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

VL - 37 SN - 02132230 (ISSN) UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85104691573&doi=10.4171%2frmi%2f1259&partnerID=40&md5=5f88bc37b87a9eea7a502ea63523ff57 IS - 6 JO - Rev. Mat. Iberoam. ER - TY - JOUR T1 - The sharp quantitative isocapacitary inequality (the case of p-capacity) JF - Advances in Calculus of Variations Y1 - 2021 A1 - Ekaterina Mukoseeva KW - isocapacitary inequality KW - Stability estimates AB -We prove a sharp quantitative form of isocapacitary inequality in the case of a general p. This work is a generalization of the author's paper with Guido De Philippis and Michele Marini, where we treated the case of 2-capacity. © 2021 Walter de Gruyter GmbH, Berlin/Boston 2021.

SN - 18648258 (ISSN) UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85106363307&doi=10.1515%2facv-2020-0106&partnerID=40&md5=26dbcad781b68c1d873512e272f0e7f4 JO - Adv. Calc. Var. ER - TY - JOUR T1 - Smoothed-adaptive perturbed inverse iteration for elliptic eigenvalue problems JF - Computational Methods in Applied Mathematics Y1 - 2021 A1 - Stefano Giani A1 - Luka Grubisic A1 - Luca Heltai A1 - Ornela Mulita VL - 21 ER - TY - JOUR T1 - A sufficient criterion to determine planar self-Cheeger sets JF - J. Convex Anal. Y1 - 2021 A1 - Saracco, G. VL - 28 UR - https://www.heldermann.de/JCA/JCA28/JCA283/jca28055.htm IS - 3 ER - TY - JOUR T1 - A supervised learning approach involving active subspaces for an efficient genetic algorithm in high-dimensional optimization problems JF - SIAM Journal on Scientific Computing Y1 - 2021 A1 - Nicola Demo A1 - Marco Tezzele A1 - Gianluigi Rozza AB -In this work, we present an extension of the genetic algorithm (GA) which exploits the active subspaces (AS) property to evolve the individuals on a lower dimensional space. In many cases, GA requires in fact more function evaluations than others optimization method to converge to the optimum. Thus, complex and high-dimensional functions may result intractable with the standard algorithm. To address this issue, we propose to linearly map the input parameter space of the original function onto its AS before the evolution, performing the mutation and mate processes in a lower dimensional space. In this contribution, we describe the novel method called ASGA, presenting differences and similarities with the standard GA method. We test the proposed method over n-dimensional benchmark functions – Rosenbrock, Ackley, Bohachevsky, Rastrigin, Schaffer N. 7, and Zakharov – and finally we apply it to an aeronautical shape optimization problem.

VL - 43 UR - https://arxiv.org/abs/2006.07282 IS - 3 ER - TY - JOUR T1 - Special Issue on Reduced Order Models in CFD JF - International Journal of Computational Fluid Dynamics Y1 - 2020 A1 - Simona Perotto A1 - Gianluigi Rozza VL - 34 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85084258805&doi=10.1080%2f10618562.2020.1756497&partnerID=40&md5=d9316aad9ba95f244e07379318ebbcba ER - TY - JOUR T1 - A spectral element reduced basis method for navier–stokes equations with geometric variations JF - Lecture Notes in Computational Science and Engineering Y1 - 2020 A1 - Martin W. Hess A1 - Annalisa Quaini A1 - Gianluigi Rozza AB -We consider the Navier-Stokes equations in a channel with a narrowing of varying height. The model is discretized with high-order spectral element ansatz functions, resulting in 6372 degrees of freedom. The steady-state snapshot solutions define a reduced order space through a standard POD procedure. The reduced order space allows to accurately and efficiently evaluate the steady-state solutions for different geometries. In particular, we detail different aspects of implementing the reduced order model in combination with a spectral element discretization. It is shown that an expansion in element-wise local degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios.

VL - 134 ER - TY - JOUR T1 - Stabilized reduced basis methods for parametrized steady Stokes and Navier–Stokes equations JF - Computers and Mathematics with Applications Y1 - 2020 A1 - Shafqat Ali A1 - F. Ballarin A1 - Gianluigi Rozza AB -It is well known in the Reduced Basis approximation of saddle point problems that the Galerkin projection on the reduced space does not guarantee the inf–sup approximation stability even if a stable high fidelity method was used to generate snapshots. For problems in computational fluid dynamics, the lack of inf–sup stability is reflected by the inability to accurately approximate the pressure field. In this context, inf–sup stability is usually recovered through the enrichment of the velocity space with suitable supremizer functions. The main goal of this work is to propose an alternative approach, which relies on the residual based stabilization techniques customarily employed in the Finite Element literature, such as Brezzi–Pitkaranta, Franca–Hughes, streamline upwind Petrov–Galerkin, Galerkin Least Square. In the spirit of offline–online reduced basis computational splitting, two such options are proposed, namely offline-only stabilization and offline–online stabilization. These approaches are then compared to (and combined with) the state of the art supremizer enrichment approach. Numerical results are discussed, highlighting that the proposed methodology allows to obtain smaller reduced basis spaces (i.e., neglecting supremizer enrichment) for which a modified inf–sup stability is still preserved at the reduced order level.

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

VL - 134 UR - http://www.sciencedirect.com/science/article/pii/S0022509619304065 ER - TY - JOUR T1 - The Serre–Swan theorem for normed modules JF - Rendiconti del Circolo Matematico di Palermo Series 2 Y1 - 2019 A1 - Danka Lučić A1 - Enrico Pasqualetto VL - 68 UR - https://doi.org/10.1007/s12215-018-0366-6 ER - TY - CONF T1 - Shape optimization through proper orthogonal decomposition with interpolation and dynamic mode decomposition enhanced by active subspaces T2 - 8th International Conference on Computational Methods in Marine Engineering, MARINE 2019 Y1 - 2019 A1 - Marco Tezzele A1 - Nicola Demo A1 - Gianluigi Rozza AB -We propose a numerical pipeline for shape optimization in naval engineering involving two different non-intrusive reduced order method (ROM) techniques. Such methods are proper orthogonal decomposition with interpolation (PODI) and dynamic mode decomposition (DMD). The ROM proposed will be enhanced by active subspaces (AS) as a pre-processing tool that reduce the parameter space dimension and suggest better sampling of the input space. We will focus on geometrical parameters describing the perturbation of a reference bulbous bow through the free form deformation (FFD) technique. The ROM are based on a finite volume method (FV) to simulate the multi-phase incompressible flow around the deformed hulls. In previous works we studied the reduction of the parameter space in naval engineering through AS [38, 10] focusing on different parts of the hull. PODI and DMD have been employed for the study of fast and reliable shape optimization cycles on a bulbous bow in [9]. The novelty of this work is the simultaneous reduction of both the input parameter space and the output fields of interest. In particular AS will be trained computing the total drag resistance of a hull advancing in calm water and its gradients with respect to the input parameters. DMD will improve the performance of each simulation of the campaign using only few snapshots of the solution fields in order to predict the regime state of the system. Finally PODI will interpolate the coefficients of the POD decomposition of the output fields for a fast approximation of all the fields at new untried parameters given by the optimization algorithm. This will result in a non-intrusive data-driven numerical optimization pipeline completely independent with respect to the full order solver used and it can be easily incorporated into existing numerical pipelines, from the reference CAD to the optimal shape.

JF - 8th International Conference on Computational Methods in Marine Engineering, MARINE 2019 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075390244&partnerID=40&md5=3e1f2e9a2539d34594caff13766c94b8 ER - TY - CHAP T1 - A Spectral Element Reduced Basis Method in Parametric CFD T2 - Numerical Mathematics and Advanced Applications - ENUMATH 2017 Y1 - 2019 A1 - Martin W. Hess A1 - Gianluigi Rozza ED - Radu, Florin Adrian ED - Kumar, Kundan ED - Berre, Inga ED - Nordbotten, Jan Martin ED - Pop, Iuliu Sorin AB -We consider the Navier-Stokes equations in a channel with varying Reynolds numbers. The model is discretized with high-order spectral element ansatz functions, resulting in 14 259 degrees of freedom. The steady-state snapshot solu- tions define a reduced order space, which allows to accurately evaluate the steady- state solutions for varying Reynolds number with a reduced order model within a fixed-point iteration. In particular, we compare different aspects of implementing the reduced order model with respect to the use of a spectral element discretization. It is shown, how a multilevel static condensation in the pressure and velocity boundary degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios.

JF - Numerical Mathematics and Advanced Applications - ENUMATH 2017 PB - Springer International Publishing VL - 126 UR - https://arxiv.org/abs/1712.06432 ER - TY - JOUR T1 - A spectral element reduced basis method in parametric CFD JF - Lecture Notes in Computational Science and Engineering Y1 - 2019 A1 - Martin W. Hess A1 - Gianluigi Rozza AB -We consider the Navier-Stokes equations in a channel with varying Reynolds numbers. The model is discretized with high-order spectral element ansatz functions, resulting in 14,259 degrees of freedom. The steady-state snapshot solutions define a reduced order space, which allows to accurately evaluate the steady-state solutions for varying Reynolds number with a reduced order model within a fixed-point iteration. In particular, we compare different aspects of implementing the reduced order model with respect to the use of a spectral element discretization. It is shown, how a multilevel static condensation (Karniadakis and Sherwin, Spectral/hp element methods for computational fluid dynamics, 2nd edn. Oxford University Press, Oxford, 2005) in the pressure and velocity boundary degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios.

VL - 126 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85060005503&doi=10.1007%2f978-3-319-96415-7_64&partnerID=40&md5=d1a900db8ddb92cd818d797ec212a4c6 ER - TY - RPRT T1 - On the square distance function from a manifold with boundary Y1 - 2019 A1 - Giovanni Bellettini A1 - Alaa Elshorbagy AB -We characterize arbitrary codimensional smooth manifolds $\mathcal{M}$ with boundary embedded in $\mathbb{R}^n$ using the square distance function and the signed distance function from $\mathcal{M}$ and from its boundary. The results are localized in an open set.

UR - http://cvgmt.sns.it/media/doc/paper/4260/manif_with_bound_dist.pdf ER - TY - JOUR T1 - Strong Novikov conjecture for low degree cohomology and exotic group C*-algebras JF - arXiv e-prints Y1 - 2019 A1 - Paolo Antonini A1 - Buss, Alcides A1 - Engel, Alexander A1 - Siebenand , Timo KW - Mathematics - K-Theory and Homology KW - Mathematics - Operator Algebras AB -We strengthen a result of Hanke–Schick about the strong Novikov conjecture for low degree cohomology by showing that their non-vanishing result for the maximal group $C^*$-algebra even holds for the reduced group $C^*$-algebra. To achieve this we provide a Fell absorption principle for certain exotic crossed product functors.

ER - TY - JOUR T1 - Swimming Euglena respond to confinement with a behavioural change enabling effective crawling JF - Nature Physics Y1 - 2019 A1 - Giovanni Noselli A1 - Alfred Beran A1 - Marino Arroyo A1 - Antonio DeSimone AB - 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. VL - 15 UR - https://doi.org/10.1038/s41567-019-0425-8 ER - TY - JOUR T1 - Second order differentiation formula on RCD(K, N) spaces JF - Rendiconti Lincei-Matematica e Applicazioni Y1 - 2018 A1 - Nicola Gigli A1 - Luca Tamanini VL - 29 ER - TY - RPRT T1 - Second order differentiation formula on RCD*(K,N) spaces Y1 - 2018 A1 - Nicola Gigli A1 - Luca Tamanini ER - TY - CONF T1 - Shape Optimization by means of Proper Orthogonal Decomposition and Dynamic Mode Decomposition T2 - Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship & Maritime Research Y1 - 2018 A1 - Nicola Demo A1 - Marco Tezzele A1 - Gianluca Gustin A1 - Gianpiero Lavini A1 - Gianluigi Rozza AB - Shape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling, applied to a naval hull design problem. The advantage introduced by this method is that the solution for a specific parameter can be expressed as the combination of few numerical solutions computed at properly chosen parametric points. The reduced model is built using the proper orthogonal decomposition with interpolation (PODI) method. We use the free form deformation (FFD) for an automated perturbation of the shape, and the finite volume method to simulate the multiphase incompressible flow around the deformed hulls. Further computational reduction is done by the dynamic mode decomposition (DMD) technique: from few high dimensional snapshots, the system evolution is reconstructed and the final state of the simulation is faithfully approximated. Finally the global optimization algorithm iterates over the reduced space: the approximated drag and lift coefficients are projected to the hull surface, hence the resistance is evaluated for the new hulls until the convergence to the optimal shape is achieved. We will present the results obtained applying the described procedure to a typical Fincantieri cruise ship. JF - Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship & Maritime Research PB - IOS Press CY - Trieste, Italy UR - http://ebooks.iospress.nl/publication/49229 ER - TY - JOUR T1 - Shape transitions in a soft incompressible sphere with residual stresses JF - Math. Mech. Solids Y1 - 2018 A1 - Davide Riccobelli A1 - Pasquale Ciarletta PB - SAGE Publications Sage UK: London, England VL - 23 ER - TY - JOUR T1 - On sinc quadrature approximations of fractional powers of regularly accretive operators JF - Journal of Numerical Mathematics Y1 - 2018 A1 - Bonito, Andrea A1 - Wenyu Lei A1 - Joseph E Pasciak PB - De Gruyter ER - TY - JOUR T1 - Singular Hartree equation in fractional perturbed Sobolev spaces JF - Journal of Nonlinear Mathematical Physics Y1 - 2018 A1 - Alessandro Michelangeli A1 - Alessandro Olgiati A1 - Raffaele Scandone AB -We establish the local and global theory for the Cauchy problem of the singular Hartree equation in three dimensions, that is, the modification of the non-linear Schrödinger equation with Hartree non-linearity, where the linear part is now given by the Hamiltonian of point interaction. The latter is a singular, self-adjoint perturbation of the free Laplacian, modelling a contact interaction at a fixed point. The resulting non-linear equation is the typical effective equation for the dynamics of condensed Bose gases with fixed point-like impurities. We control the local solution theory in the perturbed Sobolev spaces of fractional order between the mass space and the operator domain. We then control the global solution theory both in the mass and in the energy space.

PB - Taylor & Francis VL - 25 UR - https://doi.org/10.1080/14029251.2018.1503423 ER - TY - RPRT T1 - On some rigorous aspects of fragmented condensation Y1 - 2018 A1 - Daniele Dimonte A1 - Marco Falconi A1 - Alessandro Olgiati UR - https://arxiv.org/abs/1809.03586 ER - TY - JOUR T1 - Spectral triples on the Jiang-Su algebra JF - Journal of Mathematical Physics Y1 - 2018 A1 - Jacopo Bassi A1 - Ludwik Dabrowski VL - 59 UR - https://doi.org/10.1063/1.5026311 ER - TY - JOUR T1 - Spontaneous morphing of equibiaxially pre-stretched elastic bilayers: The role of sample geometry JF - International Journal of Mechanical Sciences Y1 - 2018 A1 - Noe Caruso A1 - Aleksandar Cvetković A1 - Alessandro Lucantonio A1 - Giovanni Noselli A1 - Antonio DeSimone KW - Bifurcation KW - Elastic bilayer KW - Pre-stretch KW - Shape programming AB -An elastic bilayer, consisting of an equibiaxially pre-stretched sheet bonded to a stress-free one, spontaneously morphs into curved shapes in the absence of external loads or constraints. Using experiments and numerical simulations, we explore the role of geometry for square and rectangular samples in determining the equilibrium shape of the system, for a fixed pre-stretch. We classify the observed shapes over a wide range of aspect ratios according to their curvatures and compare measured and computed values, which show good agreement. In particular, as the bilayer becomes thinner, a bifurcation of the principal curvatures occurs, which separates two scaling regimes for the energy of the system. We characterize the transition between these two regimes and show the peculiar features that distinguish square from rectangular samples. The results for our model bilayer system may help explaining morphing in more complex systems made of active materials.

VL - 149 UR - https://www.sciencedirect.com/science/article/pii/S0020740317311761 ER - TY - CONF T1 - SRTP 2.0 - The evolution of the safe return to port concept T2 - Technology and Science for the Ships of the Future - Proceedings of NAV 2018: 19th International Conference on Ship and Maritime Research Y1 - 2018 A1 - D. Cangelosi A1 - A. Bonvicini A1 - M. Nardo A1 - Andrea Mola A1 - A. Marchese A1 - Marco Tezzele A1 - Gianluigi Rozza AB -In 2010 IMO (International Maritime Organisation) introduced new rules in SOLAS with the aim of intrinsically increase the safety of passenger ships. This requirement is achieved by providing safe areas for passengers and essential services for allowing ship to Safely Return to Port (SRtP). The entry into force of these rules has changed the way to design passenger ships. In this respect big effort in the research has been done by industry to address design issues related to the impact on failure analysis of the complex interactions among systems. Today the research activity is working to bring operational matters in the design stage. This change of research focus was necessary because human factor and the way to operate the ship itself after a casualty on board may have a big impact in the design of the ship/systems. Also the management of the passengers after a casualty is becoming a major topic for safety. This paper presents the state of the art of Italian knowledge in the field of system engineering applied to passenger ship address to safety improvement and design reliability. An overview of present tools and methodologies will be offered together with future focuses in the research activity.

