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

%B Journal of Biological SystemsJournal of Biological Systems %V 30 %P 1 - 25 %8 2022/03/01 %@ 0218-3390 %G eng %U https://doi.org/10.1142/S0218339022500085 %N 01 %! J. Biol. Syst. %0 Journal Article %J Mathematical Methods in the Applied SciencesMathematical Methods in the Applied SciencesMath Meth Appl Sci %D 2022 %T Mathematical modelling of oscillating patterns for chronic autoimmune diseases %A Rossella Della Marca %A Maria da Piedade Machado Ramos %A Carolina Ribeiro %A Ana Jacinta Soares %K autoimmune diseases %K cellular interactions %K Dynamical systems %K Hopf bifurcation %K kinetic theory %K mathematical biology %XMany autoimmune diseases are chronic in nature, so that in general, patients experience periods of recurrence and remission of the symptoms characterizing their specific autoimmune ailment. In order to describe this very important feature of autoimmunity, we construct a mathematical model of kinetic type describing the immune system cellular interactions in the context of autoimmunity exhibiting recurrent dynamics. The model equations constitute a nonlinear system of integro-differential equations with quadratic terms that describe the interactions between self-antigen presenting cells, self-reactive T cells, and immunosuppressive cells. We consider a constant input of self-antigen presenting cells, due to external environmental factors that are believed to trigger autoimmunity in people with predisposition for this condition. We also consider the natural death of all cell populations involved in our model, caused by their interaction with cells of the host environment. We derive the macroscopic analogue and show positivity and well-posedness of the solution and then we study the equilibria of the corresponding dynamical system and their stability properties. By applying dynamical system theory, we prove that steady oscillations may arise due to the occurrence of a Hopf bifurcation. We perform some numerical simulations for our model, and we observe a recurrent pattern in the solutions of both the kinetic description and its macroscopic analogue, which leads us to conclude that this model is able to capture the chronic behaviour of many autoimmune diseases.

%B Mathematical Methods in the Applied SciencesMathematical Methods in the Applied SciencesMath Meth Appl Sci %V n/a %8 2022/04/01 %@ 0170-4214 %G eng %U https://doi.org/10.1002/mma.8229 %N n/a %! Mathematical Methods in the Applied Sciences %0 Journal Article %J Networks and Heterogeneous Media %D 2022 %T An SIR–like kinetic model tracking individuals' viral load %A Rossella Della Marca %A Nadia Loy %A Andrea Tosin %B Networks and Heterogeneous Media %P - %G eng %0 Unpublished Work %D 2021 %T A data-driven partitioned approach for the resolution of time-dependent optimal control problems with dynamic mode decomposition %A Eleonora Donadini %A Maria Strazzullo %A Marco Tezzele %A Gianluigi Rozza %G eng %0 Generic %D 2021 %T A Dimensionality Reduction Approach for Convolutional Neural Networks %A Laura Meneghetti %A Nicola Demo %A Gianluigi Rozza %G eng %0 Journal Article %J arXiv preprint arXiv:2110.09155 %D 2021 %T A dynamic mode decomposition extension for the forecasting of parametric dynamical systems %A Francesco Andreuzzi %A Nicola Demo %A Gianluigi Rozza %B arXiv preprint arXiv:2110.09155 %G eng %0 Journal Article %J Bolletino dell Unione Matematica Italiana %D 2021 %T An efficient computational framework for naval shape design and optimization problems by means of data-driven reduced order modeling techniques %A Nicola Demo %A Giulio Ortali %A Gianluca Gustin %A Gianluigi Rozza %A Gianpiero Lavini %XThis contribution describes the implementation of a data-driven shape optimization pipeline in a naval architecture application. We adopt reduced order models in order to improve the efficiency of the overall optimization, keeping a modular and equation-free nature to target the industrial demand. We applied the above mentioned pipeline to a realistic cruise ship in order to reduce the total drag. We begin by defining the design space, generated by deforming an initial shape in a parametric way using free form deformation. The evaluation of the performance of each new hull is determined by simulating the flux via finite volume discretization of a two-phase (water and air) fluid. Since the fluid dynamics model can result very expensive—especially dealing with complex industrial geometries—we propose also a dynamic mode decomposition enhancement to reduce the computational cost of a single numerical simulation. The real-time computation is finally achieved by means of proper orthogonal decomposition with Gaussian process regression technique. Thanks to the quick approximation, a genetic optimization algorithm becomes feasible to converge towards the optimal shape.

%B Bolletino dell Unione Matematica Italiana %V 14 %P 211-230 %G eng %R 10.1007/s40574-020-00263-4 %0 Journal Article %J Annales Henri Poincaré %D 2021 %T Exactness of Linear Response in the Quantum Hall Effect %A Sven Bachmann %A De Roeck, Wojciech %A Fraas, Martin %A Markus Lange %B Annales Henri Poincaré %I Springer Science and Business Media LLC %V 22 %P 1113–1132 %8 Jan %G eng %U http://dx.doi.org/10.1007/s00023-020-00989-z %R 10.1007/s00023-020-00989-z %0 Unpublished Work %D 2021 %T AN EXTENDED PHYSICS INFORMED NEURAL NETWORK FOR PRELIMINARY ANALYSIS OF PARAMETRIC OPTIMAL CONTROL PROBLEMS %A Nicola Demo %A Maria Strazzullo %A Gianluigi Rozza %G eng %0 Journal Article %J Journal of Marine Science and Engineering %D 2021 %T Hull Shape Design Optimization with Parameter Space and Model Reductions, and Self-Learning Mesh Morphing %A Nicola Demo %A Marco Tezzele %A Andrea Mola %A Gianluigi Rozza %XIn the field of parametric partial differential equations, shape optimization represents a challenging problem due to the required computational resources. In this contribution, a data-driven framework involving multiple reduction techniques is proposed to reduce such computational burden. Proper orthogonal decomposition (POD) and active subspace genetic algorithm (ASGA) are applied for a dimensional reduction of the original (high fidelity) model and for an efficient genetic optimization based on active subspace property. The parameterization of the shape is applied directly to the computational mesh, propagating the generic deformation map applied to the surface (of the object to optimize) to the mesh nodes using a radial basis function (RBF) interpolation. Thus, topology and quality of the original mesh are preserved, enabling application of POD-based reduced order modeling techniques, and avoiding the necessity of additional meshing steps. Model order reduction is performed coupling POD and Gaussian process regression (GPR) in a data-driven fashion. The framework is validated on a benchmark ship.

%B Journal of Marine Science and Engineering %V 9 %P 185 %G eng %U https://www.mdpi.com/2077-1312/9/2/185 %R 10.3390/jmse9020185 %0 Generic %D 2021 %T The Neural Network shifted-Proper Orthogonal Decomposition: a Machine Learning Approach for Non-linear Reduction of Hyperbolic Equations %A Davide Papapicco %A Nicola Demo %A Michele Girfoglio %A Giovanni Stabile %A Gianluigi Rozza %G eng %0 Journal Article %J Communications in Computational Physics %D 2021 %T A novel iterative penalty method to enforce boundary conditions in Finite Volume POD-Galerkin reduced order models for fluid dynamics problems %A Kelbij Star %A Giovanni Stabile %A Francesco Belloni %A Gianluigi Rozza %A Joris Degroote %X A Finite-Volume based POD-Galerkin reduced order model is developed for fluid dynamic problems where the (time-dependent) boundary conditions are controlled using two different boundary control strategies: the control function method, whose aim is to obtain homogeneous basis functions for the reduced basis space and the penalty method where the boundary conditions are enforced in the reduced order model using a penalty factor. The penalty method is improved by using an iterative solver for the determination of the penalty factor rather than tuning the factor with a sensitivity analysis or numerical experimentation. The boundary control methods are compared and tested for two cases: the classical lid driven cavity benchmark problem and a Y-junction flow case with two inlet channels and one outlet channel. The results show that the boundaries of the reduced order model can be controlled with the boundary control methods and the same order of accuracy is achieved for the velocity and pressure fields. Finally, the speedup ratio between the reduced order models and the full order model is of the order 1000 for the lid driven cavity case and of the order 100 for the Y-junction test case. %B Communications in Computational Physics %I Global Science Press %V 30 %P 34–66 %G eng %R https://doi.org/10.4208/cicp.OA-2020-0059 %0 Journal Article %J Phil. Trans. R. Soc. A %D 2021 %T Nutations in growing plant shoots as a morphoelastic flutter instability %A Daniele Agostinelli %A Giovanni Noselli %A Antonio DeSimone %XGrowing plant shoots exhibit spontaneous oscillations that Darwin observed, and termed "circumnutations". Recently, they have received renewed attention for the design and optimal actuation of bioinspired robotic devices. We discuss a possible interpretation of these spontaneous oscillations as a Hopf-type bifurcation in a growing morphoelastic rod. Using a three-dimensional model and numerical simulations, we analyse the salient features of this flutter-like phenomenon (e.g. the characteristic period of the oscillations) and their dependence on the model details (in particular, the impact of choosing different growth models) finding that, overall, these features are robust with respect to changes in the details of the growth model adopted.

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

%B Frontiers in Plant Science %I Cold Spring Harbor Laboratory %V 12 %G eng %U https://www.frontiersin.org/article/10.3389/fpls.2021.608005 %9 Journal article %R 10.3389/fpls.2021.608005 %0 Journal Article %J Applied Mathematical Modelling %D 2021 %T A POD-Galerkin reduced order model of a turbulent convective buoyant flow of sodium over a backward-facing step %A Kelbij Star %A Giovanni Stabile %A Gianluigi Rozza %A Joris Degroote %XA Finite-Volume based POD-Galerkin reduced order modeling strategy for steady-state Reynolds averaged Navier–Stokes (RANS) simulation is extended for low-Prandtl number flow. The reduced order model is based on a full order model for which the effects of buoyancy on the flow and heat transfer are characterized by varying the Richardson number. The Reynolds stresses are computed with a linear eddy viscosity model. A single gradient diffusion hypothesis, together with a local correlation for the evaluation of the turbulent Prandtl number, is used to model the turbulent heat fluxes. The contribution of the eddy viscosity and turbulent thermal diffusivity fields are considered in the reduced order model with an interpolation based data-driven method. The reduced order model is tested for buoyancy-aided turbulent liquid sodium flow over a vertical backward-facing step with a uniform heat flux applied on the wall downstream of the step. The wall heat flux is incorporated with a Neumann boundary condition in both the full order model and the reduced order model. The velocity and temperature profiles predicted with the reduced order model for the same and new Richardson numbers inside the range of parameter values are in good agreement with the RANS simulations. Also, the local Stanton number and skin friction distribution at the heated wall are qualitatively well captured. Finally, the reduced order simulations, performed on a single core, are about 105 times faster than the RANS simulations that are performed on eight cores.

%B Applied Mathematical Modelling %V 89 %P 486-503 %G eng %R 10.1016/j.apm.2020.07.029 %0 Journal Article %J Software Impacts %D 2021 %T PyGeM: Python Geometrical Morphing %A Marco Tezzele %A Nicola Demo %A Andrea Mola %A Gianluigi Rozza %K Free form deformation %K Geometrical morphing %K Inverse distance weighting %K Python %K Radial basis functions interpolation %X PyGeM is an open source Python package which allows to easily parametrize and deform 3D object described by CAD files or 3D meshes. It implements several morphing techniques such as free form deformation, radial basis function interpolation, and inverse distance weighting. Due to its versatility in dealing with different file formats it is particularly suited for researchers and practitioners both in academia and in industry interested in computational engineering simulations and optimization studies. %B Software Impacts %V 7 %P 100047 %G eng %R 10.1016/j.simpa.2020.100047 %0 Journal Article %D 2021 %T Quasistatic Limit of a Dynamic Viscoelastic Model with Memory %A Gianni Dal Maso %A Francesco Sapio %XWe study the behaviour of the solutions to a dynamic evolution problem for a viscoelastic model with long memory, when the rate of change of the data tends to zero. We prove that a suitably rescaled version of the solutions converges to the solution of the corresponding stationary problem.

%8 2021/11/30 %@ 1424-9294 %G eng %U https://doi.org/10.1007/s00032-021-00343-w %! Milan Journal of Mathematics %0 Journal Article %J International Journal for Numerical Methods in Fluids %D 2021 %T Reduced order models for the incompressible Navier-Stokes equations on collocated grids using a `discretize-then-project' approach %A Kelbij Star %A Benjamin Sanderse %A Giovanni Stabile %A Gianluigi Rozza %A Joris Degroote %B International Journal for Numerical Methods in Fluids %I Wiley %V 93 %P 2694–2722 %G eng %U https://doi.org/10.1002/fld.4994 %R 10.1002/fld.4994 %0 Journal Article %J Revista Matematica Iberoamericana %D 2021 %T The sharp quantitative isocapacitary inequality %A Guido De Philippis %A Michele Marini %A Ekaterina Mukoseeva %K Fraenkel asymmetry %K isocapacitary inequality %K Stability estimates %XWe prove a sharp quantitative form of the classical isocapacitary inequality. Namely, we show that the difference between the capacity of a set and that of a ball with the same volume bounds the square of the Fraenkel asymmetry of the set. This provides a positive answer to a conjecture of Hall, Hayman, and Weitsman (J. Analyse Math.'91). © 2021 Real Sociedad Matemática Española

%B Revista Matematica Iberoamericana %V 37 %P 2191 - 2228 %8 2021 %@ 02132230 (ISSN) %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85104691573&doi=10.4171%2frmi%2f1259&partnerID=40&md5=5f88bc37b87a9eea7a502ea63523ff57 %N 6 %! Rev. Mat. Iberoam. %0 Journal Article %J SIAM Journal on Scientific Computing %D 2021 %T A supervised learning approach involving active subspaces for an efficient genetic algorithm in high-dimensional optimization problems %A Nicola Demo %A Marco Tezzele %A Gianluigi Rozza %XIn this work, we present an extension of the genetic algorithm (GA) which exploits the active subspaces (AS) property to evolve the individuals on a lower dimensional space. In many cases, GA requires in fact more function evaluations than others optimization method to converge to the optimum. Thus, complex and high-dimensional functions may result intractable with the standard algorithm. To address this issue, we propose to linearly map the input parameter space of the original function onto its AS before the evolution, performing the mutation and mate processes in a lower dimensional space. In this contribution, we describe the novel method called ASGA, presenting differences and similarities with the standard GA method. We test the proposed method over n-dimensional benchmark functions – Rosenbrock, Ackley, Bohachevsky, Rastrigin, Schaffer N. 7, and Zakharov – and finally we apply it to an aeronautical shape optimization problem.

%B SIAM Journal on Scientific Computing %V 43 %G eng %U https://arxiv.org/abs/2006.07282 %N 3 %& B831 %R https://doi.org/10.1137/20M1345219 %0 Conference Paper %B Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018 %D 2020 %T Advances in reduced order methods for parametric industrial problems in computational fluid dynamics %A Gianluigi Rozza %A M.H. Malik %A Nicola Demo %A Marco Tezzele %A Michele Girfoglio %A Giovanni Stabile %A Andrea Mola %XReduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of model order reduction techniques in various engineering and scientific applications including but not limited to mechanical, naval and aeronautical engineering. The focus here is kept limited to computational fluid mechanics and related applications. The advances in the reduced order modeling with proper orthogonal decomposition and reduced basis method are presented as well as a brief discussion of dynamic mode decomposition and also some present advances in the parameter space reduction. Here, an overview of the challenges faced and possible solutions are presented with examples from various problems.

%B Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075395686&partnerID=40&md5=fb0b1a3cfdfd35a104db9921bc9be675 %0 Journal Article %J Computers and Mathematics with Applications %D 2020 %T The deal.II finite element library: Design, features, and insights %A Daniel Arndt %A Wolfgang Bangerth %A Denis Davydov %A Timo Heister %A Luca Heltai %A Martin Kronbichler %A Matthias Maier %A Jean-Paul Pelteret %A Bruno Turcksin %A David Wells %B Computers and Mathematics with Applications %G eng %U https://doi.org/10.1016/j.camwa.2020.02.022 %0 Journal Article %J Advanced Modeling and Simulation in Engineering Sciences %D 2020 %T Enhancing CFD predictions in shape design problems by model and parameter space reduction %A Marco Tezzele %A Nicola Demo %A Giovanni Stabile %A Andrea Mola %A Gianluigi Rozza %XIn this work we present an advanced computational pipeline for the approximation and prediction of the lift coefficient of a parametrized airfoil profile. The non-intrusive reduced order method is based on dynamic mode decomposition (DMD) and it is coupled with dynamic active subspaces (DyAS) to enhance the future state prediction of the target function and reduce the parameter space dimensionality. The pipeline is based on high-fidelity simulations carried out by the application of finite volume method for turbulent flows, and automatic mesh morphing through radial basis functions interpolation technique. The proposed pipeline is able to save 1/3 of the overall computational resources thanks to the application of DMD. Moreover exploiting DyAS and performing the regression on a lower dimensional space results in the reduction of the relative error in the approximation of the time-varying lift coefficient by a factor 2 with respect to using only the DMD.

%B Advanced Modeling and Simulation in Engineering Sciences %V 7 %G eng %U https://arxiv.org/abs/2001.05237 %N 40 %R https://doi.org/10.1186/s40323-020-00177-y %0 Journal Article %J Mathematics in Engineering %D 2020 %T MicroMotility: State of the art, recent accomplishments and perspectives on the mathematical modeling of bio-motility at microscopic scales %A Daniele Agostinelli %A Roberto Cerbino %A Del Alamo, Juan C %A Antonio DeSimone %A Stephanie Höhn %A Cristian Micheletti %A Giovanni Noselli %A Eran Sharon %A Julia Yeomans %K active matter %K adhesive locomotion %K cell motility %K cell sheet folding %K knotted DNA %K topological defects %K unicellular swimmers %K unjamming transition %XMathematical modeling and quantitative study of biological motility (in particular, of motility at microscopic scales) is producing new biophysical insight and is offering opportunities for new discoveries at the level of both fundamental science and technology. These range from the explanation of how complex behavior at the level of a single organism emerges from body architecture, to the understanding of collective phenomena in groups of organisms and tissues, and of how these forms of swarm intelligence can be controlled and harnessed in engineering applications, to the elucidation of processes of fundamental biological relevance at the cellular and sub-cellular level. In this paper, some of the most exciting new developments in the fields of locomotion of unicellular organisms, of soft adhesive locomotion across scales, of the study of pore translocation properties of knotted DNA, of the development of synthetic active solid sheets, of the mechanics of the unjamming transition in dense cell collectives, of the mechanics of cell sheet folding in volvocalean algae, and of the self-propulsion of topological defects in active matter are discussed. For each of these topics, we provide a brief state of the art, an example of recent achievements, and some directions for future research.

%B Mathematics in Engineering %V 2 %P 230 %G eng %U http://dx.doi.org/10.3934/mine.2020011 %9 Perspective %R 10.3934/mine.2020011 %0 Journal Article %J Journal of Convex Analysis %D 2020 %T A numerical study of the jerky crack growth in elastoplastic materials with localized plasticity %A Gianni Dal Maso %A Luca Heltai %B Journal of Convex Analysis %G eng %U https://arxiv.org/abs/2004.12705 %0 Journal Article %J Lecture Notes in Computational Science and Engineering %D 2020 %T Reduced order isogeometric analysis approach for pdes in parametrized domains %A Fabrizio Garotta %A Nicola Demo %A Marco Tezzele %A Massimo Carraturo %A Alessandro Reali %A Gianluigi Rozza %XIn this contribution, we coupled the isogeometric analysis to a reduced order modelling technique in order to provide a computationally efficient solution in parametric domains. In details, we adopt the free-form deformation method to obtain the parametric formulation of the domain and proper orthogonal decomposition with interpolation for the computational reduction of the model. This technique provides a real-time solution for any parameter by combining several solutions, in this case computed using isogeometric analysis on different geometrical configurations of the domain, properly mapped into a reference configuration. We underline that this reduced order model requires only the full-order solutions, making this approach non-intrusive. We present in this work the results of the application of this methodology to a heat conduction problem inside a deformable collector pipe.

%B Lecture Notes in Computational Science and Engineering %V 137 %P 153-170 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85089615035&doi=10.1007%2f978-3-030-48721-8_7&partnerID=40&md5=7b15836ae65fa28dcfe8733788d7730c %R 10.1007/978-3-030-48721-8_7 %0 Conference Paper %B 8th International Conference on Computational Methods in Marine Engineering, MARINE 2019 %D 2019 %T A complete data-driven framework for the efficient solution of parametric shape design and optimisation in naval engineering problems %A Nicola Demo %A Marco Tezzele %A Andrea Mola %A Gianluigi Rozza %XIn the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples of the ROM application, in the naval field, can be found in [31, 24]. Mandatory ingredient for the ROM methods is the relation between the high-fidelity solutions and the parameters. Dealing with geometrical parameters, especially in the industrial context, this relation may be unknown and not trivial (simulations over hand morphed geometries) or very complex (high number of parameters or many nested morphing techniques). To overcome these scenarios, we propose in this contribution an efficient and complete data-driven framework involving ROM techniques for shape design and optimization, extending the pipeline presented in [7]. By applying the singular value decomposition (SVD) to the points coordinates defining the hull geometry — assuming the topology is inaltered by the deformation —, we are able to compute the optimal space which the deformed geometries belong to, hence using the modal coefficients as the new parameters we can reconstruct the parametric formulation of the domain. Finally the output of interest is approximated using the proper orthogonal decomposition with interpolation technique. To conclude, we apply this framework to a naval shape design problem where the bulbous bow is morphed to reduce the total resistance of the ship advancing in calm water.

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

%B VIII International Conference on Computational Methods in Marine Engineering %G eng %U https://arxiv.org/abs/1905.05982 %0 Journal Article %J Journal of Numerical Mathematics %D 2019 %T The deal.II Library, Version 9.1 %A Daniel Arndt %A Wolfgang Bangerth %A Thomas C. Clevenger %A Denis Davydov %A Marc Fehling %A Garcia-Sanchez, Daniel %A Harper, Graham %A Timo Heister %A Luca Heltai %A Martin Kronbichler %A Maguire Kynch, Ross %A Matthias Maier %A Jean-Paul Pelteret %A Bruno Turcksin %A David Wells %X This paper provides an overview of the new features of the finite element library deal.II, version 9.1. %B Journal of Numerical Mathematics %G eng %R 10.1515/jnma-2019-0064 %0 Journal Article %J Journal of Numerical Mathematics %D 2019 %T The deal.II Library, Version 9.1 %A Daniel Arndt %A Wolfgang Bangerth %A Thomas C. Clevenger %A Denis Davydov %A Marc Fehling %A Garcia-Sanchez, Daniel %A Harper, Graham %A Timo Heister %A Luca Heltai %A Martin Kronbichler %A Maguire Kynch, Ross %A Matthias Maier %A Jean-Paul Pelteret %A Bruno Turcksin %A David Wells %B Journal of Numerical Mathematics %G eng %0 Journal Article %J Duke Math. J. %D 2019 %T Isomonodromy deformations at an irregular singularity with coalescing eigenvalues %A Giordano Cotti %A Boris Dubrovin %A Davide Guzzetti %XWe consider an n×n linear system of ODEs with an irregular singularity of Poincar\'e rank 1 at z=∞, holomorphically depending on parameter t within a polydisc in Cn centred at t=0. The eigenvalues of the leading matrix at z=∞ coalesce along a locus Δ contained in the polydisc, passing through t=0. Namely, z=∞ is a resonant irregular singularity for t∈Δ. We analyse the case when the leading matrix remains diagonalisable at Δ. We discuss the existence of fundamental matrix solutions, their asymptotics, Stokes phenomenon and monodromy data as t varies in the polydisc, and their limits for t tending to points of Δ. When the deformation is isomonodromic away from Δ, it is well known that a fundamental matrix solution has singularities at Δ. When the system also has a Fuchsian singularity at z=0, we show under minimal vanishing conditions on the residue matrix at z=0 that isomonodromic deformations can be extended to the whole polydisc, including Δ, in such a way that the fundamental matrix solutions and the constant monodromy data are well defined in the whole polydisc. These data can be computed just by considering the system at fixed t=0. Conversely, if the t-dependent system is isomonodromic in a small domain contained in the polydisc not intersecting Δ, if the entries of the Stokes matrices with indices corresponding to coalescing eigenvalues vanish, then we show that Δ is not a branching locus for the fundamental matrix solutions. The importance of these results for the analytic theory of Frobenius Manifolds is explained. An application to Painlev\'e equations is discussed.

%B Duke Math. J. %I Duke University Press %V 168 %P 967–1108 %8 04 %G eng %U https://doi.org/10.1215/00127094-2018-0059 %R 10.1215/00127094-2018-0059 %0 Journal Article %J Proceedings of the Royal Society A: Mathematical, Physical and Engineering SciencesProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences %D 2019 %T A neutrally stable shell in a Stokes flow: a rotational Taylor's sheet %A Giovanni Corsi %A Antonio DeSimone %A C. Maurini %A S. Vidoli %B Proceedings of the Royal Society A: Mathematical, Physical and Engineering SciencesProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences %V 475 %P 20190178 %8 2019/07/26 %G eng %U https://doi.org/10.1098/rspa.2019.0178 %N 2227 %! Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences %0 Journal Article %J Comptes Rendus - Mecanique %D 2019 %T A non-intrusive approach for the reconstruction of POD modal coefficients through active subspaces %A Nicola Demo %A Marco Tezzele %A Gianluigi Rozza %XReduced order modeling (ROM) provides an efficient framework to compute solutions of parametric problems. Basically, it exploits a set of precomputed high-fidelity solutions—computed for properly chosen parameters, using a full-order model—in order to find the low dimensional space that contains the solution manifold. Using this space, an approximation of the numerical solution for new parameters can be computed in real-time response scenario, thanks to the reduced dimensionality of the problem. In a ROM framework, the most expensive part from the computational viewpoint is the calculation of the numerical solutions using the full-order model. Of course, the number of collected solutions is strictly related to the accuracy of the reduced order model. In this work, we aim at increasing the precision of the model also for few input solutions by coupling the proper orthogonal decomposition with interpolation (PODI)—a data-driven reduced order method—with the active subspace (AS) property, an emerging tool for reduction in parameter space. The enhanced ROM results in a reduced number of input solutions to reach the desired accuracy. In this contribution, we present the numerical results obtained by applying this method to a structural problem and in a fluid dynamics one.

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

%B Journal of the Mechanics and Physics of Solids %P 103702 %G eng %U https://doi.org/10.1016/j.jmps.2019.103702 %R 10.1016/j.jmps.2019.103702 %0 Conference Paper %B International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019 %D 2019 %T POD-Galerkin Reduced Order Model of the Boussinesq Approximation for Buoyancy-Driven Enclosed Flows %A Kelbij Star %A Giovanni Stabile %A Sokratia Georgaka %A Francesco Belloni %A Gianluigi Rozza %A Joris Degroote %B International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019 %@ 9780894487699 %G eng %0 Journal Article %J International Journal for Numerical Methods in Engineering %D 2019 %T A POD-selective inverse distance weighting method for fast parametrized shape morphing %A F. Ballarin %A A. D'Amario %A Simona Perotto %A Gianluigi Rozza %XEfficient shape morphing techniques play a crucial role in the approximation of partial differential equations defined in parametrized domains, such as for fluid-structure interaction or shape optimization problems. In this paper, we focus on inverse distance weighting (IDW) interpolation techniques, where a reference domain is morphed into a deformed one via the displacement of a set of control points. We aim at reducing the computational burden characterizing a standard IDW approach without significantly compromising the accuracy. To this aim, first we propose an improvement of IDW based on a geometric criterion that automatically selects a subset of the original set of control points. Then, we combine this new approach with a dimensionality reduction technique based on a proper orthogonal decomposition of the set of admissible displacements. This choice further reduces computational costs. We verify the performances of the new IDW techniques on several tests by investigating the trade-off reached in terms of accuracy and efficiency.

%B International Journal for Numerical Methods in Engineering %V 117 %P 860-884 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85056396233&doi=10.1002%2fnme.5982&partnerID=40&md5=6aabcbdc9a0da25e36575a0ebfac034f %R 10.1002/nme.5982 %0 Report %D 2019 %T Quasi-continuous vector fields on RCD spaces %A Clément Debin %A Nicola Gigli %A Enrico Pasqualetto %G eng %0 Generic %D 2019 %T Regularity of minimizers for a model of charged droplets %A Guido De Philippis %A Jonas Hirsch %A Giulia Vescovo %G eng %0 Conference Paper %B 8th International Conference on Computational Methods in Marine Engineering, MARINE 2019 %D 2019 %T Shape optimization through proper orthogonal decomposition with interpolation and dynamic mode decomposition enhanced by active subspaces %A Marco Tezzele %A Nicola Demo %A Gianluigi Rozza %XWe propose a numerical pipeline for shape optimization in naval engineering involving two different non-intrusive reduced order method (ROM) techniques. Such methods are proper orthogonal decomposition with interpolation (PODI) and dynamic mode decomposition (DMD). The ROM proposed will be enhanced by active subspaces (AS) as a pre-processing tool that reduce the parameter space dimension and suggest better sampling of the input space. We will focus on geometrical parameters describing the perturbation of a reference bulbous bow through the free form deformation (FFD) technique. The ROM are based on a finite volume method (FV) to simulate the multi-phase incompressible flow around the deformed hulls. In previous works we studied the reduction of the parameter space in naval engineering through AS [38, 10] focusing on different parts of the hull. PODI and DMD have been employed for the study of fast and reliable shape optimization cycles on a bulbous bow in [9]. The novelty of this work is the simultaneous reduction of both the input parameter space and the output fields of interest. In particular AS will be trained computing the total drag resistance of a hull advancing in calm water and its gradients with respect to the input parameters. DMD will improve the performance of each simulation of the campaign using only few snapshots of the solution fields in order to predict the regime state of the system. Finally PODI will interpolate the coefficients of the POD decomposition of the output fields for a fast approximation of all the fields at new untried parameters given by the optimization algorithm. This will result in a non-intrusive data-driven numerical optimization pipeline completely independent with respect to the full order solver used and it can be easily incorporated into existing numerical pipelines, from the reference CAD to the optimal shape.

%B 8th International Conference on Computational Methods in Marine Engineering, MARINE 2019 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075390244&partnerID=40&md5=3e1f2e9a2539d34594caff13766c94b8 %0 Journal Article %J Nature Physics %D 2019 %T Swimming Euglena respond to confinement with a behavioural change enabling effective crawling %A Giovanni Noselli %A Alfred Beran %A Marino Arroyo %A Antonio DeSimone %X Some euglenids, a family of aquatic unicellular organisms, can develop highly concerted, large-amplitude peristaltic body deformations. This remarkable behaviour has been known for centuries. Yet, its function remains controversial, and is even viewed as a functionless ancestral vestige. Here, by examining swimming Euglena gracilis in environments of controlled crowding and geometry, we show that this behaviour is triggered by confinement. Under these conditions, it allows cells to switch from unviable flagellar swimming to a new and highly robust mode of fast crawling, which can deal with extreme geometric confinement and turn both frictional and hydraulic resistance into propulsive forces. To understand how a single cell can control such an adaptable and robust mode of locomotion, we developed a computational model of the motile apparatus of Euglena cells consisting of an active striated cell envelope. Our modelling shows that gait adaptability does not require specific mechanosensitive feedback but instead can be explained by the mechanical self-regulation of an elastic and extended motor system. Our study thus identifies a locomotory function and the operating principles of the adaptable peristaltic body deformation of Euglena cells. %B Nature Physics %V 15 %P 496–502 %G eng %U https://doi.org/10.1038/s41567-019-0425-8 %R 10.1038/s41567-019-0425-8 %0 Journal Article %J IMA Journal of Numerical Analysis %D 2019 %T Virtual element method for quasilinear elliptic problems %A Andrea Cangiani %A Chatzipantelidis, P %A Diwan, G %A E.H. Georgoulis %X A virtual element method for the quasilinear equation \\$-\\textrm\{div\} (\{\\boldsymbol \ąppa \}(u)\\operatorname\{grad\} u)=f\\$ using general polygonal and polyhedral meshes is presented and analysed. The nonlinear coefficient is evaluated with the piecewise polynomial projection of the virtual element ansatz. Well posedness of the discrete problem and optimal-order a priori error estimates in the \\$H^1\\$- and \\$L^2\\$-norm are proven. In addition, the convergence of fixed-point iterations for the resulting nonlinear system is established. Numerical tests confirm the optimal convergence properties of the method on general meshes. %B IMA Journal of Numerical Analysis %V 40 %P 2450-2472 %8 07 %G eng %U https://doi.org/10.1093/imanum/drz035 %R 10.1093/imanum/drz035 %0 Report %D 2018 %T On the Cauchy problem for the wave equation on time-dependent domains %A Gianni Dal Maso %A Rodica Toader %X We introduce a notion of solution to the wave equation on a suitable class of time-dependent domains and compare it with a previous de nition. We prove an existence result for the solution of the Cauchy problem and present some additional conditions which imply uniqueness. %I SISSA %G en %U http://preprints.sissa.it/handle/1963/35314 %1 35622 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-04-23T06:03:52Z No. of bitstreams: 1 DM-Toa-18-sissa.pdf: 404543 bytes, checksum: 73bb5b0c57b574d05b3d6f33417016e0 (MD5) %0 Journal Article %J JOURNAL OF NUMERICAL MATHEMATICS %D 2018 %T The deal.II Library, Version 9.0 %A Giovanni Alzetta %A Daniel Arndt %A Wolfgang Bangerth %A Boddu, Vishal %A Brands, Benjamin %A Denis Davydov %A Rene Gassmöller %A Timo Heister %A Luca Heltai %A Kormann, Katharina %A Martin Kronbichler %A Matthias Maier %A Jean-Paul Pelteret %A Bruno Turcksin %A David Wells %B JOURNAL OF NUMERICAL MATHEMATICS %G eng %U https://doi.org/10.1515/jnma-2018-0054 %R 10.1515/jnma-2018-0054 %0 Conference Proceedings %B The 28th International Ocean and Polar Engineering Conference %D 2018 %T An efficient shape parametrisation by free-form deformation enhanced by active subspace for hull hydrodynamic ship design problems in open source environment %A Nicola Demo %A Marco Tezzele %A Andrea Mola %A Gianluigi Rozza %K Active subspaces %K Boundary element method %K Dynamic mode decomposition %K Fluid structure interaction %K Free form deformation %K Fully nonlinear potential %K Numerical towing tank %X In this contribution, we present the results of the application of a parameter space reduction methodology based on active subspaces to the hull hydrodynamic design problem. Several parametric deformations of an initial hull shape are considered to assess the influence of the shape parameters considered on the hull total drag. The hull resistance is typically computed by means of numerical simulations of the hydrodynamic flow past the ship. Given the high number of parameters involved - which might result in a high number of time consuming hydrodynamic simulations - assessing whether the parameters space can be reduced would lead to considerable computational cost reduction. Thus, the main idea of this work is to employ the active subspaces to identify possible lower dimensional structures in the parameter space, or to verify the parameter distribution in the position of the control points. To this end, a fully automated procedure has been implemented to produce several small shape perturbations of an original hull CAD geometry which are then used to carry out high-fidelity flow simulations and collect data for the active subspaces analysis. To achieve full automation of the open source pipeline described, both the free form deformation methodology employed for the hull perturbations and the solver based on unsteady potential flow theory, with fully nonlinear free surface treatment, are directly interfaced with CAD data structures and operate using IGES vendor-neutral file formats as input files. The computational cost of the fluid dynamic simulations is further reduced through the application of dynamic mode decomposition to reconstruct the steady state total drag value given only few initial snapshots of the simulation. The active subspaces analysis is here applied to the geometry of the DTMB-5415 naval combatant hull, which is which is a common benchmark in ship hydrodynamics simulations. %B The 28th International Ocean and Polar Engineering Conference %I International Society of Offshore and Polar Engineers %C Sapporo, Japan %G eng %U https://www.onepetro.org/conference-paper/ISOPE-I-18-481 %0 Report %D 2018 %T Existence for elastodynamic Griffith fracture with a weak maximal dissipation condition %A Gianni Dal Maso %A Cristopher J. Larsen %A Rodica Toader %X We consider a model of elastodynamics with fracture evolution, based on energy-dissipation balance and a maximal dissipation condition. We prove an existence result in the case of planar elasticity with a free crack path, where the maximal dissipation condition is satisfied among suitably regular competitor cracks. %G en %U http://preprints.sissa.it/handle/1963/35308 %1 35616 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-03-19T09:02:45Z No. of bitstreams: 1 DM-Lar-Toa-sissa.pdf: 429343 bytes, checksum: 82817f96da6dcabff29c2c322590fb66 (MD5) %0 Journal Article %J The Journal of Open Source Software %D 2018 %T EZyRB: Easy Reduced Basis method %A Nicola Demo %A Marco Tezzele %A Gianluigi Rozza %B The Journal of Open Source Software %V 3 %P 661 %G eng %U https://joss.theoj.org/papers/10.21105/joss.00661 %R 10.21105/joss.00661 %0 Report %D 2018 %T Foldable structures made of hydrogel bilayers %A Virginia Agostiniani %A Antonio DeSimone %A Alessandro Lucantonio %A Danka Lučić %G eng %0 Report %D 2018 %T Local moduli of semisimple Frobenius coalescent structures %A Giordano Cotti %A Boris Dubrovin %A Davide Guzzetti %XThere is a conjectural relation, formulated by the second author, between the enumerative geometry of a wide class of smooth projective varieties and their derived category of coherent sheaves. In particular, there is an increasing interest for an explicit description of certain local invariants, called monodromy data, of semisimple quantum cohomologies in terms of characteristic classes of exceptional collections in the derived categories. Being intentioned to address this problem, which, to our opinion, is still not well understood, we have realized that some issues in the theory of Frobenius manifolds need to be preliminarily clarified, and that an extension of the theory itself is necessary, in view of the fact that quantum cohomologies of certain classes of homogeneous spaces may show a coalescence phenomenon.

%I SISSA %G en %U http://preprints.sissa.it/handle/1963/35304 %1 35610 %2 Mathematics %4 1 %# MAT/03 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-01-16T11:11:03Z No. of bitstreams: 1 Preprint_Davide.pdf: 1242726 bytes, checksum: 527d898383b9f997856370b14965bbdc (MD5) %0 Journal Article %J Annales Henri Poincaré %D 2018 %T Lp-Boundedness of Wave Operators for the Three-Dimensional Multi-Centre Point Interaction %A Gianfausto Dell'Antonio %A Alessandro Michelangeli %A Raffaele Scandone %A Kenji Yajima %XWe prove that, for arbitrary centres and strengths, the wave operators for three-dimensional Schrödinger operators with multi-centre local point interactions are bounded in Lp(R3)for 1<p<3 and unbounded otherwise.

%B Annales Henri Poincaré %V 19 %P 283–322 %8 Jan %G eng %U https://doi.org/10.1007/s00023-017-0628-4 %R 10.1007/s00023-017-0628-4 %0 Report %D 2018 %T A minimization approach to the wave equation on time-dependent domains %A Gianni Dal Maso %A Lucia De Luca %X We prove the existence of weak solutions to the homogeneous wave equation on a suitable class of time-dependent domains. Using the approach suggested by De Giorgi and developed by Serra and Tilli, such solutions are approximated by minimizers of suitable functionals in space-time. %I SISSA %G en %U http://preprints.sissa.it/handle/1963/35318 %1 35627 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-06-05T09:52:31Z No. of bitstreams: 1 DM-DeL-18-sissa.pdf: 301594 bytes, checksum: 0da772afb21ae49058bd3b54ae1dd432 (MD5) %0 Conference Paper %B Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship & Maritime Research %D 2018 %T Model Order Reduction by means of Active Subspaces and Dynamic Mode Decomposition for Parametric Hull Shape Design Hydrodynamics %A Marco Tezzele %A Nicola Demo %A Mahmoud Gadalla %A Andrea Mola %A Gianluigi Rozza %X We present the results of the application of a parameter space reduction methodology based on active subspaces (AS) to the hull hydrodynamic design problem. Several parametric deformations of an initial hull shape are considered to assess the influence of the shape parameters on the hull wave resistance. Such problem is relevant at the preliminary stages of the ship design, when several flow simulations are carried out by the engineers to establish a certain sensibility with respect to the parameters, which might result in a high number of time consuming hydrodynamic simulations. The main idea of this work is to employ the AS to identify possible lower dimensional structures in the parameter space. The complete pipeline involves the use of free form deformation to parametrize and deform the hull shape, the full order solver based on unsteady potential flow theory with fully nonlinear free surface treatment directly interfaced with CAD, the use of dynamic mode decomposition to reconstruct the final steady state given only few snapshots of the simulation, and the reduction of the parameter space by AS, and shared subspace. Response surface method is used to minimize the total drag. %B Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship & Maritime Research %I IOS Press %C Trieste, Italy %G eng %U http://ebooks.iospress.nl/publication/49270 %R 10.3233/978-1-61499-870-9-569 %0 Journal Article %J Frontiers in Robotics and AI %D 2018 %T Peristaltic Waves as Optimal Gaits in Metameric Bio-Inspired Robots %A Daniele Agostinelli %A François Alouges %A Antonio DeSimone %K Biomimetic robots %K Crawling motility %K Lumbricus terrestris %K Metameric robots %K Optimization %K Peristalsis %K Self-propulsion %K Soft robotics %X*Peristalsis*, i.e., a motion pattern arising from the propagation of muscle contraction and expansion waves along the body, is a common locomotion strategy for limbless animals. Mimicking peristalsis in bio-inspired robots has attracted considerable attention in the literature. It has recently been observed that maximal velocity in a metameric earthworm-like robot is achieved by actuating the segments using a “phase coordination” principle. This paper shows that, in fact, peristalsis (which requires not only phase coordination, but also that all segments oscillate at same frequency and amplitude) emerges from optimization principles. More precisely, basing our analysis on the assumption of small deformations, we show that peristaltic waves provide the optimal actuation solution in the ideal case of a periodic infinite system, and that this is approximately true, modulo edge effects, for the real, finite length system. Therefore, this paper confirms the effectiveness of mimicking peristalsis in bio-inspired robots, at least in the small-deformation regime. Further research will be required to test the effectiveness of this strategy if large deformations are allowed.

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.

