential nonlinearities and Dirac deltas on the right-hand side. The study arises from abelian Chern–Simons theory in self-dual regime, or from the problem of prescribing the Gaussian curvature in presence of conical singularities. A general existence result is proved using global variational methods: the analytic problem is reduced to a topological problem concerning the contractibility of a model space, the so-called space of formal barycenters, characterizing the very low sublevels of a suitable functional. PB - Elsevier UR - http://hdl.handle.net/1963/5793 U1 - 5648 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Cluster solutions for the Schrödinger-Poisson-Slater problem around a local minimum of the potential JF - Rev. Mat. Iberoamericana Y1 - 2011 A1 - David Ruiz A1 - Giusi Vaira PB - Real Sociedad Matemática Española VL - 27 UR - https://projecteuclid.org:443/euclid.rmi/1296828834 ER - TY - RPRT T1 - Compactness by maximality Y1 - 2011 A1 - Sandro Zagatti AB - We derive a compactness property in the Sobolev space $W^{1,1}(\O)$ in order to study the Dirichlet problem for the eikonal equation \begin{displaymath} \begin{cases} \ha |\n u(x)|^2 - a(x) = 0 & \ \textrm{in} \ \O\cr u(x)=\varphi(x) & \ \textrm{on} \ \partial \O, \end{cases} \end{displaymath} without continuity assumptions on the map $a$. UR - http://preprints.sissa.it/handle/1963/35317 U1 - 35626 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Concentration of solutions for a singularly perturbed Neumann problem in non-smooth domains JF - Annales de l'I.H.P. Analyse non linéaire Y1 - 2011 A1 - Serena Dipierro PB - Elsevier VL - 28 UR - http://www.numdam.org/item/AIHPC_2011__28_1_107_0 ER - TY - JOUR T1 - Crack growth with non-interpenetration : a simplified proof for the pure Neumann problem JF - Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1219-1231 Y1 - 2011 A1 - Gianni Dal Maso A1 - Giuliano Lazzaroni AB - We present a recent existence result concerning the quasi-static evolution of cracks in hyperelastic brittle materials, in the frame-work of finite elasticity with non-interpenetration. In particular, here we consider the problem where no Dirichlet conditions are imposed, the boundary is traction-free, and the body is subject only to time-dependent volume forces. This allows us to present the main ideas of the proof in a simpler way, avoiding some of the technicalities needed in the general case, studied in. PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/3801 U1 - 526 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Critical points of the Moser-Trudinger functional Y1 - 2011 A1 - Francesca De Marchis A1 - Andrea Malchiodi A1 - Luca Martinazzi KW - Moser-Trudinger inequality PB - SISSA UR - http://hdl.handle.net/1963/4592 U1 - 4353 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Cytoskeletal actin networks in motile cells are critically self-organized systems synchronized by mechanical interactions JF - PNAS 108 (2011) 13978 Y1 - 2011 A1 - Luca Cardamone A1 - Alessandro Laio A1 - Rajesh Shahapure A1 - Antonio DeSimone PB - National Academy of Sciences UR - http://hdl.handle.net/1963/4358 U1 - 4066 U2 - Physics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - A Decomposition Theorem for BV functions JF - Communications on Pure and Applied Analysis Y1 - 2011 A1 - Stefano Bianchini A1 - Daniela Tonon PB - American Institute of Mathematical Sciences VL - 10 UR - http://hdl.handle.net/20.500.11767/14599 IS - 6 U1 - 693 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Dimensional Reduction and Approximation of Measures and Weakly Differentiable Homeomorphisms Y1 - 2011 A1 - Sara Daneri AB - This thesis is devoted to the study of two different problems: the properties of the disintegration of the Lebesgue measure on the faces of a convex function and the existence of smooth approximations of bi-Lipschitz orientation-preserving homeomorphisms in the plane. PB - SISSA UR - http://hdl.handle.net/1963/5348 U1 - 5178 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Double resonance with Landesman–Lazer conditions for planar systems of ordinary differential equations JF - Journal of Differential Equations Y1 - 2011 A1 - Alessandro Fonda A1 - Maurizio Garrione KW - Double resonance KW - Landesman–Lazer conditions KW - Nonlinear planar systems AB -We prove the existence of periodic solutions for first order planar systems at resonance. The nonlinearity is indeed allowed to interact with two positively homogeneous Hamiltonians, both at resonance, and some kind of Landesman–Lazer conditions are assumed at both sides. We are thus able to obtain, as particular cases, the existence results proposed in the pioneering papers by Lazer and Leach (1969) [27], and by Frederickson and Lazer (1969) [18]. Our theorem also applies in the case of asymptotically piecewise linear systems, and in particular generalizes Fabry's results in Fabry (1995) [10], for scalar equations with double resonance with respect to the Dancer–Fučik spectrum.

VL - 250 UR - http://www.sciencedirect.com/science/article/pii/S0022039610002901 ER - TY - JOUR T1 - Embedding theorems and existence results for nonlinear Schrödinger–Poisson systems with unbounded and vanishing potentials JF - Journal of Differential Equations Y1 - 2011 A1 - Bonheure, Denis A1 - Mercuri, Carlo AB -Motivated by existence results for positive solutions of non-autonomous nonlinear Schrödinger–Poisson systems with potentials possibly unbounded or vanishing at infinity, we prove embedding theorems for weighted Sobolev spaces. We both consider a general framework and spaces of radially symmetric functions when assuming radial symmetry of the potentials.

PB - Elsevier VL - 251 UR - https://doi.org/10.1016/j.jde.2011.04.010 ER - TY - JOUR T1 - Energy release rate and stress intensity factor in antiplane elasticity JF - Journal de Mathematiques Pures et Appliquees 95 (2011) 565-584 Y1 - 2011 A1 - Giuliano Lazzaroni A1 - Rodica Toader AB - In the setting of antiplane linearized elasticity, we show the existence of the stress intensity factor and its relation with the energy release rate when the crack path is a C1,1 curve. Finally, we show that the energy release rate is continuous with respect to the Hausdorff convergence in a class of admissible cracks. PB - Elsevier UR - http://hdl.handle.net/1963/3780 U1 - 546 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Ennio De Giorgi and Γ-convergence JF - Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1017-1021 Y1 - 2011 A1 - Gianni Dal Maso AB - Γ-convergence was introduced by Ennio De Giorgi in a series of papers published between 1975 and 1983. In the same years he developed many applications of this tool to a great variety of asymptotic problems in the calculus of variations and in the theory of partial differential equations. PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/5308 U1 - 5138 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - An Estimate on the Flow Generated by Monotone Operators JF - Communications in Partial Differential Equations 36 (2011) 777-796 Y1 - 2011 A1 - Stefano Bianchini A1 - Matteo Gloyer PB - Taylor & Francis UR - http://hdl.handle.net/1963/3646 U1 - 658 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - An Existence and Uniqueness Result for the Motion of Self-Propelled Microswimmers JF - SIAM J. Math. Anal. Y1 - 2011 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Marco Morandotti AB -We present an analytical framework to study the motion of micro-swimmers in a viscous fluid. Our main result is that, under very mild regularity assumptions, the change of shape determines uniquely the motion of the swimmer. We assume that the Reynolds number is very small, so that the velocity field of the surrounding, infinite fluid is governed by the Stokes system and all inertial effects can be neglected. Moreover, we enforce the self propulsion constraint (no external forces and torques). Therefore, Newton\\\'s equations of motion reduce to the vanishing of the viscous drag force and torque acting on the body. By exploiting an integral representation of viscous force and torque, the equations of motion can be reduced to a system of six ordinary differential equations. Variational techniques are used to prove the boundedness and measurability of its coefficients, so that classical results on ordinary differential equations can be invoked to prove existence and uniqueness of the solution.

PB - Society for Industrial and Applied Mathematics VL - 43 UR - http://hdl.handle.net/1963/3894 U1 - 815 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence for wave equations on domains with arbitrary growing cracks JF - Rend. Lincei Mat. Appl. 22 (2011) 387-408 Y1 - 2011 A1 - Gianni Dal Maso A1 - Cristopher J. Larsen KW - Wave equation AB - In this paper we formulate and study scalar wave equations on domains with arbitrary growing cracks. This includes a zero Neumann condition on the crack sets, and the only assumptions on these sets are that they have bounded surface measure and are growing in the sense of set inclusion. In particular, they may be dense, so the weak formulations must fall outside of the usual weak formulations using Sobolev spaces. We study both damped and undamped equations, showing existence and, for the damped equation, uniqueness and energy conservation. PB - European Mathematical Society UR - http://hdl.handle.net/1963/4284 U1 - 4015 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Fracture and plastic models as Gamma-limits of damage models under different regimes JF - Advances in Calculus of Variations., to appear. Y1 - 2011 A1 - Flaviana Iurlano AB -We consider a variational model for damaged elastic materials. This model depends on three small parameters, which are related to the cost of the damage, to the width of the damaged regions, and to the minimum elasticity constant attained in the damaged regions. As these parameters tend to zero, our models Gamma-converge to a model for brittle fracture, for fracture with a cohesive zone, or for perfect plasticity, depending on the asymptotic ratios of the three parameters.

PB - Walter de Gruyter UR - http://hdl.handle.net/1963/5069 U1 - 4883 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Gamma-convergence of energies for nematic elastomers in the small strain limit JF - Continuum. Mech. Therm. Y1 - 2011 A1 - Virginia Agostiniani A1 - Antonio DeSimone KW - Liquid crystals AB -We study two variational models recently proposed in the literature to describe the mechanical behaviour of nematic elastomers either in the fully nonlinear regime or in the framework of a geometrically linear theory. We show that, in the small strain limit, the energy functional of the first one I\\\"-converges to the relaxation of the second one, a functional for which an explicit representation formula is available.

PB - Springer VL - 23 UR - http://hdl.handle.net/1963/4141 U1 - 3882 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Generalised functions of bounded deformation JF - J. Eur. Math. Soc. (JEMS), to appear Y1 - 2011 A1 - Gianni Dal Maso KW - free discontinuity problems, special functions of bounded deformation, jump set, rec- tifiability, slicing, approximate differentiability AB -We introduce the space GBD of generalized functions of bounded deformation and study the structure properties of these functions: the rectifiability and the slicing properties of their jump sets, and the existence of their approximate symmetric gradients. We conclude by proving a compactness results for GBD, which leads to a compactness result for the space GSBD of generalized special functions of bounded deformation. The latter is connected to the existence of solutions to a weak formulation of some variational problems arising in fracture mechanics in the framework of linearized elasticity.

PB - SISSA UR - http://hdl.handle.net/1963/6374 U1 - 6309 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Generalized Ricci Curvature Bounds for Three Dimensional Contact Subriemannian manifolds Y1 - 2011 A1 - Andrei A. Agrachev A1 - Paul Lee PB - SISSA UR - http://hdl.handle.net/1963/6507 N1 - This is a revised extended version that contains new results. U1 - 6454 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - The geometry of Maximum Principle JF - Proceedings of the Steklov Institute of mathematics. vol. 273 (2011), page: 5-27 ; ISSN: 0081-5438 Y1 - 2011 A1 - Andrei A. Agrachev A1 - Revaz Gamkrelidze AB - An invariant formulation of the maximum principle in optimal control is presented, and some second-order invariants are discussed. UR - http://hdl.handle.net/1963/6456 U1 - 6401 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - THES T1 - Homology invariants of quadratic maps Y1 - 2011 A1 - Antonio Lerario AB - Given a real projective algebraic set X we could hope that the equations describing it can give some information on its topology, e.g. on the number of its connected components. Unfortunately in the general case this hope is too vague and there is no direct way to extract such information from the algebraic description of X: Even the problem to decide whether X is empty or not is far from an easy visualization and requires some complicated algebraic machinery. A fi rst step observation is that as long as we are interested only in the topology of X, we can replace, using some Veronese embedding, the original ambient space with a much bigger RPn and assume that X is cut by quadratic equations. The price for this is the increase of the number of equations de ning our set; the advantage is that quadratic polynomials are easier to handle and our hope becomes more concrete... PB - SISSA UR - http://hdl.handle.net/1963/6245 U1 - 6145 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Infinitely many positive solutions for a Schrödinger–Poisson system JF - Nonlinear Analysis: Theory, Methods & Applications Y1 - 2011 A1 - Pietro d’Avenia A1 - Alessio Pomponio A1 - Giusi Vaira KW - Non-autonomous Schrödinger–Poisson system KW - Perturbation method AB -We are interested in the existence of infinitely many positive solutions of the Schrödinger–Poisson system −Δu+u+V(|x|)ϕu=|u|p−1u,x∈R3,−Δϕ=V(|x|)u2,x∈R3, where V(|x|) is a positive bounded function, 1<p<5 and V(r

VL - 74 UR - http://www.sciencedirect.com/science/article/pii/S0362546X11003518 ER - TY - JOUR T1 - An Integro-Extremization Approach for Non Coercive and Evolution Hamilton-Jacobi Equations JF - Journal of Convex Analysis 18 (2011) 1141-1170 Y1 - 2011 A1 - Sandro Zagatti AB - We devote the \\\\textit{integro-extremization} method to the study of the Dirichlet problem for homogeneous Hamilton-Jacobi equations \\\\begin{displaymath} \\\\begin{cases} F(Du)=0 & \\\\quad \\\\textrm{in} \\\\quad\\\\O\\\\cr u(x)=\\\\varphi(x) & \\\\quad \\\\textrm{for} \\\\quad x\\\\in \\\\partial \\\\O, \\\\end{cases} \\\\end{displaymath} with a particular interest for non coercive hamiltonians $F$, and to the Cauchy-Dirichlet problem for the corresponding homogeneous time-dependent equations \\\\begin{displaymath} \\\\begin{cases} \\\\frac{\\\\partial u}{\\\\partial t}+ F(\\\\nabla u)=0 & \\\\quad \\\\textrm{in} \\\\quad ]0,T[\\\\times \\\\O\\\\cr u(0,x)=\\\\eta(x) & \\\\quad \\\\textrm{for} \\\\quad x\\\\in\\\\O \\\\cr u(t,x)=\\\\psi(x) & \\\\quad \\\\textrm{for} \\\\quad (t,x)\\\\in[0,T]\\\\times \\\\partial \\\\O. \\\\end{cases} \\\\end{displaymath} We prove existence and some qualitative results for viscosity and almost everywhere solutions, under suitably convexity conditions on the hamiltonian $F$, on the domain $\\\\O$ and on the boundary datum, without any growth assumptions on $F$. PB - Heldermann Verlag UR - http://hdl.handle.net/1963/5538 U1 - 5375 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Invariant manifolds for a singular ordinary differential equation JF - Journal of Differential Equations 250 (2011) 1788-1827 Y1 - 2011 A1 - Stefano Bianchini A1 - Laura Spinolo PB - Elsevier UR - http://hdl.handle.net/1963/2554 U1 - 1565 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Invariants, volumes and heat kernels in sub-Riemannian geometry Y1 - 2011 A1 - Davide Barilari KW - Sub-Riemannian geometry AB - Sub-Riemannian geometry can be seen as a generalization of Riemannian geometry under non-holonomic constraints. From the theoretical point of view, sub-Riemannian geometry is the geometry underlying the theory of hypoelliptic operators (see [32, 57, 70, 92] and references therein) and many problems of geometric measure theory (see for instance [18, 79]). In applications it appears in the study of many mechanical problems (robotics, cars with trailers, etc.) and recently in modern elds of research such as mathematical models of human behaviour, quantum control or motion of self-propulsed micro-organism (see for instance [15, 29, 34])\\r\\nVery recently, it appeared in the eld of cognitive neuroscience to model the\\r\\nfunctional architecture of the area V1 of the primary visual cortex, as proposed by Petitot in [87, 86], and then by Citti and Sarti in [51]. In this context, the sub-Riemannian heat equation has been used as basis to new applications in image reconstruction (see [35]). PB - SISSA UR - http://hdl.handle.net/1963/6124 U1 - 6005 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Large Time Existence for Thin Vibrating Plates JF - Communication in Partial Differential Equations 36 (2011) 2062-2102 Y1 - 2011 A1 - Helmut Abels A1 - Maria Giovanna Mora A1 - Stefan Müller AB - We construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence of strong solutions for large\\r\\ntimes under appropriate scaling of the initial values such that the limit system as h --> 0 is either the nonlinear von Karman plate equation or the linear fourth order Germain-Lagrange equation. In the case of the\\r\\nlinear Germain-Lagrange equation we even obtain a convergence rate of the three-dimensional solution to the solution of the two-dimensional linear plate equation. PB - Taylor & Francis UR - http://hdl.handle.net/1963/3755 U1 - 562 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The matching property of infinitesimal isometries on elliptic surfaces and elasticity on thin shells JF - Archive for Rational Mechanics and Analysis 200 (2011) 1023-1050 Y1 - 2011 A1 - Marta Lewicka A1 - Maria Giovanna Mora A1 - Mohammad Reza Pakzad AB - Using the notion of Γ-convergence, we discuss the limiting behavior of the three-dimensional nonlinear elastic energy for thin elliptic shells, as their thickness h converges to zero, under the assumption that the elastic energy of deformations scales like h β with 2 < β < 4. We establish that, for the given scaling regime, the limiting theory reduces to linear pure bending. Two major ingredients of the proofs are the density of smooth infinitesimal isometries in the space of W 2,2 first order infinitesimal isometries, and a result on matching smooth infinitesimal isometries with exact isometric immersions on smooth elliptic surfaces. PB - Springer UR - http://hdl.handle.net/1963/3392 U1 - 940 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Metastable equilibria of capillary drops on solid surfaces: a phase field approach JF - Continuum Mechanics and Thermodynamics Y1 - 2011 A1 - Livio Fedeli A1 - Turco, Alessandro A1 - Antonio DeSimone AB -We discuss a phase field model for the numerical simulation of metastable equilibria of capillary drops resting on rough solid surfaces and for the description of contact angle hysteresis phenomena in wetting. The model is able to reproduce observed transitions of drops on micropillars from Cassie–Baxter to Wenzel states. When supplemented with a dissipation potential which describes energy losses due to frictional forces resisting the motion of the contact line, the model can describe metastable states such as drops in equilibrium on vertical glass plates. The reliability of the model is assessed by a detailed comparison of its predictions with experimental data on the maximal size of water drops that can stick on vertical glass plates which have undergone different surface treatments.

VL - 23 UR - https://doi.org/10.1007/s00161-011-0189-6 ER - TY - JOUR T1 - A MODEL FOR CRACK PROPAGATION BASED ON VISCOUS APPROXIMATION JF - {MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES} Y1 - 2011 A1 - Giuliano Lazzaroni A1 - Rodica Toader KW - Brittle fracture KW - Crack propagation KW - energy derivative KW - energy release rate KW - free-discontinuity problems KW - Griffith's criterion KW - local minimizers KW - stress intensity factor} KW - vanishing viscosity KW - {Variational models AB -{In the setting of antiplane linearized elasticity, we show the existence of quasistatic evolutions of cracks in brittle materials by using a vanishing viscosity approach, thus taking into account local minimization. The main feature of our model is that the path followed by the crack need not be prescribed a priori: indeed, it is found as the limit (in the sense of Hausdorff convergence) of curves obtained by an incremental procedure. The result is based on a continuity property for the energy release rate in a suitable class of admissible cracks.}

PB - {WORLD SCIENTIFIC PUBL CO PTE LTD} CY - {5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE} VL - {21} ER - TY - CONF T1 - The Monge Problem in Geodesic Spaces T2 - Nonlinear Conservation Laws and Applications Y1 - 2011 A1 - Stefano Bianchini A1 - Fabio Cavalletti ED - Alberto Bressan ED - Chen, Gui-Qiang G. ED - Marta Lewicka ED - Wang, Dehua AB -We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish non branching geodesic space. We show that we can reduce the transport problem to 1-dimensional transport problems along geodesics. We introduce an assumption on the transport problem π which implies that the conditional probabilities of the first marginal on each geodesic are continuous. It is known that this regularity is sufficient for the construction of an optimal transport map.

JF - Nonlinear Conservation Laws and Applications PB - Springer US CY - Boston, MA SN - 978-1-4419-9554-4 ER - TY - JOUR T1 - Multiplicity of solutions for a mean field equation on compact surfaces JF - Boll. Unione Mat. Ital.(9) Y1 - 2011 A1 - Francesca De Marchis AB -We consider a scalar field equation on compact surfaces which has variational structure. When the surface is a torus and a physical parameter ρ belongs to $(8\pi, 4\pi^2 )$ we show under some extra assumptions that, as conjectured in [9], the functional admits at least three saddle points other than a local minimum.

VL - 4 ER - TY - JOUR T1 - New improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces JF - Geometric and Functional Analysis 21 (2011) 1196-1217 Y1 - 2011 A1 - Andrea Malchiodi A1 - David Ruiz AB - We consider a singular Liouville equation on a compact surface, arising from the study of Chern-Simons vortices in a self dual regime. Using new improved versions of the Moser-Trudinger inequalities (whose main feature is to be scaling invariant) and a variational scheme, we prove new existence results. PB - Springer UR - http://hdl.handle.net/1963/4099 U1 - 305 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Nonlinear resonance: a comparison between Landesman-Lazer and Ahmad-Lazer-Paul conditions JF - Advanced Nonlinear Studies Y1 - 2011 A1 - Alessandro Fonda A1 - Maurizio Garrione AB -We show that the Ahmad-Lazer-Paul condition for resonant problems is more general than the Landesman-Lazer one, discussing some relations with other existence conditions, as well. As a consequence, such a relation holds, for example, when considering resonant boundary value problems associated with linear elliptic operators, the p-Laplacian and, in the scalar case, with an asymmetric oscillator.

PB - Advanced Nonlinear Studies, Inc. VL - 11 ER - TY - RPRT T1 - Nonlinear thin-walled beams with a rectangular cross-section - Part II Y1 - 2011 A1 - Lorenzo Freddi A1 - Maria Giovanna Mora A1 - Roberto Paroni KW - Thin-walled cross-section beams AB - In this paper we report the second part of our results concerning the rigorous derivation of a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section.. PB - SISSA UR - http://hdl.handle.net/1963/4169 U1 - 3891 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Nonlinear wave and Schrödinger equations on compact Lie groups and homogeneous spaces JF - Duke Mathematical Journal Y1 - 2011 A1 - Massimiliano Berti A1 - Michela Procesi AB - We develop linear and nonlinear harmonic analysis on compact Lie groups and homogeneous spaces relevant for the theory of evolutionary Hamiltonian PDEs. A basic tool is the theory of the highest weight for irreducible representations of compact Lie groups. This theory provides an accurate description of the eigenvalues of the Laplace-Beltrami operator as well as the multiplication rules of its eigenfunctions. As an application, we prove the existence of Cantor families of small amplitude time-periodic solutions for wave and Schr¨odinger equations with differentiable nonlinearities. We apply an abstract Nash-Moser implicit function theorem to overcome the small divisors problem produced by the degenerate eigenvalues of the Laplace operator. We provide a new algebraic framework to prove the key tame estimates for the inverse linearized operators on Banach scales of Sobolev functions. VL - 159 IS - 3 ER - TY - JOUR T1 - A note on a superlinear indefinite Neumann problem with multiple positive solutions JF - Journal of Mathematical Analysis and Applications Y1 - 2011 A1 - Alberto Boscaggin KW - Indefinite weight KW - Nonlinear boundary value problems KW - positive solutions KW - Shooting method AB -We prove the existence of three positive solutions for the Neumann problem associated to u″+a(t)uγ+1=0, assuming that a(t) has two positive humps and ∫0Ta−(t)dt is large enough. Actually, the result holds true for a more general class of superlinear nonlinearities.

VL - 377 UR - http://www.sciencedirect.com/science/article/pii/S0022247X10008796 ER - TY - JOUR T1 - Numerical Strategies for Stroke Optimization of Axisymmetric Microswimmers JF - Mathematical Models and Methods in Applied Sciences 21 (2011) 361-387 Y1 - 2011 A1 - François Alouges A1 - Antonio DeSimone A1 - Luca Heltai KW - Optimal swimming AB - We propose a computational method to solve optimal swimming problems, based on the boundary integral formulation of the hydrodynamic interaction between swimmer and surrounding fluid and direct constrained minimization of the energy consumed by the swimmer. We apply our method to axisymmetric model examples. We consider a classical model swimmer (the three-sphere swimmer of Golestanian et al.) as well as a novel axisymmetric swimmer inspired by the observation of biological micro-organisms. PB - World Scientific UR - http://hdl.handle.net/1963/3657 U1 - 648 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Osservazioni sui teoremi di inversione globale JF - Rendiconti Lincei - Matematica e Applicazioni 22 (2011) 3-15 Y1 - 2011 A1 - Antonio Ambrosetti AB - Some global inversion theorems with applications to semilinear elliptic equation are discussed. PB - European Mathematical Society UR - http://hdl.handle.net/1963/4068 U1 - 334 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - A planar bi-Lipschitz extension Theorem Y1 - 2011 A1 - Sara Daneri A1 - Aldo Pratelli UR - http://arxiv.org/abs/1110.6124 ER - TY - JOUR T1 - Planar loops with prescribed curvature: existence, multiplicity and uniqueness results JF - Proceedings of the American Mathematical Society 139 (2011) 4445-4459 Y1 - 2011 A1 - Roberta Musina KW - Plane curves PB - American Mathematical Society UR - http://hdl.handle.net/1963/3842 U1 - 867 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A proof of Sudakov theorem with strictly convex norms JF - Mathematische Zeitschrift 268 (2011) 371-407 Y1 - 2011 A1 - Laura Caravenna AB - We establish a solution to the Monge problem in Rn, with an asymmetric, strictly convex norm cost function, when the initial measure is absolutely continuous. We focus on the strategy, based on disintegration of measures, initially proposed by Sudakov. As known, there is a gap to fill. The missing step is completed when the unit ball is strictly convex, but not necessarily differentiable nor uniformly convex. The key disintegration is achieved following a similar proof for a variational problem. PB - Springer UR - http://hdl.handle.net/1963/2967 U1 - 1733 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasiconvex envelopes of energies for nematic elastomers in the small strain regime and applications JF - Journal of the Mechanics and Physics of Solids 59 (2011) 787-803 Y1 - 2011 A1 - Pierluigi Cesana A1 - Antonio DeSimone AB - We provide some explicit formulas for the quasiconvex envelope of energy densities for nematic elastomers in the small strain regime and plane strain conditions. We then demonstrate their use as a powerful tool for the interpretation of mechanical experiments. UR - http://hdl.handle.net/1963/4065 U1 - 337 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a Young measures approach JF - ESAIM: COCV 17 (2011) 1-27 Y1 - 2011 A1 - Filippo Cagnetti A1 - Rodica Toader AB - A new approach to irreversible quasistatic fracture growth is given, by means of Young measures. The study concerns a cohesive zone model with prescribed crack path, when the material gives different responses to loading and unloading phases. In the particular situation of constant unloading response, the result contained in [6] is recovered. In this case, the convergence of the discrete time approximations is improved. PB - Cambridge University Press / EDP Sciences UR - http://hdl.handle.net/1963/2355 U1 - 1662 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic crack growth in finite elasticity with Lipschitz data JF - {ANNALI DI MATEMATICA PURA ED APPLICATA} Y1 - 2011 A1 - Giuliano Lazzaroni KW - Brittle fracture KW - Crack propagation KW - Energy minimization KW - Finite elasticity KW - free-discontinuity problems KW - Griffith's criterion KW - Non-interpenetration} KW - Polyconvexity KW - Quasistatic evolution KW - Rate-independent processes KW - {Variational models AB -{We extend the recent existence result of Dal Maso and Lazzaroni (Ann Inst H Poincare Anal Non Lineaire 27:257-290, 2010) for quasistatic evolutions of cracks in finite elasticity, allowing for boundary conditions and external forces with discontinuous first derivatives.}

PB - {SPRINGER HEIDELBERG} CY - {TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY} VL - {190} ER - TY - JOUR T1 - Quasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling JF - Calculus of Variations and Partial Differential Equations 40 (2011) 125-181 Y1 - 2011 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Francesco Solombrino KW - Cam-Clay plasticity AB -Cam-Clay nonassociative plasticity exhibits both hardening and softening behaviour, depending on the loading. For many initial data the classical formulation of the quasistatic evolution problem has no smooth solution. We propose here a notion of generalized solution, based on a viscoplastic approximation. To study the limit of the viscoplastic evolutions we rescale time, in such a way that the plastic strain is uniformly Lipschitz with respect to the rescaled time. The limit of these rescaled solutions, as the viscosity parameter tends to zero, is characterized through an energy-dissipation balance, that can be written in a natural way using the rescaled time. As shown in [4] and [6], the proposed solution may be discontinuous with respect to the original time. Our formulation allows to compute the amount of viscous dissipation occurring instantaneously at each discontinuity time.

PB - Springer UR - http://hdl.handle.net/1963/3670 U1 - 635 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic evolution of sessile drops and contact angle hysteresis JF - Arch. Rational Mech. Anal. 202 (2011) 295-348 Y1 - 2011 A1 - Giovanni Alberti A1 - Antonio DeSimone AB - We consider the classical model of capillarity coupled with a rate-independent dissipation mechanism due to frictional forces acting on the contact line, and prove the existence of quasistatic evolutions with prescribed initial configuration. We also discuss in detail some explicit solutions to show that the model does account for contact angle hysteresis, and to compare its predictions with experimental observations. PB - Springer UR - http://hdl.handle.net/1963/4912 U1 - 4693 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Resonance and Landesman-Lazer conditions for first order systems in R^2 JF - Le Matematiche Y1 - 2011 A1 - Maurizio Garrione AB -The first part of the paper surveys the concept of resonance for $T$-periodic nonlinear problems. In the second part, some new results about existence conditions for nonlinear planar systems are presented. In particular, the Landesman-Lazer conditions are generalized to systems in $\mathbbR^2$ where the nonlinearity interacts with two resonant Hamiltonians. Such results apply to second order equations, generalizing previous theorems by Fabry [4] (for the undamped case), and Frederickson-Lazer [9] (for the case with friction). The results have been obtained with A. Fonda, and have been published in [8].

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

VL - 74 UR - http://www.sciencedirect.com/science/article/pii/S0362546X11001817 ER - TY - JOUR T1 - SBV regularity for Hamilton-Jacobi equations in R^n JF - Arch. Rational Mech. Anal. 200 (2011) 1003-1021 Y1 - 2011 A1 - Stefano Bianchini A1 - Camillo De Lellis A1 - Roger Robyr AB -In this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$ \partial_t u + H(D_{x} u)=0 \qquad \textrm{in}\quad \Omega\subset \mathbb{R}\times \mathbb{R}^{n} . $$ In particular, under the assumption that the Hamiltonian $H\in C^2(\mathbb{R}^n)$ is uniformly convex, we prove that $D_{x}u$ and $\partial_t u$ belong to the class $SBV_{loc}(\Omega)$.

PB - Springer UR - http://hdl.handle.net/1963/4911 U1 - 4695 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Singular perturbation models in phase transitions for second order materials JF - Indiana Univ. Math. J. 60 (2011) 367-409 Y1 - 2011 A1 - Milena Chermisi A1 - Gianni Dal Maso A1 - Irene Fonseca A1 - Giovanni Leoni AB - A variational model proposed in the physics literature to describe the onset of pattern formation in two-component bilayer membranes and amphiphilic monolayers leads to the analysis of a Ginzburg-Landau type energy with a negative term depending on the first derivative of the phase function. Scaling arguments motivate the study of the family of second order singular perturbed energies Fe having a negative term depending on the first derivative of the phase function. Here, the asymptotic behavior of {Fe} is studied using G-convergence techniques. In particular, compactness results and an integral representation of the limit energy are obtained. PB - Indiana University UR - http://hdl.handle.net/1963/3858 U1 - 851 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the Space of Symmetric Operators with Multiple Ground States JF - Functional Analysis and its Applications, Volume 45, Issue 4, December 2011, Pages 241-251 Y1 - 2011 A1 - Andrei A. Agrachev KW - Multiple eigenvalue AB - We study homological structure of the filtrations of the spaces of self-adjoint operators by the multiplicity of the ground state. We consider only operators acting in a finite dimensional complex or real Hilbert space but infinite dimensional generalizations are easily guessed. PB - SISSA UR - http://hdl.handle.net/1963/7069 U1 - 6392 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry JF - Journal of Dynamical and Control Systems Y1 - 2011 A1 - Bernard Bonnard A1 - Grégoire Charlot A1 - Roberta Ghezzi A1 - Gabriel Janin AB -We study the tangential case in 2-dimensional almost-Riemannian geometry. We\\r\\nanalyse the connection with the Martinet case in sub-Riemannian geometry. We\\r\\ncompute estimations of the exponential map which allow us to describe the\\r\\nconjugate locus and the cut locus at a tangency point. We prove that this last\\r\\none generically accumulates at the tangency point as an asymmetric cusp whose branches are separated by the singular set.

PB - Springer VL - 17 UR - http://hdl.handle.net/1963/4914 U1 - 4692 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - RPRT T1 - Structure of level sets and Sard-type properties of Lipschitz maps Y1 - 2011 A1 - Giovanni Alberti A1 - Stefano Bianchini A1 - Gianluca Crippa PB - SISSA UR - http://hdl.handle.net/1963/4657 U1 - 4424 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Subharmonic solutions of planar Hamiltonian systems: a rotation number approach JF - Advanced Nonlinear Studies Y1 - 2011 A1 - Alberto Boscaggin PB - Advanced Nonlinear Studies, Inc. VL - 11 ER - TY - JOUR T1 - Subharmonic solutions of planar Hamiltonian systems via the Poincaré́-Birkhoff theorem JF - Le Matematiche Y1 - 2011 A1 - Alberto Boscaggin AB -We revisit some recent results obtained in [1] about the existence of subharmonic solutions for a class of (nonautonomous) planar Hamiltonian systems, and we compare them with the existing literature. New applications to undamped second order equations are discussed, as well.

VL - 66 ER - TY - JOUR T1 - Supercritical conformal metrics on surfaces with conical singularities JF - Int Math Res Notices (2011) 2011 (24): 5625-5643 Y1 - 2011 A1 - Mauro Bardelloni A1 - Francesca De Marchis A1 - Andrea Malchiodi AB -We study the problem of prescribing the Gaussian curvature on surfaces with conical singularities in supercritical regimes. Using a Morse-theoretical approach we prove a general existence theorem on surfaces with positive genus, with a generic multiplicity result.

PB - Oxford University Press UR - http://hdl.handle.net/1963/4095 U1 - 309 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Thin-walled beams with a cross-section of arbitrary geometry: derivation of linear theories starting from 3D nonlinear elasticity Y1 - 2011 A1 - Elisa Davoli AB -The subject of this paper is the rigorous derivation of lower dimensional models for a nonlinearly elastic thin-walled beam whose cross-section is given by a thin tubular neighbourhood of a smooth curve. Denoting by h and δ_h, respectively, the diameter and the thickness of the cross-section, we analyse the case where the scaling factor of the elastic energy is of order ε_h^2, with ε_h/δ_h^2 \rightarrow l \in [0, +\infty). Different linearized models are deduced according to the relative order of magnitude of δ_h with respect to h.

