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.

10aAxiomatic Sobolev space10aCotangent module10aLocality of differentials1 aGigli, Nicola1 aPasqualetto, Enrico uhttp://www.sciencedirect.com/science/article/pii/S072308691830097500540nas a2200145 4500008004100000245007700041210006900118300001400187490000600201100002100207700002100228700002200249700001700271856010600288 2018 eng d00adeal2lkit: A toolkit library for high performance programming in deal.II0 adeal2lkit A toolkit library for high performance programming in a318–3270 v71 aSartori, Alberto1 aGiuliani, Nicola1 aBardelloni, Mauro1 aHeltai, Luca uhttps://www.math.sissa.it/publication/deal2lkit-toolkit-library-high-performance-programming-dealii-000702nas a2200253 4500008004100000245003700041210003000078100002200108700001800130700001700148700001800165700002100183700001900204700002200223700001800245700001700263700002300280700002400303700002000327700002400347700001700371700001700388856004300405 2018 eng d00aThe deal.II Library, Version 9.00 adealII Library Version 901 aAlzetta, Giovanni1 aArndt, Daniel1 aBangerth, W.1 aBoddu, Vishal1 aBrands, Benjamin1 aDavydov, Denis1 aGassmöller, Rene1 aHeister, Timo1 aHeltai, Luca1 aKormann, Katharina1 aKronbichler, Martin1 aMaier, Matthias1 aPelteret, Jean-Paul1 aTurcksin, B.1 aWells, David uhttps://doi.org/10.1515/jnma-2018-005400395nas a2200109 4500008004100000245004700041210004700088100001800135700002400153700002600177856008200203 2018 eng d00aDifferential of metric valued Sobolev maps0 aDifferential of metric valued Sobolev maps1 aGigli, Nicola1 aPasqualetto, Enrico1 aSoultanis, Elefterios uhttps://www.math.sissa.it/publication/differential-metric-valued-sobolev-maps00493nas a2200097 4500008004100000245012200041210006900163100001900232700001900251856012500270 2018 eng d00aDimension reduction for thin films with transversally varying prestrain: the oscillatory and the non-oscillatory case0 aDimension reduction for thin films with transversally varying pr1 aLewicka, Marta1 aLučić, Danka uhttps://www.math.sissa.it/publication/dimension-reduction-thin-films-transversally-varying-prestrain-oscillatory-and-non02307nas a2200169 4500008004100000245011900041210006900160260000800229300000700237490000600244520167500250100001901925700002501944700001701969700002101986856013002007 2018 eng d00aDimension reduction in heterogeneous parametric spaces with application to naval engineering shape design problems0 aDimension reduction in heterogeneous parametric spaces with appl cSep a250 v53 aWe 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.

1 aTezzele, Marco1 aSalmoiraghi, Filippo1 aMola, Andrea1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/dimension-reduction-heterogeneous-parametric-spaces-application-naval-engineering-shape00444nas a2200133 4500008004100000022001400041245008800055210006900143300001400212490000800226100001900234700002100253856003600274 2018 eng d a0564-616200aDiscriminant circle bundles over local models of Strebel graphs and Boutroux curves0 aDiscriminant circle bundles over local models of Strebel graphs a163–2070 v1971 aBertola, Marco1 aKorotkin, D., A. uhttps://doi.org/10.4213/tmf951300547nas a2200145 4500008004100000245013400041210006900175260004400244300001100288490000700299100001900306700002000325700001700345856003900362 2018 eng d00aA distributed lagrange formulation of the finite element immersed boundary method for fluids interacting with compressible solids0 adistributed lagrange formulation of the finite element immersed aChambSpringer International Publishing a1–210 v161 aBoffi, Daniele1 aGastaldi, Lucia1 aHeltai, Luca uhttps://arxiv.org/abs/1712.02545v100585nas a2200217 4500008004100000245003700041210003000078300001400108490000700122100001800129700001700147700001900164700001800183700001700201700002400218700002000242700002400262700001700286700001700303856004700320 2017 eng d00aThe deal.II Library, Version 8.50 adealII Library Version 85 a137–1450 v251 aArndt, Daniel1 