JF - Technology and Science for the Ships of the Future - Proceedings of NAV 2018: 19th International Conference on Ship and Maritime Research ER - TY - JOUR T1 - Stabilized weighted reduced basis methods for parametrized advection dominated problems with random inputs JF - SIAM-ASA Journal on Uncertainty Quantification Y1 - 2018 A1 - D. Torlo A1 - F. Ballarin A1 - Gianluigi Rozza AB -In this work, we propose viable and eficient strategies for stabilized parametrized advection dominated problems, with random inputs. In particular, we investigate the combination of the wRB (weighted reduced basis) method for stochastic parametrized problems with the stabilized RB (reduced basis) method, which is the integration of classical stabilization methods (streamline/upwind Petrov-Galerkin (SUPG) in our case) in the ofine-online structure of the RB method. Moreover, we introduce a reduction method that selectively enables online stabilization; this leads to a sensible reduction of computational costs, while keeping a very good accuracy with respect to high-fdelity solutions. We present numerical test cases to assess the performance of the proposed methods in steady and unsteady problems related to heat transfer phenomena.

VL - 6 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85058246502&doi=10.1137%2f17M1163517&partnerID=40&md5=6c54e2f0eb727cb85060e988486b8ac8 ER - TY - RPRT T1 - Stochastic homogenisation of free-discontinuity problems Y1 - 2018 A1 - Filippo Cagnetti A1 - Gianni Dal Maso A1 - Lucia Scardia A1 - Caterina Ida Zeppieri AB - In this paper we study the stochastic homogenisation of free-discontinuity functionals. Assuming stationarity for the random volume and surface integrands, we prove the existence of a homogenised random free-discontinuity functional, which is deterministic in the ergodic case. Moreover, by establishing a connection between the deterministic convergence of the functionals at any fixed realisation and the pointwise Subadditive Ergodic Theorem by Akcoglou and Krengel, we characterise the limit volume and surface integrands in terms of asymptotic cell formulas. UR - http://preprints.sissa.it/handle/1963/35309 U1 - 35617 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Symplectic invariants for parabolic orbits and cusp singularities of integrable systems JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Y1 - 2018 A1 - Alexey Bolsinov A1 - Lorenzo Guglielmi A1 - Elena Kudryavtseva AB -We discuss normal forms and symplectic invariants of parabolic orbits and cuspidal tori in integrable Hamiltonian systems with two degrees of freedom. Such singularities appear in many integrable systems in geometry and mathematical physics and can be considered as the simplest example of degenerate singularities. We also suggest some new techniques which apparently can be used for studying symplectic invariants of degenerate singularities of more general type. This article is part of the theme issue ‘Finite dimensional integrable systems: new trends and methods’.

VL - 376 UR - https://royalsocietypublishing.org/doi/abs/10.1098/rsta.2017.0424 ER - TY - RPRT T1 - Second order differentiation formula on compact RCD*(K,N) spaces Y1 - 2017 A1 - Nicola Gigli A1 - Luca Tamanini ER - TY - RPRT T1 - Self-Adjoint Extensions of Dirac Operator with Coulomb Potential Y1 - 2017 A1 - Matteo Gallone AB - In this note we give a concise review of the present state-of-art for the problem of self-adjoint realisations for the Dirac operator with a Coulomb-like singular scalar potential V(x) = Ø(x)I4. We try to follow the historical and conceptual path that leads to the present understanding of the problem and to highlight the techniques employed and the main ideas. In the final part we outline a few major open questions that concern the topical problem of the multiplicity of self-adjoint realisations of the model, and which are worth addressing in the future. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/35273 U1 - 35579 U4 - 1 ER - TY - RPRT T1 - Self-adjoint realisations of the Dirac-Coulomb Hamiltonian for heavy nuclei Y1 - 2017 A1 - Matteo Gallone A1 - Alessandro Michelangeli AB - We derive a classification of the self-adjoint extensions of the three-dimensional Dirac-Coulomb operator in the critical regime of the Coulomb coupling. Our approach is solely based upon the KreĬn-Višik- Birman extension scheme, or also on Grubb's universal classification theory, as opposite to previous works within the standard von Neu- mann framework. This let the boundary condition of self-adjointness emerge, neatly and intrinsically, as a multiplicative constraint between regular and singular part of the functions in the domain of the exten- sion, the multiplicative constant giving also immediate information on the invertibility property and on the resolvent and spectral gap of the extension. UR - http://preprints.sissa.it/handle/1963/35287 U1 - 35592 U2 - Mathematics ER - TY - RPRT T1 - Semistable Higgs Bundles on Calabi-Yau Manifolds Y1 - 2017 A1 - Ugo Bruzzo A1 - Valeriano Lanza A1 - Alessio Lo Giudice AB - We provide a partial classification of semistable Higgs bundles over a simply connected Calabi-Yau manifold. Applications to a conjecture about a special class of semistable Higgs bundles are given. In particular, the conjecture is proved for K3 and Enriques surfaces, and some related classes of surfaces. UR - http://preprints.sissa.it/handle/1963/35295 U1 - 35601 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Small Time Asymptotics on the Diagonal for Hörmander's Type Hypoelliptic Operators JF - Journal of Dynamical and Control Systems Y1 - 2017 A1 - Elisa Paoli AB -We compute the small time asymptotics of the fundamental solution of Hörmander's type hypoelliptic operators with drift, on the diagonal at a point x0. We show that the order of the asymptotics depends on the controllability of an associated control problem and of its approximating system. If the control problem of the approximating system is controllable at x0, then so is also the original control problem, and in this case we show that the fundamental solution blows up as t−N/2\$\backslashphantom {\backslashdot {i}\backslash!}t^{-\backslashmathcal {N}/2}\$, where N\$\backslashphantom {\backslashdot {i}\backslash!}\backslashmathcal {N}\$is a number determined by the Lie algebra at x0 of the fields, that define the hypoelliptic operator.

VL - 23 UR - https://doi.org/10.1007/s10883-016-9321-z ER - TY - JOUR T1 - Solid tumors are poroelastic solids with a chemo-mechanical feedback on growth JF - J. Elast. Y1 - 2017 A1 - D. Ambrosi A1 - Pezzuto, S. A1 - Davide Riccobelli A1 - Stylianopoulos, T. A1 - Pasquale Ciarletta PB - Springer Netherlands VL - 129 ER - TY - JOUR T1 - Spectral Properties of the 2+1 Fermionic Trimer with Contact Interactions Y1 - 2017 A1 - Simon Becker A1 - Alessandro Michelangeli A1 - Andrea Ottolini AB - We qualify the main features of the spectrum of the Hamiltonian of point interaction for a three-dimensional quantum system consisting of three point-like particles, two identical fermions, plus a third particle of different species, with two-body interaction of zero range. For arbitrary magnitude of the interaction, and arbitrary value of the mass parameter (the ratio between the mass of the third particle and that of each fermion) above the stability threshold, we identify the essential spectrum, localise and prove the finiteness of the discrete spectrum, qualify the angular symmetry of the eigenfunctions, and prove the monotonicity of the eigenvalues with respect to the mass parameter. We also demonstrate the existence of bound states in a physically relevant regime of masses. PB - SISSA UR - http://preprints.sissa.it/handle/1963/35303 N1 - Partially supported by the 2014-2017 MIUR-FIR grant \Cond-Math: Condensed Matter and Mathematical Physics" code RBFR13WAET (S.B., A.M., A.O.), by the DAAD International Trainership Programme (S.B.), and by a 2017 visiting research fellowship at the International Center for Mathematical Research CIRM, Trento (A.M.). U1 - 35609 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Stasis domains and slip surfaces in the locomotion of a bio-inspired two-segment crawler JF - Meccanica Y1 - 2017 A1 - Paolo Gidoni A1 - Antonio DeSimone AB -We formulate and solve the locomotion problem for a bio-inspired crawler consisting of two active elastic segments (i.e., capable of changing their rest lengths), resting on three supports providing directional frictional interactions. The problem consists in finding the motion produced by a given, slow actuation history. By focusing on the tensions in the elastic segments, we show that the evolution laws for the system are entirely analogous to the flow rules of elasto-plasticity. In particular, sliding of the supports and hence motion cannot occur when the tensions are in the interior of certain convex regions (stasis domains), while support sliding (and hence motion) can only take place when the tensions are on the boundary of such regions (slip surfaces). We solve the locomotion problem explicitly in a few interesting examples. In particular, we show that, for a suitable range of the friction parameters, specific choices of the actuation strategy can lead to net displacements also in the direction of higher friction.

VL - 52 UR - https://doi.org/10.1007/s11012-016-0408-0 ER - TY - JOUR T1 - Symplectic geometry of the moduli space of projective structures in homological coordinates JF - Inventiones Mathematicae Y1 - 2017 A1 - Marco Bertola A1 - Dmitry Korotkin A1 - Chaya Norton UR - https://arxiv.org/abs/1506.07918 ER - TY - RPRT T1 - Second-order structured deformations Y1 - 2016 A1 - Ana Cristina Barroso A1 - Jose Matias A1 - Marco Morandotti A1 - David R. Owen PB - SISSA U1 - 35497 U2 - Mathematics U4 - 1 ER - TY - CONF T1 - Ship Sinkage and Trim Predictions Based on a CAD Interfaced Fully Nonlinear Potential Model T2 - The 26th International Ocean and Polar Engineering Conference Y1 - 2016 A1 - Andrea Mola A1 - Luca Heltai A1 - Antonio DeSimone A1 - Massimiliano Berti JF - The 26th International Ocean and Polar Engineering Conference PB - International Society of Offshore and Polar Engineers VL - 3 ER - TY - JOUR T1 - Simple Lie Algebras and Topological ODEs JF - Int. Math. Res. Not. Y1 - 2016 A1 - Marco Bertola A1 - Boris Dubrovin A1 - Di Yang VL - 2016 ER - TY - JOUR T1 - On Sobolev instability of the interior problem of tomography JF - Journal of Mathematical Analysis and Applications Y1 - 2016 A1 - Marco Bertola A1 - Alexander Katsevich A1 - Alexander Tovbis ER - TY - THES T1 - Some results on quasistatic evolution problems for unidirectional processes Y1 - 2016 A1 - Vito Crismale PB - SISSA U1 - 35522 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - THES T1 - Some results on the mathematical analysis of crack problems with forces applied on the fracture lips Y1 - 2016 A1 - Stefano Almi KW - Fracture mechanics AB - This thesis is devoted to the study of some models of fracture growth in elastic materials, characterized by the presence of forces acting on the crack lips. Working in the general framework of rate-independent processes, we first discuss a variational formulation of the problem of quasi-static crack evolution in hydraulic fracture. Then, we investigate the crack growth process in a cohesive fracture model, showing the existence of an evolution satisfying a weak Griffith's criterion. Finally, in the last chapter of this work we investigate, in the static case, the interaction between the energy spent in order to create a new fracture and the energy spent by the applied surface forces. This leads us to study the lower semicontinuity properties of a free discontinuity functional F(u) that can be written as the sum of a crack term, depending on the jump set of u, and of a boundary term, depending on the trace of u. PB - SISSA U1 - 35503 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Spectral analysis and the Aharonov-Bohm effect on certain almost-Riemannian manifolds JF - Communications in Partial Differential Equations Y1 - 2016 A1 - Ugo Boscain A1 - Dario Prandi A1 - M. Seri AB -We study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. This operator contains first order diverging terms caused by the divergence of the volume. We get explicit descriptions of the spectrum and the eigenfunctions. In particular in both cases we get a Weyl's law with leading term Elog E. We then study the drastic effect of Aharonov-Bohm magnetic potentials on the spectral properties. Other generalized Riemannian structures including conic and anti-conic type manifolds are also studied. In this case, the Aharonov-Bohm magnetic potential may affect the self-adjointness of the Laplace-Beltrami operator.

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

PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/35209 U1 - 35508 U2 - Mathematics U5 - MAT/05 ER - TY - JOUR T1 - Symmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index JF - Journal of High Energy Physics Y1 - 2016 A1 - Benvenuti, Sergio A1 - Giulio Bonelli A1 - Massimiliano Ronzani A1 - Alessandro Tanzini AB -We explore $\mathcal{N}=(1,0)$ superconformal six-dimensional theories arising from M5 branes probing a transverse $A_k$ singularity. Upon circle compactification to 5 dimensions, we describe this system with a dual pq-web of five-branes and propose the spectrum of basic five-dimensional instanton operators driving global symmetry enhancement. For a single M5 brane, we find that the exact partition function of the 5d quiver gauge theory matches the 6d (1, 0) index, which we compute by letter counting. We finally show that S-duality of the pq-web implies new relations among vertex correlators of $q\mathcal{W}$ algebrae.

VL - 2016 UR - https://doi.org/10.1007/JHEP09(2016)053 ER - TY - JOUR T1 - Symmetry properties of some solutions to some semilinear elliptic equations JF - Annali della Scuola Normale Superiore di Pisa. Classe di scienze Y1 - 2016 A1 - Farina, Alberto A1 - Andrea Malchiodi A1 - Matteo Rizzi PB - Classe di Scienze VL - 16 ER - TY - RPRT T1 - Schödinger operators on half-line with shrinking potentials at the origin Y1 - 2015 A1 - Gianfausto Dell'Antonio A1 - Alessandro Michelangeli AB - We discuss the general model of a Schrödinger quantum particle constrained on a straight half-line with given self-adjoint boundary condition at the origin and an interaction potential supported around the origin. We study the limit when the range of the potential scales to zero and its magnitude blows up. We show that in the limit the dynamics is generated by a self-adjoint negative Laplacian on the half-line, with a possible preservation or modification of the boundary condition at the origin, depending on the magnitude of the scaling and of the strength of the potential. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/34439 U1 - 34566 ER - TY - RPRT T1 - Semicartesian surfaces and the relaxed area of maps from the plane to the plane with a line discontinuity Y1 - 2015 A1 - Lucia Tealdi A1 - Giovanni Bellettini A1 - Maurizio Paolini AB -We address the problem of estimating the area of the graph of a map u, defined on a bounded planar domain O and taking values in the plane, jumping on a segment J, either compactly contained in O or having both the end points on the boundary of O. We define the relaxation of the area functional w.r.t. a sort of uniform convergence, and we characterize it in terms of the infimum of the area among those surfaces in the space spanning the graphs of the traces of u on the two side of J and having what we have called a semicartesian structure. We exhibit examples showing that the relaxed area functional w.r.t the L^1 convergence may depend also on the values of u far from J, and on the relative position of J w.r.t. the boundary of O; these examples confirm the non-local behaviour of the L^1 relaxed area functional, and justify the interest in studying the relaxation w.r.t. a stronger convergence. We prove also that the L^1 relaxed area functional in non-subadditive for a rather class of maps.

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

UR - http://urania.sissa.it/xmlui/handle/1963/34489 U1 - 34672 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - THES T1 - Some results on anisotropic mean curvature and other phase-transition problems Y1 - 2015 A1 - Stefano Amato KW - Anisotropic mean curvature AB - The present thesis is divided into three parts. In the first part, we analyze a suitable regularization — which we call nonlinear multidomain model — of the motion of a hypersurface under smooth anisotropic mean curvature flow. The second part of the thesis deals with crystalline mean curvature of facets of a solid set of R^3 . Finally, in the third part we study a phase-transition model for Plateau’s type problems based on the theory of coverings and of BV functions. PB - SISSA U1 - 34733 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - Stability of closed gaps for the alternating Kronig-Penney Hamiltonian Y1 - 2015 A1 - Alessandro Michelangeli A1 - Domenico Monaco AB - We consider the Kronig-Penney model for a quantum crystal with equispaced periodic delta-interactions of alternating strength. For this model all spectral gaps at the centre of the Brillouin zone are known to vanish, although so far this noticeable property has only been proved through a very delicate analysis of the discriminant of the corresponding ODE and the associated monodromy matrix. We provide a new, alternative proof by showing that this model can be approximated, in the norm resolvent sense, by a model of regular periodic interactions with finite range for which all gaps at the centre of the Brillouin zone are still vanishing. In particular this shows that the vanishing gap property is stable in the sense that it is present also for the "physical" approximants and is not only a feature of the idealised model of zero-range interactions. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/34460 U1 - 34629 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Stability of the (2+2)-fermionic system with zero-range interaction Y1 - 2015 A1 - Alessandro Michelangeli A1 - Paul Pfeiffer AB - We introduce a 3D model, and we study its stability, consisting of two distinct pairs of identical fermions coupled with a two-body interaction between fermions of different species, whose effective range is essentially zero (a so called (2+2)-fermionic system with zero-range interaction). The interaction is modelled by implementing the the celebrated (and ubiquitous, in the literature of this field) Bethe-Peierls contact condition with given two-body scattering length within the Krein-Visik-Birman theory of extensions of semi-bounded symmetric operators, in order to make the Hamiltonian a well-defined (self-adjoint) physical observable. After deriving the expression for the associated energy quadratic form, we show analytically and numerically that the energy of the model is bounded below, thus describing a stable system. UR - http://urania.sissa.it/xmlui/handle/1963/34474 N1 - This SISSA preprint has 17 pages and recorded in PDF format U1 - 34649 U2 - Mathematics U4 - 1 U5 - MAT/07 ER - TY - JOUR T1 - Stable regular critical points of the Mumford-Shah functional are local minimizers JF - Annales de l'Institut Henri Poincare (C) Non Linear Analysis Y1 - 2015 A1 - Marco Bonacini A1 - Massimiliano Morini KW - Mumford-Shah functional AB -In this paper it is shown that any regular critical point of the Mumford–Shah functional, with positive definite second variation, is an isolated local minimizer with respect to competitors which are sufficiently close in the $L^1$

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

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

VL - 471 UR - https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2015.0054 ER - TY - JOUR T1 - Supremizer stabilization of POD-Galerkin approximation of parametrized Navier-Stokes equations Y1 - 2015 A1 - F. Ballarin A1 - Andrea Manzoni A1 - Alfio Quarteroni A1 - Gianluigi Rozza AB - In this work, we present a stable proper orthogonal decomposition–Galerkin approximation for parametrized steady incompressible Navier–Stokes equations with low Reynolds number. PB - Wiley UR - http://urania.sissa.it/xmlui/handle/1963/34701 U1 - 34915 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - Symmetry and localization in periodic crystals: triviality of Bloch bundles with a fermionic time-reversal symmetry JF - Acta Applicandae Mathematicae, vol. 137, Issue 1, 2015, pages: 185-203 Y1 - 2015 A1 - Domenico Monaco A1 - Gianluca Panati AB -We describe some applications of group- and bundle-theoretic methods in solid state physics, showing how symmetries lead to a proof of the localization of electrons in gapped crystalline solids, as e.g. insulators and semiconductors. We shortly review the Bloch-Floquet decomposition of periodic operators, and the related concepts of Bloch frames and composite Wannier functions. We show that the latter are almost-exponentially localized if and only if there exists a smooth periodic Bloch frame, and that the obstruction to the latter condition is the triviality of a Hermitian vector bundle, called the Bloch bundle. The rôle of additional Z_2-symmetries, as time-reversal and space-reflection symmetry, is discussed, showing how time-reversal symmetry implies the triviality of the Bloch bundle, both in the bosonic and in the fermionic case. Moreover, the same Z_2-symmetry allows to define a finer notion of isomorphism and, consequently, to define new topological invariants, which agree with the indices introduced by Fu, Kane and Mele in the context of topological insulators.

PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34468 N1 - The article is composed of 23 pages and recorded in PDF format U1 - 34642 U2 - Mathematics U4 - 1 U5 - MAT/07 ER - TY - JOUR T1 - SBV Regularity of Systems of Conservation Laws and Hamilton–Jacobi Equations Y1 - 2014 A1 - Stefano Bianchini AB - We review the SBV regularity for solutions to hyperbolic systems of conservation laws and Hamilton-Jacobi equations. We give an overview of the techniques involved in the proof, and a collection of related problems concludes the paper. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34691 U1 - 34904 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Second Order Asymptotic Development for the Anisotropic Cahn-Hilliard Functional Y1 - 2014 A1 - Gianni Dal Maso A1 - Irene Fonseca A1 - Giovanni Leoni KW - Gamma-convergence, Cahn-Hilliard functional, phase transitions AB - The asymptotic behavior of an anisotropic Cahn-Hilliard functional with prescribed mass and Dirichlet boundary condition is studied when the parameter $\varepsilon$ that determines the width of the transition layers tends to zero. The double-well potential is assumed to be even and equal to $|s-1|^\beta$ near $s=1$, with $1<\beta<2$. The first order term in the asymptotic development by $\Gamma$-convergence is well-known, and is related to a suitable anisotropic perimeter of the interface. Here it is shown that, under these assumptions, the second order term is zero, which gives an estimate on the rate of convergence of the minimum values. PB - SISSA UR - http://hdl.handle.net/1963/7390 N1 - This article is composed if 33 pages and recorded in PDF format U1 - 7439 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Semiclassical limit of focusing NLS for a family of square barrier initial data Y1 - 2014 A1 - Robert Jenkins A1 - Kenneth McLaughlin AB - The small dispersion limit of the focusing nonlinear Schrödinger equation (NLS) exhibits a rich structure of sharply separated regions exhibiting disparate rapid oscillations at microscopic scales. The non-self-adjoint scattering problem and ill-posed limiting Whitham equations associated to focusing NLS make rigorous asymptotic results difficult. Previous studies have focused on special classes of analytic initial data for which the limiting elliptic Whitham equations are wellposed. In this paper we consider another exactly solvable family of initial data,the family of square barriers,ψ 0(x) = qχ[-L,L] for real amplitudes q. Using Riemann-Hilbert techniques, we obtain rigorous pointwise asymptotics for the semiclassical limit of focusing NLS globally in space and up to an O(1) maximal time. In particular, we show that the discontinuities in our initial data regularize by the immediate generation of genus-one oscillations emitted into the support of the initial data. To the best of our knowledge, this is the first case in which the genus structure of the semiclassical asymptotics for focusing NLS have been calculated for nonanalytic initial data. PB - Wiley Periodicals UR - http://urania.sissa.it/xmlui/handle/1963/35066 U1 - 35301 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Shape control of active surfaces inspired by the movement of euglenids Y1 - 2014 A1 - Marino Arroyo A1 - Antonio DeSimone AB - We examine a novel mechanism for active surface morphing inspired by the cell body deformations of euglenids. Actuation is accomplished through in-plane simple shear along prescribed slip lines decorating the surface. Under general non-uniform actuation, such local deformation produces Gaussian curvature, and therefore leads to shape changes. Geometrically, a deformation that realizes the prescribed local shear is an isometric embedding. We explore the possibilities and limitations of this bio-inspired shape morphing mechanism, by first characterizing isometric embeddings under axisymmetry, understanding the limits of embeddability, and studying in detail the accessibility of surfaces of zero and constant curvature. Modeling mechanically the active surface as a non-Euclidean plate (NEP), we further examine the mechanism beyond the geometric singularities arising from embeddability, where mechanics and buckling play a decisive role. We also propose a non-axisymmetric actuation strategy to accomplish large amplitude bending and twisting motions of elongated cylindrical surfaces. Besides helping understand how euglenids delicately control their shape, our results may provide the background to engineer soft machines. PB - Elsevier UR - http://urania.sissa.it/xmlui/handle/1963/35118 U1 - 35375 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Shape Optimization by Free-Form Deformation: Existence Results and Numerical Solution for Stokes Flows Y1 - 2014 A1 - F. Ballarin A1 - Andrea Manzoni A1 - Gianluigi Rozza A1 - Sandro Salsa AB - Shape optimization problems governed by PDEs result from many applications in computational fluid dynamics. These problems usually entail very large computational costs and require also a suitable approach for representing and deforming efficiently the shape of the underlying geometry, as well as for computing the shape gradient of the cost functional to be minimized. Several approaches based on the displacement of a set of control points have been developed in the last decades, such as the so-called free-form deformations. In this paper we present a new theoretical result which allows to recast free-form deformations into the general class of perturbation of identity maps, and to guarantee the compactness of the set of admissible shapes. Moreover, we address both a general optimization framework based on the continuous shape gradient and a numerical procedure for solving efficiently three-dimensional optimal design problems. This framework is applied to the optimal design of immersed bodies in Stokes flows, for which we consider the numerical solution of a benchmark case study from literature. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34698 U1 - 34914 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Singular Value Decomposition of a Finite Hilbert Transform Defined on Several Intervals and the Interior Problem of Tomography: The Riemann-Hilbert Problem Approach JF - Comm. Pure Appl. Math. Y1 - 2014 A1 - Marco Bertola A1 - Alexander Katsevich A1 - Alexander Tovbis ER - TY - JOUR T1 - Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics Y1 - 2014 A1 - Giulio Bonelli A1 - Antonio Sciarappa A1 - Alessandro Tanzini A1 - Petr Vasko AB - We show that the exact partition function of U(N) six-dimensional gauge theory with eight supercharges on C^2 x S^2 provides the quantization of the integrable system of hydrodynamic type known as gl(N) periodic Intermediate Long Wave (ILW). We characterize this system as the hydrodynamic limit of elliptic Calogero-Moser integrable system. We compute the Bethe equations from the effective gauged linear sigma model on S^2 with target space the ADHM instanton moduli space, whose mirror computes the Yang-Yang function of gl(N) ILW. The quantum Hamiltonians are given by the local chiral ring observables of the six-dimensional gauge theory. As particular cases, these provide the gl(N) Benjamin-Ono and Korteweg-de Vries quantum Hamiltonians. In the four dimensional limit, we identify the local chiral ring observables with the conserved charges of Heisenberg plus W_N algebrae, thus providing a gauge theoretical proof of AGT correspondence. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34546 U1 - 34771 U2 - Physics U4 - 2 ER - TY - JOUR T1 - Smooth approximation of bi-Lipschitz orientation-preserving homeomorphisms JF - Annales de l'Institut Henri Poincare (C) Non Linear Analysis Y1 - 2014 A1 - Sara Daneri A1 - Aldo Pratelli AB -We show that a planar bi-Lipschitz orientation-preserving homeomorphism can be approximated in the W1,p norm, together with its inverse, with an orientation-preserving homeomorphism which is piecewise affine or smooth.

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

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

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

JF - 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014 UR - https://infoscience.epfl.ch/record/203327/files/ECCOMAS_PP_GR.pdf ER - TY - RPRT T1 - Steady nearly incompressible vector elds in 2D: chain rule and renormalization Y1 - 2014 A1 - Stefano Bianchini A1 - N.A. Gusev PB - SISSA U1 - 7464 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - The stringy instanton partition function Y1 - 2014 A1 - Giulio Bonelli A1 - Antonio Sciarappa A1 - Alessandro Tanzini A1 - Petr Vasko AB - We perform an exact computation of the gauged linear sigma model associated to a D1-D5 brane system on a resolved A_1 singularity. This is accomplished via supersymmetric localization on the blown-up two-sphere. We show that in the blow-down limit C^2/Z_2 the partition function reduces to the Nekrasov partition function evaluating the equivariant volume of the instanton moduli space. For finite radius we obtain a tower of world-sheet instanton corrections, that we identify with the equivariant Gromov-Witten invariants of the ADHM moduli space. We show that these corrections can be encoded in a deformation of the Seiberg-Witten prepotential. From the mathematical viewpoint, the D1-D5 system under study displays a twofold nature: the D1-branes viewpoint captures the equivariant quantum cohomology of the ADHM instanton moduli space in the Givental formalism, and the D5-branes viewpoint is related to higher rank equivariant Donaldson-Thomas invariants of P^1 x C^2. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34589 U1 - 34796 U2 - Physics U4 - 2 ER - TY - RPRT T1 - Structure of classical (finite and affine) W-algebras Y1 - 2014 A1 - Alberto De Sole A1 - Victor G. Kac A1 - Daniele Valeri AB - First, we derive an explicit formula for the Poisson bracket of the classical finite W-algebra W^{fin}(g,f), the algebra of polynomial functions on the Slodowy slice associated to a simple Lie algebra g and its nilpotent element f. On the other hand, we produce an explicit set of generators and we derive an explicit formula for the Poisson vertex algebra structure of the classical affine W-algebra W(g,f). As an immediate consequence, we obtain a Poisson algebra isomorphism between W^{fin}(g,f) and the Zhu algebra of W(g,f). We also study the generalized Miura map for classical W-algebras. PB - SISSA UR - http://hdl.handle.net/1963/7314 N1 - 40 pages U1 - 7359 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Structure of entropy solutions to general scalar conservation laws in one space dimension JF - Journal of Mathematical Analysis and Applications Y1 - 2014 A1 - Stefano Bianchini A1 - Lei Yu PB - SISSA VL - 428 UR - https://www.sciencedirect.com/science/article/pii/S0022247X15002218 IS - 1 U1 - 7305 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - Swelling dynamics of a thin elastomeric sheet under uniaxial pre-stretch Y1 - 2014 A1 - Alessandro Lucantonio A1 - Paola Nardinocchi A1 - Howard A. Stone AB - It has been demonstrated experimentally that pre-stretch affects the swelling of an elastomeric membrane when it is exposed to a solvent. We study theoretically the one-dimensional swelling of a pre-stretched thin elastomeric sheet, bonded to an impermeable rigid substrate, to quantify the influence of pre-stretch. We show that the solvent uptake increases when pre-stretch increases, both at equilibrium and during the swelling transient, where it exhibits two different scaling regimes. The coupling between the solvent uptake and pre-stretch may be practically exploited to design soft actuators where the swelling-induced deformations can be controlled by varying the pre-stretch. PB - American Institute of Physics UR - http://urania.sissa.it/xmlui/handle/1963/35113 U1 - 35370 U2 - Physics U4 - 1 ER - TY - JOUR T1 - Swelling-induced and controlled curving in layered gel beams Y1 - 2014 A1 - Alessandro Lucantonio A1 - Paola Nardinocchi A1 - Matteo Pezzulla AB - We describe swelling-driven curving in originally straight and non-homogeneous beams. We present and verify a structural model of swollen beams, based on a new point of view adopted to describe swelling-induced deformation processes in bilayered gel beams, that is based on the split of the swelling-induced deformation of the beam at equilibrium into two components, both depending on the elastic properties of the gel. The method allows us to: (i) determine beam stretching and curving, once assigned the characteristics of the solvent bath and of the non-homogeneous beam, and (ii) estimate the characteristics of non-homogeneous flat gel beams in such a way as to obtain, under free-swelling conditions, three-dimensional shapes. The study was pursued by means of analytical, semi-analytical and numerical tools; excellent agreement of the outcomes of the different techniques was found, thus confirming the strength of the method. PB - Royal Society of London UR - http://urania.sissa.it/xmlui/handle/1963/34987 U1 - 35229 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Self-adjoint extensions and stochastic completeness of the Laplace-Beltrami operator on conic and anticonic surfaces Y1 - 2013 A1 - Ugo Boscain A1 - Dario Prandi ER - TY - THES T1 - Semistability and Decorated Bundles Y1 - 2013 A1 - Andrea Pustetto KW - Decorated sheaves, semistability, moduli space, Mehta-Ramanathan, maximal destabilizing subsheaf AB - This thesis is devoted to the study of semistability condition of type t=(a,b,c,N) decorated bundles and sheaves in order to better understand and simplify it. We approach the problem in two different ways: on one side we “enclose” the above semistability condition between a stronger semistability condition (\epsilon-semistability) and a weaker one (k-semistability), on the other side we try, and succeed for the case of a = 2, to bound the length of weighted filtrations on which one checks the semistability condition. PB - SISSA UR - http://hdl.handle.net/1963/7130 U1 - 7132 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Softly Constrained Films Y1 - 2013 A1 - Luca Giomi AB - The shape of materials is often subject to a number of geometric constraints\r\nthat limit the size of the system or fix the structure of its boundary. In soft\r\nand biological materials, however, these constraints are not always hard, but\r\nare due to other physical mechanisms that affect the overall force balance. A\r\ncapillary film spanning a flexible piece of wire or a cell anchored to a\r\ncompliant substrate by mean of adhesive contacts are examples of these softly\r\nconstrained systems in the macroscopic and microscopic world. In this article I\r\nreview some of the important mathematical and physical developments that\r\ncontributed to our understanding of shape formation in softly constrained films\r\nand their recent application to the mechanics of adherent cells. PB - SISSA UR - http://hdl.handle.net/1963/6563 N1 - Review article, 21 pages, 16 figures, submitted to Soft Matter U1 - 6518 U2 - Mathematics U4 - 2 U5 - FIS/02 FISICA TEORICA, MODELLI E METODI MATEMATICI ER - TY - THES T1 - Some models of crack growth in brittle materials Y1 - 2013 A1 - Simone Racca KW - Quasi-static crack evolution PB - SISSA U1 - 7205 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Some open problems Y1 - 2013 A1 - Andrei A. Agrachev KW - Geometry AB - We discuss some challenging open problems in the geometric control theory and sub-Riemannian geometry. PB - SISSA UR - http://hdl.handle.net/1963/7070 U1 - 7064 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Some remarks on the viscous approximation of crack growth JF - Discrete Contin. Dyn. Syst. Ser. S Y1 - 2013 A1 - Giuliano Lazzaroni A1 - Rodica Toader KW - Variational models AB -We describe an existence result for quasistatic evolutions of cracks in antiplane elasticity obtained in [16] by a vanishing viscosity approach, with free (but regular enough) crack path. We underline in particular the motivations for the choice of the class of admissible cracks and of the dissipation potential. Moreover, we extend the result to a model with applied forces depending on time.