ER - TY - JOUR T1 - The time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity JF - Calculus of Variations and Partial Differential Equations 41 (2011) 241-259 Y1 - 2011 A1 - Helmut Abels A1 - Maria Giovanna Mora A1 - Stefan Müller AB - The asymptotic behaviour of the solutions of three-dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness $h$ of the plate tends to zero. Under appropriate scalings of the applied force and of the initial values in terms of $h$, it is shown that three-dimensional solutions of the nonlinear elastodynamic equation converge to solutions of the time-dependent von K\\\\\\\'arm\\\\\\\'an plate equation. PB - Springer UR - http://hdl.handle.net/1963/3835 U1 - 492 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Uniqueness and nondegeneracy of the ground state for a quasilinear Schrödinger equation with a small parameter JF - Nonlinear Analysis: Theory, Methods & Applications Y1 - 2011 A1 - Alessandro Selvitella KW - Bifurcation theory KW - Nonlinear Schrödinger equations KW - Stationary solutions AB -We study least energy solutions of a quasilinear Schrödinger equation with a small parameter. We prove that the ground state is nondegenerate and unique up to translations and phase shifts using bifurcation theory.

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

VL - 96 UR - http://www.sciencedirect.com/science/article/pii/S0021782411000511 ER - TY - THES T1 - Almost-Riemannian Geometry from a Control Theoretical Viewpoint Y1 - 2010 A1 - Roberta Ghezzi PB - SISSA UR - http://hdl.handle.net/1963/4705 U1 - 4482 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Concentration of solutions for some singularly perturbed mixed problems. Part I: existence results JF - Arch. Ration. Mech. Anal. 196 (2010) 907-950 Y1 - 2010 A1 - Jesus Garcia Azorero A1 - Andrea Malchiodi A1 - Luigi Montoro A1 - Ireneo Peral AB - In this paper we study the asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions. We prove that, under suitable geometric conditions on the boundary of the domain, there exist solutions which approach the intersection of the Neumann and the Dirichlet parts as the singular perturbation parameter tends to zero. UR - http://hdl.handle.net/1963/3406 U1 - 927 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Concentration of solutions for some singularly perturbed mixed problems: Asymptotics of minimal energy solutions JF - Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 37-56 Y1 - 2010 A1 - Jesus Garcia Azorero A1 - Andrea Malchiodi A1 - Luigi Montoro A1 - Ireneo Peral AB - In this paper we carry on the study of asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions, started in the first paper. Here we are mainly interested in the analysis of the location and shape of least energy solutions when the singular perturbation parameter tends to zero. We show that in many cases they coincide with the new solutions produced in. UR - http://hdl.handle.net/1963/3409 U1 - 926 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Continuity of optimal control costs and its application to weak KAM theory JF - Calculus of Variations and Partial Differential Equations. Volume 39, Issue 1, 2010, Pages 213-232 Y1 - 2010 A1 - Andrei A. Agrachev A1 - Paul Lee AB - We prove continuity of certain cost functions arising from optimal control of\\r\\naffine control systems. We give sharp sufficient conditions for this\\r\\ncontinuity. As an application, we prove a version of weak KAM theorem and\\r\\nconsider the Aubry-Mather problems corresponding to these systems. PB - SISSA UR - http://hdl.handle.net/1963/6459 N1 - 23 pages, 1 figures U1 - 6405 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - RPRT T1 - Convergence of equilibria of thin elastic rods under physical growth conditions for the energy density Y1 - 2010 A1 - Elisa Davoli A1 - Maria Giovanna Mora AB - The subject of this paper is the study of the asymptotic behaviour of the equilibrium configurations of a nonlinearly elastic thin rod, as the diameter of the cross-section tends to zero. Convergence results are established assuming physical growth conditions for the elastic energy density and suitable scalings of the applied loads, that correspond at the limit to different rod models: the constrained linear theory, the analogous of von Kármán plate theory for rods, and the linear theory. UR - http://hdl.handle.net/1963/4086 U1 - 317 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The disintegration of the Lebesgue measure on the faces of a convex function JF - J. Funct. Anal. 258 (2010) 3604-3661 Y1 - 2010 A1 - Laura Caravenna A1 - Sara Daneri AB -We consider the disintegration of the Lebesgue measure on the graph of a convex function f:\\\\Rn-> \\\\R w.r.t. the partition into its faces, which are convex sets and therefore have a well defined linear dimension, and we prove that each conditional measure is equivalent to the k-dimensional Hausdorff measure of the k-dimensional face on which it is concentrated. The remarkable fact is that a priori the directions of the faces are just Borel and no Lipschitz regularity is known. Notwithstanding that, we also prove that a Green-Gauss formula for these directions holds on special sets.

UR - http://hdl.handle.net/1963/3622 U1 - 682 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Dynamics control by a time-varying feedback JF - Journal of Dynamical and Control Systems. Volume 16, Issue 2, April 2010, Pages :149-162 Y1 - 2010 A1 - Andrei A. Agrachev A1 - Marco Caponigro KW - Discrete-time dynamics AB - We consider a smooth bracket generating control-affine system in R^d and show that any orientation preserving diffeomorphism of R^d can be approximated, in the very strong sense, by a diffeomorphism included in the flow generated by a time-varying feedback control which is polynomial with respect to the state variables and trigonometric-polynomial with respect to the time variable. PB - SISSA UR - http://hdl.handle.net/1963/6461 U1 - 6407 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Estimates on path functionals over Wasserstein Spaces JF - SIAM J. Math. Anal. 42 (2010) 1179-1217 Y1 - 2010 A1 - Stefano Bianchini A1 - Alessio Brancolini AB - In this paper we consider the class a functionals (introduced in [Brancolini, Buttazzo, and Santambrogio, J. Eur. Math. Soc. (JEMS), 8 (2006), pp. 415-434] $\\\\mathcal{G}_{r,p}$ defined on Lipschitz curves $\\\\gamma$ valued in the $p$-Wasserstein space. The problem considered is the following: given a measure $\\\\mu$, give conditions in order to assure the existence of a curve $\\\\gamma$ such that $\\\\gamma(0)=\\\\mu$, $\\\\gamma(1)=\\\\delta_{x_0}$, and $\\\\mathcal{G}_{r,p}(\\\\gamma)<+\\\\infty$. To this end, new estimates on $\\\\mathcal{G}_{r,p}(\\\\mu)$ are given, and a notion of dimension of a measure (called path dimension) is introduced: the path dimension specifies the values of the parameters $(r,p)$ for which the answer to the previous reachability problem is positive. Finally, we compare the path dimension with other known dimensions. UR - http://hdl.handle.net/1963/3583 U1 - 717 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the Euler-Lagrange equation for a variational problem : the general case II JF - Math. Z. 265 (2010) 889-923 Y1 - 2010 A1 - Stefano Bianchini A1 - Matteo Gloyer UR - http://hdl.handle.net/1963/2551 U1 - 1568 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Exact reconstruction of damaged color images using a total variation model JF - Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 1291-1331 Y1 - 2010 A1 - Irene Fonseca A1 - Giovanni Leoni A1 - Francesco Maggi A1 - Massimiliano Morini AB - In this paper the reconstruction of damaged piecewice constant color images is studied using a RGB total variation based model for colorization/inpainting. In particular, it is shown that when color is known in a uniformly distributed region, then reconstruction is possible with maximal fidelity. PB - Elsevier UR - http://hdl.handle.net/1963/4039 U1 - 363 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence of planar curves minimizing length and curvature JF - Proc. Steklov Inst. Math. 270 (2010) 43-56 Y1 - 2010 A1 - Ugo Boscain A1 - Grégoire Charlot A1 - Francesco Rossi AB - In this paper we consider the problem of reconstructing a curve that is partially hidden or corrupted by minimizing the functional $\\\\int \\\\sqrt{1+K_\\\\gamma^2} ds$, depending both on length and curvature $K$. We fix starting and ending points as well as initial and final directions.\\nFor this functional we discuss the problem of existence of minimizers on various functional spaces. We find non-existence of minimizers in cases in which initial and final directions are considered with orientation. In this case, minimizing sequences of trajectories can converge to curves with angles.\\nWe instead prove existence of minimizers for the \\\"time-reparameterized\\\" functional $$\\\\int \\\\| \\\\dot\\\\gamma(t) \\\\|\\\\sqrt{1+K_\\\\ga^2} dt$$ for all boundary conditions if initial and final directions are considered regardless to orientation. In this case, minimizers can present cusps (at most two) but not angles. PB - Springer UR - http://hdl.handle.net/1963/4107 U1 - 297 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Gene expression analysis of the emergence of epileptiform activity after focal injection of kainic acid into mouse hippocampus. JF - The European journal of neuroscience. 2010 Oct; 32(8):1364-79 Y1 - 2010 A1 - Dario Motti A1 - Caroline Le Duigou A1 - Nicole Chemaly A1 - Lucia Wittner A1 - Dejan Lazarevic A1 - Helena Krmac A1 - Troels Torben Marstrand A1 - Eivind Valen A1 - Remo Sanges A1 - Elia Stupka A1 - Albin Sandelin A1 - Enrico Cherubini A1 - Stefano Gustincich A1 - Richard Miles AB -We report gene profiling data on genomic processes underlying the progression towards recurrent seizures after injection of kainic acid (KA) into the mouse hippocampus. Focal injection enabled us to separate the effects of proepileptic stimuli initiated by KA injection. Both the injected and contralateral hippocampus participated in the status epilepticus. However, neuronal death induced by KA treatment was restricted to the injected hippocampus, although there was some contralateral axonal degeneration. We profiled gene expression changes in dorsal and ventral regions of both the injected and contralateral hippocampus. Changes were detected in the expression of 1526 transcripts in samples from three time-points: (i) during the KA-induced status epilepticus, (ii) at 2 weeks, before recurrent seizures emerged, and (iii) at 6 months after seizures emerged. Grouping genes with similar spatio-temporal changes revealed an early transcriptional response, strong immune, cell death and growth responses at 2 weeks and an activation of immune and extracellular matrix genes persisting at 6 months. Immunostaining for proteins coded by genes identified from array studies provided evidence for gliogenesis and suggested that the proteoglycan biglycan is synthesized by astrocytes and contributes to a glial scar. Gene changes at 6 months after KA injection were largely restricted to tissue from the injection site. This suggests that either recurrent seizures might depend on maintained processes including immune responses and changes in extracellular matrix proteins near the injection site or alternatively might result from processes, such as growth, distant from the injection site and terminated while seizures are maintained.

PB - Wiley UR - http://hdl.handle.net/1963/4480 U1 - 4244 U2 - Neuroscience U3 - Neurobiology U4 - -1 ER - TY - JOUR T1 - Generic multiplicity for a scalar field equation on compact surfaces JF - Journal of Functional Analysis Y1 - 2010 A1 - Francesca De Marchis KW - Generic multiplicity KW - Geometric PDE's KW - Morse inequalities KW - Scalar field equations AB -We prove generic multiplicity of solutions for a scalar field equation on compact surfaces via Morse inequalities. In particular our result improves significantly the multiplicity estimate which can be deduced from the degree-counting formula in Chen and Lin (2003) [12]. Related results are derived for the prescribed Q-curvature equation.

VL - 259 UR - http://www.sciencedirect.com/science/article/pii/S0022123610002697 ER - TY - JOUR T1 - A global compactness result for the p-Laplacian involving critical nonlinearities JF - Discrete & Continuous Dynamical Systems-A Y1 - 2010 A1 - Mercuri, Carlo A1 - Willem, Michel AB -We prove a representation theorem for Palais-Smale sequences involving the p-Laplacian and critical nonlinearities. Applications are given to a critical problem.

VL - 28 UR - http://www.aimsciences.org/journals/displayArticles.jsp?paperID=5097 ER - TY - JOUR T1 - Homogeneous binary trees as ground states of quantum critical Hamiltonians JF - Phys. Rev. A 81 (2010) 062335 Y1 - 2010 A1 - Pietro Silvi A1 - Vittorio Giovannetti A1 - Simone Montangero A1 - Matteo Rizzi A1 - J. Ignacio Cirac A1 - Rosario Fazio AB -

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

PB - American Physical Society UR - http://hdl.handle.net/1963/3909 U1 - 800 U2 - Physics U3 - Condensed Matter Theory ER - TY - JOUR T1 - Homogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems JF - New J. Phys. 12 (2010) 075018 Y1 - 2010 A1 - Matteo Rizzi A1 - Simone Montangero A1 - Pietro Silvi A1 - Vittorio Giovannetti A1 - Rosario Fazio AB -In this paper, we review the properties of homogeneous multiscale entanglement renormalization ansatz (MERA) to describe quantum critical systems.We discuss in more detail our results for one-dimensional (1D) systems (the Ising and Heisenberg models) and present new data for the 2D Ising model. Together with the results for the critical exponents, we provide a detailed description of the numerical algorithm and a discussion of new optimization\\nstrategies. The relation between the critical properties of the system and the tensor structure of the MERA is expressed using the formalism of quantum channels, which we review and extend.

PB - IOP Publishing UR - http://hdl.handle.net/1963/4067 U1 - 335 U2 - Physics U3 - Condensed Matter Theory ER - TY - JOUR T1 - Homogenization of fiber reinforced brittle material: the intermediate case JF - Adv. Calc. Var. 3 (2010) 345-370 Y1 - 2010 A1 - Gianni Dal Maso A1 - Caterina Ida Zeppieri AB - We derive a cohesive fracture model by homogenizing a periodic composite material whose microstructure is characterized by the presence of brittle inclusions in a reticulated unbreakable elastic structure. PB - Walter de Gruyter UR - http://hdl.handle.net/1963/3607 U1 - 694 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Invariant Lagrange submanifolds of dissipative systems JF - Russian Mathematical Surveys. Volume 65, Issue 5, 2010, Pages: 977-978 Y1 - 2010 A1 - Andrei A. Agrachev AB - We study solutions of modified Hamilton-Jacobi equations H(du/dq,q) + cu(q) =\\r\\n0, q \\\\in M, on a compact manifold M . PB - SISSA UR - http://hdl.handle.net/1963/6457 U1 - 6403 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - THES T1 - New approximation results for free discontinuity problems T2 - Università degli Studi di Trieste and SISSA Y1 - 2010 A1 - Flaviana Iurlano JF - Università degli Studi di Trieste and SISSA ER - TY - JOUR T1 - Nonlocal character of the reduced theory of thin films with higher order perturbations JF - Adv. Calc. Var. 3 (2010) 287-319 Y1 - 2010 A1 - Gianni Dal Maso A1 - Irene Fonseca A1 - Giovanni Leoni UR - http://hdl.handle.net/1963/3754 U1 - 563 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A normal form for generic 2-dimensional almost-Riemannian structures at a tangency point JF - arXiv preprint arXiv:1008.5036 Y1 - 2010 A1 - Ugo Boscain A1 - Grégoire Charlot A1 - Roberta Ghezzi ER - TY - RPRT T1 - On the number of positive solutions of some semilinear elliptic problems Y1 - 2010 A1 - Antonio Ambrosetti UR - http://hdl.handle.net/1963/4083 U1 - 320 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On optimality of c-cyclically monotone transference plans JF - Comptes Rendus Mathematique 348 (2010) 613-618 Y1 - 2010 A1 - Stefano Bianchini A1 - Laura Caravenna AB - Abstract. This note deals with the equivalence between the optimality of a transport plan for the Monge-Kantorovich problem and the condition of c-cyclical monotonicity, as an outcome of the construction in [7]. We emphasize the measurability assumption on the hidden structure of linear preorder, applied also to extremality and uniqueness problems. Resume. Dans la presente note nous decrivons brievement la construction introduite dans [7] a propos de l\\\'equivalence entre l\\\'optimalite d\\\'un plan de transport pour le probleme de Monge-Kantorovich et la condition de monotonie c-cyclique ainsi que d\\\'autres sujets que cela nous amene a aborder. Nous souhaitons mettre en evidence l\\\'hypothese de mesurabilite sur la structure sous-jacente de pre-ordre lineaire. PB - Elsevier UR - http://hdl.handle.net/1963/4023 U1 - 379 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Optimally swimming Stokesian Robots Y1 - 2010 A1 - François Alouges A1 - Antonio DeSimone A1 - Luca Heltai A1 - Aline Lefebvre A1 - Benoit Merlet AB - We study self propelled stokesian robots composed of assemblies of balls, in dimen-\\nsions 2 and 3, and prove that they are able to control their position and orientation. This is a result of controllability, and its proof relies on applying Chow\\\'s theorem in an analytic framework, similarly to what has been done in [3] for an axisymmetric system swimming along the axis of symmetry. However, we simplify drastically\\nthe analyticity result given in [3] and apply it to a situation where more complex swimmers move either in a plane or in three-dimensional space, hence experiencing also rotations. We then focus our attention on energetically optimal strokes, which we are able to compute numerically. Some examples of computed optimal strokes are discussed in detail. UR - http://hdl.handle.net/1963/3929 U1 - 472 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CONF T1 - A Phase Field Approach to Wetting and Contact Angle Hysteresis Phenomena T2 - IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials Y1 - 2010 A1 - Antonio DeSimone A1 - Livio Fedeli A1 - Turco, Alessandro ED - Hackl, Klaus AB -We discuss a phase field model for the numerical simulation of contact angle hysteresis phenomena in wetting. The performance of the model is assessed by comparing its predictions with experimental data on the critical size of drops that can stick on a vertical glass plate.

JF - IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials PB - Springer Netherlands CY - Dordrecht SN - 978-90-481-9195-6 ER - TY - JOUR T1 - Poles of Integrale Tritronquee and Anharmonic Oscillators. Asymptotic localization from WKB analysis JF - Nonlinearity. vol. 23, (2010), page 2501-2507 Y1 - 2010 A1 - Davide Masoero AB -Poles of integrale tritronquee are in bijection with cubic oscillators that admit the simultaneous solutions of two quantization conditions. We show that the poles lie near the solutions of a pair of Bohr-Sommerfeld quantization conditions (the Bohr-Sommerfeld-Boutroux system): the distance between a pole and the corresponding solution of the Bohr-Sommerfeld-Boutroux system vanishes asymptotically.

UR - http://hdl.handle.net/1963/3841 U1 - 486 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Positive solutions for some non-autonomous Schrödinger–Poisson systems JF - Journal of Differential Equations Y1 - 2010 A1 - Giovanna Cerami A1 - Giusi Vaira PB - Academic Press VL - 248 ER - TY - JOUR T1 - Projective Reeds-Shepp car on $S^2$ with quadratic cost JF - ESAIM COCV 16 (2010) 275-297 Y1 - 2010 A1 - Ugo Boscain A1 - Francesco Rossi AB - Fix two points $x,\\\\bar{x}\\\\in S^2$ and two directions (without orientation) $\\\\eta,\\\\bar\\\\eta$ of the velocities in these points. In this paper we are interested to the problem of minimizing the cost $$ J[\\\\gamma]=\\\\int_0^T g_{\\\\gamma(t)}(\\\\dot\\\\gamma(t),\\\\dot\\\\gamma(t))+\\nK^2_{\\\\gamma(t)}g_{\\\\gamma(t)}(\\\\dot\\\\gamma(t),\\\\dot\\\\gamma(t)) ~dt$$ along all smooth curves starting from $x$ with direction $\\\\eta$ and ending in $\\\\bar{x}$ with direction $\\\\bar\\\\eta$. Here $g$ is the standard Riemannian metric on $S^2$ and $K_\\\\gamma$ is the corresponding geodesic curvature.\\nThe interest of this problem comes from mechanics and geometry of vision. It can be formulated as a sub-Riemannian problem on the lens space L(4,1).\\nWe compute the global solution for this problem: an interesting feature is that some optimal geodesics present cusps. The cut locus is a stratification with non trivial topology. UR - http://hdl.handle.net/1963/2668 U1 - 1429 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic crack growth in elasto-plastic materials: the two-dimensional case JF - Arch. Ration. Mech. Anal. 196 (2010) 867-906 Y1 - 2010 A1 - Gianni Dal Maso A1 - Rodica Toader AB - We study a variational model for the quasistatic evolution of elasto-plastic materials with cracks in the case of planar small strain associative elasto-plasticity. UR - http://hdl.handle.net/1963/2964 U1 - 1736 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic crack growth in finite elasticity with non-interpenetration JF - Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 257-290 Y1 - 2010 A1 - Gianni Dal Maso A1 - Giuliano Lazzaroni AB -We present a variational model to study the quasistatic growth of brittle cracks in hyperelastic materials, in the framework of finite elasticity, taking\\ninto account the non-interpenetration condition.

UR - http://hdl.handle.net/1963/3397 U1 - 935 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic evolution for Cam-Clay plasticity: the spatially homogeneous case JF - Netw. Heterog. Media 5 (2010) 97-132 Y1 - 2010 A1 - Gianni Dal Maso A1 - Francesco Solombrino KW - Cam-Clay plasticity AB -We study the spatially uniform case of the problem of quasistatic evolution in small strain nonassociative elastoplasticity (Cam-Clay model). Through the introdution of a viscous approximation, the problem reduces to determine the limit behavior of the solutions of a singularly perturbed system of ODE\\\'s in a finite dimensional Banach space. Depending on the sign of two explicit scalar indicators, we see that the limit dynamics presents, under quite generic assumptions, the alternation of three possible regimes: the elastic regime, when the limit equation is just the equation of linearized elasticity, the slow dynamics, when the strain evolves smoothly on the yield surface and plastic flow is produced, and the fast dynamics, which may happen only in the softening regime, where\\nviscous solutions exhibit a jump across a heteroclinic orbit of an auxiliary system.

UR - http://hdl.handle.net/1963/3671 U1 - 634 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic evolution for plasticity with softening: The spatially homogeneous case JF - Discrete & Continuous Dynamical Systems - A Y1 - 2010 A1 - Francesco Solombrino KW - plasticity with softening KW - rate independent processes AB -The spatially uniform case of the problem of quasistatic evolution in small strain associative elastoplasticity with softening is studied. Through the introdution of a viscous approximation, the problem reduces to determine the limit behaviour of the solutions of a singularly perturbed system of ODE's in a finite dimensional Banach space. We see that the limit dynamics presents, for a generic choice of the initial data, the alternation of three possible regimes (elastic regime, slow dynamics, fast dynamics), which is determined by the sign of two scalar indicators, whose explicit expression is given.

VL - 27 UR - http://aimsciences.org//article/id/4c2301d8-f553-493e-b672-b4f76a3ede2f ER - TY - RPRT T1 - The role of membrane viscosity in the dynamics of fluid membranes Y1 - 2010 A1 - Marino Arroyo A1 - Antonio DeSimone A1 - Luca Heltai AB - Fluid membranes made out of lipid bilayers are the fundamental separation structure in eukaryotic cells. Many physiological processes rely on dramatic shape and topological changes (e.g. fusion, fission) of fluid membrane systems. Fluidity is key to the versatility and constant reorganization of lipid bilayers. Here, we study the role of the membrane intrinsic viscosity, arising from the friction of the lipid molecules as they rearrange to accommodate shape changes, in the dynamics of morphological changes of fluid vesicles. In particular, we analyze the competition between the membrane viscosity and the viscosity of the bulk fluid surrounding the vesicle as the dominant dissipative mechanism. We consider the relaxation dynamics of fluid vesicles put in an out-of-equilibrium state, but conclusions can be drawn regarding the kinetics or power consumption in regulated shape changes in the cell. On the basis of numerical calculations, we find that the dynamics arising from the membrane viscosity are qualitatively different from the dynamics arising from the bulk viscosity. When these two dissipation mechanisms are put in competition, we find that for small vesicles the membrane dissipation dominates, with a relaxation time that scales as the size of the vesicle to the power 2. For large vesicles, the bulk dissipation dominates, and the exponent in the relaxation time vs. size relation is 3. UR - http://hdl.handle.net/1963/3930 U1 - 471 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Semiclassical evolution of two rotating solitons for the Nonlinear Schrödinger Equation with electric potential JF - Adv. Differential Equations Y1 - 2010 A1 - Alessandro Selvitella PB - Khayyam Publishing, Inc. VL - 15 UR - https://projecteuclid.org:443/euclid.ade/1355854752 ER - TY - RPRT T1 - Sharp nonexistence results for a linear elliptic inequality involving Hardy and Leray potentials Y1 - 2010 A1 - Mouhamed Moustapha Fall A1 - Roberta Musina AB - In this paper we deal with nonnegative distributional supersolutions for a class of linear\\nelliptic equations involving inverse-square potentials and logarithmic weights. We prove sharp nonexistence results. UR - http://hdl.handle.net/1963/3869 U1 - 840 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Shell theories arising as low energy Gamma-limit of 3d nonlinear elasticity JF - Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. IX (2010) 253-295 Y1 - 2010 A1 - Marta Lewicka A1 - Maria Giovanna Mora A1 - Mohammad Reza Pakzad AB - We discuss the limiting behavior (using the notion of gamma-limit) of the 3d nonlinear elasticity for thin shells around an arbitrary smooth 2d surface. In particular, under the assumption that the elastic energy of deformations scales like h4, h being the thickness of a shell, we derive a limiting theory which is a generalization of the von Karman theory for plates. UR - http://hdl.handle.net/1963/2601 U1 - 1521 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Stable determination of an immersed body in a stationary Stokes fluid JF - Inverse Problems Y1 - 2010 A1 - Andrea Ballerini AB -We consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the Stokes equations, from a single measurement of force and velocity on a portion of the boundary. We obtain an estimate of the stability of log–log type.

PB - IOP Publishing VL - 26 UR - https://doi.org/10.1088%2F0266-5611%2F26%2F12%2F125015 ER - TY - JOUR T1 - A three-dimensional model for the dynamics and hydrodynamics of rowing boats JF - Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology Y1 - 2010 A1 - L. Formaggia A1 - Andrea Mola A1 - N Parolini A1 - M Pischiutta AB -This paper proposes a new model describing the dynamics of a rowing boat for general three-dimensional motions. The complex interaction between the different components of the rowers–-oars–-boat system is analysed and reduced to a set of ordinary differential equations governing the rigid motion along the six degrees of freedom. To treat the unstable nature of the physical problem, a rather simple (but effective) control model is included, which mimics the main active control techniques adopted by the rowers during their action.

VL - 224 UR - https://doi.org/10.1243/17543371jset46 ER - TY - JOUR T1 - Two-dimensional almost-Riemannian structures with tangency points JF - Ann. Inst. H. Poincare Anal. Non Lineaire Y1 - 2010 A1 - Andrei A. Agrachev A1 - Ugo Boscain A1 - Grégoire Charlot A1 - Roberta Ghezzi A1 - Mario Sigalotti AB -Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We study the relation between the topological invariants of an almost-Riemannian structure on a compact oriented surface and the rank-two vector bundle over the surface which defines the structure. We analyse the generic case including the presence of tangency points, i.e. points where two generators of the distribution and their Lie bracket are linearly dependent. The main result of the paper provides a classification of oriented almost-Riemannian structures on compact oriented surfaces in terms of the Euler number of the vector bundle corresponding to the structure. Moreover, we present a Gauss-Bonnet formula for almost-Riemannian structures with tangency points.

PB - Elsevier VL - 27 UR - http://hdl.handle.net/1963/3870 U1 - 839 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Well-posed infinite horizon variational problems on a compact manifold JF - Proceedings of the Steklov Institute of Mathematics. Volume 268, Issue 1, 2010, Pages 17-31 Y1 - 2010 A1 - Andrei A. Agrachev AB - We give an effective sufficient condition for a variational problem with infinite horizon on a compact Riemannian manifold M to admit a smooth optimal synthesis, i. e., a smooth dynamical system on M whose positive semi-trajectories are solutions to the problem. To realize the synthesis, we construct an invariant Lagrangian submanifold (well-projected to M) of the flow of extremals in the cotangent bundle T*M. The construction uses the curvature of the flow in the cotangent bundle and some ideas of hyperbolic dynamics PB - SISSA UR - http://hdl.handle.net/1963/6458 U1 - 6404 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - CHAP T1 - Biological Fluid Dynamics, Non-linear Partial Differential Equations T2 - Encyclopedia of Complexity and Systems Science / Robert A. Meyers (ed.). - Springer, 2009, 548-554 Y1 - 2009 A1 - Antonio DeSimone A1 - François Alouges A1 - Aline Lefebvre JF - Encyclopedia of Complexity and Systems Science / Robert A. Meyers (ed.). - Springer, 2009, 548-554 UR - http://hdl.handle.net/1963/2630 U1 - 1493 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The boundary Riemann solver coming from the real vanishing viscosity approximation JF - Arch. Ration. Mech. Anal. 191 (2009) 1-96 Y1 - 2009 A1 - Stefano Bianchini A1 - Laura Spinolo AB - We study the limit of the hyperbolic-parabolic approximation $$ \\\\begin{array}{lll} v_t + \\\\tilde{A} ( v, \\\\, \\\\varepsilon v_x ) v_x = \\\\varepsilon \\\\tilde{B}(v ) v_{xx} \\\\qquad v \\\\in R^N\\\\\\\\ \\\\tilde \\\\beta (v (t, \\\\, 0)) = \\\\bar g \\\\\\\\ v (0, \\\\, x) = \\\\bar v_0. \\\\\\\\ \\\\end{array} \\\\right. $$\\nThe function $\\\\tilde \\\\beta$ is defined in such a way to guarantee that the initial boundary value problem is well posed even if $\\\\tilde \\\\beta$ is not invertible.\\nThe data $\\\\bar g$ and $\\\\bar v_0$ are constant. When $\\\\tilde B$ is invertible, the previous problem takes the simpler form $$ \\\\left\\\\{ \\\\begin{array}{lll} v_t + \\\\tilde{A} \\\\big( v, \\\\, \\\\varepsilon v_x \\\\big) v_x = \\\\varepsilon \\\\tilde{B}(v ) v_{xx} \\\\qquad v \\\\in \\\\mathbb{R}^N\\\\\\\\ v (t, \\\\, 0) \\\\equiv \\\\bar v_b \\\\\\\\ v (0, \\\\, x) \\\\equiv \\\\bar{v}_0. \\\\\\\\ \\\\end{array} \\\\right. $$\\nAgain, the data $\\\\bar v_b$ and $\\\\bar v_0$ are constant. The conservative case is included in the previous formulations. It is assumed convergence of the v, smallness of the total variation and other technical hypotheses and it is provided a complete characterization of the limit. The most interesting points are the following two. First, the boundary characteristic case is considered, i.e. one eigenvalue of $\\\\tilde A$ can be 0.\\n Second, as pointed out before we take into account the possibility that $\\\\tilde B$ is not invertible. To deal with this case, we take as hypotheses conditions that were introduced by Kawashima and Shizuta relying on physically meaningful examples. We also introduce a new condition of block linear degeneracy. We prove that, if it is not satisfied, then pathological behaviours may occur. UR - http://hdl.handle.net/1963/1831 U1 - 2385 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Bubbles with prescribed mean curvature: the variational approach Y1 - 2009 A1 - Paolo Caldiroli A1 - Roberta Musina UR - http://hdl.handle.net/1963/3659 N1 - H-systems, prescribed mean curvature equation, blowup U1 - 646 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A connection between viscous profiles and singular ODEs JF - Rend. Istit. Mat. Univ. Trieste 41 (2009) 35-41 Y1 - 2009 A1 - Stefano Bianchini A1 - Laura Spinolo UR - http://hdl.handle.net/1963/2555 U1 - 1564 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Controllability of the discrete-spectrum Schrodinger equation driven by an external field JF - Ann. Inst. H. Poincare Anal. Non Lineaire 26 (2009) 329-349 Y1 - 2009 A1 - Thomas Chambrion A1 - Paolo Mason A1 - Mario Sigalotti A1 - Ugo Boscain AB - We prove approximate controllability of the bilinear Schrodinger equation in the case in which the uncontrolled Hamiltonian has discrete nonresonant\\nspectrum. The results that are obtained apply both to bounded or unbounded domains and to the case in which the control potential is bounded or unbounded. The method relies on finite-dimensional techniques applied to the\\nGalerkin approximations and permits, in addition, to get some controllability properties for the density matrix. Two examples are presented: the harmonic oscillator and the 3D well of potential controlled by suitable potentials. UR - http://hdl.handle.net/1963/2547 U1 - 1572 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Controllability on the group of diffeomorphisms JF - Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009) 2503-2509 Y1 - 2009 A1 - Andrei A. Agrachev A1 - Marco Caponigro AB - Given a compact manifold M, we prove that any bracket generating family of vector fields on M, which is invariant under multiplication by smooth functions, generates the connected component of identity of the group of diffeomorphisms of M. UR - http://hdl.handle.net/1963/3396 U1 - 936 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the convergence of viscous approximations after shock interactions JF - Discrete Contin. Dyn. Syst. 23 (2009) 29-48 Y1 - 2009 A1 - Alberto Bressan A1 - Carlotta Donadello AB - We consider a piecewise smooth solution to a scalar conservation law, with possibly interacting shocks. We show that, after the interactions have taken place, vanishing viscosity approximations can still be represented by a regular expansion on smooth regions and by a singular perturbation expansion near the shocks, in terms of powers of the viscosity coefficient. PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/3412 U1 - 923 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Differential geometry of curves in Lagrange Grassmannians with given Young diagram JF - Differential Geom. Appl. 27 (2009) 723-742 Y1 - 2009 A1 - Igor Zelenko A1 - Li Chengbo AB - Curves in Lagrange Grassmannians appear naturally in the intrinsic study of geometric structures on manifolds. By a smooth geometric structure on a manifold we mean any submanifold of its tangent bundle, transversal to the fibers. One can consider the time-optimal problem naturally associate with a geometric structure. The Pontryagin extremals of this optimal problem are integral curves of certain Hamiltonian system in the cotangent bundle. The dynamics of the fibers of the cotangent bundle w.r.t. this system along an extremal is described by certain curve in a Lagrange Grassmannian, called Jacobi curve of the extremal. Any symplectic invariant of the Jacobi curves produces the invariant of the original geometric structure. The basic characteristic of a curve in a Lagrange Grassmannian is its Young diagram. The number of boxes in its kth column is equal to the rank of the kth derivative of the curve (which is an appropriately defined linear mapping) at a generic point. We will describe the construction of the complete system of symplectic invariants for parameterized curves in a Lagrange Grassmannian with given Young diagram. It allows to develop in a unified way local differential geometry of very wide classes of geometric structures on manifolds, including both classical geometric structures such as Riemannian and Finslerian structures and less classical ones such as sub-Riemannian and sub-Finslerian structures, defined on nonholonomic distributions. PB - Elsevier UR - http://hdl.handle.net/1963/3819 U1 - 508 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Discrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers JF - Netw. Heterog. Media 4 (2009) 667-708 Y1 - 2009 A1 - Marco Cicalese A1 - Antonio DeSimone A1 - Caterina Ida Zeppieri AB - In the framework of linear elasticity, we study the limit of a class of discrete free energies modeling strain-alignment-coupled systems by a rigorous coarse-graining procedure, as the number of molecules diverges. We focus on three paradigmatic examples: magnetostrictive solids, ferroelectric crystals and nematic elastomers, obtaining in the limit three continuum models consistent with those commonly employed in the current literature. We also derive the correspondent macroscopic energies in the presence of displacement boundary conditions and of various kinds of applied external fields. PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/3788 U1 - 538 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - The Disintegration Theorem and Applications to Optimal Mass Transportation Y1 - 2009 A1 - Laura Caravenna PB - SISSA UR - http://hdl.handle.net/1963/5900 U1 - 5750 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Existence of extremals for the Maz\\\'ya and for the Caffarelli-Kohn-Nirenberg inequalities JF - Nonlinear Anal. 70 (2009) 3002-3007 Y1 - 2009 A1 - Roberta Musina AB - This paper deals with some Sobolev-type inequalities with weights that were proved by Maz\\\'ya in 1980 and by Caffarelli-Kohn-Nirenberg in 1984. UR - http://hdl.handle.net/1963/2739 U1 - 1961 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - An existence result for the Monge problem in R^n with norm cost Y1 - 2009 A1 - Laura Caravenna UR - http://hdl.handle.net/1963/3647 U1 - 657 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the extremality, uniqueness and optimality of transference plans JF - Bull. Inst. Math. Acad. Sin. (N.S.) 4 (2009) 353-458 Y1 - 2009 A1 - Stefano Bianchini A1 - Laura Caravenna AB - We consider the following standard problems appearing in optimal mass transportation theory: when a transference plan is extremal; when a transference plan is the unique transference plan concentrated on a set A,; when a transference plan is optimal. UR - http://hdl.handle.net/1963/3692 U1 - 613 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Foliations of small tubes in Riemannian manifolds by capillary minimal discs JF - Nonlinear Analysis: Theory, Methods & Applications Y1 - 2009 A1 - Fall, Mouhamed Moustapha A1 - Mercuri, Carlo AB -Letting be an embedded curve in a Riemannian manifold , we prove the existence of minimal disc-type surfaces centered at inside the surface of revolution of around , having small radius, and intersecting it with constant angles. In particular we obtain that small tubular neighborhoods can be foliated by minimal discs.