aBangerth, W.1 aDavydov, Denis1 aHeister, Timo1 aHeltai, Luca1 aKronbichler, Martin1 aMaier, Matthias1 aPelteret, Jean-Paul1 aTurcksin, B.1 aWells, David uhttps://www.dealii.org/deal85-preprint.pdf00906nas a2200121 4500008004100000245009600041210006900137520045600206100002300662700002400685700002400709856005100733 2017 en d00aDerivation of a rod theory from lattice systems with interactions beyond nearest neighbours0 aDerivation of a rod theory from lattice systems with interaction3 aWe 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.1 aAlicandro, Roberto1 aLazzaroni, Giuliano1 aPalombaro, Mariapia uhttp://urania.sissa.it/xmlui/handle/1963/3526901132nas a2200109 4500008004100000245006100041210006000102520076300162100002000925700002900945856004800974 2017 en d00aDiscrete spectra for critical Dirac-Coulomb Hamiltonians0 aDiscrete spectra for critical DiracCoulomb Hamiltonians3 aThe 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.1 aGallone, Matteo1 aMichelangeli, Alessandro uhttp://preprints.sissa.it/handle/1963/3530001416nas a2200169 4500008004100000020002200041245008400063210007000147260004400217300001400261520082100275100002001096700002301116700002901139700002901168856004901197 2017 eng d a978-3-319-58904-600aDispersive Estimates for Schrödinger Operators with Point Interactions in ℝ30 aDispersive Estimates for Schrödinger Operators with Point Intera aChambSpringer International Publishing a187–1993 aThe 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 $q \geq 3$.

1 aIandoli, Felice1 aScandone, Raffaele1 aMichelangeli, Alessandro1 aDell'Antonio, Gianfausto uhttps://doi.org/10.1007/978-3-319-58904-6_1100494nas a2200181 4500008004100000245003700041210003000078300001100108490000600119100001700125700001800142700001700160700001700177700002400194700002000218700001700238856005700255 2016 eng d00aThe deal.II Library, Version 8.30 adealII Library Version 83 a1–110 v41 aBangerth, W.1 aHeister, Timo1 aHeltai, Luca1 aKanschat, G.1 aKronbichler, Martin1 aMaier, Matthias1 aTurcksin, B. uhttp://nbn-resolving.de/urn:nbn:de:bsz:16-ans-23122600573nas a2200205 4500008004100000245003700041210003000078300001400108490000700122100001700129700001900146700001800165700001700183700001700200700002400217700002000241700001700261700001700278856007200295 2016 eng d00aThe deal.II library, Version 8.40 adealII library Version 84 a135–1410 v241 aBangerth, W.1 aDavydov, Denis1 aHeister, Timo1 aHeltai, Luca1 aKanschat, G.1 aKronbichler, Martin1 aMaier, Matthias1 aTurcksin, B.1 aWells, David uhttps://www.math.clemson.edu/ heister/preprints/deal84-preprint.pdf01640nas a2200145 4500008004100000245007700041210006900118260001000187520116500197100002101362700002101383700002201404700001701426856005101443 2015 en d00aDeal2lkit: a Toolkit Library for High Performance Programming in deal.II0 aDeal2lkit a Toolkit Library for High Performance Programming in bSISSA3 aWe 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.1 aSartori, Alberto1 aGiuliani, Nicola1 aBardelloni, Mauro1 aHeltai, Luca uhttp://urania.sissa.it/xmlui/handle/1963/3500600596nas a2200181 4500008004100000245003700041210003000078520010700108100001700215700001800232700001700250700001700267700002400284700002000308700001700328700001800345856005100363 2015 en d00aThe deal.II Library, Version 8.20 adealII Library Version 823 aThis paper provides an overview of the new features of the finite element library deal.II version 8.21 aBangerth, W.1 aHeister, Timo1 aHeltai, Luca1 aKanschat, G.1 aKronbichler, Martin1 aMaier, Matthias1 aTurcksin, B.1 aYoung, T., D. uhttp://urania.sissa.it/xmlui/handle/1963/3446400709nas a2200133 4500008004100000245007500041210007000116260002100186300001200207490000700219520027900226100002000505856005000525 2015 eng d00aDecay of correlations for invertible maps with non-Hölder observables0 aDecay of correlations for invertible maps with nonHölder observa bTaylor & Francis a341-3520 v303 aAn 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.

