In this work we present a Reduced Order Model which is specifically designed to deal with turbulent flows in a finite volume setting. The method used to build the reduced order model is based on the idea of merging/combining projection-based techniques with data-driven reduction strategies. In particular, the work presents a mixed strategy that exploits a data-driven reduction method to approximate the eddy viscosity solution manifold and a classical POD-Galerkin projection approach for the velocity and the pressure fields, respectively. The newly proposed reduced order model has been validated on benchmark test cases in both steady and unsteady settings with Reynolds up to $Re=O(10^5)$.

VL - 416 UR - https://arxiv.org/abs/1907.09909 ER - TY - JOUR T1 - The deal.II finite element library: Design, features, and insights JF - Computers and Mathematics with Applications Y1 - 2020 A1 - Daniel Arndt A1 - Wolfgang Bangerth A1 - Denis Davydov A1 - Timo Heister A1 - Luca Heltai A1 - Martin Kronbichler A1 - Matthias Maier A1 - Jean-Paul Pelteret A1 - Bruno Turcksin A1 - David Wells UR - https://doi.org/10.1016/j.camwa.2020.02.022 ER - TY - JOUR T1 - The deal.II Library, Version 9.1 JF - Journal of Numerical Mathematics Y1 - 2019 A1 - Arndt, Daniel A1 - Bangerth, Wolfgang A1 - Clevenger, Thomas C. A1 - Davydov, Denis A1 - Fehling, Marc A1 - Garcia-Sanchez, Daniel A1 - Harper, Graham A1 - Heister, Timo A1 - Heltai, Luca A1 - Kronbichler, Martin A1 - Maguire Kynch, Ross A1 - Maier, Matthias A1 - Pelteret, Jean Paul A1 - Turcksin, Bruno A1 - Wells, David AB - This paper provides an overview of the new features of the finite element library deal.II, version 9.1. ER - TY - JOUR T1 - Differential structure associated to axiomatic Sobolev spaces JF - Expositiones Mathematicae Y1 - 2019 A1 - Nicola Gigli A1 - Enrico Pasqualetto KW - Axiomatic Sobolev space KW - Cotangent module KW - Locality of differentials AB -The aim of this note is to explain in which sense an axiomatic Sobolev space over a general metric measure space (à la Gol’dshtein–Troyanov) induces – under suitable locality assumptions – a first-order differential structure.

UR - http://www.sciencedirect.com/science/article/pii/S0723086918300975 ER - TY - UNPB T1 - Discontinuous Galerkin Model Order Reduction of Geometrically Parametrized Stokes Equation Y1 - 2019 A1 - Nirav Vasant Shah A1 - Martin Hess A1 - Gianluigi Rozza AB -The present work focuses on the geometric parametrization and the reduced order modeling of the Stokes equation. We discuss the concept of a parametrized geometry and its application within a reduced order modeling technique. The full order model is based on the discontinuous Galerkin method with an interior penalty formulation. We introduce the broken Sobolev spaces as well as the weak formulation required for an affine parameter dependency. The operators are transformed from a fixed domain to a parameter dependent domain using the affine parameter dependency. The proper orthogonal decomposition is used to obtain the basis of functions of the reduced order model. By using the Galerkin projection the linear system is projected onto the reduced space. During this process, the offline-online decomposition is used to separate parameter dependent operations from parameter independent operations. Finally this technique is applied to an obstacle test problem.The numerical outcomes presented include experimental error analysis, eigenvalue decay and measurement of online simulation time. Keywords: Discontinuous Galerkin method, Stokes flow, Geometric parametrization, Proper orthogonal decomposition.

UR - https://arxiv.org/abs/1912.09787 ER - TY - JOUR T1 - A discrete districting plan JF - Netw. Heterog. Media Y1 - 2019 A1 - Saracco, A. A1 - Saracco, G. VL - 14 ER - TY - RPRT T1 - A dynamic model for viscoelastic materials with prescribed growing cracks Y1 - 2019 A1 - Maicol Caponi A1 - Francesco Sapio AB -In this paper we prove the existence of solutions for a class of viscoelastic dynamic systems on time-dependent cracked domains, with possibly degenerate viscosity coefficients. Under stronger regularity assumptions we also show a uniqueness result. Finally, we exhibit an example where the energy-dissipation balance is not satisfied, showing there is an additional dissipation due to the crack growth.

UR - http://preprints.sissa.it:8180/xmlui/handle/1963/35334 ER - TY - JOUR T1 - deal2lkit: A toolkit library for high performance programming in deal.II JF - SOFTWAREX Y1 - 2018 A1 - Alberto Sartori A1 - Nicola Giuliani A1 - Mauro Bardelloni A1 - Luca Heltai VL - 7 ER - TY - JOUR T1 - The deal.II Library, Version 9.0 JF - JOURNAL OF NUMERICAL MATHEMATICS Y1 - 2018 A1 - Giovanni Alzetta A1 - Arndt, Daniel A1 - W. Bangerth A1 - Boddu, Vishal A1 - Brands, Benjamin A1 - Denis Davydov A1 - Gassmöller, Rene A1 - Timo Heister A1 - Luca Heltai A1 - Kormann, Katharina A1 - Martin Kronbichler A1 - Matthias Maier A1 - Pelteret, Jean-Paul A1 - B. Turcksin A1 - David Wells UR - https://doi.org/10.1515/jnma-2018-0054 ER - TY - RPRT T1 - Differential of metric valued Sobolev maps Y1 - 2018 A1 - Nicola Gigli A1 - Enrico Pasqualetto A1 - Elefterios Soultanis ER - TY - RPRT T1 - Dimension reduction for thin films with transversally varying prestrain: the oscillatory and the non-oscillatory case Y1 - 2018 A1 - Marta Lewicka A1 - Danka Lučić ER - TY - JOUR T1 - Dimension reduction in heterogeneous parametric spaces with application to naval engineering shape design problems JF - Advanced Modeling and Simulation in Engineering Sciences Y1 - 2018 A1 - Marco Tezzele A1 - Filippo Salmoiraghi A1 - Andrea Mola A1 - Gianluigi Rozza AB -We present the results of the first application in the naval architecture field of a methodology based on active subspaces properties for parameters space reduction. The physical problem considered is the one of the simulation of the hydrodynamic flow past the hull of a ship advancing in calm water. Such problem is extremely relevant at the preliminary stages of the ship design, when several flow simulations are typically carried out by the engineers to assess the dependence of the hull total resistance on the geometrical parameters of the hull, and others related with flows and hull properties. Given the high number of geometric and physical parameters which might affect the total ship drag, the main idea of this work is to employ the active subspaces properties to identify possible lower dimensional structures in the parameter space. Thus, a fully automated procedure has been implemented to produce several small shape perturbations of an original hull CAD geometry, in order to exploit the resulting shapes to run high fidelity flow simulations with different structural and physical parameters as well, and then collect data for the active subspaces analysis. The free form deformation procedure used to morph the hull shapes, the high fidelity solver based on potential flow theory with fully nonlinear free surface treatment, and the active subspaces analysis tool employed in this work have all been developed and integrated within SISSA mathLab as open source tools. The contribution will also discuss several details of the implementation of such tools, as well as the results of their application to the selected target engineering problem.