PB - Elsevier VL - 70 UR - https://doi.org/10.1016/j.na.2008.10.024 ER - TY - JOUR T1 - Hardy-Sobolev-Maz\\\'ja inequalities: symmetry and breaking symmetry of extremal functions JF - Commun. Contemp. Math. 11 (2009) 993-1007 Y1 - 2009 A1 - Marita Gazzini A1 - Roberta Musina UR - http://hdl.handle.net/1963/2569 U1 - 1551 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A higher order model for image restoration: the one dimensional case JF - SIAM J. Math. Anal. 40 (2009) 2351-2391 Y1 - 2009 A1 - Gianni Dal Maso A1 - Irene Fonseca A1 - Giovanni Leoni A1 - Massimiliano Morini AB - The higher order total variation-based model for image restoration proposed by Chan, Marquina, and Mulet in [6] is analyzed in one dimension. A suitable functional framework in which the minimization problem is well posed is being proposed and it is proved analytically that the\\nhigher order regularizing term prevents the occurrence of the staircase effect. The generalized version of the model considered here includes, as particular cases, some curvature dependent functionals. UR - http://hdl.handle.net/1963/3174 U1 - 1127 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Homogenization of fiber reinforced brittle materials: the extremal cases JF - SIAM J. Math. Anal. 41 (2009) 1874-1889 Y1 - 2009 A1 - Marco Barchiesi A1 - Gianni Dal Maso AB - We analyze the behavior of a fragile material reinforced by a reticulated elastic unbreakable structure in the case of antiplane shear. The microscopic geometry of this material is described by means of two small parameters: the period $\\\\varepsilon$ of the grid and the ratio $\\\\delta$ between the thickness of the fibers and the period $\\\\varepsilon$. We show that the asymptotic behavior as $\\\\varepsilon\\\\to0^+$ and $\\\\delta\\\\to0^+$ depends dramatically on the relative size of these parameters. Indeed, in the two cases considered, i.e., $\\\\varepsilon\\\\ll\\\\delta$ and $\\\\varepsilon\\\\gg\\\\delta$, we obtain two different limit models: a perfectly elastic model and an elastic model with macroscopic cracks, respectively. PB - SIAM UR - http://hdl.handle.net/1963/2705 U1 - 1396 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups JF - J. Funct. Anal. 256 (2009) 2621-2655 Y1 - 2009 A1 - Andrei A. Agrachev A1 - Ugo Boscain A1 - Jean-Paul Gauthier A1 - Francesco Rossi AB - We present an invariant definition of the hypoelliptic Laplacian on sub-Riemannian structures with constant growth vector, using the Popp\\\'s volume form introduced by Montgomery. This definition generalizes the one of the Laplace-Beltrami operator in Riemannian geometry. In the case of left-invariant problems on unimodular Lie groups we prove that it coincides with the usual sum of squares.\\nWe then extend a method (first used by Hulanicki on the Heisenberg group) to compute explicitly the kernel of the hypoelliptic heat equation on any unimodular Lie group of type I. The main tool is the noncommutative Fourier transform. We then study some relevant cases: SU(2), SO(3), SL(2) (with the metrics inherited by the Killing form), and the group SE(2) of rototranslations of the plane.\\nOur study is motivated by some recent results about the cut and conjugate loci on these sub-Riemannian manifolds. The perspective is to understand how singularities of the sub-Riemannian distance reflect on the kernel of the corresponding hypoelliptic heat equation. UR - http://hdl.handle.net/1963/2669 U1 - 1428 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Jacobi Equations and Comparison Theorems for Corank 1 Sub-Riemannian structures with symmetries Y1 - 2009 A1 - Li Chengbo A1 - Igor Zelenko AB - The Jacobi curve of an extremal of optimal control problem is a curve in a Lagrangian Grassmannian defined up to a symplectic transformation and containing all information about the solutions of the Jacobi equations along this extremal. In our previous works we constructed the canonical\\nbundle of moving frames and the complete system of symplectic invariants, called curvature maps, for\\nparametrized curves in Lagrange Grassmannians satisfying very general assumptions. The structural\\nequation for a canonical moving frame of the Jacobi curve of an extremal can be interpreted as the\\nnormal form for the Jacobi equation along this extremal and the curvature maps can be seen as the\\n\\\"coefficients\\\"of this normal form. In the case of a Riemannian metric there is only one curvature map and it is naturally related to the Riemannian sectional curvature. In the present paper we study the curvature maps for a sub-Riemannian structure on a corank 1 distribution having an additional transversal infinitesimal symmetry. After the factorization by the integral foliation of this symmetry, such sub-Riemannian structure can be reduced to a Riemannian manifold equipped with a closed 2-form(a magnetic field). We obtain explicit expressions for the curvature maps of the original sub-Riemannian structure in terms of the curvature tensor of this Riemannian manifold and the magnetic field. We also estimate the number of conjugate points along the sub-Riemannian extremals in terms of the bounds for the curvature tensor of this Riemannian manifold and the magnetic field in the case of an uniform magnetic field. The language developed for the calculation of the curvature maps can be applied to more general sub-Riemannian structures with symmetries, including sub-Riemmannian structures appearing naturally in Yang-Mills fields. UR - http://hdl.handle.net/1963/3736 U1 - 581 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Minimal disc-type surfaces embedded in a perturbed cylinder JF - Differential and Integral Equations Y1 - 2009 A1 - Fall, Mouhamed Moustapha A1 - Mercuri, Carlo AB -In the present note we deal with small perturbations of an infinite cylinder in the 3D euclidian space. We find minimal disc-type surfaces embedded in the cylinder and intersecting its boundary perpendicularly. The existence and localization of those minimal discs is a consequence of a non-degeneracy condition for the critical points of a functional related to the oscillations of the cylinder from the flat configuration.

PB - Khayyam Publishing, Inc. VL - 22 UR - https://projecteuclid.org/euclid.die/1356019407 ER - TY - JOUR T1 - A nonlinear theory for shells with slowly varying thickness JF - C. R. Math. 347 (2009) 211-216 Y1 - 2009 A1 - Marta Lewicka A1 - Maria Giovanna Mora A1 - Mohammad Reza Pakzad AB - We study the Γ-limit of 3d nonlinear elasticity for shells of small, variable thickness, around an arbitrary smooth 2d surface. UR - http://hdl.handle.net/1963/2632 U1 - 1491 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A note on the paper \\\"Optimizing improved Hardy inequalities\\\" by S. Filippas and A. Tertikas JF - J. Funct. Anal. 256 (2009) 2741-2745 Y1 - 2009 A1 - Roberta Musina UR - http://hdl.handle.net/1963/2698 U1 - 1402 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Optimal transportation under nonholonomic constraints JF - Trans. Amer. Math. Soc. 361 (2009) 6019-6047 Y1 - 2009 A1 - Andrei A. Agrachev A1 - Paul Lee AB - We study the Monge\\\'s optimal transportation problem where the cost is given by optimal control cost. We prove the existence and uniqueness of optimal map under certain regularity conditions on the Lagrangian, absolute continuity of the measures and most importantly the absent of sharp abnormal minimizers. In particular, this result is applicable in the case of subriemannian manifolds with a 2-generating distribution and cost given by d2, where d is the subriemannian distance. Also, we discuss some properties of the optimal plan when abnormal minimizers are present. Finally, we consider some examples of displacement interpolation in the case of Grushin plane. UR - http://hdl.handle.net/1963/2176 U1 - 2068 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic evolution for Cam-Clay plasticity: examples of spatially homogeneous solutions JF - Math. Models Methods Appl. Sci. 19 (2009) 1643-1711 Y1 - 2009 A1 - Gianni Dal Maso A1 - Antonio DeSimone AB - We study a quasistatic evolution problem for Cam-Clay plasticity under a special loading program which leads to spatially homogeneous solutions. Under some initial conditions, the solutions exhibit a softening behaviour and time discontinuities.\\nThe behavior of the solutions at the jump times is studied by a viscous approximation. UR - http://hdl.handle.net/1963/3395 U1 - 937 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic evolution problems for nonhomogeneous elastic plastic materials JF - J. Convex Anal. Y1 - 2009 A1 - Francesco Solombrino AB -The paper studies the quasistatic evolution for elastoplastic materials when the yield surface depends on the position in the reference configuration. The main results are obtained when the yield surface is continuous with respect to the space variable. The case of piecewise constant dependence is also considered. The evolution is studied in the framework of the variational formulation for rate independent problems developed by Mielke. The results are proved by adapting the arguments introduced for a constant yield surface, using some properties of convex valued semicontinuous multifunctions. A strong formulation of the problem is also obtained, which includes a pointwise version of the plastic flow rule. Some examples are considered, which show that strain concentration may occur as a consequence of a nonconstant yield surface.

VL - 16 ER - TY - JOUR T1 - Relaxation dynamics of fluid membranes JF - Phys. Rev. E 79 (2009) 031915 Y1 - 2009 A1 - Marino Arroyo A1 - Antonio DeSimone AB - We study the effect of membrane viscosity in the dynamics of liquid membranes-possibly with free or internal boundaries-driven by conservative forces (curvature elasticity and line tension) and dragged by the bulk dissipation of the ambient fluid and the friction occurring when the amphiphilic molecules move relative to each other. To this end, we formulate a continuum model which includes a form of the governing equations for a two-dimensional viscous fluid moving on a curved, time-evolving surface. The effect of membrane viscosity has received very limited attention in previous continuum studies of the dynamics of fluid membranes, although recent coarse-grained discrete simulations suggest its importance. By applying our model to the study of vesiculation and membrane fusion in a simplified geometry, we conclude that membrane viscosity plays a dominant role in the relaxation dynamics of fluid membranes of sizes comparable to those found in eukaryotic cells, and is not negligible in many large synthetic systems of current interest. PB - American Physical Society UR - http://hdl.handle.net/1963/3618 U1 - 686 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On a Sobolev type inequality related to the weighted p-Laplace operator JF - J. Math. Anal. Appl. 352 (2009) 99-111 Y1 - 2009 A1 - Marita Gazzini A1 - Roberta Musina UR - http://hdl.handle.net/1963/2613 U1 - 1510 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Solutions of the Schrödinger–Poisson problem concentrating on spheres, part I: necessary conditions JF - Mathematical Models and Methods in Applied Sciences Y1 - 2009 A1 - Ianni, Isabella A1 - Giusi Vaira AB -In this paper we study a coupled nonlinear Schrödinger–Poisson problem with radial functions. This system has been introduced as a model describing standing waves for the nonlinear Schrödinger equations in the presence of the electrostatic field. We provide necessary conditions for concentration on sphere for the solutions of this kind of problem extending the results already known.

VL - 19 UR - https://doi.org/10.1142/S0218202509003589 ER - TY - JOUR T1 - Some new entire solutions of semilinear elliptic equations on Rn JF - Adv. Math. 221 (2009) 1843-1909 Y1 - 2009 A1 - Andrea Malchiodi PB - Elsevier UR - http://hdl.handle.net/1963/3645 U1 - 659 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Strain-order coupling in nematic elastomers: equilibrium configurations JF - Math. Models Methods Appl. Sci. 19 (2009) 601-630 Y1 - 2009 A1 - Pierluigi Cesana A1 - Antonio DeSimone AB - We consider models that describe liquid crystal elastomers either in a biaxial or in a uniaxial phase and in the framework of Frank\\\'s director theory. We prove existence of static equilibrium solutions in the presence of frustrations due to electro-mechanical boundary conditions and to applied loads and fields. We find explicit solutions arising in connection with special boundary conditions and the corresponding phase diagrams, leading to significant implications on possible experimental observations. UR - http://hdl.handle.net/1963/2700 U1 - 1400 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Stratos: a code for 3D free surface flows with floating constraints Y1 - 2009 A1 - Antonio DeSimone A1 - B. Bianchi A1 - Luca Heltai AB - This report presents a brief discussion of the theoretical aspects and practical implementation of STRATOS . STRATOS is a 3D code for the simulation\\nof hydrodynamic flows for incompressible fluids, in the presence of a free surface, capable of simulating the interaction between the free surface and a\\nfloating object via Lagrange multipliers...... UR - http://hdl.handle.net/1963/3701 U1 - 604 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Tools for the Solution of PDEs Defined on Curved Manifolds with deal.II Y1 - 2009 A1 - Antonio DeSimone A1 - Luca Heltai A1 - Cataldo Manigrasso AB - The deal.II finite element library was originally designed to solve partial differential equations defined on one, two or three space dimensions, mostly\\nvia the Finite Element Method. In its versions prior to version 6.2, the user could not solve problems defined on curved manifolds embedded in two or\\nthree spacial dimensions. This infrastructure is needed if one wants to solve, for example, Boundary Integral Equations. UR - http://hdl.handle.net/1963/3700 U1 - 605 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A variational model for quasistatic crack growth in nonlinear elasticity: some qualitative properties of the solutions JF - Boll. Unione Mat. Ital. (9) 2 (2009) 371-390 Y1 - 2009 A1 - Gianni Dal Maso A1 - Alessandro Giacomini A1 - Marcello Ponsiglione UR - http://hdl.handle.net/1963/2675 U1 - 1425 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On viscosity solutions of Hamilton-Jacobi equations JF - Trans. Amer. Math. Soc. 361 (2009) 41-59 Y1 - 2009 A1 - Sandro Zagatti AB - We consider the Dirichlet problem for Hamilton-Jacobi equations and prove existence, uniqueness and continuous dependence on boundary data of Lipschitz continuous maximal viscosity solutions. PB - American Mathematical Society UR - http://hdl.handle.net/1963/3420 U1 - 915 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Asymptotic evolution for the semiclassical nonlinear Schrödinger equation in presence of electric and magnetic fields JF - Journal of Differential Equations Y1 - 2008 A1 - Alessandro Selvitella AB -In this paper we study the semiclassical limit for the solutions of a subcritical focusing NLS with electric and magnetic potentials. We consider in particular the Cauchy problem for initial data close to solitons and show that, when the Planck constant goes to zero, the motion shadows that of a classical particle. Several works were devoted to the case of standing waves: differently from these we show that, in the dynamic version, the Lorentz force appears crucially.

VL - 245 UR - http://www.sciencedirect.com/science/article/pii/S002203960800243X ER - TY - JOUR T1 - Concentrating solutions of some singularly perturbed elliptic equations JF - Front. Math. China 3 (2008) 239-252 Y1 - 2008 A1 - Andrea Malchiodi AB - We study singularly perturbed elliptic equations arising from models in physics or biology, and investigate the asymptotic behavior of some special solutions. We also discuss some connections with problems arising in differential geometry. UR - http://hdl.handle.net/1963/2657 U1 - 1466 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On concentration of positive bound states for the Schrödinger-Poisson problem with potentials JF - Advanced nonlinear studies Y1 - 2008 A1 - Ianni, Isabella A1 - Giusi Vaira AB -We study the existence of semiclassical states for a nonlinear Schrödinger-Poisson system that concentrate near critical points of the external potential and of the density charge function. We use a perturbation scheme in a variational setting, extending the results in [1]. We also discuss necessary conditions for concentration.

PB - Advanced Nonlinear Studies, Inc. VL - 8 ER - TY - JOUR T1 - Convergence of equilibria of three-dimensional thin elastic beams JF - Proc. Roy. Soc. Edinburgh Sect. A 138 (2008) 873-896 Y1 - 2008 A1 - Maria Giovanna Mora A1 - Stefan Müller AB - A convergence result is proved for the equilibrium configurations of a three-dimensional thin elastic beam, as the diameter $h$ of the cross-section tends to zero. More precisely, we show that stationary points of the nonlinear elastic functional $E^h$, whose energies (per unit cross-section) are bounded by $Ch^2$, converge to stationary points of the $\\\\varGamma$-limit of $E^h/h^2$. This corresponds to a nonlinear one-dimensional model for inextensible rods, describing bending and torsion effects. The proof is based on the rigidity estimate for low-energy deformations by Friesecke, James and Müller and on a compensated compactness argument in a singular geometry. In addition, possible concentration effects of the strain are controlled by a careful truncation argument. UR - http://hdl.handle.net/1963/1896 U1 - 2339 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Decomposition results for functions with bounded variation JF - Boll. Unione Mat. Ital. (9) 1 (2008) 497-505 Y1 - 2008 A1 - Gianni Dal Maso A1 - Rodica Toader PB - Unione Matematica Italiana UR - http://hdl.handle.net/1963/3535 U1 - 729 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Entire solutions of autonomous equations on Rn with nontrivial asymptotics JF - Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 19 (2008) 65-72 Y1 - 2008 A1 - Andrea Malchiodi AB - We prove existence of a new type of solutions for the semilinear equation $- \\\\D u + u = u^p$ on $\\\\R^n$, with $1 < p < \\\\frac{n+2}{n-2}$. These solutions are positive, bounded, decay exponentially to zero away from three half-lines with a common origin, and at infinity are asymptotically periodic. UR - http://hdl.handle.net/1963/2640 U1 - 1483 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - An entropy based Glimm-type functional JF - J. Hyperbolic Differ. Equ. 5 (2008) 643-662 Y1 - 2008 A1 - Laura Caravenna PB - World Scientific UR - http://hdl.handle.net/1963/4051 U1 - 351 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Eulerian calculus for the displacement convexity in the Wasserstein distance JF - SIAM J. Math. Anal. 40 (2008) 1104-1122 Y1 - 2008 A1 - Sara Daneri A1 - Giuseppe Savarè AB - In this paper we give a new proof of the (strong) displacement convexity of a class of integral functionals defined on a compact Riemannian manifold satisfying a lower Ricci curvature bound. Our approach does not rely on existence and regularity results for optimal transport maps on Riemannian manifolds, but it is based on the Eulerian point of view recently introduced by Otto and Westdickenberg [SIAM J. Math. Anal., 37 (2005), pp. 1227-1255] and on the metric characterization of the gradient flows generated by the functionals in the Wasserstein space. PB - SIAM UR - http://hdl.handle.net/1963/3413 U1 - 922 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence of conformal metrics with constant $Q$-curvature JF - Ann. of Math. 168 (2008) 813-858 Y1 - 2008 A1 - Zindine Djadli A1 - Andrea Malchiodi AB - Given a compact four dimensional manifold, we prove existence of conformal metrics with constant $Q$-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure. Since the corresponding Euler functional is in general unbounded from above and from below, we employ topological methods and minimax schemes, jointly with a compactness result by the second author. UR - http://hdl.handle.net/1963/2308 U1 - 1708 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Forced Vibrations of a Nonhomogeneous String JF - SIAM J. Math. Anal. 40 (2008) 382-412 Y1 - 2008 A1 - P Baldi A1 - Massimiliano Berti AB - We prove existence of vibrations of a nonhomogeneous string under a nonlinear time periodic forcing term in the case in which the forcing frequency avoids resonances with the vibration modes of the string (nonresonant case). The proof relies on a Lyapunov-Schmidt reduction and a Nash-Moser iteration scheme. UR - http://hdl.handle.net/1963/2643 U1 - 1480 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Fulde-Ferrell-Larkin-Ovchinnikov pairing in one-dimensional optical lattices JF - Phys. Rev. B 77 (2008) 245105 Y1 - 2008 A1 - Matteo Rizzi A1 - Marco Polini A1 - Miguel A. Cazalilla A1 - M.R. Bakhtiari A1 - Mario P. Tosi A1 - Rosario Fazio AB -Spin-polarized attractive Fermi gases in one-dimensional (1D) optical lattices are expected to be remarkably good candidates for the observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We model these systems with an attractive Hubbard model with population imbalance. By means of the density-matrix renormalization-group method we compute the pairing correlations as well as the static spin and charge structure factors in the whole range from weak to strong coupling. We demonstrate that pairing correlations exhibit quasi-long range order and oscillations at the wave number expected from FFLO theory. However, we also show by numerically computing the mixed spin-charge static structure factor that charge and spin degrees of freedom appear to be coupled already for small imbalance. We discuss the consequences of this coupling for the observation of the FFLO phase, as well as for the stabilization of the quasi-long range order into long-range order by coupling many identical 1D systems, as in quasi-1D optical lattices.

UR - http://hdl.handle.net/1963/2694 U1 - 1406 U2 - Physics U3 - Condensed Matter Theory ER - TY - JOUR T1 - A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds JF - Discrete Contin. Dyn. Syst. 20 (2008) 801-822 Y1 - 2008 A1 - Andrei A. Agrachev A1 - Ugo Boscain A1 - Mario Sigalotti AB - We consider a generalization of Riemannian geometry that naturally arises in the framework of control theory. Let $X$ and $Y$ be two smooth vector fields on a two-dimensional manifold $M$. If $X$ and $Y$ are everywhere linearly independent, then they define a classical Riemannian metric on $M$ (the metric for which they are orthonormal) and they give to $M$ the structure of metric space. If $X$ and $Y$ become linearly dependent somewhere on $M$, then the corresponding Riemannian metric has singularities, but under generic conditions the metric structure is still well defined. Metric structures that can be defined locally in this way are called almost-Riemannian structures. They are special cases of rank-varying sub-Riemannian structures, which are naturally defined in terms of submodules of the space of smooth vector fields on $M$. Almost-Riemannian structures show interesting phenomena, in particular for what concerns the relation between curvature, presence of conjugate points, and topology of the manifold. The main result of the paper is a generalization to almost-Riemannian structures of the Gauss-Bonnet formula. UR - http://hdl.handle.net/1963/1869 U1 - 2353 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Globally stable quasistatic evolution in plasticity with softening JF - Netw. Heterog. Media 3 (2008) 567-614 Y1 - 2008 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Maria Giovanna Mora A1 - Massimiliano Morini AB - We study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is characterized by the following properties: global stability at each time and energy balance on each\\ntime interval. An example developed in detail compares the solutions obtained by this method with the ones provided by a vanishing viscosity approximation, and shows that only the latter capture a decreasing branch in the stress-strain response. UR - http://hdl.handle.net/1963/1965 U1 - 2228 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Gradient bounds for minimizers of free discontinuity problems related to cohesive zone models in fracture mechanics JF - Calc. Var. Partial Differential Equations 31 (2008) 137-145 Y1 - 2008 A1 - Gianni Dal Maso A1 - Adriana Garroni AB - In this note we consider a free discontinuity problem for a scalar function, whose energy depends also on the size of the jump. We prove that the gradient of every smooth local minimizer never exceeds a constant, determined only by the data of the problem. UR - http://hdl.handle.net/1963/1723 U1 - 2428 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Invariant Carnot-Caratheodory metrics on S3, SO(3), SL(2) and Lens Spaces JF - SIAM J. Control Optim. 47 (2008) 1851-1878 Y1 - 2008 A1 - Ugo Boscain A1 - Francesco Rossi AB - In this paper we study the invariant Carnot-Caratheodory metrics on SU(2) \\\' S3,\\nSO(3) and SL(2) induced by their Cartan decomposition. Beside computing explicitly geodesics and conjugate loci, we compute the cut loci (globally) and we give the expression of the Carnot-Caratheodory distance as the inverse of an elementary function. We then prove that the metric\\ngiven on SU(2) projects on the so called Lens Spaces L(p; q). Also for Lens Spaces, we compute\\nthe cut loci (globally). UR - http://hdl.handle.net/1963/2144 U1 - 2099 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Invariant Manifolds for Viscous Profiles of a Class of Mixed Hyperbolic-Parabolic Systems Y1 - 2008 A1 - Stefano Bianchini A1 - Laura Spinolo UR - http://hdl.handle.net/1963/3400 U1 - 932 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Limit Time Optimal Syntheses for a control-affine system on S² JF - SIAM J. Control Optim. 47 (2008) 111-143 Y1 - 2008 A1 - Paolo Mason A1 - Rebecca Salmoni A1 - Ugo Boscain A1 - Yacine Chitour AB - For $\\\\alpha \\\\in ]0,\\\\pi/2[$, let $(\\\\Sigma)_\\\\alpha$ be the control system $\\\\dot{x}=(F+uG)x$, where $x$ belongs to the two-dimensional unit sphere $S^2$, $u\\\\in [-1,1]$, and $F,G$ are $3\\\\times3$ skew-symmetric matrices generating rotations with perpendicular axes and of respective norms $\\\\cos(\\\\alpha)$ and $\\\\sin(\\\\alpha)$. In this paper, we study the time optimal synthesis (TOS) from the north pole $(0,0,1)^T$ associated to $(\\\\Sigma)_\\\\alpha$, as the parameter $\\\\alpha$ tends to zero; this problem is motivated by specific issues in the control of quantum systems. We first prove that the TOS is characterized by a \\\"two-snakes\\\" configuration on the whole $S^2$, except for a neighborhood $U_\\\\alpha$ of the south pole $(0,0,-1)^T$ of diameter at most ${\\\\cal O}(\\\\alpha)$. We next show that, inside $U_\\\\alpha$, the TOS depends on the relationship between $r(\\\\alpha):=\\\\pi/2\\\\alpha-[\\\\pi/2\\\\alpha]$ and $\\\\alpha$. More precisely, we characterize three main relationships by considering sequences $(\\\\alpha_k)_{k\\\\geq 0}$ satisfying (a) $r(\\\\alpha_k)=\\\\bar{r}$, (b) $r(\\\\alpha_k)=C\\\\alpha_k$, and (c) $r(\\\\alpha_k)=0$, where $\\\\bar{r}\\\\in (0,1)$ and $C>0$. In each case, we describe the TOS and provide, after a suitable rescaling, the limiting behavior, as $\\\\alpha$ tends to zero, of the corresponding TOS inside $U_\\\\alpha$. UR - http://hdl.handle.net/1963/1862 U1 - 2360 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Minimization of non quasiconvex functionals by integro-extremization method JF - Discrete Contin. Dyn. Syst. 21 (2008) 625-641 Y1 - 2008 A1 - Sandro Zagatti UR - http://hdl.handle.net/1963/2761 U1 - 1939 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Minimizers of non convex scalar functionals and viscosity solutions of Hamilton-Jacobi equations JF - Calc. Var. Partial Differential Equations 31 (2008) 511-519 Y1 - 2008 A1 - Sandro Zagatti UR - http://hdl.handle.net/1963/2760 U1 - 1940 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Morse theory and a scalar field equation on compact surfaces JF - Adv. Differential Equations 13 (2008) 1109-1129 Y1 - 2008 A1 - Andrea Malchiodi PB - Khayyam Publishing UR - http://hdl.handle.net/1963/3531 U1 - 733 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Multiple bound states for the Schroedinger-Poisson problem JF - Commun. Contemp. Math. 10 (2008) 391-404 Y1 - 2008 A1 - Antonio Ambrosetti A1 - David Ruiz UR - http://hdl.handle.net/1963/2679 U1 - 1421 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - A note on the differentiability of Lipschitz functions and the chain rule in Sobolev spaces Y1 - 2008 A1 - Massimiliano Morini UR - http://hdl.handle.net/1963/2654 U1 - 1469 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Optimal Strokes for Low Reynolds Number Swimmers: An Example JF - J. Nonlinear Sci. 18 (2008) 277-302 Y1 - 2008 A1 - François Alouges A1 - Antonio DeSimone A1 - Aline Lefebvre AB - Swimming, i.e., being able to advance in the absence of external forces by performing cyclic shape changes, is particularly demanding at low Reynolds numbers. This is the regime of interest for micro-organisms and micro- or nano-robots. We focus in this paper on a simple yet representative example: the three-sphere swimmer of Najafi and Golestanian (Phys. Rev. E, 69, 062901-062904, 2004). For this system, we show how to cast the problem of swimming in the language of control theory, prove global controllability (which implies that the three-sphere swimmer can indeed swim), and propose a numerical algorithm to compute optimal strokes (which turn out to be suitably defined sub-Riemannian geodesics). PB - Springer UR - http://hdl.handle.net/1963/4006 U1 - 396 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Positive solutions of nonlinear Schrödinger-Poisson systems with radial potentials vanishing at infinity JF - Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl Y1 - 2008 A1 - Mercuri, Carlo AB -We deal with a weighted nonlinear Schr¨odinger-Poisson system, allowing the potentials to vanish at infinity.