1 aRuziboev, Marks uhttps://doi.org/10.1080/14689367.2015.104681600480nas a2200133 4500008004100000022001400041245011900055210006900174300001500243490000700258100001900265700002200284856004000306 2015 eng d a0022-248800aA degeneration of two-phase solutions of the focusing nonlinear Schrödinger equation via Riemann-Hilbert problems0 adegeneration of twophase solutions of the focusing nonlinear Sch a061507, 170 v561 aBertola, Marco1 aGiavedoni, Pietro uhttp://dx.doi.org/10.1063/1.492236201006nas a2200097 4500008004100000245007800041210006900119520059600188100001900784856010500803 2015 en d00aDispersive deformations of the Hamiltonian structure of Euler's equations0 aDispersive deformations of the Hamiltonian structure of Eulers e3 aEuler'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.1 aCasati, Matteo uhttps://www.math.sissa.it/publication/dispersive-deformations-hamiltonian-structure-eulers-equations01384nas a2200133 4500008004100000245008700041210006900128260001000197520092000207100002701127700002301154700002201177856005101199 2015 en d00aDynamics of screw dislocations: a generalised minimising-movements scheme approach0 aDynamics of screw dislocations a generalised minimisingmovements bSISSA3 aThe 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.1 aBonaschi, Giovanni, A.1 aVan Meurs, Patrick1 aMorandotti, Marco uhttp://urania.sissa.it/xmlui/handle/1963/3449500423nas a2200121 4500008004100000245005500041210005500096300000700151490001100158100001900169700002000188856009300208 2014 eng d00aDarboux Transformations and Random Point Processes0 aDarboux Transformations and Random Point Processes a560 vrnu1221 aBertola, Marco1 aCafasso, Mattia uhttps://www.math.sissa.it/publication/darboux-transformations-and-random-point-processes00403nas a2200109 4500008004100000245007400041210006900115260001000184653002700194100002200221856005000243 2014 en d00aThe decomposition of optimal transportation problems with convex cost0 adecomposition of optimal transportation problems with convex cos bSISSA10aOptimal Transportation1 aBardelloni, Mauro uhttp://urania.sissa.it/xmlui/handle/1963/747500387nas a2200109 4500008004300000245007400043210006900117260001000186100002300196700002200219856003600241 2014 en_Ud 00aThe decomposition of optimal transportation problems with convex cost0 adecomposition of optimal transportation problems with convex cos bSISSA1 aBianchini, Stefano1 aBardelloni, Mauro uhttp://hdl.handle.net/1963/743300921nas a2200109 4500008004100000245010000041210006900141260001300210520051500223100002200738856005100760 2014 en d00aA density result for GSBD and its application to the approximation of brittle fracture energies0 adensity result for GSBD and its application to the approximation bSpringer3 aWe 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).

1 aIurlano, Flaviana uhttp://urania.sissa.it/xmlui/handle/1963/3464701079nas a2200133 4500008004100000245006300041210006300104260003200167520063100199100002000830700002200850700002200872856005100894 2014 en d00aDirac operators on noncommutative principal circle bundles0 aDirac operators on noncommutative principal circle bundles bWorld Scientific Publishing3 aWe 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 → S2.1 aSitarz, Andrzej1 aZucca, Alessandro1 aDabrowski, Ludwik uhttp://urania.sissa.it/xmlui/handle/1963/3512500706nas a2200133 4500008004100000245004800041210004800089260001000137520032800147100002100475700002000496700002000516856003600536 2014 en d00aDirac reduction for Poisson vertex algebras0 aDirac reduction for Poisson vertex algebras bSISSA3 aWe 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.1 aDe Sole, Alberto1 aKac, Victor, G.1 aValeri, Daniele uhttp://hdl.handle.net/1963/698001213nas a2200145 4500008004100000245011200041210006900153260001300222520069800235653001900933100002200952700002000974700002200994856005101016 2014 en d00aDiscrete one-dimensional crawlers on viscous substrates: achievable net displacements and their energy cost0 aDiscrete onedimensional crawlers on viscous substrates achievabl bElsevier3 aWe 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.10aCell migration1 aNoselli, Giovanni1 aTatone, Amabile1 aDeSimone, Antonio uhttp://urania.sissa.it/xmlui/handle/1963/3444900376nas a2200097 4500008004100000245008700041210006900128100002000197700002500217856003600242 2014 