PB - SISSA VL - 6 UR - http://hdl.handle.net/1963/4206 U1 - 3945 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - THES T1 - Some topics on Higgs bundles over projective varieties and their moduli spaces Y1 - 2013 A1 - Alessio Lo Giudice KW - Algebraic Geometry, Moduli spaces, Vector bundles AB - In this thesis we study vector bundles on projective varieties and their moduli spaces. In Chapters 2, 3 and 4 we recall some basic notions as Higgs bundles, decorated bundles and generalized parabolic sheaves and introduce the problem we want to study. In chapter 5, we study Higgs bundles on nodal curves. After moving the problem on the normalization of the curve, starting from a Higgs bundle we obtain a generalized parabolic Higgs bundle. Using decorated bundles we are able to construct a projective moduli space which parametrizes equivalence classes of Higgs bundles on a nodal curve X. This chapter is an extract of a joint work with Andrea Pustetto Later on Chapter 6 is devoted to the study of holomorphic pairs (or twisted Higgs bundles) on elliptic curve. Holomorphic pairs were introduced by Nitsure and they are a natural generalization of the concept of Higgs bundles. In this Chapter we extend a result of E. Franco, O. Garc\'ia-Prada And P.E. Newstead valid for Higgs bundles to holomorphic pairs. Finally the last Chapter describes a joint work with Professor Ugo Bruzzo. We study Higgs bundles over varieties with nef tangent bundle. In particular generalizing a result of Nitsure we prove that if a Higgs bundle $(E,\phi)$ over the variety X with nef tangent remains semisatble when pulled-back to any smooth curve then it discrimiant vanishes. PB - SISSA U1 - 7134 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Spectra of random Hermitian matrices with a small-rank external source: the supercritical and subcritical regimes JF - J. Stat. Phys. Y1 - 2013 A1 - Marco Bertola A1 - Buckingham, R. A1 - Lee, S. Y. A1 - Pierce, V. VL - 153 UR - http://dx.doi.org/10.1007/s10955-013-0845-2 ER - TY - RPRT T1 - The splitting theorem in non-smooth context Y1 - 2013 A1 - Nicola Gigli AB - We prove that an infinitesimally Hilbertian $CD(0,N)$ space containing a line splits as the product of $R$ and an infinitesimally Hilbertian $CD(0,N −1)$ space. By ‘infinitesimally Hilbertian’ we mean that the Sobolev space $W^{1,2}(X,d,m)$, which in general is a Banach space, is an Hilbert space. When coupled with a curvature-dimension bound, this condition is known to be stable with respect to measured Gromov-Hausdorff convergence. UR - http://preprints.sissa.it/handle/1963/35306 U1 - 35613 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - On the stability of continuous-discontinuous Galerkin methods for advection-diffusion-reaction problems JF - J. Sci. Comput. Y1 - 2013 A1 - Andrea Cangiani A1 - Chapman, John A1 - E.H. Georgoulis A1 - Jensen, Max VL - 57 UR - https://doi.org/10.1007/s10915-013-9707-y ER - TY - JOUR T1 - Stabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control JF - IEEE Transactions on Automatic Control. Volume 58, Issue 1, 2013, Article number6228517, Pages 74-85 Y1 - 2013 A1 - Claudio Altafini A1 - Francesco Ticozzi A1 - K. Nishio AB - In this paper, we investigate parametrization-free solutions of the problem of quantum pure state preparation and subspace stabilization by means of Hamiltonian control, continuous measurement, and quantum feedback, in the presence of a Markovian environment. In particular, we show that whenever suitable dissipative effects are induced either by the unmonitored environment, or by non-Hermitian measurements, there is no need for feedback, as open-loop time-invariant control is sufficient to achieve stabilization of the target set in probability. Constructive necessary and sufficient conditions on the form of the control Hamiltonian can be provided in this case. When time-invariant control is not sufficient, state stabilization can be attained by the addition of filtering-based feedback control UR - http://hdl.handle.net/1963/6503 U1 - 6448 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - A stable and adaptive semi-Lagrangian potential model for unsteady and nonlinear ship-wave interactions JF - Engineering Analysis with Boundary Elements, 37(1):128 – 143, 2013. Y1 - 2013 A1 - Andrea Mola A1 - Luca Heltai A1 - Antonio DeSimone KW - Unsteady ship-wave interaction AB -We present an innovative numerical discretization of the equations of inviscid potential flow for the simulation of three dimensional unsteady and nonlinear water waves generated by a ship hull advancing in water. The equations of motion are written in a semi-Lagrangian framework, and the resulting integro-diff erential equations are discretized in space via an adaptive iso-parametric collocation Boundary Element Method, and in time via adaptive implicit Backward Di erentiation Formulas (BDF) with variable step and variable order. When the velocity of the advancing ship hull is non-negligible, the semi-Lagrangian formulation (also known as Arbitrary Lagrangian Eulerian formulation, or ALE) of the free surface equations contains dominant transport terms which are stabilized with a Streamwise Upwind Petrov-Galerkin (SUPG) method. The SUPG stabilization allows automatic and robust adaptation of the spatial discretization with unstructured quadrilateral grids. Preliminary results are presented where we compare our numerical model with experimental results on the case of a Wigley hull advancing in calm water with fi xed sink and trim.

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

PB - Taylor & Francis VL - 92 UR - https://doi.org/10.1080/00036811.2011.628173 ER - TY - JOUR T1 - Stochastic optimal robin boundary control problems of advection-dominated elliptic equations JF - SIAM Journal on Numerical Analysis Y1 - 2013 A1 - Peng Chen A1 - Alfio Quarteroni A1 - Gianluigi Rozza AB - In this work we deal with a stochastic optimal Robin boundary control problem constrained by an advection-diffusion-reaction elliptic equation with advection-dominated term. We assume that the uncertainty comes from the advection field and consider a stochastic Robin boundary condition as control function. A stochastic saddle point system is formulated and proved to be equivalent to the first order optimality system for the optimal control problem, based on which we provide the existence and uniqueness of the optimal solution as well as some results on stochastic regularity with respect to the random variables. Stabilized finite element approximations in physical space and collocation approximations in stochastic space are applied to discretize the optimality system. A global error estimate in the product of physical space and stochastic space for the numerical approximation is derived. Illustrative numerical experiments are provided. VL - 51 ER - TY - JOUR T1 - Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two-matrix model JF - J. Math. Phys. Y1 - 2013 A1 - Marco Bertola A1 - Gekhtman, M. A1 - Szmigielski, J. VL - 54 ER - TY - THES T1 - The structure and regularity of admissible BV solutions to hyperbolic conservation laws in one space dimension Y1 - 2013 A1 - Lei Yu AB - This thesis is devoted to the study of the qualitative properties of admissible BV solutions to the strictly hyperbolic conservation laws in one space dimension by using wave-front tracking approximation. This thesis consists of two parts: • SBV-like regularity of vanishing viscosity BV solutions to strict hyperbolic systems of conservation laws. • Global structure of admissible BV solutions to strict hyperbolic conservation laws. PB - SISSA U1 - 7210 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Subharmonic solutions for nonlinear second order equations in presence of lower and upper solutions JF - Discrete & Continuous Dynamical Systems - A Y1 - 2013 A1 - Alberto Boscaggin A1 - Fabio Zanolin KW - lower and upper solutions KW - parameter dependent equations KW - Periodic solutions KW - Poincaré-Birkhoff twist theorem KW - subharmonic solutions AB -We study the problem of existence and multiplicity of subharmonic solutions for a second order nonlinear ODE in presence of lower and upper solutions. We show how such additional information can be used to obtain more precise multiplicity results. Applications are given to pendulum type equations and to Ambrosetti-Prodi results for parameter dependent equations.

VL - 33 UR - http://aimsciences.org//article/id/3638a93e-4f3e-4146-a927-3e8a64e6863f ER - TY - RPRT T1 - On Sudakov's type decomposition of transference plans with norm costs Y1 - 2013 A1 - Stefano Bianchini A1 - Sara Daneri PB - SISSA UR - http://hdl.handle.net/1963/7206 U1 - 7234 U2 - Mathematics U4 - -1 ER - TY - RPRT T1 - Symplectic instanton bundles on P3 and 't Hooft instantons Y1 - 2013 A1 - Ugo Bruzzo A1 - Dimitri Markushevich A1 - Alexander Tikhomirov AB - We introduce the notion of tame symplectic instantons by excluding a kind of pathological monads and show that the locus $I^*_{n,r}$ of tame symplectic instantons is irreducible and has the expected dimension, equal to $4n(r+1)-r(2r+1)$. The proof is inherently based on a relation between the spaces $I^*_{n,r}$ and the moduli spaces of 't Hooft instantons. PB - arXiv:1312.5554 [math.AG] UR - http://urania.sissa.it/xmlui/handle/1963/34486 N1 - This preprint has been published with the title "Moduli of symplectic instanton vector bundles of higher rank on projective space P-3 " in CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, Volume: 10, issue 4, Augst 2012, pages 1232-1245. U1 - 34675 U2 - Mathematics U4 - 1 U5 - MAT/03 ER - TY - JOUR T1 - SBV regularity for genuinely nonlinear, strictly hyperbolic systems of conservation laws in one space dimension JF - Communications in Mathematical Physics 313 (2012) 1-33 Y1 - 2012 A1 - Stefano Bianchini A1 - Laura Caravenna PB - Springer UR - http://hdl.handle.net/1963/4091 U1 - 313 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - SBV regularity for Hamilton-Jacobi equations with Hamiltonian depending on (t,x) JF - Siam Journal on Mathematical Analysis Y1 - 2012 A1 - Stefano Bianchini A1 - Daniela Tonon PB - SISSA VL - 44 UR - http://hdl.handle.net/20.500.11767/14066 IS - 3 U1 - 3890 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - SBV regularity of genuinely nonlinear hyperbolic systems of conservation laws in one space dimension JF - Acta Mathematica Scientia, Volume 32, Issue 1, January 2012, Pages 380-388 Y1 - 2012 A1 - Stefano Bianchini KW - Hyperbolic systems AB - The problem of the presence of Cantor part in the derivative of a solution to a hyperbolic system of conservation laws is considered. An overview of the techniques involved in the proof is given, and a collection of related problems concludes the paper. Key words hyperbolic systems; conservation laws; SBV; regularity PB - Elsevier UR - http://hdl.handle.net/1963/6535 U1 - 6510 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - SBV-like regularity for general hyperbolic systems of conservation laws in one space dimension JF - Rend. Istit. Mat. Univ. Trieste Y1 - 2012 A1 - Stefano Bianchini A1 - Lei Yu VL - 44 ER - TY - JOUR T1 - SBV-like regularity for Hamilton-Jacobi equations with a convex Hamiltonian JF - Journal of Mathematical Analysis and Applications Y1 - 2012 A1 - Stefano Bianchini A1 - Daniela Tonon PB - SISSA VL - 391 UR - http://hdl.handle.net/20.500.11767/13909 IS - 1 U1 - 4352 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Second order approximations of quasistatic evolution problems in finite dimension JF - Discrete & Continuous Dynamical Systems - A Y1 - 2012 A1 - Virginia Agostiniani KW - discrete approximations KW - perturbation methods KW - saddle-node bifurcation KW - Singular perturbations KW - vanishing viscosity AB -In this paper, we study the limit, as ε goes to zero, of a particular solution of the equation $\epsilon^2A\ddot u^ε(t)+εB\dot u^ε(t)+\nabla_xf(t,u^ε(t))=0$, where $f(t,x)$ is a potential satisfying suitable coerciveness conditions. The limit $u(t)$ of $u^ε(t)$ is piece-wise continuous and verifies $\nabla_xf(t,u(t))=0$. Moreover, certain jump conditions characterize the behaviour of $u(t)$ at the discontinuity times. The same limit behaviour is obtained by considering a different approximation scheme based on time discretization and on the solutions of suitable autonomous systems.

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

PB - Taylor & Francis VL - 6 UR - https://doi.org/10.1080/17513758.2011.611260 N1 - PMID: 22873677 ER - TY - JOUR T1 - Simulation-based uncertainty quantification of human arterial network hemodynamics JF - International Journal Numerical Methods Biomedical Engineering Y1 - 2012 A1 - Peng Chen A1 - Alfio Quarteroni A1 - Gianluigi Rozza KW - uncertainty quantification, mathematical modelling of the cardiovascular system, fluid-structure interaction AB - This work aims at identifying and quantifying uncertainties from various sources in human cardiovascular\r\nsystem based on stochastic simulation of a one dimensional arterial network. A general analysis of\r\ndifferent uncertainties and probability characterization with log-normal distribution of these uncertainties\r\nis introduced. Deriving from a deterministic one dimensional fluid structure interaction model, we establish\r\nthe stochastic model as a coupled hyperbolic system incorporated with parametric uncertainties to describe\r\nthe blood flow and pressure wave propagation in the arterial network. By applying a stochastic collocation\r\nmethod with sparse grid technique, we study systemically the statistics and sensitivity of the solution with\r\nrespect to many different uncertainties in a relatively complete arterial network with potential physiological\r\nand pathological implications for the first time. PB - Wiley U1 - 6467 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - Sobolev quasi-periodic solutions of multidimensional wave equations with a multiplicative potential JF - Nonlinearity Y1 - 2012 A1 - Massimiliano Berti A1 - Philippe Bolle AB - We prove the existence of quasi-periodic solutions for wave equations with a multiplicative potential on T d , d ≥ 1, and finitely differentiable nonlinearities, quasi-periodically forced in time. The only external parameter is the length of the frequency vector. The solutions have Sobolev regularity both in time and space. The proof is based on a Nash-Moser iterative scheme as in [5]. The key tame estimates for the inverse linearized operators are obtained by a multiscale inductive argument, which is more difficult than for NLS due to the dispersion relation of the wave equation. We prove the 'separation properties' of the small divisors assuming weaker non-resonance conditions than in [11]. © 2012 IOP Publishing Ltd. VL - 25 N1 - cited By (since 1996)3 ER - TY - JOUR T1 - Solving the Sixth Painlevé Equation: Towards the Classification of all the Critical Behaviors and the Connection Formulae JF - Int Math Res Notices (2012) 2012 (6): 1352-1413 Y1 - 2012 A1 - Davide Guzzetti AB - The critical behavior of a three real parameter class of solutions of the\\r\\nsixth Painlev\\\\\\\'e equation is computed, and parametrized in terms of monodromy\\r\\ndata of the associated $2\\\\times 2$ matrix linear Fuchsian system of ODE. The\\r\\nclass may contain solutions with poles accumulating at the critical point. The\\r\\nstudy of this class closes a gap in the description of the transcendents in one\\r\\nto one correspondence with the monodromy data. These transcendents are reviewed in the paper. Some formulas that relate the monodromy data to the critical behaviors of the four real (two complex) parameter class of solutions are\\r\\nmissing in the literature, so they are computed here. A computational procedure to write the full expansion of the four and three real parameter class of solutions is proposed. PB - Oxford University Press UR - http://hdl.handle.net/1963/6093 N1 - 53 pages, 2 figures U1 - 5979 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Some applications of the SBV Regularity Theorem for entropy solutions of 1D scalar conservation laws to ConvectionTheory and sticky particles JF - Riv. Mat. Univ. Parma Y1 - 2012 A1 - Daniela Tonon AB -We show how it is possible to apply the SBV Regularity Theorem for entropy solutions of one-dimensional scalar conservation laws, proved by Ambrosio and De Lellis, to Convection Theory and sticky particles. In the multi-dimensional case we present a counterexample which prevent us from using the same approach.

VL - 3 UR - https://hal.archives-ouvertes.fr/hal-00918409 ER - TY - THES T1 - Some aspects of spinors – classical and noncommutative Y1 - 2012 A1 - Giacomo Dossena PB - SISSA UR - http://hdl.handle.net/1963/6317 U1 - 6218 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Some remarks on quantum mechanics JF - International Journal of Geometric Methods in Modern Physics, Volume 9, Issue 2, March 2012, Article number1260018 Y1 - 2012 A1 - Gianfausto Dell'Antonio KW - Quantum mechanics AB - We discuss the similarities and differences between the formalism of Hamiltonian Classical Mechanics and of Quantum Mechanics and exemplify the differences through an analysis of tracks in a cloud chamber. PB - World Scientific Publishing UR - http://hdl.handle.net/1963/7018 U1 - 7013 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Spectra of random Hermitian matrices with a small-rank external source: the critical and near-critical regimes JF - J. Stat. Phys. Y1 - 2012 A1 - Marco Bertola A1 - Buckingham, R. A1 - Lee, S. Y. A1 - Pierce, V. VL - 146 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1007/s10955-011-0409-2 ER - TY - JOUR T1 - Stability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions JF - Rev. Math. Phys. 24 (2012), 1250017 Y1 - 2012 A1 - Michele Correggi A1 - Gianfausto Dell'Antonio A1 - Domenico Finco A1 - Alessandro Michelangeli A1 - Alessandro Teta AB - We study the stability problem for a non-relativistic quantum system in\\r\\ndimension three composed by $ N \\\\geq 2 $ identical fermions, with unit mass,\\r\\ninteracting with a different particle, with mass $ m $, via a zero-range\\r\\ninteraction of strength $ \\\\alpha \\\\in \\\\R $. We construct the corresponding\\r\\nrenormalised quadratic (or energy) form $ \\\\form $ and the so-called\\r\\nSkornyakov-Ter-Martirosyan symmetric extension $ H_{\\\\alpha} $, which is the\\r\\nnatural candidate as Hamiltonian of the system. We find a value of the mass $\\r\\nm^*(N) $ such that for $ m > m^*(N)$ the form $ \\\\form $ is closed and bounded from below. As a consequence, $ \\\\form $ defines a unique self-adjoint and bounded from below extension of $ H_{\\\\alpha}$ and therefore the system is stable. On the other hand, we also show that the form $ \\\\form $ is unbounded from below for $ m < m^*(2)$. In analogy with the well-known bosonic case, this suggests that the system is unstable for $ m < m^*(2)$ and the so-called Thomas effect occurs. PB - World Scientific UR - http://hdl.handle.net/1963/6069 U1 - 5955 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - CONF T1 - A stable semi-lagrangian potential method for the simulation of ship interaction with unsteady and nonlinear waves T2 - 17th Int. Conf. Ships Shipp. Res. Y1 - 2012 A1 - Andrea Mola A1 - Luca Heltai A1 - Antonio DeSimone JF - 17th Int. Conf. Ships Shipp. Res. ER - TY - JOUR T1 - Sub-Riemannian structures on 3D Lie groups JF - Journal of Dynamical and Control Systems. Volume 18, Issue 1, January 2012, Pages 21-44 Y1 - 2012 A1 - Andrei A. Agrachev A1 - Davide Barilari AB -We give a complete classification of left-invariant sub-Riemannian structures on three dimensional Lie groups in terms of the basic differential invariants. As a corollary we explicitly find a sub-Riemannian isometry between the nonisomorphic Lie groups $SL(2)$ and $A^+(\mathbb{R})\times S^1$, where $A^+(\mathbb{R})$ denotes the group of orientation preserving affine maps on the real line.