PB - Citeseer VL - 19 UR - http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.510.3635&rep=rep1&type=pdf ER - TY - JOUR T1 - Relaxation of some transversally isotropic energies and applications to smectic A elastomers JF - Math. Models Methods Appl. Sci. 18 (2008) 1-20 Y1 - 2008 A1 - James Adams A1 - Sergio Conti A1 - Antonio DeSimone A1 - Georg Dolzmann UR - http://hdl.handle.net/1963/1912 U1 - 2325 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A second order minimality condition for the Mumford-Shah functional JF - Calc. Var. Partial Differential Equations 33 (2008) 37-74 Y1 - 2008 A1 - Filippo Cagnetti A1 - Maria Giovanna Mora A1 - Massimiliano Morini AB - A new necessary minimality condition for the Mumford-Shah functional is derived by means of second order variations. It is expressed in terms of a sign condition for a nonlocal quadratic form on $H^1_0(\\\\Gamma)$, $\\\\Gamma$ being a submanifold of the regular part of the discontinuity set of the critical point. Two equivalent formulations are provided: one in terms of the first eigenvalue of a suitable compact operator, the other involving a sort of nonlocal capacity of $\\\\Gamma$. A sufficient condition for minimality is also deduced. Finally, an explicit example is discussed, where a complete characterization of the domains where the second variation is nonnegative can be given. UR - http://hdl.handle.net/1963/1955 U1 - 2318 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Solitons of linearly coupled systems of semilinear non-autonomous equations on Rn JF - J. Funct. Anal. 254 (2008) 2816-2845 Y1 - 2008 A1 - Antonio Ambrosetti A1 - Giovanna Cerami A1 - David Ruiz AB - Using concentration compactness type arguments, we prove some results about the existence of positive ground and bound state of linearly coupled systems of nonlinear Schrödinger equations. UR - http://hdl.handle.net/1963/2175 U1 - 2069 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Stability of planar switched systems: the nondiagonalizable case JF - Commun. Pure Appl. Anal. 7 (2008) 1-21 Y1 - 2008 A1 - Ugo Boscain A1 - Moussa Balde UR - http://hdl.handle.net/1963/1857 U1 - 2361 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Topological methods for an elliptic equation with exponential nonlinearities JF - Discrete Contin. Dyn. Syst. 21 (2008) 277-294 Y1 - 2008 A1 - Andrea Malchiodi AB - We consider a class of variational equations with exponential nonlinearities on compact surfaces. From considerations involving the Moser-Trudinger inequality, we characterize some sublevels of the Euler-Lagrange functional in terms of the topology of the surface and of the data of the equation. This is used together with a min-max argument to obtain existence results. UR - http://hdl.handle.net/1963/2594 U1 - 1528 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Transition layer for the heterogeneous Allen-Cahn equation JF - Ann. Inst. H. Poincare Anal. Non Lineaire 25 (2008) 609-631 Y1 - 2008 A1 - Fethi Mahmoudi A1 - Andrea Malchiodi A1 - Juncheng Wei AB - We consider the equation $\\\\e^{2}\\\\Delta u=(u-a(x))(u^2-1)$ in $\\\\Omega$, $\\\\frac{\\\\partial u}{\\\\partial \\\\nu} =0$ on $\\\\partial \\\\Omega$, where $\\\\Omega$ is a smooth and bounded domain in $\\\\R^n$, $\\\\nu$ the outer unit normal to $\\\\pa\\\\Omega$, and $a$ a smooth function satisfying $-10} and {a<0}. Assuming $\\\\nabla a \\\\neq 0$ on $K$ and $a\\\\ne 0$ on $\\\\partial \\\\Omega$, we show that there exists a sequence $\\\\e_j \\\\to 0$ such that the above equation has a solution $u_{\\\\e_j}$ which converges uniformly to $\\\\pm 1$ on the compact sets of $\\\\O_{\\\\pm}$ as $j \\\\to + \\\\infty$. UR - http://hdl.handle.net/1963/2656 U1 - 1467 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - Transport Rays and Applications to Hamilton–Jacobi Equations T2 - Nonlinear PDE’s and Applications : C.I.M.E. Summer School, Cetraro, Italy 2008 / Stefano Bianchini, Eric A. Carlen, Alexander Mielke, Cédric Villani. Eds. Luigi Ambrosio, Giuseppe Savaré. - Berlin : Springer, 2011. - (Lecture Notes in Mathematics ; 20 Y1 - 2008 A1 - Stefano Bianchini A1 - Matteo Gloyer AB - The aim of these notes is to introduce the readers to the use of the Disintegration Theorem for measures as an effective tool for reducing problems in transport equations to simpler ones. The basic idea is to partition Rd into one dimensional sets, on which the problem under consideration becomes one space dimensional (and thus much easier, hopefully). JF - Nonlinear PDE’s and Applications : C.I.M.E. Summer School, Cetraro, Italy 2008 / Stefano Bianchini, Eric A. Carlen, Alexander Mielke, Cédric Villani. Eds. Luigi Ambrosio, Giuseppe Savaré. - Berlin : Springer, 2011. - (Lecture Notes in Mathematics ; 20 PB - Springer SN - 978-3-642-21718-0 UR - http://hdl.handle.net/1963/5463 N1 - This volume collects the notes of the CIME course Nonlinear PDE’s and\\r\\napplications held in Cetraro (Italy) on June 23–28, 2008. The school consisted\\r\\nin 5 series of lectures, delivered by Stefano Bianchini (SISSA, Trieste), Eric A. Carlen (Rutgers University), Alexander Mielke (WIAS, Berlin), Felix Otto (Bonn University), Cedric Villani (Ecole Normale Superieure de Lyon). U1 - 5298 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - A vanishing viscosity approach to quasistatic evolution in plasticity with softening JF - Arch. Ration. Mech. Anal. 189 (2008) 469-544 Y1 - 2008 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Maria Giovanna Mora A1 - Massimiliano Morini AB - We deal with quasistatic evolution problems in plasticity with softening, in the framework of small strain associative elastoplasticity. The presence of a nonconvex term due to the softening phenomenon requires a nontrivial extension of the variational framework for rate-independent problems to the case of a nonconvex energy functional. We argue that, in this case, the use of global minimizers in the corresponding incremental problems is not justified from the mechanical point of view. Thus, we analize a different selection criterion for the solutions of the quasistatic evolution problem, based on a viscous approximation. This leads to a generalized formulation in terms of Young measures, developed in the first part of the paper. In the second part we apply our approach to some concrete examples. UR - http://hdl.handle.net/1963/1844 U1 - 2373 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Asymptotic behaviour of smooth solutions for partially dissipative hyperbolic systems with a convex entropy JF - Comm. Pure Appl. Math. 60 (2007) 1559-1622 Y1 - 2007 A1 - Stefano Bianchini A1 - Bernard Hanouzet A1 - Roberto Natalini AB - We study the asymptotic time behavior of global smooth solutions to general entropy dissipative hyperbolic systems of balance law in m space dimensions, under the Shizuta-Kawashima condition. UR - http://hdl.handle.net/1963/1780 U1 - 2764 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Asymptotic variational wave equations JF - Arch. Ration. Mech. Anal. 183 (2007) 163-185 Y1 - 2007 A1 - Alberto Bressan A1 - Zhang Ping A1 - Zheng Yuxi AB - We investigate the equation $(u_t + (f(u))_x)_x = f\\\'\\\'(u) (u_x)^2/2$ where $f(u)$ is a given smooth function. Typically $f(u)= u^2/2$ or $u^3/3$. This equation models unidirectional and weakly nonlinear waves for the variational wave equation $u_{tt} - c(u) (c(u)u_x)_x =0$ which models some liquid crystals with a natural sinusoidal $c$. The equation itself is also the Euler-Lagrange equation of a variational problem. Two natural classes of solutions can be associated with this equation. A conservative solution will preserve its energy in time, while a dissipative weak solution loses energy at the time when singularities appear. Conservative solutions are globally defined, forward and backward in time, and preserve interesting geometric features, such as the Hamiltonian structure. On the other hand, dissipative solutions appear to be more natural from the physical point of view.\\nWe establish the well-posedness of the Cauchy problem within the class of conservative solutions, for initial data having finite energy and assuming that the flux function $f$ has Lipschitz continuous second-order derivative. In the case where $f$ is convex, the Cauchy problem is well-posed also within the class of dissipative solutions. However, when $f$ is not convex, we show that the dissipative solutions do not depend continuously on the initial data. UR - http://hdl.handle.net/1963/2182 U1 - 2062 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Boundary interface for the Allen-Cahn equation JF - J. Fixed Point Theory Appl. 1 (2007) 305-336 Y1 - 2007 A1 - Andrea Malchiodi A1 - Juncheng Wei UR - http://hdl.handle.net/1963/2027 U1 - 2169 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Boundary-clustered interfaces for the Allen–Cahn equation JF - Pacific Journal of Mathematics 229 (2007), No. 2, 447–468 Y1 - 2007 A1 - Andrea Malchiodi A1 - Wei-Ming Ni A1 - Juncheng Wei PB - Mathematical Sciences Publishers UR - http://hdl.handle.net/1963/5089 U1 - 4905 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - RPRT T1 - BV instability for the Lax-Friedrichs scheme Y1 - 2007 A1 - Paolo Baiti A1 - Alberto Bressan A1 - Helge Kristian Jenssen AB - It is proved that discrete shock profiles (DSPs) for the Lax-Friedrichs scheme for a system of conservation laws do not necessarily depend continuously in BV on their speed. We construct examples of $2 \\\\times 2$-systems for which there are sequences of DSPs with speeds converging to a rational number. Due to a resonance phenomenon, the difference between the limiting DSP and any DSP in the sequence will contain an order-one amount of variation. UR - http://hdl.handle.net/1963/2335 U1 - 1681 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Concentration on minimal submanifolds for a singularly perturbed Neumann problem JF - Adv. Math. 209 (2007) 460-525 Y1 - 2007 A1 - Fethi Mahmoudi A1 - Andrea Malchiodi AB - We consider the equation $- \\\\e^2 \\\\D u + u= u^p$ in $\\\\Omega \\\\subseteq \\\\R^N$, where $\\\\Omega$ is open, smooth and bounded, and we prove concentration of solutions along $k$-dimensional minimal submanifolds of $\\\\partial \\\\O$, for $N \\\\geq 3$ and for $k \\\\in \\\\{1, ..., N-2\\\\}$. We impose Neumann boundary conditions, assuming $13 or with two inputs for n=4 and n=5, up to state-feedback transformations, preserving the affine structure. First using the Poincare series of moduli numbers we introduce the intrinsic numbers of functional moduli of each prescribed number of variables on which a classification problem depends. In order to classify affine systems with scalar input we associate with such a system the canonical frame by normalizing some structural functions in a commutative relation of the vector fields, which define our control system. Then, using this canonical frame, we introduce the canonical coordinates and find a complete system of state-feedback invariants of the system. It also gives automatically the micro-local (i.e. local in state-input space) classification of the generic non-affine n-dimensional control system with scalar input for n>2. Further we show how the problem of feedback-equivalence of affine systems with two-dimensional input in state space of dimensions 4 and 5 can be reduced to the same problem for affine systems with scalar input. In order to make this reduction we distinguish the subsystem of our control system, consisting of the directions of all extremals in dimension 4 and all abnormal extremals in dimension 5 of the time optimal problem, defined by the original control system. In each classification problem under consideration we find the intrinsic numbers of functional moduli of each prescribed number of variables according to its Poincare series. UR - http://hdl.handle.net/1963/2186 U1 - 2058 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On finite-dimensional projections of distributions for solutions of randomly forced PDE\\\'s JF - Ann. Inst. Henri Poincare-Prob. Stat. 43 (2007) 399-415 Y1 - 2007 A1 - Andrei A. Agrachev A1 - Sergei Kuksin A1 - Andrey Sarychev A1 - Armen Shirikyan AB - The paper is devoted to studying the image of probability measures on a Hilbert space under finite-dimensional analytic maps. We establish sufficient conditions under which the image of a measure has a density with respect to the Lebesgue measure and continuously depends on the map. The results obtained are applied to the 2D Navier-Stokes equations perturbed by various random forces of low dimension. UR - http://hdl.handle.net/1963/2012 U1 - 2184 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Gaussian estimates for hypoelliptic operators via optimal control JF - Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 333-342 Y1 - 2007 A1 - Ugo Boscain A1 - Sergio Polidoro AB - We obtain Gaussian lower bounds for the fundamental solution of a class of hypoelliptic equations, by using repeatedly an invariant Harnack inequality. Our main result is given in terms of the value function of a suitable optimal control problem. UR - http://hdl.handle.net/1963/1994 U1 - 2202 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - High-order angles in almost-Riemannian geometry Y1 - 2007 A1 - Ugo Boscain A1 - Mario Sigalotti AB - Let X and Y be two smooth vector fields on a two-dimensional manifold M. If X and Y are everywhere linearly independent, then they define a Riemannian metric on M (the metric for which they are orthonormal) and they give to M the structure of metric space. If X and Y become linearly dependent somewhere on M, then the corresponding Riemannian metric has singularities, but under generic conditions the metric structure is still well defined. Metric structures that can be defined locally in this way are called almost-Riemannian structures. The main result of the paper is a generalization to almost-Riemannian structures of the Gauss-Bonnet formula for domains with piecewise-C2 boundary. The main feature of such formula is the presence of terms that play the role of high-order angles at the intersection points with the set of singularities. UR - http://hdl.handle.net/1963/1995 U1 - 2201 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Luther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas JF - Phys. Rev. Lett. 98 (2007) 030404 Y1 - 2007 A1 - Gao Xianlong A1 - Matteo Rizzi A1 - Marco Polini A1 - Rosario Fazio A1 - Mario P. Tosi A1 - Vivaldo L. Jr. Campo A1 - Klaus Capelle AB -

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

UR - http://hdl.handle.net/1963/2056 U1 - 2140 U2 - Physics U3 - Condensed Matter Theory ER - TY - RPRT T1 - On the Maz\\\'ya inequalities: existence and multiplicity results for an elliptic problem involving cylindrical weights Y1 - 2007 A1 - Marita Gazzini A1 - Roberta Musina UR - http://hdl.handle.net/1963/2522 U1 - 1596 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Multi-bump solitons to linearly coupled systems of nonlinear Schrödinger equations Y1 - 2007 A1 - Antonio Ambrosetti A1 - Eduardo Colorado A1 - David Ruiz JF - Calc. Var. Partial Differential Equations 30 (2007) 85-112 UR - http://hdl.handle.net/1963/1835 U1 - 2381 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Nearly time optimal stabilizing patchy feedbacks JF - Ann. Inst. H. Poincare Anal. Non Lineaire 24 (2007) 279-310 Y1 - 2007 A1 - Fabio Ancona A1 - Alberto Bressan AB - We consider the time optimal stabilization problem for a nonlinear control system $\\\\dot x=f(x,u)$. Let $\\\\tau(y)$ be the minimum time needed to steer the system from the state $y\\\\in\\\\R^n$ to the origin, and call $\\\\A(T)$ the set of initial states that can be steered to the origin in time $\\\\tau(y)\\\\leq T$. Given any $\\\\ve>0$, in this paper we construct a patchy feedback $u=U(x)$ such that every solution of $\\\\dot x=f(x, U(x))$, $x(0)=y\\\\in \\\\A(T)$ reaches an $\\\\ve$-neighborhood of the origin within time $\\\\tau(y)+\\\\ve$. UR - http://hdl.handle.net/1963/2185 U1 - 2059 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Necessary and sufficient conditions for the chainrule in W1,1loc(RN;Rd) and BVloc(RN;Rd) JF - J. Eur. Math. Soc. (JEMS) 9 (2007) 219-252 Y1 - 2007 A1 - Giovanni Leoni A1 - Massimiliano Morini AB -In this paper we prove necessary and sufficient conditions for the validity of the classical chain rule in Sobolev spaces and in the space of functions of bounded variation.

UR - http://hdl.handle.net/1963/2037 U1 - 2159 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - A new model for contact angle hysteresis Y1 - 2007 A1 - Antonio DeSimone A1 - Natalie Gruenewald A1 - Felix Otto AB - We present a model which explains several experimental observations relating contact angle hysteresis with surface roughness. The model is based on the balance between released energy and dissipation, and it describes the stick-slip behavior of drops on a rough surface using ideas similar to those employed in dry friction, elasto-plasticity and fracture mechanics. The main results of our analysis are formulas giving the interval of stable contact angles as a function of the surface roughness. These formulas show that the difference between advancing and receding angles is much larger for a drop in complete contact with the substrate (Wenzel drop) than for one whose cavities are filled with air (Cassie-Baxter drop). This fact is used as the key tool to interpret the experimental evidence. JF - Netw. Heterog. Media 2 (2007) 211-225 UR - http://hdl.handle.net/1963/1848 U1 - 2369 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On a notion of unilateral slope for the Mumford-Shah functional JF - NoDEA 13 (2007) 713-734 Y1 - 2007 A1 - Gianni Dal Maso A1 - Rodica Toader AB - In this paper we introduce a notion of unilateral slope for the Mumford-Shah functional, and provide an explicit formula in the case of smooth cracks. We show that the slope is not lower semicontinuous and study the corresponding relaxed functional. UR - http://hdl.handle.net/1963/2059 U1 - 2137 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Parametrized curves in Lagrange Grassmannians JF - C. R. Math. 345 (2007) 647-652 Y1 - 2007 A1 - Igor Zelenko A1 - Li Chengbo UR - http://hdl.handle.net/1963/2560 U1 - 1559 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Perturbation techniques applied to the real vanishing viscosity approximation of an initial boundary value problem Y1 - 2007 A1 - Stefano Bianchini PB - SISSA UR - http://preprints.sissa.it/handle/1963/35315 U1 - 35623 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Quasistatic crack growth for a cohesive zone model with prescribed crack path Y1 - 2007 A1 - Gianni Dal Maso A1 - Chiara Zanini AB - In this paper we study the quasistatic crack growth for a cohesive zone model. We assume that the crack path is prescribed and we study the time evolution of the crack in the framework of the variational theory of rate-independent processes. JF - Proc. Roy. Soc. Edinburgh Sect. A 137 (2007) 253-279 UR - http://hdl.handle.net/1963/1686 U1 - 2447 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic evolution problems for pressure-sensitive plastic materials JF - Milan J. Math. 75 (2007) 117-134 Y1 - 2007 A1 - Gianni Dal Maso A1 - Alexey Demyanov A1 - Antonio DeSimone AB - We study quasistatic evolution problems for pressure-sensitive plastic materials in the context of small strain associative perfect plasticity. UR - http://hdl.handle.net/1963/1962 U1 - 2231 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the regularity of weak solutions to H-systems JF - Atti .Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 209-219 Y1 - 2007 A1 - Roberta Musina AB - Abstract. In this paper we prove that every weak solution to the H-surface equation is locally bounded, provided the prescibed mean curvatore H is asymptotic to a constant at infinity (with a suitable decay rate). No smoothness ssumptions are required on H. We consider also the Dirichlet problem.... UR - http://hdl.handle.net/1963/1753 U1 - 2791 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Soft elasticity and microstructure in smectic C elastomers Y1 - 2007 A1 - Antonio DeSimone A1 - James Adams A1 - Sergio Conti AB - Smectic C elastomers are layered materials exhibiting a solid-like elastic response along the layer normal and a rubbery one in the plane. The set of strains minimizing the elastic energy contains a one-parameter family of simple stretches associated with an internal degree of freedom, coming from the in-plane component of the director. We investigate soft elasticity and the corresponding microstructure by determining the quasiconvex hull of the set , and use this to propose experimental tests that should make the predicted soft response observable. JF - Contin. Mech. Thermodyn. 18 (2007) 319-334 UR - http://hdl.handle.net/1963/1811 U1 - 2403 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Solutions of vectorial Hamilton-Jacobi equations and minimizers of nonquasiconvex functionals JF - J. Math. Anal. Appl. 335 (2007) 1143-1160 Y1 - 2007 A1 - Sandro Zagatti AB - We provide a unified approach to prove existence results for the Dirichlet problem for Hamilton-Jacobi equations and for the minimum problem for nonquasiconvex functionals of the Calculus of Variations with affine boundary data. The idea relies on the definition of integro-extremal solutions introduced in the study of nonconvex scalar variational problem. UR - http://hdl.handle.net/1963/2763 U1 - 1937 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Solutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part I: study of the limit set and approximate solutions Y1 - 2007 A1 - Fethi Mahmoudi A1 - Andrea Malchiodi A1 - Marcelo Montenegro AB - We prove existence of a special class of solutions to the (elliptic) Nonlinear Schroeodinger Equation $- \\\\epsilon^2 \\\\Delta \\\\psi + V(x) \\\\psi = |\\\\psi|^{p-1} \\\\psi$, on a manifold or in the Euclidean space. Here V represents the potential, p an exponent greater than 1 and $\\\\epsilon$ a small parameter corresponding to the Planck constant. As $\\\\epsilon$ tends to zero (namely in the semiclassical limit) we prove existence of complex-valued solutions which concentrate along closed curves, and whose phase is highly oscillatory. Physically, these solutions carry quantum-mechanical momentum along the limit curves. In this first part we provide the characterization of the limit set, with natural stationarity and non-degeneracy conditions. We then construct an approximate solution up to order $\\\\epsilon^2$, showing that these conditions appear naturally in a Taylor expansion of the equation in powers of $\\\\epsilon$. Based on these, an existence result will be proved in the second part. UR - http://hdl.handle.net/1963/2112 U1 - 2577 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Solutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part II: proof of the existence result Y1 - 2007 A1 - Fethi Mahmoudi A1 - Andrea Malchiodi AB - We prove existence of a special class of solutions to the (elliptic) Nonlinear Schroedinger Equation $- \\\\epsilon^2 \\\\Delta \\\\psi + V(x) \\\\psi = |\\\\psi|^{p-1} \\\\psi$ on a manifold or in the Euclidean space. Here V represents the potential, p is an exponent greater than 1 and $\\\\epsilon$ a small parameter corresponding to the Planck constant. As $\\\\epsilon$ tends to zero (namely in the semiclassical limit) we prove existence of complex-valued solutions which concentrate along closed curves, and whose phase in highly oscillatory. Physically, these solutions carry quantum-mechanical momentum along the limit curves. In the first part of this work we identified the limit set and constructed approximate solutions, while here we give the complete proof of our main existence result. UR - http://hdl.handle.net/1963/2111 U1 - 2578 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Some existence results for the Toda system on closed surfaces JF - Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 391-412 Y1 - 2007 A1 - Andrea Malchiodi A1 - Cheikh Birahim Ndiaye AB - Given a compact closed surface $\\\\Sig$, we consider the {\\\\em generalized Toda} system of equations on $\\\\Sig$: $- \\\\D u_i = \\\\sum_{j=1}^2 \\\\rho_j a_{ij} \\\\left( \\\\frac{h_j e^{u_j}}{\\\\int_\\\\Sig h_j e^{u_j} dV_g} - 1 \\\\right)$ for $i = 1, 2$, where $\\\\rho_1, \\\\rho_2$ are real parameters and $h_1, h_2$ are smooth positive functions. Exploiting the variational structure of the problem and using a new minimax scheme we prove existence of solutions for generic values of $\\\\rho_1$ and for $\\\\rho_2 < 4 \\\\pi$. UR - http://hdl.handle.net/1963/1775 U1 - 2769 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Stability of front tracking solutions to the initial and boundary value problem for systems of conservation laws JF - NoDEA Nonlinear Differential Equations Appl. 14 (2007) 569-592 Y1 - 2007 A1 - Andrea Marson A1 - Carlotta Donadello UR - http://hdl.handle.net/1963/1769 U1 - 2775 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Standing waves of some coupled Nonlinear Schrödinger Equations Y1 - 2007 A1 - Antonio Ambrosetti A1 - Eduardo Colorado AB - We deal with a class of systems of NLS equations, proving the existence of bound and ground states provided the coupling parameter is small, respectively, large. JF - J. Lond. Math. Soc. 75 (2007) 67-82 UR - http://hdl.handle.net/1963/1821 U1 - 2393 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Surfactants in Foam Stability: A Phase-Field Model JF - Arch. Rational Mech. Anal. 183 (2007) 411-456 Y1 - 2007 A1 - Irene Fonseca A1 - Massimiliano Morini A1 - Valeriy Slastikov AB - The role of surfactants in stabilizing the formation of bubbles in foams is studied using a phase-field model. The analysis is centered on a van der Walls-Cahn-Hilliard-type energy with an added term accounting for the interplay between the presence of a surfactant density and the creation of interfaces. In particular, it is concluded that the surfactant segregates to the interfaces, and that the prescriptionof the distribution of surfactant will dictate the locus of interfaces, what is in agreement with experimentation. UR - http://hdl.handle.net/1963/2035 U1 - 2161 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Time optimal swing-up of the planar pendulum JF - 46th IEEE Conference on Decision and Control (2007) 5389 - 5394 Y1 - 2007 A1 - Mireille E. Broucke A1 - Paolo Mason A1 - Benedetto Piccoli AB - This paper presents qualitative and numerical results on the global structure of the time optimal trajectories of the planar pendulum on a cart. UR - http://hdl.handle.net/1963/1867 U1 - 2355 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Time-dependent systems of generalized Young measures Y1 - 2007 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Maria Giovanna Mora A1 - Massimiliano Morini AB - In this paper some new tools for the study of evolution problems in the framework of Young measures are introduced. A suitable notion of time-dependent system of generalized Young measures is defined, which allows to extend the classical notions of total variation and absolute continuity with respect to time, as well as the notion of time derivative. The main results are a Helly type theorem for sequences of systems of generalized Young measures and a theorem about the existence of the time derivative for systems with bounded variation with respect to time. JF - Netw. Heterog. Media 2 (2007) 1-36 UR - http://hdl.handle.net/1963/1795 U1 - 2749 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Uniqueness and continuous dependence on boundary data for integro-extremal minimizers of the functional of the gradient JF - J. Convex Anal. 14 (2007) 705-727 Y1 - 2007 A1 - Sandro Zagatti AB - We study some qualitative properties of the integro-extremal minimizers of the functional of the gradient defined on Sobolev spaces with Dirichlet boundary conditions. We discuss their use in the non-convex case via viscosity methods and give conditions under which they are unique and depend continuously on boundary data. UR - http://hdl.handle.net/1963/2762 U1 - 1938 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Viscosity solutions of Hamilton-Jacobi equations with discontinuous coefficients JF - J. Hyperbolic Differ. Equ. 4 (2007) 771-795 Y1 - 2007 A1 - Giuseppe Maria Coclite A1 - Nils Henrik Risebro AB - We consider Hamilton--Jacobi equations, where the Hamiltonian depends discontinuously on both the spatial and temporal location. Our main results are the existence and well--posedness of a viscosity solution to the Cauchy problem. We define a viscosity solution by treating the discontinuities in the coefficients analogously to \\\"internal boundaries\\\". By defining an appropriate penalization function, we prove that viscosity solutions are unique. The existence of viscosity solutions is established by showing that a sequence of front tracking approximations is compact in $L^\\\\infty$, and that the limits are viscosity solutions. PB - World Scientific UR - http://hdl.handle.net/1963/2907 U1 - 1793 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - 2-d stability of the Néel wall JF - Calc. Var. Partial Differential Equations 27 (2006) 233-253 Y1 - 2006 A1 - Antonio DeSimone A1 - Hans Knuepfer A1 - Felix Otto AB - We are interested in thin-film samples in micromagnetism, where the magnetization m is a 2-d unit-length vector field. More precisely we are interested in transition layers which connect two opposite magnetizations, so called Néel walls. UR - http://hdl.handle.net/1963/2194 U1 - 2050 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - 4e-condensation in a fully frustrated Josephson junction diamond chain JF - Phys. Rev. B 73 (2006) 100502(R) Y1 - 2006 A1 - Matteo Rizzi A1 - Vittorio Cataudella A1 - Rosario Fazio AB -Fully frustrated one-dimensional diamond Josephson chains have been shown [B. Dou\\\\c{c}ot and J. Vidal, Phys. Rev. Lett. {\\\\bf 88}, 227005 (2002)] to posses a remarkable property: The superfluid phase occurs through the condensation of pairs of Cooper pairs. By means of Monte Carlo simulations we analyze quantitatively the Insulator to $4e$-Superfluid transition. We determine the location of the critical point and discuss the behaviour of the phase-phase correlators. For comparison we also present the case of a diamond chain at zero and 1/3 frustration where the standard $2e$-condensation is observed.