%B International Journal of Mechanical Sciences %V 149 %P 481-486 %G eng %U https://www.sciencedirect.com/science/article/pii/S0020740317311761 %R https://doi.org/10.1016/j.ijmecsci.2017.08.049 %0 Report %D 2018 %T Stochastic homogenisation of free-discontinuity problems %A Filippo Cagnetti %A Gianni Dal Maso %A Lucia Scardia %A Caterina Ida Zeppieri %X In this paper we study the stochastic homogenisation of free-discontinuity functionals. Assuming stationarity for the random volume and surface integrands, we prove the existence of a homogenised random free-discontinuity functional, which is deterministic in the ergodic case. Moreover, by establishing a connection between the deterministic convergence of the functionals at any fixed realisation and the pointwise Subadditive Ergodic Theorem by Akcoglou and Krengel, we characterise the limit volume and surface integrands in terms of asymptotic cell formulas. %G en %U http://preprints.sissa.it/handle/1963/35309 %1 35617 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-03-19T09:16:27Z No. of bitstreams: 1 Cag-DM-Sca-Zep-Stochastic.pdf: 427225 bytes, checksum: 758a4e21e1c47b4a34c774f5d4bff8c2 (MD5) %0 Report %D 2018 %T Transmission conditions obtained by homogenisation %A Gianni Dal Maso %A Giovanni Franzina %A Davide Zucco %X We study the asymptotic behaviour of solutions to variational problems in perforated domains with Neumann boundary conditions. We consider perforations that in the limit concentrate on a smooth manifold. We characterise the limits of the solutions and show that they solve a variational problem with a transmission condition across the manifold. This is expressed through a measure on the manifold, vanishing on sets of capacity zero. Then, we prove that every such measure can be obtained by homogenising suitable perforations. Eventually, we provide an asymptotic formula for this measure by using some auxiliary minimum problems. %G en %U http://preprints.sissa.it/handle/1963/35310 %1 35618 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-03-19T09:23:08Z No. of bitstreams: 1 DM-Fra-Zuc-preprint.pdf: 420855 bytes, checksum: 1c4ce5133a6ab027c50e403c702aa690 (MD5) %0 Report %D 2017 %T Almost global existence of solutions for capillarity-gravity water waves equations with periodic spatial boundary conditions %A Massimiliano Berti %A Jean-Marc Delort %X The goal of this monograph is to prove that any solution of the Cauchy problem for the capillarity-gravity water waves equations, in one space dimension, with periodic, even in space, initial data of small size ϵ, is almost globally defined in time on Sobolev spaces, i.e. it exists on a time interval of length of magnitude ϵ−N for any N, as soon as the initial data are smooth enough, and the gravity-capillarity parameters are taken outside an exceptional subset of zero measure. In contrast to the many results known for these equations on the real line, with decaying Cauchy data, one cannot make use of dispersive properties of the linear flow. Instead, our method is based on a normal forms procedure, in order to eliminate those contributions to the Sobolev energy that are of lower degree of homogeneity in the solution. Since the water waves equations are a quasi-linear system, usual normal forms approaches would face the well known problem of losses of derivatives in the unbounded transformations. In this monograph, to overcome such a difficulty, after a paralinearization of the capillarity-gravity water waves equations, necessary to obtain energy estimates, and thus local existence of the solutions, we first perform several paradifferential reductions of the equations to obtain a diagonal system with constant coefficients symbols, up to smoothing remainders. Then we may start with a normal form procedure where the small divisors are compensated by the previous paradifferential regularization.The reversible structure of the water waves equations, and the fact that we look for solutions even in x, guarantees a key cancellation which prevents the growth of the Sobolev norms of the solutions. %G en %U http://preprints.sissa.it/handle/1963/35285 %1 35590 %2 Mathematics %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-05-30T09:17:49Z No. of bitstreams: 1 1702.04674.pdf: 2311619 bytes, checksum: 0765035340f77780899e30e93390092b (MD5) %0 Book Section %B Spectral and High Order Methods for Partial Differential Equations %D 2017 %T Certified Reduced Basis Method for Affinely Parametric Isogeometric Analysis NURBS Approximation %A Denis Devaud %A Gianluigi Rozza %XIn this work we apply reduced basis methods for parametric PDEs to an isogeometric formulation based on

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

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

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

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

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

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

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

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

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

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

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

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

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

%B Spectral and High Order Methods for Partial Differential Equations %7 Bittencourt, Dumont, Hesthaven. (Eds). %I Springer %C Heildeberg %V 119 %@ 978-3-319-65869-8 %G eng %0 Journal Article %J Engineering with Computers %D 2017 %T Curvature-adapted remeshing of CAD surfaces %A Franco Dassi %A Andrea Mola %A Hang Si %B Engineering with Computers %I Springer Nature %V 34 %P 565–576 %8 dec %G eng %U https://doi.org/10.1007/s00366-017-0558-2 %R 10.1007/s00366-017-0558-2 %0 Journal Article %J JOURNAL OF NUMERICAL MATHEMATICS %D 2017 %T The deal.II Library, Version 8.5 %A Daniel Arndt %A Wolfgang Bangerth %A Denis Davydov %A Timo Heister %A Luca Heltai %A Martin Kronbichler %A Matthias Maier %A Jean-Paul Pelteret %A Bruno Turcksin %A David Wells %B JOURNAL OF NUMERICAL MATHEMATICS %V 25 %P 137–145 %G eng %U https://www.dealii.org/deal85-preprint.pdf %R 10.1515/jnma-2017-0058 %0 Book Section %B Advances in Quantum Mechanics: Contemporary Trends and Open Problems %D 2017 %T Dispersive Estimates for Schrödinger Operators with Point Interactions in ℝ3 %A Felice Iandoli %A Raffaele Scandone %E Alessandro Michelangeli %E Gianfausto Dell'Antonio %XThe study of dispersive properties of Schrödinger operators with point interactions is a fundamental tool for understanding the behavior of many body quantum systems interacting with very short range potential, whose dynamics can be approximated by non linear Schrödinger equations with singular interactions. In this work we proved that, in the case of one point interaction in $\mathbb{R}^3$, the perturbed Laplacian satisfies the same $L^p$−$L^q$ estimates of the free Laplacian in the smaller regime $q \in [2,3)$. These estimates are implied by a recent result concerning the Lpboundedness of the wave operators for the perturbed Laplacian. Our approach, however, is more direct and relatively simple, and could potentially be useful to prove optimal weighted estimates also in the regime $q \geq 3$.

%B Advances in Quantum Mechanics: Contemporary Trends and Open Problems %I Springer International Publishing %C Cham %P 187–199 %@ 978-3-319-58904-6 %G eng %U https://doi.org/10.1007/978-3-319-58904-6_11 %R 10.1007/978-3-319-58904-6_11 %0 Book Section %B Advances in Quantum Mechanics: Contemporary Trends and Open Problems %D 2017 %T Effective Non-linear Dynamics of Binary Condensates and Open Problems %A Alessandro Olgiati %E Alessandro Michelangeli %E Gianfausto Dell'Antonio %XWe report on a recent result concerning the effective dynamics for a mixture of Bose-Einstein condensates, a class of systems much studied in physics and receiving a large amount of attention in the recent literature in mathematical physics; for such models, the effective dynamics is described by a coupled system of non-linear Schödinger equations. After reviewing and commenting our proof in the mean-field regime from a previous paper, we collect the main details needed to obtain the rigorous derivation of the effective dynamics in the Gross-Pitaevskii scaling limit.

%B Advances in Quantum Mechanics: Contemporary Trends and Open Problems %I Springer International Publishing %C Cham %P 239–256 %@ 978-3-319-58904-6 %G eng %U https://doi.org/10.1007/978-3-319-58904-6_14 %R 10.1007/978-3-319-58904-6_14 %0 Report %D 2017 %T Gamma-Convergence of Free-discontinuity problems %A Filippo Cagnetti %A Gianni Dal Maso %A Lucia Scardia %A Caterina Ida Zeppieri %X We study the Gamma-convergence of sequences of free-discontinuity functionals depending on vector-valued functions u which can be discontinuous across hypersurfaces whose shape and location are not known a priori. The main novelty of our result is that we work under very general assumptions on the integrands which, in particular, are not required to be periodic in the space variable. Further, we consider the case of surface integrands which are not bounded from below by the amplitude of the jump of u. We obtain three main results: compactness with respect to Gamma-convergence, representation of the Gamma-limit in an integral form and identification of its integrands, and homogenisation formulas without periodicity assumptions. In particular, the classical case of periodic homogenisation follows as a by-product of our analysis. Moreover, our result covers also the case of stochastic homogenisation, as we will show in a forthcoming paper. %I SISSA %G en %U http://preprints.sissa.it/handle/1963/35276 %1 35583 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-03-20T13:20:54Z No. of bitstreams: 1 Cag-DM-Sca-Zep-sissa.pdf: 494285 bytes, checksum: 0da567323c828153382b08fc0f967af4 (MD5) %0 Journal Article %J ESAIM: COCV %D 2017 %T On the genesis of directional friction through bristle-like mediating elements %A Paolo Gidoni %A Antonio DeSimone %XWe propose an explanation of the genesis of directional dry friction, as emergent property of the oscillations produced in a bristle-like mediating element by the interaction with microscale fluctuations on the surface. Mathematically, we extend a convergence result by Mielke, for Prandtl–Tomlinson-like systems, considering also non-homothetic scalings of a wiggly potential. This allows us to apply the result to some simple mechanical models, that exemplify the interaction of a bristle with a surface having small fluctuations. We find that the resulting friction is the product of two factors: a geometric one, depending on the bristle angle and on the fluctuation profile, and a energetic one, proportional to the normal force exchanged between the bristle-like element and the surface. Finally, we apply our result to discuss the with the nap/against the nap asymmetry.

%B ESAIM: COCV %V 23 %P 1023-1046 %G eng %U https://doi.org/10.1051/cocv/2017030 %R 10.1051/cocv/2017030 %0 Book %B SpringerBriefs in Mathematics %D 2017 %T $hp$-version discontinuous Galerkin methods on polygonal and polyhedral meshes %A Andrea Cangiani %A Dong, Zhaonan %A E.H. Georgoulis %A Houston, Paul %B SpringerBriefs in Mathematics %I Springer, Cham %P viii+131 %@ 978-3-319-67671-5; 978-3-319-67673-9 %G eng %0 Journal Article %J SIAM J. Sci. Comput. %D 2017 %T $hp$-version space-time discontinuous Galerkin methods for parabolic problems on prismatic meshes %A Andrea Cangiani %A Dong, Zhaonan %A E.H. Georgoulis %B SIAM J. Sci. Comput. %V 39 %P A1251–A1279 %G eng %U https://doi.org/10.1137/16M1073285 %R 10.1137/16M1073285 %0 Journal Article %J ArXiv e-prints %D 2017 %T The injectivity radius of Lie manifolds %A Paolo Antonini %A Guido De Philippis %A Nicola Gigli %K (58J40) %K 53C21 %K Mathematics - Differential Geometry %XWe prove in a direct, geometric way that for any compatible Riemannian metric on a Lie manifold the injectivity radius is positive

%B ArXiv e-prints %G eng %U https://arxiv.org/pdf/1707.07595.pdf %0 Journal Article %J Proceedings of the National Academy of Sciences %D 2017 %T Kinematics of flagellar swimming in Euglena gracilis: Helical trajectories and flagellar shapes %A Massimiliano Rossi %A Giancarlo Cicconofri %A Alfred Beran %A Giovanni Noselli %A Antonio DeSimone %X Active flagella provide the propulsion mechanism for a large variety of swimming eukaryotic microorganisms, from protists to sperm cells. Planar and helical beating patterns of these structures are recurrent and widely studied. The fast spinning motion of the locomotory flagellum of the alga Euglena gracilis constitutes a remarkable exception to these patterns. We report a quantitative description of the 3D flagellar beating in swimming E. gracilis. Given their complexity, these shapes cannot be directly imaged with current microscopy techniques. We show how to overcome these limitations by developing a method to reconstruct in full the 3D kinematics of the cell from conventional 2D microscopy images, based on the exact characterization of the helical motion of the cell body.The flagellar swimming of euglenids, which are propelled by a single anterior flagellum, is characterized by a generalized helical motion. The 3D nature of this swimming motion, which lacks some of the symmetries enjoyed by more common model systems, and the complex flagellar beating shapes that power it make its quantitative description challenging. In this work, we provide a quantitative, 3D, highly resolved reconstruction of the swimming trajectories and flagellar shapes of specimens of Euglena gracilis. We achieved this task by using high-speed 2D image recordings taken with a conventional inverted microscope combined with a precise characterization of the helical motion of the cell body to lift the 2D data to 3D trajectories. The propulsion mechanism is discussed. Our results constitute a basis for future biophysical research on a relatively unexplored type of eukaryotic flagellar movement. %B Proceedings of the National Academy of Sciences %V 114 %P 13085-13090 %G eng %U https://www.pnas.org/content/114/50/13085 %R 10.1073/pnas.1708064114 %0 Report %D 2017 %T Linearisation of multiwell energies %A Roberto Alicandro %A Gianni Dal Maso %A Giuliano Lazzaroni %A Mariapia Palombaro %X Linear elasticity can be rigorously derived from finite elasticity under the assumption of small loadings in terms of Gamma-convergence. This was first done in the case of one-well energies with super-quadratic growth and later generalised to different settings, in particular to the case of multi-well energies where the distance between the wells is very small (comparable to the size of the load). In this paper we study the case when the distance between the wells is independent of the size of the load. In this context linear elasticity can be derived by adding to the multi-well energy a singular higher order term which penalises jumps from one well to another. The size of the singular term has to satisfy certain scaling assumptions whose optimality is shown in most of the cases. Finally, the derivation of linear elasticty from a two-well discrete model is provided, showing that the role of the singular perturbation term is played in this setting by interactions beyond nearest neighbours. %G en %U http://preprints.sissa.it/handle/1963/35288 %1 35594 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-06-22T09:07:10Z No. of bitstreams: 1 ADMLP_linear.pdf: 364014 bytes, checksum: 305b4dcf6f1ee7c09e6747b7378ae58c (MD5) %0 Journal Article %J Advances in Calculus of Variations %D 2017 %T Lower semicontinuity of a class of integral functionals on the space of functions of bounded deformation %A Gianni Dal Maso %A Gianluca Orlando %A Rodica Toader %XWe study the lower semicontinuity of some free discontinuity functionals with linear growth defined on the space of functions with bounded deformation. The volume term is convex and depends only on the Euclidean norm of the symmetrized gradient. We introduce a suitable class of surface terms, which make the functional lower semicontinuous with respect to $L^1$ convergence.

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

%B Journal de Mathématiques Pures et Appliquées %V 108 %P 952-990 %G en %U http://hdl.handle.net/20.500.11767/15979 %N 6 %1 34731 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by salmi@sissa.it (salmi@sissa.it) on 2015-12-15T14:37:19Z No. of bitstreams: 1 Alm-DM-Toa-15-sissa.pdf: 351559 bytes, checksum: b6adddc4944478676c7d4b34028a347c (MD5) %& 952 %R 10.1016/j.matpur.2017.05.018 %0 Journal Article %J COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING %D 2017 %T A natural framework for isogeometric fluid-structure interaction based on BEM-shell coupling %A Luca Heltai %A Kiendl, J. %A Antonio DeSimone %A Alessandro Reali %B COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING %V 316 %P 522–546 %G eng %U http://cdsads.u-strasbg.fr/abs/2017CMAME.316..522H %R 10.1016/j.cma.2016.08.008 %0 Book Section %B Advances in Quantum Mechanics: Contemporary Trends and Open Problems %D 2017 %T Remarks on the Derivation of Gross-Pitaevskii Equation with Magnetic Laplacian %A Alessandro Olgiati %E Alessandro Michelangeli %E Gianfausto Dell'Antonio %XThe effective dynamics for a Bose-Einstein condensate in the regime of high dilution and subject to an external magnetic field is governed by a magnetic Gross-Pitaevskii equation. We elucidate the steps needed to adapt to the magnetic case the proof of the derivation of the Gross-Pitaevskii equation within the ``projection counting'' scheme.

%B Advances in Quantum Mechanics: Contemporary Trends and Open Problems %I Springer International Publishing %C Cham %P 257–266 %@ 978-3-319-58904-6 %G eng %U https://doi.org/10.1007/978-3-319-58904-6_15 %R 10.1007/978-3-319-58904-6_15 %0 Journal Article %J Meccanica %D 2017 %T Stasis domains and slip surfaces in the locomotion of a bio-inspired two-segment crawler %A Paolo Gidoni %A Antonio DeSimone %XWe formulate and solve the locomotion problem for a bio-inspired crawler consisting of two active elastic segments (i.e., capable of changing their rest lengths), resting on three supports providing directional frictional interactions. The problem consists in finding the motion produced by a given, slow actuation history. By focusing on the tensions in the elastic segments, we show that the evolution laws for the system are entirely analogous to the flow rules of elasto-plasticity. In particular, sliding of the supports and hence motion cannot occur when the tensions are in the interior of certain convex regions (stasis domains), while support sliding (and hence motion) can only take place when the tensions are on the boundary of such regions (slip surfaces). We solve the locomotion problem explicitly in a few interesting examples. In particular, we show that, for a suitable range of the friction parameters, specific choices of the actuation strategy can lead to net displacements also in the direction of higher friction.

%B Meccanica %V 52 %P 587–601 %8 Feb %G eng %U https://doi.org/10.1007/s11012-016-0408-0 %R 10.1007/s11012-016-0408-0 %0 Journal Article %J Phys. Rev. Lett. %D 2017 %T Universality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schrödinger Equation %A Tikan, Alexey %A Billet, Cyril %A Gennady El %A Alexander Tovbis %A Marco Bertola %A Sylvestre, Thibaut %A Gustave, Francois %A Randoux, Stephane %A Genty, Goëry %A Suret, Pierre %A Dudley, John M. %B Phys. Rev. Lett. %I American Physical Society %V 119 %P 033901 %8 Jul %G eng %U https://link.aps.org/doi/10.1103/PhysRevLett.119.033901 %R 10.1103/PhysRevLett.119.033901 %0 Journal Article %J Journal of Ship Research %D 2017 %T Wet and Dry Transom Stern Treatment for Unsteady and Nonlinear Potential Flow Model for Naval Hydrodynamics Simulations %A Andrea Mola %A Luca Heltai %A Antonio DeSimone %XWe present a model for the fast evaluation of the total drag of ship hulls operating in both wet and dry transom stern conditions, in calm or wavy water, based on the combination of an unsteady semi-Lagrangian potential flow formulation with fully nonlinear free-surface treatment, experimental correlations, and simplified viscous drag modeling. The implementation is entirely based on open source libraries. The spatial discretization is solved using a streamline upwind Petrov‐Galerkin stabilization of an iso-parametric, collocation based, boundary element method, implemented using the open source library deal.II. The resulting nonlinear differential-algebraic system is integrated in time using implicit backward differentiation formulas, implemented in the open source library SUNDIALS. The Open CASCADE library is used to interface the model directly with computer-aided design data structures. The model accounts automatically for hulls with a transom stern, both in wet and dry regimes, by using a specific treatment of the free-surface nodes on the stern edge that automatically detects when the hull advances at low speeds. In this case, the transom stern is partially immersed, and a pressure patch is applied on the water surface detaching from the transom stern, to recover the gravity effect of the recirculating water on the underlying irrotational flow domain. The parameters of the model used to impose the pressure patch are approximated from experimental relations found in the literature. The test cases considered are those of the U.S. Navy Combatant DTMB-5415 and the National Physical Laboratory hull. Comparisons with experimental data on quasi-steady test cases for both water elevation and total hull drag are presented and discussed. The quality of the results obtained on quasi-steady simulations suggests that this model can represent a promising alternative to current unsteady solvers for simulations with Froude numbers below 0.35.

%B Journal of Ship Research %V 61 %P 1–14 %G eng %R https://doi.org/10.5957/JOSR.61.1.160016 %0 Journal Article %J Phys. D %D 2016 %T Correlation functions of the KdV hierarchy and applications to intersection numbers over $\overline\CalM_g,n$ %A Marco Bertola %A Boris Dubrovin %A Di Yang %B Phys. D %V 327 %P 30–57 %G eng %U http://dx.doi.org/10.1016/j.physd.2016.04.008 %R 10.1016/j.physd.2016.04.008 %0 Journal Article %J JOURNAL OF NUMERICAL MATHEMATICS %D 2016 %T The deal.II library, Version 8.4 %A Wolfgang Bangerth %A Denis Davydov %A Timo Heister %A Luca Heltai %A G. Kanschat %A Martin Kronbichler %A Matthias Maier %A Bruno Turcksin %A David Wells %B JOURNAL OF NUMERICAL MATHEMATICS %V 24 %P 135–141 %G eng %U https://www.math.clemson.edu/ heister/preprints/deal84-preprint.pdf %R 10.1515/jnma-2016-1045 %0 Journal Article %J Journal of Differential Equations %D 2016 %T Existence and uniqueness of dynamic evolutions for a peeling test in dimension one %A Gianni Dal Maso %A Giuliano Lazzaroni %A Lorenzo Nardini %K Dynamic debonding %K Dynamic energy release rate %K Dynamic fracture %K Griffith's criterion %K Maximum dissipation principle %K Wave equation in time-dependent domains %XIn this paper we present a one-dimensional model of a dynamic peeling test for a thin film, where the wave equation is coupled with a Griffith criterion for the propagation of the debonding front. Our main results provide existence and uniqueness for the solution to this coupled problem under different assumptions on the data.

%B Journal of Differential Equations %V 261 %P 4897 - 4923 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022039616301772 %R https://doi.org/10.1016/j.jde.2016.07.012 %0 Journal Article %J Calculus of Variations and Partial Differential Equations %D 2016 %T Fracture models for elasto-plastic materials as limits of gradient damage models coupled with plasticity: the antiplane case %A Gianni Dal Maso %A Gianluca Orlando %A Rodica Toader %XWe study the asymptotic behavior of a variational model for damaged elasto-plastic materials in the case of antiplane shear. The energy functionals we consider depend on a small parameter $\varepsilon$, which forces damage concentration on regions of codimension one. We determine the $\Gamma$-limit as $\varepsilon$ tends to zero and show that it contains an energy term involving the crack opening.

%B Calculus of Variations and Partial Differential Equations %V 55 %P 45 %8 Apr %G eng %U https://doi.org/10.1007/s00526-016-0981-z %R 10.1007/s00526-016-0981-z %0 Journal Article %J ESAIM Math. Model. Numer. Anal. %D 2016 %T $hp$-version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes %A Andrea Cangiani %A Dong, Zhaonan %A E.H. Georgoulis %A Houston, Paul %B ESAIM Math. Model. Numer. Anal. %V 50 %P 699–725 %G eng %U https://doi.org/10.1051/m2an/2015059 %R 10.1051/m2an/2015059 %0 Report %D 2016 %T A model for the quasistatic growth of cracks with fractional dimension %A Gianni Dal Maso %A Marco Morandotti %X We study a variational model for the quasistatic growth of cracks with fractional dimension in brittle materials. We give a minimal set of properties of the collection of admissible cracks which ensure the existence of a quasistatic evolution. Both the antiplane and the planar cases are treated. %G en %U http://urania.sissa.it/xmlui/handle/1963/35175 %1 35459 %2 Mathematics %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2016-03-01T11:58:09Z No. of bitstreams: 1 DM-Mor-15-SISSA.pdf: 333769 bytes, checksum: f89da17dcba29091a91c253127244ede (MD5) %0 Journal Article %J The European Physical Journal E %D 2016 %T Motion planning and motility maps for flagellar microswimmers %A Giancarlo Cicconofri %A Antonio DeSimone %XWe study two microswimmers consisting of a spherical rigid head and a passive elastic tail. In the first one the tail is clamped to the head, and the system oscillates under the action of an external torque. In the second one, head and tail are connected by a joint allowing the angle between them to vary periodically, as a result of an oscillating internal torque. Previous studies on these models were restricted to sinusoidal actuations, showing that the swimmers can propel while moving on average along a straight line, in the direction given by the symmetry axis around which beating takes place. We extend these results to motions produced by generic (non-sinusoidal) periodic actuations within the regime of small compliance of the tail. We find that modulation in the velocity of actuation can provide a mechanism to select different directions of motion. With velocity-modulated inputs, the externally actuated swimmer can translate laterally with respect to the symmetry axis of beating, while the internally actuated one is able to move along curved trajectories. The governing equations are analysed with an asymptotic perturbation scheme, providing explicit formulas, whose results are expressed through motility maps. Asymptotic approximations are further validated by numerical simulations.

%B The European Physical Journal E %V 39 %P 72 %8 Jul %G eng %U https://doi.org/10.1140/epje/i2016-16072-y %R 10.1140/epje/i2016-16072-y %0 Book Section %B Noncommutative Analysis, Operator Theory and Applications %D 2016 %T Pimsner Algebras and Circle Bundles %A Francesca Arici %A Francesco D'Andrea %A Giovanni Landi %E Alpay, Daniel %E Cipriani, Fabio %E Colombo, Fabrizio %E Guido, Daniele %E Sabadini, Irene %E Sauvageot, Jean-Luc %XWe report on the connections between noncommutative principal circle bundles, Pimsner algebras and strongly graded algebras. We illustrate several results with examples of quantum weighted projective and lens spaces and θ-deformations.

%B Noncommutative Analysis, Operator Theory and Applications %I Springer International Publishing %C Cham %P 1–25 %@ 978-3-319-29116-1 %G eng %U https://doi.org/10.1007/978-3-319-29116-1_1 %R 10.1007/978-3-319-29116-1_1 %0 Book Section %B Building bridges: connections and challenges in modern approaches to numerical partial differential equations %D 2016 %T Review of discontinuous Galerkin finite element methods for partial differential equations on complicated domains %A Antonietti, Paola F. %A Andrea Cangiani %A Collis, Joe %A Dong, Zhaonan %A E.H. Georgoulis %A Stefano Giani %A Houston, Paul %B Building bridges: connections and challenges in modern approaches to numerical partial differential equations %S Lect. Notes Comput. Sci. Eng. %I Springer, [Cham] %V 114 %P 279–308 %G eng %0 Conference Paper %B The 26th International Ocean and Polar Engineering Conference %D 2016 %T Ship Sinkage and Trim Predictions Based on a CAD Interfaced Fully Nonlinear Potential Model %A Andrea Mola %A Luca Heltai %A Antonio DeSimone %A Massimiliano Berti %B The 26th International Ocean and Polar Engineering Conference %I International Society of Offshore and Polar Engineers %V 3 %P 511–518 %G eng %0 Journal Article %J Int. Math. Res. Not. %D 2016 %T Simple Lie Algebras and Topological ODEs %A Marco Bertola %A Boris Dubrovin %A Di Yang %B Int. Math. Res. Not. %V 2016 %G eng %0 Journal Article %J Correggi, M., Dimonte, D., 2016. On the third critical speed for rotating Bose-Einstein condensates. J. Math. Phys. 57, 71901 %D 2016 %T On the third critical speed for rotating Bose-Einstein condensates %A Daniele Dimonte %A Michele Correggi %X We study a two-dimensional rotating Bose-Einstein condensate confined by an anharmonic trap in the framework of the Gross-Pitaevskii theory. We consider a rapid rotation regime close to the transition to a giant vortex state. It was proven in Correggi et al. [J. Math. Phys. 53, 095203 (2012)] that such a transition occurs when the angular velocity is of order ε−4, with ε−2 denoting the coefficient of the nonlinear term in the Gross-Pitaevskii functional and ε ≪ 1 (Thomas-Fermi regime). In this paper, we identify a finite value Ωc such that if Ω = Ω0/ε4 with Ω0 > Ωc, the condensate is in the giant vortex phase. Under the same condition, we prove a refined energy asymptotics and an estimate of the winding number of any Gross-Pitaevskii minimizer. %B Correggi, M., Dimonte, D., 2016. On the third critical speed for rotating Bose-Einstein condensates. J. Math. Phys. 57, 71901 %I AIP Publisher %G en %U http://urania.sissa.it/xmlui/handle/1963/35246 %1 35557 %2 Mathematics %$ Submitted by ddimonte@sissa.it (ddimonte@sissa.it) on 2016-10-19T16:34:31Z No. of bitstreams: 1 1508.07235v4.pdf: 520340 bytes, checksum: e987bbeef8fe09e31b8ea970c4ae4b4b (MD5) %R 10.1063/1.4954805 %0 Report %D 2015 %T A class of Hamiltonians for a three-particle fermionic system at unitarity %A Michele Correggi %A Gianfausto Dell'Antonio %A Domenico Finco %A Alessandro Michelangeli %A Alessandro Teta %X We consider a quantum mechanical three-particle system made of two identical fermions of mass one and a different particle of mass $m$, where each fermion interacts via a zero-range force with the different particle. In particular we study the unitary regime, i.e., the case of infinite two-body scattering length. The Hamiltonians describing the system are, by definition, self-adjoint extensions of the free Hamiltonian restricted on smooth functions vanishing at the two-body coincidence planes, i.e., where the positions of two interacting particles coincide. It is known that for $m$ larger than a critical value $m^* \simeq (13.607)^{-1}$ a self-adjoint and lower bounded Hamiltonian $H_0$ can be constructed, whose domain is characterized in terms of the standard point-interaction boundary condition at each coincidence plane. Here we prove that for $m\in(m^*,m^{**})$, where $m^{**}\simeq (8.62)^{-1}$, there is a further family of self-adjoint and lower bounded Hamiltonians $H_{0,\beta}$, $\beta \in \mathbb{R}$, describing the system. Using a quadratic form method, we give a rigorous construction of such Hamiltonians and we show that the elements of their domains satisfy a further boundary condition, characterizing the singular behavior when the positions of all the three particles coincide. %G en %U http://urania.sissa.it/xmlui/handle/1963/34469 %1 34644 %2 Mathematics %4 1 %$ Submitted by Alessandro Michelangeli (alemiche@sissa.it) on 2015-05-21T06:33:20Z No. of bitstreams: 1 SISSA_preprint_22-2015-MATE.pdf: 438261 bytes, checksum: ca05e5e2c5d78d87225a11073cb09d47 (MD5) %0 Report %D 2015 %T Existence for constrained dynamic Griffith fracture with a weak maximal dissipation condition %A Gianni Dal Maso %A Cristopher J. Larsen %A Rodica Toader %X There are very few existence results for fracture evolution, outside of globally minimizing quasi-static evolutions. Dynamic evolutions are particularly problematic, due to the difficulty of showing energy balance, as well as of showing that solutions obey a maximal dissipation condition, or some similar condition that prevents stationary cracks from always being solutions. Here we introduce a new weak maximal dissipation condition and show that it is compatible with cracks constrained to grow smoothly on a smooth curve. In particular, we show existence of dynamic fracture evolutions satisfying this maximal dissipation condition, subject to the above smoothness constraints, and exhibit explicit examples to show that this maximal dissipation principle can indeed rule out stationary cracks as solutions. %G en %U http://urania.sissa.it/xmlui/handle/1963/35045 %1 35277 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2015-11-18T15:46:32Z No. of bitstreams: 1 DM-Lar-Toa-SISSA.pdf: 313034 bytes, checksum: 76419fd2c8c435ae7deeca773b424667 (MD5) %0 Conference Paper %B International Conference on Parallel Processing and Applied Mathematics %D 2015 %T Experience on vectorizing lattice Boltzmann kernels for multi-and many-core architectures %A Calore, Enrico %A Nicola Demo %A Schifano, Sebastiano Fabio %A Tripiccione, Raffaele %B International Conference on Parallel Processing and Applied Mathematics %I Springer %P 53–62 %G eng %0 Report %D 2015 %T Extended affine Weyl groups of BCD type, Frobenius manifolds and their Landau-Ginzburg superpotentials %A Boris Dubrovin %A Ian A.B. Strachan %A Youjin Zhang %A Dafeng Zuo %X For the root systems of type Bl, Cl and Dl, we generalize the result of [7] by showing the existence of Frobenius manifold structures on the orbit spaces of the extended affine Weyl groups that correspond to any vertex of the Dynkin diagram instead of a particular choice made in [7]. It also depends on certain additional data. We also construct LG superpotentials for these Frobenius manifold structures. %I SISSA %G en %U http://preprints.sissa.it/handle/1963/35316 %1 35625 %2 Mathematics %4 1 %# MAT/07 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-05-23T10:53:54Z No. of bitstreams: 1 1510.08690.pdf: 433692 bytes, checksum: 0cd6111d36bb3b57262400e1f1cebe3a (MD5) %0 Journal Article %J Journal of the Mechanics and Physics of Solids %D 2015 %T Liquid crystal elastomer strips as soft crawlers %A Antonio DeSimone %A Paolo Gidoni %A Giovanni Noselli %K Crawling motility %K Directional surfaces %K Frictional interactions %K Liquid crystal elastomers %K Soft biomimetic robots %XIn this paper, we speculate on a possible application of Liquid Crystal Elastomers to the field of soft robotics. In particular, we study a concept for limbless locomotion that is amenable to miniaturisation. For this purpose, we formulate and solve the evolution equations for a strip of nematic elastomer, subject to directional frictional interactions with a flat solid substrate, and cyclically actuated by a spatially uniform, time-periodic stimulus (e.g., temperature change). The presence of frictional forces that are sensitive to the direction of sliding transforms reciprocal, ‘breathing-like’ deformations into directed forward motion. We derive formulas quantifying this motion in the case of distributed friction, by solving a differential inclusion for the displacement field. The simpler case of concentrated frictional interactions at the two ends of the strip is also solved, in order to provide a benchmark to compare the continuously distributed case with a finite-dimensional benchmark. We also provide explicit formulas for the axial force along the crawler body.

%B Journal of the Mechanics and Physics of Solids %V 84 %P 254 - 272 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022509615300430 %R https://doi.org/10.1016/j.jmps.2015.07.017 %0 Journal Article %J International Journal of Non-Linear Mechanics %D 2015 %T Motility of a model bristle-bot: A theoretical analysis %A Giancarlo Cicconofri %A Antonio DeSimone %K Bristle-robots %K Crawling motility %K Frictional interactions %XBristle-bots are legged robots that can be easily made out of a toothbrush head and a small vibrating engine. Despite their simple appearance, the mechanism enabling them to propel themselves by exploiting friction with the substrate is far from trivial. Numerical experiments on a model bristle-bot have been able to reproduce such a mechanism revealing, in addition, the ability to switch direction of motion by varying the vibration frequency. This paper provides a detailed account of these phenomena through a fully analytical treatment of the model. The equations of motion are solved through an expansion in terms of a properly chosen small parameter. The convergence of the expansion is rigorously proven. In addition, the analysis delivers formulas for the average velocity of the robot and for the frequency at which the direction switch takes place. A quantitative description of the mechanism for the friction modulation underlying the motility of the bristle-bot is also provided.

%B International Journal of Non-Linear Mechanics %V 76 %P 233 - 239 %G eng %U http://www.sciencedirect.com/science/article/pii/S0020746215000025 %R https://doi.org/10.1016/j.ijnonlinmec.2014.12.010 %0 Journal Article %D 2015 %T The phototransduction machinery in the rod outer segment has a strong efficacy gradient %A Monica Mazzolini %A Giuseppe Facchetti %A L. Andolfi %A R. Proietti Zaccaria %A S. Tuccio %A J. Treud %A Claudio Altafini %A Enzo M. Di Fabrizio %A Marco Lazzarino %A G. Rapp %A Vincent Torre %I National Academy of Sciences %G en %U http://urania.sissa.it/xmlui/handle/1963/35157 %1 35382 %2 Neuroscience %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2016-01-21T09:29:28Z (GMT) No. of bitstreams: 0 %R 10.1073/pnas.1423162112 %0 Report %D 2015 %T Schödinger operators on half-line with shrinking potentials at the origin %A Gianfausto Dell'Antonio %A Alessandro Michelangeli %X We discuss the general model of a Schrödinger quantum particle constrained on a straight half-line with given self-adjoint boundary condition at the origin and an interaction potential supported around the origin. We study the limit when the range of the potential scales to zero and its magnitude blows up. We show that in the limit the dynamics is generated by a self-adjoint negative Laplacian on the half-line, with a possible preservation or modification of the boundary condition at the origin, depending on the magnitude of the scaling and of the strength of the potential. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/34439 %1 34566 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-02-09T07:28:40Z No. of bitstreams: 1 SISSA_preprint_06-2015-MATE.pdf: 177243 bytes, checksum: 383296953d36b4cec0cb4cfb55e95d7f (MD5) %0 Journal Article %J Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences %D 2015 %T A study of snake-like locomotion through the analysis of a flexible robot model %A Giancarlo Cicconofri %A Antonio DeSimone %XWe examine the problem of snake-like locomotion by studying a system consisting of a planar inextensible elastic rod with adjustable spontaneous curvature, which provides an internal actuation mechanism that mimics muscular action in a snake. Using a Cosserat model, we derive the equations of motion in two special cases: one in which the rod can only move along a prescribed curve, and one in which the rod is constrained to slide longitudinally without slipping laterally, but the path is not fixed a priori (free-path case). The second setting is inspired by undulatory locomotion of snakes on flat surfaces. The presence of constraints leads in both cases to non-standard boundary conditions that allow us to close and solve the equations of motion. The kinematics and dynamics of the system can be recovered from a one-dimensional equation, without any restrictive assumption on the followed trajectory or the actuation. We derive explicit formulae highlighting the role of spontaneous curvature in providing the driving force (and the steering, in the free-path case) needed for locomotion. We also provide analytical solutions for a special class of serpentine motions, which enable us to discuss the connection between observed trajectories, internal actuation and forces exchanged with the environment.

%B Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences %V 471 %P 20150054 %G eng %U https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2015.0054 %R 10.1098/rspa.2015.0054 %0 Journal Article %D 2015 %T Three-sphere low-Reynolds-number swimmer with a passive elastic arm %A Alessandro Montino %A Antonio DeSimone %X One of the simplest model swimmers at low Reynolds number is the three-sphere swimmer by Najafi and Golestanian. It consists of three spheres connected by two rods which change their lengths periodically in non-reciprocal fashion. Here we investigate a variant of this model in which one rod is periodically actuated while the other is replaced by an elastic spring. We show that the competition between the elastic restoring force and the hydrodynamic drag produces a delay in the response of the passive elastic arm with respect to the active one. This leads to non-reciprocal shape changes and self-propulsion. After formulating the equations of motion, we study their solutions qualitatively and numerically. The leading-order term of the solution is computed analytically. We then address questions of optimization with respect to both actuation frequency and swimmer's geometry. Our results can provide valuable conceptual guidance in the engineering of robotic microswimmers. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34530 %1 34735 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-09-22T07:16:17Z No. of bitstreams: 1 art_10.1140_epje_i2015-15042-3.pdf: 766953 bytes, checksum: 7c5396c7e15baff264376c63eaf2248b (MD5) %R 10.1140/epje/i2015-15042-3 %0 Report %D 2015 %T The wave equation on domains with cracks growing on a prescribed path: existence, uniqueness, and continuous dependence on the data %A Gianni Dal Maso %A Ilaria Lucardesi %X Given a bounded open set $\Omega \subset \mathbb R^d$ with Lipschitz boundary and an increasing family $\Gamma_t$, $t\in [0,T]$, of closed subsets of $\Omega$, we analyze the scalar wave equation $\ddot{u} - div (A \nabla u) = f$ in the time varying cracked domains $\Omega\setminus\Gamma_t$. Here we assume that the sets $\Gamma_t$ are contained into a prescribed $(d-1)$-manifold of class $C^2$. Our approach relies on a change of variables: recasting the problem on the reference configuration $\Omega\setminus \Gamma_0$, we are led to consider a hyperbolic problem of the form $\ddot{v} - div (B\nabla v) + a \cdot \nabla v - 2 b \cdot \nabla \dot{v} = g$ in $\Omega \setminus \Gamma_0$. Under suitable assumptions on the regularity of the change of variables that transforms $\Omega\setminus \Gamma_t$ into $\Omega\setminus \Gamma_0$, we prove existence and uniqueness of weak solutions for both formulations. Moreover, we provide an energy equality, which gives, as a by-product, the continuous dependence of the solutions with respect to the cracks. %G en %U http://urania.sissa.it/xmlui/handle/1963/34629 %1 34832 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by lucardes@sissa.it (lucardes@sissa.it) on 2015-10-12T09:08:37Z No. of bitstreams: 1 DM-Luc-15-SISSA.pdf: 376913 bytes, checksum: bfdcf0975c25c9366acb4195e0f08e79 (MD5) %0 Journal Article %D 2014 %T Adler-Gelfand-Dickey approach to classical W-algebras within the theory of Poisson vertex algebras %A Alberto De Sole %A Victor G. Kac %A Daniele Valeri %X We put the Adler-Gelfand-Dickey approach to classical W-algebras in the framework of Poisson vertex algebras. We show how to recover the bi-Poisson structure of the KP hierarchy, together with its generalizations and reduction to the N-th KdV hierarchy, using the formal distribution calculus and the lambda-bracket formalism. We apply the Lenard-Magri scheme to prove integrability of the corresponding hierarchies. We also give a simple proof of a theorem of Kupershmidt and Wilson in this framework. Based on this approach, we generalize all these results to the matrix case. In particular, we find (non-local) bi-Poisson structures of the matrix KP and the matrix N-th KdV hierarchies, and we prove integrability of the N-th matrix KdV hierarchy. %I SISSA %G eng %U http://hdl.handle.net/1963/7242 %0 Journal Article %J Communications in Mathematical Physics 331, nr. 2 (2014) 623-676 %D 2014 %T Classical W-algebras and generalized Drinfeld-Sokolov hierarchies for minimal and short nilpotents %A Alberto De Sole %A Victor G. Kac %A Daniele Valeri %X We derive explicit formulas for lambda-brackets of the affine classical W-algebras attached to the minimal and short nilpotent elements of any simple Lie algebra g. This is used to compute explicitly the first non-trivial PDE of the corresponding intgerable generalized Drinfeld-Sokolov hierarchies. It turns out that a reduction of the equation corresponding to a short nilpotent is Svinolupov's equation attached to a simple Jordan algebra, while a reduction of the equation corresponding to a minimal nilpotent is an integrable Hamiltonian equation on 2h-3 functions, where h is the dual Coxeter number of g. In the case when g is sl_2 both these equations coincide with the KdV equation. In the case when g is not of type C_n, we associate to the minimal nilpotent element of g yet another generalized Drinfeld-Sokolov hierarchy. %B Communications in Mathematical Physics 331, nr. 2 (2014) 623-676 %I SISSA %G en %U http://hdl.handle.net/1963/6979 %1 6967 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Daniele Valeri (dvaleri@sissa.it) on 2013-07-13T15:27:20Z No. of bitstreams: 1 1306.1684v1.pdf: 580565 bytes, checksum: de8a5fc99d3eb9f1c4f85b4a2a6592e9 (MD5) %R 10.1007/s00220-014-2049-2 %0 Journal Article %J International Journal of Non-Linear Mechanics %D 2014 %T Crawling on directional surfaces %A Paolo Gidoni %A Giovanni Noselli %A Antonio DeSimone %K Bio-mimetic micro-robots %K Cell migration %K Crawling motility %K Directional surfaces %K Self-propulsion %XIn this paper we study crawling locomotion based on directional frictional interactions, namely, frictional forces that are sensitive to the sign of the sliding velocity. Surface interactions of this type are common in biology, where they arise from the presence of inclined hairs or scales at the crawler/substrate interface, leading to low resistance when sliding ‘along the grain’, and high resistance when sliding ‘against the grain’. This asymmetry can be exploited for locomotion, in a way analogous to what is done in cross-country skiing (classic style, diagonal stride). We focus on a model system, namely, a continuous one-dimensional crawler and provide a detailed study of the motion resulting from several strategies of shape change. In particular, we provide explicit formulae for the displacements attainable with reciprocal extensions and contractions (breathing), or through the propagation of extension or contraction waves. We believe that our results will prove particularly helpful for the study of biological crawling motility and for the design of bio-mimetic crawling robots.

%B International Journal of Non-Linear Mechanics %V 61 %P 65 - 73 %G eng %U http://www.sciencedirect.com/science/article/pii/S0020746214000213 %R https://doi.org/10.1016/j.ijnonlinmec.2014.01.012 %0 Journal Article %J Procedia Engineering %D 2014 %T Curvature-adapted remeshing of CAD surfaces %A Franco Dassi %A Andrea Mola %A Hang Si %XA common representation of surfaces with complicated topology and geometry is through composite parametric surfaces as is the case for most CAD modelers. A challenging problem is how to generate a mesh of such a surface that well approximates the geometry of the surface, preserves its topology and important geometric features, and contains nicely shaped elements. In this work, we present an optimization-based surface remeshing method that is able to satisfy many of these requirements simultaneously. This method is inspired by the recent work of Lévy and Bonneel (Proc. 21th International Meshing Roundtable, October 2012), which embeds a smooth surface into a high-dimensional space and remesh it uniformly in that embedding space. Our method works directly in the 3d spaces and uses an embedding space in R6 to evaluate mesh size and mesh quality. It generates a curvatureadapted anisotropic surface mesh that well represents the geometry of the surface with a low number of elements. We illustrate our approach through various examples.