VL - 5 ER - TY - JOUR T1 - Discriminant circle bundles over local models of Strebel graphs and Boutroux curves JF - Teoret. Mat. Fiz. Y1 - 2018 A1 - Marco Bertola A1 - Korotkin, D. A. VL - 197 UR - https://doi.org/10.4213/tmf9513 ER - TY - CHAP T1 - A distributed lagrange formulation of the finite element immersed boundary method for fluids interacting with compressible solids T2 - Mathematical and Numerical Modeling of the Cardiovascular System and Applications Y1 - 2018 A1 - Boffi, Daniele A1 - Gastaldi, Lucia A1 - Luca Heltai JF - Mathematical and Numerical Modeling of the Cardiovascular System and Applications PB - Springer International Publishing CY - Cham VL - 16 UR - https://arxiv.org/abs/1712.02545v1 ER - TY - JOUR T1 - The deal.II Library, Version 8.5 JF - JOURNAL OF NUMERICAL MATHEMATICS Y1 - 2017 A1 - Arndt, Daniel A1 - W. Bangerth A1 - Denis Davydov A1 - Timo Heister A1 - Luca Heltai A1 - Martin Kronbichler A1 - Matthias Maier A1 - Pelteret, Jean-Paul A1 - B. Turcksin A1 - David Wells VL - 25 UR - https://www.dealii.org/deal85-preprint.pdf ER - TY - RPRT T1 - Derivation of a rod theory from lattice systems with interactions beyond nearest neighbours Y1 - 2017 A1 - Roberto Alicandro A1 - Giuliano Lazzaroni A1 - Mariapia Palombaro AB - We study continuum limits of discrete models for (possibly heterogeneous) nanowires. The lattice energy includes at least nearest and next-to-nearest neighbour interactions: the latter have the role of penalising changes of orientation. In the heterogeneous case, we obtain an estimate on the minimal energy spent to match different equilibria. This gives insight into the nucleation of dislocations in epitaxially grown heterostructured nanowires. UR - http://urania.sissa.it/xmlui/handle/1963/35269 U1 - 35575 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Discrete spectra for critical Dirac-Coulomb Hamiltonians Y1 - 2017 A1 - Matteo Gallone A1 - Alessandro Michelangeli AB - The one-particle Dirac Hamiltonian with Coulomb interaction is known to be realised, in a regime of large (critical) couplings, by an infinite multiplicity of distinct self-adjoint operators, including a distinguished physically most natural one. For the latter, Sommerfeld’s celebrated fine structure formula provides the well-known expression for the eigenvalues in the gap of the continuum spectrum. Exploiting our recent general classification of all other self-adjoint realisations, we generalise Sommerfeld’s formula so as to determine the discrete spectrum of all other self-adjoint versions of the Dirac-Coulomb Hamiltonian. Such discrete spectra display naturally a fibred structure, whose bundle covers the whole gap of the continuum spectrum. UR - http://preprints.sissa.it/handle/1963/35300 U1 - 35606 U2 - Mathematics U4 - 1 ER - TY - CHAP T1 - Dispersive Estimates for Schrödinger Operators with Point Interactions in ℝ3 T2 - Advances in Quantum Mechanics: Contemporary Trends and Open Problems Y1 - 2017 A1 - Felice Iandoli A1 - Raffaele Scandone ED - Alessandro Michelangeli ED - Gianfausto Dell'Antonio AB -The study of dispersive properties of Schrödinger operators with point interactions is a fundamental tool for understanding the behavior of many body quantum systems interacting with very short range potential, whose dynamics can be approximated by non linear Schrödinger equations with singular interactions. In this work we proved that, in the case of one point interaction in $\mathbb{R}^3$, the perturbed Laplacian satisfies the same $L^p$−$L^q$ estimates of the free Laplacian in the smaller regime $q \in [2,3)$. These estimates are implied by a recent result concerning the Lpboundedness of the wave operators for the perturbed Laplacian. Our approach, however, is more direct and relatively simple, and could potentially be useful to prove optimal weighted estimates also in the regime $q \geq 3$.

JF - Advances in Quantum Mechanics: Contemporary Trends and Open Problems PB - Springer International Publishing CY - Cham SN - 978-3-319-58904-6 UR - https://doi.org/10.1007/978-3-319-58904-6_11 ER - TY - JOUR T1 - The deal.II Library, Version 8.3 JF - ARCHIVE OF NUMERICAL SOFTWARE Y1 - 2016 A1 - W. Bangerth A1 - Timo Heister A1 - Luca Heltai A1 - G. Kanschat A1 - Martin Kronbichler A1 - Matthias Maier A1 - B. Turcksin VL - 4 UR - http://nbn-resolving.de/urn:nbn:de:bsz:16-ans-231226 ER - TY - JOUR T1 - The deal.II library, Version 8.4 JF - JOURNAL OF NUMERICAL MATHEMATICS Y1 - 2016 A1 - W. Bangerth A1 - Denis Davydov A1 - Timo Heister A1 - Luca Heltai A1 - G. Kanschat A1 - Martin Kronbichler A1 - Matthias Maier A1 - B. Turcksin A1 - David Wells VL - 24 UR - https://www.math.clemson.edu/ heister/preprints/deal84-preprint.pdf ER - TY - JOUR T1 - Deal2lkit: a Toolkit Library for High Performance Programming in deal.II Y1 - 2015 A1 - Alberto Sartori A1 - Nicola Giuliani A1 - Mauro Bardelloni A1 - Luca Heltai AB - We present version 1.0.0 of the deal2lkit (deal.II ToolKit) library. deal2lkit is a collection of modules and classes for the general purpose finite element library deal.II. Its principal aim is to provide a high level interface, controlled via parameter files, for those steps that are common in all finite element programs: mesh generation, selection of the finite element type, application of boundary conditions and many others. Each module can be used as a building block independently on the others, and can be integrated in existing finite element codes based on deal.II, drastically reducing the size of programs, rendering their use automatically parametrised, and reducing the overall time-to-market of finite element programming. Moreover, deal2lkit features interfaces with the SUNDIALS (SUite of Nonlinear and DIfferential/ALgebraic equation Solvers) and ASSIMP (Open Asset Import Library) libraries. Some examples are provided which show the aim and scopes of deal2lkit. The deal2lkit library is released under the GNU Lesser General Public License (LGPL) and can be retrieved from the deal2lkit repository https://github.com/mathLab/deal2lkit. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/35006 U1 - 35235 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - The deal.II Library, Version 8.2 JF - Archive of Numerical Software, vol. 3, n. 100, (2015), pages : 1-8 Y1 - 2015 A1 - W. Bangerth A1 - Timo Heister A1 - Luca Heltai A1 - G. Kanschat A1 - Martin Kronbichler A1 - Matthias Maier A1 - B. Turcksin A1 - T. D. Young AB - This paper provides an overview of the new features of the finite element library deal.II version 8.2 UR - http://urania.sissa.it/xmlui/handle/1963/34464 U1 - 34637 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - Decay of correlations for invertible maps with non-Hölder observables JF - Dynamical Systems Y1 - 2015 A1 - Marks Ruziboev AB -An invertible dynamical system with some hyperbolic structure is considered. Upper estimates for the correlations of continuous observables are given in terms of modulus of continuity. The result is applied to certain Hénon maps and Solenoid maps with intermittency.