PB - SISSA UR - http://hdl.handle.net/1963/6453 U1 - 6397 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Systems of Quadratic Inequalities JF - Proceedings of the London Mathematical Society, Volume 105, Issue 3, September 2012, Pages 622-660 Y1 - 2012 A1 - Andrei A. Agrachev A1 - Antonio Lerario AB - We present a spectral sequence which efficiently computes Betti numbers of a closed semi-algebraic subset of RP^n defined by a system of quadratic inequalities and the image of the homology homomorphism induced by the inclusion of this subset in RP^n. We do not restrict ourselves to the term E_2 of the spectral sequence and give a simple explicit formula for the differential d_2. PB - SISSA UR - http://hdl.handle.net/1963/7072 U1 - 7066 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - SBV regularity for Hamilton-Jacobi equations in R^n JF - Arch. Rational Mech. Anal. 200 (2011) 1003-1021 Y1 - 2011 A1 - Stefano Bianchini A1 - Camillo De Lellis A1 - Roger Robyr AB -In this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$ \partial_t u + H(D_{x} u)=0 \qquad \textrm{in}\quad \Omega\subset \mathbb{R}\times \mathbb{R}^{n} . $$ In particular, under the assumption that the Hamiltonian $H\in C^2(\mathbb{R}^n)$ is uniformly convex, we prove that $D_{x}u$ and $\partial_t u$ belong to the class $SBV_{loc}(\Omega)$.

PB - Springer UR - http://hdl.handle.net/1963/4911 U1 - 4695 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Semistable and numerically effective principal (Higgs) bundles JF - Advances in Mathematics 226 (2011) 3655-3676 Y1 - 2011 A1 - Ugo Bruzzo A1 - Beatriz Grana-Otero AB - We study Miyaoka-type semistability criteria for principal Higgs G-bundles E on complex projective manifolds of any dimension. We prove that E has the property of being semistable after pullback to any projective curve if and only if certain line bundles, obtained from some characters of the parabolic subgroups of G, are numerically effective. One also proves that these conditions are met for semistable principal Higgs bundles whose adjoint bundle has vanishing second Chern class.\\r\\n\\r\\nIn a second part of the paper, we introduce notions of numerical effectiveness and numerical flatness for principal (Higgs) bundles, discussing their main properties. For (non-Higgs) principal bundles, we show that a numerically flat principal bundle admits a reduction to a Levi factor which has a flat Hermitian–Yang–Mills connection, and, as a consequence, that the cohomology ring of a numerically flat principal bundle with coefficients in R is trivial. To our knowledge this notion of numerical effectiveness is new even in the case of (non-Higgs) principal bundles. PB - Elsevier UR - http://hdl.handle.net/1963/3638 U1 - 666 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Singular perturbation models in phase transitions for second order materials JF - Indiana Univ. Math. J. 60 (2011) 367-409 Y1 - 2011 A1 - Milena Chermisi A1 - Gianni Dal Maso A1 - Irene Fonseca A1 - Giovanni Leoni AB - A variational model proposed in the physics literature to describe the onset of pattern formation in two-component bilayer membranes and amphiphilic monolayers leads to the analysis of a Ginzburg-Landau type energy with a negative term depending on the first derivative of the phase function. Scaling arguments motivate the study of the family of second order singular perturbed energies Fe having a negative term depending on the first derivative of the phase function. Here, the asymptotic behavior of {Fe} is studied using G-convergence techniques. In particular, compactness results and an integral representation of the limit energy are obtained. PB - Indiana University UR - http://hdl.handle.net/1963/3858 U1 - 851 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - Solving PVI by Isomonodromy Deformations T2 - Painlevé equations and related topics : proceedings of the international conference, Saint Petersburg, Russia, June 17-23, 2011 / Aleksandr Dmitrievich Briuno; Alexander B Batkhin. - Berlin : De Gruyter, [2012]. - p. 101-105 Y1 - 2011 A1 - Davide Guzzetti KW - Painlevé Equations AB - The critical and asymptotic behaviors of solutions of the sixth Painlev\\\'e\r\nequation, an their parametrization in terms of monodromy data, are\r\nsynthetically reviewed. The explicit formulas are given. This paper has been\r\nwithdrawn by the author himself, because some improvements are necessary.\r\nThis is a proceedings of the international conference \"Painlevé Equations and Related Topics\" which was taking place at the Euler International Mathematical Institute, a branch of the Saint Petersburg Department of the SteklovInstitute of Mathematicsof theRussian Academy of Sciences, in Saint Petersburg on June 17 to 23, 2011. JF - Painlevé equations and related topics : proceedings of the international conference, Saint Petersburg, Russia, June 17-23, 2011 / Aleksandr Dmitrievich Briuno; Alexander B Batkhin. - Berlin : De Gruyter, [2012]. - p. 101-105 PB - SISSA SN - 9783110275582 UR - http://hdl.handle.net/1963/6522 N1 - 12 pages, 1 figurethis paper has been U1 - 6472 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - On the Space of Symmetric Operators with Multiple Ground States JF - Functional Analysis and its Applications, Volume 45, Issue 4, December 2011, Pages 241-251 Y1 - 2011 A1 - Andrei A. Agrachev KW - Multiple eigenvalue AB - We study homological structure of the filtrations of the spaces of self-adjoint operators by the multiplicity of the ground state. We consider only operators acting in a finite dimensional complex or real Hilbert space but infinite dimensional generalizations are easily guessed. PB - SISSA UR - http://hdl.handle.net/1963/7069 U1 - 6392 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry JF - Journal of Dynamical and Control Systems Y1 - 2011 A1 - Bernard Bonnard A1 - Grégoire Charlot A1 - Roberta Ghezzi A1 - Gabriel Janin AB -We study the tangential case in 2-dimensional almost-Riemannian geometry. We\\r\\nanalyse the connection with the Martinet case in sub-Riemannian geometry. We\\r\\ncompute estimations of the exponential map which allow us to describe the\\r\\nconjugate locus and the cut locus at a tangency point. We prove that this last\\r\\none generically accumulates at the tangency point as an asymmetric cusp whose branches are separated by the singular set.

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

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

PB - Oxford University Press UR - http://hdl.handle.net/1963/4095 U1 - 309 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A system-level approach for deciphering the transcriptional response to prion infection JF - Bioinformatics (Oxford, England). 2011 Dec; 27(24):3407-14 Y1 - 2011 A1 - Mattia Zampieri A1 - Giuseppe Legname A1 - Daniel Segrè A1 - Claudio Altafini AB - MOTIVATION: Deciphering the response of a complex biological system to an insulting event, at the gene expression level, requires adopting theoretical models that are more sophisticated than a one-to-one comparison (i.e. t-test). Here, we investigate the ability of a novel reverse engineering approach (System Response Inference) to unveil non-obvious transcriptional signatures of the system response induced by prion infection.\\r\\nRESULTS: To this end, we analyze previously published gene expression data, from which we extrapolate a putative full-scale model of transcriptional gene-gene dependencies in the mouse central nervous system. Then, we use this nominal model to interpret the gene expression changes caused by prion replication, aiming at selecting the genes primarily influenced by this perturbation. Our method sheds light on the mode of action of prions by identifying key transcripts that are the most likely to be responsible for the overall transcriptional rearrangement from a nominal regulatory network. As a first result of our inference, we have been able to predict known targets of prions (i.e. PrP(C)) and to unveil the potential role of previously unsuspected genes.\\r\\nCONTACT: altafini@sissa.it\\r\\nSUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online. PB - Oxford University Press UR - http://hdl.handle.net/1963/5745 U1 - 5600 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Semiclassical evolution of two rotating solitons for the Nonlinear Schrödinger Equation with electric potential JF - Adv. Differential Equations Y1 - 2010 A1 - Alessandro Selvitella PB - Khayyam Publishing, Inc. VL - 15 UR - https://projecteuclid.org:443/euclid.ade/1355854752 ER - TY - JOUR T1 - On semistable principal bundles over complex projective manifolds, II JF - Geom. Dedicata 146 (2010) 27-41 Y1 - 2010 A1 - Indranil Biswas A1 - Ugo Bruzzo AB - Let (X, \\\\omega) be a compact connected Kaehler manifold of complex dimension d and E_G a holomorphic principal G-bundle on X, where G is a connected reductive linear algebraic group defined over C. Let Z (G) denote the center of G. We prove that the following three statements are equivalent: (1) There is a parabolic subgroup P of G and a holomorphic reduction of the structure group of E_G to P (say, E_P) such that the bundle obtained by extending the structure group of E_P to L(P)/Z(G) (where L(P) is the Levi quotient of P) admits a flat connection; (2) The adjoint vector bundle ad(E_G) is numerically flat; (3) The principal G-bundle E_G is pseudostable, and the degree of the charateristic class c_2(ad(E_G) is zero. UR - http://hdl.handle.net/1963/3404 U1 - 928 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Sharp nonexistence results for a linear elliptic inequality involving Hardy and Leray potentials Y1 - 2010 A1 - Mouhamed Moustapha Fall A1 - Roberta Musina AB - In this paper we deal with nonnegative distributional supersolutions for a class of linear\\nelliptic equations involving inverse-square potentials and logarithmic weights. We prove sharp nonexistence results. UR - http://hdl.handle.net/1963/3869 U1 - 840 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Shell theories arising as low energy Gamma-limit of 3d nonlinear elasticity JF - Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. IX (2010) 253-295 Y1 - 2010 A1 - Marta Lewicka A1 - Maria Giovanna Mora A1 - Mohammad Reza Pakzad AB - We discuss the limiting behavior (using the notion of gamma-limit) of the 3d nonlinear elasticity for thin shells around an arbitrary smooth 2d surface. In particular, under the assumption that the elastic energy of deformations scales like h4, h being the thickness of a shell, we derive a limiting theory which is a generalization of the von Karman theory for plates. UR - http://hdl.handle.net/1963/2601 U1 - 1521 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Sobolev periodic solutions of nonlinear wave equations in higher spatial dimensions JF - Archive for Rational Mechanics and Analysis Y1 - 2010 A1 - Massimiliano Berti A1 - Philippe Bolle AB - We prove the existence of Cantor families of periodic solutions for nonlinear wave equations in higher spatial dimensions with periodic boundary conditions. We study both forced and autonomous PDEs. In the latter case our theorems generalize previous results of Bourgain to more general nonlinearities of class C k and assuming weaker non-resonance conditions. Our solutions have Sobolev regularity both in time and space. The proofs are based on a differentiable Nash-Moser iteration scheme, where it is sufficient to get estimates of interpolation-type for the inverse linearized operators. Our approach works also in presence of very large "clusters of small divisors". © Springer-Verlag (2009). VL - 195 N1 - cited By (since 1996)6 ER - TY - JOUR T1 - Solitonic asymptotics for the Korteweg-de Vries equation in the small dispersion limit JF - SIAM J. Math. Anal. 42 (2010) 2132-2154 Y1 - 2010 A1 - Tamara Grava A1 - Tom Claeys AB - We study the small dispersion limit for the Korteweg-de Vries (KdV) equation $u_t+6uu_x+\\\\epsilon^{2}u_{xxx}=0$ in a critical scaling regime where $x$ approaches the trailing edge of the region where the KdV solution shows oscillatory behavior. Using the Riemann-Hilbert approach, we obtain an asymptotic expansion for the KdV solution in a double scaling limit, which shows that the oscillations degenerate to sharp pulses near the trailing edge. Locally those pulses resemble soliton solutions of the KdV equation. UR - http://hdl.handle.net/1963/3839 U1 - 488 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - A spatial model of cellular molecular trafficking including active transport along microtubules JF - J. Theoret. Biol. Y1 - 2010 A1 - Andrea Cangiani A1 - Natalini, R. VL - 267 UR - https://doi.org/10.1016/j.jtbi.2010.08.017 ER - TY - JOUR T1 - Stable determination of an immersed body in a stationary Stokes fluid JF - Inverse Problems Y1 - 2010 A1 - Andrea Ballerini AB -We consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the Stokes equations, from a single measurement of force and velocity on a portion of the boundary. We obtain an estimate of the stability of log–log type.

PB - IOP Publishing VL - 26 UR - https://doi.org/10.1088%2F0266-5611%2F26%2F12%2F125015 ER - TY - JOUR T1 - On a Sobolev type inequality related to the weighted p-Laplace operator JF - J. Math. Anal. Appl. 352 (2009) 99-111 Y1 - 2009 A1 - Marita Gazzini A1 - Roberta Musina UR - http://hdl.handle.net/1963/2613 U1 - 1510 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Solutions of the Schrödinger–Poisson problem concentrating on spheres, part I: necessary conditions JF - Mathematical Models and Methods in Applied Sciences Y1 - 2009 A1 - Ianni, Isabella A1 - Giusi Vaira AB -In this paper we study a coupled nonlinear Schrödinger–Poisson problem with radial functions. This system has been introduced as a model describing standing waves for the nonlinear Schrödinger equations in the presence of the electrostatic field. We provide necessary conditions for concentration on sphere for the solutions of this kind of problem extending the results already known.