%B Procedia Engineering %I Elsevier %V 82 %P 253–265 %G en %U https://doi.org/10.1016/j.proeng.2014.10.388 %1 35220 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-11-11T16:19:16Z No. of bitstreams: 1 art2014.pdf: 3913220 bytes, checksum: ba78b55b28c0eed195d2abc48bd7ca4b (MD5) %R 10.1016/j.proeng.2014.10.388 %0 Journal Article %D 2014 %T Dirac operators on noncommutative principal circle bundles %A Andrzej Sitarz %A Alessandro Zucca %A Ludwik Dabrowski %X We study spectral triples over noncommutative principal U(1)-bundles of arbitrary dimension and a compatibility condition between the connection and the Dirac operator on the total space and on the base space of the bundle. Examples of low-dimensional noncommutative tori are analyzed in more detail and all connections found that are compatible with an admissible Dirac operator. Conversely, a family of new Dirac operators on the noncommutative tori, which arise from the base-space Dirac operator and a suitable connection is exhibited. These examples are extended to the theta-deformed principal U(1)-bundle S 3 θ → S2. %I World Scientific Publishing %G en %U http://urania.sissa.it/xmlui/handle/1963/35125 %1 35363 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-12-02T15:58:16Z No. of bitstreams: 1 preprint2014.pdf: 282573 bytes, checksum: 862ea930b67b00c451a0c6f093be973d (MD5) %R 10.1142/S0219887814500121 %0 Journal Article %J Communications in Mathematical Physics 331, nr. 3 (2014) 1155-1190 %D 2014 %T Dirac reduction for Poisson vertex algebras %A Alberto De Sole %A Victor G. Kac %A Daniele Valeri %X We construct an analogue of Dirac's reduction for an arbitrary local or non-local Poisson bracket in the general setup of non-local Poisson vertex algebras. This leads to Dirac's reduction of an arbitrary non-local Poisson structure. We apply this construction to an example of a generalized Drinfeld-Sokolov hierarchy. %B Communications in Mathematical Physics 331, nr. 3 (2014) 1155-1190 %I SISSA %G en %U http://hdl.handle.net/1963/6980 %1 6968 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Daniele Valeri (dvaleri@sissa.it) on 2013-07-13T15:28:44Z No. of bitstreams: 1 1306.6589v1.pdf: 417586 bytes, checksum: 261351372e0d72d5e2d46b6664f19fd4 (MD5) %R 10.1007/s00220-014-2103-0 %0 Journal Article %D 2014 %T Discrete one-dimensional crawlers on viscous substrates: achievable net displacements and their energy cost %A Giovanni Noselli %A Amabile Tatone %A Antonio DeSimone %K Cell migration %X We study model one-dimensional crawlers, namely, model mechanical systems that can achieve self-propulsion by controlled shape changes of their body (extension or contraction of portions of the body), thanks to frictional interactions with a rigid substrate. We evaluate the achievable net displacement and the related energetic cost for self-propulsion by discrete crawlers (i.e., whose body is made of a discrete number of contractile or extensile segments) moving on substrates with either a Newtonian (linear) or a Bingham-type (stick-slip) rheology. Our analysis is aimed at constructing the basic building blocks towards an integrative, multi-scale description of crawling cell motility. %I Elsevier %G en %U http://urania.sissa.it/xmlui/handle/1963/34449 %1 34591 %2 Mathematics %$ Submitted by gnoselli@sissa.it (gnoselli@sissa.it) on 2015-03-07T17:44:40Z No. of bitstreams: 1 N-link_crawlers.pdf: 1005838 bytes, checksum: 685d5b41e7de190ec65c60090d397f93 (MD5) %R 10.1016/j.mechrescom.2013.10.023 %0 Report %D 2014 %T Donagi–Markman cubic for the generalised Hitchin system %A Ugo Bruzzo %A Peter Dalakov %K Generalized Hitchin system, Donagi-Markman cubic, algebraically completely integrable systems, moduli space of Higgs G-bundles %X Donagi and Markman (1993) have shown that the infinitesimal period map for an algebraic completely integrable Hamiltonian system (ACIHS) is encoded in a section of the third symmetric power of the cotangent bundle to the base of the system. For the ordinary Hitchin system the cubic is given by a formula of Balduzzi and Pantev. We show that the Balduzzi–Pantev formula holds on maximal rank symplectic leaves of the G-generalised Hitchin system. %G en %U http://hdl.handle.net/1963/7253 %1 7294 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Ugo Bruzzo (bruzzo@sissa.it) on 2014-02-17T15:50:22Z No. of bitstreams: 1 bruzzo-dalakov-fin-2.pdf: 461019 bytes, checksum: 99e7b1cb6cd4f6f5d5fbfaa1d2d35880 (MD5) %0 Report %D 2014 %T Dynamics on a graph as the limit of the dynamics on a "fat graph" %A Gianfausto Dell'Antonio %A Alessandro Michelangeli %X We discuss how the vertex boundary conditions for the dynamics of a quantum particle constrained on a graph emerge in the limit of the dynamics of a particle in a tubular region around the graph (\fat graph") when the transversal section of this region shrinks to zero. We give evidence of the fact that if the limit dynamics exists and is induced by the Laplacian on the graph with certain self-adjoint boundary conditions, such conditions are determined by the possible presence of a zero energy resonance on the fat graph. Pictorially, one may say that in the shrinking limit the resonance acts as a bridge connecting the boundary values at the vertex along the different rays. %I SISSA %G en_US %U http://urania.sissa.it/xmlui/handle/1963/7485 %1 7598 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-12-12T13:16:15Z No. of bitstreams: 1 sissa-preprint-69-2014-mate.pdf: 137454 bytes, checksum: 4d4571bd97df46ee020c81057ce78620 (MD5) %0 Journal Article %D 2014 %T Editorial %A Ciro Ciliberto %A Gianni Dal Maso %A Pasquale Vetro %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34712 %1 34926 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-10-26T10:50:12Z (GMT) No. of bitstreams: 0 %R 10.1007/s12215-014-0172-8 %0 Journal Article %D 2014 %T An effective model for nematic liquid crystal composites with ferromagnetic inclusions %A Maria Carme Calderer %A Antonio DeSimone %A Dmitry Golovaty %A Alexander Panchenko %X Molecules of a nematic liquid crystal respond to an applied magnetic field by reorienting themselves in the direction of the field. Since the dielectric anisotropy of a nematic is small, it takes relatively large fields to elicit a significant liquid crystal response. The interaction may be enhanced in colloidal suspensions of ferromagnetic particles in a liquid crystalline matrix- ferronematics-as proposed by Brochard and de Gennes in 1970. The ability of these particles to align with the field and simultaneously cause reorientation of the nematic molecules greatly increases the magnetic response of the mixture. Essentially the particles provide an easy axis of magnetization that interacts with the liquid crystal via surface anchoring. We derive an expression for the effective energy of ferronematic in the dilute limit, that is, when the number of particles tends to infinity while their total volume fraction tends to zero. The total energy of the mixture is assumed to be the sum of the bulk elastic liquid crystal contribution, the anchoring energy of the liquid crystal on the surfaces of the particles, and the magnetic energy of interaction between the particles and the applied magnetic field. The homogenized limiting ferronematic energy is obtained rigorously using a variational approach. It generalizes formal expressions previously reported in the physical literature. %I Society for Industrial and Applied Mathematics Publications %G en %U http://urania.sissa.it/xmlui/handle/1963/34940 %1 35194 %2 Physics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-11-09T09:28:26Z No. of bitstreams: 1 preprint2014.pdf: 284611 bytes, checksum: ef4123b4aefb1a36fa198c1207a6f021 (MD5) %R 10.1137/130910348 %0 Journal Article %D 2014 %T Existence and uniqueness of the gradient flow of the Entropy in the space of probability measures %A Stefano Bianchini %A Alexander Dabrowski %X After a brief introduction on gradient flows in metric spaces and on geodesically convex functionals, we give an account of the proof (following the outline of [3, 7]) of the existence and uniqueness of the gradient flow of the Entropy in the space of Borel probability measures over a compact geodesic metric space with Ricci curvature bounded from below. %I EUT Edizioni Universita di Trieste %G en %U http://urania.sissa.it/xmlui/handle/1963/34693 %1 34907 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-10-22T09:22:40Z No. of bitstreams: 1 ExUniqGFEntropy.pdf: 344636 bytes, checksum: a918d50ab5d6b9ce9cb8683238f402e6 (MD5) %0 Conference Proceedings %B Proceedings of the 24th International Ocean and Polar Engineering Conference, Busan, 2014 %D 2014 %T A fully nonlinear potential model for ship hydrodynamics directly interfaced with CAD data structures %A Andrea Mola %A Luca Heltai %A Antonio DeSimone %K ship hydrodynamics %X We present a model for ship hydrodynamics simulations currently under development at SISSA. The model employs potential flow theory and fully nonlinear free surface boundary conditions. The spatial discretization of the equations is performed by means of a collocation BEM. This gives rise to a Differential Algbraic Equations (DAE) system, solved using an implicit BDF scheme to time advance the solution. The model has been implemented into a C++ software able to automatically generate the computational grids from the CAD geometry of the hull. Numerical results on Kriso KCS and KVLCC2 hulls are presented and discussed. %B Proceedings of the 24th International Ocean and Polar Engineering Conference, Busan, 2014 %I SISSA %G en %1 7357 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Luca Heltai (heltai@sissa.it) on 2014-03-22T15:00:37Z No. of bitstreams: 1 MolaHeltaiDeSimone2014.pdf: 1241007 bytes, checksum: 1a56d909a08f1f470c7efc14018e37f8 (MD5) %0 Report %D 2014 %T Integrability of Dirac reduced bi-Hamiltonian equations %A Alberto De Sole %A Victor G. Kac %A Daniele Valeri %X First, we give a brief review of the theory of the Lenard-Magri scheme for a non-local bi-Poisson structure and of the theory of Dirac reduction. These theories are used in the remainder of the paper to prove integrability of three hierarchies of bi-Hamiltonian PDE's, obtained by Dirac reduction from some generalized Drinfeld-Sokolov hierarchies. %I SISSA %G en %U http://hdl.handle.net/1963/7247 %1 7286 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Daniele Valeri (dvaleri@sissa.it) on 2014-01-24T09:47:51Z No. of bitstreams: 1 1401.6006v1.pdf: 249123 bytes, checksum: 3b83fabf790160e10ecb05aa89251970 (MD5) %0 Journal Article %D 2014 %T On an isomonodromy deformation equation without the Painlevé property %A Boris Dubrovin %A Andrey Kapaev %X We show that the fourth order nonlinear ODE which controls the pole dynamics in the general solution of equation $P_I^2$ compatible with the KdV equation exhibits two remarkable properties: 1) it governs the isomonodromy deformations of a $2\times2$ matrix linear ODE with polynomial coefficients, and 2) it does not possesses the Painlev\'e property. We also study the properties of the Riemann--Hilbert problem associated to this ODE and find its large $t$ asymptotic solution for the physically interesting initial data. %I Maik Nauka-Interperiodica Publishing %G en %U http://hdl.handle.net/1963/6466 %1 6410 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-08T11:29:56Z No. of bitstreams: 1 1301.7211v2.pdf: 415681 bytes, checksum: f606a3b5df4b201ae37a9d6fa1b79016 (MD5) %R 10.1134/S1061920814010026 %0 Journal Article %D 2014 %T Laplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length %A Gianni Dal Maso %A Gianluca Orlando %A Rodica Toader %K cracked domains, energy release rate, higher order derivatives, asymptotic expansion of solutions %XWe consider the weak solution of the Laplace equation in a planar domain with a straight crack, prescribing a homogeneous Neumann condition on the crack and a nonhomogeneous Dirichlet condition on the rest of the boundary. For every k we express the k-th derivative of the energy with respect to the crack length in terms of a finite number of coefficients of the asymptotic expansion of the solution near the crack tip and of a finite number of other parameters, which only depend on the shape of the domain.

%I SISSA %G en %U http://hdl.handle.net/1963/7271 %1 7316 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2014-03-11T15:17:50Z No. of bitstreams: 1 DM-Orl-Toa-sissa.pdf: 251851 bytes, checksum: 59273a217a11dcfc5a9ed89d2c34c6cd (MD5) %R 10.1007/s00030-014-0291-0 %0 Book Section %D 2014 %T Lecture notes on gradient flows and optimal transport %A Sara Daneri %A Giuseppe Savarè %X We present a short overview on the strongest variational formulation for gradient flows of geodesically λ-convex functionals in metric spaces, with applications to diffusion equations in Wasserstein spaces of probability measures. These notes are based on a series of lectures given by the second author for the Summer School "Optimal transportation: Theory and applications" in Grenoble during the week of June 22-26, 2009. %I Cambridge University Press %G en %U http://urania.sissa.it/xmlui/handle/1963/35093 %1 35348 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-12-02T11:28:52Z No. of bitstreams: 1 preprint2014.pdf: 448708 bytes, checksum: b8b01c6463b81dc26c42c74009c43406 (MD5) %R 10.1017/CBO9781107297296 %0 Journal Article %J ESAIM: Control, Optimisation and Calculus of Variations %D 2014 %T Linearized plastic plate models as Γ-limits of 3D finite elastoplasticity %A Elisa Davoli %XThe subject of this paper is the rigorous derivation of reduced models for a thin plate by means of $\Gamma$-convergence, in the framework of finite plasticity. Denoting by $\epsilon$ the thickness of the plate, we analyse the case where the scaling factor of the elasto-plastic energy per unit volume is of order $\epsilon^{2 \alpha -2}$, with $\alpha \geq 3$. According to the value of $\alpha$, partially or fully linearized models are deduced, which correspond, in the absence of plastic deformation, to the Von Kármán plate theory and the linearized plate theory.

%B ESAIM: Control, Optimisation and Calculus of Variations %I EDP Sciences %V 20 %P 725–747 %G eng %R 10.1051/cocv/2013081 %0 Journal Article %D 2014 %T Local behavior of fractional p-minimizers %A Agnese Di Castro %A Tuomo Kuusi %A Giampiero Palatucci %K fractional Sobolev spaces %XWe extend the De Giorgi-Nash Moser theory to nonlocal, possibly degerate integro-differential operators

%I SISSA %G en %1 7301 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Giampiero Palatucci (palatucc@sissa.it) on 2014-03-03T08:54:40Z No. of bitstreams: 1 DKP.pdf: 459581 bytes, checksum: 58cf9e0f905a3932505ab467eefd39e9 (MD5) %0 Journal Article %D 2014 %T Minimal Liouville gravity correlation numbers from Douglas string equation %A Alexander Belavin %A Boris Dubrovin %A Baur Mukhametzhanov %X We continue the study of $(q,p)$ Minimal Liouville Gravity with the help of Douglas string equation. We generalize the results of \cite{Moore:1991ir}, \cite{Belavin:2008kv}, where Lee-Yang series $(2,2s+1)$ was studied, to $(3,3s+p_0)$ Minimal Liouville Gravity, where $p_0=1,2$. We demonstrate that there exist such coordinates $\tau_{m,n}$ on the space of the perturbed Minimal Liouville Gravity theories, in which the partition function of the theory is determined by the Douglas string equation. The coordinates $\tau_{m,n}$ are related in a non-linear fashion to the natural coupling constants $\lambda_{m,n}$ of the perturbations of Minimal Lioville Gravity by the physical operators $O_{m,n}$. We find this relation from the requirement that the correlation numbers in Minimal Liouville Gravity must satisfy the conformal and fusion selection rules. After fixing this relation we compute three- and four-point correlation numbers when they are not zero. The results are in agreement with the direct calculations in Minimal Liouville Gravity available in the literature \cite{Goulian:1990qr}, \cite{Zamolodchikov:2005sj}, \cite{Belavin:2006ex}. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34588 %1 34795 %2 Physics %4 2 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-09-28T14:45:32Z No. of bitstreams: 1 art2014.pdf: 914777 bytes, checksum: 6f6d70a301b22d993393d16ad5abef80 (MD5) %R 10.1007/JHEP01(2014)156 %0 Journal Article %D 2014 %T New results on Gamma-limits of integral functionals %A Nadia Ansini %A Gianni Dal Maso %A Caterina Ida Zeppieri %K Gamma-convergence %I Elsevier %G en %U http://hdl.handle.net/1963/5880 %1 5745 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-05-30T12:48:08Z No. of bitstreams: 1 03M_2012_Ansini.pdf: 262251 bytes, checksum: 4e0dd5c07ab75bd2da8aa462f2ae8f0f (MD5) %R 10.1016/j.anihpc.2013.02.005 %0 Journal Article %D 2014 %T Nonsingular Isogeometric Boundary Element Method for Stokes Flows in 3D %A Luca Heltai %A Marino Arroyo %A Antonio DeSimone %K Isogeometric Analysis %X Isogeometric analysis (IGA) is emerging as a technology bridging Computer Aided Geometric Design (CAGD), most commonly based on Non-Uniform Rational B-Splines (NURBS) surfaces, and engineering analysis. In finite element and boundary element isogeometric methods (FE-IGA and IGA-BEM), the NURBS basis functions that de- scribe the geometry define also the approximation spaces. In the FE-IGA approach, the surfaces generated by the CAGD tools need to be extended to volumetric descriptions, a major open problem in 3D. This additional passage can be avoided in principle when the partial differential equations to be solved admit a formulation in terms of bound- ary integral equations, leading to Boundary Element Isogeometric Analysis (IGA-BEM). The main advantages of such an approach are given by the dimensionality reduction of the problem (from volumetric-based to surface-based), by the fact that the interface with CAGD tools is direct, and by the possibility to treat exterior problems, where the computational domain is infinite. By contrast, these methods produce system matrices which are full, and require the integration of singular kernels. In this paper we address the second point and propose a nonsingular formulation of IGA-BEM for 3D Stokes flows, whose convergence is carefully tested numerically. Standard Gaussian quadrature rules suffice to integrate the boundary integral equations, and carefully chosen known exact solutions of the interior Stokes problem are used to correct the resulting matrices, extending the work by Klaseboer et al. [27] to IGA-BEM. %I Elsevier %G en %U http://hdl.handle.net/1963/6326 %1 6250 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Luca Heltai (heltai@sissa.it) on 2012-12-03T08:19:28Z No. of bitstreams: 1 isogeo_stokes.pdf: 732320 bytes, checksum: 224ef57de6c49f03db0afaccdcb234f9 (MD5) %R 10.1016/j.cma.2013.09.017 %0 Conference Paper %B The 24th International Ocean and Polar Engineering Conference %D 2014 %T Potential Model for Ship Hydrodynamics Simulations Directly Interfaced with CAD Data Structures %A Andrea Mola %A Luca Heltai %A Antonio DeSimone %A Massimiliano Berti %B The 24th International Ocean and Polar Engineering Conference %I International Society of Offshore and Polar Engineers %V 4 %P 815–822 %G eng %0 Journal Article %D 2014 %T Quantum gauge symmetries in noncommutative geometry %A Jyotishman Bhowmick %A Francesco D'Andrea %A Biswarup Krishna Das %A Ludwik Dabrowski %X We discuss generalizations of the notion of i) the group of unitary elements of a (real or complex) finite-dimensional C*-algebra, ii) gauge transformations and iii) (real) automorphisms in the framework of compact quantum group theory and spectral triples. The quantum analogue of these groups are defined as universal (initial) objects in some natural categories. After proving the existence of the universal objects, we discuss several examples that are of interest to physics, as they appear in the noncommutative geometry approach to particle physics: in particular, the C*-algebras M n(R), Mn(C) and Mn(H), describing the finite noncommutative space of the Einstein-Yang-Mills systems, and the algebras A F = C H M3 (C) and Aev = H H M4(C), that appear in Chamseddine-Connes derivation of the Standard Model of particle physics coupled to gravity. As a byproduct, we identify a "free" version of the symplectic group Sp.n/ (quaternionic unitary group). %I European Mathematical Society Publishing House %G en %U http://urania.sissa.it/xmlui/handle/1963/34897 %1 35182 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-11-04T16:59:52Z No. of bitstreams: 1 preprint2014.pdf: 652206 bytes, checksum: d452b46b1c285be861389dcab56e1f6e (MD5) %R 10.4171/JNCG/161 %0 Journal Article %J Nonlinear Analysis %D 2014 %T Quasi-static crack growth in hydraulic fracture %A Stefano Almi %A Gianni Dal Maso %A Rodica Toader %XWe present a variational model for the quasi-static crack growth in hydraulic fracture in the framework of the energy formulation of rate-independent processes. The cracks are assumed to lie on a prescribed plane and to satisfy a very weak regularity assumption.

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

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

%B Mathematical Models and Methods in Applied Sciences %V 24 %P 2085-2153 %G eng %U https://doi.org/10.1142/S021820251450016X %R 10.1142/S021820251450016X %0 Journal Article %J Proceedings of the Royal Society A 470, 20140333 (2014) %D 2014 %T A robotic crawler exploiting directional frictional interactions: experiments, numerics, and derivation of a reduced model %A Giovanni Noselli %A Antonio DeSimone %X We present experimental and numerical results for a model crawler which is able to extract net positional changes from reciprocal shape changes, i.e. ‘breathing-like’ deformations, thanks to directional, frictional interactions with a textured solid substrate, mediated by flexible inclined feet. We also present a simple reduced model that captures the essential features of the kinematics and energetics of the gait, and compare its predictions with the results from experiments and from numerical simulations. %B Proceedings of the Royal Society A 470, 20140333 (2014) %I Royal Society Publishing %G en %1 34594 %2 Mathematics %$ Submitted by gnoselli@sissa.it (gnoselli@sissa.it) on 2015-03-07T18:10:10Z No. of bitstreams: 1 bristle_crawlers.pdf: 9309327 bytes, checksum: 10f6df9814dd01c888aa9ec7836f1dff (MD5) %R 10.1098/rspa.2014.0333 %0 Journal Article %D 2014 %T Second Order Asymptotic Development for the Anisotropic Cahn-Hilliard Functional %A Gianni Dal Maso %A Irene Fonseca %A Giovanni Leoni %K Gamma-convergence, Cahn-Hilliard functional, phase transitions %X The asymptotic behavior of an anisotropic Cahn-Hilliard functional with prescribed mass and Dirichlet boundary condition is studied when the parameter $\varepsilon$ that determines the width of the transition layers tends to zero. The double-well potential is assumed to be even and equal to $|s-1|^\beta$ near $s=1$, with $1<\beta<2$. The first order term in the asymptotic development by $\Gamma$-convergence is well-known, and is related to a suitable anisotropic perimeter of the interface. Here it is shown that, under these assumptions, the second order term is zero, which gives an estimate on the rate of convergence of the minimum values. %I SISSA %G en %U http://hdl.handle.net/1963/7390 %1 7439 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2014-06-19T16:24:43Z No. of bitstreams: 1 DM-Fon-Leo-14-sissa.pdf: 409621 bytes, checksum: 40ba0baf0686b18dcd89582772f376b5 (MD5) %0 Journal Article %D 2014 %T Shape control of active surfaces inspired by the movement of euglenids %A Marino Arroyo %A Antonio DeSimone %X We examine a novel mechanism for active surface morphing inspired by the cell body deformations of euglenids. Actuation is accomplished through in-plane simple shear along prescribed slip lines decorating the surface. Under general non-uniform actuation, such local deformation produces Gaussian curvature, and therefore leads to shape changes. Geometrically, a deformation that realizes the prescribed local shear is an isometric embedding. We explore the possibilities and limitations of this bio-inspired shape morphing mechanism, by first characterizing isometric embeddings under axisymmetry, understanding the limits of embeddability, and studying in detail the accessibility of surfaces of zero and constant curvature. Modeling mechanically the active surface as a non-Euclidean plate (NEP), we further examine the mechanism beyond the geometric singularities arising from embeddability, where mechanics and buckling play a decisive role. We also propose a non-axisymmetric actuation strategy to accomplish large amplitude bending and twisting motions of elongated cylindrical surfaces. Besides helping understand how euglenids delicately control their shape, our results may provide the background to engineer soft machines. %I Elsevier %G en %U http://urania.sissa.it/xmlui/handle/1963/35118 %1 35375 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-12-03T09:19:38Z (GMT) No. of bitstreams: 0 %R 10.1016/j.jmps.2013.09.017 %0 Journal Article %J Annales de l'Institut Henri Poincare (C) Non Linear Analysis %D 2014 %T Smooth approximation of bi-Lipschitz orientation-preserving homeomorphisms %A Sara Daneri %A Aldo Pratelli %XWe show that a planar bi-Lipschitz orientation-preserving homeomorphism can be approximated in the W1,p norm, together with its inverse, with an orientation-preserving homeomorphism which is piecewise affine or smooth.

%B Annales de l'Institut Henri Poincare (C) Non Linear Analysis %V 31 %P 567 - 589 %G eng %U http://www.sciencedirect.com/science/article/pii/S0294144913000711 %R https://doi.org/10.1016/j.anihpc.2013.04.007 %0 Journal Article %D 2014 %T Some remarks on the seismic behaviour of embedded cantilevered retaining walls %A Riccardo Conti %A F. Burali D'Arezzo %A Giulia M.B. Viggiani %X This paper is a numerical investigation of the physical phenomena that control the dynamic behaviour of embedded cantilevered retaining walls. Recent experimental observations obtained from centrifuge tests have shown that embedded cantilevered retaining walls experience permanent displacements even before the acceleration reaches its critical value, corresponding to full mobilisation of the soil strength. The motivation for this work stems from the need to incorporate these observations in simplified design procedures. A parametric study was carried out on a pair of embedded cantilevered walls in dry sand, subjected to real earthquakes scaled at different values of the maximum acceleration. The results of these analyses indicate that, for the geotechnical design of the wall, the equivalent acceleration to be used in pseudo-static calculations can be related to the maximum displacement that the structure can sustain, and can be larger than the maximum acceleration expected at the site. For the structural design of the wall, it is suggested that the maximum bending moments of the wall can be computed using a realistic distribution of contact stress and a conservative value of the pseudo-static acceleration, taking into account two-dimensional amplification effects near the walls. %I Thomas Telford %G en %U http://urania.sissa.it/xmlui/handle/1963/35073 %1 35308 %2 Physics %4 2 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-11-30T17:34:56Z No. of bitstreams: 1 art2014.pdf: 1304935 bytes, checksum: 2618504941effc8eed6dddb1077d8916 (MD5) %R 10.1680/geot.13.P.031 %0 Journal Article %D 2014 %T Spontaneous division and motility in active nematic droplets %A Luca Giomi %A Antonio DeSimone %X We investigate the mechanics of an active droplet endowed with internal nematic order and surrounded by an isotropic Newtonian fluid. Using numerical simulations we demonstrate that, due to the interplay between the active stresses and the defective geometry of the nematic director, this system exhibits two of the fundamental functions of living cells: spontaneous division and motility, by means of self-generated hydrodynamic flows. These behaviors can be selectively activated by controlling a single physical parameter, namely, an active variant of the capillary number. %I American Physical Society %G en %U http://urania.sissa.it/xmlui/handle/1963/34902 %1 35107 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-11-03T14:40:44Z No. of bitstreams: 1 preprint2014.pdf: 4005398 bytes, checksum: eebaadedd03c1077a9cb2a209b5abdcc (MD5) %R 10.1103/PhysRevLett.112.147802 %0 Report %D 2014 %T Structure of classical (finite and affine) W-algebras %A Alberto De Sole %A Victor G. Kac %A Daniele Valeri %X First, we derive an explicit formula for the Poisson bracket of the classical finite W-algebra W^{fin}(g,f), the algebra of polynomial functions on the Slodowy slice associated to a simple Lie algebra g and its nilpotent element f. On the other hand, we produce an explicit set of generators and we derive an explicit formula for the Poisson vertex algebra structure of the classical affine W-algebra W(g,f). As an immediate consequence, we obtain a Poisson algebra isomorphism between W^{fin}(g,f) and the Zhu algebra of W(g,f). We also study the generalized Miura map for classical W-algebras. %I SISSA %G en %U http://hdl.handle.net/1963/7314 %1 7359 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Daniele Valeri (dvaleri@sissa.it) on 2014-04-04T09:52:02Z No. of bitstreams: 1 1404.0715v1.pdf: 386481 bytes, checksum: bafb532b11dfa1100008853a1f4cd543 (MD5) %0 Journal Article %D 2013 %T Analytical validation of a continuum model for epitaxial growth with elasticity on vicinal surfaces %A Gianni Dal Maso %A Irene Fonseca %A Giovanni Leoni %K singular nonlinear parabolic equations, Hilbert transform, thin films %X In this paper it is shown existence of weak solutions of a variational inequality derived from the continuum model introduced by Xiang [7, formula (3.62)] (see also the work of Xiang and E [8] and Xu and Xiang [9]) to describe the self-organization of terraces and steps driven by misfit elasticity between a film and a substrate in heteroepitaxial growth. This model is obtained as a continuum limit of discrete theories of Duport, Politi, and Villain [3] and Tersoff, Phang, Zhang, and Lagally[6]. %I Springer %G en %U http://hdl.handle.net/1963/7245 %1 7284 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2014-01-15T08:47:14Z No. of bitstreams: 1 DM-Fon-Leo.pdf: 409459 bytes, checksum: 07429e936667a481a2c093217e585e84 (MD5) %R 10.1007/s00205-014-0730-4 %0 Report %D 2013 %T Attainment results for nematic elastomers %A Virginia Agostiniani %A Gianni Dal Maso %A Antonio DeSimone %X We consider a class of non-quasiconvex frame indifferent energy densities which includes Ogden-type energy densities for nematic elastomers. For the corresponding geometrically linear problem we provide an explicit minimizer of the energy functional satisfying a nontrivial boundary condition. Other attainment results, both for the nonlinear and the linearized model, are obtained by using the theory of convex integration introduced by Mueller and Sverak in the context of crystalline solids. %I SISSA %G en %U http://hdl.handle.net/1963/7174 %1 7201 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-10-22T14:32:26Z No. of bitstreams: 1 Ago-DM-DeS-13-sissa.pdf: 394672 bytes, checksum: d02690a6c7f206310d28d253ce53d0d3 (MD5) %0 Journal Article %J Math. Models Methods Appl. Sci. %D 2013 %T Basic principles of virtual element methods %A Beirão da Veiga, L. %A Brezzi, F. %A Andrea Cangiani %A Manzini, G. %A Marini, L. D. %A Russo, A. %B Math. Models Methods Appl. Sci. %V 23 %P 199–214 %G eng %U https://doi.org/10.1142/S0218202512500492 %R 10.1142/S0218202512500492 %0 Journal Article %J Communications in Mathematical Physics 323, nr. 2 (2013) 663-711 %D 2013 %T Classical W-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras %A Alberto De Sole %A Victor G. Kac %A Daniele Valeri %X We provide a description of the Drinfeld-Sokolov Hamiltonian reduction for the construction of classical W-algebras within the framework of Poisson vertex algebras. In this context, the gauge group action on the phase space is translated in terms of (the exponential of) a Lie conformal algebra action on the space of functions. Following the ideas of Drinfeld and Sokolov, we then establish under certain sufficient conditions the applicability of the Lenard-Magri scheme of integrability and the existence of the corresponding integrable hierarchy of bi-Hamiltonian equations. %B Communications in Mathematical Physics 323, nr. 2 (2013) 663-711 %I Springer %G en %U http://hdl.handle.net/1963/6978 %1 6966 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Daniele Valeri (dvaleri@sissa.it) on 2013-07-13T15:24:57Z No. of bitstreams: 1 1207.6286v3.pdf: 588052 bytes, checksum: a5630eb1399cba992d56be98f25cdc9c (MD5) %R 10.1007/s00220-013-1785-z %0 Journal Article %J Comptes Rendus Mathematique. Volume 351, Issue 15-16, August 2013, Pages 593-598 %D 2013 %T A combination between the reduced basis method and the ANOVA expansion: On the computation of sensitivity indices %A Denis Devaud %A Andrea Manzoni %A Gianluigi Rozza %K Partial differential equations %XWe consider a method to efficiently evaluate in a real-time context an output based on the numerical solution of a partial differential equation depending on a large number of parameters. We state a result allowing to improve the computational performance of a three-step RB-ANOVA-RB method. This is a combination of the reduced basis (RB) method and the analysis of variations (ANOVA) expansion, aiming at compressing the parameter space without affecting the accuracy of the output. The idea of this method is to compute a first (coarse) RB approximation of the output of interest involving all the parameter components, but with a large tolerance on the a posteriori error estimate; then, we evaluate the ANOVA expansion of the output and freeze the least important parameter components; finally, considering a restricted model involving just the retained parameter components, we compute a second (fine) RB approximation with a smaller tolerance on the a posteriori error estimate. The fine RB approximation entails lower computational costs than the coarse one, because of the reduction of parameter dimensionality. Our result provides a criterion to avoid the computation of those terms in the ANOVA expansion that are related to the interaction between parameters in the bilinear form, thus making the RB-ANOVA-RB procedure computationally more feasible.

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

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

%B Journal of Differential Equations %V 254 %P 30 - 66 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022039612003312 %R https://doi.org/10.1016/j.jde.2012.08.017 %0 Journal Article %J International Journal of Non-Linear Mechanics 56, 142-147 (2013) %D 2013 %T Crawlers in viscous environments: linear vs nonlinear rheology %A Antonio DeSimone %A Federica Guarnieri %A Giovanni Noselli %A Amabile Tatone %X We study model self-propelled crawlers which derive their propulsive capabilities from the tangential resistance to motion offered by the environment. Two types of relationships between tangential forces and slip velocities are considered: a linear, Newtonian one and a nonlinear one of Bingham-type. Different behaviors result from the two different rheologies. These differences and their implications in terms of motility performance are discussed. Our aim is to develop new tools and insight for future studies of cell motility by crawling. %B International Journal of Non-Linear Mechanics 56, 142-147 (2013) %I Elsevier %G en %1 34590 %2 Mathematics %$ Submitted by gnoselli@sissa.it (gnoselli@sissa.it) on 2015-03-07T17:29:52Z No. of bitstreams: 1 viscous_crawlers.pdf: 887755 bytes, checksum: 6022e4160d2eced97b51326bf51e0827 (MD5) %R 10.1016/j.ijnonlinmec.2013.02.007 %0 Report %D 2013 %T On critical behaviour in systems of Hamiltonian partial differential equations %A Boris Dubrovin %A Tamara Grava %A Christian Klein %A Antonio Moro %XWe study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by particular solutions to the Painlev\'e-I (P$_I$) equation or its fourth order analogue P$_I^2$. As concrete examples we discuss nonlinear Schr\"odinger equations in the semiclassical limit. A numerical study of these cases provides strong evidence in support of the conjecture.

%I SISSA %G en %1 7280 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Tamara Grava (grava@sissa.it) on 2014-01-14T18:10:19Z No. of bitstreams: 1 EHfinal_3.pdf: 7760169 bytes, checksum: 1e98e693fbceb1268a5acd269dd9b03e (MD5) %0 Journal Article %J Journal of Mathematical Physics. Volume 54, Issue 1, 22 January 2013, Article number 013518 %D 2013 %T Curved noncommutative torus and Gauss--Bonnet %A Ludwik Dabrowski %A Andrzej Sitarz %K Geometry %X We study perturbations of the flat geometry of the noncommutative two-dimensional torus T^2_\theta (with irrational \theta). They are described by spectral triples (A_\theta, \H, D), with the Dirac operator D, which is a differential operator with coefficients in the commutant of the (smooth) algebra A_\theta of T_\theta. We show, up to the second order in perturbation, that the zeta-function at 0 vanishes and so the Gauss-Bonnet theorem holds. We also calculate first two terms of the perturbative expansion of the corresponding local scalar curvature. %B Journal of Mathematical Physics. Volume 54, Issue 1, 22 January 2013, Article number 013518 %I American Institute of Physics %G en %U http://hdl.handle.net/1963/7376 %1 7424 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-06-17T13:10:21Z No. of bitstreams: 1 1204.0420v1.pdf: 126064 bytes, checksum: ffa850e50f99585d61676b1d2398af2f (MD5) %R 10.1063/1.4776202 %0 Journal Article %J Classical and Quantum Gravity. Volume 30, Issue 1, 7 January 2013, Article number 015006 %D 2013 %T Dirac operator on spinors and diffeomorphisms %A Ludwik Dabrowski %A Giacomo Dossena %K gravity %X The issue of general covariance of spinors and related objects is reconsidered. Given an oriented manifold $M$, to each spin structure $\sigma$ and Riemannian metric $g$ there is associated a space $S_{\sigma, g}$ of spinor fields on $M$ and a Hilbert space $\HH_{\sigma, g}= L^2(S_{\sigma, g},\vol{M}{g})$ of $L^2$-spinors of $S_{\sigma, g}$. The group $\diff{M}$ of orientation-preserving diffeomorphisms of $M$ acts both on $g$ (by pullback) and on $[\sigma]$ (by a suitably defined pullback $f^*\sigma$). Any $f\in \diff{M}$ lifts in exactly two ways to a unitary operator $U$ from $\HH_{\sigma, g} $ to $\HH_{f^*\sigma,f^*g}$. The canonically defined Dirac operator is shown to be equivariant with respect to the action of $U$, so in particular its spectrum is invariant under the diffeomorphisms. %B Classical and Quantum Gravity. Volume 30, Issue 1, 7 January 2013, Article number 015006 %I IOP Publishing %G en %U http://hdl.handle.net/1963/7377 %1 7425 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-06-17T13:30:17Z No. of bitstreams: 1 1209.2021v1.pdf: 201918 bytes, checksum: fe811643c070348a7dd399672ddad6f4 (MD5) %R 10.1088/0264-9381/30/1/015006 %0 Report %D 2013 %T Dislocation dynamics in crystals: a macroscopic theory in a fractional Laplace setting %A Serena Dipierro %A Giampiero Palatucci %A Enrico Valdinoci %K nonlocal Allen-Cahn equation %X We consider an evolution equation arising in the Peierls-Nabarro model for crystal dislocation. We study the evolution of such dislocation function and show that, at a macroscopic scale, the dislocations have the tendency to concentrate at single points of the crystal, where the size of the slip coincides with the natural periodicity of the medium. These dislocation points evolve according to the external stress and an interior repulsive potential. %I SISSA %G en %U http://hdl.handle.net/1963/7124 %1 7124 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Giampiero Palatucci (palatucc@sissa.it) on 2013-09-23T12:18:14Z No. of bitstreams: 1 Dipierro-Palatucci-Valdinoci.pdf: 651692 bytes, checksum: 839508f3ff7cdc4417c33991ebf3a9f3 (MD5) %0 Journal Article %J Le Matematiche (Catania), Vol. 68 (2013), no. 1: 201-216 %D 2013 %T Existence and symmetry results for a Schrodinger type problem involving the fractional Laplacian %A Serena Dipierro %A Giampiero Palatucci %A Enrico Valdinoci %XThis paper deals with the following class of nonlocal Schr\"odinger equations $$ \displaystyle (-\Delta)^s u + u = |u|^{p-1}u \ \ \text{in} \ \mathbb{R}^N, \quad \text{for} \ s\in (0,1). $$ We prove existence and symmetry results for the solutions $u$ in the fractional Sobolev space $H^s(\mathbb{R}^N)$. Our results are in clear accordance with those for the classical local counterpart, that is when $s=1$.

%B Le Matematiche (Catania), Vol. 68 (2013), no. 1: 201-216 %I University of Catania %G en %1 7318 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-03-11T16:07:36Z No. of bitstreams: 1 1202.0576v1.pdf: 219939 bytes, checksum: 822c73753d6d4194cf48cb0ff9ad0e48 (MD5) %0 Journal Article %J Communications on Pure and Applied Analysis 12 (2013) 1657-1686 %D 2013 %T Fracture models as Gamma-limits of damage models %A Gianni Dal Maso %A Flaviana Iurlano %XWe analyze the asymptotic behavior of a variational model for damaged elastic materials. This model depends on two small parameters, which govern the width of the damaged regions and the minimum elasticity constant attained in the damaged regions. When these parameters tend to zero, we find that the corresponding functionals Gamma-converge to a functional related to fracture mechanics. The corresponding problem is brittle or cohesive, depending on the asymptotic ratio of the two parameters.

%B Communications on Pure and Applied Analysis 12 (2013) 1657-1686 %I American Institute of Mathematical Sciences %G en %U http://hdl.handle.net/1963/4225 %1 3952 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-23T11:09:07Z\\r\\nNo. of bitstreams: 1\\r\\nDalMaso_Iurlano_25_M.pdf: 360594 bytes, checksum: a0e0909b1c483748ede26b7e785a1d79 (MD5) %R 10.3934/cpaa.2013.12.1657 %0 Journal Article %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %T Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations %A Cacace, S. %A Antonin Chambolle %A Antonio DeSimone %A Livio Fedeli %B ESAIM: Mathematical Modelling and Numerical Analysis %I EDP Sciences %V 47 %P 837–858 %G eng %R 10.1051/m2an/2012048 %0 Journal Article %J Communications in Mathematical Physics. Volume 318, Issue 1, 2013, Pages 111-130 %D 2013 %T Noncommutative circle bundles and new Dirac operators %A Ludwik Dabrowski %A Andrzej Sitarz %K Quantum principal bundles %X We study spectral triples over noncommutative principal U(1) bundles. Basing on the classical situation and the abstract algebraic approach, we propose an operatorial definition for a connection and compatibility between the connection and the Dirac operator on the total space and on the base space of the bundle. We analyze in details the example of the noncommutative three-torus viewed as a U(1) bundle over the noncommutative two-torus and find all connections compatible with an admissible Dirac operator. Conversely, we find a family of new Dirac operators on the noncommutative tori, which arise from the base-space Dirac operator and a suitable connection. %B Communications in Mathematical Physics. Volume 318, Issue 1, 2013, Pages 111-130 %I Springer %G en %U http://hdl.handle.net/1963/7384 %1 7432 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-06-18T10:06:43Z No. of bitstreams: 1 1012.3055v2.pdf: 181206 bytes, checksum: be182e0f568384847efe0f656a70634b (MD5) %R 10.1007/s00220-012-1550-8 %0 Journal Article %D 2013 %T One-dimensional swimmers in viscous fluids: dynamics, controllability, and existence of optimal controls %A Gianni Dal Maso %A Antonio DeSimone %A Marco Morandotti %XIn this paper we study a mathematical model of one-dimensional swimmers performing a planar motion while fully immersed in a viscous fluid. The swimmers are assumed to be of small size, and all inertial effects are neglected. Hydrodynamic interactions are treated in a simplified way, using the local drag approximation of resistive force theory. We prove existence and uniqueness of the solution of the equations of motion driven by shape changes of the swimmer. Moreover, we prove a controllability result showing that given any pair of initial and final states, there exists a history of shape changes such that the resulting motion takes the swimmer from the initial to the final state. We give a constructive proof, based on the composition of elementary maneuvers (straightening and its inverse, rotation, translation), each of which represents the solution of an interesting motion planning problem. Finally, we prove the existence of solutions for the optimal control problem of finding, among the histories of shape changes taking the swimmer from an initial to a final state, the one of minimal energetic cost.