UR - http://hdl.handle.net/1963/2400 U1 - 2297 U2 - Physics U3 - Condensed Matter Theory ER - TY - RPRT T1 - An artificial viscosity approach to quasistatic crack growth Y1 - 2006 A1 - Rodica Toader A1 - Chiara Zanini AB - We introduce a new model of irreversible quasistatic crack growth in which the evolution of cracks is the limit of a suitably modified $\\\\epsilon$-gradient flow of the energy functional, as the \\\"viscosity\\\" parameter $\\\\epsilon$ tends to zero. UR - http://hdl.handle.net/1963/1850 U1 - 2367 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A Birkhoff-Lewis-Type Theorem for Some Hamiltonian PDEs JF - SIAM J. Math. Anal. 37 (2006) 83-102 Y1 - 2006 A1 - Dario Bambusi A1 - Massimiliano Berti AB - In this paper we give an extension of the Birkhoff--Lewis theorem to some semilinear PDEs. Accordingly we prove existence of infinitely many periodic orbits with large period accumulating at the origin. Such periodic orbits bifurcate from resonant finite dimensional invariant tori of the fourth order normal form of the system. Besides standard nonresonance and nondegeneracy assumptions, our main result is obtained assuming a regularizing property of the nonlinearity. We apply our main theorem to a semilinear beam equation and to a nonlinear Schr\\\\\\\"odinger equation with smoothing nonlinearity. UR - http://hdl.handle.net/1963/2159 U1 - 2085 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Bound and ground states of coupled nonlinear Schrödinger equations JF - C. R. Acad. Sci. Paris, Ser. I 342 (2006) 453-458 Y1 - 2006 A1 - Antonio Ambrosetti A1 - Eduardo Colorado AB - We prove existence of bound and ground states of some systems of coupled nonlinear Schrodinger equations. UR - http://hdl.handle.net/1963/2149 U1 - 2094 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Bound states of Nonlinear Schroedinger Equations with Potentials Vanishing at Infinity JF - J. Anal. Math. 98 (2006) 317-348 Y1 - 2006 A1 - Antonio Ambrosetti A1 - Andrea Malchiodi A1 - David Ruiz UR - http://hdl.handle.net/1963/1756 U1 - 2788 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On Bressan\\\'s conjecture on mixing properties of vector fields JF - Self-Similar Solutions of Nonlinear PDE / Ed. Piotr Biler and Grzegorz Karch. - Banach Center Publ. 74 (2006) 13-31 Y1 - 2006 A1 - Stefano Bianchini UR - http://hdl.handle.net/1963/1806 U1 - 2408 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - A Canonical Frame for Nonholonomic Rank Two Distributions of Maximal Class Y1 - 2006 A1 - Boris Doubrov A1 - Igor Zelenko AB - In 1910 E. Cartan constructed the canonical frame and found the most symmetric case for maximally nonholonomic rank 2 distributions in R5. We solve the analogous problems for rank 2 distributions in Rn for arbitrary n > 5. Our method is a kind of symplectification of the problem and it is completely different from the Cartan method of equivalence. JF - C. R. Math. Acad. Sci. Paris 342 (2006) 589-594 UR - http://hdl.handle.net/1963/1712 U1 - 2439 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Cantor families of periodic solutions for completely resonant nonlinear wave equations JF - Duke Math. J. 134 (2006) 359-419 Y1 - 2006 A1 - Massimiliano Berti A1 - Philippe Bolle AB - We prove the existence of small amplitude, $2\\\\pi \\\\slash \\\\om$-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions, for any frequency $ \\\\om $ belonging to a Cantor-like set of positive measure and for a new set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem. In spite of the complete resonance of the equation we show that we can still reduce the problem to a {\\\\it finite} dimensional bifurcation equation. Moreover, a new simple approach for the inversion of the linearized operators required by the Nash-Moser scheme is developed. It allows to deal also with nonlinearities which are not odd and with finite spatial regularity. UR - http://hdl.handle.net/1963/2161 U1 - 2083 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Classification of stable time-optimal controls on 2-manifolds JF - J. Math. Sci. 135 (2006) 3109-3124 Y1 - 2006 A1 - Ugo Boscain A1 - Igor Nikolaev A1 - Benedetto Piccoli UR - http://hdl.handle.net/1963/2196 U1 - 2048 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Common Polynomial Lyapunov Functions for Linear Switched Systems JF - SIAM J. Control Optim. 45 (2006) 226-245 Y1 - 2006 A1 - Paolo Mason A1 - Ugo Boscain A1 - Yacine Chitour AB - In this paper, we consider linear switched systems $\\\\dot x(t)=A_{u(t)} x(t)$, $x\\\\in\\\\R^n$, $u\\\\in U$, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching ({\\\\bf UAS} for short). We first prove that, given a {\\\\bf UAS} system, it is always possible to build a common polynomial Lyapunov function. Then our main result is that the degree of that common polynomial Lyapunov function is not uniformly bounded over all the {\\\\bf UAS} systems. This result answers a question raised by Dayawansa and Martin. A generalization to a class of piecewise-polynomial Lyapunov functions is given. UR - http://hdl.handle.net/1963/2181 U1 - 2063 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Compactness of solutions to some geometric fourth-order equations JF - J. Reine Angew. Math. 594 (2006) 137-174 Y1 - 2006 A1 - Andrea Malchiodi AB - We prove compactness of solutions to some fourth order equations with exponential nonlinearities on four manifolds. The proof is based on a refined bubbling analysis, for which the main estimates are given in integral form. Our result is used in a subsequent paper to find critical points (via minimax arguments) of some geometric functional, which give rise to conformal metrics of constant $Q$-curvature. As a byproduct of our method, we also obtain compactness of such metrics. UR - http://hdl.handle.net/1963/2126 U1 - 2117 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Concentration at manifolds of arbitrary dimension for a singularly perturbed Neumann problem JF - Atti Accad. Naz Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 17 (2006) 279-290 Y1 - 2006 A1 - Fethi Mahmoudi A1 - Andrea Malchiodi AB - We consider the equation $- \\\\e^2 \\\\D u + u = u^p$ in $\\\\O \\\\subseteq \\\\R^N$, where $\\\\O$ is open, smooth and bounded, and we prove concentration of solutions along $k$-dimensional minimal submanifolds of $\\\\pa \\\\O$, for $N \\\\geq 3$ and for $k \\\\in \\\\{1, \\\\dots, N-2\\\\}$. We impose Neumann boundary conditions, assuming $1<\\\\frac{N-k+2}{N-k-2}$ and $\\\\e \\\\to 0^+$. This result settles in full generality a phenomenon previously considered only in the particular case $N = 3$ and $k = 1$. UR - http://hdl.handle.net/1963/2170 U1 - 2074 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Conservative Solutions to a Nonlinear Variational Wave Equation JF - Comm. Math. Phys. 266 (2006) 471-497 Y1 - 2006 A1 - Alberto Bressan A1 - Zheng Yuxi AB - We establish the existence of a conservative weak solution to the Cauchy problem for the nonlinear variational wave equation $u_{tt} - c(u)(c(u)u_x)_x=0$, for initial data of finite energy. Here $c(\\\\cdot)$ is any smooth function with uniformly positive bounded values. UR - http://hdl.handle.net/1963/2184 U1 - 2060 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The Dirichlet problem for H-systems with small boundary data: blowup phenomena and nonexistence results JF - Arch. Ration. Mech. Anal. 181 (2006) 1-42 Y1 - 2006 A1 - Paolo Caldiroli A1 - Roberta Musina UR - http://hdl.handle.net/1963/2252 U1 - 1995 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - An estimation of the controllability time for single-input systems on compact Lie Groups JF - ESAIM Control Optim. Calc. Var. 12 (2006) 409-441 Y1 - 2006 A1 - Andrei A. Agrachev A1 - Thomas Chambrion AB - Geometric control theory and Riemannian techniques are used to describe the reachable set at time t of left invariant single-input control systems on semi-simple compact Lie groups and to estimate the minimal time needed to reach any point from identity. This method provides an effective way to give an upper and a lower bound for the minimal time needed to transfer a controlled quantum system with a drift from a given initial position to a given final position. The bounds include diameters of the flag manifolds; the latter are also explicitly computed in the paper. UR - http://hdl.handle.net/1963/2135 U1 - 2108 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Experimental and modeling studies of desensitization of P2X3 receptors. JF - Molecular pharmacology. 2006 Jul; 70(1):373-82 Y1 - 2006 A1 - Elena Sokolova A1 - Andrei Skorinkin A1 - Igor Moiseev A1 - Andrei A. Agrachev A1 - Andrea Nistri A1 - Rashid Giniatullin AB - The function of ATP-activated P2X3 receptors involved in pain sensation is modulated by desensitization, a phenomenon poorly understood. The present study used patch-clamp recording from cultured rat or mouse sensory neurons and kinetic modeling to clarify the properties of P2X3 receptor desensitization. Two types of desensitization were observed, a fast process (t1/2 = 50 ms; 10 microM ATP) following the inward current evoked by micromolar agonist concentrations, and a slow process (t1/2 = 35 s; 10 nM ATP) that inhibited receptors without activating them. We termed the latter high-affinity desensitization (HAD). Recovery from fast desensitization or HAD was slow and agonist-dependent. When comparing several agonists, there was analogous ranking order for agonist potency, rate of desensitization and HAD effectiveness, with 2-methylthioadenosine triphosphate the strongest and beta,gamma-methylene-ATP the weakest. HAD was less developed with recombinant (ATP IC50 = 390 nM) than native P2X3 receptors (IC50 = 2.3 nM). HAD could also be induced by nanomolar ATP when receptors seemed to be nondesensitized, indicating that resting receptors could express high-affinity binding sites. Desensitization properties were well accounted for by a cyclic model in which receptors could be desensitized from either open or closed states. Recovery was assumed to be a multistate process with distinct kinetics dependent on the agonist-dependent dissociation rate from desensitized receptors. Thus, the combination of agonist-specific mechanisms such as desensitization onset, HAD, and resensitization could shape responsiveness of sensory neurons to P2X3 receptor agonists. By using subthreshold concentrations of an HAD-potent agonist, it might be possible to generate sustained inhibition of P2X3 receptors for controlling chronic pain. PB - the American Society for Pharmacology and Experimental Therapeutics UR - http://hdl.handle.net/1963/4974 U1 - 4799 U2 - Neuroscience U3 - Neurobiology U4 - -1 ER - TY - JOUR T1 - Forced vibrations of wave equations with non-monotone nonlinearities JF - Ann. Inst. H. Poincaré Anal. Non Linéaire 23 (2006) 439-474 Y1 - 2006 A1 - Massimiliano Berti A1 - Luca Biasco AB - We prove existence and regularity of periodic in time solutions of completely resonant nonlinear forced wave equations with Dirichlet boundary conditions for a large class of non-monotone forcing terms. Our approach is based on a variational Lyapunov-Schmidt reduction. It turns out that the infinite dimensional bifurcation equation exhibits an intrinsic lack of compactness. We solve it via a minimization argument and a-priori estimate methods inspired to regularity theory of Rabinowitz. UR - http://hdl.handle.net/1963/2160 U1 - 2084 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Fundamental form and Cartan tensor of (2,5)-distributions coincide JF - J. Dyn. Control Syst. 12 (2006) 247-276 Y1 - 2006 A1 - Igor Zelenko AB - In our previous paper for generic rank 2 vector distributions on n-dimensional manifold (n greater or equal to 5) we constructed a special differential invariant, the fundamental form. In the case n=5 this differential invariant has the same algebraic nature, as the covariant binary biquadratic form, constructed by E.Cartan in 1910, using his ``reduction- prolongation\\\'\\\' procedure (we call this form Cartan\\\'s tensor). In the present paper we prove that our fundamental form coincides (up to constant factor -35) with Cartan\\\'s tensor. This result explains geometric reason for existence of Cartan\\\'s tensor (originally this tensor was obtained by very sophisticated algebraic manipulations) and gives the true analogs of this tensor in Riemannian geometry. In addition, as a part of the proof, we obtain a new useful formula for Cartan\\\'s tensor in terms of structural functions of any frame naturally adapted to the distribution. UR - http://hdl.handle.net/1963/2187 U1 - 2057 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on distributions of corank 1 JF - J. Math. Sci. 135 (2006) 3168-3194 Y1 - 2006 A1 - Igor Zelenko AB - The present paper is devoted to the problem of (local) geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on generic corank 1 distributions. Using Pontryagin Maximum Principle, we treat Riemannian and sub-Riemannian cases in an unified way and obtain some algebraic necessary conditions for the geodesic equivalence of (sub-)Riemannian metrics. In this way first we obtain a new elementary proof of classical Levi-Civita\\\'s Theorem about the classification of all Riemannian geodesically equivalent metrics in a neighborhood of so-called regular (stable) point w.r.t. these metrics. Secondly we prove that sub-Riemannian metrics on contact distributions are geodesically equivalent iff they are constantly proportional. Then we describe all geodesically equivalent sub-Riemannian metrics on quasi-contact distributions. Finally we make the classification of all pairs of geodesically equivalent Riemannian metrics on a surface, which proportional in an isolated point. This is the simplest case, which was not covered by Levi-Civita\\\'s Theorem. UR - http://hdl.handle.net/1963/2205 U1 - 2039 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Glimm interaction functional for BGK schemes Y1 - 2006 A1 - Stefano Bianchini UR - http://hdl.handle.net/1963/1770 U1 - 2774 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Infinite Horizon Noncooperative Differential Games Y1 - 2006 A1 - Alberto Bressan A1 - Fabio Simone Priuli AB - For a non-cooperative differential game, the value functions of the various players satisfy a system of Hamilton-Jacobi equations. In the present paper, we consider a class of infinite-horizon games with nonlinear costs exponentially discounted in time. By the analysis of the value\\nfunctions, we establish the existence of Nash equilibrium solutions in feedback form and provide results and counterexamples on their uniqueness and stability. JF - J. Differential Equations 227 (2006) 230-257 UR - http://hdl.handle.net/1963/1720 U1 - 2431 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - An instability of the Godunov scheme JF - Comm. Pure Appl. Math. 59 (2006) 1604-1638 Y1 - 2006 A1 - Alberto Bressan A1 - Helge Kristian Jenssen A1 - Paolo Baiti AB - We construct a solution to a $2\\\\times 2$ strictly hyperbolic system of conservation laws, showing that the Godunov scheme \\\\cite{Godunov59} can produce an arbitrarily large amount of oscillations. This happens when the speed of a shock is close to rational, inducing a resonance with the grid. Differently from the Glimm scheme or the vanishing viscosity method, for systems of conservation laws our counterexample indicates that no a priori BV bounds or $L^1$ stability estimates can in general be valid for finite difference schemes. UR - http://hdl.handle.net/1963/2183 U1 - 2061 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On Palais-Smale sequences for H-systems: some examples JF - Adv. Differential Equations 11 (2006) 931-960 Y1 - 2006 A1 - Paolo Caldiroli A1 - Roberta Musina AB - We exhibit a series of examples of Palais-Smale sequences for the Dirichlet problem associated to the mean curvature equation with null boundary condition, and we show that in the case of nonconstant mean curvature functions different kinds of blow up phenomena appear and Palais-Smale sequences may have quite wild behaviour. UR - http://hdl.handle.net/1963/2157 U1 - 2087 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Q-curvature flow on S^4 JF - J. Differential Geom. 73 (2006) 1-44 Y1 - 2006 A1 - Andrea Malchiodi A1 - Michael Struwe UR - http://hdl.handle.net/1963/2193 U1 - 2051 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasi-periodic solutions of completely resonant forced wave equations JF - Comm. Partial Differential Equations 31 (2006) 959 - 985 Y1 - 2006 A1 - Massimiliano Berti A1 - Michela Procesi AB - We prove existence of quasi-periodic solutions with two frequencies of completely resonant, periodically forced nonlinear wave equations with periodic spatial boundary conditions. We consider both the cases the forcing frequency is: (Case A) a rational number and (Case B) an irrational number. UR - http://hdl.handle.net/1963/2234 U1 - 2010 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic evolution problems for linearly elastic-perfectly plastic materials JF - Arch. Ration. Mech. Anal. 180 (2006) 237-291 Y1 - 2006 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Maria Giovanna Mora AB - The problem of quasistatic evolution in small strain associative elastoplasticity is studied in the framework of the variational theory for rate-independent processes. Existence of solutions is proved through the use of incremental variational problems in spaces of functions with bounded deformation. This provides a new approximation result for the solutions of the quasistatic evolution problem, which are shown to be absolutely continuous in time. Four equivalent formulations of the problem in rate form are derived. A strong formulation of the flow rule is obtained by introducing a precise definition of the stress on the singular set of the plastic strain. UR - http://hdl.handle.net/1963/2129 U1 - 2114 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Radial solutions concentrating on spheres of nonlinear Schrödinger equations with vanishing potentials JF - Proc. Roy. Soc. Edinburgh Sect. A 136 (2006) 889-907 Y1 - 2006 A1 - Antonio Ambrosetti A1 - David Ruiz AB - We prove the existence of radial solutions of 1.2) concentrating at a sphere for potentials which might be zero and might decay to zero at\\r\\ninfinity. The proofs use a perturbation technique in a variational setting, through a Lyapunov-Schmidt reduction. UR - http://hdl.handle.net/1963/1755 U1 - 2789 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - Recent analytical developments in micromagnetics T2 - The science of hysteresis / eds. Giorgio Bertotti, Isaak D. Mayergoyz. - Amsterdam: Elsevier, 2006. Vol.2, 269-381. Y1 - 2006 A1 - Antonio DeSimone A1 - Robert V. Kohn A1 - Stefan Müller A1 - Felix Otto JF - The science of hysteresis / eds. Giorgio Bertotti, Isaak D. Mayergoyz. - Amsterdam: Elsevier, 2006. Vol.2, 269-381. SN - 978-0-12-480874-4 UR - http://hdl.handle.net/1963/2230 U1 - 2014 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Stability of planar nonlinear switched systems Y1 - 2006 A1 - Ugo Boscain A1 - Grégoire Charlot A1 - Mario Sigalotti AB - We consider the time-dependent nonlinear system ˙ q(t) = u(t)X(q(t)) + (1 − u(t))Y (q(t)), where q ∈ R2, X and Y are two smooth vector fields, globally asymptotically stable at the origin and u : [0,∞) → {0, 1} is an arbitrary measurable function. Analysing the topology of the set where X and Y are parallel, we give some sufficient and some necessary conditions for global asymptotic stability, uniform with respect to u(.). Such conditions can be verified without any integration or construction of a Lyapunov function, and they are robust under small perturbations of the vector fields. JF - Discrete Contin. Dyn. Syst. 15 (2006) 415-432 UR - http://hdl.handle.net/1963/1710 U1 - 2441 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Time Minimal Trajectories for a Spin 1/2 Particle in a Magnetic field Y1 - 2006 A1 - Ugo Boscain A1 - Paolo Mason AB - In this paper we consider the minimum time population transfer problem for the z-component\\nof the spin of a (spin 1/2) particle driven by a magnetic field, controlled along the x axis, with bounded amplitude. On the Bloch sphere (i.e. after a suitable Hopf projection), this problem can be attacked with techniques of optimal syntheses on 2-D manifolds. Let (-E,E) be the two energy levels, and |omega (t)| ≤ M the bound on the field amplitude. For each couple of values E and M, we determine the time optimal synthesis starting from the level -E and we provide the explicit expression of the time optimal trajectories steering the state one to the state two, in terms of a parameter that can be computed solving numerically a suitable equation. For M/E << 1, every time optimal trajectory is bang-bang and in particular the corresponding control is periodic with frequency of the order of the resonance frequency wR = 2E. On the other side, for M/E > 1, the time optimal trajectory steering the state one to the state two is bang-bang with exactly one switching. Fixed E we also prove that for M → ∞ the time needed to reach the state two tends to zero. In the case M/E > 1 there are time optimal trajectories containing a singular arc. Finally we compare these results with some known results of Khaneja, Brockett and Glaser and with those obtained by controlling the magnetic field both on the x and y directions (or with one external field, but in the rotating wave approximation). As byproduct we prove that the qualitative shape of the time optimal synthesis presents different patterns, that cyclically alternate as M/E → 0, giving a partial proof of a conjecture formulated in a previous paper. JF - Journal of Mathematical Physics 47, 062101 (2006) UR - http://hdl.handle.net/1963/1734 U1 - 2418 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On variational approach to differential invariants of rank two distributions JF - Differential Geom. Appl. 24 (2006) 235-259 Y1 - 2006 A1 - Igor Zelenko AB - n the present paper we construct differential invariants for generic rank 2 vector distributions on n-dimensional manifold. In the case n=5 (the first case containing functional parameters) E. Cartan found in 1910 the covariant fourth-order tensor invariant for such distributions, using his \\\"reduction-prolongation\\\" procedure. After Cartan\\\'s work the following questions remained open: first the geometric reason for existence of Cartan\\\'s tensor was not clear; secondly it was not clear how to generalize this tensor to other classes of distributions; finally there were no explicit formulas for computation of Cartan\\\'s tensor. Our paper is the first in the series of papers, where we develop an alternative approach, which gives the answers to the questions mentioned above. It is based on the investigation of dynamics of the field of so-called abnormal extremals (singular curves) of rank 2 distribution and on the general theory of unparametrized curves in the Lagrange Grassmannian, developed in our previous works with A. Agrachev . In this way we construct the fundamental form and the projective Ricci curvature of rank 2 vector distributions for arbitrary n greater than 4.\\nFor n=5 we give an explicit method for computation of these invariants and demonstrate it on several examples. In our next paper we show that in the case n=5 our fundamental form coincides with Cartan\\\'s tensor. UR - http://hdl.handle.net/1963/2188 U1 - 2056 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Variational problems in fracture mechanics Y1 - 2006 A1 - Gianni Dal Maso AB - We present some recent existence results for the variational model of crack growth in brittle materials proposed by Francfort and Marigo in 1998. These results, obtained in collaboration with Francfort and Toader, cover the case of arbitrary space dimension with a general quasiconvex bulk energy and with prescribed boundary deformations and applied loads. UR - http://hdl.handle.net/1963/1816 U1 - 2398 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Asymptotic Morse theory for the equation $\\\\Delta v=2v\\\\sb x\\\\wedge v\\\\sb y$ JF - Comm. Anal. Geom. 13 (2005) 187-252 Y1 - 2005 A1 - Sagun Chanillo A1 - Andrea Malchiodi AB - Given a smooth bounded domain ${\\\\O}\\\\subseteq \\\\R^2$, we consider the equation $\\\\D v = 2 v_x \\\\wedge v_y$ in $\\\\O$, where $v: {\\\\O}\\\\to \\\\R^3$. We prescribe Dirichlet boundary datum, and consider the case in which this datum converges to zero. An asymptotic study of the corresponding Euler functional is performed, analyzing multiple-bubbling phenomena. This allows us to settle a particular case of a question raised by H. Brezis and J.M. Coron. PB - International Press UR - http://hdl.handle.net/1963/3533 U1 - 731 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the attainable set for Temple class systems with boundary controls JF - SIAM J. Control Optim. 43 (2005) 2166-2190 Y1 - 2005 A1 - Fabio Ancona A1 - Giuseppe Maria Coclite AB - Consider the initial-boundary value problem for a strictly hyperbolic, genuinely nonlinear, Temple class system of conservation laws % $$ u_t+f(u)_x=0, \\\\qquad u(0,x)=\\\\ov u(x), \\\\qquad {{array}{ll} &u(t,a)=\\\\widetilde u_a(t), \\\\noalign{\\\\smallskip} &u(t,b)=\\\\widetilde u_b(t), {array}. \\\\eqno(1) $$ on the domain $\\\\Omega =\\\\{(t,x)\\\\in\\\\R^2 : t\\\\geq 0, a \\\\le x\\\\leq b\\\\}.$ We study the mixed problem (1) from the point of view of control theory, taking the initial data $\\\\bar u$ fixed, and regarding the boundary data $\\\\widetilde u_a, \\\\widetilde u_b$ as control functions that vary in prescribed sets $\\\\U_a, \\\\U_b$, of $\\\\li$ boundary controls. In particular, we consider the family of configurations $$ \\\\A(T) \\\\doteq \\\\big\\\\{u(T,\\\\cdot); ~ u {\\\\rm is a sol. to} (1), \\\\quad \\\\widetilde u_a\\\\in \\\\U_a, \\\\widetilde u_b \\\\in \\\\U_b \\\\big\\\\} $$ that can be attained by the system at a given time $T>0$, and we give a description of the attainable set $\\\\A(T)$ in terms of suitable Oleinik-type conditions. We also establish closure and compactness of the set $\\\\A(T)$ in the $lu$ topology. PB - SISSA Library UR - http://hdl.handle.net/1963/1581 U1 - 2537 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the Blow-up for a Discrete Boltzmann Equation in the Plane JF - Discrete Contin. Dyn. Syst. 13 (2005) 1-12 Y1 - 2005 A1 - Alberto Bressan A1 - Massimo Fonte AB - We study the possibility of finite-time blow-up for a two dimensional Broadwell model. In a set of rescaled variables, we prove that no self-similar blow-up solution exists, and derive some a priori bounds on the blow-up rate. In the final section, a possible blow-up scenario is discussed. UR - http://hdl.handle.net/1963/2244 U1 - 2000 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - Complete systems of invariants for rank 1 curves in Lagrange Grassmannians T2 - Differential geometry and its applications, 367-382, Matfyzpress, Prague, 2005 Y1 - 2005 A1 - Igor Zelenko AB - Curves in Lagrange Grassmannians naturally appear when one studies intrinsically \\\"the Jacobi equations for extremals\\\", associated with control systems and geometric structures. In this way one reduces the problem of construction of the curvature-type invariants for these objects to the much more concrete problem of finding of invariants of curves in Lagrange Grassmannians w.r.t. the action of the linear Symplectic group. In the present paper we develop a new approach to differential geometry of so-called rank 1 curves in Lagrange Grassmannian, i.e., the curves with velocities being rank one linear mappings (under the standard identification of the tangent space to a point of the Lagrange Grassmannian with an appropriate space of linear mappings). The curves of this class are associated with \\\"the Jacobi equations for extremals\\\", corresponding to control systems with scalar control and to rank 2 vector distributions. In particular, we construct the tuple of m principal invariants, where m is equal to half of dimension of the ambient linear symplectic space, such that for a given tuple of arbitrary m smooth functions there exists the unique, up to a symplectic transformation, rank 1 curve having this tuple, as the tuple of the principal invariants. This approach extends and essentially simplifies some results of our previous paper (J. Dynamical and Control Systems, 8, 2002, No. 1, 93-140), where only the uniqueness part was proved and in rather cumbersome way. It is based on the construction of the new canonical moving frame with the most simple structural equation. JF - Differential geometry and its applications, 367-382, Matfyzpress, Prague, 2005 UR - http://hdl.handle.net/1963/2310 N1 - Proceedings of 9th Conference on Differential Geometry and its Applications, Prague 2004 U1 - 1706 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Concentration at curves for a singularly perturbed Neumann problem in three-dimensional domains JF - Geometric and Functional Analysis 15 (6) 1162-1222 (2005) Y1 - 2005 A1 - Andrea Malchiodi AB - We prove new concentration phenomena for the equation −ɛ2 Δu + u = up in a smooth bounded domain R3 and with Neumann boundary conditions. Here p > 1 and ɛ > 0 is small. We show that concentration of solutions occurs at some geodesics of ∂Ω when ɛ → 0. PB - Springer UR - http://hdl.handle.net/1963/4866 U1 - 4645 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Conservation laws with time dependent discontinuous coefficients JF - SIAM J. Math. Anal. 36 (2005) 1293-1309 Y1 - 2005 A1 - Giuseppe Maria Coclite A1 - Nils Henrik Risebro AB - We consider scalar conservation laws where the flux function depends discontinuously on both the spatial and temporal location. Our main results are the existence and well-posedness of an entropy solution to the Cauchy problem. The existence is established by showing that a sequence of front tracking approximations is compact in L1, and that the limits are entropy solutions. Then, using the definition of an entropy solution taken form [11], we show that the solution operator is L1 contractive. These results generalize the corresponding results from [16] and [11]. PB - SISSA Library UR - http://hdl.handle.net/1963/1666 U1 - 2452 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On curvatures and focal points of distributions of dynamical Lagrangian distributions and their reductions by first integrals JF - J. Dyn. Control Syst. 11 (2005) 297-327 Y1 - 2005 A1 - Andrei A. Agrachev A1 - Natalia N. Chtcherbakova A1 - Igor Zelenko AB - Pairs (Hamiltonian system, Lagrangian distribution), called dynamical Lagrangian distributions, appear naturally in Differential Geometry, Calculus of Variations and Rational Mechanics. The basic differential invariants of a dynamical Lagrangian distribution w.r.t. the action of the group of symplectomorphisms of the ambient symplectic manifold are the curvature operator and the curvature form. These invariants can be seen as generalizations of the classical curvature tensor in Riemannian Geometry. In particular, in terms of these invariants one can localize the focal points along extremals of the corresponding variational problems. In the present paper we study the behavior of the curvature operator, the curvature form and the focal points of a dynamical Lagrangian distribution after its reduction by arbitrary first integrals in involution. The interesting phenomenon is that the curvature form of so-called monotone increasing Lagrangian dynamical distributions, which appear naturally in mechanical systems, does not decrease after reduction. It also turns out that the set of focal points to the given point w.r.t. the monotone increasing dynamical Lagrangian distribution and the corresponding set of focal points w.r.t. its reduction by one integral are alternating sets on the corresponding integral curve of the Hamiltonian system of the considered dynamical distributions. Moreover, the first focal point corresponding to the reduced Lagrangian distribution comes before any focal point related to the original dynamical distribution. We illustrate our results on the classical $N$-body problem. UR - http://hdl.handle.net/1963/2254 U1 - 1993 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A fourth order uniformization theorem on some four manifolds with large total Q-curvature JF - C. R. Acad. Sci. Paris, Ser. I 340 (2005) 341-346. Y1 - 2005 A1 - Zindine Djadli A1 - Andrea Malchiodi AB - Given a four-dimensional manifold (M,g), we study the existence of a conformal metric for which the Q-curvature, associated to a conformally invariant fourth-order operator (the Paneitz operator), is constant. Using a topological argument, we obtain a new result in cases which were still open. PB - Elsevier UR - http://hdl.handle.net/1963/4868 U1 - 4649 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Global solutions of the Hunter-Saxton equation JF - SIAM J. Math. Anal. 37 (2005) 996-1026 Y1 - 2005 A1 - Alberto Bressan A1 - Adrian Constantin AB - We construct a continuous semigroup of weak, dissipative solutions to a nonlinear partial differential equations modeling nematic liquid crystals. A new distance functional, determined by a problem of optimal transportation, yields sharp estimates on the continuity of solutions with respect to the initial data. UR - http://hdl.handle.net/1963/2256 U1 - 1991 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Ground states of nonlinear Schroedinger equations with potentials vanishing at infinity JF - J. Eur. Math. Soc. 7 (2005) 117-144 Y1 - 2005 A1 - Antonio Ambrosetti A1 - Veronica Felli A1 - Andrea Malchiodi AB - We deal with a class on nonlinear Schr\\\\\\\"odinger equations \\\\eqref{eq:1} with potentials $V(x)\\\\sim |x|^{-\\\\a}$, $0<\\\\a<2$, and $K(x)\\\\sim |x|^{-\\\\b}$, $\\\\b>0$. Working in weighted Sobolev spaces, the existence of ground states $v_{\\\\e}$ belonging to $W^{1,2}(\\\\Rn)$ is proved under the assumption that $p$ satisfies \\\\eqref{eq:p}. Furthermore, it is shown that $v_{\\\\e}$ are {\\\\em spikes} concentrating at a minimum of ${\\\\cal A}=V^{\\\\theta}K^{-2/(p-1)}$, where $\\\\theta= (p+1)/(p-1)-1/2$. UR - http://hdl.handle.net/1963/2352 U1 - 1664 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Hybrid necessary principle JF - SIAM J. Control Optim. 43 (2005) 1867-1887 Y1 - 2005 A1 - Mauro Garavello A1 - Benedetto Piccoli AB - We consider a hybrid control system and general optimal control problems for this system. We suppose that the switching strategy imposes restrictions on control sets and we provide necessary conditions for an optimal hybrid trajectory, stating a hybrid necessary principle (HNP). Our result generalizes various necessary principles available in the literature. PB - SIAM UR - http://hdl.handle.net/1963/1641 N1 - Proceedings of IFAC Conference on Analysis and Design of Hybrid Systems, Saint Malo, France U1 - 2477 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Minimal surfaces in pseudohermitian geometry JF - Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (5), 4 (2005) 129-177. Y1 - 2005 A1 - Jih-Hsin Cheng A1 - JennFang Hwang A1 - Andrea Malchiodi A1 - Paul Yang AB - We consider surfaces immersed in three-dimensional pseudohermitian manifolds. We define the notion of (p-)mean curvature and of the associated (p-)minimal surfaces, extending some concepts previously given for the (flat) Heisenberg group. We interpret the p-mean curvature not only as the tangential sublaplacian of a defining function, but also as the curvature of a characteristic curve, and as a quantity in terms of calibration geometry. As a differential equation, the p-minimal surface equation is degenerate (hyperbolic and elliptic). To analyze the singular set, we formulate some {\em extension} theorems, which describe how the characteristic curves meet the singular set. This allows us to classify the entire solutions to this equation and to solve a Bernstein-type problem (for graphs over the $xy$-plane) in the Heisenberg group $H_1$. In $H_{1}$, identified with the Euclidean space $R^{3}$, the p-minimal surfaces are classical ruled surfaces with the rulings generated by Legendrian lines. We also prove a uniqueness theorem for the Dirichlet problem under a condition on the size of the singular set in two dimensions, and generalize to higher dimensions without any size control condition. We also show that there are no closed, connected, $C^{2}$ smoothly immersed constant p-mean curvature or p-minimal surfaces of genus greater than one in the standard $S^{3}.$ This fact continues to hold when $S^{3}$ is replaced by a general spherical pseudohermitian 3-manifold. PB - Scuola Normale Superiore UR - http://hdl.handle.net/1963/4579 U1 - 4347 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - On the Minimum Problem for Nonconvex Scalar Functionals JF - SIAM J. Math. Anal. 37 (2005) 982-995 Y1 - 2005 A1 - Sandro Zagatti AB - We study the minimum problem for scalar nonconvex functionals defined on Sobolev maps satisfying a Dirichlet boundary condition and refine well-known existence results under standard regularity assumptions. UR - http://hdl.handle.net/1963/2764 U1 - 1936 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Multiple clustered layer solutions for semilinear Neumann problems on a ball JF - Ann. Inst. H. Poincare Anal. Non Lineaire 22 (2005) 143-163 Y1 - 2005 A1 - Andrea Malchiodi A1 - Wei-Ming Ni A1 - Juncheng Wei PB - Elsevier UR - http://hdl.handle.net/1963/3532 U1 - 732 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Nonisotropic 3-level quantum systems: complete solutions for minimum time and minimum energy JF - Discrete Contin. Dyn. Syst. Ser. B 5 (2005) 957-990 Y1 - 2005 A1 - Ugo Boscain A1 - Thomas Chambrion A1 - Grégoire Charlot AB - We apply techniques of subriemannian geometry on Lie groups and of optimal synthesis on 2-D manifolds to the population transfer problem in a three-level quantum system driven by two laser pulses, of arbitrary shape and frequency. In the rotating wave approximation, we consider a nonisotropic model i.e. a model in which the two coupling constants of the lasers are different. The aim is to induce transitions from the first to the third level, minimizing 1) the time of the transition (with bounded laser amplitudes),\\n2) the energy of lasers (with fixed final time). After reducing the problem to real variables, for the purpose 1) we develop a theory of time optimal syntheses for distributional problem on 2-D-manifolds, while for the purpose 2) we use techniques of subriemannian geometry on 3-D Lie groups. The complete optimal syntheses are computed. UR - http://hdl.handle.net/1963/2259 U1 - 1988 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Nonlinear Schrödinger Equations with vanishing and decaying potentials Y1 - 2005 A1 - Antonio Ambrosetti A1 - Wang Zhi-Qiang JF - Differential Integral Equations 18 (2005), no. 12, 1321-1332 UR - http://hdl.handle.net/1963/1760 U1 - 2784 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - An Optimal Transportation Metric for Solutions of the Camassa-Holm Equation Y1 - 2005 A1 - Alberto Bressan A1 - Massimo Fonte AB - In this paper we construct a global, continuous flow of solutions to the Camassa-Holm equation on the entire space H1. Our solutions are conservative, in the sense that the total energy int[(u2 + u2x) dx] remains a.e. constant in time. Our new approach is based on a distance functional J(u, v), defined in terms of an optimal transportation problem, which satisfies d dtJ(u(t), v(t)) ≤ κ · J(u(t), v(t)) for every couple of solutions. Using this new distance functional, we can construct arbitrary solutions as the uniform limit of multi-peakon solutions, and prove a general uniqueness result. JF - Methods Appl. Anal. 12 (2005) 191-219 UR - http://hdl.handle.net/1963/1719 U1 - 2432 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Periodic solutions of nonlinear wave equations with non-monotone forcing terms JF - Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 16 (2005), no. 2, 117-124 Y1 - 2005 A1 - Massimiliano Berti A1 - Luca Biasco PB - Accademia Nazionale dei Lincei UR - http://hdl.handle.net/1963/4581 U1 - 4349 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Quasi-periodic oscillations for wave equations under periodic forcing JF - Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 16 (2005), no. 2, 109-116 Y1 - 2005 A1 - Massimiliano Berti A1 - Michela Procesi PB - Accademia Nazionale dei Lincei UR - http://hdl.handle.net/1963/4583 U1 - 4350 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Quasistatic Crack Growth in Nonlinear Elasticity JF - Arch. Ration. Mech. Anal. 176 (2005) 165-225 Y1 - 2005 A1 - Gianni Dal Maso A1 - Gilles A. Francfort A1 - Rodica Toader AB - In this paper, we prove a new existence result for a variational model of crack growth in brittle materials proposed in [15]. We consider the case of $n$-dimensional finite elasticity, for an arbitrary $n\\\\ge1$, with a quasiconvex bulk energy and with prescribed boundary deformations and applied loads, both depending on time. UR - http://hdl.handle.net/1963/2293 U1 - 1723 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Regularity properties of optimal trajectories of single-input control systems in dimension three JF - Journal of Mathematical Sciences 126 (2005) 1561-1573 Y1 - 2005 A1 - Mario Sigalotti AB - Let q=f(q)+ug(q) be a smooth control system on a three-dimensional manifold. Given a point q 0 of the manifold at which the iterated Lie brackets of f and g satisfy some prescribed independence condition, we analyze the structure of a control function u(t) corresponding to a time-optimal trajectory lying in a neighborhood of q 0. The control turns out to be the concatenation of some bang-bang and some singular arcs. More general optimality criteria than time-optimality are considered. The paper is a step toward to the analysis of generic single-input systems affine in the control in dimension 3. The main techniques used are second-order optimality conditions and, in particular, the index of the second variation of the switching times for bang-bang trajectories. PB - Springer UR - http://hdl.handle.net/1963/4794 U1 - 4564 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Self-similar folding patterns and energy scaling in compressed elastic sheets JF - Comput. Methods Appl. Mech. Engrg. 194 (2005) 2534-2549 Y1 - 2005 A1 - Sergio Conti A1 - Antonio DeSimone A1 - Stefan Müller AB - Thin elastic sheets under isotropic compression, such as for example blisters formed by thin films which debonded from the substrate, can exhibit remarkably complex folding patterns. We discuss the scaling of the elastic energy with respect to the film thickness, and show that in certain regimes the optimal energy scaling can be reached\\nby self-similar folding patterns that refine towards the boundary, in agreement with experimental observations. We then extend the analysis\\nto anisotropic compression, and discuss a simplified scalar model which suggests the presence of a transition between a regime where\\nthe deformation is governed by global properties of the domain and another one where the direction of maximal compression dominates and the scale of the folds is mainly determined by the distance to the boundary in the direction of the folds themselves. PB - Elsevier UR - http://hdl.handle.net/1963/3000 U1 - 1333 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - A short introduction to optimal control T2 - Contrôle non linéaire et applications: Cours donnés à l\\\'école d\\\'été du Cimpa de l\\\'Université de Tlemcen / Sari Tewfit [ed.]. - Paris: Hermann, 2005 Y1 - 2005 A1 - Ugo Boscain A1 - Benedetto Piccoli JF - Contrôle non linéaire et applications: Cours donnés à l\\\'école d\\\'été du Cimpa de l\\\'Université de Tlemcen / Sari Tewfit [ed.]. - Paris: Hermann, 2005 SN - 2 7056 6511 0 UR - http://hdl.handle.net/1963/2257 U1 - 1990 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - ABST T1 - Solutions of Neumann problems in domains with cracks and applications to fracture mechanics Y1 - 2005 A1 - Gianni Dal Maso UR - http://hdl.handle.net/1963/1684 U1 - 79 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Stability of solutions of quasilinear parabolic equations JF - J. Math. Anal. Appl. 308 (2005) 221-239 Y1 - 2005 A1 - Giuseppe Maria Coclite A1 - Helge Holden AB - We bound the difference between solutions $u$ and $v$ of $u_t = a\\\\Delta u+\\\\Div_x f+h$ and $v_t = b\\\\Delta v+\\\\Div_x g+k$ with initial data $\\\\phi$ and $ \\\\psi$, respectively, by $\\\\Vert u(t,\\\\cdot)-v(t,\\\\cdot)\\\\Vert_{L^p(E)}\\\\le A_E(t)\\\\Vert \\\\phi-\\\\psi\\\\Vert_{L^\\\\infty(\\\\R^n)}^{2\\\\rho_p}+ B(t)(\\\\Vert a-b\\\\Vert_{\\\\infty}+ \\\\Vert \\\\nabla_x\\\\cdot f-\\\\nabla_x\\\\cdot g\\\\Vert_{\\\\infty}+ \\\\Vert f_u-g_u\\\\Vert_{\\\\infty} + \\\\Vert h-k\\\\Vert_{\\\\infty})^{\\\\rho_p} \\\\abs{E}^{\\\\eta_p}$. Here all functions $a$, $f$, and $h$ are smooth and bounded, and may depend on $u$, $x\\\\in\\\\R^n$, and $t$. The functions $a$ and $h$ may in addition depend on $\\\\nabla u$. Identical assumptions hold for the functions that determine the solutions $v$. Furthermore, $E\\\\subset\\\\R^n$ is assumed to be a bounded set, and $\\\\rho_p$ and $\\\\eta_p$ are fractions that depend on $n$ and $p$. The diffusion coefficients $a$ and $b$ are assumed to be strictly positive and the initial data are smooth. PB - Elsevier UR - http://hdl.handle.net/1963/2892 U1 - 1808 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Stress-dilatancy based modelling of granular materials and extensions to soils with crushable grains JF - Int. J. Numer. Anal. Met. 29 (2005) 73-101 Y1 - 2005 A1 - Antonio DeSimone A1 - Claudio Tamagnini AB - Stress-dilatancy relations have played a crucial role in the understanding of the mechanical behaviour of soils and in the development of realistic constitutive models for their response. Recent investigations on the mechanical behaviour of materials with crushable grains have called into question the validity of classical relations such as those used in critical state soil mechanics.\\nIn this paper, a method to construct thermodynamically consistent (isotropic, three-invariant) elasto-plastic models based on a given stress-dilatancy relation is discussed. Extensions to cover the case of granular materials with crushable grains are also presented, based on the interpretation of some classical model parameters (e.g. the stress ratio at critical state) as internal variables that evolve according to suitable hardening laws. UR - http://hdl.handle.net/1963/2165 U1 - 2079 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Time minimal trajectories for two-level quantum systems with drift Y1 - 2005 A1 - Ugo Boscain A1 - Paolo Mason AB - On a two-level quantum system driven by an external field, we consider the population transfer problem from the first to the second level, minimizing the time of transfer, with bounded field amplitude. On the Bloch sphere (i.e. after a suitable Hopf projection), this problem can be attacked with techniques of optimal syntheses on 2-D manifolds. JF - Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC \\\'05. 44th IEEE Conference on UR - http://hdl.handle.net/1963/1688 U1 - 2445 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Time Optimal Synthesis for Left-Invariant Control Systems on SO(3) JF - SIAM J. Control Optim. 44 (2005) 111-139 Y1 - 2005 A1 - Ugo Boscain A1 - Yacine Chitour AB - Consider the control system given by $\\\\dot x=x(f+ug)$, where $x\\\\in SO(3)$, $|u|\\\\leq 1$ and $f,g\\\\in so(3)$ define two perpendicular left-invariant vector fields normalized so that $\\\\|f\\\\|=\\\\cos(\\\\al)$ and $\\\\|g\\\\|=\\\\sin(\\\\al)$, $\\\\al\\\\in ]0,\\\\pi/4[$. In this paper, we provide an upper bound and a lower bound for $N(\\\\alpha)$, the maximum number of switchings for time-optimal trajectories. More precisely, we show that $N_S(\\\\al)\\\\leq N(\\\\al)\\\\leq N_S(\\\\al)+4$, where $N_S(\\\\al)$ is a suitable integer function of $\\\\al$ which for $\\\\al\\\\to 0$ is of order $\\\\pi/(4\\\\alpha).$ The result is obtained by studying the time optimal synthesis of a projected control problem on $R P^2$, where the projection is defined by an appropriate Hopf fibration. Finally, we study the projected control problem on the unit sphere $S^2$. It exhibits interesting features which will be partly rigorously derived and partially described by numerical simulations. UR - http://hdl.handle.net/1963/2258 U1 - 1989 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Traffic flow on a road network JF - SIAM J. Math. Anal. 36 (2005) 1862-1886 Y1 - 2005 A1 - Giuseppe Maria Coclite A1 - Benedetto Piccoli A1 - Mauro Garavello AB - This paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from conservation of the number of cars,\\ndefined on a road network that is a collection of roads with junctions. The evolution problem is underdetermined at junctions, hence we choose to have some fixed rules for the distribution of traffic plus an optimization criteria for the flux. We prove existence, uniqueness and stability of solutions to the Cauchy problem. Our method is based on wave front tracking approach, see [6], and works also for boundary data and time dependent coefficients of traffic distribution at junctions, so including traffic lights. PB - SISSA Library UR - http://hdl.handle.net/1963/1584 U1 - 2534 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Vanishing viscosity solutions of nonlinear hyperbolic systems JF - Ann. of Math. 161 (2005) 223-342 Y1 - 2005 A1 - Stefano Bianchini A1 - Alberto Bressan AB - We consider the Cauchy problem for a strictly hyperbolic, $n\\\\times n$ system in one space dimension: $u_t+A(u)u_x=0$, assuming that the initial data has small total variation.\\nWe show that the solutions of the viscous approximations $u_t+A(u)u_x=\\\\ve u_{xx}$ are defined globally in time and satisfy uniform BV estimates, independent of $\\\\ve$. Moreover, they depend continuously on the initial data in the $\\\\L^1$ distance, with a Lipschitz constant independent of $t,\\\\ve$. Letting $\\\\ve\\\\to 0$, these viscous solutions converge to a unique limit, depending Lipschitz continuously on the initial data. In the conservative case where $A=Df$ is the Jacobian of some flux function $f:\\\\R^n\\\\mapsto\\\\R^n$, the vanishing viscosity limits are precisely the unique entropy weak solutions to the system of conservation laws $u_t+f(u)_x=0$. PB - Annals of Mathematics UR - http://hdl.handle.net/1963/3074 U1 - 1259 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Wetting of rough surfaces: a homogenization approach JF - Proc. R. Soc. Lon. Ser. A 461 (2005) 79-97 Y1 - 2005 A1 - Antonio DeSimone A1 - Giovanni Alberti AB - The contact angle of a drop in equilibrium on a solid is strongly affected by the roughness of the surface on which it rests. We study the roughness-induced enhancement of the hydrophobic or hydrophilic properties of a solid surface through homogenization theory. By relying on a variational formulation of the problem, we show that the macroscopic contact angle is associated with the solution of two cell problems, giving the minimal energy per unit macroscopic area for a transition layer between the rough solid surface and a liquid or vapor phase. Our results are valid for both chemically heterogeneous and homogeneous surfaces. In the latter case, a very transparent structure emerges from the variational\\napproach: the classical laws of Wenzel and Cassie-Baxter give bounds for the optimal energy, and configurations of minimal energy are those leading to the smallest macroscopic contact angle in the hydrophobic case, to the largest one in the hydrophilic case. UR - http://hdl.handle.net/1963/2253 U1 - 1994 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains JF - Ann. Inst. H. Poincaré. Anal. Non Linéaire 21 (2004), (4), p. 445-486. Y1 - 2004 A1 - Gianni Dal Maso A1 - Francois Murat AB - We consider a sequence of Dirichlet problems in varying domains (or, more generally, of relaxed Dirichlet problems involving measures in M_0) for second order linear elliptic operators in divergence form with varying matrices of coefficients. When the matrices H-converge to a matrix A^0, we prove that there exist a subsequence and a measure mu^0 in M_0 such that the limit problem is the relaxed Dirichlet problem corresponding to A^0 and mu^0. We also prove a corrector result which provides an explicit approximation of the solutions in the H^1-norm, and which is obtained by multiplying the corrector for the H-converging matrices by some special test function which depends both on the varying matrices and on the varying domains. PB - SISSA Library UR - http://hdl.handle.net/1963/1611 U1 - 2507 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Bifurcation of free vibrations for completely resonant wave equations JF - Boll. Unione Mat. Ital. Sez. B 7 (2004) 519-528 Y1 - 2004 A1 - Massimiliano Berti A1 - Philippe Bolle AB - We prove existence of small amplitude, 2 pi/omega -periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for any frequency omega belonging to a Cantor-like set of positive measure and for a generic set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem. UR - http://hdl.handle.net/1963/2245 U1 - 1999 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Calculation of impulsively started incompressible viscous flows JF - Int. J. Numer. Meth. Fluids Y1 - 2004 A1 - Marra, Andrea A1 - Andrea Mola A1 - Quartapelle, Luigi A1 - Riviello, Luca VL - 46 ER - TY - JOUR T1 - Coarse-grained models of materials with non-convex free-energy: two case studies JF - Computer methods in applied mechanics and engineering , 193 (2004) 5129-5141 Y1 - 2004 A1 - Antonio DeSimone AB - Bridging across length scales is one of the fundamental challenges in the computational modelling of material systems whose mechanical response is driven by rough energy landscapes. The typical feature of such systems is that of exhibiting fine scale microstructures. Two case studies, namely, nematic elastomers and ferromagnetic shape memory alloys, are presented to illustrate the use of modern techniques from (non-convex) calculus of variations in developing coarse-grained models of microstructure-driven material response. PB - Elsevier UR - http://hdl.handle.net/1963/4884 U1 - 4664 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - On the convergence rate of vanishing viscosity approximations JF - Comm. Pure Appl. Math. 57 (2004) 1075-1109 Y1 - 2004 A1 - Alberto Bressan A1 - Tong Yang AB - Given a strictly hyperbolic, genuinely nonlinear system of conservation laws, we prove the a priori bound $\\\\big\\\\|u(t,\\\\cdot)-u^\\\\ve(t,\\\\cdot)\\\\big\\\\|_{\\\\L^1}= \\\\O(1)(1+t)\\\\cdot \\\\sqrt\\\\ve|\\\\ln\\\\ve|$ on the distance between an exact BV solution $u$ and a viscous approximation $u^\\\\ve$, letting the viscosity coefficient $\\\\ve\\\\to 0$. In the proof, starting from $u$ we construct an approximation of the viscous solution $u^\\\\ve$ by taking a mollification $u*\\\\phi_{\\\\strut \\\\sqrt\\\\ve}$ and inserting viscous shock profiles at the locations of finitely many large shocks, for each fixed $\\\\ve$. Error estimates are then obtained by introducing new Lyapunov functionals which control shock interactions, interactions between waves of different families and by using sharp decay estimates for positive nonlinear waves. PB - Wiley UR - http://hdl.handle.net/1963/2915 U1 - 1785 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Energetics and switching of quasi-uniform states in small ferromagnetic particles JF - M2AN Math. Model. Numer. Anal. 38 (2004) 235-248 Y1 - 2004 A1 - François Alouges A1 - Sergio Conti A1 - Antonio DeSimone A1 - Ivo Pokern AB - We present a numerical algorithm to solve the micromagnetic equations based on tangential-plane minimization for the magnetization update and a homothethic-layer decomposition of outer space for the computation of the demagnetization field. As a first application, detailed results on the flower-vortex transition in the cube of Micromagnetic Standard Problem number 3 are obtained, which confirm, with a different method, those already present in the literature, and validate our method and code. We then turn to switching of small cubic or almost-cubic particles, in the single-domain limit. Our data show systematic deviations from the Stoner-Wohlfarth model due to the non-ellipsoidal shape of the particle, and in particular a non-monotone dependence on the particle size. PB - EDP Sciences UR - http://hdl.handle.net/1963/2999 U1 - 1334 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence of H-bubbles in a perturbative setting JF - Rev. Mat. Iberoamericana 20 (2004) 611-626 Y1 - 2004 A1 - Paolo Caldiroli A1 - Roberta Musina AB - Given a $C^{1}$ function $H: \\\\mathbb{R}^3 \\\\to \\\\mathbb{R}$, we look for $H$-bubbles, i.e., surfaces in $\\\\mathbb{R}^3$ parametrized by the sphere $\\\\mathbb{S}^2$ with mean curvature $H$ at every regular point. Here we study the case $H(u)=H_{0}(u)+\\\\epsilon H_{1}(u)$ where $H_{0}$ is some \\\"good\\\" curvature (for which there exist $H_{0}$-bubbles with minimal energy, uniformly bounded in $L^{\\\\infty}$), $\\\\epsilon$ is the smallness parameter, and $H_{1}$ is {\\\\em any} $C^{1}$ function. PB - SISSA Library UR - http://hdl.handle.net/1963/1606 U1 - 2512 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - H-bubbles in a perturbative setting: the finite-dimensional reduction\\\'s method JF - Duke Math. J. 122 (2004), no. 3, 457--484 Y1 - 2004 A1 - Paolo Caldiroli A1 - Roberta Musina AB - Given a regular function $H\\\\colon\\\\mathbb{R}^{3}\\\\to\\\\mathbb{R}$, we look for $H$-bubbles, that is, regular surfaces in $\\\\mathbb{R}^{3}$ parametrized on the sphere $\\\\mathbb{S}+^{2}$ with mean curvature $H$ at every point. Here we study the case of $H(u)=H_{0}+\\\\varepsilon H_{1}(u)=:H_{\\\\varepsilon}(u)$, where $H_{0}$ is a nonzero constant, $\\\\varepsilon$ is the smallness parameter, and $H_{1}$ is any $C^{2}$-function. We prove that if $\\\\bar p\\\\in\\\\mathbb{R}^{3}$ is a ``good\\\'\\\' stationary point for the Melnikov-type function $\\\\Gamma(p)=-\\\\int_{|q-p|<|H_{0}|^{-1}}H_{1}(q)\\\\,dq$, then for $|\\\\varepsilon|$ small there exists an $H_{\\\\varepsilon}$-bubble $\\\\omega^{\\\\varepsilon}$ that converges to a sphere of radius $|H_{0}|^{-1}$ centered at $\\\\bar p$, as $\\\\varepsilon\\\\to 0$. PB - SISSA Library UR - http://hdl.handle.net/1963/1607 U1 - 2511 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Higher order quasiconvexity reduces to quasiconvexity JF - Arch. Ration. Mech. Anal. 171 (2004) 55-81 Y1 - 2004 A1 - Gianni Dal Maso A1 - Irene Fonseca A1 - Giovanni Leoni A1 - Massimiliano Morini AB - In this paper it is shown that higher order quasiconvex functions suitable in the variational treatment of problems involving second derivatives may be extended to the space of all matrices as classical quasiconvex functions. Precisely, it is proved that a smooth strictly 2-quasiconvex function with p-growth at infinity, p>1, is the restriction to symmetric matrices of a 1-quasiconvex function with the same growth. As a consequence, lower semicontinuity results for second-order variational problems are deduced as corollaries of well-known first order theorems. PB - Springer UR - http://hdl.handle.net/1963/2911 U1 - 1789 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - Generic T1 - On the minimal degree of a common Lyapunov function for planar switched systems T2 - 43rd IEEE Conference on Decision and Control, 2004, 2786 - 2791 Vol.3 Y1 - 2004 A1 - Paolo Mason A1 - Ugo Boscain A1 - Yacine Chitour AB - In this paper, we consider linear switched systems x(t) = Au(t)x(t), x ε Rn, u ε U, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching (UAS for short). We first prove that, given a UAS system, it is always possible to build a polynomial common Lyapunov function. Then our main result is that the degree of that the common polynomial Lyapunov function is not uniformly bounded over all the UAS systems. This result answers a question raised by Dayawansa and Martin. JF - 43rd IEEE Conference on Decision and Control, 2004, 2786 - 2791 Vol.3 PB - IEEE UR - http://hdl.handle.net/1963/4834 U1 - 4611 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Multidimensional boundary layers for a singularly perturbed Neumann problem JF - Duke Math. J. 124 (2004) 105-143 Y1 - 2004 A1 - Andrea Malchiodi A1 - Marcelo Montenegro PB - Duke University Press UR - http://hdl.handle.net/1963/2960 U1 - 1740 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Multiplicity of periodic solutions of nonlinear wave equations JF - Nonlinear Anal. 56 (2004) 1011-1046 Y1 - 2004 A1 - Massimiliano Berti A1 - Philippe Bolle PB - Elsevier UR - http://hdl.handle.net/1963/2974 U1 - 1359 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Periodic orbits close to elliptic tori and applications to the three-body problem JF - Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 3 (2004) 87-138 Y1 - 2004 A1 - Massimiliano Berti A1 - Luca Biasco A1 - Enrico Valdinoci AB - We prove, under suitable non-resonance and non-degeneracy ``twist\\\'\\\' conditions, a Birkhoff-Lewis type result showing the existence of infinitely many periodic solutions, with larger and larger minimal period, accumulating onto elliptic invariant tori (of Hamiltonian systems). We prove the applicability of this result to the spatial planetary three-body problem in the small eccentricity-inclination regime. Furthermore, we find other periodic orbits under some restrictions on the period and the masses of the ``planets\\\'\\\'. The proofs are based on averaging theory, KAM theory and variational methods. (Supported by M.U.R.S.T. Variational Methods and Nonlinear Differential Equations.) PB - Scuola Normale Superiore di Pisa UR - http://hdl.handle.net/1963/2985 U1 - 1348 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasi-static evolution in brittle fracture: the case of bounded solutions JF - Quad. Mat. Dip. Mat. Seconda Univ. Napoli 14 (2004) 245-266 Y1 - 2004 A1 - Gianni Dal Maso A1 - Gilles A. Francfort A1 - Rodica Toader AB - The main steps of the proof of the existence result for the quasi-static evolution of cracks in brittle materials, obtained in [7] in the vector case and for a general quasiconvex elastic energy, are presented here under the simplifying assumption that the minimizing sequences involved in the problem are uniformly bounded in $L^\\\\infty$. UR - http://hdl.handle.net/1963/2229 U1 - 2015 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Resonance of minimizers for n-level quantum systems with an arbitrary cost JF - ESAIM COCV 10 (2004) 593-614 Y1 - 2004 A1 - Ugo Boscain A1 - Grégoire Charlot AB - We consider an optimal control problem describing a laser-induced population transfer on a $n$-level quantum system.\\nFor a convex cost depending only on the moduli of controls (i.e. the lasers intensities), we prove that there always exists a minimizer in resonance. This permits to justify some strategies used in experimental physics. It is also quite important because it permits to reduce remarkably the complexity of the problem (and extend some of our previous results for $n=2$ and $n=3$): instead of looking for minimizers on the sphere $S^{2n-1}\\\\subset\\\\C^n$ one is reduced to look just for minimizers on the sphere $S^{n-1}\\\\subset \\\\R^n$. Moreover, for the reduced problem, we investigate on the question of existence of strict abnormal minimizer. PB - EDP Sciences UR - http://hdl.handle.net/1963/2910 U1 - 1790 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The role of the spectrum of the Laplace operator on \\\\S2 in the H-bubble problem JF - J. Anal. Math. 94 (2004) 265-291 Y1 - 2004 A1 - Roberta Musina PB - Hebrew University Magnes Press UR - http://hdl.handle.net/1963/2894 U1 - 1806 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Semi-cooperative strategies for differential games JF - Internat. J. Game Theory 32 (2004) 561-593 Y1 - 2004 A1 - Alberto Bressan A1 - Wen Shen AB - The paper is concerned with a non-cooperative differential game for two players. We first consider Nash equilibrium solutions in feedback form. In this case, we show that the Cauchy problem for the value functions is generically ill-posed. Looking at vanishing viscosity approximations, one can construct special solutions in the form of chattering controls, but these also appear to be unstable. In the second part of the paper we propose an alternative \\\"semi-cooperative\\\" pair of strategies for the two players, seeking a Pareto optimum instead of a Nash equilibrium. In this case, we prove that the corresponding Hamiltonian system for the value functions is always weakly hyperbolic. PB - Springer UR - http://hdl.handle.net/1963/2893 U1 - 1807 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A sharp decay estimate for positive nonlinear waves JF - SIAM J. Math. Anal. 36 (2004) 659-677 Y1 - 2004 A1 - Alberto Bressan A1 - Tong Yang AB - We consider a strictly hyperbolic, genuinely nonlinear system of conservation laws in one space dimension. A sharp decay estimate is proved for the positive waves in an entropy weak solution. The result is stated in terms of a partial ordering among positive measures, using symmetric rearrangements and a comparison with a solution of Burgers\\\' equation with impulsive sources. PB - SIAM UR - http://hdl.handle.net/1963/2916 U1 - 1784 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Singularity perturbed elliptic equations with symmetry: existence of solutions concetrating on spheres, Part II JF - Indiana Univ. Math. J. 53 (2004) 297-392 Y1 - 2004 A1 - Antonio Ambrosetti A1 - Andrea Malchiodi A1 - Wei-Ming Ni PB - Indiana University Mathematics Journal UR - http://hdl.handle.net/1963/1663 U1 - 2455 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Small BV solutions of hyperbolic noncooperative differential games JF - SIAM J. Control Optim. 43 (2004) 194-215 Y1 - 2004 A1 - Alberto Bressan A1 - Wen Shen AB - The paper is concerned with an n-persons differential game in one space dimension. We state conditions for which the system of Hamilton-Jacobi equations for the value functions is strictly hyperbolic. In the positive case, we show that the weak solution of a corresponding system of conservation laws determines an n-tuple of feedback strategies. These yield a Nash equilibrium solution to the non-cooperative differential game. PB - SIAM UR - http://hdl.handle.net/1963/2917 U1 - 1783 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Solitary waves for Maxwell Schrodinger equations JF - Electron. J. Differential Equations (2004) 94 Y1 - 2004 A1 - Giuseppe Maria Coclite A1 - Vladimir Georgiev AB - In this paper we study solitary waves for the coupled system of Schrodinger-Maxwell equations in the three-dimensional space. We prove the existence of a sequence of radial solitary waves for these equations with a fixed L^2 norm. We study the asymptotic behavior and the smoothness of these solutions. We show also that the eigenvalues are negative and the first one is isolated. PB - SISSA Library UR - http://hdl.handle.net/1963/1582 U1 - 2536 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Solutions concentrating at curves for some singularly perturbed elliptic problems JF - C. R. Acad. Sci. Paris, Ser. I 338 (2004) 775-780 Y1 - 2004 A1 - Andrea Malchiodi PB - Elsevier UR - http://hdl.handle.net/1963/4869 U1 - 4647 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Soluzioni periodiche di PDEs Hamiltoniane JF - Bollettino dell\\\'Unione Matematica Italiana Serie 8 7-B (2004), p. 647-661 Y1 - 2004 A1 - Massimiliano Berti PB - Unione Matematica Italiana UR - http://hdl.handle.net/1963/4582 U1 - 4351 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Some remarks on multidimensional systems of conservation laws JF - Rend. Mat. Acc. Lincei, s. 9, v. 15 (2004) 3-4, pp. 225 - 233 Y1 - 2004 A1 - Alberto Bressan AB - This note is concerned with the Cauchy problem for hyperbolic systems of conservation\\nlaws in several space dimensions. We first discuss an example of ill-posedness, for a special system\\nhaving a radial symmetry property. Some conjectures are formulated, on the compactness of the set of\\nflow maps generated by vector fields with bounded variation. PB - Accademia Nazionale dei Lincei UR - http://hdl.handle.net/1963/3642 U1 - 662 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Stability rates for patchy vector fields JF - ESAIM COCV 10 (2004) 168-200 Y1 - 2004 A1 - Fabio Ancona A1 - Alberto Bressan AB - This paper is concerned with the stability of the set of trajectories of a patchy vector field, in the presence of impulsive perturbations. Patchy vector fields are discontinuous, piecewise smooth vector fields that were introduced in Ancona and Bressan (1999) to study feedback stabilization problems. For patchy vector fields in the plane, with polygonal patches in generic position, we show that the distance between a perturbed trajectory and an unperturbed one is of the same order of magnitude as the impulsive forcing term. PB - EDP Sciences UR - http://hdl.handle.net/1963/2959 U1 - 1741 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Well-posedness for general 2x2 systems of conservation laws JF - Mem. Amer. Math. Soc. 169 (2004), no. 801, x+170 pp. Y1 - 2004 A1 - Fabio Ancona A1 - Andrea Marson PB - SISSA Library UR - http://hdl.handle.net/1963/1241 U1 - 2702 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Autonomous integral functionals with discontinous nonconvex integrands: Lipschitz regularity of mimimizers, DuBois-Reymond necessary conditions and Hamilton-Jacobi equations JF - Applied Math.Optim. 48 (2003), no.1, p.39-66 Y1 - 2003 A1 - Gianni Dal Maso A1 - Helene Frankowska PB - SISSA Library UR - http://hdl.handle.net/1963/1625 U1 - 2493 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The calibration method for the Mumford-Shah functional and free-discontinuity problems JF - Calc. Var. Partial Differential Equations 16 (2003) 299-333 Y1 - 2003 A1 - Giovanni Alberti A1 - Guy Bouchitte A1 - Gianni Dal Maso AB - We present a minimality criterion for the Mumford-Shah functional, and more generally for non convex variational integrals on SBV which couple a surface and a bulk term. This method provides short and easy proofs for several minimality results. PB - Springer UR - http://hdl.handle.net/1963/3051 U1 - 1282 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Control Problems for Systems of Conservation Laws Y1 - 2003 A1 - Giuseppe Maria Coclite KW - Asymptotic Stabilization PB - SISSA UR - http://hdl.handle.net/1963/5325 U1 - 5154 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Drift in phase space: a new variational mechanism with optimal diffusion time JF - J. Math. Pures Appl. 82 (2003) 613-664 Y1 - 2003 A1 - Massimiliano Berti A1 - Luca Biasco A1 - Philippe Bolle AB - We consider non-isochronous, nearly integrable, a-priori unstable Hamiltonian systems with a (trigonometric polynomial) $O(\\\\mu)$-perturbation which does not preserve the unperturbed tori. We prove the existence of Arnold diffusion with diffusion time $ T_d = O((1/ \\\\mu) \\\\log (1/ \\\\mu))$ by a variational method which does not require the existence of ``transition chains of tori\\\'\\\' provided by KAM theory. We also prove that our estimate of the diffusion time $T_d $ is optimal as a consequence of a general stability result derived from classical perturbation theory. PB - Elsevier UR - http://hdl.handle.net/1963/3020 U1 - 1313 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A finite element approximation of the Griffith\\\'s model in fracture mechanics JF - Numer. Math., 2003, 95, 653 Y1 - 2003 A1 - Matteo Negri AB - The Griffith model for the mechanics of fractures in brittle materials is consider in the weak formulation of SBD spaces. We suggest an approximation, in the sense of Gamma-convergence, by a sequence of discrete functionals defined on finite elements spaces over structured and adaptive triangulations. The quasi-static evolution for boundary value problems is also taken into account and some numerical results are shown. PB - SISSA Library UR - http://hdl.handle.net/1963/1548 U1 - 2570 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Hybrid optimal control: case study of a car with gears JF - Int. J. Control 76 (2003) 1272-1284 Y1 - 2003 A1 - Ciro D'Apice A1 - Mauro Garavello A1 - Rosanna Manzo A1 - Benedetto Piccoli AB - The purpose of this paper is to show the use of some analytical tools for hybrid optimal control. We illustrate both the hybrid maximum principle and the hybrid necessary principle at work on a simple example of a car with gears. The model is sufficiently rich to generate non-trivial optimization problems and the obtained results match with intuition. Finally, computer simulations confirm the theoretical analysis. PB - Taylor and Francis UR - http://hdl.handle.net/1963/3022 U1 - 1311 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - An ill posed Cauchy problem for a hyperbolic system in two space dimensions Y1 - 2003 A1 - Alberto Bressan AB - The theory of weak solutions for nonlinear conservation laws is now well developed in the case of scalar equations [3] and for one-dimensional hyperbolic systems [1, 2]. For systems in several space dimensions, however, even the global existence of solutions to the Cauchy problem remains a challenging open question. In this note we construct a conterexample showing that, even for a simple class of hyperbolic systems, in two space dimensions the Cauchy problem can be ill posed. PB - Università di Padova UR - http://hdl.handle.net/1963/2913 U1 - 1787 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - An interior estimate for a nonlinear parabolic equation JF - J.Math.Anal.Appl. 284 (2003) no.1, 49 Y1 - 2003 A1 - Giuseppe Maria Coclite PB - SISSA Library UR - http://hdl.handle.net/1963/1622 U1 - 2496 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A lemma and a conjecture on the cost of rearrangements JF - Rend. Sem. Mat. Univ. Padova 110 (2003) 97-102 Y1 - 2003 A1 - Alberto Bressan AB - Consider a stack of books, containing both white and black books. Suppose that we want to sort them out, putting the white books on the right, and the black books on the left (fig.~1). This will be done by a finite sequence of elementary transpositions. In other words, if we have a stack of all black books of length $a$ followed by a stack of all white books of length $b$, we are allowed to reverse their order at the cost of $a+b$. We are interested in a lower bound on the total cost of the rearrangement. PB - Università di Padova UR - http://hdl.handle.net/1963/2914 U1 - 1786 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the local structure of optimal trajectories in R3 JF - SIAM J. Control Optim. 42 (2003) 513-531 Y1 - 2003 A1 - Andrei A. Agrachev A1 - Mario Sigalotti AB - We analyze the structure of a control function u(t) corresponding to an optimal trajectory for the system $\\\\dot q =f(q)+u\\\\, g(q)$ in a three-dimensional manifold, near a point where some nondegeneracy conditions are satisfied. The kind of optimality which is studied includes time-optimality. The control turns out to be the concatenation of some bang and some singular arcs. Studying the index of the second variation of the switching times, the number of such arcs is bounded by four. PB - SISSA Library UR - http://hdl.handle.net/1963/1612 U1 - 2506 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A note on singular limits to hyperbolic systems of conservation laws JF - Commun. Pure Appl. Ana., 2003, 2, 51-64 Y1 - 2003 A1 - Stefano Bianchini AB - In this note we consider two different singular limits to hyperbolic system of conservation laws, namely the standard backward schemes for non linear semigroups and the semidiscrete scheme. \\nUnder the assumption that the rarefaction curve of the corresponding hyperbolic system are straight lines, we prove the stability of the solution and the convergence to the perturbed system to the unique solution of the limit system for initial data with small total variation. PB - SISSA Library UR - http://hdl.handle.net/1963/1542 U1 - 2621 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A note on the integral representation of functionals in the space SBD(O) JF - Rend. Mat. Appl. 23 (2003) 189-201 Y1 - 2003 A1 - Francois Ebobisse A1 - Rodica Toader AB - In this paper we study the integral representation in the space SBD(O) of special functions with bounded deformation of some L^1-norm lower semicontinuous functionals invariant with respect to rigid motions. PB - Rendiconti di Matematica UR - http://hdl.handle.net/1963/3064 U1 - 1269 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Periodic solutions of nonlinear wave equations with general nonlinearities JF - Comm.Math.Phys. 243 (2003) no.2, 315 Y1 - 2003 A1 - Massimiliano Berti A1 - Philippe Bolle PB - SISSA Library UR - http://hdl.handle.net/1963/1648 U1 - 2470 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Positive solutions to a class of quasilinear elliptic equations on R JF - Discrete Contin.Dyn.Syst. 9 (2003), no.1, 55-68 Y1 - 2003 A1 - Antonio Ambrosetti A1 - Wang Zhi-Qiang AB - We discuss the existence of positive solutions of perturbation to a class of quasilinear elliptic equations on R. PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/1628 U1 - 2490 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Prescribing scalar and boundary mean curvature on the three dimensional half sphere JF - J. Geom. Anal. 13 (2003) 255-289 Y1 - 2003 A1 - Zindine Djadli A1 - Andrea Malchiodi A1 - Mohameden Ould Ahmedou AB - We consider the problem of prescribing the scalar curvature and the boundary mean curvature of the standard half three sphere, by deforming conformally its standard metric. Using blow up analysis techniques and minimax arguments, we prove some existence and compactness results. PB - Springer UR - http://hdl.handle.net/1963/3086 U1 - 1247 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Sequences of Singularly Perturbed Functionals Generating Free-Discontinuity Problems JF - SIAM J. Math. Anal. 35 (2003) 759-805 Y1 - 2003 A1 - Massimiliano Morini AB - We prove that a wide class of singularly perturbed functionals generates as $\\\\Gamma$-limit a functional related to a free-discontinuity problem. Several applications of the result are shown. PB - SIAM UR - http://hdl.handle.net/1963/3071 U1 - 1262 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Single-Input Control Affine Systems: Local Regularity of Optimal Trajectories and a Geometric Controllability Problem Y1 - 2003 A1 - Mario Sigalotti PB - SISSA UR - http://hdl.handle.net/1963/5342 U1 - 5170 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres, Part I JF - Comm. Math. Phys. 235 (2003) no.3, 427-466 Y1 - 2003 A1 - Antonio Ambrosetti A1 - Andrea Malchiodi A1 - Wei-Ming Ni PB - Springer UR - http://hdl.handle.net/1963/1633 U1 - 2485 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Some results on the boundary control of systems of conservation laws JF - SIAM J.Control Optim. 41 (2003),no.2, 607 Y1 - 2003 A1 - Alberto Bressan A1 - Fabio Ancona A1 - Giuseppe Maria Coclite PB - SISSA Library UR - http://hdl.handle.net/1963/1615 U1 - 2503 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A stability result for nonlinear Neumann problems under boundary variations JF - J.Math. Pures Appl. (9) 82 (2003) no.5 , 503 Y1 - 2003 A1 - Gianni Dal Maso A1 - Francois Ebobisse A1 - Marcello Ponsiglione AB - 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. PB - SISSA Library UR - http://hdl.handle.net/1963/1618 U1 - 2500 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Admissible Riemann solvers for genuinely nonlinear P-systems of mixed type JF - J. Differ. Equations, 2002, 180, 395 Y1 - 2002 A1 - Jean-Marc Mercier A1 - Benedetto Piccoli PB - SISSA Library UR - http://hdl.handle.net/1963/1491 U1 - 2672 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Arnold diffusion: a functional analysis approach JF - Pr. Inst. Mat. Nats. Akad. Nauk Ukr. Mat. Zastos., 43, Part 1, 2, Natsīonal. Akad. Nauk Ukraïni, Īnst. Mat., Kiev, 2002 Y1 - 2002 A1 - Massimiliano Berti AB - 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. PB - Natsīonal. Akad. Nauk Ukraïni U1 - 7269 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - On the Boundary Control of Systems of Conservation Laws JF - SIAM J. Control Optim. 41 (2002) 607-622 Y1 - 2002 A1 - Alberto Bressan A1 - Giuseppe Maria Coclite AB - 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. PB - SIAM UR - http://hdl.handle.net/1963/3070 U1 - 1263 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The Calibration Method for Free-Discontinuity Problems on Vector-Valued Maps JF - J. Convex Anal. 9 (2002) 1-29 Y1 - 2002 A1 - Maria Giovanna Mora AB - 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. PB - Heldermann Verlag UR - http://hdl.handle.net/1963/3049 U1 - 1284 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A center manifold technique for tracing viscous waves JF - Commun. Pure Appl. Anal. 1 (2002) 161-190 Y1 - 2002 A1 - Stefano Bianchini A1 - Alberto Bressan AB - 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. PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/3075 U1 - 1258 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Chaotic dynamics for perturbations of infinite-dimensional Hamiltonian systems JF - Nonlinear Anal. 48 (2002) 481-504 Y1 - 2002 A1 - Massimiliano Berti A1 - Carlo Carminati PB - Elsevier UR - http://hdl.handle.net/1963/1279 U1 - 3176 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Curvature theory of boundary phases: the two-dimensional case JF - Interfaces Free Bound. 7 (2002) 345-370 Y1 - 2002 A1 - Andrea Braides A1 - Andrea Malchiodi AB - 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. PB - European Mathematical Society UR - http://hdl.handle.net/1963/3537 U1 - 1164 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence of minimal H-bubbles JF - Commun. Contemp. Math. 4 (2002) 177-209 Y1 - 2002 A1 - Paolo Caldiroli A1 - Roberta Musina PB - SISSA Library UR - http://hdl.handle.net/1963/1525 U1 - 2638 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Fast Arnold diffusion in systems with three time scales JF - Discrete Contin. Dyn. Syst. 8 (2002) 795-811 Y1 - 2002 A1 - Massimiliano Berti A1 - Philippe Bolle AB - 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. PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/3058 U1 - 1275 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Flow Stability of Patchy Vector Fields and Robust Feedback Stabilization JF - SIAM J. Control Optim. 41 (2002) 1455-1476 Y1 - 2002 A1 - Fabio Ancona A1 - Alberto Bressan AB - 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. PB - SIAM UR - http://hdl.handle.net/1963/3073 U1 - 1260 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A functional analysis approach to Arnold diffusion JF - Ann. Inst. H. Poincare Anal. Non Lineaire 19 (2002) 395-450 Y1 - 2002 A1 - Massimiliano Berti A1 - Philippe Bolle AB - 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. PB - Elsevier UR - http://hdl.handle.net/1963/3151 U1 - 1182 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Geometry of Jacobi Curves I JF - J. Dynam. Control Systems 8 (2002) 93-140 Y1 - 2002 A1 - Andrei A. Agrachev A1 - Igor Zelenko AB - 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\\\". PB - Springer UR - http://hdl.handle.net/1963/3110 U1 - 1223 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Geometry of Jacobi curves II JF - J. Dynam. Control Systems 8 (2002), no. 2, 167--215 Y1 - 2002 A1 - Andrei A. Agrachev A1 - Igor Zelenko PB - SISSA Library UR - http://hdl.handle.net/1963/1589 U1 - 2529 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Global calibrations for the non-homogeneous Mumford-Shah functional JF - Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 1 (2002) 603-648 Y1 - 2002 A1 - Massimiliano Morini AB - 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. PB - Scuola Normale Superiore di Pisa UR - http://hdl.handle.net/1963/3089 U1 - 1244 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the K+P problem for a three-level quantum system: optimality implies resonance JF - J.Dynam. Control Systems 8 (2002),no.4, 547 Y1 - 2002 A1 - Ugo Boscain A1 - Thomas Chambrion A1 - Jean-Paul Gauthier PB - SISSA Library UR - http://hdl.handle.net/1963/1601 U1 - 2517 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Linearized elasticity as gamma-limit of finite elasticity JF - Set-Valued Anal. 10 (2002), p.165-183 Y1 - 2002 A1 - Gianni Dal Maso A1 - Matteo Negri A1 - Danilo Percivale PB - Springer UR - http://hdl.handle.net/1963/3052 U1 - 1281 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Local calibrations for minimizers of the Mumford-Shah functional with a triple junction JF - Commun. Contemp. Math. 4 (2002) 297-326 Y1 - 2002 A1 - Maria Giovanna Mora AB - 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. PB - World Scientific UR - http://hdl.handle.net/1963/3050 U1 - 1283 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On a Lyapunov functional relating shortening curves and viscous conservation laws JF - Nonlinear Anal. 51 (2002) 649-662 Y1 - 2002 A1 - Stefano Bianchini A1 - Alberto Bressan AB - 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. PB - Elsevier UR - http://hdl.handle.net/1963/1337 U1 - 3118 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A model for the quasi-static growth of a brittle fracture: existence and approximation results JF - Math. Models Methods Appl. Sci., 12 (2002), no. 12, 1773 Y1 - 2002 A1 - Gianni Dal Maso A1 - Rodica Toader AB - 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. PB - SISSA Library UR - http://hdl.handle.net/1963/1571 U1 - 2547 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A model for the quasi-static growth of brittle fractures based on local minimization JF - Math.Models Methods Appl. Sci., 12 (2002) , p.1773-1800. Y1 - 2002 A1 - Gianni Dal Maso A1 - Rodica Toader AB - 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. PB - SISSA Library UR - http://hdl.handle.net/1963/1621 U1 - 2497 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A Model for the Quasi-Static Growth of Brittle Fractures: Existence and Approximation Results JF - Arch. Ration. Mech. Anal. 162 (2002) 101-135 Y1 - 2002 A1 - Gianni Dal Maso A1 - Rodica Toader AB - 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. PB - Springer UR - http://hdl.handle.net/1963/3056 U1 - 1277 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A multiplicity result for the Schrodinger-Maxwell equations with negative potential JF - Ann. Pol. Math. 79 (2002) 21-30 Y1 - 2002 A1 - Giuseppe Maria Coclite AB - 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. PB - IMPAN UR - http://hdl.handle.net/1963/3053 U1 - 1280 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Multiplicity results for the Yamabe problem on Sn JF - Proceedings of the National Academy of Sciences of the United States of America. 2002 Nov; 99(24):15252-6 Y1 - 2002 A1 - Antonio Ambrosetti AB - We discuss some results related to the existence of multiple solutions for the Yamabe problem. PB - National Academy of Sciences UR - http://hdl.handle.net/1963/5885 U1 - 5757 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - An optimal fast-diffusion variational method for non isochronous system Y1 - 2002 A1 - Luca Biasco A1 - Massimiliano Berti A1 - Philippe Bolle PB - SISSA Library UR - http://hdl.handle.net/1963/1579 U1 - 2539 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Optimal stability and instability results for a class of nearly integrable Hamiltonian systems JF - Atti.Accad.Naz.Lincei Cl.Sci.Fis.Mat.Natur.Rend.Lincei (9) Mat.Appl.13(2002),no.2,77-84 Y1 - 2002 A1 - Massimiliano Berti A1 - Luca Biasco A1 - Philippe Bolle PB - SISSA Library UR - http://hdl.handle.net/1963/1596 U1 - 2522 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The passage from nonconvex discrete systems to variational problems in Sobolev spaces: the one-dimensional case JF - Proc. Steklov Inst. Math. 236 (2002) 395-414 Y1 - 2002 A1 - Andrea Braides A1 - Maria Stella Gelli A1 - Mario Sigalotti PB - MAIK Nauka/Interperiodica UR - http://hdl.handle.net/1963/3130 U1 - 1203 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Prescribing a fourth oder conformal invariant on the standard sphere - Part II: blow up analysis and applications JF - Ann. Sc. Norm. Super. Pisa Cl. Sci., 2002, 1, 387 Y1 - 2002 A1 - Zindine Djadli A1 - Andrea Malchiodi A1 - Mohameden Ould Ahmedou PB - SISSA Library UR - http://hdl.handle.net/1963/1540 U1 - 2623 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Prescribing a fourth oder conformal invariant on the standard sphere - Part I: a perturbation result JF - Commun. Contemp. Math., 2002, 4, 375 Y1 - 2002 A1 - Zindine Djadli A1 - Mohameden Ould Ahmedou A1 - Andrea Malchiodi PB - SISSA Library UR - http://hdl.handle.net/1963/1539 U1 - 2624 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the reachability of quantized control systems JF - IEEE Trans. Automat. Contr. 47 (2002) 546-563 Y1 - 2002 A1 - Antonio Bicchi A1 - Alessia Marigo A1 - Benedetto Piccoli AB - 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. PB - SISSA Library UR - http://hdl.handle.net/1963/1501 U1 - 2662 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The scalar curvature problem on $S\\\\sp n$: an approach via Morse theory JF - Calc. Var. Partial Differential Equations 14 (2002), no. 4, 429-445 Y1 - 2002 A1 - Andrea Malchiodi PB - Springer UR - http://hdl.handle.net/1963/1331 U1 - 3124 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Singular elliptic problems with critical growth JF - Comm. Partial Differential Equations 27 (2002), no. 5-6, 847-876 Y1 - 2002 A1 - Paolo Caldiroli A1 - Andrea Malchiodi PB - Dekker UR - http://hdl.handle.net/1963/1268 U1 - 3187 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Solutions concentrating on spheres to symmetric singularly perturbed problems JF - C.R.Math.Acad.Sci. Paris 335 (2002),no.2,145-150 Y1 - 2002 A1 - Antonio Ambrosetti A1 - Andrea Malchiodi A1 - Wei-Ming Ni AB - We discuss some existence results concerning problems (NLS) and (N), proving the existence of radial solutions concentrating on a sphere. PB - SISSA Library UR - http://hdl.handle.net/1963/1594 U1 - 2524 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Stability of planar switched systems: the linear single input case JF - SIAM J. Control Optim. 41 (2002), no. 1, 89-112 Y1 - 2002 A1 - Ugo Boscain AB - 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. PB - SIAM UR - http://hdl.handle.net/1963/1529 U1 - 2634 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the Stability of the Standard Riemann Semigroup JF - P. Am. Math. Soc., 2002, 130, 1961 Y1 - 2002 A1 - Stefano Bianchini A1 - Rinaldo M. Colombo PB - SISSA Library UR - http://hdl.handle.net/1963/1528 U1 - 2635 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the Yamabe problem and the scalar curvature problems under boundary conditions JF - Math. Ann., 2002, 322, 667 Y1 - 2002 A1 - Antonio Ambrosetti A1 - Li YanYan A1 - Andrea Malchiodi PB - SISSA Library UR - http://hdl.handle.net/1963/1510 U1 - 2653 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Adiabatic limits of closed orbits for some Newtonian systems in R-n JF - Asymptotic Anal., 2001, 25, 149-181 Y1 - 2001 A1 - Andrea Malchiodi AB - 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. PB - SISSA Library UR - http://hdl.handle.net/1963/1511 U1 - 2652 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A case study in vanishing viscosity JF - Discrete Cont. Dyn. Syst. 7 (2001) 449-476 Y1 - 2001 A1 - Stefano Bianchini A1 - Alberto Bressan PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/3091 U1 - 1242 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Controllability for discrete systems with a finite control set JF - Math. Control Signals Systems 14 (2001) 173-193 Y1 - 2001 A1 - Yacine Chitour A1 - Benedetto Piccoli PB - Springer UR - http://hdl.handle.net/1963/3114 U1 - 1219 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Dieletric breakdown: optimal bounds JF - Proc. of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences 457 (2001): p. 2317-2335, OCT. 8, 2001 Y1 - 2001 A1 - Adriana Garroni A1 - Vincenzo Nesi A1 - Marcello Ponsiglione PB - SISSA Library UR - http://hdl.handle.net/1963/1569 U1 - 2549 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence and nonexistence results for a class of nonlinear, singular Sturm-Liouville equations JF - Adv. Differential Equations 6 (2001), no. 3, 303-326 Y1 - 2001 A1 - Paolo Caldiroli A1 - Roberta Musina PB - SISSA Library UR - http://hdl.handle.net/1963/1319 U1 - 3136 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Extremal synthesis for generic planar systems JF - J. Dynam. Control Systems, 2001, 7, 209 Y1 - 2001 A1 - Ugo Boscain A1 - Benedetto Piccoli PB - SISSA Library UR - http://hdl.handle.net/1963/1503 U1 - 2660 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Finite Difference Approximation of Free Discontinuity Problems JF - Proc. Royal Soc. Edinb. Ser. A 131 (2001), no. 3, 567-595 Y1 - 2001 A1 - Massimo Gobbino A1 - Maria Giovanna Mora PB - SISSA Library UR - http://hdl.handle.net/1963/1228 U1 - 2715 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Free-discontinuity problems: calibration and approximation of solutions Y1 - 2001 A1 - Massimiliano Morini KW - Calibration of solutions PB - SISSA UR - http://hdl.handle.net/1963/5398 U1 - 5223 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Gamma-limit of periodic obstacles JF - Acta Appl. Math., 2001, 65, 207-215 Y1 - 2001 A1 - Gianni Dal Maso A1 - Paola Trebeschi AB - We compute the Gamma-limit of a sequence obstacle functionals in the case of periodic obstacles. PB - SISSA Library UR - http://hdl.handle.net/1963/1495 U1 - 2668 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A Glimm type functional for a special Jin-Xin relaxation model JF - Ann. Inst. H. Poincare\\\' Anal. Non Lineaire 18 (2001), no. 1, 19-42 Y1 - 2001 A1 - Stefano Bianchini PB - Elsevier UR - http://hdl.handle.net/1963/1355 U1 - 3100 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Global continuous Riemann solver for nonlinear elasticity JF - Arch. Ration. Mech. An., 2001, 156, 89 Y1 - 2001 A1 - Jean-Marc Mercier A1 - Benedetto Piccoli PB - SISSA Library UR - http://hdl.handle.net/1963/1493 U1 - 2670 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Local calibrations for minimizers of the Mumford-Shah functional with a regular discontinuity set JF - Ann. I. H. Poincare - An., 2001, 18, 403 Y1 - 2001 A1 - Maria Giovanna Mora A1 - Massimiliano Morini PB - SISSA Library UR - http://hdl.handle.net/1963/1479 U1 - 2684 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A monotonicity approach to nonlinear Dirichlet problems in perforated domains JF - Adv. Math. Sci. Appl. 11 (2001) 721-751 Y1 - 2001 A1 - Gianni Dal Maso A1 - Igor V. Skrypnik AB - 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. PB - SISSA Library UR - http://hdl.handle.net/1963/1555 U1 - 2563 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Morse properties for the minimum time function on 2-D manifolds JF - J. Dynam. Control Systems 7 (2001), no. 3, 385--423 Y1 - 2001 A1 - Ugo Boscain A1 - Benedetto Piccoli PB - SISSA Library UR - http://hdl.handle.net/1963/1541 U1 - 2622 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Multiple positive solutions of some elliptic equations in \\\\bold R\\\\sp N JF - Nonlinear Anal. 43 (2001) 159-172 Y1 - 2001 A1 - Andrea Malchiodi PB - Elsevier UR - http://hdl.handle.net/1963/3094 U1 - 1239 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Multiplicity results for some nonlinear Schrodinger equations with potentials JF - Arch. Ration. Mech. An., 2001, 159, 253 Y1 - 2001 A1 - Antonio Ambrosetti A1 - Andrea Malchiodi A1 - Simone Secchi PB - SISSA Library UR - http://hdl.handle.net/1963/1564 U1 - 2554 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Non-compactness and multiplicity results for the Yamabe problem on Sn JF - J. Funct. Anal. 180 (2001) 210-241 Y1 - 2001 A1 - Massimiliano Berti A1 - Andrea Malchiodi PB - Elsevier UR - http://hdl.handle.net/1963/1345 U1 - 3110 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Numerical Methods for Free-Discontinuity Problems Based on Approximations by Γ-Convergence Y1 - 2001 A1 - Matteo Negri KW - Mumford-Shah functional PB - SISSA UR - http://hdl.handle.net/1963/5399 U1 - 5226 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Numerical minimization of the Mumford-Shah functional JF - Calcolo, 2001, 38, 67 Y1 - 2001 A1 - Matteo Negri A1 - Maurizio Paolini PB - SISSA Library UR - http://hdl.handle.net/1963/1461 U1 - 3079 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - S^2 type parametric surfaces with prescribed mean curvature and minimal energy T2 - 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 Y1 - 2001 A1 - Paolo Caldiroli A1 - Roberta Musina JF - 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 PB - Birkhauser UR - http://hdl.handle.net/1963/1605 U1 - 2513 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the spreading of characteristics for non-convex conservation laws JF - Proc. Roy. Soc. Edinburgh Sect. A 131 (2001) 909-925 Y1 - 2001 A1 - Helge Kristian Jenssen A1 - Carlo Sinestrari AB - 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. PB - Cambridge University Press UR - http://hdl.handle.net/1963/3265 U1 - 1436 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Stability of L-infinity solutions for hyperbolic systems with coinciding shocks and rarefactions JF - Siam J. Math. Anal., 2001, 33, 959 Y1 - 2001 A1 - Stefano Bianchini AB - 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. PB - SISSA Library UR - http://hdl.handle.net/1963/1523 U1 - 2640 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Stationary states for a two-dimensional singular Schrodinger equation JF - Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 4 (2001), no. 3, 609-633. Y1 - 2001 A1 - Paolo Caldiroli A1 - Roberta Musina PB - SISSA Library UR - http://hdl.handle.net/1963/1249 U1 - 3206 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the subanalyticity of Carnot-Caratheodory distances JF - Ann. I. H. Poincare - An., 2001, 18, 359 Y1 - 2001 A1 - Andrei A. Agrachev A1 - Jean-Paul Gauthier PB - SISSA Library UR - http://hdl.handle.net/1963/1483 U1 - 2680 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the symmetric scalar curvature problem on S\\\\sp n JF - J. Differential Equations 170 (2001) 228-245 Y1 - 2001 A1 - Antonio Ambrosetti A1 - Andrea Malchiodi AB - We discuss some existence results dealing with the scalar curvature problem on S\\\\sp n in the presence of various symmetries. PB - Elsevier UR - http://hdl.handle.net/1963/3095 U1 - 1238 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Uniqueness of classical and nonclassical solutions for nonlinear hyperbolic systems JF - J. Differential Equations 172 (2001) 59-82 Y1 - 2001 A1 - Paolo Baiti A1 - Philippe G. LeFloch A1 - Benedetto Piccoli PB - Elsevier UR - http://hdl.handle.net/1963/3113 U1 - 1220 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Uniqueness of solutions to Hamilton-Jacobi equations arising in the Calculus of Variations JF - Optimal control and partial differential equations : in honour of professor Alain Bensoussan\\\'s 60th birthday / edited by José Luis Menaldi, Edmundo Rofman, and Agnès Sulem.,Amsterdam : IOS Press, 2001, p. 335-345 Y1 - 2001 A1 - Gianni Dal Maso A1 - Helene Frankowska AB - We prove the uniqueness of the viscosity solution to the Hamilton-Jacobi equation associated with a Bolza problem of the Calculus of Variations, assuming that the Lagrangian is autonomous, continuous, superlinear, and satisfies the usual convexity hypothesis. Under the same assumptions we prove also the uniqueness, in a class of lower semicontinuous functions, of a slightly different notion of solution, where classical derivatives are replaced only by subdifferentials. These results follow from a new comparison theorem for lower semicontinuous viscosity supersolutions of the Hamilton-Jacobi equation, that is proved in the general case of lower semicontinuous Lagrangians. PB - SISSA Library UR - http://hdl.handle.net/1963/1515 U1 - 2648 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Abnormal extremals for minimum time on the plane Y1 - 2000 A1 - Ugo Boscain A1 - Benedetto Piccoli PB - SISSA Library UR - http://hdl.handle.net/1963/1508 U1 - 2655 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Arnold's Diffusion in nearly integrable isochronous Hamiltonian systems Y1 - 2000 A1 - Massimiliano Berti A1 - Philippe Bolle PB - SISSA Library UR - http://hdl.handle.net/1963/1554 U1 - 2564 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - BV estimates for multicomponent chromatography with relaxation JF - Discrete Contin. Dynam. Systems 6 (2000) 21-38 Y1 - 2000 A1 - Alberto Bressan A1 - Wen Shen AB - We consider the Cauchy problem for a system of $2n$ balance laws which arises from the modelling of multi-component chromatography: $$\\\\left\\\\{ \\\\eqalign{u_t+u_x&=-{1\\\\over\\\\ve}\\\\big( F(u)-v\\\\big),\\\\cr v_t&={1\\\\over\\\\ve}\\\\big( F(u)-v\\\\big),\\\\cr}\\\\right. \\\\eqno(1)$$ This model describes a liquid flowing with unit speed over a solid bed. Several chemical substances are partly dissolved in the liquid, partly deposited on the solid bed. Their concentrations are represented respectively by the vectors $u=(u_1,\\\\ldots,u_n)$ and $v=(v_1,\\\\ldots,v_n)$. We show that, if the initial data have small total variation, then the solution of (1) remains with small variation for all times $t\\\\geq 0$. Moreover, using the $\\\\L^1$ distance, this solution depends Lipschitz continuously on the initial data, with a Lipschitz constant uniform w.r.t.~$\\\\ve$. Finally we prove that as $\\\\ve\\\\to 0$, the solutions of (1) converge to a limit described by the system $$\\\\big(u+F(u)\\\\big)_t+u_x=0,\\\\qquad\\\\qquad v=F(u).\\\\eqno(2)$$ The proof of the uniform BV estimates relies on the application of probabilistic techniques. It is shown that the components of the gradients $v_x,u_x$ can be interpreted as densities of random particles travelling with speed 0 or 1. The amount of coupling between different components is estimated in terms of the expected number of crossing of these random particles. This provides a first example where BV estimates are proved for general solutions to a class of $2n\\\\times 2n$ systems with relaxation. PB - SISSA Library UR - http://hdl.handle.net/1963/1336 U1 - 3119 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - BV solutions for a class of viscous hyperbolic systems JF - Indiana Univ. Math. J. 49 (2000) 1673-1714 Y1 - 2000 A1 - Stefano Bianchini A1 - Alberto Bressan PB - Indiana University Mathematics Journal UR - http://hdl.handle.net/1963/3194 U1 - 1107 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The Calibration Method for Free Discontinuity Problems JF - European Congress of Mathematics. Volume I : Barcelona, July 10-14, 2000 / Carles Casacuberta ... [et al.], editors. , Boston : Birkhauser, 2001, p. 317-326. Y1 - 2000 A1 - Gianni Dal Maso AB - The calibration method is used to identify some minimizers of the Mumford-Shah functional. The method is then extended to more general free discontinuity problems. PB - SISSA Library UR - http://hdl.handle.net/1963/1496 U1 - 2667 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the convergence of Godunov scheme for nonlinear hyperbolic systems JF - Chinese Ann. Math. B, 2000, 21, 269 Y1 - 2000 A1 - Alberto Bressan A1 - Helge Kristian Jenssen PB - SISSA Library UR - http://hdl.handle.net/1963/1473 U1 - 2690 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Diffusion time and splitting of separatrices for nearly integrable JF - Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei Mat. Appl., 2000, 11, 235 Y1 - 2000 A1 - Massimiliano Berti A1 - Philippe Bolle PB - SISSA Library UR - http://hdl.handle.net/1963/1547 U1 - 2571 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Elliptic variational problems in $ R\\\\sp N$ with critical growth JF - J. Differential Equations 168 (2000), no. 1, 10--32 Y1 - 2000 A1 - Antonio Ambrosetti A1 - Jesus Garcia Azorero A1 - Ireneo Peral PB - SISSA Library UR - http://hdl.handle.net/1963/1258 U1 - 3197 ER - TY - JOUR T1 - Existence and multiplicity results for some nonlinear elliptic equations: a survey. JF - Rend. Mat. Appl., 2000, 20, 167 Y1 - 2000 A1 - Antonio Ambrosetti A1 - Jesus Garcia Azorero A1 - Ireneo Peral PB - SISSA Library UR - http://hdl.handle.net/1963/1462 U1 - 3078 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Existence and multiplicity results for some problems in Riemannian geometry Y1 - 2000 A1 - Andrea Malchiodi KW - Yamabe problem PB - SISSA UR - http://hdl.handle.net/1963/5948 U1 - 5808 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Functionals depending on curvatures with constraints JF - Rend. Sem. Mat. Univ. Padova 104 (2000), 173--199 Y1 - 2000 A1 - Maria Giovanna Mora A1 - Massimiliano Morini PB - SISSA Library UR - http://hdl.handle.net/1963/1299 U1 - 3156 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - High-order Averaging and Stability of Time-Varying Systems Y1 - 2000 A1 - Andrey Sarychev PB - SISSA Library UR - http://hdl.handle.net/1963/1465 U1 - 3075 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Local calibrations for minimizers of the Mumford-Shah functional with rectilinear discontinuity sets JF - J. Math. Pures Appl. 79, 2 (2000) 141-162 Y1 - 2000 A1 - Gianni Dal Maso A1 - Maria Giovanna Mora A1 - Massimiliano Morini PB - SISSA Library UR - http://hdl.handle.net/1963/1261 U1 - 3194 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Minimization of functionals of the gradient by Baire's theorem JF - SIAM J. Control Optim. 38 (2000) 384-399 Y1 - 2000 A1 - Sandro Zagatti AB -We give sufficient conditions for the existence of solutions of the minimum problem $$ {\mathcal{P}}_{u_0}: \qquad \hbox{Minimize}\quad \int_\Omega g(Du(x))dx, \quad u\in u_0 + W_0^{1,p}(\Omega,{\mathbb{R}}), $$ based on the structure of the epigraph of the lower convex envelope of g, which is assumed be lower semicontinuous and to grow at infinity faster than the power p with p larger than the dimension of the space. No convexity conditions are required on g, and no assumptions are made on the boundary datum $u_0\in W_0^{1,p}(\Omega,\mathbb{R})$.