eng d00aDislocations at the continuum scale: functional setting and variational properties0 aDislocations at the continuum scale functional setting and varia1 aScala, Riccardo1 aVan Goethem, Nicolas uhttp://cvgmt.sns.it/paper/2294/00943nas a2200121 4500008004100000245006300041210006200104520045300166653013100619100001600750700001900766856003600785 2014 en d00aDonagi–Markman cubic for the generalised Hitchin system0 aDonagi–Markman cubic for the generalised Hitchin system3 aDonagi 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.10aGeneralized Hitchin system, Donagi-Markman cubic, algebraically completely integrable systems, moduli space of Higgs G-bundles1 aBruzzo, Ugo1 aDalakov, Peter uhttp://hdl.handle.net/1963/725301107nas a2200121 4500008004300000245007000043210006800113260001000181520068600191100002900877700002900906856005000935 2014 en_Ud 00aDynamics on a graph as the limit of the dynamics on a "fat graph"0 aDynamics on a graph as the limit of the dynamics on a fat graph bSISSA3 aWe 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.1 aDell'Antonio, Gianfausto1 aMichelangeli, Alessandro uhttp://urania.sissa.it/xmlui/handle/1963/748500604nas a2200193 4500008004100000245003700041210003000078260001000108520010800118100001700226700001800243700001700261700001700278700002400295700002000319700001700339700001800356856003600374 2013 en d00aThe deal.II Library, Version 8.10 adealII Library Version 81 bSISSA3 aThis paper provides an overview of the new features of the finite element library deal.II version 8.0.1 aBangerth, W.1 aHeister, Timo1 aHeltai, Luca1 aKanschat, G.1 aKronbichler, Martin1 aMaier, Matthias1 aTurcksin, B.1 aYoung, T., D. uhttp://hdl.handle.net/1963/723601298nas a2200145 4500008004100000245006100041210006100102260001000163520087100173100001601044700002101060700001101081700002401092856003601116 2013 en d00aDefect annihilation and proliferation in active nematics0 aDefect annihilation and proliferation in active nematics bSISSA3 aLiquid 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.1 aGiomi, Luca1 aBowick, Mark, J.1 aMa, Xu1 aMarchetti, Cristina uhttp://hdl.handle.net/1963/656601138nas a2200121 4500008004100000245007900041210006900120260001000189520073700199653002500936100001900961856003600980 2013 en d00aOn deformations of multidimensional Poisson brackets of hydrodynamic type0 adeformations of multidimensional Poisson brackets of hydrodynami bSISSA3 aThe 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.10aHamiltonian operator1 aCasati, Matteo uhttp://hdl.handle.net/1963/723500420nas a2200097 4500008004100000245008000041210006900121260001000190100001900200856010300219 2013 en d00aOn the desingularization of Kahler orbifolds with constant scalar curvature0 adesingularization of Kahler orbifolds with constant scalar curva bSISSA1 aLena, Riccardo uhttps://www.math.sissa.it/publication/desingularization-kahler-orbifolds-constant-scalar-curvature01202nas a2200133 4500008004100000245005000041210005000091260001900141520081700160653001200977100002200989700002101011856003601032 2013 en d00aDirac operator on spinors and diffeomorphisms0 aDirac operator on spinors and diffeomorphisms bIOP Publishing3 aThe 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.10agravity1 aDabrowski, Ludwik1 aDossena, Giacomo uhttp://hdl.handle.net/1963/737700951nas a2200145 4500008004100000245009100041210006900132260001000201520045700211653003300668100002100701700002500722700002200747856003600769 2013 en d00aDislocation dynamics in crystals: a macroscopic theory in a fractional Laplace setting0 aDislocation dynamics in crystals a macroscopic theory in a fract bSISSA3 aWe 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.10anonlocal Allen-Cahn equation1 aDipierro, Serena1 aPalatucci, Giampiero1 aValdinoci, Enrico uhttp://hdl.handle.net/1963/712401414nas a2200145 4500008004100000245008300041210006900124260002800193520092600221100002001147700002201167700002101189700002201210856003601232 2012 en d00aDecompositions of large-scale biological systems based on dynamical properties0 aDecompositions of largescale biological systems based on dynamic bOxford University Press3 aMOTIVATION: 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.1 aSoranzo, Nicola1 aRamezani, Fahimeh1 aIacono, Giovanni1 aAltafini, Claudio uhttp://hdl.handle.net/1963/522602150nas a2200157 