%I SISSA %G en %U http://hdl.handle.net/1963/6467 %1 6412 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-02-11T12:13:39Z No. of bitstreams: 1 DM-DeS-Mor-12-v10 sissa.pdf: 606490 bytes, checksum: 45f448186465b198ec31beb54afb0edf (MD5) %0 Journal Article %J Annales de l'Institut Henri Poincare (C) Non Linear Analysis %D 2013 %T A quasistatic evolution model for perfectly plastic plates derived by Γ-convergence %A Elisa Davoli %A Maria Giovanna Mora %K -convergence %K Perfect plasticity %K Prandtl–Reuss plasticity %K Quasistatic evolution %K Rate-independent processes %K Thin plates %XThe subject of this paper is the rigorous derivation of a quasistatic evolution model for a linearly elastic–perfectly plastic thin plate. As the thickness of the plate tends to zero, we prove via Γ-convergence techniques that solutions to the three-dimensional quasistatic evolution problem of Prandtl–Reuss elastoplasticity converge to a quasistatic evolution of a suitable reduced model. In this limiting model the admissible displacements are of Kirchhoff–Love type and the stretching and bending components of the stress are coupled through a plastic flow rule. Some equivalent formulations of the limiting problem in rate form are derived, together with some two-dimensional characterizations for suitable choices of the data.

%B Annales de l'Institut Henri Poincare (C) Non Linear Analysis %V 30 %P 615 - 660 %G eng %U http://www.sciencedirect.com/science/article/pii/S0294144912001035 %R https://doi.org/10.1016/j.anihpc.2012.11.001 %0 Book Section %B CEMRACS 2013 - Modelling and simulation of complex systems: stochastic and deterministic approaches %D 2013 %T Reduced Basis Approximation for the Structural-Acoustic Design based on Energy Finite Element Analysis (RB-EFEA) %A Denis Devaud %A Gianluigi Rozza %B CEMRACS 2013 - Modelling and simulation of complex systems: stochastic and deterministic approaches %V 48 %P 98-115 %G eng %R http://dx.doi.org/10.1051/proc/201448004 %0 Journal Article %J Engineering Analysis with Boundary Elements, 37(1):128 – 143, 2013. %D 2013 %T A stable and adaptive semi-Lagrangian potential model for unsteady and nonlinear ship-wave interactions %A Andrea Mola %A Luca Heltai %A Antonio DeSimone %K Unsteady ship-wave interaction %XWe present an innovative numerical discretization of the equations of inviscid potential flow for the simulation of three dimensional unsteady and nonlinear water waves generated by a ship hull advancing in water. The equations of motion are written in a semi-Lagrangian framework, and the resulting integro-diff erential equations are discretized in space via an adaptive iso-parametric collocation Boundary Element Method, and in time via adaptive implicit Backward Di erentiation Formulas (BDF) with variable step and variable order. When the velocity of the advancing ship hull is non-negligible, the semi-Lagrangian formulation (also known as Arbitrary Lagrangian Eulerian formulation, or ALE) of the free surface equations contains dominant transport terms which are stabilized with a Streamwise Upwind Petrov-Galerkin (SUPG) method. The SUPG stabilization allows automatic and robust adaptation of the spatial discretization with unstructured quadrilateral grids. Preliminary results are presented where we compare our numerical model with experimental results on the case of a Wigley hull advancing in calm water with fi xed sink and trim.

%B Engineering Analysis with Boundary Elements, 37(1):128 – 143, 2013. %I SISSA %G en %U http://hdl.handle.net/1963/5669 %1 5457 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-03-16T11:19:51Z\\nNo. of bitstreams: 1\\nMolaHeltaiDeSimone-2012-aa.pdf: 1981527 bytes, checksum: 8a82da009242da0cf884e2c7f04009a6 (MD5) %0 Report %D 2013 %T On Sudakov's type decomposition of transference plans with norm costs %A Stefano Bianchini %A Sara Daneri %I SISSA %G en %U http://hdl.handle.net/1963/7206 %1 7234 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-11-08T11:08:16Z No. of bitstreams: 1 Sudakov_160813 (1).pdf: 1030337 bytes, checksum: 121734a60b7c507acb1e0ca656676a37 (MD5) %0 Journal Article %J Discrete Contin. Dyn. Syst. 33, nr.7 (2012): 2777-2790 %D 2012 %T Asymptotics of the s-perimeter as s →0 %A Serena Dipierro %A Alessio Figalli %A Giampiero Palatucci %A Enrico Valdinoci %XWe deal with the asymptotic behavior of the $s$-perimeter of a set $E$ inside a domain $\Omega$ as $s\searrow0$. We prove necessary and sufficient conditions for the existence of such limit, by also providing an explicit formulation in terms of the Lebesgue measure of $E$ and $\Omega$. Moreover, we construct examples of sets for which the limit does not exist.

%B Discrete Contin. Dyn. Syst. 33, nr.7 (2012): 2777-2790 %I American Institute of Mathematical Sciences %G en %1 7317 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-03-11T15:55:21Z No. of bitstreams: 1 1204.0750v2.pdf: 216883 bytes, checksum: 3ee8d497a2c0f9a211ec5327e8aa6b9a (MD5) %R 10.3934/dcds.2013.33.2777 %0 Journal Article %J Theoretical and Mathematical Physics. Volume 172, Issue 1, July 2012, Pages 911-931 %D 2012 %T Classical double, R-operators, and negative flows of integrable hierarchies %A Boris Dubrovin %A Taras V. Skrypnyk %X Using the classical double G of a Lie algebra g equipped with the classical R-operator, we define two sets of functions commuting with respect to the initial Lie–Poisson bracket on g and its extensions. We consider examples of Lie algebras g with the “Adler–Kostant–Symes” R-operators and the two corresponding sets of mutually commuting functions in detail. Using the constructed commutative Hamiltonian flows on different extensions of g, we obtain zero-curvature equations with g-valued U–V pairs. The so-called negative flows of soliton hierarchies are among such equations. We illustrate the proposed approach with examples of two-dimensional Abelian and non-Abelian Toda field equations. %B Theoretical and Mathematical Physics. Volume 172, Issue 1, July 2012, Pages 911-931 %I SISSA %G en %U http://hdl.handle.net/1963/6468 %1 6413 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-02-11T14:56:54Z (GMT) No. of bitstreams: 0 %R 10.1007/s11232-012-0086-6 %0 Book Section %B Natural locomotion in fluids and on surfaces : swimming, flying, and sliding / editors Stephen Childress, Anette Hosoi, William W. Schultz, and Z. Jane Wang, editors, %D 2012 %T Computing optimal strokes for low reynolds number swimmers %A Antonio DeSimone %A Luca Heltai %A François Alouges %A Lefebvre-Lepot Aline %K Numerical analysis. %XWe discuss connections between low-Reynolds-number swimming and geometric control theory, and present a general algorithm for the numerical computation of energetically optimal strokes. As an illustration of our approach, we show computed motility maps and optimal strokes for two model swimmers.

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

%B Communications in Contemporary Mathematics %I World Scientific %V 14 %P 1250009 %G eng %U https://doi.org/10.1142/S0219199712500095 %R 10.1142/S0219199712500095 %0 Journal Article %J The European Physical Journal E, Volume 35, Issue 9, September 2012, Article number85 %D 2012 %T Crawling motility through the analysis of model locomotors: two case studies %A Antonio DeSimone %A Amabile Tatone %X We study model locomotors on a substrate, which derive their propulsive capabilities from the tangential (viscous or frictional) resistance offered by the substrate. Our aim is to develop new tools and insight for future studies of cellular motility by crawling and of collective bacterial motion. The purely viscous case (worm) is relevant for cellular motility by crawling of individual cells. We re-examine some recent results on snail locomotion in order to assess the role of finely regulated adhesion mechanisms in crawling motility. Our main conclusion is that such regulation, although well documented in several biological systems, is not indispensable to accomplish locomotion driven by internal deformations, provided that the crawler may execute sufficiently large body deformations. Thus, there is no snail theorem. Namely, the crawling analog of the scallop theorem of low Reynolds number hydrodynamics does not hold for snail-like crawlers. The frictional case is obtained by assuming that the viscous coefficient governing tangential resistance forces, which act parallel and in the direction opposite to the velocity of the point to which they are applied, depends on the normal force acting at that point. We combine these surface interactions with inertial effects in order to investigate the mechanisms governing the motility of a bristle-robot. This model locomotor is easily manufactured and has been proposed as an effective tool to replicate and study collective bacterial motility. %B The European Physical Journal E, Volume 35, Issue 9, September 2012, Article number85 %I Springer %G en %U http://hdl.handle.net/1963/7017 %1 7014 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-08-12T11:01:46Z No. of bitstreams: 0 %R 10.1140/epje/i2012-12085-x %0 Journal Article %J Russian Journal of Mathematical Physics. Volume 19, Issue 4, December 2012, Pages 449-460 %D 2012 %T On the critical behavior in nonlinear evolutionary PDEs with small viscocity %A Boris Dubrovin %A Maria Elaeva %X We address the problem of general dissipative regularization of the quasilinear transport equation. We argue that the local behavior of solutions to the regularized equation near the point of gradient catastrophe for the transport equation is described by the logarithmic derivative of the Pearcey function, a statement generalizing the result of A.M.Il\\\'in \\\\cite{ilin}. We provide some analytic arguments supporting such conjecture and test it numerically. %B Russian Journal of Mathematical Physics. Volume 19, Issue 4, December 2012, Pages 449-460 %I SISSA %G en %U http://hdl.handle.net/1963/6465 %1 6409 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-08T11:28:04Z\\nNo. of bitstreams: 1\\ndubrovin_elaeva.pdf: 8618184 bytes, checksum: 3c56d1922af7001581ca4ceb4c79cc3b (MD5) %R 10.1134/S106192081204005X %0 Journal Article %J Biophysical Journal. Volume 102, Issue 12, 20 June 2012, Pages 2677-2686 %D 2012 %T A dynamical feedback model for adaptation in the olfactory transduction pathway %A Giovanna De Palo %A Anna Boccaccio %A Andrew Miri %A Anna Menini %A Claudio Altafini %X Olfactory transduction exhibits two distinct types of adaptation, which we denote multipulse and step adaptation. In terms of measured transduction current, multipulse adaptation appears as a decrease in the amplitude of the second of two consecutive responses when the olfactory neuron is stimulated with two brief pulses. Step adaptation occurs in response to a sustained steplike stimulation and is characterized by a return to a steady-state current amplitude close to the prestimulus value, after a transient peak. In this article, we formulate a dynamical model of the olfactory transduction pathway, which includes the kinetics of the CNG channels, the concentration of Ca ions flowing through them, and the Ca-complexes responsible for the regulation. Based on this model, a common dynamical explanation for the two types of adaptation is suggested. We show that both forms of adaptation can be well described using different time constants for the kinetics of Ca ions (faster) and the kinetics of the feedback mechanisms (slower). The model is validated on experimental data collected in voltage-clamp conditions using different techniques and animal species. %B Biophysical Journal. Volume 102, Issue 12, 20 June 2012, Pages 2677-2686 %I Biophysical Society, Elsevier %G en %U http://hdl.handle.net/1963/7019 %1 7012 %2 Neuroscience %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-08-12T10:21:18Z No. of bitstreams: 1 1-s2.0-S0006349512005140-main.pdf: 607871 bytes, checksum: b57c678e05477bb1551bc379bc674a88 (MD5) %R 10.1016/j.bpj.2012.04.040 %0 Journal Article %J Journal de Mathématiques Pures et Appliquées, Available online 12 September 2012 %D 2012 %T Gamma-convergence and H-convergence of linear elliptic operators %A Nadia Ansini %A Gianni Dal Maso %A Caterina Ida Zeppieri %K Linear elliptic operators %B Journal de Mathématiques Pures et Appliquées, Available online 12 September 2012 %I Elsevier %G en %U http://hdl.handle.net/1963/5878 %1 5746 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-05-30T13:02:32Z\\r\\nNo. of bitstreams: 1\\r\\n04M_2012_Ansini.pdf: 226441 bytes, checksum: 789582b685e552b522a3e8a896e091f8 (MD5) %R 10.1016/j.matpur.2012.09.004 %0 Journal Article %J Russian Journal of Mathematical Physics. Volume 19, Issue 3, September 2012, Pages 273-298 %D 2012 %T On the genus two free energies for semisimple Frobenius manifolds %A Boris Dubrovin %A Si-Qi Liu %A Youjin Zhang %X We represent the genus two free energy of an arbitrary semisimple Frobenius\\r\\nmanifold as a sum of contributions associated with dual graphs of certain\\r\\nstable algebraic curves of genus two plus the so-called \\\"genus two G-function\\\".\\r\\nConjecturally the genus two G-function vanishes for a series of important\\r\\nexamples of Frobenius manifolds associated with simple singularities as well as\\r\\nfor ${\\\\bf P}^1$-orbifolds with positive Euler characteristics. We explain the\\r\\nreasons for such Conjecture and prove it in certain particular cases. %B Russian Journal of Mathematical Physics. Volume 19, Issue 3, September 2012, Pages 273-298 %I SISSA %G en %U http://hdl.handle.net/1963/6464 %1 6411 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-08T11:35:38Z\\nNo. of bitstreams: 1\\n1205.5990v1.pdf: 547320 bytes, checksum: 9c9d894fbe3241c632b6cab13379f9c9 (MD5) %R 10.1134/S1061920812030028 %0 Journal Article %J Nanoscale. 2012 Mar; 4(5):1734-41 %D 2012 %T Hybridization in nanostructured DNA monolayers probed by AFM: theory versus experiment %A Alessandro Bosco %A Fouzia Bano %A Pietro Parisse %A Loredana Casalis %A Antonio DeSimone %A Cristian Micheletti %X Nanografted monolayers (NAMs) of DNA show novel physico-chemical properties that make them ideally suited for advanced biosensing applications. In comparison with alternative solid-phase techniques for diagnostic DNA detection, NAMs have the advantage of combining a small size with a high homogeneity of the DNA surface coverage. These two properties favour the extreme miniaturization and ultrasensitivity in high-throughput biosensing devices. The systematic use of NAMs for quantitative DNA (and protein) detection has so far suffered from the lack of a control on key fabrication parameters, such as the ss- or ds-DNA surface coverage. Here we report on a combined experimental-computational study that allows us to estimate the surface density of the grafted DNA by analyzing the sample mechanical response, that is the DNA patch height vs. applied tip load curves. It is shown that the same analysis scheme can be used to detect the occurrence of hybridization with complementary strands in solution and estimate its efficiency. Thanks to these quantitative relationships it is possible to use a single AFM-based setup to: (i) fabricate a DNA NAM, (ii) control the DNA surface coverage, and (iii) characterize its level of hybridization helping the design of NAMs with pre-determined fabrication parameters. %B Nanoscale. 2012 Mar; 4(5):1734-41 %I Royal Society of Chemistry %G en %1 6998 %2 Physics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-08-08T07:48:55Z No. of bitstreams: 0 %R 10.1039/c2nr11662f %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire %D 2012 %T Linear elasticity obtained from finite elasticity by Gamma-convergence under weak coerciveness conditions %A Virginia Agostiniani %A Gianni Dal Maso %A Antonio DeSimone %K Nonlinear elasticity %XThe energy functional of linear elasticity is obtained as G-limit of suitable rescalings of the energies of finite elasticity...

%B Ann. Inst. H. Poincare Anal. Non Lineaire %I Gauthier-Villars;Elsevier %V 29 %P 715-735 %G en %U http://hdl.handle.net/1963/4267 %1 3996 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-26T15:11:45Z\\r\\nNo. of bitstreams: 1\\r\\nAgostiniani_DalMaso_30_M.pdf: 407057 bytes, checksum: 2009d1218f7735191a1c768a73b400a3 (MD5) %R 10.1016/j.anihpc.2012.04.001 %0 Conference Proceedings %B Materials Research Society Symposium Proceedings. Volume 1403, 2012, Pages 125-130 %D 2012 %T Mathematical and numerical modeling of liquid crystal elastomer phase transition and deformation %A Mariarita De Luca %A Antonio DeSimone %K Artificial muscle %X Liquid crystal (in particular, nematic) elastomers consist of cross-linked flexible polymer chains with embedded stiff rod molecules that allow them to behave as a rubber and a liquid crystal. Nematic elastomers are characterized by a phase transition from isotropic to nematic past a temperature threshold. They behave as rubber at high temperature and show nematic behavior below the temperature threshold. Such transition is reversible. While in the nematic phase, the rod molecules are aligned along the direction of the "nematic director". This molecular rearrangement induces a stretch in the polymer chains and hence macroscopic spontaneous deformations. The coupling between nematic order parameter and deformation gives rise to interesting phenomena with a potential for new interesting applications. In the biological field, the ability to considerably change their length makes them very promising as artificial muscles actuators. Their tunable optical properties make them suitable, for example, as lenses for new imaging systems. We present a mathematical model able to describe the behavior of nematic elastomers and numerical simulations reproducing such peculiar behavior. We use a geometrically linear version of the Warner and Terentjev model [1] and consider cooling experiments and stretching experiments in the direction perpendicular to the one of the director at cross-linking. %B Materials Research Society Symposium Proceedings. Volume 1403, 2012, Pages 125-130 %I Cambridge University Press %@ 9781605113807 %G en %U http://hdl.handle.net/1963/7020 %1 7011 %2 Physics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-08-12T10:02:18Z No. of bitstreams: 0 %R 10.1557/opl.2012.249 %0 Journal Article %J Acta Geotechnica, Volume 7, Issue 3, September 2012, Pages 219-237 %D 2012 %T Numerical modelling of installation effects for diaphragm walls in sand %A Riccardo Conti %A Luca de Sanctis %A Giulia M.B. Viggiani %K Constitutive relations %X The scopes of this work are to study the mechanisms of load transfer and the deformations of the ground during slurry trenching and concreting in dry sand and to evaluate their effects on service structural loads, wall deflections and ground displacements behind the wall caused by subsequent excavation. A series of three-dimensional finite element analyses was carried out modelling the installation of diaphragm walls consisting of panels of different length. The soil was modelled as either linearly elastic-perfectly plastic or incrementally non-linear (hypoplastic) with elastic strain range. Plane strain analyses of diaphragm walls of identical cross section were also carried out in which wall installation was either modelled or the wall was wished in place (WIP). The analyses predict ground movements consistent with the experimental observations both in magnitude and trend. The results also show that the maximum horizontal wall deflections and structural loads reduce with increasing panel aspect ratio towards a minimum which is about twice the value computed for WIP analyses. Panel aspect ratios should be larger than about three to take advantage of the three-dimensional effects. The pattern and magnitude of surface vertical displacements obtained from linearly elastic-perfectly plastic analyses, no matter whether three- or two-dimensional, are unrealistic. %B Acta Geotechnica, Volume 7, Issue 3, September 2012, Pages 219-237 %I Springer %G en %U http://hdl.handle.net/1963/6934 %1 6916 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-05-30T10:23:32Z No. of bitstreams: 0 %R 10.1007/s11440-011-0157-0 %0 Journal Article %J International Journal of Non-Linear mechanics %D 2012 %T Ogden-type energies for nematic elastomers %A Virginia Agostiniani %A Antonio DeSimone %K Nonlinear elasticity %XOgden-type extensions of the free-energy densities currently used to model the mechanical behavior of nematic elastomers are proposed and analyzed. Based on a multiplicative decomposition of the deformation gradient into an elastic and a spontaneous or remanent part, they provide a suitable framework to study the stiffening response at high imposed stretches. Geometrically linear versions of the models (Taylor expansions at order two) are provided and discussed. These small strain theories provide a clear illustration of the geometric structure of the underlying energy landscape (the energy grows quadratically with the distance from a non-convex set of spontaneous strains or energy wells). The comparison between small strain and finite deformation theories may also be useful in the opposite direction, inspiring finite deformation generalizations of small strain theories currently used in the mechanics of active and phase-transforming materials. The energy well structure makes the free-energy densities non-convex. Explicit quasi-convex envelopes are provided, and applied to compute the stiffening response of a specimen tested in plane strain extension experiments (pure shear).

%B International Journal of Non-Linear mechanics %I Elsevier %V 47 %P 402-412 %G en %N 2 %1 6971 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-07-15T14:33:38Z No. of bitstreams: 0 %R 10.1016/j.ijnonlinmec.2011.10.001 %0 Journal Article %J Calculus of variations and partial differential equations 44 (2012) 495-541 %D 2012 %T Quasistatic evolution for Cam-Clay plasticity: properties of the viscosity solution %A Gianni Dal Maso %A Antonio DeSimone %A Francesco Solombrino %XCam-Clay plasticity is a well established model for the description of the mechanics of fine grained soils. As solutions can develop discontinuities in time, a weak notion of solution, in terms of a rescaled time s , has been proposed in [8] to give a meaning to this discontinuous evolution. In this paper we first prove that this rescaled evolution satisfies the flow-rule for the rate of plastic strain, in a suitable measure-theoretical sense. In the second part of the paper we consider the behavior of the evolution in terms of the original time variable t . We prove that the unrescaled solution satisfies an energy-dissipation balance and an evolution law for the internal variable, which can be expressed in terms of integrals depending only on the original time. Both these integral identities contain terms concentrated on the jump times, whose size can only be determined by looking at the rescaled formulation.

%B Calculus of variations and partial differential equations 44 (2012) 495-541 %I Springer %G en_US %U http://hdl.handle.net/1963/3900 %1 809 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-07-26T09:17:50Z\\r\\nNo. of bitstreams: 1\\r\\nSolombrino_46M.pdf: 382911 bytes, checksum: dd118cc7f80d4cb1902713eb18747ac6 (MD5) %R 10.1007/s00526-011-0443-6 %0 Journal Article %J Proceedings of the National Academy of Sciences of the United States of America. Volume 109, Issue 44, 30 October 2012, Pages 17874-17879 %D 2012 %T Reverse engineering the euglenoid movement %A Marino Arroyo %A Luca Heltai %A Daniel Millán %A Antonio DeSimone %K microswimmers %X Euglenids exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large-amplitude highly concerted deformations of the entire body (euglenoid movement or metaboly). A plastic cell envelope called pellicle mediates these deformations. Unlike ciliary or flagellar motility, the biophysics of this mode is not well understood, including its efficiency and molecular machinery. We quantitatively examine video recordings of four euglenids executing such motions with statistical learning methods. This analysis reveals strokes of high uniformity in shape and pace. We then interpret the observations in the light of a theory for the pellicle kinematics, providing a precise understanding of the link between local actuation by pellicle shear and shape control. We systematically understand common observations, such as the helical conformations of the pellicle, and identify previously unnoticed features of metaboly. While two of our euglenids execute their stroke at constant body volume, the other two exhibit deviations of about 20% from their average volume, challenging current models of low Reynolds number locomotion. We find that the active pellicle shear deformations causing shape changes can reach 340%, and estimate the velocity of the molecular motors. Moreover, we find that metaboly accomplishes locomotion at hydrodynamic efficiencies comparable to those of ciliates and flagellates. Our results suggest new quantitative experiments, provide insight into the evolutionary history of euglenids, and suggest that the pellicle may serve as a model for engineered active surfaces with applications in microfluidics. %B Proceedings of the National Academy of Sciences of the United States of America. Volume 109, Issue 44, 30 October 2012, Pages 17874-17879 %G en %U http://hdl.handle.net/1963/6444 %1 6380 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Luca Heltai (heltai@sissa.it) on 2013-02-01T17:29:31Z\\nNo. of bitstreams: 0 %R 10.1073/pnas.1213977109 %0 Thesis %D 2012 %T Some aspects of spinors – classical and noncommutative %A Giacomo Dossena %I SISSA %G en %U http://hdl.handle.net/1963/6317 %1 6218 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Giacomo Dossena (dossena@sissa.it) on 2012-11-13T11:13:08Z\\nNo. of bitstreams: 1\\nthesis.pdf: 1569621 bytes, checksum: 1ab89dce9cdc2097b3692da5a63ad82b (MD5) %0 Journal Article %J International Journal of Geometric Methods in Modern Physics, Volume 9, Issue 2, March 2012, Article number1260018 %D 2012 %T Some remarks on quantum mechanics %A Gianfausto Dell'Antonio %K Quantum mechanics %X We discuss the similarities and differences between the formalism of Hamiltonian Classical Mechanics and of Quantum Mechanics and exemplify the differences through an analysis of tracks in a cloud chamber. %B International Journal of Geometric Methods in Modern Physics, Volume 9, Issue 2, March 2012, Article number1260018 %I World Scientific Publishing %G en %U http://hdl.handle.net/1963/7018 %1 7013 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-08-12T10:45:49Z No. of bitstreams: 0 %R 10.1142/S0219887812600183 %0 Journal Article %J Rev. Math. Phys. 24 (2012), 1250017 %D 2012 %T Stability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions %A Michele Correggi %A Gianfausto Dell'Antonio %A Domenico Finco %A Alessandro Michelangeli %A Alessandro Teta %X We study the stability problem for a non-relativistic quantum system in\\r\\ndimension three composed by $ N \\\\geq 2 $ identical fermions, with unit mass,\\r\\ninteracting with a different particle, with mass $ m $, via a zero-range\\r\\ninteraction of strength $ \\\\alpha \\\\in \\\\R $. We construct the corresponding\\r\\nrenormalised quadratic (or energy) form $ \\\\form $ and the so-called\\r\\nSkornyakov-Ter-Martirosyan symmetric extension $ H_{\\\\alpha} $, which is the\\r\\nnatural candidate as Hamiltonian of the system. We find a value of the mass $\\r\\nm^*(N) $ such that for $ m > m^*(N)$ the form $ \\\\form $ is closed and bounded from below. As a consequence, $ \\\\form $ defines a unique self-adjoint and bounded from below extension of $ H_{\\\\alpha}$ and therefore the system is stable. On the other hand, we also show that the form $ \\\\form $ is unbounded from below for $ m < m^*(2)$. In analogy with the well-known bosonic case, this suggests that the system is unstable for $ m < m^*(2)$ and the so-called Thomas effect occurs. %B Rev. Math. Phys. 24 (2012), 1250017 %I World Scientific %G en %U http://hdl.handle.net/1963/6069 %1 5955 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-08-02T07:19:59Z\\nNo. of bitstreams: 1\\n1201.5740v1.pdf: 303047 bytes, checksum: eb2df0afd547514c235422e82f494584 (MD5) %R 10.1142/S0129055X12500171 %0 Conference Paper %B 17th Int. Conf. Ships Shipp. Res. %D 2012 %T A stable semi-lagrangian potential method for the simulation of ship interaction with unsteady and nonlinear waves %A Andrea Mola %A Luca Heltai %A Antonio DeSimone %B 17th Int. Conf. Ships Shipp. Res. %G eng %0 Journal Article %J Proc. R. Soc. A 8 March 2012 vol. 468 no. 2139 701-719 %D 2012 %T Thermodynamic phase transitions and shock singularities %A Giuseppe De Nittis %A Antonio Moro %X We show that under rather general assumptions on the form of the entropy\\r\\nfunction, the energy balance equation for a system in thermodynamic equilibrium is equivalent to a set of nonlinear equations of hydrodynamic type. This set of equations is integrable via the method of the characteristics and it provides the equation of state for the gas. The shock wave catastrophe set identifies the phase transition. A family of explicitly solvable models of\\r\\nnon-hydrodynamic type such as the classical plasma and the ideal Bose gas are\\r\\nalso discussed. %B Proc. R. Soc. A 8 March 2012 vol. 468 no. 2139 701-719 %I The Royal Society %G en %U http://hdl.handle.net/1963/6090 %1 5978 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-08-02T11:53:22Z\\nNo. of bitstreams: 1\\n1107.0394v2.pdf: 610849 bytes, checksum: be0b8d83ff44e0468c3133f7ab3ca18d (MD5) %R 10.1098/rspa.2011.0459 %0 Journal Article %J IET systems biology. 2011 Jul; 5(4):269-79 %D 2011 %T Adaptation as a genome-wide autoregulatory principle in the stress response of yeast. %A F Eduati %A B Di Camillo %A G Toffolo %A Claudio Altafini %A Giovanna De Palo %A Mattia Zampieri %X The gene expression response of yeast to various types of stresses/perturbations shows a common functional and dynamical pattern for the vast majority of genes, characterised by a quick transient peak (affecting primarily short genes) followed by a return to the pre-stimulus level. Kinetically, this process of adaptation following the transient excursion can be modelled using a genome-wide autoregulatory mechanism by means of which yeast aims at maintaining a preferential concentration in its mRNA levels. The resulting feedback system explains well the different time constants observable in the transient response, while being in agreement with all the known experimental dynamical features. For example, it suggests that a very rapid transient can be induced also by a slowly varying concentration of the gene products. %B IET systems biology. 2011 Jul; 5(4):269-79 %I The Institution of Engineering and Technology %G en %U http://hdl.handle.net/1963/5106 %1 4922 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-11-25T13:05:49Z\\r\\nNo. of bitstreams: 1\\r\\nDePaEdal10.pdf: 2390366 bytes, checksum: f6550b1052efeb53942e47cae9632899 (MD5) %R 10.1049/iet-syb.2009.0050 %0 Journal Article %J Annales de l'I.H.P. Analyse non linéaire %D 2011 %T Concentration of solutions for a singularly perturbed Neumann problem in non-smooth domains %A Serena Dipierro %B Annales de l'I.H.P. Analyse non linéaire %I Elsevier %V 28 %P 107-126 %G eng %U http://www.numdam.org/item/AIHPC_2011__28_1_107_0 %R 10.1016/j.anihpc.2010.11.003 %0 Journal Article %J Le Matematiche (Catania), volume 66, Issue no.2, (2011), pages : 153-187 %D 2011 %T Cones of divisors of blow-ups of projective spaces %A Alessio Lo Giudice %A Salvatore Cacciola %A M. Donten-Bury %A O. Dumitrescu %A J. Park %K Mori dream space %X We investigate Mori dream spaces obtained by blowing-up the n-dimensional complex projective space at n+1, n+2 or n+3 points in very general position. Using toric techniques we study the movable cone of the blow-up of Pn at n+1 points, its decomposition into nef chambers and the action of theWeyl group on the set of chambers. Moreover, using different methods, we explicitly write down the equations of the movable cone also for Pn blown-up at n+2 points. %B Le Matematiche (Catania), volume 66, Issue no.2, (2011), pages : 153-187 %I Università degli Studi di Catania. Dipartimento di matematica %G en %U http://hdl.handle.net/1963/6613 %1 6462 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Alessio Lo Giudice (logiudic@sissa.it) on 2013-03-01T08:45:50Z No. of bitstreams: 1 CONES OF DIVISORS OF BLOW-UPS OF PROJECTIVE SPACES: 409758 bytes, checksum: 15d01ca131c41cf5f244bb4621177e36 (MD5) %R 10.4418/2011.66.2.13 %0 Journal Article %J Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1219-1231 %D 2011 %T Crack growth with non-interpenetration : a simplified proof for the pure Neumann problem %A Gianni Dal Maso %A Giuliano Lazzaroni %X We present a recent existence result concerning the quasi-static evolution of cracks in hyperelastic brittle materials, in the frame-work of finite elasticity with non-interpenetration. In particular, here we consider the problem where no Dirichlet conditions are imposed, the boundary is traction-free, and the body is subject only to time-dependent volume forces. This allows us to present the main ideas of the proof in a simpler way, avoiding some of the technicalities needed in the general case, studied in. %B Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1219-1231 %I American Institute of Mathematical Sciences %G en_US %U http://hdl.handle.net/1963/3801 %1 526 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-11-27T10:24:55Z\\r\\nNo. of bitstreams: 1\\r\\nDM-Laz-proc-pre.pdf: 195002 bytes, checksum: 44e408b134f19e4d31e77b3e0762cd73 (MD5) %R 10.3934/dcds.2011.31.1219 %0 Report %D 2011 %T Critical points of the Moser-Trudinger functional %A Francesca De Marchis %A Andrea Malchiodi %A Luca Martinazzi %K Moser-Trudinger inequality %I SISSA %G en %U http://hdl.handle.net/1963/4592 %1 4353 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-10-07T11:40:39Z\\nNo. of bitstreams: 1\\n46M_Malchiodi.pdf: 234581 bytes, checksum: 365098bf21692bfa547056b200acb4c6 (MD5) %0 Journal Article %J PNAS 108 (2011) 13978 %D 2011 %T Cytoskeletal actin networks in motile cells are critically self-organized systems synchronized by mechanical interactions %A Luca Cardamone %A Alessandro Laio %A Rajesh Shahapure %A Antonio DeSimone %B PNAS 108 (2011) 13978 %I National Academy of Sciences %G en %U http://hdl.handle.net/1963/4358 %1 4066 %2 Physics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-28T06:31:24Z\\nNo. of bitstreams: 0 %R 10.1073/pnas.1100549108 %0 Report %D 2011 %T D-branes, surface operators, and ADHM quiver representations %A Ugo Bruzzo %A Duiliu-Emanuel Diaconescu %A M. Yardim %A G. Pan %A Yi Zhang %A Chuang Wu-yen %X A supersymmetric quantum mechanical model is constructed for BPS states bound to surface operators in five dimensional SU(r) gauge theories using D-brane engineering. This model represents the effective action of a certain D2-brane configuration, and is naturally obtained by dimensional reduction of a quiver $(0,2)$ gauged linear sigma model. In a special stability chamber, the resulting moduli space of quiver representations is shown to be smooth and isomorphic to a moduli space of framed quotients on the projective plane. A precise conjecture relating a K-theoretic partition function of this moduli space to refined open string invariants of toric lagrangian branes is formulated for conifold and local P^1 x P^1 geometries. %I SISSA %G en %U http://hdl.handle.net/1963/4133 %1 3873 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-15T08:27:03Z\\r\\nNo. of bitstreams: 1\\r\\n1012.1826v2.pdf: 536824 bytes, checksum: 38cd256a97e7244dc3eaac8073827cc2 (MD5) %0 Thesis %D 2011 %T Dimensional Reduction and Approximation of Measures and Weakly Differentiable Homeomorphisms %A Sara Daneri %X This thesis is devoted to the study of two different problems: the properties of the disintegration of the Lebesgue measure on the faces of a convex function and the existence of smooth approximations of bi-Lipschitz orientation-preserving homeomorphisms in the plane. %I SISSA %G en %U http://hdl.handle.net/1963/5348 %1 5178 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-02-02T16:17:40Z\\nNo. of bitstreams: 1\\nTesiPhDDaneriFinal.pdf: 1042283 bytes, checksum: be3ac0827af99c78eafc9395b4670544 (MD5) %0 Journal Article %J Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1017-1021 %D 2011 %T Ennio De Giorgi and Γ-convergence %A Gianni Dal Maso %X Γ-convergence was introduced by Ennio De Giorgi in a series of papers published between 1975 and 1983. In the same years he developed many applications of this tool to a great variety of asymptotic problems in the calculus of variations and in the theory of partial differential equations. %B Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1017-1021 %I American Institute of Mathematical Sciences %G en %U http://hdl.handle.net/1963/5308 %1 5138 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-01-31T12:04:34Z\\nNo. of bitstreams: 0 %R 10.3934/dcds.2011.31.1017 %0 Journal Article %J SIAM J. Math. Anal. %D 2011 %T An Existence and Uniqueness Result for the Motion of Self-Propelled Microswimmers %A Gianni Dal Maso %A Antonio DeSimone %A Marco Morandotti %XWe present an analytical framework to study the motion of micro-swimmers in a viscous fluid. Our main result is that, under very mild regularity assumptions, the change of shape determines uniquely the motion of the swimmer. We assume that the Reynolds number is very small, so that the velocity field of the surrounding, infinite fluid is governed by the Stokes system and all inertial effects can be neglected. Moreover, we enforce the self propulsion constraint (no external forces and torques). Therefore, Newton\\\'s equations of motion reduce to the vanishing of the viscous drag force and torque acting on the body. By exploiting an integral representation of viscous force and torque, the equations of motion can be reduced to a system of six ordinary differential equations. Variational techniques are used to prove the boundedness and measurability of its coefficients, so that classical results on ordinary differential equations can be invoked to prove existence and uniqueness of the solution.

%B SIAM J. Math. Anal. %I Society for Industrial and Applied Mathematics %V 43 %P 1345-1368 %G en_US %U http://hdl.handle.net/1963/3894 %1 815 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-07-23T11:44:06Z\\r\\nNo. of bitstreams: 1\\r\\nMorandotti_44M.pdf: 217358 bytes, checksum: 4c362016bb2220e7a97805254b7fb870 (MD5) %R 10.1137/10080083X %0 Journal Article %J Rend. Lincei Mat. Appl. 22 (2011) 387-408 %D 2011 %T Existence for wave equations on domains with arbitrary growing cracks %A Gianni Dal Maso %A Cristopher J. Larsen %K Wave equation %X In this paper we formulate and study scalar wave equations on domains with arbitrary growing cracks. This includes a zero Neumann condition on the crack sets, and the only assumptions on these sets are that they have bounded surface measure and are growing in the sense of set inclusion. In particular, they may be dense, so the weak formulations must fall outside of the usual weak formulations using Sobolev spaces. We study both damped and undamped equations, showing existence and, for the damped equation, uniqueness and energy conservation. %B Rend. Lincei Mat. Appl. 22 (2011) 387-408 %I European Mathematical Society %G en %U http://hdl.handle.net/1963/4284 %1 4015 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-27T09:09:30Z\\r\\nNo. of bitstreams: 1\\r\\nDM-Lar_32_M.pdf: 223891 bytes, checksum: 7c6c66b6d21936b33ed0c21574928e24 (MD5) %R 10.4171/RLM/606 %0 Journal Article %J Continuum. Mech. Therm. %D 2011 %T Gamma-convergence of energies for nematic elastomers in the small strain limit %A Virginia Agostiniani %A Antonio DeSimone %K Liquid crystals %XWe study two variational models recently proposed in the literature to describe the mechanical behaviour of nematic elastomers either in the fully nonlinear regime or in the framework of a geometrically linear theory. We show that, in the small strain limit, the energy functional of the first one I\\\"-converges to the relaxation of the second one, a functional for which an explicit representation formula is available.

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

%B J. Eur. Math. Soc. (JEMS), to appear %I SISSA %G en %U http://hdl.handle.net/1963/6374 %1 6309 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-10T18:54:48Z\\nNo. of bitstreams: 1\\nDM-11.pdf: 413971 bytes, checksum: eca2a953ba1b97755da281bca4e099e4 (MD5) %0 Journal Article %J Matematische Annalen 349 (2011) 75-115 %D 2011 %T Infinite-dimensional Frobenius manifolds for 2 + 1 integrable systems %A Guido Carlet %A Boris Dubrovin %A Luca Philippe Mertens %X We introduce a structure of an infinite-dimensional Frobenius manifold on a subspace in the space of pairs of functions analytic inside/outside the unit circle with simple poles at 0/infinity respectively. The dispersionless 2D Toda equations are embedded into a bigger integrable hierarchy associated with this Frobenius manifold. %B Matematische Annalen 349 (2011) 75-115 %I Springer %G en_US %U http://hdl.handle.net/1963/3584 %1 716 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-03-09T09:29:31Z\\r\\nNo. of bitstreams: 1\\r\\n0902.1245.pdf: 343930 bytes, checksum: 421342a05bb8986c1bf542d6446f5792 (MD5) %R 10.1007/s00208-010-0509-3 %0 Journal Article %J Nonlinear Analysis: Theory, Methods & Applications %D 2011 %T Infinitely many positive solutions for a Schrödinger–Poisson system %A Pietro d’Avenia %A Alessio Pomponio %A Giusi Vaira %K Non-autonomous Schrödinger–Poisson system %K Perturbation method %XWe are interested in the existence of infinitely many positive solutions of the Schrödinger–Poisson system −Δu+u+V(|x|)ϕu=|u|p−1u,x∈R3,−Δϕ=V(|x|)u2,x∈R3, where V(|x|) is a positive bounded function, 1<p<5 and V(r

%B Nonlinear Analysis: Theory, Methods & Applications %V 74 %P 5705 - 5721 %G eng %U http://www.sciencedirect.com/science/article/pii/S0362546X11003518 %R https://doi.org/10.1016/j.na.2011.05.057 %0 Journal Article %J Functional Analysis and Its Applications. Volume 45, Issue 4, December 2011, Pages 278-290 %D 2011 %T Linearly degenerate Hamiltonian PDEs and a new class of solutions to the WDVV associativity equations %A Boris Dubrovin %A M.V. Pavlov %A Sergei A. Zykov %K Frobenius manifold %X We define a new class of solutions to the WDVV associativity equations. This class is determined by the property that one of the commuting PDEs associated with such a WDVV solution is linearly degenerate. We reduce the problem of classifying such solutions of the WDVV equations to the particular case of the so-called algebraic Riccati equation and, in this way, arrive at a complete classification of irreducible solutions. %B Functional Analysis and Its Applications. Volume 45, Issue 4, December 2011, Pages 278-290 %I Springer %G en %U http://hdl.handle.net/1963/6430 %1 6367 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-01-29T11:15:30Z No. of bitstreams: 1 dubrovin_linearly.pdf: 298813 bytes, checksum: 568feaa543b4082cc8e8fab4643dce71 (MD5) %R 10.1007/s10688-011-0030-9 %0 Journal Article %J Continuum Mechanics and Thermodynamics %D 2011 %T Metastable equilibria of capillary drops on solid surfaces: a phase field approach %A Livio Fedeli %A Turco, Alessandro %A Antonio DeSimone %XWe discuss a phase field model for the numerical simulation of metastable equilibria of capillary drops resting on rough solid surfaces and for the description of contact angle hysteresis phenomena in wetting. The model is able to reproduce observed transitions of drops on micropillars from Cassie–Baxter to Wenzel states. When supplemented with a dissipation potential which describes energy losses due to frictional forces resisting the motion of the contact line, the model can describe metastable states such as drops in equilibrium on vertical glass plates. The reliability of the model is assessed by a detailed comparison of its predictions with experimental data on the maximal size of water drops that can stick on vertical glass plates which have undergone different surface treatments.

%B Continuum Mechanics and Thermodynamics %V 23 %P 453–471 %8 Sep %G eng %U https://doi.org/10.1007/s00161-011-0189-6 %R 10.1007/s00161-011-0189-6 %0 Journal Article %J Boll. Unione Mat. Ital.(9) %D 2011 %T Multiplicity of solutions for a mean field equation on compact surfaces %A Francesca De Marchis %XWe consider a scalar field equation on compact surfaces which has variational structure. When the surface is a torus and a physical parameter ρ belongs to $(8\pi, 4\pi^2 )$ we show under some extra assumptions that, as conjectured in [9], the functional admits at least three saddle points other than a local minimum.