PB - SIAM UR - http://hdl.handle.net/1963/3511 U1 - 753 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A note on the scalar curvature problem in the presence of symmetries JF - Ricerche Mat. 49 (2000), suppl., 169-176 Y1 - 2000 A1 - Antonio Ambrosetti A1 - Li YanYan A1 - Andrea Malchiodi PB - SISSA Library UR - http://hdl.handle.net/1963/1365 U1 - 3090 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - Principal invariants of Jacobi curves T2 - Nonlinear control in the Year 2000 / Alberto Isidori, Francoise Lamnabhi-Lagarrigue, Witold Respondek (eds.) - Springer : Berlin, 2001. - (Lecture notes in control and information sciences ; 258). - ISBN 1-85233-363-4 (v. 1). - p. 9-22. Y1 - 2000 A1 - Andrei A. Agrachev A1 - Igor Zelenko AB - Jacobi curves are far going generalizations of the spaces of \\\"Jacobi fields\\\" along Riemannian geodesics. Actually, Jacobi curves are curves in the Lagrange Grassmannians. Differential geometry of these curves provides basic feedback or gauge invariants for a wide class of smooth control systems and geometric structures. In the present paper we mainly discuss two principal invariants: the generalized Ricci curvature, which is an invariant of the parametrized curve in the Lagrange Grassmanian providing the curve with a natural projective structure, and a fundamental form, which is a 4-oder differential on the curve. JF - Nonlinear control in the Year 2000 / Alberto Isidori, Francoise Lamnabhi-Lagarrigue, Witold Respondek (eds.) - Springer : Berlin, 2001. - (Lecture notes in control and information sciences ; 258). - ISBN 1-85233-363-4 (v. 1). - p. 9-22. PB - Springer UR - http://hdl.handle.net/1963/3825 U1 - 502 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quantized control systems and discrete nonholonomy JF - Lagrangian and Hamiltonian Methods for Nonlinear Control : a proc. volume from the IFAC Workshop. Princeton, New Jersey, 16-18 March 2000 / ed. by N.E. Leonard, R. Ortega. - Oxford : Pergamon, 2000 Y1 - 2000 A1 - Alessia Marigo A1 - Benedetto Piccoli A1 - Antonio Bicchi PB - Elsevier SN - 0-08-043658-7 UR - http://hdl.handle.net/1963/1502 U1 - 2661 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - Reachability Analysis for a Class of Quantized Control Systems T2 - Proc. 39th IEEE Int. Conf. on Decision and Control 4 (2000) 3963-3968 Y1 - 2000 A1 - Alessia Marigo A1 - Benedetto Piccoli A1 - Antonio Bicchi AB - We study control systems whose input sets are quantized. 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 on some results on the reachable set of linear quantized systems, and study in detail an interesting class of nonlinear systems, forming the discrete counterpart of driftless nonholonomic continuous systems. For such systems, we provide a complete characterization of the reachable set, and, in the case the set is discrete, a computable method to describe its lattice structure. JF - Proc. 39th IEEE Int. Conf. on Decision and Control 4 (2000) 3963-3968 PB - IEEE UR - http://hdl.handle.net/1963/3518 U1 - 746 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Regular Synthesis and Sufficiency Conditions for Optimality JF - SIAM J. Control Optim. 39 (2000) 359-410 Y1 - 2000 A1 - Benedetto Piccoli A1 - Hector J. Sussmann AB - We propose a definition of \\\"regular synthesis\\\" that is more general than those suggested by other authors such as Boltyanskii and Brunovsky, and an even more general notion of \\\"regular presynthesis.\\\" We give a complete proof of the corresponding sufficiency theorem, a slightly weaker version of which had been stated in an earlier article, with only a rough outline of the proof. We illustrate the strength of our result by showing that the optimal synthesis for the famous Fuller problem satisfies our hypotheses. We also compare our concept of synthesis with the simpler notion of a \\\"family of solutions of the closed-loop equation arising from an optimal feedback law,\\\" and show by means of examples why the latter is inadequate, and why the difficulty cannot be resolved byusing other concepts of solution--such as Filippov solutions, or the limits of sample-and-hold solutions recently proposed as feedback solutions by Clarke, Ledyaev, Subbotin and Sontag -for equations with a non-Lipschitz and possibly discontinuous right-hand side. PB - SIAM UR - http://hdl.handle.net/1963/3213 U1 - 1088 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Scalar curvature under boundary conditions JF - Cr. Acad. Sci. I-Math, 2000, 330, 1013 Y1 - 2000 A1 - Antonio Ambrosetti A1 - Li YanYan A1 - Andrea Malchiodi PB - SISSA Library UR - http://hdl.handle.net/1963/1506 U1 - 2657 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The semigroup generated by a Temple class system with non-convex flux function JF - Differential Integral Equations 13 (2000) 1529-1550 Y1 - 2000 A1 - Stefano Bianchini AB - We consider the Cauchy problem for a nonlinear n × n system of conservation laws of Temple class, i.e. with coinciding shock and rarefaction curves and with a coordinate system made of Riemann invariants. Without any assumption on the convexity of the flux function, we prove the existence of a semigroup made of weak solutions of the equations and depending Lipschitz continuously on the initial data with bounded total variation. PB - Khayyam Publishing UR - http://hdl.handle.net/1963/3221 U1 - 1080 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the shift differentiability of the flow generated by a hyperbolic system of conservation laws JF - Discrete Contin. Dynam. Systems 6 (2000), no. 2, 329-350 Y1 - 2000 A1 - Stefano Bianchini PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/1274 U1 - 3181 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Stability of L^infty Solutions of Temple Class Systems JF - Differential Integral Equations 13 (2000) 1503-1528 Y1 - 2000 A1 - Alberto Bressan A1 - Paola Goatin AB -Let $u_t+f(u)_x=0$ be a strictly hyperbolic, genuinely nonlinear system of conservation laws of Temple class. In this paper, a continuous semigroup of solutions is constructed on a domain of $L^\infty$ functions, with possibly unbounded variation. Trajectories depend Lipschitz continuously on the initial data, in the $L^1$ distance. Moreover, we show that a weak solution of the Cauchy problem coincides with the corresponding semigroup trajectory if and only if it satisfies an entropy condition of Oleinik type, concerning the decay of positive waves.