4500008004100000245008500041210006900126260003000195520152900225653003001754100003001784700002301814700001901837700002001856856011601876 2012 en d00aDeformed Lorentz symmetry and relative locality in a curved/expanding spacetime0 aDeformed Lorentz symmetry and relative locality in a curvedexpan bAmerican Physical Society3 aThe 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.10aDoubly special relativity1 aAmelino-Camelia, Giovanni1 aMarciano, Antonino1 aMatassa, Marco1 aRosati, Giacomo uhttps://www.math.sissa.it/publication/deformed-lorentz-symmetry-and-relative-locality-curvedexpanding-spacetime02153nas a2200181 4500008004100000245015200041210006900193260001000262520154500272100001101817700002101828700001601849700001501865700001401880700001901894700002201913856003601935 2012 en d00aDetection of transcriptional triggers in the dynamics of microbial growth: application to the respiratory-versatile bacterium Shewanella oneidensis0 aDetection of transcriptional triggers in the dynamics of microbi bSISSA3 aThe 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 systems1 aBeg, Q1 aZampieri, Mattia1 aKlitgord, N1 aCollins, S1 aSerres, M1 aSegrè, Daniel1 aAltafini, Claudio uhttp://hdl.handle.net/1963/650601693nas a2200157 4500008004100000245008400041210006900125260003400194520117300228100002201401700002001423700001701443700001701460700002201477856003601499 2012 en d00aA dynamical feedback model for adaptation in the olfactory transduction pathway0 adynamical feedback model for adaptation in the olfactory transdu bBiophysical Society, Elsevier3 aOlfactory 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.1 aDe Palo, Giovanna1 aBoccaccio, Anna1 aMiri, Andrew1 aMenini, Anna1 aAltafini, Claudio uhttp://hdl.handle.net/1963/701901344nas a2200109 4500008004100000245007300041210006900114260000900183520098400192100002201176856003601198 2012 en d00aDynamics of opinion forming in structurally balanced social networks0 aDynamics of opinion forming in structurally balanced social netw bPLoS3 aA 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.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/605101229nas a2200169 4500008004100000245006500041210006200106260001000168520073800178100001600916700003100932700001500963700001200978700001400990700001901004856003601023 2011 en d00aD-branes, surface operators, and ADHM quiver representations0 aDbranes surface operators and ADHM quiver representations bSISSA3 aA 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.1 aBruzzo, Ugo1 aDiaconescu, Duiliu-Emanuel1 aYardim, M.1 aPan, G.1 aZhang, Yi1 aWu-yen, Chuang uhttp://hdl.handle.net/1963/413300421nas a2200133 4500008004300000245004500043210004300088260004800131300001400179490000700193100002300200700001900223856004500242 2011 en_Ud 00aA Decomposition Theorem for BV functions0 aDecomposition Theorem for BV functions bAmerican Institute of Mathematical Sciences a1549-15660 v101 aBianchini, Stefano1 aTonon, Daniela uhttp://hdl.handle.net/20.500.11767/1459900919nas a2200157 4500008004100000022001300041245006100054210006100115300001400176490000800190520040200198100001900600700002400619700002300643856009500666 2011 eng d a0022039600aDegenerate KAM theory for partial differential equations0 aDegenerate KAM theory for partial differential equations a3379-33970 v2503 aThis 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.1 aBambusi, Dario1 aBerti, Massimiliano1 aMagistrelli, Elena uhttps://www.math.sissa.it/publication/degenerate-kam-theory-partial-differential-equations00653nas a2200109 4500008004100000245009700041210006900138260001000207520027300217100001700490856003600507 2011 en d00aDimensional Reduction and Approximation of Measures and Weakly Differentiable Homeomorphisms0 aDimensional Reduction and Approximation of Measures and Weakly D bSISSA3 aThis 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.1 aDaneri, Sara uhttp://hdl.handle.net/1963/534801344nas a2200181 4500008004100000022001400041245010900055210007100164300001600235490000800251520070400259653002100963653003300984653002901017100002201046700002301068856007101091 2011 eng d a0022-039600aDouble resonance with Landesman–Lazer conditions for planar systems of ordinary differential equations0 aDouble resonance with Landesman–Lazer conditions for planar syst a1052 - 10820 v2503 aWe 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.