PB - Taylor & Francis VL - 30 UR - https://doi.org/10.1080/14689367.2015.1046816 ER - TY - JOUR T1 - A degeneration of two-phase solutions of the focusing nonlinear Schrödinger equation via Riemann-Hilbert problems JF - J. Math. Phys. Y1 - 2015 A1 - Marco Bertola A1 - Giavedoni, Pietro VL - 56 UR - http://dx.doi.org/10.1063/1.4922362 ER - TY - JOUR T1 - Dispersive deformations of the Hamiltonian structure of Euler's equations Y1 - 2015 A1 - Matteo Casati AB - Euler's equations for a two-dimensional system can be written in Hamiltonian form, where the Poisson bracket is the Lie-Poisson bracket associated to the Lie algebra of divergence free vector fields. We show how to derive the Poisson brackets of 2d hydrodynamics of ideal fluids as a reduction from the one associated to the full algebra of vector fields. Motivated by some recent results about the deformations of Lie-Poisson brackets of vector fields, we study the dispersive deformations of the Poisson brackets of Euler's equation and show that, up to the second order, they are trivial. U1 - 34700 U2 - Mathematics U4 - 1 U5 - MAT/07 ER - TY - RPRT T1 - Dynamics of screw dislocations: a generalised minimising-movements scheme approach Y1 - 2015 A1 - Giovanni A. Bonaschi A1 - Patrick Van Meurs A1 - Marco Morandotti AB - The gradient flow structure of the model introduced in [CG99] for the dynamics of screw dislocations is investigated by means of a generalised minimising-movements scheme approach. The assumption of a finite number of available glide directions, together with the "maximal dissipation criterion" that governs the equations of motion, results into solving a differential inclusion rather than an ODE. This paper addresses how the model in [CG99] is connected to a time-discrete evolution scheme which explicitly confines dislocations to move each time step along a single glide direction. It is proved that the time-continuous model in [CG99] is the limit of these time-discrete minimising-movement schemes when the time step converges to 0. The study presented here is a first step towards a generalization of the setting in [AGS08, Chap. 2 and 3] that allows for dissipations which cannot be described by a metric. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/34495 U1 - 34692 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Darboux Transformations and Random Point Processes JF - IMRN Y1 - 2014 A1 - Marco Bertola A1 - Mattia Cafasso VL - rnu122 ER - TY - RPRT T1 - The decomposition of optimal transportation problems with convex cost Y1 - 2014 A1 - Stefano Bianchini A1 - Mauro Bardelloni PB - SISSA UR - http://hdl.handle.net/1963/7433 U1 - 7527 ER - TY - THES T1 - The decomposition of optimal transportation problems with convex cost Y1 - 2014 A1 - Mauro Bardelloni KW - Optimal Transportation PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7475 U1 - 7570 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - A density result for GSBD and its application to the approximation of brittle fracture energies Y1 - 2014 A1 - Flaviana Iurlano AB -We present an approximation result for functions u: Ω → ℝ^n belonging to the space GSBD(Ω) ∩ L2(Ω, ℝn) with e(u) square integrable and Hn-1(Ju) finite. The approximating functions uk are piecewise continuous functions such that uk → u in (Formula Presented). As an application, we provide the extension to the vector-valued case of the Γ-convergence result in GSBV(Ω) proved by Ambrosio and Tortorelli (Commun Pure Appl Math 43:999-1036, 1990; Boll. Un. Mat. Ital. B (7) 6:105-123, 1992).

PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34647 U1 - 34851 U2 - Mathematics ER - TY - JOUR T1 - Dirac operators on noncommutative principal circle bundles Y1 - 2014 A1 - Andrzej Sitarz A1 - Alessandro Zucca A1 - Ludwik Dabrowski AB - We study spectral triples over noncommutative principal U(1)-bundles of arbitrary dimension and a compatibility condition between the connection and the Dirac operator on the total space and on the base space of the bundle. Examples of low-dimensional noncommutative tori are analyzed in more detail and all connections found that are compatible with an admissible Dirac operator. Conversely, a family of new Dirac operators on the noncommutative tori, which arise from the base-space Dirac operator and a suitable connection is exhibited. These examples are extended to the theta-deformed principal U(1)-bundle S 3 θ → S2. PB - World Scientific Publishing UR - http://urania.sissa.it/xmlui/handle/1963/35125 U1 - 35363 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Dirac reduction for Poisson vertex algebras JF - Communications in Mathematical Physics 331, nr. 3 (2014) 1155-1190 Y1 - 2014 A1 - Alberto De Sole A1 - Victor G. Kac A1 - Daniele Valeri AB - We construct an analogue of Dirac's reduction for an arbitrary local or non-local Poisson bracket in the general setup of non-local Poisson vertex algebras. This leads to Dirac's reduction of an arbitrary non-local Poisson structure. We apply this construction to an example of a generalized Drinfeld-Sokolov hierarchy. PB - SISSA UR - http://hdl.handle.net/1963/6980 N1 - 31 pages U1 - 6968 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Discrete one-dimensional crawlers on viscous substrates: achievable net displacements and their energy cost Y1 - 2014 A1 - Giovanni Noselli A1 - Amabile Tatone A1 - Antonio DeSimone KW - Cell migration AB - We study model one-dimensional crawlers, namely, model mechanical systems that can achieve self-propulsion by controlled shape changes of their body (extension or contraction of portions of the body), thanks to frictional interactions with a rigid substrate. We evaluate the achievable net displacement and the related energetic cost for self-propulsion by discrete crawlers (i.e., whose body is made of a discrete number of contractile or extensile segments) moving on substrates with either a Newtonian (linear) or a Bingham-type (stick-slip) rheology. Our analysis is aimed at constructing the basic building blocks towards an integrative, multi-scale description of crawling cell motility. PB - Elsevier UR - http://urania.sissa.it/xmlui/handle/1963/34449 U1 - 34591 U2 - Mathematics ER - TY - RPRT T1 - Dislocations at the continuum scale: functional setting and variational properties Y1 - 2014 A1 - Riccardo Scala A1 - Nicolas Van Goethem UR - http://cvgmt.sns.it/paper/2294/ ER - TY - RPRT T1 - Donagi–Markman cubic for the generalised Hitchin system Y1 - 2014 A1 - Ugo Bruzzo A1 - Peter Dalakov KW - Generalized Hitchin system, Donagi-Markman cubic, algebraically completely integrable systems, moduli space of Higgs G-bundles AB - Donagi and Markman (1993) have shown that the infinitesimal period map for an algebraic completely integrable Hamiltonian system (ACIHS) is encoded in a section of the third symmetric power of the cotangent bundle to the base of the system. For the ordinary Hitchin system the cubic is given by a formula of Balduzzi and Pantev. We show that the Balduzzi–Pantev formula holds on maximal rank symplectic leaves of the G-generalised Hitchin system. UR - http://hdl.handle.net/1963/7253 U1 - 7294 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - RPRT T1 - Dynamics on a graph as the limit of the dynamics on a "fat graph" Y1 - 2014 A1 - Gianfausto Dell'Antonio A1 - Alessandro Michelangeli AB - We discuss how the vertex boundary conditions for the dynamics of a quantum particle constrained on a graph emerge in the limit of the dynamics of a particle in a tubular region around the graph (\fat graph") when the transversal section of this region shrinks to zero. We give evidence of the fact that if the limit dynamics exists and is induced by the Laplacian on the graph with certain self-adjoint boundary conditions, such conditions are determined by the possible presence of a zero energy resonance on the fat graph. Pictorially, one may say that in the shrinking limit the resonance acts as a bridge connecting the boundary values at the vertex along the different rays. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7485 U1 - 7598 ER - TY - RPRT T1 - The deal.II Library, Version 8.1 Y1 - 2013 A1 - W. Bangerth A1 - Timo Heister A1 - Luca Heltai A1 - G. Kanschat A1 - Martin Kronbichler A1 - Matthias Maier A1 - B. Turcksin A1 - T. D. Young AB - This paper provides an overview of the new features of the finite element library deal.II version 8.0. PB - SISSA UR - http://hdl.handle.net/1963/7236 N1 - 5 pages U1 - 7272 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - RPRT T1 - Defect annihilation and proliferation in active nematics Y1 - 2013 A1 - Luca Giomi A1 - Mark J. Bowick A1 - Xu Ma A1 - M. Cristina Marchetti AB - Liquid crystals inevitably possess topological defect excitations generated\r\nthrough boundary conditions, applied fields or in quenches to the ordered\r\nphase. In equilibrium pairs of defects coarsen and annihilate as the uniform\r\nground state is approached. Here we show that defects in active liquid crystals\r\nexhibit profoundly different behavior, depending on the degree of activity and\r\nits contractile or extensile character. While contractile systems enhance the\r\nannihilation dynamics of passive systems, extensile systems act to drive\r\ndefects apart so that they swarm around in the manner of topologically\r\nwell-characterized self-propelled particles. We develop a simple analytical\r\nmodel for the defect dynamics which reproduces the key features of both the\r\nnumerical solutions and recent experiments on microtuble-kinesin assemblies. PB - SISSA UR - http://hdl.handle.net/1963/6566 N1 - 5 pages, 4 figures U1 - 6517 U2 - Mathematics U4 - 2 U5 - FIS/02 FISICA TEORICA, MODELLI E METODI MATEMATICI ER - TY - RPRT T1 - On deformations of multidimensional Poisson brackets of hydrodynamic type Y1 - 2013 A1 - Matteo Casati KW - Hamiltonian operator AB - The theory of Poisson Vertex Algebras (PVAs) is a good framework to treat Hamiltonian partial differential equations. A PVA consist of a pair $(\mathcal{A},\{\cdot_{\lambda}\cdot\})$ of a differential algebra $\mathcal{A}$ and a bilinear operation called the $\lambda$-bracket. We extend the definition to the class of algebras $\mathcal{A}$ endowed with $d\geq 1$ commuting derivations. We call this structure a multidimensional PVA: it is a suitable setting to the study of deformations of the Poisson bracket of hydrodynamic type associated to the Euler's equation of motion of $d$-dimensional incompressible fluids. We prove that for $d=2$ all the first order deformations of such class of Poisson brackets are trivial. PB - SISSA UR - http://hdl.handle.net/1963/7235 U1 - 7271 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - THES T1 - On the desingularization of Kahler orbifolds with constant scalar curvature Y1 - 2013 A1 - Riccardo Lena PB - SISSA U1 - 7263 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Dirac operator on spinors and diffeomorphisms JF - Classical and Quantum Gravity. Volume 30, Issue 1, 7 January 2013, Article number 015006 Y1 - 2013 A1 - Ludwik Dabrowski A1 - Giacomo Dossena KW - gravity AB - The issue of general covariance of spinors and related objects is reconsidered. Given an oriented manifold $M$, to each spin structure $\sigma$ and Riemannian metric $g$ there is associated a space $S_{\sigma, g}$ of spinor fields on $M$ and a Hilbert space $\HH_{\sigma, g}= L^2(S_{\sigma, g},\vol{M}{g})$ of $L^2$-spinors of $S_{\sigma, g}$. The group $\diff{M}$ of orientation-preserving diffeomorphisms of $M$ acts both on $g$ (by pullback) and on $[\sigma]$ (by a suitably defined pullback $f^*\sigma$). Any $f\in \diff{M}$ lifts in exactly two ways to a unitary operator $U$ from $\HH_{\sigma, g} $ to $\HH_{f^*\sigma,f^*g}$. The canonically defined Dirac operator is shown to be equivariant with respect to the action of $U$, so in particular its spectrum is invariant under the diffeomorphisms. PB - IOP Publishing UR - http://hdl.handle.net/1963/7377 N1 - This article is composed of 13 pages and is recorded in PDF format U1 - 7425 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - RPRT T1 - Dislocation dynamics in crystals: a macroscopic theory in a fractional Laplace setting Y1 - 2013 A1 - Serena Dipierro A1 - Giampiero Palatucci A1 - Enrico Valdinoci KW - nonlocal Allen-Cahn equation AB - We consider an evolution equation arising in the Peierls-Nabarro model for crystal dislocation. We study the evolution of such dislocation function and show that, at a macroscopic scale, the dislocations have the tendency to concentrate at single points of the crystal, where the size of the slip coincides with the natural periodicity of the medium. These dislocation points evolve according to the external stress and an interior repulsive potential. PB - SISSA UR - http://hdl.handle.net/1963/7124 U1 - 7124 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Decompositions of large-scale biological systems based on dynamical properties JF - Bioinformatics (Oxford, England). 2012 Jan; 28(1):76-83 Y1 - 2012 A1 - Nicola Soranzo A1 - Fahimeh Ramezani A1 - Giovanni Iacono A1 - Claudio Altafini AB - MOTIVATION: Given a large-scale biological network represented as an influence graph, in this article we investigate possible decompositions of the network aimed at highlighting specific dynamical properties.\\r\\nRESULTS: The first decomposition we study consists in finding a maximal directed acyclic subgraph of the network, which dynamically corresponds to searching for a maximal open-loop subsystem of the given system. Another dynamical property investigated is strong monotonicity. We propose two methods to deal with this property, both aimed at decomposing the system into strongly monotone subsystems, but with different structural characteristics: one method tends to produce a single large strongly monotone component, while the other typically generates a set of smaller disjoint strongly monotone subsystems.