%B Boll. Unione Mat. Ital.(9) %V 4 %P 245–257 %G eng %0 Journal Article %J J. Phys. A 44 (2011) 315302 %D 2011 %T On the number of eigenvalues of a model operator related to a system of three particles on lattices %A Gianfausto Dell'Antonio %A Zahriddin I. Muminov %A Y.M. Shermatova %B J. Phys. A 44 (2011) 315302 %I IOP Publishing %G en %U http://hdl.handle.net/1963/5496 %1 5340 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-02-16T07:58:53Z\\nNo. of bitstreams: 0 %] We consider a quantum mechanical system on a lattice \\\\mathbb {Z}^3 in which three particles, two of them being identical, interact through a zero-range potential. We admit a very general form for the \\\'kinetic\\\' part H0γ of the Hamiltonian, which contains a parameter γ to distinguish the two identical particles from the third one (in the continuum case this parameter would be the inverse of the mass). We prove that there is a value γ* of the parameter such that only for γ < γ* the Efimov effect (infinite number of bound states if the two-body interactions have a resonance) is absent for the sector of the Hilbert space which contains functions which are antisymmetric with respect to the two identical particles, while it is present for all values of γ on the symmetric sector. We comment briefly on the relation of this result with previous investigations on the Thomas effect. We also establish the following asymptotics for the number N(z) of eigenvalues z below Emin, the lower limit of the essential spectrum of H0. In the symmetric subspace \\\\lim _{z \\\\rightarrow E_{\\\\rm min}^- } { N^s(z) \\\\over | \\\\log | E_{\\\\rm min} -z| | } = \\\\mathcal {U}_0^s (\\\\gamma ), \\\\quad \\\\forall\\\\ \\\\gamma, whereas in the antisymmetric subspace \\\\lim _{z \\\\rightarrow E_{\\\\rm min}^- } { N^{as}(z) \\\\over | \\\\log | E_{\\\\rm min} -z| | } = \\\\mathcal {U}_0^{as} (\\\\gamma ), \\\\quad \\\\forall\\\\ \\\\gamma \\\\gt \\\\gamma ^*, where \\\\mathcal {U}_0^{ as } (\\\\gamma ), \\\\mathcal {U}_0^s (\\\\gamma ) are written explicitly as a function of the integral kernel of operators acting on L^2((0,r) \\\\times (L^2 (\\\\mathbb {S}^2) \\\\otimes L^2 (\\\\mathbb {S}^2)) (\\\\mathbb {S}^2 is the unit sphere in \\\\mathbb {R}^3). %R 10.1088/1751-8113/44/31/315302 %0 Journal Article %J Mathematical Models and Methods in Applied Sciences 21 (2011) 361-387 %D 2011 %T Numerical Strategies for Stroke Optimization of Axisymmetric Microswimmers %A François Alouges %A Antonio DeSimone %A Luca Heltai %K Optimal swimming %X We propose a computational method to solve optimal swimming problems, based on the boundary integral formulation of the hydrodynamic interaction between swimmer and surrounding fluid and direct constrained minimization of the energy consumed by the swimmer. We apply our method to axisymmetric model examples. We consider a classical model swimmer (the three-sphere swimmer of Golestanian et al.) as well as a novel axisymmetric swimmer inspired by the observation of biological micro-organisms. %B Mathematical Models and Methods in Applied Sciences 21 (2011) 361-387 %I World Scientific %G en_US %U http://hdl.handle.net/1963/3657 %1 648 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-06-23T17:30:51Z\\r\\nNo. of bitstreams: 1\\r\\nSissa33_2009M.pdf: 708341 bytes, checksum: 6134bd52f083488620fb5bb24bcf9b93 (MD5) %R 10.1142/S0218202511005088 %0 Journal Article %J SIAM J. Appl. Math. 71 (2011) 983-1008 %D 2011 %T Numerical Study of breakup in generalized Korteweg-de Vries and Kawahara equations %A Boris Dubrovin %A Tamara Grava %A Christian Klein %X This article is concerned with a conjecture in [B. Dubrovin, Comm. Math. Phys., 267 (2006), pp. 117–139] on the formation of dispersive shocks in a class of Hamiltonian dispersive regularizations of the quasi-linear transport equation. The regularizations are characterized by two arbitrary functions of one variable, where the condition of integrability implies that one of these functions must not vanish. It is shown numerically for a large class of equations that the local behavior of their solution near the point of gradient catastrophe for the transport equation is described by a special solution of a Painlevé-type equation. This local description holds also for solutions to equations where blowup can occur in finite time. Furthermore, it is shown that a solution of the dispersive equations away from the point of gradient catastrophe is approximated by a solution of the transport equation with the same initial data, modulo terms of order $\\\\epsilon^2$, where $\\\\epsilon^2$ is the small dispersion parameter. Corrections up to order $\\\\epsilon^4$ are obtained and tested numerically. %B SIAM J. Appl. Math. 71 (2011) 983-1008 %I SIAM %G en %U http://hdl.handle.net/1963/4951 %1 4732 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-27T12:18:45Z\\nNo. of bitstreams: 1\\n1101.0268v1.pdf: 522533 bytes, checksum: d9e2df220724f918ec3b888cef3593d4 (MD5) %R 10.1137/100819783 %0 Report %D 2011 %T A planar bi-Lipschitz extension Theorem %A Sara Daneri %A Aldo Pratelli %G eng %U http://arxiv.org/abs/1110.6124 %0 Journal Article %J Physics Letters A 375 (2011) 3496-3498 %D 2011 %T Poincaré covariance and κ-Minkowski spacetime %A Ludwik Dabrowski %A Gherardo Piacitelli %X A fully Poincaré covariant model is constructed out of the k-Minkowski spacetime. Covariance is implemented by a unitary representation of the Poincaré group, and thus complies with the original Wigner approach to quantum symmetries. This provides yet another example (besides the DFR model), where Poincaré covariance is realised á la Wigner in the presence of two characteristic dimensionful parameters: the light speed and the Planck length. In other words, a Doubly Special Relativity (DSR) framework may well be realised without deforming the meaning of \\\"Poincaré covariance\\\". %B Physics Letters A 375 (2011) 3496-3498 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3893 %1 816 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-07-23T11:27:21Z\\r\\nNo. of bitstreams: 1\\r\\npiacitelli_43FM.pdf: 292672 bytes, checksum: 3aaa83de9dbf151351756897dbbcda09 (MD5) %R 10.1016/j.physleta.2011.08.011 %0 Journal Article %J International Journal of Geometric Methods in Modern Physics 8 (2011) 1833-1848 %D 2011 %T Product of real spectral triples %A Ludwik Dabrowski %A Giacomo Dossena %X We construct the product of real spectral triples of arbitrary finite dimension (and arbitrary parity) taking into account the fact that in the even case there are two possible real structures, in the odd case there are two inequivalent representations of the gamma matrices (Clifford algebra), and in the even-even case there are two natural candidates for the Dirac operator of the product triple. %B International Journal of Geometric Methods in Modern Physics 8 (2011) 1833-1848 %I World Scientific %G en %U http://hdl.handle.net/1963/5510 %1 5345 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-02-16T16:08:08Z\\nNo. of bitstreams: 1\\n1011.4456v1.pdf: 279 bytes, checksum: 44d0388a861dfb41e598ee6d79dc9d01 (MD5) %R 10.1142/S021988781100597X %0 Journal Article %J Commun. Math. Phys. 308 (2011) 567-589 %D 2011 %T Quantum Geometry on Quantum Spacetime: Distance, Area and Volume Operators %A Dorothea Bahns %A Sergio Doplicher %A Klaus Fredenhagen %A Gherardo Piacitelli %X We develop the first steps towards an analysis of geometry on the quantum\\r\\nspacetime proposed in Doplicher et al. (Commun Math Phys 172:187–220, 1995). The homogeneous elements of the universal differential algebra are naturally identified with operators living in tensor powers of Quantum Spacetime; this allows us to compute their spectra. In particular, we consider operators that can be interpreted as distances, areas, 3- and 4-volumes. The Minkowski distance operator between two independent events is shown to have pure Lebesgue spectrum with infinite multiplicity. The Euclidean distance operator is shown to have spectrum bounded below by a constant of the order of the Planck length. The corresponding statement is proved also for both the space-space and space-time area operators, as well as for the Euclidean length of the vector representing the 3-volume operators. However, the space 3-volume operator (the time component of that vector) is shown to have spectrum equal to the whole complex plane. All these operators are normal, while the distance operators are also selfadjoint. The Lorentz invariant spacetime volume operator, representing the 4- volume spanned by five\\r\\nindependent events, is shown to be normal. Its spectrum is pure point with a\\r\\nfinite distance (of the order of the fourth power of the Planck length) away\\r\\nfrom the origin. The mathematical formalism apt to these problems is developed and its relation to a general formulation of Gauge Theories on Quantum Spaces is outlined. As a byproduct, a Hodge Duality between the absolute differential and the Hochschild boundary is pointed out. %B Commun. Math. Phys. 308 (2011) 567-589 %I Springer %G en %U http://hdl.handle.net/1963/5203 %1 5025 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-12-16T08:24:01Z\\nNo. of bitstreams: 1\\n1005.2130v1.pdf: 270027 bytes, checksum: d12021458a91ccdbfdaf8adfbb2ec89d (MD5) %R 10.1007/s00220-011-1358-y %0 Journal Article %J Commun. Math. Phys. 307:101-131, 2011 %D 2011 %T Quantum Isometries of the finite noncommutative geometry of the Standard Model %A Jyotishman Bhowmick %A Francesco D'Andrea %A Ludwik Dabrowski %X We compute the quantum isometry group of the finite noncommutative geometry F describing the internal degrees of freedom in the Standard Model of particle physics. We show that this provides genuine quantum symmetries of the spectral triple corresponding to M x F where M is a compact spin manifold. We also prove that the bosonic and fermionic part of the spectral action are preserved by these symmetries. %B Commun. Math. Phys. 307:101-131, 2011 %I Springer %G en %U http://hdl.handle.net/1963/4906 %1 4688 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-25T07:42:04Z\\nNo. of bitstreams: 1\\n1009.2850v3.pdf: 383426 bytes, checksum: 9d28d3070f7e7c39ec9486f40fd4f13b (MD5) %R 10.1007/s00220-011-1301-2 %0 Journal Article %J Journal of the Mechanics and Physics of Solids 59 (2011) 787-803 %D 2011 %T Quasiconvex envelopes of energies for nematic elastomers in the small strain regime and applications %A Pierluigi Cesana %A Antonio DeSimone %X We provide some explicit formulas for the quasiconvex envelope of energy densities for nematic elastomers in the small strain regime and plane strain conditions. We then demonstrate their use as a powerful tool for the interpretation of mechanical experiments. %B Journal of the Mechanics and Physics of Solids 59 (2011) 787-803 %G en_US %U http://hdl.handle.net/1963/4065 %1 337 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-09-15T10:43:52Z\\r\\nNo. of bitstreams: 1\\r\\nCesana_DeSimone_62M.pdf: 1146834 bytes, checksum: 514b1b282763c0351f234702f96e73f4 (MD5) %0 Journal Article %J Calculus of Variations and Partial Differential Equations 40 (2011) 125-181 %D 2011 %T Quasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling %A Gianni Dal Maso %A Antonio DeSimone %A Francesco Solombrino %K Cam-Clay plasticity %XCam-Clay nonassociative plasticity exhibits both hardening and softening behaviour, depending on the loading. For many initial data the classical formulation of the quasistatic evolution problem has no smooth solution. We propose here a notion of generalized solution, based on a viscoplastic approximation. To study the limit of the viscoplastic evolutions we rescale time, in such a way that the plastic strain is uniformly Lipschitz with respect to the rescaled time. The limit of these rescaled solutions, as the viscosity parameter tends to zero, is characterized through an energy-dissipation balance, that can be written in a natural way using the rescaled time. As shown in [4] and [6], the proposed solution may be discontinuous with respect to the original time. Our formulation allows to compute the amount of viscous dissipation occurring instantaneously at each discontinuity time.

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

%B Arch. Rational Mech. Anal. 200 (2011) 1003-1021 %I Springer %G en %U http://hdl.handle.net/1963/4911 %1 4695 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-25T10:18:41Z\\nNo. of bitstreams: 1\\n1002.4087v1.pdf: 272486 bytes, checksum: 551dab603b0252ec9c22800b33360d02 (MD5) %R 10.1007/s00205-010-0381-z %0 Journal Article %J Indiana Univ. Math. J. 60 (2011) 367-409 %D 2011 %T Singular perturbation models in phase transitions for second order materials %A Milena Chermisi %A Gianni Dal Maso %A Irene Fonseca %A Giovanni Leoni %X A variational model proposed in the physics literature to describe the onset of pattern formation in two-component bilayer membranes and amphiphilic monolayers leads to the analysis of a Ginzburg-Landau type energy with a negative term depending on the first derivative of the phase function. Scaling arguments motivate the study of the family of second order singular perturbed energies Fe having a negative term depending on the first derivative of the phase function. Here, the asymptotic behavior of {Fe} is studied using G-convergence techniques. In particular, compactness results and an integral representation of the limit energy are obtained. %B Indiana Univ. Math. J. 60 (2011) 367-409 %I Indiana University %G en_US %U http://hdl.handle.net/1963/3858 %1 851 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-04-27T10:47:12Z\\r\\nNo. of bitstreams: 1\\r\\nCheDMaFonLeo_2010.pdf: 350746 bytes, checksum: b384a4d0b82dd9713e1849ad3ef6a2be (MD5) %R 10.1512/iumj.2011.60.4346 %0 Journal Article %J Int Math Res Notices (2011) 2011 (24): 5625-5643 %D 2011 %T Supercritical conformal metrics on surfaces with conical singularities %A Mauro Bardelloni %A Francesca De Marchis %A Andrea Malchiodi %XWe study the problem of prescribing the Gaussian curvature on surfaces with conical singularities in supercritical regimes. Using a Morse-theoretical approach we prove a general existence theorem on surfaces with positive genus, with a generic multiplicity result.

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

%G eng %0 Journal Article %J Journal de Mathématiques Pures et Appliquées %D 2011 %T The well-posedness issue for the density-dependent Euler equations in endpoint Besov spaces %A Raphaël Danchin %A Francesco Fanelli %K Blow-up criterion %K Critical regularity %K Incompressible Euler equations %K Lifespan %K Nonhomogeneous inviscid fluids %XThis work is the continuation of the recent paper (Danchin, 2010) [9] devoted to the density-dependent incompressible Euler equations. Here we concentrate on the well-posedness issue in Besov spaces of type B∞,rs embedded in the set of Lipschitz continuous functions, a functional framework which contains the particular case of Hölder spaces C1,α and of the endpoint Besov space B∞,11. For such data and under the non-vacuum assumption, we establish the local well-posedness and a continuation criterion in the spirit of that of Beale, Kato and Majda (1984) [2]. In the last part of the paper, we give lower bounds for the lifespan of a solution. In dimension two, we point out that the lifespan tends to infinity when the initial density tends to be a constant. This is, to our knowledge, the first result of this kind for the density-dependent incompressible Euler equations. Résumé Ce travail complète lʼarticle récent (Danchin, 2010) [9] consacré au système dʼEuler incompressible à densité variable. Lorsque lʼétat initial ne comporte pas de vide, on montre ici que le système est bien posé dans tous les espaces de Besov B∞,rs inclus dans lʼensemble des fonctions lipschitziennes. Ce cadre fonctionnel contient en particulier les espaces de Hölder C1,α et lʼespace de Besov limite B∞,11. On établit également un critère de prolongement dans lʼesprit de celui de Beale, Kato et Majda (1984) [2] pour le cas homogène. Dans la dernière partie de lʼarticle, on donne des minorations pour le temps de vie des solutions du système. En dimension deux, on montre que ce temps de vie tend vers lʼinfini lorsque la densité tend à être homogène. À notre connaissance, il sʼagit du premier résultat de ce type pour le système dʼEuler incompressible à densité variable.

%B Journal de Mathématiques Pures et Appliquées %V 96 %P 253 - 278 %G eng %U http://www.sciencedirect.com/science/article/pii/S0021782411000511 %R https://doi.org/10.1016/j.matpur.2011.04.005 %0 Report %D 2010 %T Canonical k-Minkowski Spacetime %A Gherardo Piacitelli %A Ludwik Dabrowski %X A complete classification of the regular representations of the relations [T,X_j] = (i/k)X_j, j=1,...,d, is given. The quantisation of RxR^d canonically (in the sense of Weyl) associated with the universal representation of the above relations is intrinsically \\\"radial\\\", this meaning that it only involves the time variable and the distance from the origin; angle variables remain classical. The time axis through the origin is a spectral singularity of the model: in the large scale limit it is topologically disjoint from the rest. The symbolic calculus is developed; in particular there is a trace functional on symbols. For suitable choices of states localised very close to the origin, the uncertainties of all spacetime coordinates can be made simultaneously small at wish. On the contrary, uncertainty relations become important at \\\"large\\\" distances: Planck scale effects should be visible at LHC energies, if processes are spread in a region of size 1mm (order of peak nominal beam size) around the origin of spacetime. %G en_US %U http://hdl.handle.net/1963/3863 %1 846 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-04-30T11:01:45Z\\r\\nNo. of bitstreams: 1\\r\\n1004.5091v1.pdf: 302332 bytes, checksum: 923a85fa3b4bef96bcf59c115bc3a61e (MD5) %0 Report %D 2010 %T Convergence of equilibria of thin elastic rods under physical growth conditions for the energy density %A Elisa Davoli %A Maria Giovanna Mora %X The subject of this paper is the study of the asymptotic behaviour of the equilibrium configurations of a nonlinearly elastic thin rod, as the diameter of the cross-section tends to zero. Convergence results are established assuming physical growth conditions for the elastic energy density and suitable scalings of the applied loads, that correspond at the limit to different rod models: the constrained linear theory, the analogous of von Kármán plate theory for rods, and the linear theory. %G en_US %U http://hdl.handle.net/1963/4086 %1 317 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-10-05T08:49:01Z\\nNo. of bitstreams: 1\\nDavoli-Mora_67M_2010.pdf: 243056 bytes, checksum: 8542ff47b9dc1ae7275fe95bc296a870 (MD5) %0 Journal Article %J Comm. Math. Phys. 295 (2010) 731-790 %D 2010 %T Dirac Operators on Quantum Projective Spaces %A Francesco D'Andrea %A Ludwik Dabrowski %X We construct a family of self-adjoint operators D_N which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space CP_q(l), for any l>1 and 0We consider the disintegration of the Lebesgue measure on the graph of a convex function f:\\\\Rn-> \\\\R w.r.t. the partition into its faces, which are convex sets and therefore have a well defined linear dimension, and we prove that each conditional measure is equivalent to the k-dimensional Hausdorff measure of the k-dimensional face on which it is concentrated. The remarkable fact is that a priori the directions of the faces are just Borel and no Lipschitz regularity is known. Notwithstanding that, we also prove that a Green-Gauss formula for these directions holds on special sets. %B J. Funct. Anal. 258 (2010) 3604-3661 %G en_US %U http://hdl.handle.net/1963/3622 %1 682 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-04-24T15:53:31Z\\nNo. of bitstreams: 1\\ndisconvCaravDaneri.pdf: 759110 bytes, checksum: e22e069339fc07c3bde1855b76e61d1e (MD5) %R 10.1016/j.jfa.2010.01.024 %0 Journal Article %J J. Phys. A 43 (2010) 474014 %D 2010 %T Effective Schroedinger dynamics on $ ε$-thin Dirichlet waveguides via Quantum Graphs I: star-shaped graphs %A Gianfausto Dell'Antonio %A Emanuele Costa %X We describe the boundary conditions at the vertex that one must choose to obtain a dynamical system that best describes the low-energy part of the evolution of a quantum system confined to a very small neighbourhood of a star-shaped metric graph. %B J. Phys. A 43 (2010) 474014 %I IOP Publishing %G en_US %U http://hdl.handle.net/1963/4106 %1 298 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-12-06T13:09:12Z\\nNo. of bitstreams: 1\\n1004.4750v2.pdf: 273649 bytes, checksum: ff34b6647ba206615715d6c764115064 (MD5) %R 10.1088/1751-8113/43/47/474014 %0 Journal Article %J Journal of Functional Analysis %D 2010 %T Generic multiplicity for a scalar field equation on compact surfaces %A Francesca De Marchis %K Generic multiplicity %K Geometric PDE's %K Morse inequalities %K Scalar field equations %XWe prove generic multiplicity of solutions for a scalar field equation on compact surfaces via Morse inequalities. In particular our result improves significantly the multiplicity estimate which can be deduced from the degree-counting formula in Chen and Lin (2003) [12]. Related results are derived for the prescribed Q-curvature equation.

%B Journal of Functional Analysis %V 259 %P 2165 - 2192 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022123610002697 %R https://doi.org/10.1016/j.jfa.2010.07.003 %0 Report %D 2010 %T The geometry emerging from the symmetries of a quantum system %A Giuseppe De Nittis %A Gianluca Panati %X We investigate the relation between the symmetries of a quantum system and its topological quantum numbers, in a general C*-algebraic framework. We prove that, under suitable assumptions on the symmetry algebra, there exists a generalization of the Bloch-Floquet transform which induces a direct-integral decomposition of the algebra of observables. Such generalized transform selects uniquely the set of \\\"continuous sections\\\" in the direct integral, thus yielding a Hilbert bundle. The emerging geometric structure provides some topological invariants of the quantum system. Two running examples provide an Ariadne\\\'s thread through the paper. For the sake of completeness, we review two related theorems by von Neumann and Maurin and compare them with our result. %G en_US %U http://hdl.handle.net/1963/3834 %1 493 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-01-26T16:38:34Z\\nNo. of bitstreams: 1\\n0911.5270v2.pdf: 578198 bytes, checksum: a06ef54ebf418d5d7b6d0a7c3410c054 (MD5) %0 Journal Article %J Journal of Physics A: Mathematical and Theoretical. Volume 43, Issue 43, 29 October 2010, Article number 434002 %D 2010 %T Hamiltonian PDEs: deformations, integrability, solutions %A Boris Dubrovin %X We review recent classification results on the theory of systems of nonlinear\\r\\nHamiltonian partial differential equations with one spatial dimension, including\\r\\na perturbative approach to the integrability theory of such systems, and discuss\\r\\nuniversality conjectures describing critical behaviour of solutions to such\\r\\nsystems. %B Journal of Physics A: Mathematical and Theoretical. Volume 43, Issue 43, 29 October 2010, Article number 434002 %I SISSA %G en %U http://hdl.handle.net/1963/6469 %1 6414 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T14:36:26Z\\nNo. of bitstreams: 0 %R 10.1088/1751-8113/43/43/434002 %0 Journal Article %J Adv. Calc. Var. 3 (2010) 345-370 %D 2010 %T Homogenization of fiber reinforced brittle material: the intermediate case %A Gianni Dal Maso %A Caterina Ida Zeppieri %X We derive a cohesive fracture model by homogenizing a periodic composite material whose microstructure is characterized by the presence of brittle inclusions in a reticulated unbreakable elastic structure. %B Adv. Calc. Var. 3 (2010) 345-370 %I Walter de Gruyter %G en_US %U http://hdl.handle.net/1963/3607 %1 694 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-04-02T10:43:00Z\\r\\nNo. of bitstreams: 1\\r\\nDM-Zep.pdf: 294507 bytes, checksum: 5ba95ca12abb15953a564aeedf353087 (MD5) %R 10.1515/ACV.2010.011 %0 Journal Article %J Phys. Rev. D 81 (2010) 125024 %D 2010 %T Lorentz Covariant k-Minkowski Spacetime %A Ludwik Dabrowski %A Michal Godlinski %A Gherardo Piacitelli %X In recent years, different views on the interpretation of Lorentz covariance of non commuting coordinates were discussed. Here, by a general procedure, we construct the minimal canonical central covariantisation of the k-Minkowski spacetime. We then show that, though the usual k-Minkowski spacetime is covariant under deformed (or twisted) Lorentz action, the resulting framework is equivalent to taking a non covariant restriction of the covariantised model. We conclude with some general comments on the approach of deformed covariance. %B Phys. Rev. D 81 (2010) 125024 %G en_US %U http://hdl.handle.net/1963/3829 %1 498 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-01-26T15:05:30Z\\nNo. of bitstreams: 1\\n0912.5451v2.pdf: 189407 bytes, checksum: e0a9a6af9e79410c0a199250cb168d04 (MD5) %R 10.1103/PhysRevD.81.125024 %0 Journal Article %J Adv. Calc. Var. 3 (2010) 287-319 %D 2010 %T Nonlocal character of the reduced theory of thin films with higher order perturbations %A Gianni Dal Maso %A Irene Fonseca %A Giovanni Leoni %B Adv. Calc. Var. 3 (2010) 287-319 %G en_US %U http://hdl.handle.net/1963/3754 %1 563 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-09-15T09:06:42Z\\nNo. of bitstreams: 1\\nDM-Fon-Leo.pdf: 288658 bytes, checksum: 7815e9376b53eb044b2fb2b57cd49b53 (MD5) %R 10.1515/ACV.2010.012, /July/2010 %0 Report %D 2010 %T Optimally swimming Stokesian Robots %A François Alouges %A Antonio DeSimone %A Luca Heltai %A Aline Lefebvre %A Benoit Merlet %X We study self propelled stokesian robots composed of assemblies of balls, in dimen-\\nsions 2 and 3, and prove that they are able to control their position and orientation. This is a result of controllability, and its proof relies on applying Chow\\\'s theorem in an analytic framework, similarly to what has been done in [3] for an axisymmetric system swimming along the axis of symmetry. However, we simplify drastically\\nthe analyticity result given in [3] and apply it to a situation where more complex swimmers move either in a plane or in three-dimensional space, hence experiencing also rotations. We then focus our attention on energetically optimal strokes, which we are able to compute numerically. Some examples of computed optimal strokes are discussed in detail. %G en_US %U http://hdl.handle.net/1963/3929 %1 472 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-07-29T11:02:56Z\\nNo. of bitstreams: 1\\nHeltai_54M_2010.pdf: 993075 bytes, checksum: 77225380bab031438ac940e694ea0e6c (MD5) %0 Conference Paper %B IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials %D 2010 %T A Phase Field Approach to Wetting and Contact Angle Hysteresis Phenomena %A Antonio DeSimone %A Livio Fedeli %A Turco, Alessandro %E Hackl, Klaus %XWe discuss a phase field model for the numerical simulation of contact angle hysteresis phenomena in wetting. The performance of the model is assessed by comparing its predictions with experimental data on the critical size of drops that can stick on a vertical glass plate.

%B IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials %I Springer Netherlands %C Dordrecht %P 51–63 %@ 978-90-481-9195-6 %G eng %0 Journal Article %J Arch. Ration. Mech. Anal. 196 (2010) 867-906 %D 2010 %T Quasistatic crack growth in elasto-plastic materials: the two-dimensional case %A Gianni Dal Maso %A Rodica Toader %X We study a variational model for the quasistatic evolution of elasto-plastic materials with cracks in the case of planar small strain associative elasto-plasticity. %B Arch. Ration. Mech. Anal. 196 (2010) 867-906 %G en_US %U http://hdl.handle.net/1963/2964 %1 1736 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-23T17:17:34Z\\nNo. of bitstreams: 1\\nDM-Toa-07-preprint.pdf: 320979 bytes, checksum: e4f2a1856f9bd91d63fc45557cbd6a16 (MD5) %R 10.1007/s00205-009-0258-1 %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 257-290 %D 2010 %T Quasistatic crack growth in finite elasticity with non-interpenetration %A Gianni Dal Maso %A Giuliano Lazzaroni %XWe present a variational model to study the quasistatic growth of brittle cracks in hyperelastic materials, in the framework of finite elasticity, taking\\ninto account the non-interpenetration condition.