PB - Khayyam Publishing UR - http://hdl.handle.net/1963/3256 U1 - 1445 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On a Steffen\\\'s result about parametric surfaces with prescribed mean curvature Y1 - 2000 A1 - Roberta Musina A1 - Paolo Caldiroli PB - SISSA Library UR - http://hdl.handle.net/1963/1558 U1 - 2560 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A Uniqueness Condition for Hyperbolic Systems of Conservation Laws JF - Discrete Contin. Dynam. Systems 6 (2000) 673-682 Y1 - 2000 A1 - Alberto Bressan A1 - Marta Lewicka AB - Consider the Cauchy problem for a hyperbolic $n\\\\times n$ system of conservation laws in one space dimension: $$u_t+f(u)_x=0, u(0,x)=\\\\bar u(x).\\\\eqno(CP)$$ Relying on the existence of a continuous semigroup of solutions, we prove that the entropy admissible solution of (CP) is unique within the class of functions $u=u(t,x)$ which have bounded variation along a suitable family of space-like curves. PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/3195 U1 - 1106 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Value Functions for Bolza Problems with Discontinuous Lagrangians and Hamilton-Jacobi inequalities JF - ESAIM Control Optim. Calc. Var., 5 (2000), n. 5, p. 369-393. Y1 - 2000 A1 - Gianni Dal Maso A1 - Helene Frankowska PB - SISSA Library UR - http://hdl.handle.net/1963/1514 U1 - 2649 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - BOOK T1 - Well-posedness of the Cauchy problem for n x n systems of conservation laws T2 - Mem. Amer. Math. Soc. 146 (2000), no. 694, 134 p. Y1 - 2000 A1 - Alberto Bressan A1 - Graziano Crasta A1 - Benedetto Piccoli JF - Mem. Amer. Math. Soc. 146 (2000), no. 694, 134 p. PB - American Mathematical Society UR - http://hdl.handle.net/1963/3495 N1 - Chapter 1 and 2 U1 - 769 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The anisotropy introduced by the mesh in the finite element approximation of the Mumford-Shah functional JF - Numer. Funct. Anal. Optim. 20 (1999), no. 9-10, 957-982 Y1 - 1999 A1 - Matteo Negri AB - We compute explicitly the anisotropy effect in the H1 term, generated in the approximation of the Mumford-Shah functional by finite element spaces defined on structured triangulations. PB - Taylor and Francis UR - http://hdl.handle.net/1963/1276 U1 - 3179 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Approximation, Stability and control for Conservation Laws Y1 - 1999 A1 - Andrea Marson PB - SISSA UR - http://hdl.handle.net/1963/5500 U1 - 5331 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Asymptotic behaviour of nonlinear elliptic higher order equations in perforated domains JF - Journal d\\\'Analyse Mathematique, Volume 79, 1999, Pages: 63-112 Y1 - 1999 A1 - Gianni Dal Maso A1 - Igor V. Skrypnik SN - 1618-1891 UR - http://hdl.handle.net/1963/6433 U1 - 6374 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Blowup asymptotics for scalar conservation laws with a source JF - Comm. in Partial Differential Equations 24 (1999) 2237-2261 Y1 - 1999 A1 - Helge Kristian Jenssen A1 - Carlo Sinestrari PB - Taylor and Francis UR - http://hdl.handle.net/1963/3482 U1 - 782 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The calibration method for the Mumford-Shah functional JF - C. R. Acad. Sci. Paris Ser. I Math. 329 (1999), no. 3, 249-254 Y1 - 1999 A1 - Giovanni Alberti A1 - Guy Bouchitte A1 - Gianni Dal Maso AB - In this Note we adapt the calibration method to functionals of Mumford-Shah type, and provide a criterion (Theorem 1) to verify that a given function is energy minimizing. Among other applications, we use this criterion to show that certain triple-junction configurations are minimizing (Example 3). PB - Elsevier UR - http://hdl.handle.net/1963/1235 U1 - 2708 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Discrete approximation of the Mumford-Shah functional in dimension two JF - M2AN 33 (1999) 651-672 Y1 - 1999 A1 - Antonin Chambolle A1 - Gianni Dal Maso PB - EDP Sciences UR - http://hdl.handle.net/1963/3588 U1 - 712 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Evans-Vasilesco theorem in Dirichlet spaces JF - Rendiconti di Matematica e delle sue Applicazioni. vol. 19, Issue 7, (1999), pages : 1-15 Y1 - 1999 A1 - Gianni Dal Maso A1 - Virginia De Cicco PB - SISSA UR - http://hdl.handle.net/1963/6436 U1 - 6376 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Extremal faces of the range of a vector measure and a theorem of Lyapunov JF - J. Math. Anal. Appl. 231 (1999) 301-318 Y1 - 1999 A1 - Stefano Bianchini PB - Elsevier UR - http://hdl.handle.net/1963/3370 U1 - 960 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Hyperbolic Systems of Conservation Laws JF - Rev. Mat. Complut. 12 (1999) 135-200 Y1 - 1999 A1 - Alberto Bressan AB - This is a survey paper, written in the occasion of an invited talk given by the author at the Universidad Complutense in Madrid, October 1998. Its purpose is to provide an account of some recent advances in the mathematical theory of hyperbolic systems of conservation laws in one space dimension. After a brief review of basic concepts, we describe in detail the method of wave-front tracking approximation and present some of the latest results on uniqueness and stability of entropy weak solutions. UR - http://hdl.handle.net/1963/1855 U1 - 77 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - L-1 stability estimates for n x n conservation laws JF - Arch. Ration. Mech. Anal. 149 (1999), no. 1, 1--22 Y1 - 1999 A1 - Alberto Bressan A1 - Tai-Ping Liu A1 - Tong Yang AB - Let $u_t+f(u)_x=0$ be a strictly hyperbolic $n\\\\times n$ system of conservation laws, each characteristic field being linearly degenerate or genuinely nonlinear. In this paper we explicitly define a functional $\\\\Phi=\\\\Phi(u,v)$, equivalent to the $L^1$ distance, which is `almost decreasing\\\', i.e., $\\\\Phi(u(t),v(t))-\\\\Phi(u(s),v(s))\\\\leq\\\\break O (\\\\epsilon)·(t-s)$ for all $t>s\\\\geq 0$, for every pair of $\\\\epsilon$-approximate solutions $u,v$ with small total variation, generated by a wave-front-tracking algorithm. The small parameter $\\\\epsilon$ here controls the errors in the wave speeds, the maximum size of rarefaction fronts and the total strength of all non-physical waves in $u$ and in $v$. From the above estimate, it follows that front-tracking approximations converge to a unique limit solution, depending Lipschitz continuously on the initial data, in the $L^1$ norm. This provides a new proof of the existence of the standard Riemann semigroup generated by an $n\\\\times n$ system of conservation laws.\\\'\\\' PB - Springer UR - http://hdl.handle.net/1963/3373 U1 - 957 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A Lipschitz selection from the set of minimizers of a nonconvex functional of the gradient JF - Nonlinear Analysis, Theory, Methods and Applications. Volume 37, Issue 6, September 1999, Pages 707-717 Y1 - 1999 A1 - Gianni Dal Maso A1 - Vladimir V. Goncharov A1 - Antonio Ornelas AB - A constructive and improved version of the proof that there exist a continuous map that solves the convexified problem is presented. A Lipschitz continuous map is analyzed such that a map vector minimizes the functional at each vector satisfying Cellina\\\'s condition of existence of minimum. This map is explicitly given by a direct constructive algorithm. PB - SISSA UR - http://hdl.handle.net/1963/6439 U1 - 6379 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - A multiplicity result for the Yamabe problem on $S\\\\sp n$ JF - J. Funct. Anal. 168 (1999), no. 2, 529-561 Y1 - 1999 A1 - Antonio Ambrosetti A1 - Andrea Malchiodi AB - We prove a multiplicity result for the Yamabe problem on the manifold (S, g), where g is a perturbation of the standard metric g0 of Sn. Solutions are found by variational methods via an abstract perturbation result. PB - Elsevier UR - http://hdl.handle.net/1963/1264 U1 - 3191 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Nonclassical Shocks and the Cauchy Problem for Nonconvex Conservation Laws JF - J. Differential Equations 151 (1999) 345-372 Y1 - 1999 A1 - Debora Amadori A1 - Paolo Baiti A1 - Philippe G. LeFloch A1 - Benedetto Piccoli AB - The Riemann problem for a conservation law with a nonconvex (cubic) flux can be solved in a class of admissible nonclassical solutions that may violate the Oleinik entropy condition but satisfy a single entropy inequality and a kinetic relation. We use such a nonclassical Riemann solver in a front tracking algorithm, and prove that the approximate solutions remain bounded in the total variation norm. The nonclassical shocks induce an increase of the total variation and, therefore, the classical measure of total variation must be modified accordingly. We prove that the front tracking scheme converges strongly to a weak solution satisfying the entropy inequality. PB - Elsevier UR - http://hdl.handle.net/1963/3312 U1 - 1018 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Oleinik type estimates and uniqueness for n x n conservation laws JF - J. Differential Equations 156 (1999), no. 1, 26--49 Y1 - 1999 A1 - Alberto Bressan A1 - Paola Goatin AB - Let $u_t+f(u)_x=0$ be a strictly hyperbolic $n\\\\times n$ system of conservation laws in one space dimension. Relying on the existence of a semigroup of solutions, we first establish the uniqueness of entropy admissible weak solutions to the Cauchy problem, under a mild assumption on the local oscillation of $u$ in a forward neighborhood of each point in the $t\\\\text{-}x$ plane. In turn, this yields the uniqueness of weak solutions which satisfy a decay estimate on positive waves of genuinely nonlinear families, thus extending a classical result proved by Oleĭnik in the scalar case. PB - Elsevier UR - http://hdl.handle.net/1963/3375 U1 - 955 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Perturbation of $\Delta u+u^(N+2)/(N-2)=0$, the scalar curvature problem in $R^N$, and related topics JF - J. Funct. Anal. 165 (1999) 117-149 Y1 - 1999 A1 - Antonio Ambrosetti A1 - Jesus Garcia Azorero A1 - Ireneo Peral AB -Some nonlinear elliptic equations on $R^N$ which arise perturbing the problem with the critical Sobolev exponent are studied. In particular, some results dealing with the scalar curvature problem in $R^N$ are given.