10aDouble resonance10aLandesman–Lazer conditions10aNonlinear planar systems1 aFonda, Alessandro1 aGarrione, Maurizio uhttp://www.sciencedirect.com/science/article/pii/S002203961000290100433nas a2200121 4500008004100000022001400041245007500055210006900130300001400199490000800213100001900221856007100240 2010 eng d a0010-361600aThe dependence on the monodromy data of the isomonodromic tau function0 adependence on the monodromy data of the isomonodromic tau functi a539–5790 v2941 aBertola, Marco uhttp://0-dx.doi.org.mercury.concordia.ca/10.1007/s00220-009-0961-700681nas a2200109 4500008004300000245004900043210004900092520034800141100002400489700002200513856003600535 2010 en_Ud 00aDirac Operators on Quantum Projective Spaces0 aDirac Operators on Quantum Projective Spaces3 aWe 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.1 aCaravenna, Laura1 aDaneri, Sara uhttp://hdl.handle.net/1963/362200778nas a2200133 4500008004100000245004800041210004700089260001000136520038900146653002700535100002500562700002100587856003600608 2010 en d00aDynamics control by a time-varying feedback0 aDynamics control by a timevarying feedback bSISSA3 aWe 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.10aDiscrete-time dynamics1 aAgrachev, Andrei, A.1 aCaponigro, Marco uhttp://hdl.handle.net/1963/646101270nas a2200133 4500008004300000245010000043210006900143520080600212100002001018700002401038700002401062700001401086856003601100 2009 en_Ud 00aDecoupling A and B model in open string theory: topological adventures in the world of tadpoles0 aDecoupling A and B model in open string theory topological adven3 aIn 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.1 aBonelli, Giulio1 aPrudenziati, Andrea1 aTanzini, Alessandro1 aJie, Yang uhttp://hdl.handle.net/1963/363201885nas a2200121 4500008004300000245008700043210006900130260001300199520148100212100001801693700001601711856003601727 2009 en_Ud 00aDifferential geometry of curves in Lagrange Grassmannians with given Young diagram0 aDifferential geometry of curves in Lagrange Grassmannians with g bElsevier3 aCurves 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.1 aZelenko, Igor1 aChengbo, Li uhttp://hdl.handle.net/1963/381901141nas a2200133 4500008004300000245014200043210006900185260004800254520060000302100002000902700002200922700002700944856003600971 2009 en_Ud 00aDiscrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers0 aDiscretetocontinuum limits for strainalignmentcoupled systems Ma bAmerican Institute of Mathematical Sciences3 aIn 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.1 aCicalese, Marco1 aDeSimone, Antonio1 aZeppieri, Caterina Ida uhttp://hdl.handle.net/1963/378800354nas a2200097 4500008004100000245007900041210006900120260001000189100002100199856003600220 2009 en d00aThe Disintegration Theorem and Applications to Optimal Mass Transportation0 aDisintegration Theorem and Applications to Optimal Mass Transpor bSISSA1 aCaravenna, Laura uhttp://hdl.handle.net/1963/590000386nas a2200109 4500008004300000245006300043210006300106260003100169100002100200700001900221856003600240 2008 en_Ud 00aDecomposition results for functions with bounded variation0 aDecomposition results for functions with bounded variation bUnione Matematica Italiana1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/1963/353502210nas a2200121 4500008004300000245009000043210006900133520178700202100002101989700002002010700002202030856003602052 2008 en_Ud 00aDiscerning static and causal interactions in genome-wide reverse engineering problems0 aDiscerning static and causal interactions in genomewide reverse 3 aBackground. 