VL - 19 UR - https://doi.org/10.1142/S0218202509003589 ER - TY - JOUR T1 - Some new entire solutions of semilinear elliptic equations on Rn JF - Adv. Math. 221 (2009) 1843-1909 Y1 - 2009 A1 - Andrea Malchiodi PB - Elsevier UR - http://hdl.handle.net/1963/3645 U1 - 659 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Strain-order coupling in nematic elastomers: equilibrium configurations JF - Math. Models Methods Appl. Sci. 19 (2009) 601-630 Y1 - 2009 A1 - Pierluigi Cesana A1 - Antonio DeSimone AB - We consider models that describe liquid crystal elastomers either in a biaxial or in a uniaxial phase and in the framework of Frank\\\'s director theory. We prove existence of static equilibrium solutions in the presence of frustrations due to electro-mechanical boundary conditions and to applied loads and fields. We find explicit solutions arising in connection with special boundary conditions and the corresponding phase diagrams, leading to significant implications on possible experimental observations. UR - http://hdl.handle.net/1963/2700 U1 - 1400 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Stratos: a code for 3D free surface flows with floating constraints Y1 - 2009 A1 - Antonio DeSimone A1 - B. Bianchi A1 - Luca Heltai AB - This report presents a brief discussion of the theoretical aspects and practical implementation of STRATOS . STRATOS is a 3D code for the simulation\\nof hydrodynamic flows for incompressible fluids, in the presence of a free surface, capable of simulating the interaction between the free surface and a\\nfloating object via Lagrange multipliers...... UR - http://hdl.handle.net/1963/3701 U1 - 604 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A second order minimality condition for the Mumford-Shah functional JF - Calc. Var. Partial Differential Equations 33 (2008) 37-74 Y1 - 2008 A1 - Filippo Cagnetti A1 - Maria Giovanna Mora A1 - Massimiliano Morini AB - A new necessary minimality condition for the Mumford-Shah functional is derived by means of second order variations. It is expressed in terms of a sign condition for a nonlocal quadratic form on $H^1_0(\\\\Gamma)$, $\\\\Gamma$ being a submanifold of the regular part of the discontinuity set of the critical point. Two equivalent formulations are provided: one in terms of the first eigenvalue of a suitable compact operator, the other involving a sort of nonlocal capacity of $\\\\Gamma$. A sufficient condition for minimality is also deduced. Finally, an explicit example is discussed, where a complete characterization of the domains where the second variation is nonnegative can be given. UR - http://hdl.handle.net/1963/1955 U1 - 2318 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On semistable principal bundles over a complex projective manifold JF - Int. Math. Res. Not. vol. 2008, article ID rnn035 Y1 - 2008 A1 - Indranil Biswas A1 - Ugo Bruzzo AB - Let G be a simple linear algebraic group defined over the complex numbers. Fix a proper parabolic subgroup P of G and a nontrivial antidominant character \\\\chi of P. We prove that a holomorphic principal G-bundle E over a connected complex projective manifold M is semistable and the second Chern class of its adjoint bundle vanishes in rational cohomology if and only if the line bundle over E/P defined by \\\\chi is numerically effective. Similar results remain valid for principal bundles with a reductive linear algebraic group as the structure group. These generalize an earlier work of Y. Miyaoka where he gave a characterization of semistable vector bundles over a smooth projective curve. Using these characterizations one can also produce similar criteria for the semistability of parabolic principal bundles over a compact Riemann surface. PB - Oxford University Press UR - http://hdl.handle.net/1963/3418 U1 - 917 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Solitons of linearly coupled systems of semilinear non-autonomous equations on Rn JF - J. Funct. Anal. 254 (2008) 2816-2845 Y1 - 2008 A1 - Antonio Ambrosetti A1 - Giovanna Cerami A1 - David Ruiz AB - Using concentration compactness type arguments, we prove some results about the existence of positive ground and bound state of linearly coupled systems of nonlinear Schrödinger equations. UR - http://hdl.handle.net/1963/2175 U1 - 2069 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Stability of planar switched systems: the nondiagonalizable case JF - Commun. Pure Appl. Anal. 7 (2008) 1-21 Y1 - 2008 A1 - Ugo Boscain A1 - Moussa Balde UR - http://hdl.handle.net/1963/1857 U1 - 2361 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Symmetric obstruction theories and Hilbert schemes of points on threefolds JF - Algebra Number Theory 2 (2008) 313-345 Y1 - 2008 A1 - Kai Behrend A1 - Barbara Fantechi AB - In an earlier paper by one of us (Behrend), Donaldson-Thomas type invariants were expressed as certain weighted Euler characteristics of the moduli space. The Euler characteristic is weighted by a certain canonical\\nZ-valued constructible function on the moduli space. This constructible function associates to\\nany point of the moduli space a certain invariant of the singularity of the space at the point. Here we evaluate this invariant for the case of a singularity that is an isolated point of a C∗-action and that admits a symmetric obstruction theory compatible with the C∗-action. The answer is (-1)d, where d\\nis the dimension of the Zariski tangent space. We use this result to prove that for any threefold, proper or not, the weighted Euler characteristic of the Hilbert scheme of n points on the threefold is, up to sign, equal to the usual Euler characteristic. For the case of a projective Calabi-Yau threefold, we deduce that the Donaldson-Thomas invariant of the Hilbert scheme of n points is, up to sign, equal to the Euler characteristic. This proves a conjecture of Maulik, Nekrasov, Okounkov and Pandharipande. UR - http://hdl.handle.net/1963/2709 U1 - 1392 U2 - Mathematics U3 - Mathematical Physics ER - TY - THES T1 - Symmetries of noncommutative spaces and equivariant cohomology Y1 - 2008 A1 - Lucio Cirio KW - Noncommutative spaces AB - As the title suggests, the main subject of this thesis is the study of symmetries of noncommutative spaces and related equivariant cohomologies. We focus on deformations of classical geometries coming from the action of some symmetry. A close relation between the deformation of the symmetry and the deformation of the space on which it acts is at the heart of our approach; we will use this idea to generate noncommutative geometries, and to de¯ne algebraic models for the equivariant cohomology of such actions. PB - SISSA UR - http://hdl.handle.net/1963/5254 U1 - 5077 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - RPRT T1 - Semistable principal Higgs bundles Y1 - 2007 A1 - Ugo Bruzzo A1 - Beatriz Grana-Otero UR - http://hdl.handle.net/1963/2533 U1 - 1585 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Smooth toric DM stacks Y1 - 2007 A1 - Barbara Fantechi A1 - Etienne Mann A1 - Fabio Nironi AB - We give a new definition of smooth toric DM stacks in the same spirit of toric varieties. We show that our definition is equivalent to the one of Borisov, Chen and Smith in terms of stacky fans. In particular, we give a geometric interpretation of the combinatorial data contained in a stacky fan. We also give a bottom up classification in terms of simplicial toric varieties and fiber products of root stacks. UR - http://hdl.handle.net/1963/2120 U1 - 2123 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Soft elasticity and microstructure in smectic C elastomers Y1 - 2007 A1 - Antonio DeSimone A1 - James Adams A1 - Sergio Conti AB - Smectic C elastomers are layered materials exhibiting a solid-like elastic response along the layer normal and a rubbery one in the plane. The set of strains minimizing the elastic energy contains a one-parameter family of simple stretches associated with an internal degree of freedom, coming from the in-plane component of the director. We investigate soft elasticity and the corresponding microstructure by determining the quasiconvex hull of the set , and use this to propose experimental tests that should make the predicted soft response observable. JF - Contin. Mech. Thermodyn. 18 (2007) 319-334 UR - http://hdl.handle.net/1963/1811 U1 - 2403 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Solutions of vectorial Hamilton-Jacobi equations and minimizers of nonquasiconvex functionals JF - J. Math. Anal. Appl. 335 (2007) 1143-1160 Y1 - 2007 A1 - Sandro Zagatti AB - We provide a unified approach to prove existence results for the Dirichlet problem for Hamilton-Jacobi equations and for the minimum problem for nonquasiconvex functionals of the Calculus of Variations with affine boundary data. The idea relies on the definition of integro-extremal solutions introduced in the study of nonconvex scalar variational problem. UR - http://hdl.handle.net/1963/2763 U1 - 1937 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Solutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part I: study of the limit set and approximate solutions Y1 - 2007 A1 - Fethi Mahmoudi A1 - Andrea Malchiodi A1 - Marcelo Montenegro AB - We prove existence of a special class of solutions to the (elliptic) Nonlinear Schroeodinger Equation $- \\\\epsilon^2 \\\\Delta \\\\psi + V(x) \\\\psi = |\\\\psi|^{p-1} \\\\psi$, on a manifold or in the Euclidean space. Here V represents the potential, p an exponent greater than 1 and $\\\\epsilon$ a small parameter corresponding to the Planck constant. As $\\\\epsilon$ tends to zero (namely in the semiclassical limit) we prove existence of complex-valued solutions which concentrate along closed curves, and whose phase is highly oscillatory. Physically, these solutions carry quantum-mechanical momentum along the limit curves. In this first part we provide the characterization of the limit set, with natural stationarity and non-degeneracy conditions. We then construct an approximate solution up to order $\\\\epsilon^2$, showing that these conditions appear naturally in a Taylor expansion of the equation in powers of $\\\\epsilon$. Based on these, an existence result will be proved in the second part. UR - http://hdl.handle.net/1963/2112 U1 - 2577 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Solutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part II: proof of the existence result Y1 - 2007 A1 - Fethi Mahmoudi A1 - Andrea Malchiodi AB - We prove existence of a special class of solutions to the (elliptic) Nonlinear Schroedinger Equation $- \\\\epsilon^2 \\\\Delta \\\\psi + V(x) \\\\psi = |\\\\psi|^{p-1} \\\\psi$ on a manifold or in the Euclidean space. Here V represents the potential, p is an exponent greater than 1 and $\\\\epsilon$ a small parameter corresponding to the Planck constant. As $\\\\epsilon$ tends to zero (namely in the semiclassical limit) we prove existence of complex-valued solutions which concentrate along closed curves, and whose phase in highly oscillatory. Physically, these solutions carry quantum-mechanical momentum along the limit curves. In the first part of this work we identified the limit set and constructed approximate solutions, while here we give the complete proof of our main existence result. UR - http://hdl.handle.net/1963/2111 U1 - 2578 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Some existence results for the Toda system on closed surfaces JF - Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 391-412 Y1 - 2007 A1 - Andrea Malchiodi A1 - Cheikh Birahim Ndiaye AB - Given a compact closed surface $\\\\Sig$, we consider the {\\\\em generalized Toda} system of equations on $\\\\Sig$: $- \\\\D u_i = \\\\sum_{j=1}^2 \\\\rho_j a_{ij} \\\\left( \\\\frac{h_j e^{u_j}}{\\\\int_\\\\Sig h_j e^{u_j} dV_g} - 1 \\\\right)$ for $i = 1, 2$, where $\\\\rho_1, \\\\rho_2$ are real parameters and $h_1, h_2$ are smooth positive functions. Exploiting the variational structure of the problem and using a new minimax scheme we prove existence of solutions for generic values of $\\\\rho_1$ and for $\\\\rho_2 < 4 \\\\pi$. UR - http://hdl.handle.net/1963/1775 U1 - 2769 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Stability of front tracking solutions to the initial and boundary value problem for systems of conservation laws JF - NoDEA Nonlinear Differential Equations Appl. 14 (2007) 569-592 Y1 - 2007 A1 - Andrea Marson A1 - Carlotta Donadello UR - http://hdl.handle.net/1963/1769 U1 - 2775 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Standing waves of some coupled Nonlinear Schrödinger Equations Y1 - 2007 A1 - Antonio Ambrosetti A1 - Eduardo Colorado AB - We deal with a class of systems of NLS equations, proving the existence of bound and ground states provided the coupling parameter is small, respectively, large. JF - J. Lond. Math. Soc. 75 (2007) 67-82 UR - http://hdl.handle.net/1963/1821 U1 - 2393 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Strengthened convergence of marginals to the cubic nonlinear Schroedinger equation Y1 - 2007 A1 - Alessandro Michelangeli AB - We rewrite a recent derivation of the cubic non-linear Schroedinger equation by Adami, Golse, and Teta in the more natural formof the asymptotic factorisation of marginals at any fixed time and in the trace norm. This is the standard form in which the emergence of the\\nnon-linear effective dynamics of a large system of interacting bosons is\\nproved in the literature. UR - http://hdl.handle.net/1963/1977 U1 - 2218 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Surfactants in Foam Stability: A Phase-Field Model JF - Arch. Rational Mech. Anal. 183 (2007) 411-456 Y1 - 2007 A1 - Irene Fonseca A1 - Massimiliano Morini A1 - Valeriy Slastikov AB - The role of surfactants in stabilizing the formation of bubbles in foams is studied using a phase-field model. The analysis is centered on a van der Walls-Cahn-Hilliard-type energy with an added term accounting for the interplay between the presence of a surfactant density and the creation of interfaces. In particular, it is concluded that the surfactant segregates to the interfaces, and that the prescriptionof the distribution of surfactant will dictate the locus of interfaces, what is in agreement with experimentation. UR - http://hdl.handle.net/1963/2035 U1 - 2161 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Semiclassical orthogonal polynomials, matrix models and isomonodromic tau functions JF - Comm. Math. Phys. Y1 - 2006 A1 - Marco Bertola A1 - B. Eynard A1 - Harnad, J. VL - 263 ER - TY - JOUR T1 - Semistability vs. nefness for (Higgs) vector bundles JF - Differential Geom. Appl. 24 (2006) 403-416 Y1 - 2006 A1 - Ugo Bruzzo A1 - Daniel Hernandez Ruiperez AB - According to Miyaoka, a vector bundle E on a smooth projective curve is semistable if and only if a certain numerical class in the projectivized bundle PE is nef. We establish a similar criterion for the semistability of Higgs bundles: namely, such a bundle is semistable if and only if for every integer s between 0 and the rank of E, a suitable numerical class in the scheme parametrizing the rank s locally-free Higgs quotients of E is nef. We also extend this result to higher-dimensional complex projective varieties by showing that the nefness of the above mentioned classes is equivalent to the semistability of the Higgs bundle E together with the vanishing of the discriminant of E. UR - http://hdl.handle.net/1963/2237 U1 - 2007 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - On Separation of Variables for Homogeneous SL(r) Gaudin Systems Y1 - 2006 A1 - Gregorio Falqui A1 - Fabio Musso AB - By means of a recently introduced bihamiltonian structure for the homogeneous Gaudin models, we find a new set of Separation Coordinates for the sl(r) case. JF - Math. Phys. Anal. Geom. 9 (2006), n. 3, 233-262 (2007) UR - http://hdl.handle.net/1963/2538 U1 - 1581 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Spectral geometry of k-Minkowski space JF - J. Math. Phys. 47 (2006) 062105 Y1 - 2006 A1 - Francesco D'Andrea AB -After recalling Snyder's idea of using vector fields over a smooth manifold as "coordinates on a noncommutative space", we discuss a two dimensional toy-model whose "dual" noncommutative coordinates form a Lie algebra: this is the well known $\kappa$-Minkowski space. We show how to improve Snyder's idea using the tools of quantum groups and noncommutative geometry. We find a natural representation of the coordinate algebra of $\kappa$-Minkowski as linear operators on an Hilbert space study its "spectral properties" and discuss how to obtain a Dirac operator for this space. We describe two Dirac operators. The first is associated with a spectral triple. We prove that the cyclic integral of M. Dimitrijevic et al. can be obtained as Dixmier trace associated to this triple. The second Dirac operator is equivariant for the action of the quantum Euclidean group, but it has unbounded commutators with the algebra.