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

%B Netw. Heterog. Media 5 (2010) 97-132 %G en_US %U http://hdl.handle.net/1963/3671 %1 634 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-07-20T08:35:17Z\\nNo. of bitstreams: 1\\nDM-Sol2-39_2009_preprint.pdf: 345995 bytes, checksum: 073ce622e3320be1f56a1cc9f8904fae (MD5) %R 10.3934/nhm.2010.5.97 %0 Report %D 2010 %T The role of membrane viscosity in the dynamics of fluid membranes %A Marino Arroyo %A Antonio DeSimone %A Luca Heltai %X Fluid membranes made out of lipid bilayers are the fundamental separation structure in eukaryotic cells. Many physiological processes rely on dramatic shape and topological changes (e.g. fusion, fission) of fluid membrane systems. Fluidity is key to the versatility and constant reorganization of lipid bilayers. Here, we study the role of the membrane intrinsic viscosity, arising from the friction of the lipid molecules as they rearrange to accommodate shape changes, in the dynamics of morphological changes of fluid vesicles. In particular, we analyze the competition between the membrane viscosity and the viscosity of the bulk fluid surrounding the vesicle as the dominant dissipative mechanism. We consider the relaxation dynamics of fluid vesicles put in an out-of-equilibrium state, but conclusions can be drawn regarding the kinetics or power consumption in regulated shape changes in the cell. On the basis of numerical calculations, we find that the dynamics arising from the membrane viscosity are qualitatively different from the dynamics arising from the bulk viscosity. When these two dissipation mechanisms are put in competition, we find that for small vesicles the membrane dissipation dominates, with a relaxation time that scales as the size of the vesicle to the power 2. For large vesicles, the bulk dissipation dominates, and the exponent in the relaxation time vs. size relation is 3. %G en_US %U http://hdl.handle.net/1963/3930 %1 471 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-07-29T11:13:35Z\\nNo. of bitstreams: 1\\nArroyo_55M.pdf: 4419667 bytes, checksum: ca8a9c175a457ad33996d46a08e85e44 (MD5) %0 Journal Article %J Annales Henri Poincare 11 (2010) 539-564 %D 2010 %T A time-dependent perturbative analysis for a quantum particle in a cloud chamber %A Gianfausto Dell'Antonio %A Rodolfo Figari %A Alessandro Teta %X We consider a simple model of a cloud chamber consisting of a test particle (the alpha-particle) interacting with two other particles (the atoms of the vapour) subject to attractive potentials centered in $a_1, a_2 \\\\in \\\\mathbb{R}^3$. At time zero the alpha-particle is described by an outgoing spherical wave centered in the origin and the atoms are in their ground state. We show that, under suitable assumptions on the physical parameters of the system and up to second order in perturbation theory, the probability that both atoms are ionized is negligible unless $a_2$ lies on the line joining the origin with $a_1$. The work is a fully time-dependent version of the original analysis proposed by Mott in 1929. %B Annales Henri Poincare 11 (2010) 539-564 %I Springer %G en_US %U http://hdl.handle.net/1963/3969 %1 432 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-08-05T08:05:00Z\\nNo. of bitstreams: 1\\n0907.5503v1.pdf: 273181 bytes, checksum: 781ee2f8d4ce957ebbfbf866bcc40d2b (MD5) %R 10.1007/s00023-010-0037-4 %0 Book Section %B Encyclopedia of Complexity and Systems Science / Robert A. Meyers (ed.). - Springer, 2009, 548-554 %D 2009 %T Biological Fluid Dynamics, Non-linear Partial Differential Equations %A Antonio DeSimone %A François Alouges %A Aline Lefebvre %B Encyclopedia of Complexity and Systems Science / Robert A. Meyers (ed.). - Springer, 2009, 548-554 %G en_US %U http://hdl.handle.net/1963/2630 %1 1493 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-04-16T08:35:02Z\\nNo. of bitstreams: 1\\nEncyclopedia_SISSA_Preprint.pdf: 157119 bytes, checksum: 6db74c2f0a9ba80b7b1e5375bd550c0c (MD5) %0 Journal Article %J Discrete Contin. Dyn. Syst. 23 (2009) 29-48 %D 2009 %T On the convergence of viscous approximations after shock interactions %A Alberto Bressan %A Carlotta Donadello %X We consider a piecewise smooth solution to a scalar conservation law, with possibly interacting shocks. We show that, after the interactions have taken place, vanishing viscosity approximations can still be represented by a regular expansion on smooth regions and by a singular perturbation expansion near the shocks, in terms of powers of the viscosity coefficient. %B Discrete Contin. Dyn. Syst. 23 (2009) 29-48 %I American Institute of Mathematical Sciences %G en_US %U http://hdl.handle.net/1963/3412 %1 923 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-09T12:23:11Z\\nNo. of bitstreams: 1\\n019.pdf: 273198 bytes, checksum: 4513df79a27da75ea57c4374c83b0cf6 (MD5) %R 10.3934/dcds.2009.23.29 %0 Journal Article %J Netw. Heterog. Media 4 (2009) 667-708 %D 2009 %T Discrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers %A Marco Cicalese %A Antonio DeSimone %A Caterina Ida Zeppieri %X In the framework of linear elasticity, we study the limit of a class of discrete free energies modeling strain-alignment-coupled systems by a rigorous coarse-graining procedure, as the number of molecules diverges. We focus on three paradigmatic examples: magnetostrictive solids, ferroelectric crystals and nematic elastomers, obtaining in the limit three continuum models consistent with those commonly employed in the current literature. We also derive the correspondent macroscopic energies in the presence of displacement boundary conditions and of various kinds of applied external fields. %B Netw. Heterog. Media 4 (2009) 667-708 %I American Institute of Mathematical Sciences %G en_US %U http://hdl.handle.net/1963/3788 %1 538 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-11-25T10:31:11Z\\nNo. of bitstreams: 1\\nCDSZ08.pdf: 390765 bytes, checksum: 2b3fcd3668352c286200e0a3b7e12c1a (MD5) %R 10.3934/nhm.2009.4.667 %0 Book Section %B New Trends in Mathematical Physics : Selected contributions of the XVth International Congress on Mathematical Physics, Springer Netherlands, 2009, pp. 231-276. %D 2009 %T Hamiltonian perturbations of hyperbolic PDEs: from classification results to the properties of solutions %A Boris Dubrovin %X We begin with presentation of classi cation results in the theory of Hamiltonian\\r\\nPDEs with one spatial dimension depending on a small parameter. Special\\r\\nattention is paid to the deformation theory of integrable hierarchies, including an\\r\\nimportant subclass of the so-called integrable hierarchies of the topological type\\r\\nassociated with semisimple Frobenius manifolds. Many well known equations of\\r\\nmathematical physics, such as KdV, NLS, Toda, Boussinesq etc., belong to this\\r\\nsubclass, but there are many new integrable PDEs, some of them being of interest\\r\\nfor applications. Connections with the theory of Gromov{Witten invariants\\r\\nand random matrices are outlined. We then address the problem of comparative\\r\\nstudy of singularities of solutions to the systems of first order quasilinear\\r\\nPDEs and their Hamiltonian perturbations containing higher derivatives. We\\r\\nformulate Universality Conjectures describing different types of critical behavior\\r\\nof perturbed solutions near the point of gradient catastrophe of the unperturbed\\r\\none. %B New Trends in Mathematical Physics : Selected contributions of the XVth International Congress on Mathematical Physics, Springer Netherlands, 2009, pp. 231-276. %I SISSA %@ 978-90-481-2810-5 %G en %U http://hdl.handle.net/1963/6470 %1 6415 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T14:43:17Z\\nNo. of bitstreams: 1\\ndubrovin_icmp.pdf: 902220 bytes, checksum: a35a8999aa1c5c58113eda66180935d9 (MD5) %0 Journal Article %J SIAM J. Math. Anal. 40 (2009) 2351-2391 %D 2009 %T A higher order model for image restoration: the one dimensional case %A Gianni Dal Maso %A Irene Fonseca %A Giovanni Leoni %A Massimiliano Morini %X The higher order total variation-based model for image restoration proposed by Chan, Marquina, and Mulet in [6] is analyzed in one dimension. A suitable functional framework in which the minimization problem is well posed is being proposed and it is proved analytically that the\\nhigher order regularizing term prevents the occurrence of the staircase effect. The generalized version of the model considered here includes, as particular cases, some curvature dependent functionals. %B SIAM J. Math. Anal. 40 (2009) 2351-2391 %G en_US %U http://hdl.handle.net/1963/3174 %1 1127 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-23T07:52:52Z\\nNo. of bitstreams: 1\\nDM-Fon-Leo-Mor-08-preprint.pdf: 336946 bytes, checksum: 32db893a2b928f559b6744296e1d4f2c (MD5) %R 10.1137/070697823 %0 Journal Article %J SIAM J. Math. Anal. 41 (2009) 1874-1889 %D 2009 %T Homogenization of fiber reinforced brittle materials: the extremal cases %A Marco Barchiesi %A Gianni Dal Maso %X We analyze the behavior of a fragile material reinforced by a reticulated elastic unbreakable structure in the case of antiplane shear. The microscopic geometry of this material is described by means of two small parameters: the period $\\\\varepsilon$ of the grid and the ratio $\\\\delta$ between the thickness of the fibers and the period $\\\\varepsilon$. We show that the asymptotic behavior as $\\\\varepsilon\\\\to0^+$ and $\\\\delta\\\\to0^+$ depends dramatically on the relative size of these parameters. Indeed, in the two cases considered, i.e., $\\\\varepsilon\\\\ll\\\\delta$ and $\\\\varepsilon\\\\gg\\\\delta$, we obtain two different limit models: a perfectly elastic model and an elastic model with macroscopic cracks, respectively. %B SIAM J. Math. Anal. 41 (2009) 1874-1889 %I SIAM %G en_US %U http://hdl.handle.net/1963/2705 %1 1396 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-08-13T12:57:01Z\\nNo. of bitstreams: 1\\nmicrofibre.pdf: 236545 bytes, checksum: 53ef9ce789d27bba7dcac550930f306b (MD5) %0 Journal Article %J Math. Models Methods Appl. Sci. 19 (2009) 1643-1711 %D 2009 %T Quasistatic evolution for Cam-Clay plasticity: examples of spatially homogeneous solutions %A Gianni Dal Maso %A Antonio DeSimone %X We study a quasistatic evolution problem for Cam-Clay plasticity under a special loading program which leads to spatially homogeneous solutions. Under some initial conditions, the solutions exhibit a softening behaviour and time discontinuities.\\nThe behavior of the solutions at the jump times is studied by a viscous approximation. %B Math. Models Methods Appl. Sci. 19 (2009) 1643-1711 %G en_US %U http://hdl.handle.net/1963/3395 %1 937 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-12-10T11:56:05Z\\nNo. of bitstreams: 1\\nDal_Maso-DeSimone.pdf: 1160572 bytes, checksum: fd49c80a369183f1941b0fcf3cd65341 (MD5) %R 10.1142/S0218202509003942 %0 Journal Article %J Phys. Rev. E 79 (2009) 031915 %D 2009 %T Relaxation dynamics of fluid membranes %A Marino Arroyo %A Antonio DeSimone %X We study the effect of membrane viscosity in the dynamics of liquid membranes-possibly with free or internal boundaries-driven by conservative forces (curvature elasticity and line tension) and dragged by the bulk dissipation of the ambient fluid and the friction occurring when the amphiphilic molecules move relative to each other. To this end, we formulate a continuum model which includes a form of the governing equations for a two-dimensional viscous fluid moving on a curved, time-evolving surface. The effect of membrane viscosity has received very limited attention in previous continuum studies of the dynamics of fluid membranes, although recent coarse-grained discrete simulations suggest its importance. By applying our model to the study of vesiculation and membrane fusion in a simplified geometry, we conclude that membrane viscosity plays a dominant role in the relaxation dynamics of fluid membranes of sizes comparable to those found in eukaryotic cells, and is not negligible in many large synthetic systems of current interest. %B Phys. Rev. E 79 (2009) 031915 %I American Physical Society %G en_US %U http://hdl.handle.net/1963/3618 %1 686 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-04-22T08:29:29Z\\nNo. of bitstreams: 1\\nmembrane_dynamics_PRE_2.pdf: 1000677 bytes, checksum: e7ab0f6e2046800e154d399808ea314c (MD5) %R 10.1103/PhysRevE.79.031915 %0 Journal Article %J Math. Models Methods Appl. Sci. 19 (2009) 601-630 %D 2009 %T Strain-order coupling in nematic elastomers: equilibrium configurations %A Pierluigi Cesana %A Antonio DeSimone %X We consider models that describe liquid crystal elastomers either in a biaxial or in a uniaxial phase and in the framework of Frank\\\'s director theory. We prove existence of static equilibrium solutions in the presence of frustrations due to electro-mechanical boundary conditions and to applied loads and fields. We find explicit solutions arising in connection with special boundary conditions and the corresponding phase diagrams, leading to significant implications on possible experimental observations. %B Math. Models Methods Appl. Sci. 19 (2009) 601-630 %G en_US %U http://hdl.handle.net/1963/2700 %1 1400 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-07-25T15:04:59Z\\nNo. of bitstreams: 1\\nprprCdS.pdf: 504721 bytes, checksum: 2ef9aff006dbc9353a50a122cb98d381 (MD5) %0 Report %D 2009 %T Stratos: a code for 3D free surface flows with floating constraints %A Antonio DeSimone %A B. Bianchi %A Luca Heltai %X This report presents a brief discussion of the theoretical aspects and practical implementation of STRATOS . STRATOS is a 3D code for the simulation\\nof hydrodynamic flows for incompressible fluids, in the presence of a free surface, capable of simulating the interaction between the free surface and a\\nfloating object via Lagrange multipliers...... %G en_US %U http://hdl.handle.net/1963/3701 %1 604 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-07-30T14:37:01Z\\nNo. of bitstreams: 1\\nBianchiDeSimoneHeltai.pdf: 899803 bytes, checksum: aff44eb1a39c6fd4acd4b3cb285e2d64 (MD5) %0 Report %D 2009 %T Tools for the Solution of PDEs Defined on Curved Manifolds with deal.II %A Antonio DeSimone %A Luca Heltai %A Cataldo Manigrasso %X The deal.II finite element library was originally designed to solve partial differential equations defined on one, two or three space dimensions, mostly\\nvia the Finite Element Method. In its versions prior to version 6.2, the user could not solve problems defined on curved manifolds embedded in two or\\nthree spacial dimensions. This infrastructure is needed if one wants to solve, for example, Boundary Integral Equations. %G en_US %U http://hdl.handle.net/1963/3700 %1 605 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-07-30T14:20:01Z\\nNo. of bitstreams: 1\\nDeSimoneHeltaiManigrasso.pdf: 915137 bytes, checksum: c3144348b6aab67a5f547060049c7847 (MD5) %0 Journal Article %J J. Nonlinear Sci. 19 (2009) 57-94 %D 2009 %T On universality of critical behaviour in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the \\\\it tritronquée solution to the Painlevé-I equation %A Boris Dubrovin %A Tamara Grava %A Christian Klein %X We argue that the critical behaviour near the point of ``gradient catastrophe\\\" of the solution to the Cauchy problem for the focusing nonlinear Schr\\\\\\\"odinger equation $ i\\\\epsilon \\\\psi_t +\\\\frac{\\\\epsilon^2}2\\\\psi_{xx}+ |\\\\psi|^2 \\\\psi =0$ with analytic initial data of the form $\\\\psi(x,0;\\\\epsilon) =A(x) e^{\\\\frac{i}{\\\\epsilon} S(x)}$ is approximately described by a particular solution to the Painlev\\\\\\\'e-I equation. %B J. Nonlinear Sci. 19 (2009) 57-94 %G en_US %U http://hdl.handle.net/1963/2525 %1 1593 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-11T13:11:26Z\\nNo. of bitstreams: 1\\n0704.0501v3.pdf: 568190 bytes, checksum: cf8471fc01eea53ce252339eda81b3cd (MD5) %R 10.1007/s00332-008-9025-y %0 Journal Article %J Boll. Unione Mat. Ital. (9) 2 (2009) 371-390 %D 2009 %T A variational model for quasistatic crack growth in nonlinear elasticity: some qualitative properties of the solutions %A Gianni Dal Maso %A Alessandro Giacomini %A Marcello Ponsiglione %B Boll. Unione Mat. Ital. (9) 2 (2009) 371-390 %G en_US %U http://hdl.handle.net/1963/2675 %1 1425 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-06-26T15:44:13Z\\nNo. of bitstreams: 1\\nDM-Gia-Pon.pdf: 242504 bytes, checksum: 3b08c25331a3436a5766d41df8e937f7 (MD5) %0 Journal Article %J Boll. Unione Mat. Ital. (9) 1 (2008) 497-505 %D 2008 %T Decomposition results for functions with bounded variation %A Gianni Dal Maso %A Rodica Toader %B Boll. Unione Mat. Ital. (9) 1 (2008) 497-505 %I Unione Matematica Italiana %G en_US %U http://hdl.handle.net/1963/3535 %1 729 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-23T10:23:36Z\\nNo. of bitstreams: 1\\nDM-Toa.pdf: 186814 bytes, checksum: bbc754f60013f0d8fd61b90a278ac837 (MD5) %0 Journal Article %J SIAM J. Math. Anal. 40 (2008) 1104-1122 %D 2008 %T Eulerian calculus for the displacement convexity in the Wasserstein distance %A Sara Daneri %A Giuseppe Savarè %X In this paper we give a new proof of the (strong) displacement convexity of a class of integral functionals defined on a compact Riemannian manifold satisfying a lower Ricci curvature bound. Our approach does not rely on existence and regularity results for optimal transport maps on Riemannian manifolds, but it is based on the Eulerian point of view recently introduced by Otto and Westdickenberg [SIAM J. Math. Anal., 37 (2005), pp. 1227-1255] and on the metric characterization of the gradient flows generated by the functionals in the Wasserstein space. %B SIAM J. Math. Anal. 40 (2008) 1104-1122 %I SIAM %G en_US %U http://hdl.handle.net/1963/3413 %1 922 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-09T12:32:55Z\\nNo. of bitstreams: 1\\n0801.2455v1.pdf: 504916 bytes, checksum: 7ccfac515ef559e376c7e7d213bd4091 (MD5) %R 10.1137/08071346X %0 Journal Article %J Ann. of Math. 168 (2008) 813-858 %D 2008 %T Existence of conformal metrics with constant $Q$-curvature %A Zindine Djadli %A Andrea Malchiodi %X Given a compact four dimensional manifold, we prove existence of conformal metrics with constant $Q$-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure. Since the corresponding Euler functional is in general unbounded from above and from below, we employ topological methods and minimax schemes, jointly with a compactness result by the second author. %B Ann. of Math. 168 (2008) 813-858 %G en_US %U http://hdl.handle.net/1963/2308 %1 1708 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-29T14:05:55Z\\nNo. of bitstreams: 1\\nDjadliMalchiodiFinal.pdf: 342979 bytes, checksum: fc2b0b8e4e01a5327ed8e01dc1bae6c5 (MD5) %0 Journal Article %J Adv. Math. 219 (2008) 780-837 %D 2008 %T Frobenius Manifolds and Central Invariants for the Drinfeld - Sokolov Bihamiltonian Structures %A Boris Dubrovin %A Liu Si-Qi %A Zhang Youjin %X The Drinfeld - Sokolov construction associates a hierarchy of bihamiltonian integrable systems with every untwisted affine Lie algebra. We compute the complete set of invariants of the related bihamiltonian structures with respect to the group of Miura type transformations. %B Adv. Math. 219 (2008) 780-837 %G en_US %U http://hdl.handle.net/1963/2523 %1 1595 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-11T12:52:04Z\\nNo. of bitstreams: 1\\n0710.3115v1.pdf: 569666 bytes, checksum: e3e72944ffd5f097ccaf975d2df90986 (MD5) %R 10.1016/j.aim.2008.06.009 %0 Journal Article %J Netw. Heterog. Media 3 (2008) 567-614 %D 2008 %T Globally stable quasistatic evolution in plasticity with softening %A Gianni Dal Maso %A Antonio DeSimone %A Maria Giovanna Mora %A Massimiliano Morini %X We study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is characterized by the following properties: global stability at each time and energy balance on each\\ntime interval. An example developed in detail compares the solutions obtained by this method with the ones provided by a vanishing viscosity approximation, and shows that only the latter capture a decreasing branch in the stress-strain response. %B Netw. Heterog. Media 3 (2008) 567-614 %G en_US %U http://hdl.handle.net/1963/1965 %1 2228 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-05-15T11:03:21Z\\nNo. of bitstreams: 1\\nDM-DeS-Mor-Mor-05-3-final.pdf: 395475 bytes, checksum: 5789494df44986207d416d5d1ea15d22 (MD5) %0 Journal Article %J Calc. Var. Partial Differential Equations 31 (2008) 137-145 %D 2008 %T Gradient bounds for minimizers of free discontinuity problems related to cohesive zone models in fracture mechanics %A Gianni Dal Maso %A Adriana Garroni %X In this note we consider a free discontinuity problem for a scalar function, whose energy depends also on the size of the jump. We prove that the gradient of every smooth local minimizer never exceeds a constant, determined only by the data of the problem. %B Calc. Var. Partial Differential Equations 31 (2008) 137-145 %G en_US %U http://hdl.handle.net/1963/1723 %1 2428 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-01-26T12:52:13Z\\nNo. of bitstreams: 1\\nmath.AP0507088.pdf: 132125 bytes, checksum: 444c743b7852d0f6e97bb318f49b4467 (MD5) %R 10.1007/s00526-006-0084-3 %0 Journal Article %J Russian Mathematical Surveys. Volume 63, Issue 6, 2008, Pages 999-1010 %D 2008 %T Hamiltonian partial differential equations and Frobenius manifolds %A Boris Dubrovin %X In the first part of this paper the theory of Frobenius manifolds\\r\\nis applied to the problem of classification of Hamiltonian systems of partial\\r\\ndifferential equations depending on a small parameter. Also developed is\\r\\na deformation theory of integrable hierarchies including the subclass of\\r\\nintegrable hierarchies of topological type. Many well-known examples\\r\\nof integrable hierarchies, such as the Korteweg–de Vries, non-linear\\r\\nSchr¨odinger, Toda, Boussinesq equations, and so on, belong to this\\r\\nsubclass that also contains new integrable hierarchies. Some of these new\\r\\nintegrable hierarchies may be important for applications. Properties of the\\r\\nsolutions to these equations are studied in the second part. Consideration\\r\\nis given to the comparative study of the local properties of perturbed and\\r\\nunperturbed solutions near a point of gradient catastrophe. A Universality\\r\\nConjecture is formulated describing the various types of critical behaviour\\r\\nof solutions to perturbed Hamiltonian systems near the point of gradient\\r\\ncatastrophe of the unperturbed solution. %B Russian Mathematical Surveys. Volume 63, Issue 6, 2008, Pages 999-1010 %I SISSA %G en %U http://hdl.handle.net/1963/6471 %1 6416 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T14:46:43Z\\nNo. of bitstreams: 1\\ndubrovin_2008_umn.pdf: 417000 bytes, checksum: 093ef887f6154d0c26771476cae72503 (MD5) %R 10.1070/RM2008v063n06ABEH004575 %0 Journal Article %J Comm. Math. Phys. 279 (2008) 77-116 %D 2008 %T The Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere %A Francesco D'Andrea %A Ludwik Dabrowski %A Giovanni Landi %X Equivariance under the action of Uq(so(5)) is used to compute the left regular and (chiral) spinorial representations of the algebra of the quantum Euclidean 4-sphere S^4_q. These representations are the constituents of a spectral triple on this sphere with a Dirac operator which is isospectral to the canonical one of the spin structure of the round undeformed four-sphere and which gives metric dimension four for the noncommutative geometry. Non-triviality of the geometry is proved by pairing the associated Fredholm module with an `instanton\\\' projection. A real structure which satisfies all required properties modulo a suitable ideal of `infinitesimals\\\' is also introduced. %B Comm. Math. Phys. 279 (2008) 77-116 %G en_US %U http://hdl.handle.net/1963/2567 %1 1553 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-01-18T11:00:40Z\\nNo. of bitstreams: 1\\n0611100v1.pdf: 351975 bytes, checksum: 8dd0f817683bd7782e5110ca6b585b91 (MD5) %R 10.1007/s00220-008-0420-x %0 Journal Article %J Rev. Math. Phys. 20 (2008) 979-1006 %D 2008 %T The Noncommutative Geometry of the Quantum Projective Plane %A Francesco D'Andrea %A Ludwik Dabrowski %A Giovanni Landi %X We study the spectral geometry of the quantum projective plane CP^2_q. In particular, we construct a Dirac operator which gives a 0^+ summable triple, equivariant under U_q(su(3)). %B Rev. Math. Phys. 20 (2008) 979-1006 %G en_US %U http://hdl.handle.net/1963/2548 %1 1571 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-01-14T08:17:29Z\\nNo. of bitstreams: 1\\n0712.3401v1.pdf: 305773 bytes, checksum: 85ef21e8ac9485f12064685740331fc2 (MD5) %R 10.1142/S0129055X08003493 %0 Journal Article %J J. Nonlinear Sci. 18 (2008) 277-302 %D 2008 %T Optimal Strokes for Low Reynolds Number Swimmers: An Example %A François Alouges %A Antonio DeSimone %A Aline Lefebvre %X Swimming, i.e., being able to advance in the absence of external forces by performing cyclic shape changes, is particularly demanding at low Reynolds numbers. This is the regime of interest for micro-organisms and micro- or nano-robots. We focus in this paper on a simple yet representative example: the three-sphere swimmer of Najafi and Golestanian (Phys. Rev. E, 69, 062901-062904, 2004). For this system, we show how to cast the problem of swimming in the language of control theory, prove global controllability (which implies that the three-sphere swimmer can indeed swim), and propose a numerical algorithm to compute optimal strokes (which turn out to be suitably defined sub-Riemannian geodesics). %B J. Nonlinear Sci. 18 (2008) 277-302 %I Springer %G en_US %U http://hdl.handle.net/1963/4006 %1 396 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-08-26T10:49:24Z\\nNo. of bitstreams: 1\\nADL2008a.pdf: 273047 bytes, checksum: 36ba2c2914fff62c05124f1ac1453733 (MD5) %R 10.1007/s00332-007-9013-7 %0 Journal Article %J Math. Models Methods Appl. Sci. 18 (2008) 1-20 %D 2008 %T Relaxation of some transversally isotropic energies and applications to smectic A elastomers %A James Adams %A Sergio Conti %A Antonio DeSimone %A Georg Dolzmann %B Math. Models Methods Appl. Sci. 18 (2008) 1-20 %G en_US %U http://hdl.handle.net/1963/1912 %1 2325 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-02-02T14:15:25Z\\nNo. of bitstreams: 1\\nsma_Preprint_SISSA.pdf: 271875 bytes, checksum: eb0cf2c367021718506356a73bda219a (MD5) %R 10.1142/S0218202508002693 %0 Journal Article %J Arch. Ration. Mech. Anal. 189 (2008) 469-544 %D 2008 %T A vanishing viscosity approach to quasistatic evolution in plasticity with softening %A Gianni Dal Maso %A Antonio DeSimone %A Maria Giovanna Mora %A Massimiliano Morini %X We deal with quasistatic evolution problems in plasticity with softening, in the framework of small strain associative elastoplasticity. The presence of a nonconvex term due to the softening phenomenon requires a nontrivial extension of the variational framework for rate-independent problems to the case of a nonconvex energy functional. We argue that, in this case, the use of global minimizers in the corresponding incremental problems is not justified from the mechanical point of view. Thus, we analize a different selection criterion for the solutions of the quasistatic evolution problem, based on a viscous approximation. This leads to a generalized formulation in terms of Young measures, developed in the first part of the paper. In the second part we apply our approach to some concrete examples. %B Arch. Ration. Mech. Anal. 189 (2008) 469-544 %G en_US %U http://hdl.handle.net/1963/1844 %1 2373 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-07-21T11:03:58Z\\nNo. of bitstreams: 1\\nmath.AP-0606718.pdf: 563956 bytes, checksum: 80e8ac8a9120c15b452698af3abc77d1 (MD5) %R 10.1007/s00205-008-0117-5 %0 Journal Article %J Comm. Math. Phys. 271 (2007) 289-373 %D 2007 %T Canonical structure and symmetries of the Schlesinger equations %A Boris Dubrovin %A Marta Mazzocco %X The Schlesinger equations S (n,m) describe monodromy preserving deformations of order m Fuchsian systems with n+1 poles. They can be considered as a family of commuting time-dependent Hamiltonian systems on the direct product of n copies of m×m matrix algebras equipped with the standard linear Poisson bracket. In this paper we present a new canonical Hamiltonian formulation ofthe general Schlesinger equations S (n,m) for all n, m and we compute the action of the symmetries of the Schlesinger equations in these coordinates. %B Comm. Math. Phys. 271 (2007) 289-373 %G en_US %U http://hdl.handle.net/1963/1997 %1 2199 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-08-30T08:59:18Z\\nNo. of bitstreams: 1\\nmathDG0311261v4.pdf: 748258 bytes, checksum: c550bb118062fa82741da16a2735b68f (MD5) %R 10.1007/s00220-006-0165-3 %0 Report %D 2007 %T The complete one-loop spin chain for N=2 Super-Yang-Mills %A Paolo Di Vecchia %A Alessandro Tanzini %X We show that the complete planar one-loop mixing matrix of the N=2 Super Yang--Mills theory can be obtained from a reduction of that of the N=4 theory. For composite operators of scalar fields, this yields an anisotropic XXZ spin chain, whose spectrum of excitations displays a mass gap. %G en_US %U http://hdl.handle.net/1963/2309 %1 1707 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-29T14:28:13Z\\nNo. of bitstreams: 1\\n0412283v1.pdf: 110673 bytes, checksum: 9f881078e3eb69765e2c6e294569fd70 (MD5) %0 Journal Article %J Eur. Phys. J. E 24 (2007) 303-310 %D 2007 %T Critical voltages and blocking stresses in nematic gels %A Antonio DeSimone %A Antonio Di Carlo %A Luciano Teresi %X We use a recently proposed model to study the dynamics of director remodeling in nematic gels under combined electro-mechanical loading. Focusing on a model specimen, we describe the critical volt-ages that must be exceeded to achieve mesogen reorientation, and the blocking stresses that prevent alignment of the nematic mesogens with the electric field. The corresponding phase diagram shows that the dynamic thresholds defined above are different from those predicted on the sole basis of energetics. Multistep loading programs are used to explore the energy landscape of our model specimen, showing the existence of multiple local minima under the same voltage and applied stress. This leads us to conclude that hysteresis should be expected in the electro-mechanical response of nematic gels. %B Eur. Phys. J. E 24 (2007) 303-310 %G en_US %U http://hdl.handle.net/1963/2553 %1 1566 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-01-15T10:18:57Z\\nNo. of bitstreams: 1\\nBlockStress-Preprint.pdf: 477394 bytes, checksum: 8cab00d44de821fc24a7ef2b832ea48c (MD5) %R 10.1140/epje/i2007-10240-2 %0 Journal Article %J J. Noncomm. Geom. 1 (2007) 213-239 %D 2007 %T Dirac operators on all Podles quantum spheres %A Francesco D'Andrea %A Ludwik Dabrowski %A Giovanni Landi %A Elmar Wagner %X We construct spectral triples on all Podles quantum spheres. These noncommutative geometries are equivariant for a left action of $U_q(su(2))$ and are regular, even and of metric dimension 2. They are all isospectral to the undeformed round geometry of the 2-sphere. There is also an equivariant real structure for which both the commutant property and the first order condition for the Dirac operators are valid up to infinitesimals of arbitrary order. %B J. Noncomm. Geom. 1 (2007) 213-239 %G en_US %U http://hdl.handle.net/1963/2177 %1 2067 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-04T09:28:47Z\\nNo. of bitstreams: 1\\n0606480v2.pdf: 249691 bytes, checksum: b7ae4969eee716046a815f5e66a249fb (MD5) %R 10.4171/JNCG/5 %0 Report %D 2007 %T A new model for contact angle hysteresis %A Antonio DeSimone %A Natalie Gruenewald %A Felix Otto %X We present a model which explains several experimental observations relating contact angle hysteresis with surface roughness. The model is based on the balance between released energy and dissipation, and it describes the stick-slip behavior of drops on a rough surface using ideas similar to those employed in dry friction, elasto-plasticity and fracture mechanics. The main results of our analysis are formulas giving the interval of stable contact angles as a function of the surface roughness. These formulas show that the difference between advancing and receding angles is much larger for a drop in complete contact with the substrate (Wenzel drop) than for one whose cavities are filled with air (Cassie-Baxter drop). This fact is used as the key tool to interpret the experimental evidence. %B Netw. Heterog. Media 2 (2007) 211-225 %G en_US %U http://hdl.handle.net/1963/1848 %1 2369 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-07-26T09:50:36Z\\nNo. of bitstreams: 1\\n37-2006M.pdf: 313357 bytes, checksum: ac507409dc660fba3ec468e50c4fe9b1 (MD5) %0 Thesis %D 2007 %T Noncommutative geometry and quantum group symmetries %A Francesco D'Andrea %K Noncommutative geometry %X It is a widespread belief that mathematics originates from the desire to understand (and eventually to formalize) some aspects of the real world. Quoting [Man07], «we are doing mathematics in order to understand, create, and handle things, and perhaps this understanding is mathematics» . Let me thus begin with a brief discussion of the physical ideas that motivated the development of Noncommutative Geometry and Quantum Group Theory - the areas of mathematics to which this dissertation belongs. Some physicists believe, and Einstein himself expressed this view in [Ein98a], that physics progresses in stages: there is no `final\\\' theory of Nature, but simply a sequence of theories which provide more and more accurate descriptions of the real world... %I SISSA %G en %U http://hdl.handle.net/1963/5269 %1 5093 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-01-24T08:56:37Z\\nNo. of bitstreams: 1\\nPhD_D\\\'Andrea_Francesco.pdf: 1636959 bytes, checksum: 0d673f9b1d591a36bd4883bedc49422a (MD5) %0 Journal Article %J NoDEA 13 (2007) 713-734 %D 2007 %T On a notion of unilateral slope for the Mumford-Shah functional %A Gianni Dal Maso %A Rodica Toader %X In this paper we introduce a notion of unilateral slope for the Mumford-Shah functional, and provide an explicit formula in the case of smooth cracks. We show that the slope is not lower semicontinuous and study the corresponding relaxed functional. %B NoDEA 13 (2007) 713-734 %G en_US %U http://hdl.handle.net/1963/2059 %1 2137 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-06T14:02:51Z\\nNo. of bitstreams: 1\\n0410525v1.pdf: 214576 bytes, checksum: 3722f413401cdb51f778a8c15eeebe71 (MD5) %R 10.1007/s00030-006-4054-4 %0 Journal Article %J J. Phys. A 40 (2007) 14819-14842 %D 2007 %T The number of eigenvalues of three-particle Schrödinger operators on lattices %A Sergio Albeverio %A Gianfausto Dell'Antonio %A Saidakhmat N. Lakaev %X We consider the Hamiltonian of a system of three quantum mechanical particles (two identical fermions and boson)on the three-dimensional lattice $\\\\Z^3$ and interacting by means of zero-range attractive potentials. We describe the location and structure of the essential spectrum of the three-particle discrete Schr\\\\\\\"{o}dinger operator $H_{\\\\gamma}(K),$ $K$ being the total quasi-momentum and $\\\\gamma>0$ the ratio of the mass of fermion and boson.\\nWe choose for $\\\\gamma>0$ the interaction $v(\\\\gamma)$ in such a way the system consisting of one fermion and one boson has a zero energy resonance.\\nWe prove for any $\\\\gamma> 0$ the existence infinitely many eigenvalues of the operator $H_{\\\\gamma}(0).$ We establish for the number $N(0,\\\\gamma; z;)$ of eigenvalues lying below $z<0$ the following asymptotics $$ \\\\lim_{z\\\\to 0-}\\\\frac{N(0,\\\\gamma;z)}{\\\\mid \\\\log \\\\mid z\\\\mid \\\\mid}={U} (\\\\gamma) .$$ Moreover, for all nonzero values of the quasi-momentum $K \\\\in T^3 $ we establish the finiteness of the number $ N(K,\\\\gamma;\\\\tau_{ess}(K))$ of eigenvalues of $H(K)$ below the bottom of the essential spectrum and we give an asymptotics for the number $N(K,\\\\gamma;0)$ of eigenvalues below zero. %B J. Phys. A 40 (2007) 14819-14842 %G en_US %U http://hdl.handle.net/1963/2576 %1 1545 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-01-28T14:20:38Z\\nNo. of bitstreams: 1\\n0703191v1.pdf: 254244 bytes, checksum: a662f118f430d7b424e751fa5f07ed92 (MD5) %R 10.1088/1751-8113/40/49/015 %0 Report %D 2007 %T Quasistatic crack growth for a cohesive zone model with prescribed crack path %A Gianni Dal Maso %A Chiara Zanini %X In this paper we study the quasistatic crack growth for a cohesive zone model. We assume that the crack path is prescribed and we study the time evolution of the crack in the framework of the variational theory of rate-independent processes. %B Proc. Roy. Soc. Edinburgh Sect. A 137 (2007) 253-279 %G en_US %U http://hdl.handle.net/1963/1686 %1 2447 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2005-06-20T12:05:32Z\\nNo. of bitstreams: 1\\nDM-Zan-04.pdf: 312529 bytes, checksum: 2373a684663d7901c85daad77c7aa8b6 (MD5) %R 10.1017/S030821050500079X %0 Journal Article %J Milan J. Math. 75 (2007) 117-134 %D 2007 %T Quasistatic evolution problems for pressure-sensitive plastic materials %A Gianni Dal Maso %A Alexey Demyanov %A Antonio DeSimone %X We study quasistatic evolution problems for pressure-sensitive plastic materials in the context of small strain associative perfect plasticity. %B Milan J. Math. 75 (2007) 117-134 %G en_US %U http://hdl.handle.net/1963/1962 %1 2231 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-05-15T10:32:12Z\\nNo. of bitstreams: 1\\nSissa27_2007M.pdf: 223083 bytes, checksum: a4cdbb7a1018403355c560749680e47a (MD5) %R 10.1007/s00032-007-0071-y %0 Journal Article %J Differential equations and quantum groups, IRMA Lect. Math. Theor. Phys. 9 (2007) 157-187 %D 2007 %T On the reductions and classical solutions of the Schlesinger equations %A Boris Dubrovin %A Marta Mazzocco %X The Schlesinger equations S(n,m) describe monodromy preserving\\r\\ndeformations of order m Fuchsian systems with n+1 poles. They\\r\\ncan be considered as a family of commuting time-dependent Hamiltonian\\r\\nsystems on the direct product of n copies of m×m matrix algebras\\r\\nequipped with the standard linear Poisson bracket. In this paper we address\\r\\nthe problem of reduction of particular solutions of “more complicated”\\r\\nSchlesinger equations S(n,m) to “simpler” S(n′,m′) having n′ < n\\r\\nor m′ < m. %B Differential equations and quantum groups, IRMA Lect. Math. Theor. Phys. 9 (2007) 157-187 %I SISSA %G en %U http://hdl.handle.net/1963/6472 %1 6418 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T14:52:15Z\\nNo. of bitstreams: 1\\ndubrovin_mazzocco_2007_irma.pdf: 300042 bytes, checksum: 85252eedf7d0fbbdf06061c20b471d44 (MD5) %0 Report %D 2007 %T Soft elasticity and microstructure in smectic C elastomers %A Antonio DeSimone %A James Adams %A Sergio Conti %X Smectic C elastomers are layered materials exhibiting a solid-like elastic response along the layer normal and a rubbery one in the plane. The set of strains minimizing the elastic energy contains a one-parameter family of simple stretches associated with an internal degree of freedom, coming from the in-plane component of the director. We investigate soft elasticity and the corresponding microstructure by determining the quasiconvex hull of the set , and use this to propose experimental tests that should make the predicted soft response observable. %B Contin. Mech. Thermodyn. 18 (2007) 319-334 %G en_US %U http://hdl.handle.net/1963/1811 %1 2403 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-04-12T09:42:24Z\\nNo. of bitstreams: 1\\nsissa05M-06.pdf: 394760 bytes, checksum: 95c4183d6cb1210bf2a689ae083a3cb7 (MD5) %R 10.1007/s00161-006-0031-8 %0 Journal Article %J NoDEA Nonlinear Differential Equations Appl. 14 (2007) 569-592 %D 2007 %T Stability of front tracking solutions to the initial and boundary value problem for systems of conservation laws %A Andrea Marson %A Carlotta Donadello %B NoDEA Nonlinear Differential Equations Appl. 14 (2007) 569-592 %G en_US %U http://hdl.handle.net/1963/1769 %1 2775 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-28T10:29:02Z\\nNo. of bitstreams: 1\\n68M.pdf: 209186 bytes, checksum: 79dcb94eb1405cbadb411592b2cffe66 (MD5) %R 10.1007/s00030-007-5010-7 %0 Report %D 2007 %T Time-dependent systems of generalized Young measures %A Gianni Dal Maso %A Antonio DeSimone %A Maria Giovanna Mora %A Massimiliano Morini %X In this paper some new tools for the study of evolution problems in the framework of Young measures are introduced. A suitable notion of time-dependent system of generalized Young measures is defined, which allows to extend the classical notions of total variation and absolute continuity with respect to time, as well as the notion of time derivative. The main results are a Helly type theorem for sequences of systems of generalized Young measures and a theorem about the existence of the time derivative for systems with bounded variation with respect to time. %B Netw. Heterog. Media 2 (2007) 1-36 %G en_US %U http://hdl.handle.net/1963/1795 %1 2749 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-04-04T13:16:42Z\\nNo. of bitstreams: 1\\n98M-2005.pdf: 339547 bytes, checksum: 695874ce74733dc0020a7e357f04cb1b (MD5) %0 Journal Article %J Calc. Var. Partial Differential Equations 27 (2006) 233-253 %D 2006 %T 2-d stability of the Néel wall %A Antonio DeSimone %A Hans Knuepfer %A Felix Otto %X We are interested in thin-film samples in micromagnetism, where the magnetization m is a 2-d unit-length vector field. More precisely we are interested in transition layers which connect two opposite magnetizations, so called Néel walls. %B Calc. Var. Partial Differential Equations 27 (2006) 233-253 %G en_US %U http://hdl.handle.net/1963/2194 %1 2050 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-10T12:14:45Z\\nNo. of bitstreams: 1\\nstability.pdf: 226255 bytes, checksum: dec90ada941ac865d9451848ca2faa5f (MD5) %R 10.1007/s00526-006-0019-z %0 Report %D 2006 %T A Canonical Frame for Nonholonomic Rank Two Distributions of Maximal Class %A Boris Doubrov %A Igor Zelenko %X In 1910 E. Cartan constructed the canonical frame and found the most symmetric case for maximally nonholonomic rank 2 distributions in R5. We solve the analogous problems for rank 2 distributions in Rn for arbitrary n > 5. Our method is a kind of symplectification of the problem and it is completely different from the Cartan method of equivalence. %B C. R. Math. Acad. Sci. Paris 342 (2006) 589-594 %G en_US %U http://hdl.handle.net/1963/1712 %1 2439 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-01-18T10:08:04Z\\nNo. of bitstreams: 1\\nmath.DG0504319.pdf: 158321 bytes, checksum: 4a76e9fa42a9ea4440d0fcd628df9c34 (MD5) %R 10.1016/j.crma.2006.02.010 %0 Journal Article %J Int. J. Mod. Phys. A 21 (2006) 3133-3150 %D 2006 %T A cyclic integral on k-Minkowski noncommutative space-time %A Alessandra Agostini %A Giovanni Amelino-Camelia %A Michele Arzano %A Francesco D'Andrea %X We examine some alternative possibilities for an action functional for $\\\\kappa$-Minkowski noncommutative spacetime, with an approach which should be applicable to other spacetimes with coordinate-dependent commutators of the spacetime coordinates ($[x_\\\\mu,x_\\\\nu]=f_{\\\\mu,\\\\nu}(x)$). Early works on $\\\\kappa$-Minkowski focused on $\\\\kappa$-Poincar\\\\\\\'e covariance and the dependence of the action functional on the choice of Weyl map, renouncing to invariance under cyclic permutations of the factors composing the argument of the action functional. A recent paper (hep-th/0307149), by Dimitrijevic, Jonke, Moller, Tsouchnika, Wess and Wohlgenannt, focused on a specific choice of Weyl map and, setting aside the issue of $\\\\kappa$-Poincar\\\\\\\'e covariance of the action functional, introduced in implicit form a cyclicity-inducing measure. We provide an explicit formula for (and derivation of) a choice of measure which indeed ensures cyclicity of the action functional, and we show that the same choice of measure is applicable to all the most used choices of Weyl map. We find that this ``cyclicity-inducing measure\\\'\\\' is not covariant under $\\\\kappa$-Poincar\\\\\\\'e transformations. We also notice that the cyclicity-inducing measure can be straightforwardly derived using a map which connects the $\\\\kappa$-Minkowski spacetime coordinates and the spacetime coordinates of a ``canonical\\\'\\\' noncommutative spacetime, with coordinate-independent commutators. %B Int. J. Mod. Phys. A 21 (2006) 3133-3150 %G en_US %U http://hdl.handle.net/1963/2158 %1 2086 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-02T08:56:14Z\\nNo. of bitstreams: 1\\n0407227v1.pdf: 219700 bytes, checksum: 4a7f6665bddfb66793e39aa4a8e3ce25 (MD5) %R 10.1142/S0217751X06031077 %0 Report %D 2006 %T Extended affine Weyl groups and Frobenius manifolds -- II %A Boris Dubrovin %A Zhang Youjin %A Zuo Dafeng %X For the root system of type $B_l$ and $C_l$, we generalize the result of \\\\cite{DZ1998} by showing the existence of a Frobenius manifold structure on the orbit space of the extended affine Weyl group that corresponds to any vertex of the Dynkin diagram instead of a particular choice of \\\\cite{DZ1998}. %G en_US %U http://hdl.handle.net/1963/1787 %1 2757 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-30T13:34:27Z\\nNo. of bitstreams: 1\\n90FM-2005.pdf: 254524 bytes, checksum: abdf833c0cf0b01fb79663489dd6acc2 (MD5) %0 Journal Article %J Comm. Pure Appl. Math. 59 (2006) 559-615 %D 2006 %T On Hamiltonian perturbations of hyperbolic systems of conservation laws I: quasitriviality of bihamiltonian perturbations %A Boris Dubrovin %A Liu Si-Qi %A Zhang Youjin %X We study the general structure of formal perturbative solutions to the Hamiltonian perturbations of spatially one-dimensional systems of hyperbolic PDEs. Under certain genericity assumptions it is proved that any bihamiltonian perturbation can be eliminated in all orders of the perturbative expansion by a change of coordinates on the infinite jet space depending rationally on the derivatives. The main tools is in constructing of the so-called quasi-Miura transformation of jet coordinates eliminating an arbitrary deformation of a semisimple bihamiltonian structure of hydrodynamic type (the quasitriviality theorem). We also describe, following \\\\cite{LZ1}, the invariants of such bihamiltonian structures with respect to the group of Miura-type transformations depending polynomially on the derivatives. %B Comm. Pure Appl. Math. 59 (2006) 559-615 %G en_US %U http://hdl.handle.net/1963/2535 %1 1583 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-18T13:01:41Z\\nNo. of bitstreams: 1\\n0410027v2.pdf: 508002 bytes, checksum: 4e8fc8db5fc7512dd54eb832cc52192d (MD5) %R 10.1002/cpa.20111 %0 Report %D 2006 %T On Hamiltonian perturbations of hyperbolic systems of conservation laws, II: universality of critical behaviour %A Boris Dubrovin %X Hamiltonian perturbations of the simplest hyperbolic equation $u_t + a(u) u_x=0$ are studied. We argue that the behaviour of solutions to the perturbed equation near the point of gradient catastrophe of the unperturbed one should be essentially independent on the choice of generic perturbation neither on the choice of generic solution. Moreover, this behaviour is described by a special solution to an integrable fourth order ODE. %B Comm. Math. Phys. 267 (2006) 117-139 %G en_US %U http://hdl.handle.net/1963/1786 %1 2758 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-30T13:22:52Z\\nNo. of bitstreams: 1\\n89FM-2005.pdf: 250067 bytes, checksum: 1e057f524c879ec57fa25833b141b6b6 (MD5) %R 10.1007/s00220-006-0021-5 %0 Report %D 2006 %T Local Index Formula on the Equatorial Podles Sphere %A Francesco D'Andrea %A Ludwik Dabrowski %X We discuss spectral properties of the equatorial Podles sphere. As a preparation we also study the `degenerate\\\' (i.e. $q=0$) case (related to the quantum disk). We consider two different spectral triples: one related to the Fock representation of the Toeplitz algebra and the isopectral one.... %B Lett. Math. Phys. 75 (2006) 235-254 %G en_US %U http://hdl.handle.net/1963/1782 %1 2762 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-30T11:54:30Z\\nNo. of bitstreams: 1\\n85FM-2005.pdf: 241084 bytes, checksum: 22ea5eb072a67393221cdb0284ab323d (MD5) %R 10.1007/s11005-005-0047-1 %0 Journal Article %J Arch. Ration. Mech. Anal. 180 (2006) 237-291 %D 2006 %T Quasistatic evolution problems for linearly elastic-perfectly plastic materials %A Gianni Dal Maso %A Antonio DeSimone %A Maria Giovanna Mora %X The problem of quasistatic evolution in small strain associative elastoplasticity is studied in the framework of the variational theory for rate-independent processes. Existence of solutions is proved through the use of incremental variational problems in spaces of functions with bounded deformation. This provides a new approximation result for the solutions of the quasistatic evolution problem, which are shown to be absolutely continuous in time. Four equivalent formulations of the problem in rate form are derived. A strong formulation of the flow rule is obtained by introducing a precise definition of the stress on the singular set of the plastic strain. %B Arch. Ration. Mech. Anal. 180 (2006) 237-291 %G en_US %U http://hdl.handle.net/1963/2129 %1 2114 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-18T10:14:12Z\\nNo. of bitstreams: 1\\n0412212v1.pdf: 419970 bytes, checksum: fa4e3c2a5db22bfa28aa4f682cb55da4 (MD5) %R 10.1007/s00205-005-0407-0 %0 Book Section %B The science of hysteresis / eds. Giorgio Bertotti, Isaak D. Mayergoyz. - Amsterdam: Elsevier, 2006. Vol.2, 269-381. %D 2006 %T Recent analytical developments in micromagnetics %A Antonio DeSimone %A Robert V. Kohn %A Stefan Müller %A Felix Otto %B The science of hysteresis / eds. Giorgio Bertotti, Isaak D. Mayergoyz. - Amsterdam: Elsevier, 2006. Vol.2, 269-381. %@ 978-0-12-480874-4 %G en_US %U http://hdl.handle.net/1963/2230 %1 2014 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-15T15:16:57Z\\nNo. of bitstreams: 1\\nDKMO.pdf: 1644450 bytes, checksum: 4c1079e4854e372d31af9a285f87f400 (MD5) %0 Journal Article %J J. Math. Phys. 47 (2006) 062105 %D 2006 %T Spectral geometry of k-Minkowski space %A Francesco D'Andrea %XAfter recalling Snyder's idea of using vector fields over a smooth manifold as "coordinates on a noncommutative space", we discuss a two dimensional toy-model whose "dual" noncommutative coordinates form a Lie algebra: this is the well known $\kappa$-Minkowski space. We show how to improve Snyder's idea using the tools of quantum groups and noncommutative geometry. We find a natural representation of the coordinate algebra of $\kappa$-Minkowski as linear operators on an Hilbert space study its "spectral properties" and discuss how to obtain a Dirac operator for this space. We describe two Dirac operators. The first is associated with a spectral triple. We prove that the cyclic integral of M. Dimitrijevic et al. can be obtained as Dixmier trace associated to this triple. The second Dirac operator is equivariant for the action of the quantum Euclidean group, but it has unbounded commutators with the algebra.