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.1 aZampieri, Mattia1 aSoranzo, Nicola1 aAltafini, Claudio uhttp://hdl.handle.net/1963/275700907nas a2200109 4500008004300000245006400043210006300107520054600170100002500716700002000741856003600761 2007 en_Ud 00aDerivation of a rod theory for phase-transforming materials0 aDerivation of a rod theory for phasetransforming materials3 aA 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.1 aMora, Maria Giovanna1 aMüller, Stefan uhttp://hdl.handle.net/1963/175100855nas a2200133 4500008004300000245005000043210005000093520045800143100002400601700002200625700002000647700001800667856003600685 2007 en_Ud 00aDirac operators on all Podles quantum spheres0 aDirac operators on all Podles quantum spheres3 aWe 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.1 aD'Andrea, Francesco1 aDabrowski, Ludwik1 aLandi, Giovanni1 aWagner, Elmar uhttp://hdl.handle.net/1963/217700395nas a2200097 4500008004300000245010800043210006900151100002100220700002000241856003600261 2006 en_Ud 00aThe Dirichlet problem for H-systems with small boundary data: blowup phenomena and nonexistence results0 aDirichlet problem for Hsystems with small boundary data blowup p1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/225200818nas a2200109 4500008004300000245007400043210006900117520043500186100002200621700002900643856003600672 2005 en_Ud 00aDecay of a bound state under a time-periodic perturbation: a toy case0 aDecay of a bound state under a timeperiodic perturbation a toy c3 aWe 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.1 aCorreggi, Michele1 aDell'Antonio, Gianfausto uhttp://hdl.handle.net/1963/229801006nas a2200157 4500008004100000245003400041210002700075260001300102520058600115100002200701700002000723700002000743700002600763700002300789856003600812 2005 en d00aThe Dirac operator on SU_q(2)0 aDirac operator on SUq2 bSpringer3 aWe 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.1 aDabrowski, Ludwik1 aLandi, Giovanni1 aSitarz, Andrzej1 avan Suijlekom, Walter1 aVarilly, Joseph C. uhttp://hdl.handle.net/1963/442500596nas a2200145 4500008004100000022001400041245012600055210006900181300001400250490000800264100001900272700001500291700001500306856012900321 2003 eng d a0010-361600aDifferential systems for biorthogonal polynomials appearing in 2-matrix models and the associated Riemann-Hilbert problem0 aDifferential systems for biorthogonal polynomials appearing in 2 a193–2400 v2431 aBertola, Marco1 aEynard, B.1 aHarnad, J. uhttps://www.math.sissa.it/publication/differential-systems-biorthogonal-polynomials-appearing-2-matrix-models-and-associated01027nas a2200133 4500008004300000245008200043210006900125260001300194520058900207100002400796700001700820700002000837856003600857 2003 en_Ud 00aDrift in phase space: a new variational mechanism with optimal diffusion time0 aDrift in phase space a new variational mechanism with optimal di bElsevier3 aWe 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.1 aBerti, Massimiliano1 aBiasco, Luca1 aBolle, Philippe uhttp://hdl.handle.net/1963/302000495nas a2200145 4500008004100000022001400041245006800055210006300123300001200186490000800198100001900206700001500225700001800240856009100258 2003 eng d a0564-616200aThe duality of spectral curves that arises in two-matrix models0 aduality of spectral curves that arises in twomatrix models a32–450 v1341 aBertola, Marco1 aEynard, B.1 aKharnad, Dzh. uhttps://www.math.sissa.it/publication/duality-spectral-curves-arises-two-matrix-models00492nas a2200145 4500008004100000022001400041245006200055210006000117300001300177490000800190100001900198700001500217700001500232856009900247 2002 eng d a0010-361600aDuality, biorthogonal polynomials and multi-matrix models0 aDuality biorthogonal polynomials and multimatrix models a73–1200 v2291 aBertola, Marco1 aEynard, B.1 aHarnad, J. uhttps://www.math.sissa.it/publication/duality-biorthogonal-polynomials-and-multi-matrix-models00362nas a2200121 4500008004100000245004000041210003900081260001800120100002100138700001900159700002600178856003600204 2001 en d00aDieletric breakdown: optimal bounds0 aDieletric breakdown optimal bounds bSISSA Library1 aGarroni, Adriana1 aNesi, Vincenzo1 aPonsiglione, Marcello uhttp://hdl.handle.net/1963/156900361nas a2200109 4500008004100000245005700041210005700098260001800155100002200173700002000195856003600215 2001 en d00aDirac operator on the standard Podles quantum sphere0 aDirac operator on the standard Podles quantum sphere bSISSA Library1 aDabrowski, Ludwik1 aSitarz, Andrzej uhttp://hdl.handle.net/1963/166800505nas