\\r\\nAVAILABILITY: Original heuristics for the methods investigated are described in the article. PB - Oxford University Press UR - http://hdl.handle.net/1963/5226 U1 - 5049 U2 - Physics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Deformed Lorentz symmetry and relative locality in a curved/expanding spacetime JF - Phys. Rev. D 86 (2012) 124035 Y1 - 2012 A1 - Giovanni Amelino-Camelia A1 - Antonino Marciano A1 - Marco Matassa A1 - Giacomo Rosati KW - Doubly special relativity AB - The interest of part of the quantum-gravity community in the possibility of\r\nPlanck-scale-deformed Lorentz symmetry is also fueled by the opportunities for testing the relevant scenarios with analyses, from a signal-propagation perspective, of observations of bursts of particles from cosmological distances. In this respect the fact that so far the implications of deformed Lorentz symmetry have been investigated only for flat (Minkowskian) spacetimes represents a very significant limitation, since for propagation over cosmological distances the curvature/expansion of spacetime is evidently tangible. We here provide a significant step toward filling this gap by exhibiting an explicit example of Planck-scale-deformed relativistic symmetries of a spacetime with constant rate of expansion (deSitterian). Technically we obtain the first ever example of a relativistic theory of worldlines of particles with 3 nontrivial relativistic invariants: a large speed scale (\"speed-of-light scale\"), a large distance scale (inverse of the \"expansion-rate scale\"), and a large momentum scale (\"Planck scale\"). We address some of the challenges that had obstructed success for previous attempts by exploiting the recent understanding of the connection between deformed Lorentz symmetry and relativity of spacetime locality. We also offer a preliminary analysis of the differences between the scenario we here propose and the most studied scenario for broken (rather than deformed) Lorentz symmetry in expanding spacetimes. PB - American Physical Society N1 - 12 pages, 5 figures U1 - 6496 U2 - Physics U4 - -1 ER - TY - JOUR T1 - Detection of transcriptional triggers in the dynamics of microbial growth: application to the respiratory-versatile bacterium Shewanella oneidensis JF - Nucleic Acids Research, Volume 40, Issue 15, August 2012, Pages 7132-7149 Y1 - 2012 A1 - Q Beg A1 - Mattia Zampieri A1 - N Klitgord A1 - S Collins A1 - M Serres A1 - Daniel Segrè A1 - Claudio Altafini AB - The capacity of microorganisms to respond to variable external conditions requires a coordination of environment-sensing mechanisms and decisionmaking regulatory circuits. Here, we seek to understand the interplay between these two processes by combining high-throughput measurement of time-dependent mRNA profiles with a novel computational approach that searches for key genetic triggers of transcriptional changes. Our approach helped us understand the regulatory strategies of a respiratorily versatile bacterium with promising bioenergy and bioremediation applications, Shewanella oneidensis, in minimal and rich media. By comparing expression profiles across these two conditions, we unveiled components of the transcriptional program that depend mainly on the growth phase. Conversely, by integrating our time-dependent data with a previously available large compendium of static perturbation responses, we identified transcriptional changes that cannot be explained solely by internal network dynamics, but are rather triggered by specific genes acting as key mediators of an environment-dependent response. These transcriptional triggers include known and novel regulators that respond to carbon, nitrogen and oxygen limitation. Our analysis suggests a sequence of physiological responses, including a coupling between nitrogen depletion and glycogen storage, partially recapitulated through dynamic flux balance analysis, and experimentally confirmed by metabolite measurements. Our approach is broadly applicable to other systems PB - SISSA UR - http://hdl.handle.net/1963/6506 U1 - 6452 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - A dynamical feedback model for adaptation in the olfactory transduction pathway JF - Biophysical Journal. Volume 102, Issue 12, 20 June 2012, Pages 2677-2686 Y1 - 2012 A1 - Giovanna De Palo A1 - Anna Boccaccio A1 - Andrew Miri A1 - Anna Menini A1 - Claudio Altafini AB - Olfactory transduction exhibits two distinct types of adaptation, which we denote multipulse and step adaptation. In terms of measured transduction current, multipulse adaptation appears as a decrease in the amplitude of the second of two consecutive responses when the olfactory neuron is stimulated with two brief pulses. Step adaptation occurs in response to a sustained steplike stimulation and is characterized by a return to a steady-state current amplitude close to the prestimulus value, after a transient peak. In this article, we formulate a dynamical model of the olfactory transduction pathway, which includes the kinetics of the CNG channels, the concentration of Ca ions flowing through them, and the Ca-complexes responsible for the regulation. Based on this model, a common dynamical explanation for the two types of adaptation is suggested. We show that both forms of adaptation can be well described using different time constants for the kinetics of Ca ions (faster) and the kinetics of the feedback mechanisms (slower). The model is validated on experimental data collected in voltage-clamp conditions using different techniques and animal species. PB - Biophysical Society, Elsevier UR - http://hdl.handle.net/1963/7019 U1 - 7012 U2 - Neuroscience U4 - -1 ER - TY - JOUR T1 - Dynamics of opinion forming in structurally balanced social networks JF - PloS one. 2012 ; 7(6):e38135 Y1 - 2012 A1 - Claudio Altafini AB - A structurally balanced social network is a social community that splits into two antagonistic factions (typical example being a two-party political system). The process of opinion forming on such a community is most often highly predictable, with polarized opinions reflecting the bipartition of the network. The aim of this paper is to suggest a class of dynamical systems, called monotone systems, as natural models for the dynamics of opinion forming on structurally balanced social networks. The high predictability of the outcome of a decision process is explained in terms of the order-preserving character of the solutions of this class of dynamical systems. If we represent a social network as a signed graph in which individuals are the nodes and the signs of the edges represent friendly or hostile relationships, then the property of structural balance corresponds to the social community being splittable into two antagonistic factions, each containing only friends. PB - PLoS UR - http://hdl.handle.net/1963/6051 U1 - 5942 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - RPRT T1 - D-branes, surface operators, and ADHM quiver representations Y1 - 2011 A1 - Ugo Bruzzo A1 - Duiliu-Emanuel Diaconescu A1 - M. Yardim A1 - G. Pan A1 - Yi Zhang A1 - Chuang Wu-yen AB - A supersymmetric quantum mechanical model is constructed for BPS states bound to surface operators in five dimensional SU(r) gauge theories using D-brane engineering. This model represents the effective action of a certain D2-brane configuration, and is naturally obtained by dimensional reduction of a quiver $(0,2)$ gauged linear sigma model. In a special stability chamber, the resulting moduli space of quiver representations is shown to be smooth and isomorphic to a moduli space of framed quotients on the projective plane. A precise conjecture relating a K-theoretic partition function of this moduli space to refined open string invariants of toric lagrangian branes is formulated