UR - http://hdl.handle.net/1963/2131 U1 - 2112 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Stability of planar nonlinear switched systems Y1 - 2006 A1 - Ugo Boscain A1 - Grégoire Charlot A1 - Mario Sigalotti AB - We consider the time-dependent nonlinear system ˙ q(t) = u(t)X(q(t)) + (1 − u(t))Y (q(t)), where q ∈ R2, X and Y are two smooth vector fields, globally asymptotically stable at the origin and u : [0,∞) → {0, 1} is an arbitrary measurable function. Analysing the topology of the set where X and Y are parallel, we give some sufficient and some necessary conditions for global asymptotic stability, uniform with respect to u(.). Such conditions can be verified without any integration or construction of a Lyapunov function, and they are robust under small perturbations of the vector fields. JF - Discrete Contin. Dyn. Syst. 15 (2006) 415-432 UR - http://hdl.handle.net/1963/1710 U1 - 2441 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Self-similar folding patterns and energy scaling in compressed elastic sheets JF - Comput. Methods Appl. Mech. Engrg. 194 (2005) 2534-2549 Y1 - 2005 A1 - Sergio Conti A1 - Antonio DeSimone A1 - Stefan Müller AB - Thin elastic sheets under isotropic compression, such as for example blisters formed by thin films which debonded from the substrate, can exhibit remarkably complex folding patterns. We discuss the scaling of the elastic energy with respect to the film thickness, and show that in certain regimes the optimal energy scaling can be reached\\nby self-similar folding patterns that refine towards the boundary, in agreement with experimental observations. We then extend the analysis\\nto anisotropic compression, and discuss a simplified scalar model which suggests the presence of a transition between a regime where\\nthe deformation is governed by global properties of the domain and another one where the direction of maximal compression dominates and the scale of the folds is mainly determined by the distance to the boundary in the direction of the folds themselves. PB - Elsevier UR - http://hdl.handle.net/1963/3000 U1 - 1333 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - A short introduction to optimal control T2 - Contrôle non linéaire et applications: Cours donnés à l\\\'école d\\\'été du Cimpa de l\\\'Université de Tlemcen / Sari Tewfit [ed.]. - Paris: Hermann, 2005 Y1 - 2005 A1 - Ugo Boscain A1 - Benedetto Piccoli JF - Contrôle non linéaire et applications: Cours donnés à l\\\'école d\\\'été du Cimpa de l\\\'Université de Tlemcen / Sari Tewfit [ed.]. - Paris: Hermann, 2005 SN - 2 7056 6511 0 UR - http://hdl.handle.net/1963/2257 U1 - 1990 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - ABST T1 - Solutions of Neumann problems in domains with cracks and applications to fracture mechanics Y1 - 2005 A1 - Gianni Dal Maso UR - http://hdl.handle.net/1963/1684 U1 - 79 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The spectral geometry of the equatorial Podles sphere JF - C. R. Math. 340 (2005) 819-822 Y1 - 2005 A1 - Ludwik Dabrowski A1 - Giovanni Landi A1 - Mario Paschke A1 - Andrzej Sitarz AB - We propose a slight modification of the properties of a spectral geometry a la Connes, which allows for some of the algebraic relations to be satisfied only modulo compact operators. On the equatorial Podles sphere we construct suq2-equivariant Dirac operator and real structure which satisfy these modified properties. UR - http://hdl.handle.net/1963/2275 U1 - 1972 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Stability of solutions of quasilinear parabolic equations JF - J. Math. Anal. Appl. 308 (2005) 221-239 Y1 - 2005 A1 - Giuseppe Maria Coclite A1 - Helge Holden AB - We bound the difference between solutions $u$ and $v$ of $u_t = a\\\\Delta u+\\\\Div_x f+h$ and $v_t = b\\\\Delta v+\\\\Div_x g+k$ with initial data $\\\\phi$ and $ \\\\psi$, respectively, by $\\\\Vert u(t,\\\\cdot)-v(t,\\\\cdot)\\\\Vert_{L^p(E)}\\\\le A_E(t)\\\\Vert \\\\phi-\\\\psi\\\\Vert_{L^\\\\infty(\\\\R^n)}^{2\\\\rho_p}+ B(t)(\\\\Vert a-b\\\\Vert_{\\\\infty}+ \\\\Vert \\\\nabla_x\\\\cdot f-\\\\nabla_x\\\\cdot g\\\\Vert_{\\\\infty}+ \\\\Vert f_u-g_u\\\\Vert_{\\\\infty} + \\\\Vert h-k\\\\Vert_{\\\\infty})^{\\\\rho_p} \\\\abs{E}^{\\\\eta_p}$. Here all functions $a$, $f$, and $h$ are smooth and bounded, and may depend on $u$, $x\\\\in\\\\R^n$, and $t$. The functions $a$ and $h$ may in addition depend on $\\\\nabla u$. Identical assumptions hold for the functions that determine the solutions $v$. Furthermore, $E\\\\subset\\\\R^n$ is assumed to be a bounded set, and $\\\\rho_p$ and $\\\\eta_p$ are fractions that depend on $n$ and $p$. The diffusion coefficients $a$ and $b$ are assumed to be strictly positive and the initial data are smooth. PB - Elsevier UR - http://hdl.handle.net/1963/2892 U1 - 1808 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Stress-dilatancy based modelling of granular materials and extensions to soils with crushable grains JF - Int. J. Numer. Anal. Met. 29 (2005) 73-101 Y1 - 2005 A1 - Antonio DeSimone A1 - Claudio Tamagnini AB - Stress-dilatancy relations have played a crucial role in the understanding of the mechanical behaviour of soils and in the development of realistic constitutive models for their response. Recent investigations on the mechanical behaviour of materials with crushable grains have called into question the validity of classical relations such as those used in critical state soil mechanics.\\nIn this paper, a method to construct thermodynamically consistent (isotropic, three-invariant) elasto-plastic models based on a given stress-dilatancy relation is discussed. Extensions to cover the case of granular materials with crushable grains are also presented, based on the interpretation of some classical model parameters (e.g. the stress ratio at critical state) as internal variables that evolve according to suitable hardening laws. UR - http://hdl.handle.net/1963/2165 U1 - 2079 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Semiclassical analysis of constrained quantum systems JF - J. Phys. A 37 (2004) 5605-5624 Y1 - 2004 A1 - Gianfausto Dell'Antonio A1 - Lucattilio Tenuta AB - We study the dynamics of a quantum particle in R^(n+m) constrained by a strong potential force to stay within a distance of order hbar (in suitable units) from a smooth n-dimensional submanifold M. We prove that in the semiclassical limit the evolution of the wave function is approximated in norm, up to terms of order hbar^(1/2), by the evolution of a semiclassical wave packet centred on the trajectory of the corresponding classical constrained system. PB - IOP Publishing UR - http://hdl.handle.net/1963/2997 U1 - 1336 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Semi-cooperative strategies for differential games JF - Internat. J. Game Theory 32 (2004) 561-593 Y1 - 2004 A1 - Alberto Bressan A1 - Wen Shen AB - The paper is concerned with a non-cooperative differential game for two players. We first consider Nash equilibrium solutions in feedback form. In this case, we show that the Cauchy problem for the value functions is generically ill-posed. Looking at vanishing viscosity approximations, one can construct special solutions in the form of chattering controls, but these also appear to be unstable. In the second part of the paper we propose an alternative \\\"semi-cooperative\\\" pair of strategies for the two players, seeking a Pareto optimum instead of a Nash equilibrium. In this case, we prove that the corresponding Hamiltonian system for the value functions is always weakly hyperbolic. PB - Springer UR - http://hdl.handle.net/1963/2893 U1 - 1807 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A sharp decay estimate for positive nonlinear waves JF - SIAM J. Math. Anal. 36 (2004) 659-677 Y1 - 2004 A1 - Alberto Bressan A1 - Tong Yang AB - We consider a strictly hyperbolic, genuinely nonlinear system of conservation laws in one space dimension. A sharp decay estimate is proved for the positive waves in an entropy weak solution. The result is stated in terms of a partial ordering among positive measures, using symmetric rearrangements and a comparison with a solution of Burgers\\\' equation with impulsive sources. PB - SIAM UR - http://hdl.handle.net/1963/2916 U1 - 1784 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Singular Z_N curves, Riemann-Hilbert problem and modular solutions of the Schlesinger equation JF - Int. Math. Res. Not. 2004, no. 32, 1619-1683 Y1 - 2004 A1 - Victor Z. Enolski A1 - Tamara Grava AB - We are solving the classical Riemann-Hilbert problem of rank N>1 on the extended complex plane punctured in 2m+2 points, for NxN quasi-permutation monodromy matrices. Following Korotkin we solve the Riemann-Hilbert problem in terms of the Szego kernel of certain Riemann surfaces branched over the given 2m+2 points. These Riemann surfaces are constructed from a permutation representation of the symmetric group S_N to which the quasi-permutation monodromy representation has been reduced. The permutation representation of our problem generates the cyclic subgroup Z_N. For this reason the corresponding Riemann surfaces of genus N(m-1) have Z_N symmetry. This fact enables us to write the matrix entries of the solution of the NxN Riemann-Hilbert problem as a product of an algebraic function and theta-function quotients. The algebraic function turns out to be related to the Szego kernel with zero characteristics. From the solution of the Riemann- Hilbert problem we automatically obtain a particular solution of the Schlesinger system. The tau-function of the Schlesinger system is computed explicitly. The rank 3 problem with four singular points (0,t,1,\\\\infty) is studied in detail. The corresponding solution of the Riemann-Hilbert problem and the Schlesinger system is given in terms of Jacobi\\\'s theta-function with modulus T=T(t), Im(T)>0. The function T=T(t) is invertible if it belongs to the Siegel upper half space modulo the subgroup \\\\Gamma_0(3) of the modular group. The inverse function t=t(T) generates a solution of a general Halphen system. UR - http://hdl.handle.net/1963/2540 U1 - 1579 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Singularity perturbed elliptic equations with symmetry: existence of solutions concetrating on spheres, Part II JF - Indiana Univ. Math. J. 53 (2004) 297-392 Y1 - 2004 A1 - Antonio Ambrosetti A1 - Andrea Malchiodi A1 - Wei-Ming Ni PB - Indiana University Mathematics Journal UR - http://hdl.handle.net/1963/1663 U1 - 2455 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Small BV solutions of hyperbolic noncooperative differential games JF - SIAM J. Control Optim. 43 (2004) 194-215 Y1 - 2004 A1 - Alberto Bressan A1 - Wen Shen AB - The paper is concerned with an n-persons differential game in one space dimension. We state conditions for which the system of Hamilton-Jacobi equations for the value functions is strictly hyperbolic. In the positive case, we show that the weak solution of a corresponding system of conservation laws determines an n-tuple of feedback strategies. These yield a Nash equilibrium solution to the non-cooperative differential game. PB - SIAM UR - http://hdl.handle.net/1963/2917 U1 - 1783 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Solitary waves for Maxwell Schrodinger equations JF - Electron. J. Differential Equations (2004) 94 Y1 - 2004 A1 - Giuseppe Maria Coclite A1 - Vladimir Georgiev AB - In this paper we study solitary waves for the coupled system of Schrodinger-Maxwell equations in the three-dimensional space. We prove the existence of a sequence of radial solitary waves for these equations with a fixed L^2 norm. We study the asymptotic behavior and the smoothness of these solutions. We show also that the eigenvalues are negative and the first one is isolated. PB - SISSA Library UR - http://hdl.handle.net/1963/1582 U1 - 2536 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Solutions concentrating at curves for some singularly perturbed elliptic problems JF - C. R. Acad. Sci. Paris, Ser. I 338 (2004) 775-780 Y1 - 2004 A1 - Andrea Malchiodi PB - Elsevier UR - http://hdl.handle.net/1963/4869 U1 - 4647 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Soluzioni periodiche di PDEs Hamiltoniane JF - Bollettino dell\\\'Unione Matematica Italiana Serie 8 7-B (2004), p. 647-661 Y1 - 2004 A1 - Massimiliano Berti PB - Unione Matematica Italiana UR - http://hdl.handle.net/1963/4582 U1 - 4351 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Some remarks on multidimensional systems of conservation laws JF - Rend. Mat. Acc. Lincei, s. 9, v. 15 (2004) 3-4, pp. 225 - 233 Y1 - 2004 A1 - Alberto Bressan AB - This note is concerned with the Cauchy problem for hyperbolic systems of conservation\\nlaws in several space dimensions. We first discuss an example of ill-posedness, for a special system\\nhaving a radial symmetry property. Some conjectures are formulated, on the compactness of the set of\\nflow maps generated by vector fields with bounded variation. PB - Accademia Nazionale dei Lincei UR - http://hdl.handle.net/1963/3642 U1 - 662 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Stability rates for patchy vector fields JF - ESAIM COCV 10 (2004) 168-200 Y1 - 2004 A1 - Fabio Ancona A1 - Alberto Bressan AB - This paper is concerned with the stability of the set of trajectories of a patchy vector field, in the presence of impulsive perturbations. Patchy vector fields are discontinuous, piecewise smooth vector fields that were introduced in Ancona and Bressan (1999) to study feedback stabilization problems. For patchy vector fields in the plane, with polygonal patches in generic position, we show that the distance between a perturbed trajectory and an unperturbed one is of the same order of magnitude as the impulsive forcing term. PB - EDP Sciences UR - http://hdl.handle.net/1963/2959 U1 - 1741 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Superlocalization formulas and supersymmetric Yang-Mills theories JF - Nucl. Phys. B 678 (2004) 638-655 Y1 - 2004 A1 - Ugo Bruzzo A1 - Francesco Fucito AB - By using supermanifold techniques we prove a generalization of the localization formula in equivariant cohomology which is suitable for studying supersymmetric Yang-Mills theories in terms of ADHM data. With these techniques one can compute the reduced partition functions of topological super Yang-Mills theory with 4, 8 or 16 supercharges. More generally, the superlocalization formula can be applied to any topological field theory in any number of dimensions. PB - Elsevier UR - http://hdl.handle.net/1963/2886 U1 - 1814 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Second and third order observables of the two-matrix model JF - J. High Energy Phys. Y1 - 2003 A1 - Marco Bertola ER - TY - JOUR T1 - Separation of variables for Bi-Hamiltonian systems JF - Math. Phys. Anal. Geom. 6 (2003) 139-179 Y1 - 2003 A1 - Gregorio Falqui A1 - Marco Pedroni AB - We address the problem of the separation of variables for the Hamilton-Jacobi equation within the theoretical scheme of bi-Hamiltonian geometry. We use the properties of a special class of bi-Hamiltonian manifolds, called omega-N manifolds, to give intrisic tests of separability (and Staeckel separability) for Hamiltonian systems. The separation variables are naturally associated with the geometrical structures of the omega-N manifold itself. We apply these results to bi-Hamiltonian systems of the Gel\\\'fand-Zakharevich type and we give explicit procedures to find the separated coordinates and the separation relations. PB - SISSA Library UR - http://hdl.handle.net/1963/1598 U1 - 2520 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Sequences of Singularly Perturbed Functionals Generating Free-Discontinuity Problems JF - SIAM J. Math. Anal. 35 (2003) 759-805 Y1 - 2003 A1 - Massimiliano Morini AB - We prove that a wide class of singularly perturbed functionals generates as $\\\\Gamma$-limit a functional related to a free-discontinuity problem. Several applications of the result are shown. PB - SIAM UR - http://hdl.handle.net/1963/3071 U1 - 1262 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Single-Input Control Affine Systems: Local Regularity of Optimal Trajectories and a Geometric Controllability Problem Y1 - 2003 A1 - Mario Sigalotti PB - SISSA UR - http://hdl.handle.net/1963/5342 U1 - 5170 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres, Part I JF - Comm. Math. Phys. 235 (2003) no.3, 427-466 Y1 - 2003 A1 - Antonio Ambrosetti A1 - Andrea Malchiodi A1 - Wei-Ming Ni PB - Springer UR - http://hdl.handle.net/1963/1633 U1 - 2485 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Some results on the boundary control of systems of conservation laws JF - SIAM J.Control Optim. 41 (2003),no.2, 607 Y1 - 2003 A1 - Alberto Bressan A1 - Fabio Ancona A1 - Giuseppe Maria Coclite PB - SISSA Library UR - http://hdl.handle.net/1963/1615 U1 - 2503 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Space-adiabatic perturbation theory JF - Adv. Theor. Math. Phys. 7 (2003) 145-204 Y1 - 2003 A1 - Gianluca Panati A1 - Herbert Spohn A1 - Stefan Teufel AB - We study approximate solutions to the Schr\\\\\\\"odinger equation $i\\\\epsi\\\\partial\\\\psi_t(x)/\\\\partial t = H(x,-i\\\\epsi\\\\nabla_x) \\\\psi_t(x)$ with the Hamiltonian given as the Weyl quantization of the symbol $H(q,p)$ taking values in the space of bounded operators on the Hilbert space $\\\\Hi_{\\\\rm f}$ of fast ``internal\\\'\\\' degrees of freedom. By assumption $H(q,p)$ has an isolated energy band. Using a method of Nenciu and Sordoni \\\\cite{NS} we prove that interband transitions are suppressed to any order in $\\\\epsi$. As a consequence, associated to that energy band there exists a subspace of $L^2(\\\\mathbb{R}^d,\\\\Hi _{\\\\rm f})$ almost invariant under the unitary time evolution. We develop a systematic perturbation scheme for the computation of effective Hamiltonians which govern approximately the intraband time evolution. As examples for the general perturbation scheme we discuss the Dirac and Born-Oppenheimer type Hamiltonians and we reconsider also the time-adiabatic theory. PB - International Press UR - http://hdl.handle.net/1963/3041 U1 - 1292 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - A stability result for nonlinear Neumann problems under boundary variations JF - J.Math. Pures Appl. (9) 82 (2003) no.5 , 503 Y1 - 2003 A1 - Gianni Dal Maso A1 - Francois Ebobisse A1 - Marcello Ponsiglione AB - In this paper we study, in dimension two, the stability of the solutions of some nonlinear elliptic equations with Neumann boundary conditions, under perturbations of the domains in the Hausdorff complementary topology. PB - SISSA Library UR - http://hdl.handle.net/1963/1618 U1 - 2500 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The scalar curvature problem on $S\\\\sp n$: an approach via Morse theory JF - Calc. Var. Partial Differential Equations 14 (2002), no. 4, 429-445 Y1 - 2002 A1 - Andrea Malchiodi PB - Springer UR - http://hdl.handle.net/1963/1331 U1 - 3124 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Singular elliptic problems with critical growth JF - Comm. Partial Differential Equations 27 (2002), no. 5-6, 847-876 Y1 - 2002 A1 - Paolo Caldiroli A1 - Andrea Malchiodi PB - Dekker UR - http://hdl.handle.net/1963/1268 U1 - 3187 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Solutions concentrating on spheres to symmetric singularly perturbed problems JF - C.R.Math.Acad.Sci. Paris 335 (2002),no.2,145-150 Y1 - 2002 A1 - Antonio Ambrosetti A1 - Andrea Malchiodi A1 - Wei-Ming Ni AB - We discuss some existence results concerning problems (NLS) and (N), proving the existence of radial solutions concentrating on a sphere. PB - SISSA Library UR - http://hdl.handle.net/1963/1594 U1 - 2524 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Space-adiabatic Decoupling in Quantum Dynamics Y1 - 2002 A1 - Gianluca Panati PB - SISSA UR - http://hdl.handle.net/1963/6360 U1 - 6292 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - Space-adiabatic perturbation theory in quantum dynamics JF - Physical review letters. 2002 Jun; 88(25 Pt 1):250405 Y1 - 2002 A1 - Gianluca Panati A1 - Herbert Spohn A1 - Stefan Teufel AB - A systematic perturbation scheme is developed for approximate solutions to the time-dependent Schrödinger equation with a space-adiabatic Hamiltonian. For a particular isolated energy band, the basic approach is to separate kinematics from dynamics. The kinematics is defined through a subspace of the full Hilbert space for which transitions to other band subspaces are suppressed to all orders, and the dynamics operates in that subspace in terms of an effective intraband Hamiltonian. As novel applications, we discuss the Born-Oppenheimer theory to second order and derive for the first time the nonperturbative definition of the g factor of the electron within nonrelativistic quantum electrodynamics. PB - American Physical Society UR - http://hdl.handle.net/1963/5985 U1 - 5841 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Stability of planar switched systems: the linear single input case JF - SIAM J. Control Optim. 41 (2002), no. 1, 89-112 Y1 - 2002 A1 - Ugo Boscain AB - We study the stability of the origin for the dynamical system $\\\\dot x(t)=u(t)Ax(t)+(1-u(t))Bx(t),$ where A and B are two 2 × 2 real matrices with eigenvalues having strictly negative real part, $x\\\\in {\\\\mbox{{\\\\bf R}}}^2$, and $u(.):[0,\\\\infty[\\\\to[0,1]$ is a completely random measurable function. More precisely, we find a (coordinates invariant) necessary and sufficient condition on A and B for the origin to be asymptotically stable for each function u(.). The result is obtained without looking for a common Lyapunov function but studying the locus in which the two vector fields Ax and Bx are collinear. There are only three relevant parameters: the first depends only on the eigenvalues of A, the second depends only on the eigenvalues of B, and the third contains the interrelation among the two systems, and it is the cross ratio of the four eigenvectors of A and B in the projective line CP1. In the space of these parameters, the shape and the convexity of the region in which there is stability are studied. PB - SIAM UR - http://hdl.handle.net/1963/1529 U1 - 2634 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the Stability of the Standard Riemann Semigroup JF - P. Am. Math. Soc., 2002, 130, 1961 Y1 - 2002 A1 - Stefano Bianchini A1 - Rinaldo M. Colombo PB - SISSA Library UR - http://hdl.handle.net/1963/1528 U1 - 2635 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - S^2 type parametric surfaces with prescribed mean curvature and minimal energy T2 - Nonlinear equations : methods, models and applications (Bergamo, 2001) / Daniela Lupo, Carlo D. Pagani, Bernhard Ruf, editors. - Basel : Birkhäuser, 2003. - (Progress in nonlinear differential equations and their applications; 54). - p. 61-77 Y1 - 2001 A1 - Paolo Caldiroli A1 - Roberta Musina JF - Nonlinear equations : methods, models and applications (Bergamo, 2001) / Daniela Lupo, Carlo D. Pagani, Bernhard Ruf, editors. - Basel : Birkhäuser, 2003. - (Progress in nonlinear differential equations and their applications; 54). - p. 61-77 PB - Birkhauser UR - http://hdl.handle.net/1963/1605 U1 - 2513 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the spreading of characteristics for non-convex conservation laws JF - Proc. Roy. Soc. Edinburgh Sect. A 131 (2001) 909-925 Y1 - 2001 A1 - Helge Kristian Jenssen A1 - Carlo Sinestrari AB - We study the spreading of characteristics for a class of one-dimensional scalar conservation laws for which the flux function has one point of inflection. It is well known that in the convex case the characteristic speed satisfies a one-sided Lipschitz estimate. Using Dafermos\\\' theory of generalized characteristics, we show that the characteristic speed in the non-convex case satisfies an Hölder estimate. In addition, we give a one-sided Lipschitz estimate with an error term given by the decrease of the total variation of the solution. PB - Cambridge University Press UR - http://hdl.handle.net/1963/3265 U1 - 1436 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Stability of L-infinity solutions for hyperbolic systems with coinciding shocks and rarefactions JF - Siam J. Math. Anal., 2001, 33, 959 Y1 - 2001 A1 - Stefano Bianchini AB - We consider a hyperbolic system of conservation laws u_t + f(u)_x = 0 and u(0,\\\\cdot) = u_0, where each characteristic field is either linearly degenerate or genuinely nonlinear. Under the assumption of coinciding shock and rarefaction curves and the existence of a set of Riemann coordinates $w$, we prove that there exists a semigroup of solutions $u(t) = \\\\mathcal{S}_t u_0$, defined on initial data $u_0 \\\\in L^\\\\infty$. The semigroup $\\\\mathcal{S}$ is continuous w.r.t. time and the initial data $u_0$ in the $L^1_{\\\\text{loc}}$ topology. Moreover $\\\\mathcal{S}$ is unique and its trajectories are obtained as limits of wave front tracking approximations. PB - SISSA Library UR - http://hdl.handle.net/1963/1523 U1 - 2640 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Stationary states for a two-dimensional singular Schrodinger equation JF - Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 4 (2001), no. 3, 609-633. Y1 - 2001 A1 - Paolo Caldiroli A1 - Roberta Musina PB - SISSA Library UR - http://hdl.handle.net/1963/1249 U1 - 3206 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the subanalyticity of Carnot-Caratheodory distances JF - Ann. I. H. Poincare - An., 2001, 18, 359 Y1 - 2001 A1 - Andrei A. Agrachev A1 - Jean-Paul Gauthier PB - SISSA Library UR - http://hdl.handle.net/1963/1483 U1 - 2680 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the symmetric scalar curvature problem on S\\\\sp n JF - J. Differential Equations 170 (2001) 228-245 Y1 - 2001 A1 - Antonio Ambrosetti A1 - Andrea Malchiodi AB - We discuss some existence results dealing with the scalar curvature problem on S\\\\sp n in the presence of various symmetries. PB - Elsevier UR - http://hdl.handle.net/1963/3095 U1 - 1238 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Scalar curvature under boundary conditions JF - Cr. Acad. Sci. I-Math, 2000, 330, 1013 Y1 - 2000 A1 - Antonio Ambrosetti A1 - Li YanYan A1 - Andrea Malchiodi PB - SISSA Library UR - http://hdl.handle.net/1963/1506 U1 - 2657 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The semigroup generated by a Temple class system with non-convex flux function JF - Differential Integral Equations 13 (2000) 1529-1550 Y1 - 2000 A1 - Stefano Bianchini AB - We consider the Cauchy problem for a nonlinear n × n system of conservation laws of Temple class, i.e. with coinciding shock and rarefaction curves and with a coordinate system made of Riemann invariants. Without any assumption on the convexity of the flux function, we prove the existence of a semigroup made of weak solutions of the equations and depending Lipschitz continuously on the initial data with bounded total variation. PB - Khayyam Publishing UR - http://hdl.handle.net/1963/3221 U1 - 1080 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the shift differentiability of the flow generated by a hyperbolic system of conservation laws JF - Discrete Contin. Dynam. Systems 6 (2000), no. 2, 329-350 Y1 - 2000 A1 - Stefano Bianchini PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/1274 U1 - 3181 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Some Properties of Non-linear sigma-Models in Noncommutative Geometry JF - Int. J. Mod. Phys. B 14 (2000) 2367-2382 Y1 - 2000 A1 - Ludwik Dabrowski A1 - Thomas Krajewski A1 - Giovanni Landi AB - 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. PB - SISSA Library UR - http://hdl.handle.net/1963/1373 U1 - 3082 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Stability of L^infty Solutions of Temple Class Systems JF - Differential Integral Equations 13 (2000) 1503-1528 Y1 - 2000 A1 - Alberto Bressan A1 - Paola Goatin AB -Let $u_t+f(u)_x=0$ be a strictly hyperbolic, genuinely nonlinear system of conservation laws of Temple class. In this paper, a continuous semigroup of solutions is constructed on a domain of $L^\infty$ functions, with possibly unbounded variation. Trajectories depend Lipschitz continuously on the initial data, in the $L^1$ distance. Moreover, we show that a weak solution of the Cauchy problem coincides with the corresponding semigroup trajectory if and only if it satisfies an entropy condition of Oleinik type, concerning the decay of positive waves.