a2200169 4500008004100000022001400041245004100055210004100096300001400137490000800151100001900159700001800178700002100196700001900217700002300236856007600259 2000 eng d a0550-321300aDecomposing quantum fields on branes0 aDecomposing quantum fields on branes a575–6030 v5811 aBertola, Marco1 aBros, Jacques1 aGorini, Vittorio1 aMoschella, Ugo1 aSchaeffer, Richard uhttps://www.math.sissa.it/publication/decomposing-quantum-fields-branes00389nas a2200109 4500008004100000245007100041210006900112260001800181100002400199700002000223856003600243 2000 en d00aDiffusion time and splitting of separatrices for nearly integrable0 aDiffusion time and splitting of separatrices for nearly integrab bSISSA Library1 aBerti, Massimiliano1 aBolle, Philippe uhttp://hdl.handle.net/1963/154700394nas a2200109 4500008004300000245007500043210006900118260001700187100002300204700002100227856003600248 1999 en_Ud 00aDiscrete approximation of the Mumford-Shah functional in dimension two0 aDiscrete approximation of the MumfordShah functional in dimensio bEDP Sciences1 aChambolle, Antonin1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/358800609nas a2200109 4500008004300000245006800043210006800111260002400179520024000203100002000443856003600463 1998 en_Ud 00aDifferential geometry of the space of orbits of a Coxeter group0 aDifferential geometry of the space of orbits of a Coxeter group bInternational Press3 aDifferential-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.1 aDubrovin, Boris uhttp://hdl.handle.net/1963/356200418nas a2200121 4500008004100000245006600041210006600107260001800173100002900191700002000220700002100240856003500261 1998 en d00aDiffusion of a particle in presence of N moving point sources0 aDiffusion of a particle in presence of N moving point sources bSISSA Library1 aDell'Antonio, Gianfausto1 aFigari, Rodolfo1 aTeta, Alessandro uhttp://hdl.handle.net/1963/13400762nas a2200109 4500008004300000245006900043210006100112260000900173520041400182100002000596856003600616 1998 en_Ud 00aOn the Dirichlet problem for vectorial Hamilton-Jacobi equations0 aDirichlet problem for vectorial HamiltonJacobi equations bSIAM3 aWe 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.1 aZagatti, Sandro uhttp://hdl.handle.net/1963/351200684nas a2200121 4500008004100000020001500041245007100056210006900127260001000196520030000206100002000506856003600526 1993 en d a354055913200aDispersion relations for non-linear waves and the Schottky problem0 aDispersion relations for nonlinear waves and the Schottky proble bSISSA3 aAn 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.1 aDubrovin, Boris uhttp://hdl.handle.net/1963/648001022nas a2200109 4500008004100000245012700041210006900168260003700237520058200274100002000856856003600876 1991 en d00aDifferential geometry of moduli spaces and its applications to soliton equations and to topological conformal field theory0 aDifferential geometry of moduli spaces and its applications to s bScuola Normale Superiore di Pisa3 aWe 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.1 aDubrovin, Boris uhttp://hdl.handle.net/1963/647500375nas a2200109 4500008004100000245006700041210006200108260001800170100002100188700002100209856003500230 1988 en d00aOn differential systems with vector-valued impulsive controls.0 adifferential systems with vectorvalued impulsive controls bSISSA Library1 aBressan, Alberto1 aRampazzo, Franco uhttp://hdl.handle.net/1963/53500389nas a2200121 4500008004100000245005200041210005200093260001800145100002500163700002300188700002100211856003500232 1986 en d00aDirichlet problems for demicoercive functionals0 aDirichlet problems for demicoercive functionals bSISSA Library1 aAnzellotti, Gabriele1 aButtazzo, Giuseppe1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/39000370nas a2200097 4500008004100000245008500041210006900126260001800195100002400213856003500237 1982 en d00aDifferential equations with multiple solutions and nonlinear functional analysis0 aDifferential equations with multiple solutions and nonlinear fun bSISSA Library1 aAmbrosetti, Antonio uhttp://hdl.handle.net/1963/222