%B J. Math. Phys. 47 (2006) 062105 %G en_US %U http://hdl.handle.net/1963/2131 %1 2112 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-18T11:48:16Z\\nNo. of bitstreams: 1\\n0503012v4.pdf: 270606 bytes, checksum: b96bcb17609481fbf7d542681a2c0cfa (MD5) %R 10.1063/1.2204808 %0 Book Section %B Geometry, topology, and mathematical physics : S.P. Novikov\\\'s seminar : 2006-2007 / V.M. Buchstaber, I.M. Krichever, editors. - Providence, R.I. : American Mathematical Society, 2008. - pages : 59-109 %D 2006 %T On universality of critical behaviour in Hamiltonian PDEs %A Boris Dubrovin %X Our main goal is the comparative study of singularities of solutions to\\r\\nthe systems of rst order quasilinear PDEs and their perturbations containing higher\\r\\nderivatives. The study is focused on the subclass of Hamiltonian PDEs with one\\r\\nspatial dimension. For the systems of order one or two we describe the local structure\\r\\nof singularities of a generic solution to the unperturbed system near the point of\\r\\n\\\\gradient catastrophe\\\" in terms of standard objects of the classical singularity theory;\\r\\nwe argue that their perturbed companions must be given by certain special solutions\\r\\nof Painlev e equations and their generalizations. %B Geometry, topology, and mathematical physics : S.P. Novikov\\\'s seminar : 2006-2007 / V.M. Buchstaber, I.M. Krichever, editors. - Providence, R.I. : American Mathematical Society, 2008. - pages : 59-109 %I American Mathematical Society %@ 978-0-8218-4674-2 %G en %U http://hdl.handle.net/1963/6491 %1 6417 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T14:49:10Z\\nNo. of bitstreams: 1\\ndubrovin_2008_ams.pdf: 671674 bytes, checksum: 08be98e78f30199030c7a4062cfcb8cf (MD5) %0 Report %D 2006 %T Variational problems in fracture mechanics %A Gianni Dal Maso %X We present some recent existence results for the variational model of crack growth in brittle materials proposed by Francfort and Marigo in 1998. These results, obtained in collaboration with Francfort and Toader, cover the case of arbitrary space dimension with a general quasiconvex bulk energy and with prescribed boundary deformations and applied loads. %G en_US %U http://hdl.handle.net/1963/1816 %1 2398 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-04-18T12:50:25Z\\nNo. of bitstreams: 1\\nmath.AP0602614.pdf: 122115 bytes, checksum: 8a582db939c08c52510bcc1c7da7c563 (MD5) %0 Book Section %B Encyclopedia of Mathematical Physics. Vol 1 A : A-C. Oxford: Elsevier, 2006, p. 438-447 %D 2006 %T WDVV equations and Frobenius manifolds %A Boris Dubrovin %B Encyclopedia of Mathematical Physics. Vol 1 A : A-C. Oxford: Elsevier, 2006, p. 438-447 %I SISSA %@ 0125126611 %G en %U http://hdl.handle.net/1963/6473 %1 6419 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T14:55:56Z\\nNo. of bitstreams: 1\\ndubrovin_2006_enc.pdf: 16392102 bytes, checksum: 90fed38af94f1692c7c4375ca8bf30c3 (MD5) %0 Journal Article %J J. Phys. A 38 (2005) 4769-4781 %D 2005 %T Decay of a bound state under a time-periodic perturbation: a toy case %A Michele Correggi %A Gianfausto Dell'Antonio %X We study the time evolution of a three dimensional quantum particle, initially in a bound state, under the action of a time-periodic zero range interaction with ``strength\\\'\\\' (\\\\alpha(t)). Under very weak generic conditions on the Fourier coefficients of (\\\\alpha(t)), we prove complete ionization as (t \\\\to \\\\infty). We prove also that, under the same conditions, all the states of the system are scattering states. %B J. Phys. A 38 (2005) 4769-4781 %G en_US %U http://hdl.handle.net/1963/2298 %1 1718 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-25T08:22:58Z\\nNo. of bitstreams: 1\\n0408003v2.pdf: 207599 bytes, checksum: 256b29c96ea071184e9455fd1dd92717 (MD5) %R 10.1088/0305-4470/38/22/002 %0 Journal Article %J Commun. Math. Phys. 259 (2005) 729-759 %D 2005 %T The Dirac operator on SU_q(2) %A Ludwik Dabrowski %A Giovanni Landi %A Andrzej Sitarz %A Walter van Suijlekom %A Joseph C. Varilly %X We construct a 3^+ summable spectral triple (A(SU_q(2)),H,D) over the quantum group SU_q(2) which is equivariant with respect to a left and a right action of U_q(su(2)). The geometry is isospectral to the classical case since the spectrum of the operator D is the same as that of the usual Dirac operator on the 3-dimensional round sphere. The presence of an equivariant real structure J demands a modification in the axiomatic framework of spectral geometry, whereby the commutant and first-order properties need be satisfied only modulo infinitesimals of arbitrary high order. %B Commun. Math. Phys. 259 (2005) 729-759 %I Springer %G en %U http://hdl.handle.net/1963/4425 %1 4175 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-04T08:01:47Z No. of bitstreams: 1 math_0411609v2.pdf: 293099 bytes, checksum: cfa2846ded2ecf161e83f4269b65e9b2 (MD5) %R 10.1007/s00220-005-1383-9 %0 Journal Article %J C. R. Acad. Sci. Paris, Ser. I 340 (2005) 341-346. %D 2005 %T A fourth order uniformization theorem on some four manifolds with large total Q-curvature %A Zindine Djadli %A Andrea Malchiodi %X Given a four-dimensional manifold (M,g), we study the existence of a conformal metric for which the Q-curvature, associated to a conformally invariant fourth-order operator (the Paneitz operator), is constant. Using a topological argument, we obtain a new result in cases which were still open. %B C. R. Acad. Sci. Paris, Ser. I 340 (2005) 341-346. %I Elsevier %G en %U http://hdl.handle.net/1963/4868 %1 4649 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-20T14:43:43Z\\nNo. of bitstreams: 1\\nexistencep81.pdf: 151457 bytes, checksum: 024bd42cba2f35fe4c206a1ef0f9a125 (MD5) %R 10.1016/j.crma.2005.01.013 %0 Journal Article %J Comm. Math. Phys. 257 (2005) 169-192 %D 2005 %T Ionization for Three Dimensional Time-dependent Point Interactions %A Michele Correggi %A Gianfausto Dell'Antonio %A Rodolfo Figari %A Andrea Mantile %X We study the time evolution of a three dimensional quantum particle under the action of a time-dependent point interaction fixed at the origin. We assume that the ``strength\\\'\\\' of the interaction (\\\\alpha(t)) is a periodic function with an arbitrary mean. Under very weak conditions on the Fourier coefficients of (\\\\alpha(t)), we prove that there is complete ionization as (t \\\\to \\\\infty), starting from a bound state at time (t = 0). Moreover we prove also that, under the same conditions, all the states of the system are scattering states. %B Comm. Math. Phys. 257 (2005) 169-192 %G en_US %U http://hdl.handle.net/1963/2297 %1 1719 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-25T08:14:45Z\\nNo. of bitstreams: 1\\n0402011v2.pdf: 306766 bytes, checksum: 7efb2bcceb4c2699d662ae1af9e7dd76 (MD5) %R 10.1007/s00220-005-1293-x %0 Journal Article %J K-Theory 35 (2005) 375-394 %D 2005 %T The local index formula for SUq(2) %A Walter van Suijlekom %A Ludwik Dabrowski %A Giovanni Landi %A Andrzej Sitarz %A Joseph C. Varilly %X We discuss the local index formula of Connes-Moscovici for the isospectral noncommutative geometry that we have recently constructed on quantum SU(2). We work out the cosphere bundle and the dimension spectrum as well as the local cyclic cocycles yielding the index formula. %B K-Theory 35 (2005) 375-394 %G en_US %U http://hdl.handle.net/1963/1713 %1 2438 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-01-18T10:14:50Z\\nNo. of bitstreams: 1\\nmath.QA0501287.pdf: 189281 bytes, checksum: 75a780cbe958f6093e340102ad9bf176 (MD5) %R 10.1007/s10977-005-3116-4 %0 Journal Article %J Arch. Ration. Mech. Anal. 176 (2005) 165-225 %D 2005 %T Quasistatic Crack Growth in Nonlinear Elasticity %A Gianni Dal Maso %A Gilles A. Francfort %A Rodica Toader %X In this paper, we prove a new existence result for a variational model of crack growth in brittle materials proposed in [15]. We consider the case of $n$-dimensional finite elasticity, for an arbitrary $n\\\\ge1$, with a quasiconvex bulk energy and with prescribed boundary deformations and applied loads, both depending on time. %B Arch. Ration. Mech. Anal. 176 (2005) 165-225 %G en_US %U http://hdl.handle.net/1963/2293 %1 1723 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-24T09:12:09Z\\nNo. of bitstreams: 1\\n0401196v1.pdf: 664295 bytes, checksum: cb1000c44e6ae356984e24b55ee97117 (MD5) %R 10.1007/s00205-004-0351-4 %0 Journal Article %J Comput. Methods Appl. Mech. Engrg. 194 (2005) 2534-2549 %D 2005 %T Self-similar folding patterns and energy scaling in compressed elastic sheets %A Sergio Conti %A Antonio DeSimone %A Stefan Müller %X Thin elastic sheets under isotropic compression, such as for example blisters formed by thin films which debonded from the substrate, can exhibit remarkably complex folding patterns. We discuss the scaling of the elastic energy with respect to the film thickness, and show that in certain regimes the optimal energy scaling can be reached\\nby self-similar folding patterns that refine towards the boundary, in agreement with experimental observations. We then extend the analysis\\nto anisotropic compression, and discuss a simplified scalar model which suggests the presence of a transition between a regime where\\nthe deformation is governed by global properties of the domain and another one where the direction of maximal compression dominates and the scale of the folds is mainly determined by the distance to the boundary in the direction of the folds themselves. %B Comput. Methods Appl. Mech. Engrg. 194 (2005) 2534-2549 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3000 %1 1333 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-01T10:37:14Z\\nNo. of bitstreams: 1\\npreprint2004_3.pdf: 907333 bytes, checksum: 2b22c209b91ba2ddacc1a1c14a9054a2 (MD5) %R 10.1016/j.cma.2004.07.044 %0 Generic %D 2005 %T Solutions of Neumann problems in domains with cracks and applications to fracture mechanics %A Gianni Dal Maso %G en_US %U http://hdl.handle.net/1963/1684 %1 79 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2005-05-20T07:18:38Z\\nNo. of bitstreams: 1\\nmath.AP0105132.pdf: 225826 bytes, checksum: d7308b70020a416522235ed54b404379 (MD5) %0 Journal Article %J C. R. Math. 340 (2005) 819-822 %D 2005 %T The spectral geometry of the equatorial Podles sphere %A Ludwik Dabrowski %A Giovanni Landi %A Mario Paschke %A Andrzej Sitarz %X We propose a slight modification of the properties of a spectral geometry a la Connes, which allows for some of the algebraic relations to be satisfied only modulo compact operators. On the equatorial Podles sphere we construct suq2-equivariant Dirac operator and real structure which satisfy these modified properties. %B C. R. Math. 340 (2005) 819-822 %G en_US %U http://hdl.handle.net/1963/2275 %1 1972 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-22T09:37:10Z\\nNo. of bitstreams: 1\\n0408034v2.pdf: 95565 bytes, checksum: 1c0e7836d4006a796eb943f128938773 (MD5) %R 10.1016/j.crma.2005.04.003 %0 Journal Article %J Int. J. Numer. Anal. Met. 29 (2005) 73-101 %D 2005 %T Stress-dilatancy based modelling of granular materials and extensions to soils with crushable grains %A Antonio DeSimone %A Claudio Tamagnini %X Stress-dilatancy relations have played a crucial role in the understanding of the mechanical behaviour of soils and in the development of realistic constitutive models for their response. Recent investigations on the mechanical behaviour of materials with crushable grains have called into question the validity of classical relations such as those used in critical state soil mechanics.\\nIn this paper, a method to construct thermodynamically consistent (isotropic, three-invariant) elasto-plastic models based on a given stress-dilatancy relation is discussed. Extensions to cover the case of granular materials with crushable grains are also presented, based on the interpretation of some classical model parameters (e.g. the stress ratio at critical state) as internal variables that evolve according to suitable hardening laws. %B Int. J. Numer. Anal. Met. 29 (2005) 73-101 %G en_US %U http://hdl.handle.net/1963/2165 %1 2079 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-02T12:02:04Z\\nNo. of bitstreams: 1\\nDeSimoneTamagnini_2005.pdf: 1179767 bytes, checksum: 23b892b2314ea8e2199cc2b2449386b0 (MD5) %R 10.1002/nag.405 %0 Journal Article %J Proc. R. Soc. Lon. Ser. A 461 (2005) 79-97 %D 2005 %T Wetting of rough surfaces: a homogenization approach %A Antonio DeSimone %A Giovanni Alberti %X The contact angle of a drop in equilibrium on a solid is strongly affected by the roughness of the surface on which it rests. We study the roughness-induced enhancement of the hydrophobic or hydrophilic properties of a solid surface through homogenization theory. By relying on a variational formulation of the problem, we show that the macroscopic contact angle is associated with the solution of two cell problems, giving the minimal energy per unit macroscopic area for a transition layer between the rough solid surface and a liquid or vapor phase. Our results are valid for both chemically heterogeneous and homogeneous surfaces. In the latter case, a very transparent structure emerges from the variational\\napproach: the classical laws of Wenzel and Cassie-Baxter give bounds for the optimal energy, and configurations of minimal energy are those leading to the smallest macroscopic contact angle in the hydrophobic case, to the largest one in the hydrophilic case. %B Proc. R. Soc. Lon. Ser. A 461 (2005) 79-97 %G en_US %U http://hdl.handle.net/1963/2253 %1 1994 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-18T07:46:26Z\\nNo. of bitstreams: 1\\n75-04.pdf: 370259 bytes, checksum: 3ac1bc80248a4e54ff5294b7baffa66f (MD5) %R 10.1098/rspa.2004.1364 %0 Journal Article %J Amer. Math. Soc. Transl. 212 (2004)\\n75-132. %D 2004 %T On almost duality for Frobenius manifolds %A Boris Dubrovin %X We present a universal construction of almost duality for Frobenius manifolds. The analytic setup of this construction is described in details for the case of semisimple Frobenius manifolds. We illustrate the general considerations by examples from the singularity theory, mirror symmetry, the theory of Coxeter groups and Shephard groups, from the Seiberg - Witten duality. %B Amer. Math. Soc. Transl. 212 (2004)\\n75-132. %G en_US %U http://hdl.handle.net/1963/2543 %1 1576 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-21T12:40:01Z\\nNo. of bitstreams: 1\\n0307374v2.pdf: 617411 bytes, checksum: 7c8c52a06ea53850475a3e7055ce9af1 (MD5) %0 Journal Article %J Astérisque. Issue 297, 2004, Pages 35-65 %D 2004 %T On analytic families of invariant tori for PDEs %A Boris Dubrovin %X We propose to apply a version of the classical Stokes\\r\\nexpansion method to the perturbative construction of invariant tori for\\r\\nPDEs corresponding to solutions quasiperiodic in space and time variables.\\r\\nWe argue that, for integrable PDEs all but finite number of the\\r\\nsmall divisors arising in the perturbative analysis cancel. As an illustrative\\r\\nexample we establish such cancellations for the case of KP equation.\\r\\nIt is proved that, under mild assumptions about decay of the magnitude\\r\\nof the Fourier modes all analytic families of finite-dimensional invariant\\r\\ntori for KP are given by the Krichever construction in terms of thetafunctions\\r\\nof Riemann surfaces. We also present an explicit construction\\r\\nof infinite dimensional real theta-functions and corresponding quasiperiodic\\r\\nsolutions to KP as sums of infinite number of interacting plane\\r\\nwaves. %B Astérisque. Issue 297, 2004, Pages 35-65 %I SISSA %G en %U http://hdl.handle.net/1963/6474 %1 6420 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T14:58:35Z\\nNo. of bitstreams: 1\\ndubrovin_2004_asterisque.pdf: 318797 bytes, checksum: 3fe6968166d8ac662d44abd508bde574 (MD5) %0 Journal Article %J Ann. Inst. H. Poincaré. Anal. Non Linéaire 21 (2004), (4), p. 445-486. %D 2004 %T Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains %A Gianni Dal Maso %A Francois Murat %X We consider a sequence of Dirichlet problems in varying domains (or, more generally, of relaxed Dirichlet problems involving measures in M_0) for second order linear elliptic operators in divergence form with varying matrices of coefficients. When the matrices H-converge to a matrix A^0, we prove that there exist a subsequence and a measure mu^0 in M_0 such that the limit problem is the relaxed Dirichlet problem corresponding to A^0 and mu^0. We also prove a corrector result which provides an explicit approximation of the solutions in the H^1-norm, and which is obtained by multiplying the corrector for the H-converging matrices by some special test function which depends both on the varying matrices and on the varying domains. %B Ann. Inst. H. Poincaré. Anal. Non Linéaire 21 (2004), (4), p. 445-486. %I SISSA Library %G en %U http://hdl.handle.net/1963/1611 %1 2507 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:17Z (GMT). No. of bitstreams: 1\\r\\nmath.AP0205225.pdf: 404809 bytes, checksum: 472524cb28afed2e55fcf0a7c46e7598 (MD5)\\r\\n Previous issue date: 2002 %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire 21 (2004) 121-137 %D 2004 %T Blow-up solutions for the Schrödinger equation in dimension three with a concentrated nonlinearity %A Riccardo Adami %A Gianfausto Dell'Antonio %A Rodolfo Figari %A Alessandro Teta %X We present some results on the blow-up phenomenon for the Schroedinger equation in dimension three with a nonlinear term supported in a fixed point. We find sufficient conditions for the blow up exploiting the moment of inertia of the solution and the uncertainty principle. In the critical case, we discuss the additional symmetry of the equation and construct a family of explicit blow up solutions. %B Ann. Inst. H. Poincare Anal. Non Lineaire 21 (2004) 121-137 %I Elsevier %G en_US %U http://hdl.handle.net/1963/2998 %1 1335 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-01T10:06:49Z\\nNo. of bitstreams: 1\\nadami.pdf: 209114 bytes, checksum: ea6a7059ff0728c6d55cdc3a16071631 (MD5) %R 10.1016/j.anihpc.2003.01.002 %0 Journal Article %J Computer methods in applied mechanics and engineering , 193 (2004) 5129-5141 %D 2004 %T Coarse-grained models of materials with non-convex free-energy: two case studies %A Antonio DeSimone %X Bridging across length scales is one of the fundamental challenges in the computational modelling of material systems whose mechanical response is driven by rough energy landscapes. The typical feature of such systems is that of exhibiting fine scale microstructures. Two case studies, namely, nematic elastomers and ferromagnetic shape memory alloys, are presented to illustrate the use of modern techniques from (non-convex) calculus of variations in developing coarse-grained models of microstructure-driven material response. %B Computer methods in applied mechanics and engineering , 193 (2004) 5129-5141 %I Elsevier %G en %U http://hdl.handle.net/1963/4884 %1 4664 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-24T06:59:37Z\\nNo. of bitstreams: 0 %R 10.1016/j.cma.2003.12.064 %0 Journal Article %J M2AN Math. Model. Numer. Anal. 38 (2004) 235-248 %D 2004 %T Energetics and switching of quasi-uniform states in small ferromagnetic particles %A François Alouges %A Sergio Conti %A Antonio DeSimone %A Ivo Pokern %X We present a numerical algorithm to solve the micromagnetic equations based on tangential-plane minimization for the magnetization update and a homothethic-layer decomposition of outer space for the computation of the demagnetization field. As a first application, detailed results on the flower-vortex transition in the cube of Micromagnetic Standard Problem number 3 are obtained, which confirm, with a different method, those already present in the literature, and validate our method and code. We then turn to switching of small cubic or almost-cubic particles, in the single-domain limit. Our data show systematic deviations from the Stoner-Wohlfarth model due to the non-ellipsoidal shape of the particle, and in particular a non-monotone dependence on the particle size. %B M2AN Math. Model. Numer. Anal. 38 (2004) 235-248 %I EDP Sciences %G en_US %U http://hdl.handle.net/1963/2999 %1 1334 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-01T10:25:50Z\\nNo. of bitstreams: 1\\npreprint2003_88.pdf: 297354 bytes, checksum: d907d5a9d74d0a3dcb244e26ff2af68a (MD5) %R 10.1051/m2an:2004011 %0 Journal Article %J Moscow Math. J. 4 (2004)\\n313-332. %D 2004 %T The Extended Toda Hierarchy %A Guido Carlet %A Boris Dubrovin %A Zhang Youjin %B Moscow Math. J. 4 (2004)\\n313-332. %G en_US %U http://hdl.handle.net/1963/2542 %1 1577 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-21T12:22:27Z\\nNo. of bitstreams: 1\\n0306060v2.pdf: 242352 bytes, checksum: 7a4fc53dbf549eb7046e75be6c087368 (MD5) %0 Journal Article %J Arch. Ration. Mech. Anal. 171 (2004) 55-81 %D 2004 %T Higher order quasiconvexity reduces to quasiconvexity %A Gianni Dal Maso %A Irene Fonseca %A Giovanni Leoni %A Massimiliano Morini %X In this paper it is shown that higher order quasiconvex functions suitable in the variational treatment of problems involving second derivatives may be extended to the space of all matrices as classical quasiconvex functions. Precisely, it is proved that a smooth strictly 2-quasiconvex function with p-growth at infinity, p>1, is the restriction to symmetric matrices of a 1-quasiconvex function with the same growth. As a consequence, lower semicontinuity results for second-order variational problems are deduced as corollaries of well-known first order theorems. %B Arch. Ration. Mech. Anal. 171 (2004) 55-81 %I Springer %G en_US %U http://hdl.handle.net/1963/2911 %1 1789 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T12:36:19Z\\nNo. of bitstreams: 1\\nmath.AP0305138.pdf: 272082 bytes, checksum: 245f93702444ac3eb1de7c86c1f83551 (MD5) %R 10.1007/s00205-003-0278-1 %0 Journal Article %J Quad. Mat. Dip. Mat. Seconda Univ. Napoli 14 (2004) 245-266 %D 2004 %T Quasi-static evolution in brittle fracture: the case of bounded solutions %A Gianni Dal Maso %A Gilles A. Francfort %A Rodica Toader %X The main steps of the proof of the existence result for the quasi-static evolution of cracks in brittle materials, obtained in [7] in the vector case and for a general quasiconvex elastic energy, are presented here under the simplifying assumption that the minimizing sequences involved in the problem are uniformly bounded in $L^\\\\infty$. %B Quad. Mat. Dip. Mat. Seconda Univ. Napoli 14 (2004) 245-266 %G en_US %U http://hdl.handle.net/1963/2229 %1 2015 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-15T15:04:28Z\\r\\nNo. of bitstreams: 1\\r\\n0401198v1.pdf: 166634 bytes, checksum: c21fba2b1fbbaec4fe14c56595b0664e (MD5) %0 Journal Article %J Ann. Henri Poincare 5 (2004) 773-808 %D 2004 %T Rotating Singular Perturbations of the Laplacian %A Michele Correggi %A Gianfausto Dell'Antonio %X We study a system of a quantum particle interacting with a singular time-dependent uniformly rotating potential in 2 and 3 dimensions: in particular we consider an interaction with support on a point (rotating point interaction) and on a set of codimension 1 (rotating blade). We prove the existence of the Hamiltonians of such systems as suitable self-adjoint operators and we give an explicit expression for their unitary semigroups. Moreover we analyze the asymptotic limit of large angular velocity and we prove strong convergence of the time-dependent propagator to some one-parameter unitary group as (\\\\omega \\\\to \\\\infty). %B Ann. Henri Poincare 5 (2004) 773-808 %I Springer %G en_US %U http://hdl.handle.net/1963/2945 %1 1755 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-15T08:20:31Z\\nNo. of bitstreams: 1\\nmath-ph0307056.pdf: 360658 bytes, checksum: 16a12ce4dfd525b63e0a6e703ef9d7bf (MD5) %R 10.1007/s00023-004-0182-8 %0 Journal Article %J J. Phys. A 37 (2004) 5605-5624 %D 2004 %T Semiclassical analysis of constrained quantum systems %A Gianfausto Dell'Antonio %A Lucattilio Tenuta %X We study the dynamics of a quantum particle in R^(n+m) constrained by a strong potential force to stay within a distance of order hbar (in suitable units) from a smooth n-dimensional submanifold M. We prove that in the semiclassical limit the evolution of the wave function is approximated in norm, up to terms of order hbar^(1/2), by the evolution of a semiclassical wave packet centred on the trajectory of the corresponding classical constrained system. %B J. Phys. A 37 (2004) 5605-5624 %I IOP Publishing %G en_US %U http://hdl.handle.net/1963/2997 %1 1336 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-01T08:52:42Z\\nNo. of bitstreams: 1\\n0312034v2.pdf: 270295 bytes, checksum: ade82e7ba05cc6dbf50709fd277e1323 (MD5) %R 10.1088/0305-4470/37/21/007 %0 Journal Article %J Comm. Math.\\nPhys. 250 (2004) 161-193. %D 2004 %T Virasoro Symmetries of the Extended Toda Hierarchy %A Boris Dubrovin %A Zhang Youjin %X We prove that the extended Toda hierarchy of \\\\cite{CDZ} admits nonabelian Lie algebra of infinitesimal symmetries isomorphic to the half of the Virasoro algebra. The generators $L_m$, $m\\\\geq -1$ of the Lie algebra act by linear differential operators onto the tau function of the hierarchy. We also prove that the tau function of a generic solution to the extended Toda hierarchy is annihilated by a combination of the Virasoro operators and the flows of the hierarchy. As an application we show that the validity of the Virasoro constraints for the $CP^1$ Gromov-Witten invariants and their descendents implies that their generating function is the logarithm of a particular tau function of the extended Toda hierarchy. %B Comm. Math.\\nPhys. 250 (2004) 161-193. %G en_US %U http://hdl.handle.net/1963/2544 %1 1575 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-21T12:53:52Z\\nNo. of bitstreams: 1\\n0308152v2.pdf: 341202 bytes, checksum: 306b1f696e6ec01c0eabbeeeca895290 (MD5) %R 10.1007/s00220-004-1084-9 %0 Journal Article %J Applied Math.Optim. 48 (2003), no.1, p.39-66 %D 2003 %T Autonomous integral functionals with discontinous nonconvex integrands: Lipschitz regularity of mimimizers, DuBois-Reymond necessary conditions and Hamilton-Jacobi equations %A Gianni Dal Maso %A Helene Frankowska %B Applied Math.Optim. 48 (2003), no.1, p.39-66 %I SISSA Library %G en %U http://hdl.handle.net/1963/1625 %1 2493 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:30Z (GMT). No. of bitstreams: 1\\r\\nmath.AP0207230.pdf: 302400 bytes, checksum: e660ec855386e1a29edd2e20f7abc796 (MD5)\\r\\n Previous issue date: 2002 %R 10.1007/s00245-003-0768-4 %0 Journal Article %J Calc. Var. Partial Differential Equations 16 (2003) 299-333 %D 2003 %T The calibration method for the Mumford-Shah functional and free-discontinuity problems %A Giovanni Alberti %A Guy Bouchitte %A Gianni Dal Maso %X We present a minimality criterion for the Mumford-Shah functional, and more generally for non convex variational integrals on SBV which couple a surface and a bulk term. This method provides short and easy proofs for several minimality results. %B Calc. Var. Partial Differential Equations 16 (2003) 299-333 %I Springer %G en_US %U http://hdl.handle.net/1963/3051 %1 1282 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-09T15:00:19Z\\nNo. of bitstreams: 1\\n0105013v1.pdf: 428802 bytes, checksum: de75d15134f2a74b36b0d71355e04835 (MD5) %R 10.1007/s005260100152 %0 Journal Article %J Int. J. Control 76 (2003) 1272-1284 %D 2003 %T Hybrid optimal control: case study of a car with gears %A Ciro D'Apice %A Mauro Garavello %A Rosanna Manzo %A Benedetto Piccoli %X The purpose of this paper is to show the use of some analytical tools for hybrid optimal control. We illustrate both the hybrid maximum principle and the hybrid necessary principle at work on a simple example of a car with gears. The model is sufficiently rich to generate non-trivial optimization problems and the obtained results match with intuition. Finally, computer simulations confirm the theoretical analysis. %B Int. J. Control 76 (2003) 1272-1284 %I Taylor and Francis %G en_US %U http://hdl.handle.net/1963/3022 %1 1311 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-02T15:37:32Z\\nNo. of bitstreams: 1\\ndgb.pdf: 374355 bytes, checksum: 5c6cc02be9e07396a29d5c6ff22db238 (MD5) %R 10.1080/0020717031000147520 %0 Journal Article %J Mod. Phys. Lett. A 18 (2003) 2371-2379 %D 2003 %T Non-linear sigma-models in noncommutative geometry: fields with values in finite spaces %A Ludwik Dabrowski %A Thomas Krajewski %A Giovanni Landi %X We study sigma-models on noncommutative spaces, notably on noncommutative tori. We construct instanton solutions carrying a nontrivial topological charge q and satisfying a Belavin-Polyakov bound. The moduli space of these instantons is conjectured to consists of an ordinary torus endowed with a complex structure times a projective space $CP^{q-1}$. %B Mod. Phys. Lett. A 18 (2003) 2371-2379 %I World Scientific %G en_US %U http://hdl.handle.net/1963/3215 %1 1086 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-30T11:23:21Z\\nNo. of bitstreams: 1\\n0309143v1.pdf: 165627 bytes, checksum: c79b1a62edf34ae51819b5e8d752db8b (MD5) %R 10.1142/S0217732303012593 %0 Journal Article %J J. Geom. Anal. 13 (2003) 255-289 %D 2003 %T Prescribing scalar and boundary mean curvature on the three dimensional half sphere %A Zindine Djadli %A Andrea Malchiodi %A Mohameden Ould Ahmedou %X We consider the problem of prescribing the scalar curvature and the boundary mean curvature of the standard half three sphere, by deforming conformally its standard metric. Using blow up analysis techniques and minimax arguments, we prove some existence and compactness results. %B J. Geom. Anal. 13 (2003) 255-289 %I Springer %G en_US %U http://hdl.handle.net/1963/3086 %1 1247 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-13T14:32:25Z\\nNo. of bitstreams: 1\\n0211227v1.pdf: 359886 bytes, checksum: e4e0c1b0979d1cb348e41f2351b74254 (MD5) %R 10.1007/BF02930697 %0 Journal Article %J J. Phys. A 36 (2003), no. 13, 3829-3840 %D 2003 %T Quantum spin coverings and statistics %A Ludwik Dabrowski %A Cesare Reina %X SL_q(2) at odd roots of unity q^l =1 is studied as a quantum cover of the complex rotation group SO(3,C), in terms of the associated Hopf algebras of (quantum) polynomial functions. We work out the irreducible corepresentations, the decomposition of their tensor products and a coquasitriangular structure, with the associated braiding (or statistics). As an example, the case l=3 is discussed in detail. %B J. Phys. A 36 (2003), no. 13, 3829-3840 %I IOP Publishing %G en %U http://hdl.handle.net/1963/1667 %1 2451 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T13:06:10Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002 %R 10.1088/0305-4470/36/13/314 %0 Journal Article %J J.Math. Pures Appl. (9) 82 (2003) no.5 , 503 %D 2003 %T A stability result for nonlinear Neumann problems under boundary variations %A Gianni Dal Maso %A Francois Ebobisse %A Marcello Ponsiglione %X In this paper we study, in dimension two, the stability of the solutions of some nonlinear elliptic equations with Neumann boundary conditions, under perturbations of the domains in the Hausdorff complementary topology. %B J.Math. Pures Appl. (9) 82 (2003) no.5 , 503 %I SISSA Library %G en %U http://hdl.handle.net/1963/1618 %1 2500 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:23Z (GMT). No. of bitstreams: 1\\nmath.AP0206215.pdf: 329673 bytes, checksum: 40d537fd197fbaec56be0729d3a72ee3 (MD5)\\n Previous issue date: 2002 %R 10.1016/S0021-7824(03)00014-X %0 Journal Article %J J. Math. Phys. %D 2002 %T Coherent state realizations of $\rm su(n+1)$ on the $n$-torus %A de Guise, Hubert %A Marco Bertola %B J. Math. Phys. %V 43 %P 3425–3444 %G eng %0 Journal Article %J Differential Geom. Appl. 16 (2002) 277-284 %D 2002 %T Instanton algebras and quantum 4-spheres %A Ludwik Dabrowski %A Giovanni Landi %X We study some generalized instanton algebras which are required to describe `instantonic complex rank 2 bundles\\\'. The spaces on which the bundles are defined are not prescribed from the beginning but rather are obtained from some natural requirements on the instantons. They turn out to be quantum 4-spheres $S^4_q$, with $q\\\\in\\\\IC$, and the instantons are described by self-adjoint idempotents e. We shall also clarify some issues related to the vanishing of the first Chern-Connes class $ch_1(e)$ and on the use of the second Chern-Connes class $ch_2(e)$ as a volume form. %B Differential Geom. Appl. 16 (2002) 277-284 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3134 %1 1199 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-17T09:39:17Z\\nNo. of bitstreams: 1\\n0101177v2.pdf: 131163 bytes, checksum: 6756bdd801d3c677c7a70ee74fefd158 (MD5) %R 10.1016/S0926-2245(02)00066-9 %0 Journal Article %J Set-Valued Anal. 10 (2002), p.165-183 %D 2002 %T Linearized elasticity as gamma-limit of finite elasticity %A Gianni Dal Maso %A Matteo Negri %A Danilo Percivale %B Set-Valued Anal. 10 (2002), p.165-183 %I Springer %G en_US %U http://hdl.handle.net/1963/3052 %1 1281 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-09T15:20:52Z\\r\\nNo. of bitstreams: 1\\r\\nDM-Neg-Per-01.pdf: 199909 bytes, checksum: ddd0bf6c6890234f6d9c820fd6ab7f47 (MD5) %R 10.1023/A:1016577431636 %0 Journal Article %J Math. Models Methods Appl. Sci., 12 (2002), no. 12, 1773 %D 2002 %T A model for the quasi-static growth of a brittle fracture: existence and approximation results %A Gianni Dal Maso %A Rodica Toader %X We study a variant of the variational model for the quasi-static growth of brittle fractures proposed by Francfort and Marigo.9 The main feature of our model is that, in the discrete-time formulation, in each step we do not consider absolute minimizers of the energy, but, in a sense, we look for local minimizers which are sufficiently close to the approximate solution obtained in the previous step. This is done by introducing in the variational problem an additional term which penalizes the L2-distance between the approximate solutions at two consecutive times. We study the continuous-time version of this model, obtained by passing to the limit as the time step tends to zero, and show that it satisfies (for almost every time) some minimality conditions which are slightly different from those considered in Refs. 9 and 8, but are still enough to prove (under suitable regularity assumptions on the crack path) that the classical Griffith\\\'s criterion holds at the crack tips. We also prove that, if no initial crack is present and if the data of the problem are sufficiently smooth, no crack will develop in this model, provided the penalization term is large enough. %B Math. Models Methods Appl. Sci., 12 (2002), no. 12, 1773 %I SISSA Library %G en %U http://hdl.handle.net/1963/1571 %1 2547 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:18Z (GMT). No. of bitstreams: 1\\nmath.AP0101089.pdf: 313965 bytes, checksum: 0373da7254cb4d172659dd2402174562 (MD5)\\n Previous issue date: 2000 %R 10.1142/S0218202502002331 %0 Journal Article %J Math.Models Methods Appl. Sci., 12 (2002) , p.1773-1800. %D 2002 %T A model for the quasi-static growth of brittle fractures based on local minimization %A Gianni Dal Maso %A Rodica Toader %X We study a variant of the variational model for the quasi-static growth of brittle fractures proposed by Francfort and Marigo.9 The main feature of our model is that, in the discrete-time formulation, in each step we do not consider absolute minimizers of the energy, but, in a sense, we look for local minimizers which are sufficiently close to the approximate solution obtained in the previous step. This is done by introducing in the variational problem an additional term which penalizes the L2-distance between the approximate solutions at two consecutive times. We study the continuous-time version of this model, obtained by passing to the limit as the time step tends to zero, and show that it satisfies (for almost every time) some minimality conditions which are slightly different from those considered in Refs. 9 and 8, but are still enough to prove (under suitable regularity assumptions on the crack path) that the classical Griffith\\\'s criterion holds at the crack tips. We also prove that, if no initial crack is present and if the data of the problem are sufficiently smooth, no crack will develop in this model, provided the penalization term is large enough. %B Math.Models Methods Appl. Sci., 12 (2002) , p.1773-1800. %I SISSA Library %G en %U http://hdl.handle.net/1963/1621 %1 2497 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:26Z (GMT). No. of bitstreams: 1\\r\\nmath.AP0207002.pdf: 268810 bytes, checksum: 00401d0491ec9d938b05dcdb884832b7 (MD5)\\r\\n Previous issue date: 2002 %R 10.1142/S0218202502002331 %0 Journal Article %J Arch. Ration. Mech. Anal. 162 (2002) 101-135 %D 2002 %T A Model for the Quasi-Static Growth of Brittle Fractures: Existence and Approximation Results %A Gianni Dal Maso %A Rodica Toader %X We give a precise mathematical formulation of a variational model for the irreversible quasi-static evolution of brittle fractures proposed by G.A. Francfort and J.-J. Marigo, and based on Griffith\\\'s theory of crack growth. In the two-dimensional case we prove an existence result for the quasi-static evolution and show that the total energy is an absolutely continuous function of time, although we can not exclude that the bulk energy and the surface energy may present some jump discontinuities. This existence result is proved by a time discretization process, where at each step a global energy minimization is performed, with the constraint that the new crack contains all cracks formed at the previous time steps. This procedure provides an effective way to approximate the continuous time evolution. %B Arch. Ration. Mech. Anal. 162 (2002) 101-135 %I Springer %G en_US %U http://hdl.handle.net/1963/3056 %1 1277 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-09T16:01:33Z\\nNo. of bitstreams: 1\\n0103221v1.pdf: 340988 bytes, checksum: 433e8545f072a326fc7a6d80a9e7a401 (MD5) %R 10.1007/s002050100187 %0 Journal Article %J Ann. Sc. Norm. Super. Pisa Cl. Sci., 2002, 1, 387 %D 2002 %T Prescribing a fourth oder conformal invariant on the standard sphere - Part II: blow up analysis and applications %A Zindine Djadli %A Andrea Malchiodi %A Mohameden Ould Ahmedou %B Ann. Sc. Norm. Super. Pisa Cl. Sci., 2002, 1, 387 %I SISSA Library %G en %U http://hdl.handle.net/1963/1540 %1 2623 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:51Z (GMT). No. of bitstreams: 1\\nmath.AP0104091.pdf: 438502 bytes, checksum: 97c6b7ab20d77a3a40904db3f08928d1 (MD5)\\n Previous issue date: 2000 %0 Journal Article %J Commun. Contemp. Math., 2002, 4, 375 %D 2002 %T Prescribing a fourth oder conformal invariant on the standard sphere - Part I: a perturbation result %A Zindine Djadli %A Mohameden Ould Ahmedou %A Andrea Malchiodi %B Commun. Contemp. Math., 2002, 4, 375 %I SISSA Library %G en %U http://hdl.handle.net/1963/1539 %1 2624 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:50Z (GMT). No. of bitstreams: 1\\nmath.AP0101101.pdf: 273679 bytes, checksum: 772598ac956e1f555f866f6330ec1fd6 (MD5)\\n Previous issue date: 2000 %R 10.1142/S0219199702000695 %0 Journal Article %J Noncommutative geometry and quantum groups (Warsaw 2001),49,Banach Center Publ., 61, Polish Acad.Sci., Warsaw,2003 %D 2001 %T Dirac operator on the standard Podles quantum sphere %A Ludwik Dabrowski %A Andrzej Sitarz %B Noncommutative geometry and quantum groups (Warsaw 2001),49,Banach Center Publ., 61, Polish Acad.Sci., Warsaw,2003 %I SISSA Library %G en %U http://hdl.handle.net/1963/1668 %1 2450 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T13:06:10Z (GMT). No. of bitstreams: 1\\nmath.QA0209048.pdf: 89749 bytes, checksum: e1bc2f04a36a957d4fb3131860296c18 (MD5)\\n Previous issue date: 2002 %0 Journal Article %J Acta Appl. Math., 2001, 65, 207-215 %D 2001 %T Gamma-limit of periodic obstacles %A Gianni Dal Maso %A Paola Trebeschi %X We compute the Gamma-limit of a sequence obstacle functionals in the case of periodic obstacles. %B Acta Appl. Math., 2001, 65, 207-215 %I SISSA Library %G en %U http://hdl.handle.net/1963/1495 %1 2668 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:12Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1023/A:1010668530972 %0 Journal Article %J Comm. Math. Phys. 221 (2001) 161-168 %D 2001 %T Instantons on the Quantum 4-Spheres S^4_q %A Ludwik Dabrowski %A Giovanni Landi %A Tetsuya Masuda %X We introduce noncommutative algebras $A_q$ of quantum 4-spheres $S^4_q$, with $q\\\\in\\\\IR$, defined via a suspension of the quantum group $SU_q(2)$, and a quantum instanton bundle described by a selfadjoint idempotent $e\\\\in \\\\Mat_4(A_q)$, $e^2=e=e^*$. Contrary to what happens for the classical case or for the noncommutative instanton constructed in Connes-Landi, the first Chern-Connes class $ch_1(e)$ does not vanish thus signaling a dimension drop. The second Chern-Connes class $ch_2(e)$ does not vanish as well and the couple $(ch_1(e), ch_2(e))$ defines a cycle in the $(b,B)$ bicomplex of cyclic homology. %B Comm. Math. Phys. 221 (2001) 161-168 %I Springer %G en_US %U http://hdl.handle.net/1963/3135 %1 1198 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-17T09:47:38Z\\nNo. of bitstreams: 1\\n0012103v2.pdf: 128667 bytes, checksum: 86c8b564b4eb5008fad8371fcfd5f265 (MD5) %R 10.1007/PL00005572 %0 Journal Article %J Adv. Math. Sci. Appl. 11 (2001) 721-751 %D 2001 %T A monotonicity approach to nonlinear Dirichlet problems in perforated domains %A Gianni Dal Maso %A Igor V. Skrypnik %X We study the asymptotic behaviour of solutions to Dirichlet problems in perforated domains for nonlinear elliptic equations associated with monotone operators. The main difference with respect to the previous papers on this subject is that no uniformity is assumed in the monotonicity condition. Under a very general hypothesis on the holes of the domains, we construct a limit equation, which is satisfied by the weak limits of the solutions. The additional term in the limit problem depends only on the local behaviour of the holes, which can be expressed in terms of suitable nonlinear capacities associated with the monotone operator. %B Adv. Math. Sci. Appl. 11 (2001) 721-751 %I SISSA Library %G en %U http://hdl.handle.net/1963/1555 %1 2563 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:04Z (GMT). No. of bitstreams: 1\\nmath.AP0010232.pdf: 246554 bytes, checksum: 691b6fb5c795a48324b128ced5a3cc44 (MD5)\\n Previous issue date: 2000 %0 Journal Article %J 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 %D 2001 %T Uniqueness of solutions to Hamilton-Jacobi equations arising in the Calculus of Variations %A Gianni Dal Maso %A Helene Frankowska %X 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. %B 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 %I SISSA Library %G en %U http://hdl.handle.net/1963/1515 %1 2648 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:29Z (GMT). No. of bitstreams: 1\\r\\nmath.AP0006015.pdf: 143977 bytes, checksum: 23794ed600a1b20f94c6b1eca86fcc54 (MD5)\\r\\n Previous issue date: 2000 %0 Journal Article %J Lett. Math. Phys., 2000, 52, 339 %D 2000 %T A(SLq(2)) at roots of unity is a free module over A(SL(2)) %A Ludwik Dabrowski %A Cesare Reina %A Alessandro Zampa %B Lett. Math. Phys., 2000, 52, 339 %I SISSA Library %G en %U http://hdl.handle.net/1963/1500 %1 2663 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T13:03:17Z (GMT). No. of bitstreams: 1\\nmath.QA0004092.pdf: 71107 bytes, checksum: ad69901d378f79db9f98cc05c5caabb4 (MD5)\\n Previous issue date: 2000 %R 10.1023/A:1007601131002 %0 Journal Article %J European Congress of Mathematics. Volume I : Barcelona, July 10-14, 2000 / Carles Casacuberta ... [et al.], editors. , Boston : Birkhauser, 2001, p. 317-326. %D 2000 %T The Calibration Method for Free Discontinuity Problems %A Gianni Dal Maso %X 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. %B European Congress of Mathematics. Volume I : Barcelona, July 10-14, 2000 / Carles Casacuberta ... [et al.], editors. , Boston : Birkhauser, 2001, p. 317-326. %I SISSA Library %G en %U http://hdl.handle.net/1963/1496 %1 2667 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:13Z (GMT). No. of bitstreams: 1\\r\\nmath.OC0006016.pdf: 150581 bytes, checksum: dde42438e52ad82f5980d68f697f90c8 (MD5)\\r\\n Previous issue date: 2000 %0 Journal Article %J J. Math. Pures Appl. 79, 2 (2000) 141-162 %D 2000 %T Local calibrations for minimizers of the Mumford-Shah functional with rectilinear discontinuity sets %A Gianni Dal Maso %A Maria Giovanna Mora %A Massimiliano Morini %B J. Math. Pures Appl. 79, 2 (2000) 141-162 %I SISSA Library %G en %U http://hdl.handle.net/1963/1261 %1 3194 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:27Z (GMT). No. of bitstreams: 1\\nmath-FA0006073.pdf: 195688 bytes, checksum: 199483eeec8fa727b6f84ce5270d3f32 (MD5)\\n Previous issue date: 1999 %R 10.1016/S0021-7824(99)00140-3 %0 Journal Article %J Invent. Math. 141 (2000) 55-147 %D 2000 %T Monodromy of certain Painlevé-VI transcendents and reflection groups %A Boris Dubrovin %A Marta Mazzocco %X We study the global analytic properties of the solutions of a particular family of Painleve\\\' VI equations with the parameters $\\\\beta=\\\\gamma=0$, $\\\\delta={1\\\\over2}$ and $\\\\alpha$ arbitrary. We introduce a class of solutions having critical behaviour of algebraic type, and completely compute the structure of the analytic continuation of these solutions in terms of an auxiliary reflection group in the three dimensional space. The analytic continuation is given in terms of an action of the braid group on the triples of generators of the reflection group. This result is used to classify all the algebraic solutions of our Painleve\\\' VI equation. %B Invent. Math. 141 (2000) 55-147 %I Springer %G en_US %U http://hdl.handle.net/1963/2882 %1 1818 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-10T09:24:50Z\\nNo. of bitstreams: 1\\n9806056v1.pdf: 604033 bytes, checksum: f49a9c54ad1f165a94c653239d2c08dd (MD5) %R 10.1007/PL00005790 %0 Journal Article %J Int. J. Mod. Phys. B 14 (2000) 721-727 %D 2000 %T A Remark on One-Dimensional Many-Body Problems with Point Interactions %A Sergio Albeverio %A Ludwik Dabrowski %A Shao-Ming Fei %X The integrability of one dimensional quantum mechanical many-body problems with general contact interactions is extensively studied. It is shown that besides the pure (repulsive or attractive) $\\\\delta$-function interaction there is another singular point interactions which gives rise to a new one-parameter family of integrable quantum mechanical many-body systems. The bound states and scattering matrices are calculated for both bosonic and fermionic statistics. %B Int. J. Mod. Phys. B 14 (2000) 721-727 %I World Scientific %G en_US %U http://hdl.handle.net/1963/3214 %1 1087 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-30T11:10:07Z\\nNo. of bitstreams: 1\\n0001089v1.pdf: 116474 bytes, checksum: e9cac488b17f06674f7abc822769dc6a (MD5) %R 10.1142/S0217979200000601 %0 Journal Article %J Int. J. Mod. Phys. B 14 (2000) 2367-2382 %D 2000 %T Some Properties of Non-linear sigma-Models in Noncommutative Geometry %A Ludwik Dabrowski %A Thomas Krajewski %A Giovanni Landi %X We introduce non-linear $\\\\sigma$-models in the framework of noncommutative geometry with special emphasis on models defined on the noncommutative torus. We choose as target spaces the two point space and the circle and illustrate some characteristic features of the corresponding $\\\\sigma$-models. In particular we construct a $\\\\sigma$-model instanton with topological charge equal to 1. We also define and investigate some properties of a noncommutative analogue of the Wess-Zumino-Witten model. %B Int. J. Mod. Phys. B 14 (2000) 2367-2382 %I SISSA Library %G en %U http://hdl.handle.net/1963/1373 %1 3082 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:57:00Z (GMT). No. of bitstreams: 1\\nhep-th0003099.pdf: 185777 bytes, checksum: 30806664c895808c1cb1afe5e6364f9f (MD5)\\n Previous issue date: 1999 %R 10.1142/S0217979200001898 %0 Journal Article %J ESAIM Control Optim. Calc. Var., 5 (2000), n. 5, p. 369-393. %D 2000 %T Value Functions for Bolza Problems with Discontinuous Lagrangians and Hamilton-Jacobi inequalities %A Gianni Dal Maso %A Helene Frankowska %B ESAIM Control Optim. Calc. Var., 5 (2000), n. 5, p. 369-393. %I SISSA Library %G en %U http://hdl.handle.net/1963/1514 %1 2649 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:28Z (GMT). No. of bitstreams: 1\\r\\nmath.AP0006013.pdf: 255518 bytes, checksum: 30b8f57e76e4104aa6c3efc013b76620 (MD5)\\r\\n Previous issue date: 2000 %R 10.1051/cocv:2000114 %0 Journal Article %J Journal d\\\'Analyse Mathematique, Volume 79, 1999, Pages: 63-112 %D 1999 %T Asymptotic behaviour of nonlinear elliptic higher order equations in perforated domains %A Gianni Dal Maso %A Igor V. Skrypnik %B Journal d\\\'Analyse Mathematique, Volume 79, 1999, Pages: 63-112 %@ 1618-1891 %G en %U http://hdl.handle.net/1963/6433 %1 6374 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-31T18:25:49Z\\nNo. of bitstreams: 0 %R 10.1007/BF01759365 %0 Journal Article %J C. R. Acad. Sci. Paris Ser. I Math. 329 (1999), no. 3, 249-254 %D 1999 %T The calibration method for the Mumford-Shah functional %A Giovanni Alberti %A Guy Bouchitte %A Gianni Dal Maso %X 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). %B C. R. Acad. Sci. Paris Ser. I Math. 329 (1999), no. 3, 249-254 %I Elsevier %G en %U http://hdl.handle.net/1963/1235 %1 2708 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:07Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %R 10.1016/S0764-4442(00)88602-4 %0 Journal Article %J M2AN 33 (1999) 651-672 %D 1999 %T Discrete approximation of the Mumford-Shah functional in dimension two %A Antonin Chambolle %A Gianni Dal Maso %B M2AN 33 (1999) 651-672 %I EDP Sciences %G en_US %U http://hdl.handle.net/1963/3588 %1 712 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-03-09T13:50:04Z\\nNo. of bitstreams: 1\\nDalMaso1999.pdf: 462659 bytes, checksum: 04dc23ba4544d5be9ebdd703da477c7e (MD5) %R 10.1051/m2an:1999156 %0 Journal Article %J Rendiconti di Matematica e delle sue Applicazioni. vol. 19, Issue 7, (1999), pages : 1-15 %D 1999 %T Evans-Vasilesco theorem in Dirichlet spaces %A Gianni Dal Maso %A Virginia De Cicco %B Rendiconti di Matematica e delle sue Applicazioni. vol. 19, Issue 7, (1999), pages : 1-15 %I SISSA %G en %U http://hdl.handle.net/1963/6436 %1 6376 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-31T18:39:11Z\\nNo. of bitstreams: 2\\nDM-DeC-96.pdf: 145467 bytes, checksum: 0cf974ac5cc090ff7f9faae3d433043f (MD5)\\nDM-DeC-96-cover.pdf: 35849 bytes, checksum: cde85af897042e1ee2c1b1a8c724b8eb (MD5) %0 Journal Article %J Selecta Math. (N.S.) 5 (1999) 423-466 %D 1999 %T Frobenius manifolds and Virasoro constraints %A Boris Dubrovin %A Zhang Youjin %X For an arbitrary Frobenius manifold a system of Virasoro constraints is constructed. In the semisimple case these constraints are proved to hold true in the genus one approximation. Particularly, the genus $\\\\leq 1$ Virasoro conjecture of T.Eguchi, K.Hori, M.Jinzenji, and C.-S.Xiong and of S.Katz is proved for smooth projective varieties having semisimple quantum cohomology. %B Selecta Math. (N.S.) 5 (1999) 423-466 %I Springer %G en_US %U http://hdl.handle.net/1963/2883 %1 1817 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-10T09:34:57Z\\nNo. of bitstreams: 1\\n9808048v2.pdf: 352376 bytes, checksum: 12496406fad546b37d3f66131d2d51ee (MD5) %R 10.1007/s000290050053 %0 Journal Article %J Nonlinear Analysis, Theory, Methods and Applications. Volume 37, Issue 6, September 1999, Pages 707-717 %D 1999 %T A Lipschitz selection from the set of minimizers of a nonconvex functional of the gradient %A Gianni Dal Maso %A Vladimir V. Goncharov %A Antonio Ornelas %X A constructive and improved version of the proof that there exist a continuous map that solves the convexified problem is presented. A Lipschitz continuous map is analyzed such that a map vector minimizes the functional at each vector satisfying Cellina\\\'s condition of existence of minimum. This map is explicitly given by a direct constructive algorithm. %B Nonlinear Analysis, Theory, Methods and Applications. Volume 37, Issue 6, September 1999, Pages 707-717 %I SISSA %G en %U http://hdl.handle.net/1963/6439 %1 6379 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-31T18:52:31Z\\nNo. of bitstreams: 1\\nDM-Gon-Orn-96-sissa.pdf: 182850 bytes, checksum: e2288b2be15f6e2f0d0dfc3fc74af3cd (MD5) %R 10.1016/S0362-546X(98)00067-4 %0 Book Section %B The Painlevé property : one century later / Robert Conte ed. - New York : Springer-Verlag, 1999. - (CRM series in mathematical physics). - p. 287-412 %D 1999 %T Painlevé transcendents in two-dimensional topological field theory %A Boris Dubrovin %B The Painlevé property : one century later / Robert Conte ed. - New York : Springer-Verlag, 1999. - (CRM series in mathematical physics). - p. 287-412 %I Springer %@ 0-387-98888-2 %G en_US %U http://hdl.handle.net/1963/3238 %1 1463 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-11-04T11:08:16Z\\nNo. of bitstreams: 1\\n9803107v2.pdf: 723839 bytes, checksum: 3066b99f8c826fa005eb229ddd03d8dc (MD5) %0 Report %D 1999 %T Recurrent procedure for the determination of the free energy ε^2 expansion in the topological string theory %A Boris Dubrovin %A Andrei Ya A Maltsev %XWe present here the iteration procedure for the determination of free energy ǫ2-expansion using the theory of KdV - type equations. In our approach we use the conservation laws for KdV - type equations depending explicitly on times t1, t2, . . . to find the ǫ2-expansion of u(x, t1, t2, . . .) after the infinite number of shifts of u(x, 0, 0, . . .) ≡ x along t1, t2, . . . in recurrent form. The formulas for the free energy expansion are just obtained then as a result of quite simple integration procedure applied to un(x).