for conifold and local P^1 x P^1 geometries. PB - SISSA UR - http://hdl.handle.net/1963/4133 N1 - 45 pages, v2: minor corrections U1 - 3873 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - A Decomposition Theorem for BV functions JF - Communications on Pure and Applied Analysis Y1 - 2011 A1 - Stefano Bianchini A1 - Daniela Tonon PB - American Institute of Mathematical Sciences VL - 10 UR - http://hdl.handle.net/20.500.11767/14599 IS - 6 U1 - 693 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Degenerate KAM theory for partial differential equations JF - Journal of Differential Equations Y1 - 2011 A1 - Dario Bambusi A1 - Massimiliano Berti A1 - Elena Magistrelli AB - This paper deals with degenerate KAM theory for lower dimensional elliptic tori of infinite dimensional Hamiltonian systems, depending on one parameter only. We assume that the linear frequencies are analytic functions of the parameter, satisfy a weak non-degeneracy condition of Rüssmann type and an asymptotic behavior. An application to nonlinear wave equations is given. © 2010 Elsevier Inc. VL - 250 N1 - cited By (since 1996)3 ER - TY - THES T1 - Dimensional Reduction and Approximation of Measures and Weakly Differentiable Homeomorphisms Y1 - 2011 A1 - Sara Daneri AB - This thesis is devoted to the study of two different problems: the properties of the disintegration of the Lebesgue measure on the faces of a convex function and the existence of smooth approximations of bi-Lipschitz orientation-preserving homeomorphisms in the plane. PB - SISSA UR - http://hdl.handle.net/1963/5348 U1 - 5178 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Double resonance with Landesman–Lazer conditions for planar systems of ordinary differential equations JF - Journal of Differential Equations Y1 - 2011 A1 - Alessandro Fonda A1 - Maurizio Garrione KW - Double resonance KW - Landesman–Lazer conditions KW - Nonlinear planar systems AB -We prove the existence of periodic solutions for first order planar systems at resonance. The nonlinearity is indeed allowed to interact with two positively homogeneous Hamiltonians, both at resonance, and some kind of Landesman–Lazer conditions are assumed at both sides. We are thus able to obtain, as particular cases, the existence results proposed in the pioneering papers by Lazer and Leach (1969) [27], and by Frederickson and Lazer (1969) [18]. Our theorem also applies in the case of asymptotically piecewise linear systems, and in particular generalizes Fabry's results in Fabry (1995) [10], for scalar equations with double resonance with respect to the Dancer–Fučik spectrum.

VL - 250 UR - http://www.sciencedirect.com/science/article/pii/S0022039610002901 ER - TY - JOUR T1 - The dependence on the monodromy data of the isomonodromic tau function JF - Comm. Math. Phys. Y1 - 2010 A1 - Marco Bertola VL - 294 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00220-009-0961-7 ER - TY - JOUR T1 - Dirac Operators on Quantum Projective Spaces JF - Comm. Math. Phys. 295 (2010) 731-790 Y1 - 2010 A1 - Francesco D'Andrea A1 - Ludwik Dabrowski AB - We construct a family of self-adjoint operators D_N which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space CP_q(l), for any l>1 and 0We consider the disintegration of the Lebesgue measure on the graph of a convex function f:\\\\Rn-> \\\\R w.r.t. the partition into its faces, which are convex sets and therefore have a well defined linear dimension, and we prove that each conditional measure is equivalent to the k-dimensional Hausdorff measure of the k-dimensional face on which it is concentrated. The remarkable fact is that a priori the directions of the faces are just Borel and no Lipschitz regularity is known. Notwithstanding that, we also prove that a Green-Gauss formula for these directions holds on special sets. UR - http://hdl.handle.net/1963/3622 U1 - 682 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Dynamics control by a time-varying feedback JF - Journal of Dynamical and Control Systems. Volume 16, Issue 2, April 2010, Pages :149-162 Y1 - 2010 A1 - Andrei A. Agrachev A1 - Marco Caponigro KW - Discrete-time dynamics AB - We consider a smooth bracket generating control-affine system in R^d and show that any orientation preserving diffeomorphism of R^d can be approximated, in the very strong sense, by a diffeomorphism included in the flow generated by a time-varying feedback control which is polynomial with respect to the state variables and trigonometric-polynomial with respect to the time variable. PB - SISSA UR - http://hdl.handle.net/1963/6461 U1 - 6407 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Decoupling A and B model in open string theory: topological adventures in the world of tadpoles JF - JHEP 06 (2009) 046 Y1 - 2009 A1 - Giulio Bonelli A1 - Andrea Prudenziati A1 - Alessandro Tanzini A1 - Yang Jie AB - In this paper we analyze the problem of tadpole cancellation in open topological strings. We prove that the inclusion of unorientable worldsheet diagrams guarantees a consistent decoupling of A and B model for open superstring amplitudes at all genera. This is proven by direct microscopic computation in Super Conformal Field Theory. For the B-model we explicitly calculate one loop amplitudes in terms of analytic Ray-Singer torsions of appropriate vector bundles and obtain that the decoupling corresponds to the cancellation of D-brane and orientifold charges. Local tadpole cancellation on the worldsheet then guarantees the decoupling at all loops. The holomorphic anomaly equations for open topological strings at one loop are also obtained and compared with the results of the Quillen formula. UR - http://hdl.handle.net/1963/3632 U1 - 672 U2 - Physics U3 - Mathematical Physics ER - TY - JOUR T1 - Differential geometry of curves in Lagrange Grassmannians with given Young diagram JF - Differential Geom. Appl. 27 (2009) 723-742 Y1 - 2009 A1 - Igor Zelenko A1 - Li Chengbo AB - Curves in Lagrange Grassmannians appear naturally in the intrinsic study of geometric structures on manifolds. By a smooth geometric structure on a manifold we mean any submanifold of its tangent bundle, transversal to the fibers. One can consider the time-optimal problem naturally associate with a geometric structure. The Pontryagin extremals of this optimal problem are integral curves of certain Hamiltonian system in the cotangent bundle. The dynamics of the fibers of the cotangent bundle w.r.t. this system along an extremal is described by certain curve in a Lagrange Grassmannian, called Jacobi curve of the extremal. Any symplectic invariant of the Jacobi curves produces the invariant of the original geometric structure. The basic characteristic of a curve in a Lagrange Grassmannian is its Young diagram. The number of boxes in its kth column is equal to the rank of the kth derivative of the curve (which is an appropriately defined linear mapping) at a generic point. We will describe the construction of the complete system of symplectic invariants for parameterized curves in a Lagrange Grassmannian with given Young diagram. It allows to develop in a unified way local differential geometry of very wide classes of geometric structures on manifolds, including both classical geometric structures