PB - Elsevier UR - http://hdl.handle.net/1963/3255 U1 - 1446 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Projection singularities of extremals for planar systems Y1 - 1999 A1 - Ugo Boscain A1 - Benedetto Piccoli PB - SISSA Library UR - http://hdl.handle.net/1963/1304 U1 - 3151 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Renormalized solutions of elliptic equations with general measure data JF - Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 28 (1999), no. 4, 741-808 Y1 - 1999 A1 - Gianni Dal Maso A1 - Francois Murat A1 - Luigi Orsina A1 - Alain Prignet PB - Scuola Normale Superiore di Pisa UR - http://hdl.handle.net/1963/1236 U1 - 2707 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the scalar curvature problem under symmetry Y1 - 1999 A1 - Antonio Ambrosetti A1 - Andrea Malchiodi PB - SISSA Library UR - http://hdl.handle.net/1963/1287 U1 - 3168 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Some properties of the solutions of obstacle problems with measure data JF - Ricerche Matematiche., Supplemento dedicato a Ennio De Giorgi, vol. 48 (1999), page : 99-116 Y1 - 1999 A1 - Paolo Dall'Aglio A1 - Gianni Dal Maso UR - http://hdl.handle.net/1963/6432 U1 - 6372 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Structural stability and regularity of entropy solutions to hyperbolic systems of conservation laws JF - Indiana Univ. Math. J. 48 (1999), no. 1, 43--84 Y1 - 1999 A1 - Alberto Bressan A1 - Philippe G. LeFloch AB - The paper is concerned with the qualitative structure of entropy solutions to a strictly hyperbolic, genuinely nonlinear system of conservation laws. We first give an accurate description of the local and global wave-front structure of a BV solution, generated by a front tracking algorithm. PB - Indiana University UR - http://hdl.handle.net/1963/3374 U1 - 956 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Vanishing viscosity solutions of hyperbolic systems on manifolds Y1 - 1999 A1 - Stefano Bianchini A1 - Alberto Bressan PB - SISSA Library UR - http://hdl.handle.net/1963/1238 U1 - 2705 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Variational formulation of softening phenomena in fracture mechanics. The one-dimensional case JF - Arch. Ration. Mech. Anal. 146 (1999), no. 1, 23--58 Y1 - 1999 A1 - Andrea Braides A1 - Gianni Dal Maso A1 - Adriana Garroni AB - Starting from experimental evidence, the authors justify a variational model for softening phenomena in fracture of one-dimensional bars where the energy is given by the contribution and interaction of two terms: a typical bulk energy term depending on elastic strain and a discrete part that depends upon the jump discontinuities that occur in fracture. A more formal, rigorous derivation of the model is presented by examining the $\\\\Gamma$-convergence of discrete energy functionals associated to an array of masses and springs. Close attention is paid to the softening and fracture regimes. \\nOnce the continuous model is derived, it is fully analyzed without losing sight of its discrete counterpart. In particular, the associated boundary value problem is studied and a detailed analysis of the stationary points under the presence of a dead load is performed. A final, interesting section on the scale effect on the model is included. PB - Springer UR - http://hdl.handle.net/1963/3371 U1 - 959 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The vector measures whose range is strictly convex JF - J. Math. Anal. Appl. 232 (1999) 1-19 Y1 - 1999 A1 - Stefano Bianchini A1 - Carlo Mariconda PB - Elsevier UR - http://hdl.handle.net/1963/3546 U1 - 1155 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Asymptotic behavior of nonlinear Dirichlet problems in perforated domains JF - Ann. Mat. Pura Appl. (4) 174 (1998), 13--72 Y1 - 1998 A1 - Gianni Dal Maso A1 - Igor V. Skrypnik PB - SISSA Library UR - http://hdl.handle.net/1963/1064 U1 - 2738 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Branching points for a class of variational operators JF - J. Anal. Math. 76 (1998) 321-335 Y1 - 1998 A1 - Antonio Ambrosetti PB - Springer UR - http://hdl.handle.net/1963/3314 U1 - 1016 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the Dirichlet problem for vectorial Hamilton-Jacobi equations JF - SIAM J. Math. Anal. 29 (1998) 1481-1491 Y1 - 1998 A1 - Sandro Zagatti AB - We give sufficient conditions for the existence of solutions to the Hamilton--Jacobi equations with Dirichlet boundary condition: $$ \\\\cases{ g(x,{\\\\hbox{\\\\rm det}}Du(x))=0, \\\\ & for a.e. $x\\\\in\\\\Omega,$\\\\cr u(x)=\\\\varphi(x), & for $x\\\\in\\\\partial\\\\Omega,$} $$ obtaining, in addition, an application to the theory of existence of minimizers for a class of nonconvex variational problems. PB - SIAM UR - http://hdl.handle.net/1963/3512 U1 - 752 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Error bounds for a deterministic version of the Glimm scheme JF - Arch. Rational Mech. Anal. 142 (1998), no. 2, 155-176 Y1 - 1998 A1 - Andrea Marson A1 - Alberto Bressan AB - Consider the hyperbolic system of conservation laws $u_t F(u)_x=0. Let $u$ be the unique viscosity solution with initial condition $u(0,x)=\\\\bar u(x)$ and let $u^\\\\varepsilon$ be an approximate solution constructed by the Glimm scheme, corresponding to the mesh sizes $\\\\Delta x,\\\\Delta t=O(\\\\Delta x). With a suitable choise of the sampling sequence, we prove the estimate $$ \\\\left\\\\Vert u^\\\\varepsilon(t,\\\\cdot)-u(t,\\\\cdot) \\\\right\\\\Vert_1=o(1)\\\\cdot\\\\sqrt{\\\\Delta x}\\\\vert\\\\ln\\\\Delta x\\\\vert. $$ PB - Springer UR - http://hdl.handle.net/1963/1045 U1 - 2811 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A generic classification of time-optimal planar stabilizing feedbacks JF - SIAM J. Control Optim. 36 (1998) 12-32 Y1 - 1998 A1 - Alberto Bressan A1 - Benedetto Piccoli AB - Consider the problem of stabilization at the origin in minimum time for a planar control system affine with respect to the control. For a family of generic vector fields, a topological equivalence relation on the corresponding time-optimal feedback synthesis was introduced in a previous paper [Dynamics of Continuous, Discrete and Impulsive Systems, 3 (1997), pp. 335--371]. The set of equivalence classes can be put in a one-to-one correspondence with a discrete family of graphs. This provides a classification of the global structure of generic time-optimal stabilizing feedbacks in the plane, analogous to the classification of smooth dynamical systems developed by Peixoto. PB - SISSA Library UR - http://hdl.handle.net/1963/998 U1 - 2858 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Geometric control approach to synthesis theory JF - Rend. Sem. Mat. Univ. Politec. Torino 56 (1998), no. 4, 53-68 (2001) Y1 - 1998 A1 - Ugo Boscain A1 - Benedetto Piccoli PB - SISSA Library UR - http://hdl.handle.net/1963/1277 U1 - 3178 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Infinite time regular synthesis JF - ESAIM: COCV 3 (1998) 381-405 Y1 - 1998 A1 - Benedetto Piccoli AB - In this paper we provide a new sufficiency theorem for regular syntheses. The concept of regular synthesis is discussed in [12], where a sufficiency theorem for finite time syntheses is proved. There are interesting examples of optimal syntheses that are very regular, but whose trajectories have time domains not necessarily bounded. The regularity assumptions of the main theorem in [12] are verified by every piecewise smooth feedback control generating extremal trajectories that reach the target in finite time with a finite number of switchings. In the case of this paper the situation is even more complicate, since we admit both trajectories with finite and infinite time. We use weak differentiability assumptions on the synthesis and weak continuity assumptions on the associated value function. PB - EDP Sciences UR - http://hdl.handle.net/1963/3517 U1 - 747 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Limits of variational problems for Dirichlet forms in varying domains JF - Journal des Mathematiques Pures et Appliquees. Volume 77, Issue 1, January 1998, Pages 89-116 Y1 - 1998 A1 - Gianni Dal Maso A1 - Virginia De Cicco A1 - Lino Notarantonio A1 - Nicoletta A. Tchou PB - SISSA UR - http://hdl.handle.net/1963/6440 U1 - 6377 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Special functions with bounded variation and with weakly differentiable traces on the jump set JF - NoDEA Nonlinear Differential Equations Appl. 5 (1998), no. 2, 219--243 Y1 - 1998 A1 - Luigi Ambrosio A1 - Andrea Braides A1 - Adriana Garroni PB - SISSA Library UR - http://hdl.handle.net/1963/1025 U1 - 2831 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Uniqueness for discontinuous ODE and conservation laws JF - Nonlinear Analysis 34 (1998) 637-652 Y1 - 1998 A1 - Alberto Bressan A1 - Wen Shen AB - Consider a scalar O.D.E. of the form $\\\\dot x=f(t,x),$ where $f$ is possibly discontinuous w.r.t. both variables $t,x$. Under suitable assumptions, we prove that the corresponding Cauchy problem admits a unique solution, which depends H\\\\\\\"older continuously on the initial data.\\nOur result applies in particular to the case where $f$ can be written in the form $f(t,x)\\\\doteq g\\\\big( u(t,x)\\\\big)$, for some function $g$ and some solution $u$ of a scalar conservation law, say $u_t+F(u)_x=0$. In turn, this yields the uniqueness and continuous dependence of solutions to a class of $2\\\\times 2$ strictly hyperbolic systems, with initial data in $\\\\L^\\\\infty$. PB - Elsevier UR - http://hdl.handle.net/1963/3699 U1 - 606 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Capacity theory for monotone operators JF - Potential Anal. 7 (1997), no. 4, 765-803 Y1 - 1997 A1 - Gianni Dal Maso A1 - Igor V. Skrypnik AB - If $Au=-div(a(x,Du))$ is a monotone operator defined on the Sobolev space $W^{1,p}(R^n)$, $1< p <+\\\\infty$, with $a(x,0)=0$ for a.e. $x\\\\in R^n$, the capacity $C_A(E,F)$ relative to $A$ can be defined for every pair $(E,F)$ of bounded sets in $R^n$ with $E\\\\subset F$. We prove that $C_A(E,F)$ is increasing and countably subadditive with respect to $E$ and decreasing with respect to $F$. Moreover we investigate the continuity properties of $C_A(E,F)$ with respect to $E$ and $F$. PB - Springer UR - http://hdl.handle.net/1963/911 U1 - 2880 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Comportamento asintotico delle soluzioni di problemi di Dirichlet JF - Bollettino della Unione Matematica Italiana A. Volume 7, Issue SUPPL. 11 part 2, June 1997, Pages 253-277 Y1 - 1997 A1 - Gianni Dal Maso UR - http://hdl.handle.net/1963/6438 N1 - This is the title of the conference which was delivered by prof. Dal Maso in Padova during the XV Congress of the \\\"Unione Mathematica Italiana\\\" (Padova, 11-16 settembre 1995) U1 - 6378 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - THES T1 - On Existence and Continuous Dependence for Systems of Conservation Laws Y1 - 1997 A1 - Paolo Baiti KW - Conservation laws PB - SISSA UR - http://hdl.handle.net/1963/5588 U1 - 5418 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Homogeneous tangent vectors and high order necessary conditions for optimal controls JF - J. Dynam. Control Systems 3 (1997), no. 2, 205--240 Y1 - 1997 A1 - Fabio Ancona PB - SISSA Library UR - http://hdl.handle.net/1963/1015 U1 - 2841 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The semigroup generated by a temple class system with large data JF - Differential Integral Equations 10 (1997), no. 3, 401-418 Y1 - 1997 A1 - Paolo Baiti A1 - Alberto Bressan AB - We consider the Cauchy problem $$u_t + [F(u)]_x=0, u(0,x)=\\\\bar u(x) (*)$$ for a nonlinear $n\\\\times n$ system of conservation laws with coinciding shock and rarefaction curves. Assuming the existence of a coordinates system made of Riemann invariants, we prove the existence of a weak solution of (*) that depends in a lipschitz continuous way on the initial data, in the class of functions with arbitrarily large but bounded total variation. PB - SISSA Library UR - http://hdl.handle.net/1963/1023 U1 - 2833 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Shift-differentiability of the flow generated by a conservation law JF - Discrete Contin. Dynam. Systems 3 (1997), no. 1, 35--58. Y1 - 1997 A1 - Alberto Bressan A1 - Graziano Guerra AB - The paper introduces a notion of \\\"shift-differentials\\\" for maps with values in the space BV. These differentials describe first order variations of a given functin $u$, obtained by horizontal shifts of the points of its graph. The flow generated by a scalar conservation law is proved to be generically shift-differentiable, according to the new definition. PB - SISSA Library UR - http://hdl.handle.net/1963/1033 U1 - 2823 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Some Problems in the Asymptotic Analysis of Partial Differential Equations in Perforated Domains Y1 - 1997 A1 - Rodica Toader KW - Dirichlet problems PB - SISSA UR - http://hdl.handle.net/1963/5698 U1 - 5541 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Some properties of reachable solutions of nonlinear elliptic equations with measure data JF - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. Sér. 4, 25 no. 1-2 (1997), p. 375-396 Y1 - 1997 A1 - Gianni Dal Maso A1 - Annalisa Malusa PB - SISSA UR - http://hdl.handle.net/1963/6434 U1 - 6375 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Structural stability for time-optimal planar sytheses JF - Dynam. Contin. Discrete Impuls. Systems 3 (1997), no. 3, 335--371 Y1 - 1997 A1 - Alberto Bressan A1 - Benedetto Piccoli PB - SISSA Library UR - http://hdl.handle.net/1963/997 U1 - 2859 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Viscosity solutions and uniquenessfor systems of inhomogeneous balance laws JF - Discrete Contin. Dynam. Systems 3 (1997), no. 4, 477--5 Y1 - 1997 A1 - Graziano Crasta A1 - Benedetto Piccoli PB - SISSA Library UR - http://hdl.handle.net/1963/969 U1 - 3485 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A capacity method for the study of Dirichlet problems for elliptic systems in varying domains JF - Rend. Sem. Mat. Univ. Padova 96 (1996), 257--277 Y1 - 1996 A1 - Gianni Dal Maso A1 - Rodica Toader PB - SISSA Library UR - http://hdl.handle.net/1963/989 U1 - 2867 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The semigroup approach to systems of conservation laws JF - Mat. Contemp. 10 (1996) 21-74 Y1 - 1996 A1 - Alberto Bressan PB - Sociedade Brasileira de Matematica UR - http://hdl.handle.net/1963/1037 U1 - 2819 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Solving Honig generic problem about Volterra integral equations JF - Bull. Polish Acad. Sci. Math. 44 (1996), no. 4, 495--498 Y1 - 1996 A1 - Giovanni Vidossich PB - SISSA Library UR - http://hdl.handle.net/1963/941 U1 - 3513 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Capacity and Dirichlet problems in varying domains Y1 - 1995 A1 - Gianni Dal Maso PB - SISSA Library UR - http://hdl.handle.net/1963/950 U1 - 3504 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - An existence result in a problem of the vectorial case of the calculus of variations Y1 - 1995 A1 - Arrigo Cellina A1 - Sandro Zagatti AB - SIAM J. Control Optim. 33 (1995) 960-970 PB - SIAM UR - http://hdl.handle.net/1963/3513 U1 - 751 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Some control problems for the pendulum JF - Proceedings of the 34th IEEE Conference on Decision and Control 4 (1995) 3313-3318 Y1 - 1995 A1 - Benedetto Piccoli AB - The aim of this paper is to illustrate some geometric techniques for the study of nonlinear systems. The pendulum on one hand is good for its simplicity, on the other it presents many of the difficulties one can encounter treating nonlinear systems. PB - IEEE UR - http://hdl.handle.net/1963/982 U1 - 2874 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Special functions of bounded deformation Y1 - 1995 A1 - Giovanni Bellettini A1 - Alessandra Coscia A1 - Gianni Dal Maso PB - SISSA Library UR - http://hdl.handle.net/1963/978 U1 - 3476 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Unique solutions of 2x2 conservation laws with large data JF - Indiana Univ. Math. J. 44 (1995), no. 3, 677-725 Y1 - 1995 A1 - Alberto Bressan A1 - Rinaldo M. Colombo AB - For a 2x2 hyperbolic system of conservation laws, we first consider a Riemann problem with arbitrarily large data. A stability assumption is introduced, which yields the existence of a Lipschitz semigroup of solutions, defined on a domain containing all suitably small BV perturbations of the Riemann data. We then establish a uniqueness result for large BV solutions, valid within the same class of functions where a local existence theorem can be proved. PB - Indiana University Mathematics Journal UR - http://hdl.handle.net/1963/975 U1 - 3479 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Asymptotic Behaviour of Dirichlet Problems in Perforated Domains Y1 - 1994 A1 - Adriana Garroni KW - Dirichlet problems PB - SISSA UR - http://hdl.handle.net/1963/5714 U1 - 5566 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Limits of Dirichlet problems in perforated domains: a new formulation JF - Rend. Istit. Mat. Univ. Trieste 26 (1994) 339-360 Y1 - 1994 A1 - Gianni Dal Maso A1 - Rodica Toader PB - Università degli Studi di Trieste, Dipartimento di Scienze Matematiche UR - http://hdl.handle.net/1963/3649 U1 - 656 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A version of Olech\\\'s lemma in a problem of the calculus of variations JF - SIAM J. Control Optim. 32 (1994) 1114-1127 Y1 - 1994 A1 - Arrigo Cellina A1 - Sandro Zagatti AB - This paper studies the solutions of the minimum problem for a functional of the gradient under linear boundary conditions. A necessary and sufficient condition, based on the facial structure of the epigraph of the integrand, is provided for the continuous dependence of the solutions on boundary data. PB - SIAM UR - http://hdl.handle.net/1963/3514 U1 - 750 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Some Problems in the Calculus of the Variations Y1 - 1992 A1 - Sandro Zagatti KW - Calculus of variations PB - SISSA UR - http://hdl.handle.net/1963/5428 U1 - 5260 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - A variational method in image segmentation: existence and approximation result JF - Acta Math. 168 (1992), no.1-2, p. 89-151 Y1 - 1992 A1 - Gianni Dal Maso A1 - Jean-Michel Morel A1 - Sergio Solimini PB - SISSA Library UR - http://hdl.handle.net/1963/808 U1 - 2983 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A class of absolute retracts of dwarf spheroidal galaxies JF - Proc.Amer.Math.Soc. 112 (1991), no.2, 413 Y1 - 1991 A1 - Alberto Bressan A1 - Arrigo Cellina A1 - Andrzej Fryszkowski PB - SISSA Library UR - http://hdl.handle.net/1963/837 U1 - 2954 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Shape optimization for Dirichlet problems: relaxed formulations and optimally conditions JF - Appl.Math.Optim. 23 (1991), no.1, p. 17-49. Y1 - 1991 A1 - Giuseppe Buttazzo A1 - Gianni Dal Maso PB - SISSA Library UR - http://hdl.handle.net/1963/880 U1 - 2911 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On systems of ordinary differential equations with measures as controls JF - Differential Integral Equations 4 (1991), no.4, p.739-765. Y1 - 1991 A1 - Gianni Dal Maso A1 - Franco Rampazzo PB - SISSA Library UR - http://hdl.handle.net/1963/840 U1 - 2951 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Correctors for the homogeneization of monotone operators JF - Differential Integral Equations 3 (1990), no.6, p.1151-1166. Y1 - 1990 A1 - Gianni Dal Maso A1 - Anneliese Defranceschi PB - SISSA Library UR - http://hdl.handle.net/1963/812 U1 - 2979 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence and continuous dependence for discontinuous O.D.E.s JF - Boll. Un. Mat. Ital. B (7) 4 (1990), no. 2, 295--311 Y1 - 1990 A1 - Alberto Bressan A1 - Giovanni Colombo PB - SISSA Library UR - http://hdl.handle.net/1963/716 U1 - 3210 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence of solutions for a class of non-convex differential inclusions JF - Rend.Sem.Mat.Univ. Padova, 83 (1990), 71-76 Y1 - 1990 A1 - Fabio Ancona A1 - Giovanni Colombo PB - SISSA Library UR - http://hdl.handle.net/1963/792 U1 - 2999 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - G-convergence of monotone operators JF - Ann. Inst. H. Poincare\\\' Anal. Non Linére 7 (1990), no. 3, 123-160 Y1 - 1990 A1 - Valeria Chiadò Piat A1 - Gianni Dal Maso A1 - Anneliese Defranceschi PB - SISSA Library UR - http://hdl.handle.net/1963/680 U1 - 3246 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A general chain rule for distributional derivatives JF - Proc. Amer. Math. Soc. 108 (1990), no. 3, 691-702 Y1 - 1990 A1 - Luigi Ambrosio A1 - Gianni Dal Maso PB - SISSA Library UR - http://hdl.handle.net/1963/650 U1 - 3276 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A general existence theorem for boundary value problems for ordinary differential equations JF - Nonlinear Anal. 15 (1990), no. 10, 897--914 Y1 - 1990 A1 - Giovanni Vidossich PB - SISSA Library UR - http://hdl.handle.net/1963/632 U1 - 3821 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Shape optimization for Dirichlet problems: relaxed solutions and optimality conditions JF - Bull. Amer. Math. Soc. (N.S.) , 23 (1990), no.2, 531-535. Y1 - 1990 A1 - Giuseppe Buttazzo A1 - Gianni Dal Maso PB - SISSA Library UR - http://hdl.handle.net/1963/809 U1 - 2982 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - An approach to the thin obstacle problem for variational functionals depending on vector JF - Comm. Partial Differential Equations, 14 (1989), no.12, 1717-1743. Y1 - 1989 A1 - Gianni Dal Maso A1 - Roberta Musina PB - SISSA Library UR - http://hdl.handle.net/1963/802 U1 - 2989 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the continuous dependence of solutions of boundary value problems for ordinary differential equations (Revised version) JF - J. Differential Equations 82 (1989), no. 1, 1-14 Y1 - 1989 A1 - Giovanni Vidossich PB - SISSA Library UR - http://hdl.handle.net/1963/666 U1 - 3260 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the continuous dependence of solutions of boundary value problems for ordinary differential equations JF - J. Differential Equations 82 (1989), no. 1, 1--14 Y1 - 1989 A1 - Giovanni Vidossich PB - SISSA Library UR - http://hdl.handle.net/1963/633 U1 - 3820 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Convergence of unilateral problems for monotone operators JF - J. Analyse Math. 53 (1989), 269--289 Y1 - 1989 A1 - Gianni Dal Maso A1 - Anneliese Defranceschi PB - SISSA Library UR - http://hdl.handle.net/1963/722 U1 - 3069 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Hyperbolic equations as ordinary differential equations in Banach spaces Y1 - 1989 A1 - Giovanni Vidossich PB - SISSA Library UR - http://hdl.handle.net/1963/773 U1 - 3018 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Limits of obstacle problems for the area functional. JF - Partial differential equations and the calculus of variations : essays in honor of Ennio De Giorgi. - Boston : Birkhauser, 1989. - p. 285-309 Y1 - 1989 A1 - Gianni Dal Maso A1 - G. Carere A1 - Antonio Leaci A1 - Eduardo Pascali PB - SISSA Library UR - http://hdl.handle.net/1963/577 U1 - 3327 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A pointwise regularity theory for the two-obstacle problem JF - Acta Math. 163 (1989), no. 1-2, 57-107 Y1 - 1989 A1 - Gianni Dal Maso A1 - Umberto Mosco A1 - Maria Agostina Vivaldi PB - SISSA Library UR - http://hdl.handle.net/1963/643 U1 - 3810 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the solvability of boundary value problems for higher order ordinary differential equations (Revised version) JF - Nonlinear Anal. 13 (1989), no. 10, 1171-1179 Y1 - 1989 A1 - Giovanni Vidossich PB - SISSA Library UR - http://hdl.handle.net/1963/662 U1 - 3264 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the solvability of boundary value problems for higher order ordinary differential equations JF - Nonlinear Anal. 13 (1989), no. 10, 1171-179 Y1 - 1989 A1 - Giovanni Vidossich PB - SISSA Library UR - http://hdl.handle.net/1963/631 U1 - 3822 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Surfaces of minimal area enclosing a given body in R\\\\sp 3. JF - Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 16 (1989), no. 3, 331--354 (1990). Y1 - 1989 A1 - Giovanni Mancini A1 - Roberta Musina PB - SISSA Library UR - http://hdl.handle.net/1963/619 U1 - 3285 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Upper semicontinuous differential inclusions without convexity JF - Proc. Amer. Math. Soc. 106 (1989), no. 3, 771-775 Y1 - 1989 A1 - Alberto Bressan A1 - Arrigo Cellina A1 - Giovanni Colombo PB - SISSA Library UR - http://hdl.handle.net/1963/670 U1 - 3256 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On differential systems with vector-valued impulsive controls. JF - Boll. Un. Mat. Ital. B (7) 2 (1988), no. 3, 641-656 Y1 - 1988 A1 - Alberto Bressan A1 - Franco Rampazzo PB - SISSA Library UR - http://hdl.handle.net/1963/535 U1 - 3369 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Generalized Baire category and differential inclusions in Banach spaces. JF - J. Differential Equations 76 (1988), no. 1, 135-158. Y1 - 1988 A1 - Alberto Bressan A1 - Giovanni Colombo PB - SISSA Library UR - http://hdl.handle.net/1963/538 U1 - 3366 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Holes and obstacles JF - Ann. Inst. H. Poincare Anal. Non Lineaire 5 (1988), no. 4, 323-345 Y1 - 1988 A1 - Roberta Musina A1 - Giovanni Mancini PB - SISSA Library UR - http://hdl.handle.net/1963/501 U1 - 3403 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - H-surfaces with obstacles. (Italian) JF - Ann. Univ. Ferrara Sez. VII (N.S.) 34 (1988), 1-14 Y1 - 1988 A1 - Roberta Musina PB - SISSA Library UR - http://hdl.handle.net/1963/491 U1 - 3413 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A Kellogg property for µ-capacities JF - Boll. Un. Mat. Ital. A (7) 2, 1988, no. 1, 127-135 Y1 - 1988 A1 - Gianni Dal Maso A1 - Anneliese Defranceschi PB - SISSA Library UR - http://hdl.handle.net/1963/492 U1 - 3412 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Limits of nonlinear Dirichlet problems in varying domains. JF - Manuscripta Math. 61 (1988), no. 3, 251-278. Y1 - 1988 A1 - Gianni Dal Maso A1 - Anneliese Defranceschi AB - We study the general form of the limit, in the sense of gamma-convergence, of a sequence of nonlinear variational problems in varying domains with Dirichlet boudary conditions. The asymptotic problem is characterized in terms of the limit of suitable nonlinear capacities associated to the domains. PB - SISSA Library UR - http://hdl.handle.net/1963/536 U1 - 3368 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Some properties of a class of nonlinear variational $m$-capacities JF - J.Funct.Anal. 79, 1988, no. 2, 476-492 Y1 - 1988 A1 - Gianni Dal Maso A1 - Anneliese Defranceschi PB - SISSA Library UR - http://hdl.handle.net/1963/485 U1 - 3419 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Variational inequalities for the biharmonic operator with variable obstacles. JF - Ann. Mat. Pura Appl. (4) 153 (1988), 203-227 (1989) Y1 - 1988 A1 - Gianni Dal Maso A1 - Gabriella Paderni PB - SISSA Library UR - http://hdl.handle.net/1963/531 U1 - 3373 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Variational Problems with Obstructions Y1 - 1988 A1 - Roberta Musina PB - SISSA UR - http://hdl.handle.net/1963/5832 U1 - 5683 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Integral representation of some convex local functionals. JF - Ricerche Mat. 36 (1987), no. 2, 197-214 Y1 - 1987 A1 - Gianni Dal Maso A1 - Gabriella Paderni PB - SISSA Library UR - http://hdl.handle.net/1963/497 U1 - 3407 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Limits of nonlinear Dirichlet problems in varying domains. (Italian) JF - Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 81, 1987, no. 2, 111-118 Y1 - 1987 A1 - Gianni Dal Maso A1 - Anneliese Defranceschi PB - SISSA Library UR - http://hdl.handle.net/1963/486 U1 - 3418 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Solutions with minimal period for Hamiltonian systems in a potential well. JF - Ann. Inst. H. Poincare Anal. Non Lineaire 4 (1987), no. 3, 275-296 Y1 - 1987 A1 - Antonio Ambrosetti A1 - Vittorio Coti Zelati PB - SISSA Library UR - http://hdl.handle.net/1963/466 U1 - 3437 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Symmetry breaking in Hamiltonian systems JF - J. Differential Equations 67 (1987), no. 2, 165-184 Y1 - 1987 A1 - Antonio Ambrosetti A1 - Vittorio Coti Zelati A1 - Ivar Ekeland PB - SISSA Library UR - http://hdl.handle.net/1963/409 U1 - 3558 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Convergence of unilateral convex sets. Optimization and related fields (Erice, 1984) JF - Berlin : Springer-Verlag, 1986, Lecture notes in mathematics, v.1190, p. 181-190 Y1 - 1986 A1 - Gianni Dal Maso PB - SISSA Library UR - http://hdl.handle.net/1963/353 U1 - 3614 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Dirichlet problems for demicoercive functionals JF - Nonlinear anal. 10(1986), no.6, 603-613 Y1 - 1986 A1 - Gabriele Anzellotti A1 - Giuseppe Buttazzo A1 - Gianni Dal Maso PB - SISSA Library UR - http://hdl.handle.net/1963/390 U1 - 3577 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Some necessary and sufficient conditions for the convergence of sequences of unilateral convex sets JF - J. Funct. Anal. 62 (1985), no. 2, 119--159 Y1 - 1985 A1 - Gianni Dal Maso PB - SISSA Library UR - http://hdl.handle.net/1963/318 U1 - 3649 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Some singular perturbation problems in the calculus of variations. JF - Ennio De Giorgi Colloquium, p. 41-49, Research Notes in Mathematics, v.125, London : Pitman, 1985 Y1 - 1985 A1 - Gianni Dal Maso PB - SISSA Library UR - http://hdl.handle.net/1963/297 U1 - 3670 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The two-point boundary value problem from the Cauchy problem JF - J. Differential Equations 60 (1985), no. 1, 1--20 Y1 - 1985 A1 - Giovanni Vidossich PB - SISSA Library UR - http://hdl.handle.net/1963/332 U1 - 3635 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Weak convergence of measures on spaces of semicontinuous functions. JF - Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 79 (1985), no. 5, 98-106 Y1 - 1985 A1 - Gianni Dal Maso A1 - Ennio De Giorgi A1 - Luciano Modica PB - SISSA Library UR - http://hdl.handle.net/1963/463 U1 - 3440 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - On the asymptotic behaviour of solutions to Pazy\\\'s class of evolution equations Y1 - 1983 A1 - Giovanni Vidossich PB - SISSA Library UR - http://hdl.handle.net/1963/276 U1 - 3691 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Towards a theory for periodic solutions to first order ordinary differential equations. Y1 - 1983 A1 - Giovanni Vidossich PB - SISSA Library UR - http://hdl.handle.net/1963/295 U1 - 3672 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A criterion for he existence of maximal solutions of strongly nonlinear elliptic problems Y1 - 1982 A1 - Giovanni Vidossich PB - SISSA Library UR - http://hdl.handle.net/1963/161 U1 - 3806 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Differential equations with multiple solutions and nonlinear functional analysis JF - Equadiff 82 (Wurzburg, 1982), 10--37, Lecture Notes in Math., 1017, Springer, Berlin, 1983 Y1 - 1982 A1 - Antonio Ambrosetti PB - SISSA Library UR - http://hdl.handle.net/1963/222 U1 - 3745 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the obstacle problem for strongly nonlinear elliptic equations Y1 - 1982 A1 - Giovanni Vidossich PB - SISSA Library UR - http://hdl.handle.net/1963/162 U1 - 3805 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Three uniqueness theorems for strongly non-linear elliptic problems Y1 - 1982 A1 - Giovanni Vidossich PB - SISSA Library UR - http://hdl.handle.net/1963/167 U1 - 3800 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Recent advances in the study of the existence of periodic orbits of Hamiltonian systems JF - Advances in Hamiltonian systems (Rome, 1981), 1--22, Ann. CEREMADE, Birkhauser Boston, Boston, MA, 1983. Y1 - 1981 A1 - Antonio Ambrosetti PB - SISSA Library UR - http://hdl.handle.net/1963/159 U1 - 3808 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Uniqueness and multiplicity of periodic solutions to first order ordinary differential equations JF - Not Found Y1 - 0 A1 - Giovanni Vidossich PB - SISSA Library UR - http://hdl.handle.net/1963/321 U1 - 3646 U2 - Mathematics U3 - Functional Analysis and Applications ER -