%B arXiv:solv-int/990400 %I SISSA %G en %U http://hdl.handle.net/1963/6489 %1 6421 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T15:03:06Z No. of bitstreams: 1 dubrovin_maltsev_1999.pdf: 156918 bytes, checksum: b8e98c45d6ed83c8762446339a79418a (MD5) %0 Journal Article %J Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 28 (1999), no. 4, 741-808 %D 1999 %T Renormalized solutions of elliptic equations with general measure data %A Gianni Dal Maso %A Francois Murat %A Luigi Orsina %A Alain Prignet %B Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 28 (1999), no. 4, 741-808 %I Scuola Normale Superiore di Pisa %G en %U http://hdl.handle.net/1963/1236 %1 2707 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:08Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %0 Journal Article %J Ricerche Matematiche., Supplemento dedicato a Ennio De Giorgi, vol. 48 (1999), page : 99-116 %D 1999 %T Some properties of the solutions of obstacle problems with measure data %A Paolo Dall'Aglio %A Gianni Dal Maso %B Ricerche Matematiche., Supplemento dedicato a Ennio De Giorgi, vol. 48 (1999), page : 99-116 %G en %U http://hdl.handle.net/1963/6432 %1 6372 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-31T18:18:45Z\\nNo. of bitstreams: 1\\nDAgl-DM-98.pdf: 205798 bytes, checksum: 96a8209dd814b3087f68a24a5f79d5b5 (MD5) %0 Journal Article %J Arch. Ration. Mech. Anal. 146 (1999), no. 1, 23--58 %D 1999 %T Variational formulation of softening phenomena in fracture mechanics. The one-dimensional case %A Andrea Braides %A Gianni Dal Maso %A Adriana Garroni %X Starting from experimental evidence, the authors justify a variational model for softening phenomena in fracture of one-dimensional bars where the energy is given by the contribution and interaction of two terms: a typical bulk energy term depending on elastic strain and a discrete part that depends upon the jump discontinuities that occur in fracture. A more formal, rigorous derivation of the model is presented by examining the $\\\\Gamma$-convergence of discrete energy functionals associated to an array of masses and springs. Close attention is paid to the softening and fracture regimes. \\nOnce the continuous model is derived, it is fully analyzed without losing sight of its discrete counterpart. In particular, the associated boundary value problem is studied and a detailed analysis of the stationary points under the presence of a dead load is performed. A final, interesting section on the scale effect on the model is included. %B Arch. Ration. Mech. Anal. 146 (1999), no. 1, 23--58 %I Springer %G en_US %U http://hdl.handle.net/1963/3371 %1 959 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-11-28T17:18:31Z\\nNo. of bitstreams: 1\\nVariational_formulation.pdf: 2100868 bytes, checksum: 88bfc4cfb6072391f1c6d7cd06e7b8ec (MD5) %R 10.1007/s002050050135 %0 Journal Article %J Ann. Mat. Pura Appl. (4) 174 (1998), 13--72 %D 1998 %T Asymptotic behavior of nonlinear Dirichlet problems in perforated domains %A Gianni Dal Maso %A Igor V. Skrypnik %B Ann. Mat. Pura Appl. (4) 174 (1998), 13--72 %I SISSA Library %G en %U http://hdl.handle.net/1963/1064 %1 2738 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:42:20Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Journal Article %J Comm. Math. Phys. 198 (1998) 311-361 %D 1998 %T Bihamiltonian Hierarchies in 2D Topological Field Theory At One-Loop Approximation %A Boris Dubrovin %A Zhang Youjin %X We compute the genus one correction to the integrable hierarchy describing coupling to gravity of a 2D topological field theory. The bihamiltonian structure of the hierarchy is given by a classical W-algebra; we compute the central charge of this algebra. We also express the generating function of elliptic Gromov - Witten invariants via tau-function of the isomonodromy deformation problem arising in the theory of WDVV equations of associativity. %B Comm. Math. Phys. 198 (1998) 311-361 %I Springer %G en_US %U http://hdl.handle.net/1963/3696 %1 609 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-07-27T12:07:27Z\\nNo. of bitstreams: 1\\n9712232v2.pdf: 436927 bytes, checksum: 47b60da0e628b29d60ba56f9071105ee (MD5) %R 10.1007/s002200050480 %0 Journal Article %J J. Differential Geometry Suppl.4 (1998) 181-211 %D 1998 %T Differential geometry of the space of orbits of a Coxeter group %A Boris Dubrovin %X Differential-geometric structures on the space of orbits of a finite Coxeter group, determined by Groth\\\\\\\'endieck residues, are calculated. This gives a construction of a 2D topological field theory for an arbitrary Coxeter group. %B J. Differential Geometry Suppl.4 (1998) 181-211 %I International Press %G en_US %U http://hdl.handle.net/1963/3562 %1 1140 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-03-03T18:46:23Z\\nNo. of bitstreams: 1\\n29-93-FM.pdf: 243594 bytes, checksum: 4ed9f8d24e959397f629a8e6b6c8114d (MD5) %0 Journal Article %J Annales Poincare Phys.Theor.69:413-424,1998 %D 1998 %T Diffusion of a particle in presence of N moving point sources %A Gianfausto Dell'Antonio %A Rodolfo Figari %A Alessandro Teta %B Annales Poincare Phys.Theor.69:413-424,1998 %I SISSA Library %G en %U http://hdl.handle.net/1963/134 %1 75 %2 LISNU %3 Interdisciplinary Laboratory for Advanced Studies %$ Made available in DSpace on 2004-09-01T12:22:22Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1996 %0 Journal Article %J Compositio Mathematica. Volume 111, Issue 2, 1998, Pages 167-219 %D 1998 %T Extended affine Weyl groups and Frobenius manifolds %A Boris Dubrovin %A Youjin Zhang %B Compositio Mathematica. Volume 111, Issue 2, 1998, Pages 167-219 %I Kluwer %G en %U http://hdl.handle.net/1963/6486 %1 6424 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T15:13:49Z\\nNo. of bitstreams: 1\\ndubrovin_zhang_1998_compositio.pdf: 321250 bytes, checksum: 49608b8d8e6245677c302db09170d85e (MD5) %R 10.1023/A:1000258122329 %0 Book Section %B Proceedings of the International Congress of Mathematicians : Berlin 1998, August 18 - 27. II, Invited lectures. - Bielefeld : Universität Bielefeld, Fakultät für Mathematik cop. 1998. - pages : 315-326 %D 1998 %T Geometry and analytic theory of Frobenius manifolds %A Boris Dubrovin %X Main mathematical applications of Frobenius manifolds are\\r\\nin the theory of Gromov - Witten invariants, in singularity theory, in\\r\\ndifferential geometry of the orbit spaces of reflection groups and of their\\r\\nextensions, in the hamiltonian theory of integrable hierarchies. The theory\\r\\nof Frobenius manifolds establishes remarkable relationships between\\r\\nthese, sometimes rather distant, mathematical theories. %B Proceedings of the International Congress of Mathematicians : Berlin 1998, August 18 - 27. II, Invited lectures. - Bielefeld : Universität Bielefeld, Fakultät für Mathematik cop. 1998. - pages : 315-326 %G en %U http://hdl.handle.net/1963/6488 %1 6422 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T15:05:37Z\\nNo. of bitstreams: 1\\nicm98.pdf: 184775 bytes, checksum: 33db28beb5919405d7396b9f6ba40c56 (MD5) %0 Journal Article %J Journal des Mathematiques Pures et Appliquees. Volume 77, Issue 1, January 1998, Pages 89-116 %D 1998 %T Limits of variational problems for Dirichlet forms in varying domains %A Gianni Dal Maso %A Virginia De Cicco %A Lino Notarantonio %A Nicoletta A. Tchou %B Journal des Mathematiques Pures et Appliquees. Volume 77, Issue 1, January 1998, Pages 89-116 %I SISSA %G en %U http://hdl.handle.net/1963/6440 %1 6377 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-31T18:44:35Z\\nNo. of bitstreams: 2\\nDM-DeC-96.pdf: 145467 bytes, checksum: 0cf974ac5cc090ff7f9faae3d433043f (MD5)\\nDM-DeC-96-cover.pdf: 35849 bytes, checksum: cde85af897042e1ee2c1b1a8c724b8eb (MD5) %R 10.1016/S0362-546X(98)00067-4 %0 Journal Article %J Potential Anal. 7 (1997), no. 4, 765-803 %D 1997 %T Capacity theory for monotone operators %A Gianni Dal Maso %A Igor V. Skrypnik %X 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 $F$. %B Potential Anal. 7 (1997), no. 4, 765-803 %I Springer %G en %U http://hdl.handle.net/1963/911 %1 2880 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:40:26Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %R 10.1023/A:1017987405983 %0 Journal Article %J Bollettino della Unione Matematica Italiana A. Volume 7, Issue SUPPL. 11 part 2, June 1997, Pages 253-277 %D 1997 %T Comportamento asintotico delle soluzioni di problemi di Dirichlet %A Gianni Dal Maso %B Bollettino della Unione Matematica Italiana A. Volume 7, Issue SUPPL. 11 part 2, June 1997, Pages 253-277 %G it %U http://hdl.handle.net/1963/6438 %1 6378 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-31T18:47:36Z\\nNo. of bitstreams: 1\\nDM-97-UMI.pdf: 232404 bytes, checksum: 9b45a539545e2635c8ffedf2ec7a0648 (MD5) %0 Book Section %B Integrable systems and algebraic geometry : proceedings of the Taniguchi symposium 1997, Kobe, June 30 - July 4, 1997 and Research Institute for Mathematical Sciences, Kyoto University, July 7 - 11, 1997 / eds. M.-H. Saito, Y. Shimizu and K. Ueno. - Sing %D 1997 %T Flat pencils of metrics and Frobenius manifolds %A Boris Dubrovin %X This paper is based on the author\\\'s talk at 1997 Taniguchi Symposium \\\"Integrable Systems and Algebraic Geometry\\\". We consider an approach to the theory of Frobenius manifolds based on the geometry of flat pencils of contravariant metrics. It is shown that, under certain homogeneity assumptions, these two objects are identical. The flat pencils of contravariant metrics on a manifold $M$ appear naturally in the classification of bihamiltonian structures of hydrodynamics type on the loop space $L(M)$. This elucidates the relations between Frobenius manifolds and integrable hierarchies. %B Integrable systems and algebraic geometry : proceedings of the Taniguchi symposium 1997, Kobe, June 30 - July 4, 1997 and Research Institute for Mathematical Sciences, Kyoto University, July 7 - 11, 1997 / eds. M.-H. Saito, Y. Shimizu and K. Ueno. - Sing %I World Scientific %@ 981-02-3266-7 %G en_US %U http://hdl.handle.net/1963/3237 %1 1065 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-11-04T10:55:32Z\\nNo. of bitstreams: 1\\n9803106v1.pdf: 198515 bytes, checksum: bd38d2f5dc411787c3b0d0660cc0b783 (MD5) %0 Book Section %B Solitons, geometry, and topology : on the crossroad / V. M. Buchstaber, S. P. Novikov editors.- Providence : American Mathematical Society, 1997. - ( American mathematical society translations. Series 2. - vol. 179). - pages : 35-44 %D 1997 %T Functionals of the Peierls - Fröhlich Type and the Variational Principle for the Whitham Equations %A Boris Dubrovin %B Solitons, geometry, and topology : on the crossroad / V. M. Buchstaber, S. P. Novikov editors.- Providence : American Mathematical Society, 1997. - ( American mathematical society translations. Series 2. - vol. 179). - pages : 35-44 %I American Mathematical Society %@ 0821806661 %G en %U http://hdl.handle.net/1963/6485 %1 6425 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T15:16:27Z\\nNo. of bitstreams: 1\\npeierls.pdf: 108417 bytes, checksum: 9821dab3c135a3be76e7cb5cb4ec401e (MD5) %0 Journal Article %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. Sér. 4, 25 no. 1-2 (1997), p. 375-396 %D 1997 %T Some properties of reachable solutions of nonlinear elliptic equations with measure data %A Gianni Dal Maso %A Annalisa Malusa %B Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. Sér. 4, 25 no. 1-2 (1997), p. 375-396 %I SISSA %G en %U http://hdl.handle.net/1963/6434 %1 6375 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-31T18:33:05Z\\nNo. of bitstreams: 1\\nDM-Mal-97-sissa.pdf: 261079 bytes, checksum: bc786a00522c2b2dd3ee0acf0e9c3759 (MD5) %0 Journal Article %J Lett. Math. Phys. 40 (1997), no. 3, 235-256 %D 1997 %T Statistics in space dimension two %A Gianfausto Dell'Antonio %A Rodolfo Figari %A Alessandro Teta %X We construct as a selfadjoint operator the Schroedinger hamiltonian for a system of $N$ identical particles on a plane, obeying the statistics defined by a representation $\\\\pi_1$ of the braid group. We use quadratic forms and potential theory, and give details only for the free case; standard arguments provide the extension of our approach to the case of potentials which are small in the sense of forms with respect to the laplacian. We also comment on the relation between the analysis given here and other approaches to the problem, and also on the connection with the description of a quantum particle on a plane under the influence of a shielded magnetic field (Aharanov-Bohm effect). %B Lett. Math. Phys. 40 (1997), no. 3, 235-256 %I SISSA Library %G en %U http://hdl.handle.net/1963/130 %1 12 %2 LISNU %3 Interdisciplinary Laboratory for Advanced Studies %$ Made available in DSpace on 2004-09-01T12:22:20Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1996 %R 10.1023/A:1007361832622 %0 Journal Article %J Studies in Applied Mathematics. Year : 1997 ; Volume: 99 ; Issue: 2 ; Pages: 137-203 %D 1997 %T Three-Phase Solutions of the Kadomtsev - Petviashvili Equation %A Boris Dubrovin %A Ron Flickinger %A Harvey Segur %X The Kadomtsev]Petviashvili KP. equation is known to admit explicit periodic\\r\\nand quasiperiodic solutions with N independent phases, for any integer\\r\\nN, based on a Riemann theta-function of N variables. For Ns1 and 2,\\r\\nthese solutions have been used successfully in physical applications. This\\r\\narticle addresses mathematical problems that arise in the computation of\\r\\ntheta-functions of three variables and with the corresponding solutions of\\r\\nthe KP equation. We identify a set of parameters and their corresponding\\r\\nranges, such that e¨ery real-valued, smooth KP solution associated with a\\r\\nRiemann theta-function of three variables corresponds to exactly one choice\\r\\nof these parameters in the proper range. Our results are embodied in a\\r\\nprogram that computes these solutions efficiently and that is available to the\\r\\nreader. We also discuss some properties of three-phase solutions. %B Studies in Applied Mathematics. Year : 1997 ; Volume: 99 ; Issue: 2 ; Pages: 137-203 %I SISSA %G en %U http://hdl.handle.net/1963/6484 %1 6426 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T15:19:00Z\\nNo. of bitstreams: 1\\ndubrovin_flickinger_segur.pdf: 1081636 bytes, checksum: a10c5af7339b1422cb469d18823c5c92 (MD5) %R 10.1111/1467-9590.00059 %0 Journal Article %J Rend. Sem. Mat. Univ. Padova 96 (1996), 257--277 %D 1996 %T A capacity method for the study of Dirichlet problems for elliptic systems in varying domains %A Gianni Dal Maso %A Rodica Toader %B Rend. Sem. Mat. Univ. Padova 96 (1996), 257--277 %I SISSA Library %G en %U http://hdl.handle.net/1963/989 %1 2867 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:41:21Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Journal Article %D 1995 %T Capacity and Dirichlet problems in varying domains %A Gianni Dal Maso %I SISSA Library %G en %U http://hdl.handle.net/1963/950 %1 3504 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:40:53Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Journal Article %J Topological nonlinear analysis, II (Frascati, 1995), 1--86, Progr. Nonlinear Differential Equations Appl., 27, Birkhauser Boston, Boston, MA, 1997 %D 1995 %T Classical solutions for a perturbed N-body system %A Gianfausto Dell'Antonio %B Topological nonlinear analysis, II (Frascati, 1995), 1--86, Progr. Nonlinear Differential Equations Appl., 27, Birkhauser Boston, Boston, MA, 1997 %I SISSA Library %G en %U http://hdl.handle.net/1963/126 %1 16 %2 LISNU %3 Interdisciplinary Laboratory for Advanced Studies %$ Made available in DSpace on 2004-09-01T12:22:18Z (GMT). No. of bitstreams: 1\\nILAS_1_96.pdf: 4461254 bytes, checksum: eae522e49d94ff9b35a3067aa9f62b0a (MD5)\\n Previous issue date: 1996 %0 Book Section %B Integrable systems and quantum groups : lectures given at the 1st session of the Centro internazionale matematico estivo (C.I.M.E.) held in Montecatini Terme, Italy, June 14-22, 1995 / R. Donagi, B. Dubrovin, E. Frenkel... [et al.] ; editors, M. Francavig %D 1995 %T Geometry of 2D topological field theories %A Boris Dubrovin %X These notes are devoted to the theory of “equations of associativity”\\r\\ndescribing geometry of moduli spaces of 2D topological field theories. %B Integrable systems and quantum groups : lectures given at the 1st session of the Centro internazionale matematico estivo (C.I.M.E.) held in Montecatini Terme, Italy, June 14-22, 1995 / R. Donagi, B. Dubrovin, E. Frenkel... [et al.] ; editors, M. Francavig %I SISSA %@ 3-540-60542-8 %G en %U http://hdl.handle.net/1963/6483 %1 6427 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T15:22:39Z\\nNo. of bitstreams: 1\\nmonte.pdf: 1437681 bytes, checksum: ecddb1d7310dbda2a35388d25609d3aa (MD5) %0 Journal Article %D 1995 %T Special functions of bounded deformation %A Giovanni Bellettini %A Alessandra Coscia %A Gianni Dal Maso %I SISSA Library %G en %U http://hdl.handle.net/1963/978 %1 3476 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:41:13Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Report %D 1994 %T Algebraic-geometrical Darboux coordinates in R-matrix formalism %A P. Diener %A Boris Dubrovin %I SISSA %G en_US %U http://hdl.handle.net/1963/3655 %1 650 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-06-19T09:50:48Z\\nNo. of bitstreams: 1\\nconvert_SCAN-9409240.pdf: 910778 bytes, checksum: 4c51b62625fe5debfdaa55aa2db61ff8 (MD5) %0 Journal Article %J Duke Mathematical Journal. Volume: 76, Issue: 2, Pages: 645-668 %D 1994 %T Integrable functional equations and algebraic geometry %A Boris Dubrovin %A A.S. Fokas %A P.M. Santini %B Duke Mathematical Journal. Volume: 76, Issue: 2, Pages: 645-668 %I SISSA %G en %U http://hdl.handle.net/1963/6482 %1 6428 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T15:25:35Z\\nNo. of bitstreams: 1\\ndubrovin_fokas_santini_1994.pdf: 19581899 bytes, checksum: 25c6a7352fa60a95d891bf8ae238f20c (MD5) %R 10.1215/S0012-7094-94-07623-0 %0 Journal Article %J Rend. Istit. Mat. Univ. Trieste 26 (1994) 339-360 %D 1994 %T Limits of Dirichlet problems in perforated domains: a new formulation %A Gianni Dal Maso %A Rodica Toader %B Rend. Istit. Mat. Univ. Trieste 26 (1994) 339-360 %I Università degli Studi di Trieste, Dipartimento di Scienze Matematiche %G en_US %U http://hdl.handle.net/1963/3649 %1 656 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-06-16T11:02:31Z\\nNo. of bitstreams: 1\\ndalmaso18.pdf: 255148 bytes, checksum: e857ab6de9d63e187905170895a65ccf (MD5) %0 Book Section %B Important developments in soliton theory / A. S. Fokas, V. E. Zakharov (eds.) - Berlin : Springer-Verlag, 1993. - pages : 86-98 %D 1993 %T Dispersion relations for non-linear waves and the Schottky problem %A Boris Dubrovin %X An approach to the Schottky problem of specification of periods of holomorphic differentials\\r\\non Riemann surfaces (or, equivalently, specification of Jacobians among all principaly\\r\\npolarized Abelian varieties) based on the theory of Kadomtsev - Petviashvili equation,\\r\\nis discussed. %B Important developments in soliton theory / A. S. Fokas, V. E. Zakharov (eds.) - Berlin : Springer-Verlag, 1993. - pages : 86-98 %I SISSA %@ 3540559132 %G en %U http://hdl.handle.net/1963/6480 %1 6430 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T15:31:24Z\\nNo. of bitstreams: 1\\ndubrovin_1993_schottky.pdf: 162204 bytes, checksum: a23db6fee2ea5f3db9c3a3562ae196f5 (MD5) %0 Journal Article %J Communications in Mathematical Physics. Volume 152, Issue 3, March 1993, Pages 539-564 %D 1993 %T Geometry and integrability of topological-antitopological fusion %A Boris Dubrovin %X Integrability of equations of topological-antitopological fusion (being proposed\\r\\nby Cecotti and Vafa) describing the ground state metric on a given 2D topological\\r\\nfield theory (TFT) model, is proved. For massive TFT models these equations\\r\\nare reduced to a universal form (being independent on the given TFT model) by\\r\\ngauge transformations. For massive perturbations of topological conformal field theory\\r\\nmodels the separatrix solutions of the equations bounded at infinity are found\\r\\nby the isomonodromy deformations method. Also it is shown that the ground state\\r\\nmetric together with some part of the underlined TFT structure can be parametrized\\r\\nby pluriharmonic maps of the coupling space to the symmetric space of real positive\\r\\ndefinite quadratic forms. %B Communications in Mathematical Physics. Volume 152, Issue 3, March 1993, Pages 539-564 %I SISSA %G en %U http://hdl.handle.net/1963/6481 %1 6429 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T15:28:15Z\\nNo. of bitstreams: 1\\ndubrovin_1993_cmp.pdf: 1218370 bytes, checksum: 6e082400ac3ed51e3b01ec532f9a598d (MD5) %R 10.1007/BF02096618 %0 Book Section %B Integrable systems : the Verdier memorial conference : actes du colloque international de Luminy / Olivier Babelon, Pierre Cartier, Yvette Kosmann-Schwarzbach editors. - Boston [etc.] : Birkhauser, c1993. - p. 313-359 %D 1993 %T Integrable systems and classification of 2D topological field theories %A Boris Dubrovin %X In this paper we consider from the point of view of differential geometry and of the\\r\\ntheory of integrable systems the so-called WDVV equations as defining relations of 2-\\r\\ndimensional topological field theory. A complete classification of massive topological conformal\\r\\nfield theories (TCFT) is obtained in terms of monodromy data of an auxillary\\r\\nlinear operator with rational coefficients. Procedure of coupling of a TCFT to topological\\r\\ngravity is described (at tree level) via certain integrable bihamiltonian hierarchies of\\r\\nhydrodynamic type and their τ -functions. A possible role of bihamiltonian formalism in\\r\\ncalculation of high genus corrections is discussed. As a biproduct of this discussion new\\r\\nexamples of infinite dimensional Virasoro-type Lie algebras and their nonlinear analogues\\r\\nare constructed. As an algebro-geometrical applications it is shown that WDVV is just the\\r\\nuniversal system of integrable differential equations (high order analogue of the Painlev´e-\\r\\nVI) specifying periods of Abelian differentials on Riemann surfaces as functions on moduli\\r\\nof these surfaces. %B Integrable systems : the Verdier memorial conference : actes du colloque international de Luminy / Olivier Babelon, Pierre Cartier, Yvette Kosmann-Schwarzbach editors. - Boston [etc.] : Birkhauser, c1993. - p. 313-359 %I SISSA %@ 0817636536 %G en %U http://hdl.handle.net/1963/6478 %1 6432 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T15:43:16Z\\nNo. of bitstreams: 1\\ndubrovin_1993_verdier.pdf: 341620 bytes, checksum: 7aeca49fd73426f29caffc6712ae6b94 (MD5) %0 Book Section %B Integrable quantum field theories / edited by L. Bonora ... \et al.! - New York : Plenum Press, 1993. - page : 283 - 302. %D 1993 %T Topological conformal field theory from the point of view of integrable systems %A Boris Dubrovin %X Recent results on classification of massive topological conformal field theories (TCFT) in terms of monodromy data of auxiliary linear operators with rational coefficients are presented. Procedure of coupling of a TCFT to topological gravity is described (at tree-level approximation) via certain integrable hierarchies of hydrodynamic type and their tau-functions. It is explained how the calculation of the ground state metric on TCFT can be interpreted in terms of harmonic maps. Also a construction of some models via Coxeter groups is described. %B Integrable quantum field theories / edited by L. Bonora ... \et al.! - New York : Plenum Press, 1993. - page : 283 - 302. %I SISSA %@ 0306445344 %G en %U http://hdl.handle.net/1963/6479 %1 6431 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T15:39:39Z No. of bitstreams: 1 dubrovin_1993_como.pdf: 5585529 bytes, checksum: ab3c2666b211166f3722fb8ef2b5716f (MD5) %0 Journal Article %D 1993 %T Workshop on point interactions, Trieste, 21-23 December 1992 %A Gianfausto Dell'Antonio %I SISSA Library %G en %U http://hdl.handle.net/1963/71 %1 52 %2 LISNU %3 Interdisciplinary Laboratory for Advanced Studies %$ Made available in DSpace on 2004-09-01T12:03:40Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1993 %0 Journal Article %J Communications in Mathematical Physics. Volume 145, Issue 1, March 1992, Pages 195-207 %D 1992 %T Hamiltonian formalism of Whitham-type hierarchies and topological Landau - Ginsburg models %A Boris Dubrovin %X We show that the bi-hamiltonian structure of the averaged Gelfand-Dikii\\r\\nhierarchy is involved in the Landau-Ginsburg topological models (for An-Series):\\r\\nthe Casimirs for the first P.B. give the correct coupling parameters for the perturbed\\r\\ntopological minimal model; the correspondence {coupling parameters} ~ {primary\\r\\nfields} is determined by the second P.B. The partition function (at the tree level) and\\r\\nthe chiral algebra for LG models are calculated for any genus g. %B Communications in Mathematical Physics. Volume 145, Issue 1, March 1992, Pages 195-207 %I SISSA %G en %U http://hdl.handle.net/1963/6476 %1 6434 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T15:47:41Z\\nNo. of bitstreams: 1\\ndubrovin_1992_cmp.pdf: 603608 bytes, checksum: 2f99a3ad40552bd6108f212c3ab48d36 (MD5) %R 10.1007/BF02099286 %0 Journal Article %J Nuclear Physics B. Volume 379, Issue 3, 1992, pages : 627-689 %D 1992 %T Integrable systems in topological field theory %A Boris Dubrovin %X Integrability of the system of PDE for dependence on coupling parameters of the (tree-level) primary partition function in massive topological field theories, being imposed by the associativity of the perturbed primary chiral algebra, is proved. In the conformal case it is shown that all the topological field theories are classified as solutions of a universal high-order Painlevé-type equation. Another integrable hierarchy (of systems of hydrodynamic type) is shown to describe coupling to gravity of the matter sector of any topological field theory. Different multicritical models with the given structure of primary correlators are identified with particular self-similar solutions of the hierarchy. The partition function of any of the models is calculated as the corresponding tau-function of the hierarchy. %B Nuclear Physics B. Volume 379, Issue 3, 1992, pages : 627-689 %I SISSA %G en %U http://hdl.handle.net/1963/6477 %1 6433 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T15:45:42Z\\nNo. of bitstreams: 1\\ndubrovin_1992_npb.pdf: 2696879 bytes, checksum: 163a16f37434f88134edaeaa900f7d1e (MD5) %0 Journal Article %J Acta Math. 168 (1992), no.1-2, p. 89-151 %D 1992 %T A variational method in image segmentation: existence and approximation result %A Gianni Dal Maso %A Jean-Michel Morel %A Sergio Solimini %B Acta Math. 168 (1992), no.1-2, p. 89-151 %I SISSA Library %G en %U http://hdl.handle.net/1963/808 %1 2983 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:38:13Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1989 %0 Report %D 1991 %T Differential geometry of moduli spaces and its applications to soliton equations and to topological conformal field theory %A Boris Dubrovin %X We construct flat Riemannian metrics on moduli spaces of algebraic curves with marked meromorphic function. This gives a new class of exact algebraic-geometry solutions to certain non-linear equations in terms of functions on the moduli spaces. We show that the Riemannian metrics on the moduli spaces coincide with two-point correlators in topological conformal field theory and calculate the partition function for A_n model for arbitrary genus. A universal method for constructing complete families of conservation laws for Whitham-type hierarchies of PDEs is also proposed. %B Preprint n.117, Scuola Normale Superiore, Pisa, November 1991, 31 pp. Published in: Surveys in Differential Geometry , Vol. IV (1999), p. 213 - 238. %I Scuola Normale Superiore di Pisa %G en %U http://hdl.handle.net/1963/6475 %1 6435 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T15:53:59Z\\nNo. of bitstreams: 1\\ndubrovin_1991_pisa.pdf: 53312802 bytes, checksum: d2f189e9a1439fd386fc50d3fa79b40b (MD5) %0 Journal Article %J Appl.Math.Optim. 23 (1991), no.1, p. 17-49. %D 1991 %T Shape optimization for Dirichlet problems: relaxed formulations and optimally conditions %A Giuseppe Buttazzo %A Gianni Dal Maso %B Appl.Math.Optim. 23 (1991), no.1, p. 17-49. %I SISSA Library %G en %U http://hdl.handle.net/1963/880 %1 2911 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:39:05Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1989 %0 Journal Article %J Differential Integral Equations 4 (1991), no.4, p.739-765. %D 1991 %T On systems of ordinary differential equations with measures as controls %A Gianni Dal Maso %A Franco Rampazzo %B Differential Integral Equations 4 (1991), no.4, p.739-765. %I SISSA Library %G en %U http://hdl.handle.net/1963/840 %1 2951 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:38:35Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1989 %0 Journal Article %J Differential Integral Equations 3 (1990), no.6, p.1151-1166. %D 1990 %T Correctors for the homogeneization of monotone operators %A Gianni Dal Maso %A Anneliese Defranceschi %B Differential Integral Equations 3 (1990), no.6, p.1151-1166. %I SISSA Library %G en %U http://hdl.handle.net/1963/812 %1 2979 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:38:16Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1989 %0 Journal Article %J Ann. Inst. H. Poincare\\\' Anal. Non Linére 7 (1990), no. 3, 123-160 %D 1990 %T G-convergence of monotone operators %A Valeria Chiadò Piat %A Gianni Dal Maso %A Anneliese Defranceschi %B Ann. Inst. H. Poincare\\\' Anal. Non Linére 7 (1990), no. 3, 123-160 %I SISSA Library %G en %U http://hdl.handle.net/1963/680 %1 3246 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:36:13Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1988 %0 Journal Article %J Proc. Amer. Math. Soc. 108 (1990), no. 3, 691-702 %D 1990 %T A general chain rule for distributional derivatives %A Luigi Ambrosio %A Gianni Dal Maso %B Proc. Amer. Math. Soc. 108 (1990), no. 3, 691-702 %I SISSA Library %G en %U http://hdl.handle.net/1963/650 %1 3276 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:35:52Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1988 %0 Journal Article %J Bull. Amer. Math. Soc. (N.S.) , 23 (1990), no.2, 531-535. %D 1990 %T Shape optimization for Dirichlet problems: relaxed solutions and optimality conditions %A Giuseppe Buttazzo %A Gianni Dal Maso %B Bull. Amer. Math. Soc. (N.S.) , 23 (1990), no.2, 531-535. %I SISSA Library %G en %U http://hdl.handle.net/1963/809 %1 2982 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:38:13Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1989 %0 Journal Article %J Comm. Partial Differential Equations, 14 (1989), no.12, 1717-1743. %D 1989 %T An approach to the thin obstacle problem for variational functionals depending on vector %A Gianni Dal Maso %A Roberta Musina %B Comm. Partial Differential Equations, 14 (1989), no.12, 1717-1743. %I SISSA Library %G en %U http://hdl.handle.net/1963/802 %1 2989 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:38:08Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1989 %0 Journal Article %J J. Analyse Math. 53 (1989), 269--289 %D 1989 %T Convergence of unilateral problems for monotone operators %A Gianni Dal Maso %A Anneliese Defranceschi %B J. Analyse Math. 53 (1989), 269--289 %I SISSA Library %G en %U http://hdl.handle.net/1963/722 %1 3069 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:36:45Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1988 %0 Journal Article %J Partial differential equations and the calculus of variations : essays in honor of Ennio De Giorgi. - Boston : Birkhauser, 1989. - p. 285-309 %D 1989 %T Limits of obstacle problems for the area functional. %A Gianni Dal Maso %A G. Carere %A Antonio Leaci %A Eduardo Pascali %B Partial differential equations and the calculus of variations : essays in honor of Ennio De Giorgi. - Boston : Birkhauser, 1989. - p. 285-309 %I SISSA Library %G en %U http://hdl.handle.net/1963/577 %1 3327 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:34:36Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1987 %0 Journal Article %J Boll. Un. Mat. Ital. B (7) 3 (1989), no. 3, 579-590 %D 1989 %T On the number of families of periodic solutions of a Hamiltonian system near equilibrium. II. (English. Italian summary) %A Gianfausto Dell'Antonio %A Biancamaria D'Onofrio %B Boll. Un. Mat. Ital. B (7) 3 (1989), no. 3, 579-590 %I SISSA Library %G en %U http://hdl.handle.net/1963/609 %1 3295 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:35:24Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1988 %0 Journal Article %J Acta Math. 163 (1989), no. 1-2, 57-107 %D 1989 %T A pointwise regularity theory for the two-obstacle problem %A Gianni Dal Maso %A Umberto Mosco %A Maria Agostina Vivaldi %B Acta Math. 163 (1989), no. 1-2, 57-107 %I SISSA Library %G en %U http://hdl.handle.net/1963/643 %1 3810 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:35:48Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1988 %0 Journal Article %J Boll. Un. Mat. Ital. A (7) 2, 1988, no. 1, 127-135 %D 1988 %T A Kellogg property for µ-capacities %A Gianni Dal Maso %A Anneliese Defranceschi %B Boll. Un. Mat. Ital. A (7) 2, 1988, no. 1, 127-135 %I SISSA Library %G en %U http://hdl.handle.net/1963/492 %1 3412 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:33:34Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1987 %0 Journal Article %J Manuscripta Math. 61 (1988), no. 3, 251-278. %D 1988 %T Limits of nonlinear Dirichlet problems in varying domains. %A Gianni Dal Maso %A Anneliese Defranceschi %X 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. %B Manuscripta Math. 61 (1988), no. 3, 251-278. %I SISSA Library %G en %U http://hdl.handle.net/1963/536 %1 3368 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:34:06Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1987 %0 Journal Article %J Stochastic processes, physics and geompetry (Ascona and Locarno, 1988), 302, World Sci.Publishing,NJ(1990) %D 1988 %T Methods of stochastic stability and properties of the Gribov horizon in the stochastic quantization of gauge theories %A Gianfausto Dell'Antonio %B Stochastic processes, physics and geompetry (Ascona and Locarno, 1988), 302, World Sci.Publishing,NJ(1990) %I SISSA Library %G en %U http://hdl.handle.net/1963/817 %1 2974 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:38:19Z (GMT). No. of bitstreams: 1\\n57_89.pdf: 1633846 bytes, checksum: a43a1ffeb9c51682ffce41b843c16bf9 (MD5)\\n Previous issue date: 1989 %0 Journal Article %J J.Funct.Anal. 79, 1988, no. 2, 476-492 %D 1988 %T Some properties of a class of nonlinear variational $m$-capacities %A Gianni Dal Maso %A Anneliese Defranceschi %B J.Funct.Anal. 79, 1988, no. 2, 476-492 %I SISSA Library %G en %U http://hdl.handle.net/1963/485 %1 3419 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:33:29Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1987 %R 10.1016/0022-1236(88)90022-5 %0 Journal Article %J Ann. Mat. Pura Appl. (4) 153 (1988), 203-227 (1989) %D 1988 %T Variational inequalities for the biharmonic operator with variable obstacles. %A Gianni Dal Maso %A Gabriella Paderni %B Ann. Mat. Pura Appl. (4) 153 (1988), 203-227 (1989) %I SISSA Library %G en %U http://hdl.handle.net/1963/531 %1 3373 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:34:03Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1987 %0 Journal Article %J Ricerche Mat. 36 (1987), no. 2, 197-214 %D 1987 %T Integral representation of some convex local functionals. %A Gianni Dal Maso %A Gabriella Paderni %B Ricerche Mat. 36 (1987), no. 2, 197-214 %I SISSA Library %G en %U http://hdl.handle.net/1963/497 %1 3407 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:33:38Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1987 %0 Journal Article %J Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 81, 1987, no. 2, 111-118 %D 1987 %T Limits of nonlinear Dirichlet problems in varying domains. (Italian) %A Gianni Dal Maso %A Anneliese Defranceschi %B Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 81, 1987, no. 2, 111-118 %I SISSA Library %G en %U http://hdl.handle.net/1963/486 %1 3418 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:33:30Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1987 %0 Journal Article %J Berlin : Springer-Verlag, 1986, Lecture notes in mathematics, v.1190, p. 181-190 %D 1986 %T Convergence of unilateral convex sets. Optimization and related fields (Erice, 1984) %A Gianni Dal Maso %B Berlin : Springer-Verlag, 1986, Lecture notes in mathematics, v.1190, p. 181-190 %I SISSA Library %G en %U http://hdl.handle.net/1963/353 %1 3614 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:28:39Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1984 %0 Journal Article %J Nonlinear anal. 10(1986), no.6, 603-613 %D 1986 %T Dirichlet problems for demicoercive functionals %A Gabriele Anzellotti %A Giuseppe Buttazzo %A Gianni Dal Maso %B Nonlinear anal. 10(1986), no.6, 603-613 %I SISSA Library %G en %U http://hdl.handle.net/1963/390 %1 3577 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:31:55Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1985 %R 10.1016/0362-546X(86)90145-8 %0 Journal Article %J Phys. Lett. A 108 (1985), no. 7, 311-314 %D 1985 %T Flat connections for Lax hierarchies on coadjoint orbits %A Giovanni Landi %A Sergio De Filippo %B Phys. Lett. A 108 (1985), no. 7, 311-314 %I SISSA Library %G en %U http://hdl.handle.net/1963/460 %1 3443 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:32:42Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1985 %R 10.1016/0375-9601(85)90102-1 %0 Journal Article %J J. Funct. Anal. 62 (1985), no. 2, 119--159 %D 1985 %T Some necessary and sufficient conditions for the convergence of sequences of unilateral convex sets %A Gianni Dal Maso %B J. Funct. Anal. 62 (1985), no. 2, 119--159 %I SISSA Library %G en %U http://hdl.handle.net/1963/318 %1 3649 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:28:20Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1984 %0 Journal Article %J Ennio De Giorgi Colloquium, p. 41-49, Research Notes in Mathematics, v.125, London : Pitman, 1985 %D 1985 %T Some singular perturbation problems in the calculus of variations. %A Gianni Dal Maso %B Ennio De Giorgi Colloquium, p. 41-49, Research Notes in Mathematics, v.125, London : Pitman, 1985 %I SISSA Library %G en %U http://hdl.handle.net/1963/297 %1 3670 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:27:46Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1983 %0 Journal Article %J Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 79 (1985), no. 5, 98-106 %D 1985 %T Weak convergence of measures on spaces of semicontinuous functions. %A Gianni Dal Maso %A Ennio De Giorgi %A Luciano Modica %B Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 79 (1985), no. 5, 98-106 %I SISSA Library %G en %U http://hdl.handle.net/1963/463 %1 3440 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:32:44Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1985 %0 Thesis %D 1984 %T Spin Structures and Global Conformal Transformations %A Ludwik Dabrowski %K Spinors %I SISSA %G en %U http://hdl.handle.net/1963/5854 %1 5718 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-05-18T10:02:53Z No. of bitstreams: 1 PhD_Dabrowski_Ludwik.pdf: 6031109 bytes, checksum: 45b102e8d5da1cb9575902b552e7b4e1 (MD5)