such as Riemannian and Finslerian structures and less classical ones such as sub-Riemannian and sub-Finslerian structures, defined on nonholonomic distributions. PB - Elsevier UR - http://hdl.handle.net/1963/3819 U1 - 508 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Discrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers JF - Netw. Heterog. Media 4 (2009) 667-708 Y1 - 2009 A1 - Marco Cicalese A1 - Antonio DeSimone A1 - Caterina Ida Zeppieri AB - In the framework of linear elasticity, we study the limit of a class of discrete free energies modeling strain-alignment-coupled systems by a rigorous coarse-graining procedure, as the number of molecules diverges. We focus on three paradigmatic examples: magnetostrictive solids, ferroelectric crystals and nematic elastomers, obtaining in the limit three continuum models consistent with those commonly employed in the current literature. We also derive the correspondent macroscopic energies in the presence of displacement boundary conditions and of various kinds of applied external fields. PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/3788 U1 - 538 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - The Disintegration Theorem and Applications to Optimal Mass Transportation Y1 - 2009 A1 - Laura Caravenna PB - SISSA UR - http://hdl.handle.net/1963/5900 U1 - 5750 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Decomposition results for functions with bounded variation JF - Boll. Unione Mat. Ital. (9) 1 (2008) 497-505 Y1 - 2008 A1 - Gianni Dal Maso A1 - Rodica Toader PB - Unione Matematica Italiana UR - http://hdl.handle.net/1963/3535 U1 - 729 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Discerning static and causal interactions in genome-wide reverse engineering problems JF - Bioinformatics 24 (2008) 1510-1515 Y1 - 2008 A1 - Mattia Zampieri A1 - Nicola Soranzo A1 - Claudio Altafini AB - Background. In the past years devicing methods for discovering gene regulatory mechanisms at a genome-wide level has become a fundamental topic in the field of system biology. The aim is to infer gene-gene interactions in a more sophisticated and reliable way through the continuously improvement of reverse engineering algorithms exploiting microarray technologies. Motivation. This work is inspired by the several studies suggesting that co-expression is mostly related to \\\"static\\\" stable binding relationships, like belonging to the same protein complex, rather than other types of interactions more of a \\\"causal\\\" and transient nature (metabolic pathway or transcription factor-binding site interaction). Discerning static relationships from causal ones on the basis of their characteristic regulatory structures and in particular identifing \\\"dense modules\\\" with protein complex, and \\\"sparse modules\\\" with causal interactions such as those between transcription factor and corresponding binding site, the performances of different network inference algorithms in artificial and real networks (derived from E.coli and S.cerevisiae) can be tested and compared. Results. Our study shows that methods that try to prune indirect interactions from the inferred gene networks may fail to retrieve genes co-participating in a protein complex. On the other hand they are more robust in the identification of transcription factor-binding sites dependences when multiple transcription factors regulate the expression of the same gene. In the end we confirm the stronger co-expression regarding genes belonging to a protein complex than transcription factor-binding site, according, also, to the effect of multiple transcription factors and a low expression variance. UR - http://hdl.handle.net/1963/2757 U1 - 1943 U2 - Physics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Derivation of a rod theory for phase-transforming materials Y1 - 2007 A1 - Maria Giovanna Mora A1 - Stefan Müller AB - A rigorous derivation is given of a rod theory for a multiphase material,starting from three-dimensional nonlinear elasticity. The stored energy density is supposed to be nonnegative and to vanish exactly on a set consisting of two copies of the group of rotations SO(3). The two potential wells correspond to the two crystalline configurations preferred by the material. We find the optimal scaling of the energy in terms of the diameter of the rod and we identify the limit, as the diameter goes to zero, in the sense of Gamma-convergence. JF - Calc. Var. Partial Differential Equations 28 (2007) 161-178 UR - http://hdl.handle.net/1963/1751 U1 - 2793 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Dirac operators on all Podles quantum spheres JF - J. Noncomm. Geom. 1 (2007) 213-239 Y1 - 2007 A1 - Francesco D'Andrea A1 - Ludwik Dabrowski A1 - Giovanni Landi A1 - Elmar Wagner AB - We construct spectral triples on all Podles quantum spheres. These noncommutative geometries are equivariant for a left action of $U_q(su(2))$ and are regular, even and of metric dimension 2. They are all isospectral to the undeformed round geometry of the 2-sphere. There is also an equivariant real structure for which both the commutant property and the first order condition for the Dirac operators are valid up to infinitesimals of arbitrary order. UR - http://hdl.handle.net/1963/2177 U1 - 2067 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - The Dirichlet problem for H-systems with small boundary data: blowup phenomena and nonexistence results JF - Arch. Ration. Mech. Anal. 181 (2006) 1-42 Y1 - 2006 A1 - Paolo Caldiroli A1 - Roberta Musina UR - http://hdl.handle.net/1963/2252 U1 - 1995 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Decay of a bound state under a time-periodic perturbation: a toy case JF - J. Phys. A 38 (2005) 4769-4781 Y1 - 2005 A1 - Michele Correggi A1 - Gianfausto Dell'Antonio AB - We study the time evolution of a three dimensional quantum particle, initially in a bound state, under the action of a time-periodic zero range interaction with ``strength\\\'\\\' (\\\\alpha(t)). Under very weak generic conditions on the Fourier coefficients of (\\\\alpha(t)), we prove complete ionization as (t \\\\to \\\\infty). We prove also that, under the same conditions, all the states of the system are scattering states. UR - http://hdl.handle.net/1963/2298 U1 - 1718 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - The Dirac operator on SU_q(2) JF - Commun. Math. Phys. 259 (2005) 729-759 Y1 - 2005 A1 - Ludwik Dabrowski A1 - Giovanni Landi A1 - Andrzej Sitarz A1 - Walter van Suijlekom A1 - Joseph C. Varilly AB - We construct a 3^+ summable spectral triple (A(SU_q(2)),H,D) over the quantum group SU_q(2) which is equivariant with respect to a left and a right action of U_q(su(2)). The geometry is isospectral to the classical case since the spectrum of the operator D is the same as that of the usual Dirac operator on the 3-dimensional round sphere. The presence of an equivariant real structure J demands a modification in the axiomatic framework of spectral geometry, whereby the commutant and first-order properties need be satisfied only modulo infinitesimals of arbitrary high order. PB - Springer UR - http://hdl.handle.net/1963/4425 N1 - v2: minor changes U1 - 4175 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Differential systems for biorthogonal polynomials appearing in 2-matrix models and the associated Riemann-Hilbert problem JF - Comm. Math. Phys. Y1 - 2003 A1 - Marco Bertola A1 - B. Eynard A1 - Harnad, J. VL - 243 ER - TY - JOUR T1 - Drift in phase space: a new variational mechanism with optimal diffusion time JF - J. Math. Pures Appl. 82 (2003) 613-664 Y1 - 2003 A1 - Massimiliano Berti A1 - Luca Biasco A1 - Philippe Bolle AB - We consider non-isochronous, nearly integrable, a-priori unstable Hamiltonian systems with a (trigonometric polynomial) $O(\\\\mu)$-perturbation which does not preserve the unperturbed tori. We prove the existence of Arnold diffusion with diffusion time $ T_d = O((1/ \\\\mu) \\\\log (1/ \\\\mu))$ by a variational method which does not require the existence of ``transition chains of tori\\\'\\\' provided by KAM theory. We also prove that our estimate of the diffusion time $T_d $ is optimal as a consequence of a general stability result derived from classical perturbation theory. PB - Elsevier UR - http://hdl.handle.net/1963/3020 U1 - 1313 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The duality of spectral curves that arises in two-matrix models JF - Teoret. Mat. Fiz. Y1 - 2003 A1 - Marco Bertola A1 - B. Eynard A1 - Kharnad, Dzh. VL - 134 ER - TY - JOUR T1 - Duality, biorthogonal polynomials and multi-matrix models JF - Comm. Math. Phys. Y1 - 2002 A1 - Marco Bertola A1 - B. Eynard A1 - Harnad, J. VL - 229 ER - TY - JOUR T1 - Dieletric breakdown: optimal bounds JF - Proc. of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences 457 (2001): p. 2317-2335, OCT. 8, 2001 Y1 - 2001 A1 - Adriana Garroni A1 - Vincenzo Nesi A1 - Marcello Ponsiglione PB - SISSA Library UR - http://hdl.handle.net/1963/1569 U1 - 2549 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Dirac operator on the standard Podles quantum sphere JF - Noncommutative geometry and quantum groups (Warsaw 2001),49,Banach Center Publ., 61, Polish Acad.Sci., Warsaw,2003 Y1 - 2001 A1 - Ludwik Dabrowski A1 - Andrzej Sitarz PB - SISSA Library UR - http://hdl.handle.net/1963/1668 U1 - 2450 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Decomposing quantum fields on branes JF - Nuclear Phys. B Y1 - 2000 A1 - Marco Bertola A1 - Bros, Jacques A1 - Gorini, Vittorio A1 - Moschella, Ugo A1 - Schaeffer, Richard VL - 581 ER - TY - JOUR T1 - Diffusion time and splitting of separatrices for nearly integrable JF - Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei Mat. Appl., 2000, 11, 235 Y1 - 2000 A1 - Massimiliano Berti A1 - Philippe Bolle PB - SISSA Library UR - http://hdl.handle.net/1963/1547 U1 - 2571 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Discrete approximation of the Mumford-Shah functional in dimension two JF - M2AN 33 (1999) 651-672 Y1 - 1999 A1 - Antonin Chambolle A1 - Gianni Dal Maso PB - EDP Sciences UR - http://hdl.handle.net/1963/3588 U1 - 712 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Differential geometry of the space of orbits of a Coxeter group JF - J. Differential Geometry Suppl.4 (1998) 181-211 Y1 - 1998 A1 - Boris Dubrovin AB - Differential-geometric structures on the space of orbits of a finite Coxeter group, determined by Groth\\\\\\\'endieck residues, are calculated. This gives a construction of a 2D topological field theory for an arbitrary Coxeter group. PB - International Press UR - http://hdl.handle.net/1963/3562 U1 - 1140 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Diffusion of a particle in presence of N moving point sources JF - Annales Poincare Phys.Theor.69:413-424,1998 Y1 - 1998 A1 - Gianfausto Dell'Antonio A1 - Rodolfo Figari A1 - Alessandro Teta PB - SISSA Library UR - http://hdl.handle.net/1963/134 U1 - 75 U2 - LISNU U3 - Interdisciplinary Laboratory for Advanced Studies ER - TY - JOUR T1 - On the Dirichlet problem for vectorial Hamilton-Jacobi equations JF - SIAM J. Math. Anal. 29 (1998) 1481-1491 Y1 - 1998 A1 - Sandro Zagatti AB - We give sufficient conditions for the existence of solutions to the Hamilton--Jacobi equations with Dirichlet boundary condition: $$ \\\\cases{ g(x,{\\\\hbox{\\\\rm det}}Du(x))=0, \\\\ & for a.e. $x\\\\in\\\\Omega,$\\\\cr u(x)=\\\\varphi(x), & for $x\\\\in\\\\partial\\\\Omega,$} $$ obtaining, in addition, an application to the theory of existence of minimizers for a class of nonconvex variational problems. PB - SIAM UR - http://hdl.handle.net/1963/3512 U1 - 752 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - Dispersion relations for non-linear waves and the Schottky problem T2 - Important developments in soliton theory / A. S. Fokas, V. E. Zakharov (eds.) - Berlin : Springer-Verlag, 1993. - pages : 86-98 Y1 - 1993 A1 - Boris Dubrovin AB - An approach to the Schottky problem of specification of periods of holomorphic differentials\\r\\non Riemann surfaces (or, equivalently, specification of Jacobians among all principaly\\r\\npolarized Abelian varieties) based on the theory of Kadomtsev - Petviashvili equation,\\r\\nis discussed. JF - Important developments in soliton theory / A. S. Fokas, V. E. Zakharov (eds.) - Berlin : Springer-Verlag, 1993. - pages : 86-98 PB - SISSA SN - 3540559132 UR - http://hdl.handle.net/1963/6480 U1 - 6430 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - RPRT T1 - Differential geometry of moduli spaces and its applications to soliton equations and to topological conformal field theory Y1 - 1991 A1 - Boris Dubrovin AB - We construct flat Riemannian metrics on moduli spaces of algebraic curves with marked meromorphic function. This gives a new class of exact algebraic-geometry solutions to certain non-linear equations in terms of functions on the moduli spaces. We show that the Riemannian metrics on the moduli spaces coincide with two-point correlators in topological conformal field theory and calculate the partition function for A_n model for arbitrary genus. A universal method for constructing complete families of conservation laws for Whitham-type hierarchies of PDEs is also proposed. JF - Preprint n.117, Scuola Normale Superiore, Pisa, November 1991, 31 pp. Published in: Surveys in Differential Geometry , Vol. IV (1999), p. 213 - 238. PB - Scuola Normale Superiore di Pisa UR - http://hdl.handle.net/1963/6475 U1 - 6435 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - On differential systems with vector-valued impulsive controls. JF - Boll. Un. Mat. Ital. B (7) 2 (1988), no. 3, 641-656 Y1 - 1988 A1 - Alberto Bressan A1 - Franco Rampazzo PB - SISSA Library UR - http://hdl.handle.net/1963/535 U1 - 3369 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Dirichlet problems for demicoercive functionals JF - Nonlinear anal. 10(1986), no.6, 603-613 Y1 - 1986 A1 - Gabriele Anzellotti A1 - Giuseppe Buttazzo A1 - Gianni Dal Maso PB - SISSA Library UR - http://hdl.handle.net/1963/390 U1 - 3577 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Differential equations with multiple solutions and nonlinear functional analysis JF - Equadiff 82 (Wurzburg, 1982), 10--37, Lecture Notes in Math., 1017, Springer, Berlin, 1983 Y1 - 1982 A1 - Antonio Ambrosetti PB - SISSA Library UR - http://hdl.handle.net/1963/222 U1 - 3745 U2 - Mathematics U3 - Functional Analysis and Applications ER -