PB - Khayyam Publishing UR - http://hdl.handle.net/1963/3256 U1 - 1445 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On a Steffen\\\'s result about parametric surfaces with prescribed mean curvature Y1 - 2000 A1 - Roberta Musina A1 - Paolo Caldiroli PB - SISSA Library UR - http://hdl.handle.net/1963/1558 U1 - 2560 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - Stokes Matrices for Frobenius Manifolds and the 6 Painlevé Equation T2 - Rokko Lectures in Mathematics, Vol 7 [Issue title: Perspective of Painleve equations], (2000), pages : 101-109 Y1 - 2000 A1 - Davide Guzzetti KW - Painlevé equation AB - These notes are a short review on the theory of Frobenius manifolds and its connection to problems of isomonodromy deformations and to Painlev'e equations. JF - Rokko Lectures in Mathematics, Vol 7 [Issue title: Perspective of Painleve equations], (2000), pages : 101-109 PB - Kobe University, Japan SN - 4-907719-07-8 UR - http://hdl.handle.net/1963/6546 U1 - 6478 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Super KP equations and Darboux transformations: another perspective on the Jacobian super KP hierarchy JF - J. Geom. Phys. 35 (2000), no. 2-3, 239-272 Y1 - 2000 A1 - Gregorio Falqui A1 - Cesare Reina A1 - Alessandro Zampa PB - SISSA Library UR - http://hdl.handle.net/1963/1367 U1 - 3088 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - On the scalar curvature problem under symmetry Y1 - 1999 A1 - Antonio Ambrosetti A1 - Andrea Malchiodi PB - SISSA Library UR - http://hdl.handle.net/1963/1287 U1 - 3168 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Some properties of the solutions of obstacle problems with measure data JF - Ricerche Matematiche., Supplemento dedicato a Ennio De Giorgi, vol. 48 (1999), page : 99-116 Y1 - 1999 A1 - Paolo Dall'Aglio A1 - Gianni Dal Maso UR - http://hdl.handle.net/1963/6432 U1 - 6372 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Stokes matrices and monodromy of the quantum cohomology of projective spaces JF - Comm. Math. Phys. 207 (1999) 341-383 Y1 - 1999 A1 - Davide Guzzetti AB - n this paper we compute Stokes matrices and monodromy of the quantum cohomology of projective spaces. This problem can be formulated in a \\\"classical\\\" framework, as the problem of computation of Stokes matrices and monodromy of differential equations with regular and irregular singularities. We prove that the Stokes\\\' matrix of the quantum cohomology coincides with the Gram matrix in the theory of derived categories of coherent sheaves. We also study the monodromy group of the quantum cohomology and we show that it is related to hyperbolic triangular groups. PB - Springer UR - http://hdl.handle.net/1963/3475 U1 - 789 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Structural stability and regularity of entropy solutions to hyperbolic systems of conservation laws JF - Indiana Univ. Math. J. 48 (1999), no. 1, 43--84 Y1 - 1999 A1 - Alberto Bressan A1 - Philippe G. LeFloch AB - The paper is concerned with the qualitative structure of entropy solutions to a strictly hyperbolic, genuinely nonlinear system of conservation laws. We first give an accurate description of the local and global wave-front structure of a BV solution, generated by a front tracking algorithm. PB - Indiana University UR - http://hdl.handle.net/1963/3374 U1 - 956 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Special functions with bounded variation and with weakly differentiable traces on the jump set JF - NoDEA Nonlinear Differential Equations Appl. 5 (1998), no. 2, 219--243 Y1 - 1998 A1 - Luigi Ambrosio A1 - Andrea Braides A1 - Adriana Garroni PB - SISSA Library UR - http://hdl.handle.net/1963/1025 U1 - 2831 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The semigroup generated by a temple class system with large data JF - Differential Integral Equations 10 (1997), no. 3, 401-418 Y1 - 1997 A1 - Paolo Baiti A1 - Alberto Bressan AB - We consider the Cauchy problem $$u_t + [F(u)]_x=0, u(0,x)=\\\\bar u(x) (*)$$ for a nonlinear $n\\\\times n$ system of conservation laws with coinciding shock and rarefaction curves. Assuming the existence of a coordinates system made of Riemann invariants, we prove the existence of a weak solution of (*) that depends in a lipschitz continuous way on the initial data, in the class of functions with arbitrarily large but bounded total variation. PB - SISSA Library UR - http://hdl.handle.net/1963/1023 U1 - 2833 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Shift-differentiability of the flow generated by a conservation law JF - Discrete Contin. Dynam. Systems 3 (1997), no. 1, 35--58. Y1 - 1997 A1 - Alberto Bressan A1 - Graziano Guerra AB - The paper introduces a notion of \\\"shift-differentials\\\" for maps with values in the space BV. These differentials describe first order variations of a given functin $u$, obtained by horizontal shifts of the points of its graph. The flow generated by a scalar conservation law is proved to be generically shift-differentiable, according to the new definition. PB - SISSA Library UR - http://hdl.handle.net/1963/1033 U1 - 2823 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Some Problems in the Asymptotic Analysis of Partial Differential Equations in Perforated Domains Y1 - 1997 A1 - Rodica Toader KW - Dirichlet problems PB - SISSA UR - http://hdl.handle.net/1963/5698 U1 - 5541 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Some properties of reachable solutions of nonlinear elliptic equations with measure data JF - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. Sér. 4, 25 no. 1-2 (1997), p. 375-396 Y1 - 1997 A1 - Gianni Dal Maso A1 - Annalisa Malusa PB - SISSA UR - http://hdl.handle.net/1963/6434 U1 - 6375 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Statistics in space dimension two JF - Lett. Math. Phys. 40 (1997), no. 3, 235-256 Y1 - 1997 A1 - Gianfausto Dell'Antonio A1 - Rodolfo Figari A1 - Alessandro Teta AB - 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). PB - SISSA Library UR - http://hdl.handle.net/1963/130 U1 - 12 U2 - LISNU U3 - Interdisciplinary Laboratory for Advanced Studies ER - TY - JOUR T1 - Structural stability for time-optimal planar sytheses JF - Dynam. Contin. Discrete Impuls. Systems 3 (1997), no. 3, 335--371 Y1 - 1997 A1 - Alberto Bressan A1 - Benedetto Piccoli PB - SISSA Library UR - http://hdl.handle.net/1963/997 U1 - 2859 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The semigroup approach to systems of conservation laws JF - Mat. Contemp. 10 (1996) 21-74 Y1 - 1996 A1 - Alberto Bressan PB - Sociedade Brasileira de Matematica UR - http://hdl.handle.net/1963/1037 U1 - 2819 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Solving Honig generic problem about Volterra integral equations JF - Bull. Polish Acad. Sci. Math. 44 (1996), no. 4, 495--498 Y1 - 1996 A1 - Giovanni Vidossich PB - SISSA Library UR - http://hdl.handle.net/1963/941 U1 - 3513 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Some control problems for the pendulum JF - Proceedings of the 34th IEEE Conference on Decision and Control 4 (1995) 3313-3318 Y1 - 1995 A1 - Benedetto Piccoli AB - The aim of this paper is to illustrate some geometric techniques for the study of nonlinear systems. The pendulum on one hand is good for its simplicity, on the other it presents many of the difficulties one can encounter treating nonlinear systems. PB - IEEE UR - http://hdl.handle.net/1963/982 U1 - 2874 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Special functions of bounded deformation Y1 - 1995 A1 - Giovanni Bellettini A1 - Alessandra Coscia A1 - Gianni Dal Maso PB - SISSA Library UR - http://hdl.handle.net/1963/978 U1 - 3476 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Some Problems in the Calculus of the Variations Y1 - 1992 A1 - Sandro Zagatti KW - Calculus of variations PB - SISSA UR - http://hdl.handle.net/1963/5428 U1 - 5260 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Shape optimization for Dirichlet problems: relaxed formulations and optimally conditions JF - Appl.Math.Optim. 23 (1991), no.1, p. 17-49. Y1 - 1991 A1 - Giuseppe Buttazzo A1 - Gianni Dal Maso PB - SISSA Library UR - http://hdl.handle.net/1963/880 U1 - 2911 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On systems of ordinary differential equations with measures as controls JF - Differential Integral Equations 4 (1991), no.4, p.739-765. Y1 - 1991 A1 - Gianni Dal Maso A1 - Franco Rampazzo PB - SISSA Library UR - http://hdl.handle.net/1963/840 U1 - 2951 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Shape optimization for Dirichlet problems: relaxed solutions and optimality conditions JF - Bull. Amer. Math. Soc. (N.S.) , 23 (1990), no.2, 531-535. Y1 - 1990 A1 - Giuseppe Buttazzo A1 - Gianni Dal Maso PB - SISSA Library UR - http://hdl.handle.net/1963/809 U1 - 2982 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Singular perturbation of the Laplacian and connections with models of random media Y1 - 1989 A1 - Alessandro Teta PB - SISSA UR - http://hdl.handle.net/1963/6348 U1 - 6281 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - On the solvability of boundary value problems for higher order ordinary differential equations (Revised version) JF - Nonlinear Anal. 13 (1989), no. 10, 1171-1179 Y1 - 1989 A1 - Giovanni Vidossich PB - SISSA Library UR - http://hdl.handle.net/1963/662 U1 - 3264 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the solvability of boundary value problems for higher order ordinary differential equations JF - Nonlinear Anal. 13 (1989), no. 10, 1171-179 Y1 - 1989 A1 - Giovanni Vidossich PB - SISSA Library UR - http://hdl.handle.net/1963/631 U1 - 3822 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Surfaces of minimal area enclosing a given body in R\\\\sp 3. JF - Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 16 (1989), no. 3, 331--354 (1990). Y1 - 1989 A1 - Giovanni Mancini A1 - Roberta Musina PB - SISSA Library UR - http://hdl.handle.net/1963/619 U1 - 3285 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Some properties of a class of nonlinear variational $m$-capacities JF - J.Funct.Anal. 79, 1988, no. 2, 476-492 Y1 - 1988 A1 - Gianni Dal Maso A1 - Anneliese Defranceschi PB - SISSA Library UR - http://hdl.handle.net/1963/485 U1 - 3419 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Susy-curves and supermoduli Y1 - 1988 A1 - Gregorio Falqui A1 - Cesare Reina PB - SISSA Library UR - http://hdl.handle.net/1963/761 U1 - 3030 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Solutions with minimal period for Hamiltonian systems in a potential well. JF - Ann. Inst. H. Poincare Anal. Non Lineaire 4 (1987), no. 3, 275-296 Y1 - 1987 A1 - Antonio Ambrosetti A1 - Vittorio Coti Zelati PB - SISSA Library UR - http://hdl.handle.net/1963/466 U1 - 3437 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Symmetry breaking in Hamiltonian systems JF - J. Differential Equations 67 (1987), no. 2, 165-184 Y1 - 1987 A1 - Antonio Ambrosetti A1 - Vittorio Coti Zelati A1 - Ivar Ekeland PB - SISSA Library UR - http://hdl.handle.net/1963/409 U1 - 3558 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Some necessary and sufficient conditions for the convergence of sequences of unilateral convex sets JF - J. Funct. Anal. 62 (1985), no. 2, 119--159 Y1 - 1985 A1 - Gianni Dal Maso PB - SISSA Library UR - http://hdl.handle.net/1963/318 U1 - 3649 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Some singular perturbation problems in the calculus of variations. JF - Ennio De Giorgi Colloquium, p. 41-49, Research Notes in Mathematics, v.125, London : Pitman, 1985 Y1 - 1985 A1 - Gianni Dal Maso PB - SISSA Library UR - http://hdl.handle.net/1963/297 U1 - 3670 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Spin Structures and Global Conformal Transformations Y1 - 1984 A1 - Ludwik Dabrowski KW - Spinors PB - SISSA UR - http://hdl.handle.net/1963/5854 U1 - 5718 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER -