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.

%B Expositiones Mathematicae %G eng %U http://www.sciencedirect.com/science/article/pii/S0723086918300975 %R https://doi.org/10.1016/j.exmath.2019.01.002 %0 Journal Article %J SOFTWAREX %D 2018 %T deal2lkit: A toolkit library for high performance programming in deal.II %A Alberto Sartori %A Nicola Giuliani %A Mauro Bardelloni %A Luca Heltai %B SOFTWAREX %V 7 %P 318–327 %G eng %R 10.1016/j.softx.2018.09.004 %0 Journal Article %J JOURNAL OF NUMERICAL MATHEMATICS %D 2018 %T The deal.II Library, Version 9.0 %A Giovanni Alzetta %A Arndt, Daniel %A W. Bangerth %A Boddu, Vishal %A Brands, Benjamin %A Denis Davydov %A Gassmöller, Rene %A Timo Heister %A Luca Heltai %A Kormann, Katharina %A Martin Kronbichler %A Matthias Maier %A Pelteret, Jean-Paul %A B. Turcksin %A David Wells %B JOURNAL OF NUMERICAL MATHEMATICS %G eng %U https://doi.org/10.1515/jnma-2018-0054 %R 10.1515/jnma-2018-0054 %0 Report %D 2018 %T Differential of metric valued Sobolev maps %A Nicola Gigli %A Enrico Pasqualetto %A Elefterios Soultanis %G eng %0 Report %D 2018 %T Dimension reduction for thin films with transversally varying prestrain: the oscillatory and the non-oscillatory case %A Marta Lewicka %A Danka Lučić %G eng %0 Journal Article %J Advanced Modeling and Simulation in Engineering Sciences %D 2018 %T Dimension reduction in heterogeneous parametric spaces with application to naval engineering shape design problems %A Marco Tezzele %A Filippo Salmoiraghi %A Andrea Mola %A Gianluigi Rozza %XWe 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.

%B Advanced Modeling and Simulation in Engineering Sciences %V 5 %P 25 %8 Sep %G eng %R 10.1186/s40323-018-0118-3 %0 Journal Article %J Teoret. Mat. Fiz. %D 2018 %T Discriminant circle bundles over local models of Strebel graphs and Boutroux curves %A Marco Bertola %A Korotkin, D. A. %B Teoret. Mat. Fiz. %V 197 %P 163–207 %G eng %U https://doi.org/10.4213/tmf9513 %R 10.4213/tmf9513 %0 Book Section %B Mathematical and Numerical Modeling of the Cardiovascular System and Applications %D 2018 %T A distributed lagrange formulation of the finite element immersed boundary method for fluids interacting with compressible solids %A Boffi, Daniele %A Gastaldi, Lucia %A Luca Heltai %B Mathematical and Numerical Modeling of the Cardiovascular System and Applications %I Springer International Publishing %C Cham %V 16 %P 1–21 %G eng %U https://arxiv.org/abs/1712.02545v1 %R 10.1007/978-3-319-96649-6_1 %0 Journal Article %J JOURNAL OF NUMERICAL MATHEMATICS %D 2017 %T The deal.II Library, Version 8.5 %A Arndt, Daniel %A W. Bangerth %A Denis Davydov %A Timo Heister %A Luca Heltai %A Martin Kronbichler %A Matthias Maier %A Pelteret, Jean-Paul %A B. Turcksin %A David Wells %B JOURNAL OF NUMERICAL MATHEMATICS %V 25 %P 137–145 %G eng %U https://www.dealii.org/deal85-preprint.pdf %R 10.1515/jnma-2017-0058 %0 Report %D 2017 %T Derivation of a rod theory from lattice systems with interactions beyond nearest neighbours %A Roberto Alicandro %A Giuliano Lazzaroni %A Mariapia Palombaro %X We study continuum limits of discrete models for (possibly heterogeneous) nanowires. The lattice energy includes at least nearest and next-to-nearest neighbour interactions: the latter have the role of penalising changes of orientation. In the heterogeneous case, we obtain an estimate on the minimal energy spent to match different equilibria. This gives insight into the nucleation of dislocations in epitaxially grown heterostructured nanowires. %G en %U http://urania.sissa.it/xmlui/handle/1963/35269 %1 35575 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-01-16T12:46:44Z No. of bitstreams: 1 Lazzaroni_Preprint_58_2016.pdf: 305384 bytes, checksum: 9e6300f0e04681ca5ebd4b457ddea10e (MD5) %0 Report %D 2017 %T Discrete spectra for critical Dirac-Coulomb Hamiltonians %A Matteo Gallone %A Alessandro Michelangeli %X 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. %G en %U http://preprints.sissa.it/handle/1963/35300 %1 35606 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-11-06T14:27:38Z No. of bitstreams: 1 SISSA_preprint_44-2017-MATE.pdf: 1573857 bytes, checksum: 728e94322471701d89ed5741cda85d99 (MD5) %0 Book Section %B Advances in Quantum Mechanics: Contemporary Trends and Open Problems %D 2017 %T Dispersive Estimates for Schrödinger Operators with Point Interactions in ℝ3 %A Felice Iandoli %A Raffaele Scandone %E Alessandro Michelangeli %E Dell'Antonio, Gianfausto %XThe study of dispersive properties of Schrödinger operators with point interactions is a fundamental tool for understanding the behavior of many body quantum systems interacting with very short range potential, whose dynamics can be approximated by non linear Schrödinger equations with singular interactions. In this work we proved that, in the case of one point interaction in $\mathbb{R}^3$, the perturbed Laplacian satisfies the same $L^p$−$L^q$ estimates of the free Laplacian in the smaller regime $q \in [2,3)$. These estimates are implied by a recent result concerning the Lpboundedness of the wave operators for the perturbed Laplacian. Our approach, however, is more direct and relatively simple, and could potentially be useful to prove optimal weighted estimates also in the regime $q \geq 3$.

%B Advances in Quantum Mechanics: Contemporary Trends and Open Problems %I Springer International Publishing %C Cham %P 187–199 %@ 978-3-319-58904-6 %G eng %U https://doi.org/10.1007/978-3-319-58904-6_11 %R 10.1007/978-3-319-58904-6_11 %0 Journal Article %J ARCHIVE OF NUMERICAL SOFTWARE %D 2016 %T The deal.II Library, Version 8.3 %A W. Bangerth %A Timo Heister %A Luca Heltai %A G. Kanschat %A Martin Kronbichler %A Matthias Maier %A B. Turcksin %B ARCHIVE OF NUMERICAL SOFTWARE %V 4 %P 1–11 %G eng %U http://nbn-resolving.de/urn:nbn:de:bsz:16-ans-231226 %R 10.11588/ans.2016.100.23122 %0 Journal Article %J JOURNAL OF NUMERICAL MATHEMATICS %D 2016 %T The deal.II library, Version 8.4 %A W. Bangerth %A Denis Davydov %A Timo Heister %A Luca Heltai %A G. Kanschat %A Martin Kronbichler %A Matthias Maier %A B. Turcksin %A David Wells %B JOURNAL OF NUMERICAL MATHEMATICS %V 24 %P 135–141 %G eng %U https://www.math.clemson.edu/ heister/preprints/deal84-preprint.pdf %R 10.1515/jnma-2016-1045 %0 Journal Article %D 2015 %T Deal2lkit: a Toolkit Library for High Performance Programming in deal.II %A Alberto Sartori %A Nicola Giuliani %A Mauro Bardelloni %A Luca Heltai %X We present version 1.0.0 of the deal2lkit (deal.II ToolKit) library. deal2lkit is a collection of modules and classes for the general purpose finite element library deal.II. Its principal aim is to provide a high level interface, controlled via parameter files, for those steps that are common in all finite element programs: mesh generation, selection of the finite element type, application of boundary conditions and many others. Each module can be used as a building block independently on the others, and can be integrated in existing finite element codes based on deal.II, drastically reducing the size of programs, rendering their use automatically parametrised, and reducing the overall time-to-market of finite element programming. Moreover, deal2lkit features interfaces with the SUNDIALS (SUite of Nonlinear and DIfferential/ALgebraic equation Solvers) and ASSIMP (Open Asset Import Library) libraries. Some examples are provided which show the aim and scopes of deal2lkit. The deal2lkit library is released under the GNU Lesser General Public License (LGPL) and can be retrieved from the deal2lkit repository https://github.com/mathLab/deal2lkit. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/35006 %1 35235 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by asartori@sissa.it (asartori@sissa.it) on 2015-11-13T13:12:29Z No. of bitstreams: 1 paper_deal2lkit.pdf: 1085486 bytes, checksum: 1dc7e9b9790fe38d2ced7b5328633cd8 (MD5) %0 Journal Article %J Archive of Numerical Software, vol. 3, n. 100, (2015), pages : 1-8 %D 2015 %T The deal.II Library, Version 8.2 %A W. Bangerth %A Timo Heister %A Luca Heltai %A G. Kanschat %A Martin Kronbichler %A Matthias Maier %A B. Turcksin %A T. D. Young %X This paper provides an overview of the new features of the finite element library deal.II version 8.2 %B Archive of Numerical Software, vol. 3, n. 100, (2015), pages : 1-8 %G en %U http://urania.sissa.it/xmlui/handle/1963/34464 %1 34637 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Luca Heltai (heltai@sissa.it) on 2015-04-20T15:40:46Z No. of bitstreams: 1 18031-44567-1-PB (1).pdf: 137014 bytes, checksum: 9a5fddeccfa389c32ca89a466e653074 (MD5) %R 10.11588/ans.2015.100.18031 %0 Journal Article %J Dynamical Systems %D 2015 %T Decay of correlations for invertible maps with non-Hölder observables %A Marks Ruziboev %XAn invertible dynamical system with some hyperbolic structure is considered. Upper estimates for the correlations of continuous observables are given in terms of modulus of continuity. The result is applied to certain Hénon maps and Solenoid maps with intermittency.

%B Dynamical Systems %I Taylor & Francis %V 30 %P 341-352 %G eng %U https://doi.org/10.1080/14689367.2015.1046816 %R 10.1080/14689367.2015.1046816 %0 Journal Article %J J. Math. Phys. %D 2015 %T A degeneration of two-phase solutions of the focusing nonlinear Schrödinger equation via Riemann-Hilbert problems %A Marco Bertola %A Giavedoni, Pietro %B J. Math. Phys. %V 56 %P 061507, 17 %G eng %U http://dx.doi.org/10.1063/1.4922362 %R 10.1063/1.4922362 %0 Journal Article %D 2015 %T Dispersive deformations of the Hamiltonian structure of Euler's equations %A Matteo Casati %X 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. %G en %1 34700 %2 Mathematics %4 1 %# MAT/07 %$ Submitted by Matteo Casati (mcasati@sissa.it) on 2015-09-09T13:27:08Z No. of bitstreams: 1 defoHD.pdf: 195202 bytes, checksum: 9ee41e73fc37dd79f1659dda2e742b57 (MD5) %0 Report %D 2015 %T Dynamics of screw dislocations: a generalised minimising-movements scheme approach %A Giovanni A. Bonaschi %A Patrick Van Meurs %A Marco Morandotti %X The gradient flow structure of the model introduced in [CG99] for the dynamics of screw dislocations is investigated by means of a generalised minimising-movements scheme approach. The assumption of a finite number of available glide directions, together with the "maximal dissipation criterion" that governs the equations of motion, results into solving a differential inclusion rather than an ODE. This paper addresses how the model in [CG99] is connected to a time-discrete evolution scheme which explicitly confines dislocations to move each time step along a single glide direction. It is proved that the time-continuous model in [CG99] is the limit of these time-discrete minimising-movement schemes when the time step converges to 0. The study presented here is a first step towards a generalization of the setting in [AGS08, Chap. 2 and 3] that allows for dissipations which cannot be described by a metric. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/34495 %1 34692 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-09-04T08:36:59Z No. of bitstreams: 1 BvMM_03_9_15-MM.pdf: 773084 bytes, checksum: 686749d206d2f9c676ab004b860799f4 (MD5) %0 Journal Article %J IMRN %D 2014 %T Darboux Transformations and Random Point Processes %A Marco Bertola %A Mattia Cafasso %B IMRN %V rnu122 %P 56 %G eng %0 Thesis %D 2014 %T The decomposition of optimal transportation problems with convex cost %A Mauro Bardelloni %K Optimal Transportation %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/7475 %1 7570 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Mauro Bardelloni (mbarde@sissa.it) on 2014-10-27T10:15:30Z No. of bitstreams: 1 Bardelloni-thesis.pdf: 1162347 bytes, checksum: f2b57d7f3054afe4fae1c207b090121f (MD5) %0 Report %D 2014 %T The decomposition of optimal transportation problems with convex cost %A Stefano Bianchini %A Mauro Bardelloni %I SISSA %G en_US %U http://hdl.handle.net/1963/7433 %1 7527 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-09-22T14:16:35Z No. of bitstreams: 1 sissa _45_2014_MATE.pdf: 893572 bytes, checksum: c4334710f599da624c2e1cfb56aac415 (MD5) %0 Journal Article %D 2014 %T A density result for GSBD and its application to the approximation of brittle fracture energies %A Flaviana Iurlano %XWe present an approximation result for functions u: Ω → ℝ^n belonging to the space GSBD(Ω) ∩ L2(Ω, ℝn) with e(u) square integrable and Hn-1(Ju) finite. The approximating functions uk are piecewise continuous functions such that uk → u in (Formula Presented). As an application, we provide the extension to the vector-valued case of the Γ-convergence result in GSBV(Ω) proved by Ambrosio and Tortorelli (Commun Pure Appl Math 43:999-1036, 1990; Boll. Un. Mat. Ital. B (7) 6:105-123, 1992).

%I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34647 %1 34851 %2 Mathematics %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-10-14T17:02:41Z No. of bitstreams: 1 preprint2014.pdf: 543013 bytes, checksum: 1d1170449f762ffdaf48812b31671bc2 (MD5) %R 10.1007/s00526-013-0676-7 %0 Journal Article %D 2014 %T Dirac operators on noncommutative principal circle bundles %A Andrzej Sitarz %A Alessandro Zucca %A Ludwik Dabrowski %X We study spectral triples over noncommutative principal U(1)-bundles of arbitrary dimension and a compatibility condition between the connection and the Dirac operator on the total space and on the base space of the bundle. Examples of low-dimensional noncommutative tori are analyzed in more detail and all connections found that are compatible with an admissible Dirac operator. Conversely, a family of new Dirac operators on the noncommutative tori, which arise from the base-space Dirac operator and a suitable connection is exhibited. These examples are extended to the theta-deformed principal U(1)-bundle S 3 θ → S2. %I World Scientific Publishing %G en %U http://urania.sissa.it/xmlui/handle/1963/35125 %1 35363 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-12-02T15:58:16Z No. of bitstreams: 1 preprint2014.pdf: 282573 bytes, checksum: 862ea930b67b00c451a0c6f093be973d (MD5) %R 10.1142/S0219887814500121 %0 Journal Article %J Communications in Mathematical Physics 331, nr. 3 (2014) 1155-1190 %D 2014 %T Dirac reduction for Poisson vertex algebras %A Alberto De Sole %A Victor G. Kac %A Daniele Valeri %X We construct an analogue of Dirac's reduction for an arbitrary local or non-local Poisson bracket in the general setup of non-local Poisson vertex algebras. This leads to Dirac's reduction of an arbitrary non-local Poisson structure. We apply this construction to an example of a generalized Drinfeld-Sokolov hierarchy. %B Communications in Mathematical Physics 331, nr. 3 (2014) 1155-1190 %I SISSA %G en %U http://hdl.handle.net/1963/6980 %1 6968 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Daniele Valeri (dvaleri@sissa.it) on 2013-07-13T15:28:44Z No. of bitstreams: 1 1306.6589v1.pdf: 417586 bytes, checksum: 261351372e0d72d5e2d46b6664f19fd4 (MD5) %R 10.1007/s00220-014-2103-0 %0 Journal Article %D 2014 %T Discrete one-dimensional crawlers on viscous substrates: achievable net displacements and their energy cost %A Giovanni Noselli %A Amabile Tatone %A Antonio DeSimone %K Cell migration %X We study model one-dimensional crawlers, namely, model mechanical systems that can achieve self-propulsion by controlled shape changes of their body (extension or contraction of portions of the body), thanks to frictional interactions with a rigid substrate. We evaluate the achievable net displacement and the related energetic cost for self-propulsion by discrete crawlers (i.e., whose body is made of a discrete number of contractile or extensile segments) moving on substrates with either a Newtonian (linear) or a Bingham-type (stick-slip) rheology. Our analysis is aimed at constructing the basic building blocks towards an integrative, multi-scale description of crawling cell motility. %I Elsevier %G en %U http://urania.sissa.it/xmlui/handle/1963/34449 %1 34591 %2 Mathematics %$ Submitted by gnoselli@sissa.it (gnoselli@sissa.it) on 2015-03-07T17:44:40Z No. of bitstreams: 1 N-link_crawlers.pdf: 1005838 bytes, checksum: 685d5b41e7de190ec65c60090d397f93 (MD5) %R 10.1016/j.mechrescom.2013.10.023 %0 Report %D 2014 %T Dislocations at the continuum scale: functional setting and variational properties %A Riccardo Scala %A Nicolas Van Goethem %G eng %U http://cvgmt.sns.it/paper/2294/ %0 Report %D 2014 %T Donagi–Markman cubic for the generalised Hitchin system %A Ugo Bruzzo %A Peter Dalakov %K Generalized Hitchin system, Donagi-Markman cubic, algebraically completely integrable systems, moduli space of Higgs G-bundles %X Donagi and Markman (1993) have shown that the infinitesimal period map for an algebraic completely integrable Hamiltonian system (ACIHS) is encoded in a section of the third symmetric power of the cotangent bundle to the base of the system. For the ordinary Hitchin system the cubic is given by a formula of Balduzzi and Pantev. We show that the Balduzzi–Pantev formula holds on maximal rank symplectic leaves of the G-generalised Hitchin system. %G en %U http://hdl.handle.net/1963/7253 %1 7294 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Ugo Bruzzo (bruzzo@sissa.it) on 2014-02-17T15:50:22Z No. of bitstreams: 1 bruzzo-dalakov-fin-2.pdf: 461019 bytes, checksum: 99e7b1cb6cd4f6f5d5fbfaa1d2d35880 (MD5) %0 Report %D 2014 %T Dynamics on a graph as the limit of the dynamics on a "fat graph" %A Gianfausto Dell'Antonio %A Alessandro Michelangeli %X We discuss how the vertex boundary conditions for the dynamics of a quantum particle constrained on a graph emerge in the limit of the dynamics of a particle in a tubular region around the graph (\fat graph") when the transversal section of this region shrinks to zero. We give evidence of the fact that if the limit dynamics exists and is induced by the Laplacian on the graph with certain self-adjoint boundary conditions, such conditions are determined by the possible presence of a zero energy resonance on the fat graph. Pictorially, one may say that in the shrinking limit the resonance acts as a bridge connecting the boundary values at the vertex along the different rays. %I SISSA %G en_US %U http://urania.sissa.it/xmlui/handle/1963/7485 %1 7598 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-12-12T13:16:15Z No. of bitstreams: 1 sissa-preprint-69-2014-mate.pdf: 137454 bytes, checksum: 4d4571bd97df46ee020c81057ce78620 (MD5) %0 Report %D 2013 %T The deal.II Library, Version 8.1 %A W. Bangerth %A Timo Heister %A Luca Heltai %A G. Kanschat %A Martin Kronbichler %A Matthias Maier %A B. Turcksin %A T. D. Young %X This paper provides an overview of the new features of the finite element library deal.II version 8.0. %I SISSA %G en %U http://hdl.handle.net/1963/7236 %1 7272 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Luca Heltai (heltai@sissa.it) on 2013-12-10T10:43:08Z No. of bitstreams: 1 1312.2266v1.pdf: 245445 bytes, checksum: e00fcd6d7d9ac6e2076208958b07eef3 (MD5) %0 Report %D 2013 %T Defect annihilation and proliferation in active nematics %A Luca Giomi %A Mark J. Bowick %A Xu Ma %A M. Cristina Marchetti %X Liquid crystals inevitably possess topological defect excitations generated\r\nthrough boundary conditions, applied fields or in quenches to the ordered\r\nphase. In equilibrium pairs of defects coarsen and annihilate as the uniform\r\nground state is approached. Here we show that defects in active liquid crystals\r\nexhibit profoundly different behavior, depending on the degree of activity and\r\nits contractile or extensile character. While contractile systems enhance the\r\nannihilation dynamics of passive systems, extensile systems act to drive\r\ndefects apart so that they swarm around in the manner of topologically\r\nwell-characterized self-propelled particles. We develop a simple analytical\r\nmodel for the defect dynamics which reproduces the key features of both the\r\nnumerical solutions and recent experiments on microtuble-kinesin assemblies. %I SISSA %G en %U http://hdl.handle.net/1963/6566 %1 6517 %2 Mathematics %4 2 %# FIS/02 FISICA TEORICA, MODELLI E METODI MATEMATICI %$ Submitted by Luca Giomi (lgiomi@sissa.it) on 2013-04-04T08:03:17Z\nNo. of bitstreams: 1\n1303.4720v1.pdf: 2660135 bytes, checksum: 5fdf2d289b9b42a28ae3d000faee65fb (MD5) %0 Report %D 2013 %T On deformations of multidimensional Poisson brackets of hydrodynamic type %A Matteo Casati %K Hamiltonian operator %X 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. %I SISSA %G en %U http://hdl.handle.net/1963/7235 %1 7271 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Matteo Casati (mcasati@sissa.it) on 2013-12-09T15:48:14Z No. of bitstreams: 1 1312.1878v1.pdf: 416883 bytes, checksum: d561f4d57afd0607190ba24368e563ae (MD5) %] 1. Introduction 1.1 Poisson Vertex Algebras 1.2 Poisson brackets of hydrodynamic type and their deformations 2. Multidimensional Poisson Vertex Algebras 2.1 Formal map space 2.2 Poisson bivector and Poisson brackets 2.3 Poisson Vertex Algebras 2.4 Proof of Master formula 2.5 Cohomology of Poisson Vertex Algebras 3. Multidimensional Poisson brackets of hydrodynamic type 3.1 Deformation of Lie-Poisson bracket of hydrodynamic type 3.2 Proof of Theorem 5 4. Concluding remarks %0 Thesis %D 2013 %T On the desingularization of Kahler orbifolds with constant scalar curvature %A Riccardo Lena %I SISSA %G en %1 7263 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Riccardo Lena (lena@sissa.it) on 2013-12-03T10:06:16Z No. of bitstreams: 1 Lena - On the desingularization of Kahler orbifolds with constant scalar curvature.pdf: 1229721 bytes, checksum: 6e1cc67d3ba8db21345b068a638d4bf4 (MD5) %0 Journal Article %J Classical and Quantum Gravity. Volume 30, Issue 1, 7 January 2013, Article number 015006 %D 2013 %T Dirac operator on spinors and diffeomorphisms %A Ludwik Dabrowski %A Giacomo Dossena %K gravity %X The issue of general covariance of spinors and related objects is reconsidered. Given an oriented manifold $M$, to each spin structure $\sigma$ and Riemannian metric $g$ there is associated a space $S_{\sigma, g}$ of spinor fields on $M$ and a Hilbert space $\HH_{\sigma, g}= L^2(S_{\sigma, g},\vol{M}{g})$ of $L^2$-spinors of $S_{\sigma, g}$. The group $\diff{M}$ of orientation-preserving diffeomorphisms of $M$ acts both on $g$ (by pullback) and on $[\sigma]$ (by a suitably defined pullback $f^*\sigma$). Any $f\in \diff{M}$ lifts in exactly two ways to a unitary operator $U$ from $\HH_{\sigma, g} $ to $\HH_{f^*\sigma,f^*g}$. The canonically defined Dirac operator is shown to be equivariant with respect to the action of $U$, so in particular its spectrum is invariant under the diffeomorphisms. %B Classical and Quantum Gravity. Volume 30, Issue 1, 7 January 2013, Article number 015006 %I IOP Publishing %G en %U http://hdl.handle.net/1963/7377 %1 7425 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-06-17T13:30:17Z No. of bitstreams: 1 1209.2021v1.pdf: 201918 bytes, checksum: fe811643c070348a7dd399672ddad6f4 (MD5) %R 10.1088/0264-9381/30/1/015006 %0 Report %D 2013 %T Dislocation dynamics in crystals: a macroscopic theory in a fractional Laplace setting %A Serena Dipierro %A Giampiero Palatucci %A Enrico Valdinoci %K nonlocal Allen-Cahn equation %X We consider an evolution equation arising in the Peierls-Nabarro model for crystal dislocation. We study the evolution of such dislocation function and show that, at a macroscopic scale, the dislocations have the tendency to concentrate at single points of the crystal, where the size of the slip coincides with the natural periodicity of the medium. These dislocation points evolve according to the external stress and an interior repulsive potential. %I SISSA %G en %U http://hdl.handle.net/1963/7124 %1 7124 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Giampiero Palatucci (palatucc@sissa.it) on 2013-09-23T12:18:14Z No. of bitstreams: 1 Dipierro-Palatucci-Valdinoci.pdf: 651692 bytes, checksum: 839508f3ff7cdc4417c33991ebf3a9f3 (MD5) %0 Journal Article %J Bioinformatics (Oxford, England). 2012 Jan; 28(1):76-83 %D 2012 %T Decompositions of large-scale biological systems based on dynamical properties %A Nicola Soranzo %A Fahimeh Ramezani %A Giovanni Iacono %A Claudio Altafini %X 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. %B Bioinformatics (Oxford, England). 2012 Jan; 28(1):76-83 %I Oxford University Press %G en %U http://hdl.handle.net/1963/5226 %1 5049 %2 Physics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-01-16T15:13:23Z\\nNo. of bitstreams: 1\\nSoIaRaAl10.pdf: 185656 bytes, checksum: df5605453eb314d79ada4355b16ad3cd (MD5) %R 10.1093/bioinformatics/btr620 %0 Journal Article %J Phys. Rev. D 86 (2012) 124035 %D 2012 %T Deformed Lorentz symmetry and relative locality in a curved/expanding spacetime %A Giovanni Amelino-Camelia %A Antonino Marciano %A Marco Matassa %A Giacomo Rosati %K Doubly special relativity %X 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. %B Phys. Rev. D 86 (2012) 124035 %I American Physical Society %G en %1 6496 %2 Physics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-03-18T13:28:49Z\nNo. of bitstreams: 1\n1206.5315v1.pdf: 659285 bytes, checksum: 97c0ba29c809a911f9abb22708bae66c (MD5) %R 10.1103/PhysRevD.86.124035 %0 Journal Article %J Nucleic Acids Research, Volume 40, Issue 15, August 2012, Pages 7132-7149 %D 2012 %T Detection of transcriptional triggers in the dynamics of microbial growth: application to the respiratory-versatile bacterium Shewanella oneidensis %A Q Beg %A Mattia Zampieri %A N Klitgord %A S Collins %A M Serres %A Daniel Segrè %A Claudio Altafini %X The capacity of microorganisms to respond to variable external conditions requires a coordination of environment-sensing mechanisms and decisionmaking regulatory circuits. Here, we seek to understand the interplay between these two processes by combining high-throughput measurement of time-dependent mRNA profiles with a novel computational approach that searches for key genetic triggers of transcriptional changes. Our approach helped us understand the regulatory strategies of a respiratorily versatile bacterium with promising bioenergy and bioremediation applications, Shewanella oneidensis, in minimal and rich media. By comparing expression profiles across these two conditions, we unveiled components of the transcriptional program that depend mainly on the growth phase. Conversely, by integrating our time-dependent data with a previously available large compendium of static perturbation responses, we identified transcriptional changes that cannot be explained solely by internal network dynamics, but are rather triggered by specific genes acting as key mediators of an environment-dependent response. These transcriptional triggers include known and novel regulators that respond to carbon, nitrogen and oxygen limitation. Our analysis suggests a sequence of physiological responses, including a coupling between nitrogen depletion and glycogen storage, partially recapitulated through dynamic flux balance analysis, and experimentally confirmed by metabolite measurements. Our approach is broadly applicable to other systems %B Nucleic Acids Research, Volume 40, Issue 15, August 2012, Pages 7132-7149 %I SISSA %G en %U http://hdl.handle.net/1963/6506 %1 6452 %2 Mathematics %4 1 %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-02-27T15:39:07Z (GMT) No. of bitstreams: 0 %R 10.1093/nar/gks467 %0 Journal Article %J Biophysical Journal. Volume 102, Issue 12, 20 June 2012, Pages 2677-2686 %D 2012 %T A dynamical feedback model for adaptation in the olfactory transduction pathway %A Giovanna De Palo %A Anna Boccaccio %A Andrew Miri %A Anna Menini %A Claudio Altafini %X Olfactory transduction exhibits two distinct types of adaptation, which we denote multipulse and step adaptation. In terms of measured transduction current, multipulse adaptation appears as a decrease in the amplitude of the second of two consecutive responses when the olfactory neuron is stimulated with two brief pulses. Step adaptation occurs in response to a sustained steplike stimulation and is characterized by a return to a steady-state current amplitude close to the prestimulus value, after a transient peak. In this article, we formulate a dynamical model of the olfactory transduction pathway, which includes the kinetics of the CNG channels, the concentration of Ca ions flowing through them, and the Ca-complexes responsible for the regulation. Based on this model, a common dynamical explanation for the two types of adaptation is suggested. We show that both forms of adaptation can be well described using different time constants for the kinetics of Ca ions (faster) and the kinetics of the feedback mechanisms (slower). The model is validated on experimental data collected in voltage-clamp conditions using different techniques and animal species. %B Biophysical Journal. Volume 102, Issue 12, 20 June 2012, Pages 2677-2686 %I Biophysical Society, Elsevier %G en %U http://hdl.handle.net/1963/7019 %1 7012 %2 Neuroscience %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-08-12T10:21:18Z No. of bitstreams: 1 1-s2.0-S0006349512005140-main.pdf: 607871 bytes, checksum: b57c678e05477bb1551bc379bc674a88 (MD5) %R 10.1016/j.bpj.2012.04.040 %0 Journal Article %J PloS one. 2012 ; 7(6):e38135 %D 2012 %T Dynamics of opinion forming in structurally balanced social networks %A Claudio Altafini %X 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. %B PloS one. 2012 ; 7(6):e38135 %I PLoS %G en %U http://hdl.handle.net/1963/6051 %1 5942 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-08-01T07:37:37Z\\nNo. of bitstreams: 1\\njournal.pone.0038135.pdf: 460419 bytes, checksum: 94138ada3b8a6340ae8f7b5d3ec08c4e (MD5) %R 10.1371/journal.pone.0038135 %0 Report %D 2011 %T D-branes, surface operators, and ADHM quiver representations %A Ugo Bruzzo %A Duiliu-Emanuel Diaconescu %A M. Yardim %A G. Pan %A Yi Zhang %A Chuang Wu-yen %X A supersymmetric quantum mechanical model is constructed for BPS states bound to surface operators in five dimensional SU(r) gauge theories using D-brane engineering. This model represents the effective action of a certain D2-brane configuration, and is naturally obtained by dimensional reduction of a quiver $(0,2)$ gauged linear sigma model. In a special stability chamber, the resulting moduli space of quiver representations is shown to be smooth and isomorphic to a moduli space of framed quotients on the projective plane. A precise conjecture relating a K-theoretic partition function of this moduli space to refined open string invariants of toric lagrangian branes is formulated for conifold and local P^1 x P^1 geometries. %I SISSA %G en %U http://hdl.handle.net/1963/4133 %1 3873 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-15T08:27:03Z\\r\\nNo. of bitstreams: 1\\r\\n1012.1826v2.pdf: 536824 bytes, checksum: 38cd256a97e7244dc3eaac8073827cc2 (MD5) %0 Journal Article %J Communications on Pure and Applied Analysis %D 2011 %T A Decomposition Theorem for BV functions %A Stefano Bianchini %A Daniela Tonon %B Communications on Pure and Applied Analysis %I American Institute of Mathematical Sciences %V 10 %P 1549-1566 %G en_US %U http://hdl.handle.net/20.500.11767/14599 %N 6 %1 693 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-04-07T15:11:02Z\\r\\nNo. of bitstreams: 1\\r\\narticoloBV-preprint.pdf: 278021 bytes, checksum: db1d8f4c30a60313b69e105977010165 (MD5) %R 10.3934/cpaa.2011.10.1549 %0 Journal Article %J Journal of Differential Equations %D 2011 %T Degenerate KAM theory for partial differential equations %A Dario Bambusi %A Massimiliano Berti %A Elena Magistrelli %X 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. %B Journal of Differential Equations %V 250 %P 3379-3397 %G eng %R 10.1016/j.jde.2010.11.002 %0 Thesis %D 2011 %T Dimensional Reduction and Approximation of Measures and Weakly Differentiable Homeomorphisms %A Sara Daneri %X This thesis is devoted to the study of two different problems: the properties of the disintegration of the Lebesgue measure on the faces of a convex function and the existence of smooth approximations of bi-Lipschitz orientation-preserving homeomorphisms in the plane. %I SISSA %G en %U http://hdl.handle.net/1963/5348 %1 5178 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-02-02T16:17:40Z\\nNo. of bitstreams: 1\\nTesiPhDDaneriFinal.pdf: 1042283 bytes, checksum: be3ac0827af99c78eafc9395b4670544 (MD5) %0 Journal Article %J Journal of Differential Equations %D 2011 %T Double resonance with Landesman–Lazer conditions for planar systems of ordinary differential equations %A Alessandro Fonda %A Maurizio Garrione %K Double resonance %K Landesman–Lazer conditions %K Nonlinear planar systems %XWe prove the existence of periodic solutions for first order planar systems at resonance. The nonlinearity is indeed allowed to interact with two positively homogeneous Hamiltonians, both at resonance, and some kind of Landesman–Lazer conditions are assumed at both sides. We are thus able to obtain, as particular cases, the existence results proposed in the pioneering papers by Lazer and Leach (1969) [27], and by Frederickson and Lazer (1969) [18]. Our theorem also applies in the case of asymptotically piecewise linear systems, and in particular generalizes Fabry's results in Fabry (1995) [10], for scalar equations with double resonance with respect to the Dancer–Fučik spectrum.

%B Journal of Differential Equations %V 250 %P 1052 - 1082 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022039610002901 %R https://doi.org/10.1016/j.jde.2010.08.006 %0 Journal Article %J Comm. Math. Phys. %D 2010 %T The dependence on the monodromy data of the isomonodromic tau function %A Marco Bertola %B Comm. Math. Phys. %V 294 %P 539–579 %G eng %U http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00220-009-0961-7 %R 10.1007/s00220-009-0961-7 %0 Journal Article %J Comm. Math. Phys. 295 (2010) 731-790 %D 2010 %T Dirac Operators on Quantum Projective Spaces %A Francesco D'Andrea %A Ludwik Dabrowski %X We construct a family of self-adjoint operators D_N which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space CP_q(l), for any l>1 and 0We consider the disintegration of the Lebesgue measure on the graph of a convex function f:\\\\Rn-> \\\\R w.r.t. the partition into its faces, which are convex sets and therefore have a well defined linear dimension, and we prove that each conditional measure is equivalent to the k-dimensional Hausdorff measure of the k-dimensional face on which it is concentrated. The remarkable fact is that a priori the directions of the faces are just Borel and no Lipschitz regularity is known. Notwithstanding that, we also prove that a Green-Gauss formula for these directions holds on special sets. %B J. Funct. Anal. 258 (2010) 3604-3661 %G en_US %U http://hdl.handle.net/1963/3622 %1 682 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-04-24T15:53:31Z\\nNo. of bitstreams: 1\\ndisconvCaravDaneri.pdf: 759110 bytes, checksum: e22e069339fc07c3bde1855b76e61d1e (MD5) %R 10.1016/j.jfa.2010.01.024 %0 Journal Article %J Journal of Dynamical and Control Systems. Volume 16, Issue 2, April 2010, Pages :149-162 %D 2010 %T Dynamics control by a time-varying feedback %A Andrei A. Agrachev %A Marco Caponigro %K Discrete-time dynamics %X We consider a smooth bracket generating control-affine system in R^d and show that any orientation preserving diffeomorphism of R^d can be approximated, in the very strong sense, by a diffeomorphism included in the flow generated by a time-varying feedback control which is polynomial with respect to the state variables and trigonometric-polynomial with respect to the time variable. %B Journal of Dynamical and Control Systems. Volume 16, Issue 2, April 2010, Pages :149-162 %I SISSA %G en %U http://hdl.handle.net/1963/6461 %1 6407 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-02-06T09:37:23Z (GMT) No. of bitstreams: 0 %R 10.1007/s10883-010-9087-7 %0 Journal Article %J JHEP 06 (2009) 046 %D 2009 %T Decoupling A and B model in open string theory: topological adventures in the world of tadpoles %A Giulio Bonelli %A Andrea Prudenziati %A Alessandro Tanzini %A Yang Jie %X 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. %B JHEP 06 (2009) 046 %G en_US %U http://hdl.handle.net/1963/3632 %1 672 %2 Physics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-05-14T12:10:45Z\\nNo. of bitstreams: 1\\n0905.1286v1.pdf: 335944 bytes, checksum: fe5d3723cd904f1c7123c5bc83356013 (MD5) %R 10.1088/1126-6708/2009/06/046 %0 Journal Article %J Differential Geom. Appl. 27 (2009) 723-742 %D 2009 %T Differential geometry of curves in Lagrange Grassmannians with given Young diagram %A Igor Zelenko %A Li Chengbo %X Curves in Lagrange Grassmannians appear naturally in the intrinsic study of geometric structures on manifolds. By a smooth geometric structure on a manifold we mean any submanifold of its tangent bundle, transversal to the fibers. One can consider the time-optimal problem naturally associate with a geometric structure. The Pontryagin extremals of this optimal problem are integral curves of certain Hamiltonian system in the cotangent bundle. The dynamics of the fibers of the cotangent bundle w.r.t. this system along an extremal is described by certain curve in a Lagrange Grassmannian, called Jacobi curve of the extremal. Any symplectic invariant of the Jacobi curves produces the invariant of the original geometric structure. The basic characteristic of a curve in a Lagrange Grassmannian is its Young diagram. The number of boxes in its kth column is equal to the rank of the kth derivative of the curve (which is an appropriately defined linear mapping) at a generic point. We will describe the construction of the complete system of symplectic invariants for parameterized curves in a Lagrange Grassmannian with given Young diagram. It allows to develop in a unified way local differential geometry of very wide classes of geometric structures on manifolds, including both classical geometric structures such as Riemannian and Finslerian structures and less classical ones such as sub-Riemannian and sub-Finslerian structures, defined on nonholonomic distributions. %B Differential Geom. Appl. 27 (2009) 723-742 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3819 %1 508 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-01-18T16:06:20Z\\nNo. of bitstreams: 1\\n0708.1100v1.pdf: 330722 bytes, checksum: 31be09831ca0758a658e2fc9fe6a900f (MD5) %R 10.1016/j.difgeo.2009.07.002 %0 Journal Article %J Netw. Heterog. Media 4 (2009) 667-708 %D 2009 %T Discrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers %A Marco Cicalese %A Antonio DeSimone %A Caterina Ida Zeppieri %X In the framework of linear elasticity, we study the limit of a class of discrete free energies modeling strain-alignment-coupled systems by a rigorous coarse-graining procedure, as the number of molecules diverges. We focus on three paradigmatic examples: magnetostrictive solids, ferroelectric crystals and nematic elastomers, obtaining in the limit three continuum models consistent with those commonly employed in the current literature. We also derive the correspondent macroscopic energies in the presence of displacement boundary conditions and of various kinds of applied external fields. %B Netw. Heterog. Media 4 (2009) 667-708 %I American Institute of Mathematical Sciences %G en_US %U http://hdl.handle.net/1963/3788 %1 538 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-11-25T10:31:11Z\\nNo. of bitstreams: 1\\nCDSZ08.pdf: 390765 bytes, checksum: 2b3fcd3668352c286200e0a3b7e12c1a (MD5) %R 10.3934/nhm.2009.4.667 %0 Thesis %D 2009 %T The Disintegration Theorem and Applications to Optimal Mass Transportation %A Laura Caravenna %I SISSA %G en %U http://hdl.handle.net/1963/5900 %1 5750 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-06-08T09:44:06Z\\nNo. of bitstreams: 1\\nPhDThesisCaravenna.pdf: 1700326 bytes, checksum: 9638dd5ad25fc3e1fb91399b1b12c293 (MD5) %0 Journal Article %J Boll. Unione Mat. Ital. (9) 1 (2008) 497-505 %D 2008 %T Decomposition results for functions with bounded variation %A Gianni Dal Maso %A Rodica Toader %B Boll. Unione Mat. Ital. (9) 1 (2008) 497-505 %I Unione Matematica Italiana %G en_US %U http://hdl.handle.net/1963/3535 %1 729 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-23T10:23:36Z\\nNo. of bitstreams: 1\\nDM-Toa.pdf: 186814 bytes, checksum: bbc754f60013f0d8fd61b90a278ac837 (MD5) %0 Journal Article %J Bioinformatics 24 (2008) 1510-1515 %D 2008 %T Discerning static and causal interactions in genome-wide reverse engineering problems %A Mattia Zampieri %A Nicola Soranzo %A Claudio Altafini %X 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. %B Bioinformatics 24 (2008) 1510-1515 %G en_US %U http://hdl.handle.net/1963/2757 %1 1943 %2 Physics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-08-29T08:29:34Z\\nNo. of bitstreams: 1\\nZaSoAl08.pdf: 5513978 bytes, checksum: a0f45096ba7e82edddd03194f8623b1f (MD5) %R 10.1093/bioinformatics/btn220 %0 Report %D 2007 %T Derivation of a rod theory for phase-transforming materials %A Maria Giovanna Mora %A Stefan Müller %X 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. %B Calc. Var. Partial Differential Equations 28 (2007) 161-178 %G en_US %U http://hdl.handle.net/1963/1751 %1 2793 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-16T14:39:50Z\\nNo. of bitstreams: 1\\n21M.pdf: 23269 bytes, checksum: 46cdfa0d7b7b8d6710cc814108473dce (MD5) %R 10.1007/s00526-006-0039-8 %0 Journal Article %J J. Noncomm. Geom. 1 (2007) 213-239 %D 2007 %T Dirac operators on all Podles quantum spheres %A Francesco D'Andrea %A Ludwik Dabrowski %A Giovanni Landi %A Elmar Wagner %X We construct spectral triples on all Podles quantum spheres. These noncommutative geometries are equivariant for a left action of $U_q(su(2))$ and are regular, even and of metric dimension 2. They are all isospectral to the undeformed round geometry of the 2-sphere. There is also an equivariant real structure for which both the commutant property and the first order condition for the Dirac operators are valid up to infinitesimals of arbitrary order. %B J. Noncomm. Geom. 1 (2007) 213-239 %G en_US %U http://hdl.handle.net/1963/2177 %1 2067 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-04T09:28:47Z\\nNo. of bitstreams: 1\\n0606480v2.pdf: 249691 bytes, checksum: b7ae4969eee716046a815f5e66a249fb (MD5) %R 10.4171/JNCG/5 %0 Journal Article %J Arch. Ration. Mech. Anal. 181 (2006) 1-42 %D 2006 %T The Dirichlet problem for H-systems with small boundary data: blowup phenomena and nonexistence results %A Paolo Caldiroli %A Roberta Musina %B Arch. Ration. Mech. Anal. 181 (2006) 1-42 %G en_US %U http://hdl.handle.net/1963/2252 %1 1995 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-18T07:32:51Z\\nNo. of bitstreams: 1\\nCaldiroliMusina04.pdf: 395788 bytes, checksum: f37ad36b2fc2eb85d6430053a575ed8c (MD5) %R 10.1007/s00205-005-0398-x %0 Journal Article %J J. Phys. A 38 (2005) 4769-4781 %D 2005 %T Decay of a bound state under a time-periodic perturbation: a toy case %A Michele Correggi %A Gianfausto Dell'Antonio %X We study the time evolution of a three dimensional quantum particle, initially in a bound state, under the action of a time-periodic zero range interaction with ``strength\\\'\\\' (\\\\alpha(t)). Under very weak generic conditions on the Fourier coefficients of (\\\\alpha(t)), we prove complete ionization as (t \\\\to \\\\infty). We prove also that, under the same conditions, all the states of the system are scattering states. %B J. Phys. A 38 (2005) 4769-4781 %G en_US %U http://hdl.handle.net/1963/2298 %1 1718 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-25T08:22:58Z\\nNo. of bitstreams: 1\\n0408003v2.pdf: 207599 bytes, checksum: 256b29c96ea071184e9455fd1dd92717 (MD5) %R 10.1088/0305-4470/38/22/002 %0 Journal Article %J Commun. Math. Phys. 259 (2005) 729-759 %D 2005 %T The Dirac operator on SU_q(2) %A Ludwik Dabrowski %A Giovanni Landi %A Andrzej Sitarz %A Walter van Suijlekom %A Joseph C. Varilly %X We construct a 3^+ summable spectral triple (A(SU_q(2)),H,D) over the quantum group SU_q(2) which is equivariant with respect to a left and a right action of U_q(su(2)). The geometry is isospectral to the classical case since the spectrum of the operator D is the same as that of the usual Dirac operator on the 3-dimensional round sphere. The presence of an equivariant real structure J demands a modification in the axiomatic framework of spectral geometry, whereby the commutant and first-order properties need be satisfied only modulo infinitesimals of arbitrary high order. %B Commun. Math. Phys. 259 (2005) 729-759 %I Springer %G en %U http://hdl.handle.net/1963/4425 %1 4175 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-04T08:01:47Z No. of bitstreams: 1 math_0411609v2.pdf: 293099 bytes, checksum: cfa2846ded2ecf161e83f4269b65e9b2 (MD5) %R 10.1007/s00220-005-1383-9 %0 Journal Article %J Comm. Math. Phys. %D 2003 %T Differential systems for biorthogonal polynomials appearing in 2-matrix models and the associated Riemann-Hilbert problem %A Marco Bertola %A B. Eynard %A Harnad, J. %B Comm. Math. Phys. %V 243 %P 193–240 %G eng %0 Journal Article %J J. Math. Pures Appl. 82 (2003) 613-664 %D 2003 %T Drift in phase space: a new variational mechanism with optimal diffusion time %A Massimiliano Berti %A Luca Biasco %A Philippe Bolle %X We consider non-isochronous, nearly integrable, a-priori unstable Hamiltonian systems with a (trigonometric polynomial) $O(\\\\mu)$-perturbation which does not preserve the unperturbed tori. We prove the existence of Arnold diffusion with diffusion time $ T_d = O((1/ \\\\mu) \\\\log (1/ \\\\mu))$ by a variational method which does not require the existence of ``transition chains of tori\\\'\\\' provided by KAM theory. We also prove that our estimate of the diffusion time $T_d $ is optimal as a consequence of a general stability result derived from classical perturbation theory. %B J. Math. Pures Appl. 82 (2003) 613-664 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3020 %1 1313 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-02T15:07:59Z\\nNo. of bitstreams: 1\\n0205307v1.pdf: 505505 bytes, checksum: 2dab01ff574df56912b2fe8d3c56108a (MD5) %R 10.1016/S0021-7824(03)00032-1 %0 Journal Article %J Teoret. Mat. Fiz. %D 2003 %T The duality of spectral curves that arises in two-matrix models %A Marco Bertola %A B. Eynard %A Kharnad, Dzh. %B Teoret. Mat. Fiz. %V 134 %P 32–45 %G eng %0 Journal Article %J Comm. Math. Phys. %D 2002 %T Duality, biorthogonal polynomials and multi-matrix models %A Marco Bertola %A B. Eynard %A Harnad, J. %B Comm. Math. Phys. %V 229 %P 73–120 %G eng %0 Journal Article %J Proc. of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences 457 (2001): p. 2317-2335, OCT. 8, 2001 %D 2001 %T Dieletric breakdown: optimal bounds %A Adriana Garroni %A Vincenzo Nesi %A Marcello Ponsiglione %B Proc. of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences 457 (2001): p. 2317-2335, OCT. 8, 2001 %I SISSA Library %G en %U http://hdl.handle.net/1963/1569 %1 2549 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:17Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 2000 %0 Journal Article %J Noncommutative geometry and quantum groups (Warsaw 2001),49,Banach Center Publ., 61, Polish Acad.Sci., Warsaw,2003 %D 2001 %T Dirac operator on the standard Podles quantum sphere %A Ludwik Dabrowski %A Andrzej Sitarz %B Noncommutative geometry and quantum groups (Warsaw 2001),49,Banach Center Publ., 61, Polish Acad.Sci., Warsaw,2003 %I SISSA Library %G en %U http://hdl.handle.net/1963/1668 %1 2450 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T13:06:10Z (GMT). No. of bitstreams: 1\\nmath.QA0209048.pdf: 89749 bytes, checksum: e1bc2f04a36a957d4fb3131860296c18 (MD5)\\n Previous issue date: 2002 %0 Journal Article %J Nuclear Phys. B %D 2000 %T Decomposing quantum fields on branes %A Marco Bertola %A Bros, Jacques %A Gorini, Vittorio %A Moschella, Ugo %A Schaeffer, Richard %B Nuclear Phys. B %V 581 %P 575–603 %G eng %0 Journal Article %J Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei Mat. Appl., 2000, 11, 235 %D 2000 %T Diffusion time and splitting of separatrices for nearly integrable %A Massimiliano Berti %A Philippe Bolle %B Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei Mat. Appl., 2000, 11, 235 %I SISSA Library %G en %U http://hdl.handle.net/1963/1547 %1 2571 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:57Z (GMT). No. of bitstreams: 1\\nmath.DS0009176.pdf: 135686 bytes, checksum: 0da5be3a4a495a53dbf6cadb69d7cb2e (MD5)\\n Previous issue date: 2000 %0 Journal Article %J M2AN 33 (1999) 651-672 %D 1999 %T Discrete approximation of the Mumford-Shah functional in dimension two %A Antonin Chambolle %A Gianni Dal Maso %B M2AN 33 (1999) 651-672 %I EDP Sciences %G en_US %U http://hdl.handle.net/1963/3588 %1 712 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-03-09T13:50:04Z\\nNo. of bitstreams: 1\\nDalMaso1999.pdf: 462659 bytes, checksum: 04dc23ba4544d5be9ebdd703da477c7e (MD5) %R 10.1051/m2an:1999156 %0 Journal Article %J J. Differential Geometry Suppl.4 (1998) 181-211 %D 1998 %T Differential geometry of the space of orbits of a Coxeter group %A Boris Dubrovin %X Differential-geometric structures on the space of orbits of a finite Coxeter group, determined by Groth\\\\\\\'endieck residues, are calculated. This gives a construction of a 2D topological field theory for an arbitrary Coxeter group. %B J. Differential Geometry Suppl.4 (1998) 181-211 %I International Press %G en_US %U http://hdl.handle.net/1963/3562 %1 1140 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-03-03T18:46:23Z\\nNo. of bitstreams: 1\\n29-93-FM.pdf: 243594 bytes, checksum: 4ed9f8d24e959397f629a8e6b6c8114d (MD5) %0 Journal Article %J Annales Poincare Phys.Theor.69:413-424,1998 %D 1998 %T Diffusion of a particle in presence of N moving point sources %A Gianfausto Dell'Antonio %A Rodolfo Figari %A Alessandro Teta %B Annales Poincare Phys.Theor.69:413-424,1998 %I SISSA Library %G en %U http://hdl.handle.net/1963/134 %1 75 %2 LISNU %3 Interdisciplinary Laboratory for Advanced Studies %$ Made available in DSpace on 2004-09-01T12:22:22Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1996 %0 Journal Article %J SIAM J. Math. Anal. 29 (1998) 1481-1491 %D 1998 %T On the Dirichlet problem for vectorial Hamilton-Jacobi equations %A Sandro Zagatti %X 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. %B SIAM J. Math. Anal. 29 (1998) 1481-1491 %I SIAM %G en_US %U http://hdl.handle.net/1963/3512 %1 752 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-12T14:49:49Z\\nNo. of bitstreams: 1\\nzagatti.pdf: 317134 bytes, checksum: c87dbe5a12fbc58c5c2ca97bd0a72a7d (MD5) %R 10.1137/S0036141097321279 %0 Book Section %B Important developments in soliton theory / A. S. Fokas, V. E. Zakharov (eds.) - Berlin : Springer-Verlag, 1993. - pages : 86-98 %D 1993 %T Dispersion relations for non-linear waves and the Schottky problem %A Boris Dubrovin %X An approach to the Schottky problem of specification of periods of holomorphic differentials\\r\\non Riemann surfaces (or, equivalently, specification of Jacobians among all principaly\\r\\npolarized Abelian varieties) based on the theory of Kadomtsev - Petviashvili equation,\\r\\nis discussed. %B Important developments in soliton theory / A. S. Fokas, V. E. Zakharov (eds.) - Berlin : Springer-Verlag, 1993. - pages : 86-98 %I SISSA %@ 3540559132 %G en %U http://hdl.handle.net/1963/6480 %1 6430 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T15:31:24Z\\nNo. of bitstreams: 1\\ndubrovin_1993_schottky.pdf: 162204 bytes, checksum: a23db6fee2ea5f3db9c3a3562ae196f5 (MD5) %0 Report %D 1991 %T Differential geometry of moduli spaces and its applications to soliton equations and to topological conformal field theory %A Boris Dubrovin %X We construct flat Riemannian metrics on moduli spaces of algebraic curves with marked meromorphic function. This gives a new class of exact algebraic-geometry solutions to certain non-linear equations in terms of functions on the moduli spaces. We show that the Riemannian metrics on the moduli spaces coincide with two-point correlators in topological conformal field theory and calculate the partition function for A_n model for arbitrary genus. A universal method for constructing complete families of conservation laws for Whitham-type hierarchies of PDEs is also proposed. %B Preprint n.117, Scuola Normale Superiore, Pisa, November 1991, 31 pp. Published in: Surveys in Differential Geometry , Vol. IV (1999), p. 213 - 238. %I Scuola Normale Superiore di Pisa %G en %U http://hdl.handle.net/1963/6475 %1 6435 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T15:53:59Z\\nNo. of bitstreams: 1\\ndubrovin_1991_pisa.pdf: 53312802 bytes, checksum: d2f189e9a1439fd386fc50d3fa79b40b (MD5) %0 Journal Article %J Boll. Un. Mat. Ital. B (7) 2 (1988), no. 3, 641-656 %D 1988 %T On differential systems with vector-valued impulsive controls. %A Alberto Bressan %A Franco Rampazzo %B Boll. Un. Mat. Ital. B (7) 2 (1988), no. 3, 641-656 %I SISSA Library %G en %U http://hdl.handle.net/1963/535 %1 3369 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:34:05Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1987 %0 Journal Article %J Nonlinear anal. 10(1986), no.6, 603-613 %D 1986 %T Dirichlet problems for demicoercive functionals %A Gabriele Anzellotti %A Giuseppe Buttazzo %A Gianni Dal Maso %B Nonlinear anal. 10(1986), no.6, 603-613 %I SISSA Library %G en %U http://hdl.handle.net/1963/390 %1 3577 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:31:55Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1985 %R 10.1016/0362-546X(86)90145-8 %0 Journal Article %J Equadiff 82 (Wurzburg, 1982), 10--37, Lecture Notes in Math., 1017, Springer, Berlin, 1983 %D 1982 %T Differential equations with multiple solutions and nonlinear functional analysis %A Antonio Ambrosetti %B Equadiff 82 (Wurzburg, 1982), 10--37, Lecture Notes in Math., 1017, Springer, Berlin, 1983 %I SISSA Library %G en %U http://hdl.handle.net/1963/222 %1 3745 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:26:35Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1982