In the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples of the ROM application, in the naval field, can be found in [31, 24]. Mandatory ingredient for the ROM methods is the relation between the high-fidelity solutions and the parameters. Dealing with geometrical parameters, especially in the industrial context, this relation may be unknown and not trivial (simulations over hand morphed geometries) or very complex (high number of parameters or many nested morphing techniques). To overcome these scenarios, we propose in this contribution an efficient and complete data-driven framework involving ROM techniques for shape design and optimization, extending the pipeline presented in [7]. By applying the singular value decomposition (SVD) to the points coordinates defining the hull geometry –- assuming the topology is inaltered by the deformation –-, we are able to compute the optimal space which the deformed geometries belong to, hence using the modal coefficients as the new parameters we can reconstruct the parametric formulation of the domain. Finally the output of interest is approximated using the proper orthogonal decomposition with interpolation technique. To conclude, we apply this framework to a naval shape design problem where the bulbous bow is morphed to reduce the total resistance of the ship advancing in calm water.

1 aDemo, Nicola1 aTezzele, Marco1 aMola, Andrea1 aRozza, Gianluigi uhttp://www.math.sissa.it/publication/complete-data-driven-framework-efficient-solution-parametric-shape-design-and00883nas a2200109 4500008004100000245008200041210006900123260001000192520050500202100001800707856004800725 2019 en d00aA continuous dependence result for a dynamic debonding model in dimension one0 acontinuous dependence result for a dynamic debonding model in di bSISSA3 aIn this paper we address the problem of continuous dependence on initial and boundary data for a one-dimensional debonding model describing a thin ﬁlm peeled away from a substrate. The system underlying the process couples the weakly damped wave equation with a Griﬃth’s criterion which rules the evolution of the debonded region. We show that under general convergence assumptions on the data the corresponding solutions converge to the limit one with respect to diﬀerent natural topologies.1 aRiva, Filippo uhttp://preprints.sissa.it/handle/1963/3532902566nas a2200169 4500008004100000245009100041210006900132520193100201100001702132700001902149700002102168700002502189700001902214700002102233700002102254856012102275 2019 eng d00aEfficient Reduction in Shape Parameter Space Dimension for Ship Propeller Blade Design0 aEfficient Reduction in Shape Parameter Space Dimension for Ship 3 aIn this work, we present the results of a ship propeller design optimization campaign carried out in the framework of the research project PRELICA, funded by the Friuli Venezia Giulia regional government. The main idea of this work is to operate on a multidisciplinary level to identify propeller shapes that lead to reduced tip vortex-induced pressure and increased efficiency without altering the thrust. First, a specific tool for the bottom-up construction of parameterized propeller blade geometries has been developed. The algorithm proposed operates with a user defined number of arbitrary shaped or NACA airfoil sections, and employs arbitrary degree NURBS to represent the chord, pitch, skew and rake distribution as a function of the blade radial coordinate. The control points of such curves have been modified to generate, in a fully automated way, a family of blade geometries depending on as many as 20 shape parameters. Such geometries have then been used to carry out potential flow simulations with the Boundary Element Method based software PROCAL. Given the high number of parameters considered, such a preliminary stage allowed for a fast evaluation of the performance of several hundreds of shapes. In addition, the data obtained from the potential flow simulation allowed for the application of a parameter space reduction methodology based on active subspaces (AS) property, which suggested that the main propeller performance indices are, at a first but rather accurate approximation, only depending on a single parameter which is a linear combination of all the original geometric ones. AS analysis has also been used to carry out a constrained optimization exploiting response surface method in the reduced parameter space, and a sensitivity analysis based on such surrogate model. The few selected shapes were finally used to set up high fidelity RANS simulations and select an optimal shape.

1 aMola, Andrea1 aTezzele, Marco1 aGadalla, Mahmoud1 aValdenazzi, Federica1 aGrassi, Davide1 aPadovan, Roberta1 aRozza, Gianluigi uhttp://www.math.sissa.it/publication/efficient-reduction-shape-parameter-space-dimension-ship-propeller-blade-design02454nas a2200121 4500008004100000245014200041210006900183520189700252100001902149700001702168700002102185856012602206 2019 eng d00aShape optimization through proper orthogonal decomposition with interpolation and dynamic mode decomposition enhanced by active subspaces0 aShape optimization through proper orthogonal decomposition with 3 aWe propose a numerical pipeline for shape optimization in naval engineering involving two different non-intrusive reduced order method (ROM) techniques. Such methods are proper orthogonal decomposition with interpolation (PODI) and dynamic mode decomposition (DMD). The ROM proposed will be enhanced by active subspaces (AS) as a pre-processing tool that reduce the parameter space dimension and suggest better sampling of the input space. We will focus on geometrical parameters describing the perturbation of a reference bulbous bow through the free form deformation (FFD) technique. The ROM are based on a finite volume method (FV) to simulate the multi-phase incompressible flow around the deformed hulls. In previous works we studied the reduction of the parameter space in naval engineering through AS [38, 10] focusing on different parts of the hull. PODI and DMD have been employed for the study of fast and reliable shape optimization cycles on a bulbous bow in [9]. The novelty of this work is the simultaneous reduction of both the input parameter space and the output fields of interest. In particular AS will be trained computing the total drag resistance of a hull advancing in calm water and its gradients with respect to the input parameters. DMD will improve the performance of each simulation of the campaign using only few snapshots of the solution fields in order to predict the regime state of the system. Finally PODI will interpolate the coefficients of the POD decomposition of the output fields for a fast approximation of all the fields at new untried parameters given by the optimization algorithm. This will result in a non-intrusive data-driven numerical optimization pipeline completely independent with respect to the full order solver used and it can be easily incorporated into existing numerical pipelines, from the reference CAD to the optimal shape.

1 aTezzele, Marco1 aDemo, Nicola1 aRozza, Gianluigi uhttp://www.math.sissa.it/publication/shape-optimization-through-proper-orthogonal-decomposition-interpolation-and-dynamic01019nas a2200181 4500008004100000245008500041210006900126260000800195300002100203520034100224653004000565653003600605100002000641700001800661700002100679700002000700856011700720 2019 eng d00aStrong Novikov conjecture for low degree cohomology and exotic group C*-algebras0 aStrong Novikov conjecture for low degree cohomology and exotic g cMay aarXiv:1905.077303 aWe strengthen a result of Hanke–Schick about the strong Novikov conjecture for low degree cohomology by showing that their non-vanishing result for the maximal group $C^*$-algebra even holds for the reduced group $C^*$-algebra. To achieve this we provide a Fell absorption principle for certain exotic crossed product functors.

10aMathematics - K-Theory and Homology10aMathematics - Operator Algebras1 aAntonini, Paolo1 aBuss, Alcides1 aEngel, Alexander1 aSiebenand, Timo uhttp://www.math.sissa.it/publication/strong-novikov-conjecture-low-degree-cohomology-and-exotic-group-c-algebras00814nas a2200121 4500008004100000245006700041210006000108260001000168520042500178100002200603700001900625856004800644 2019 en d00aOn the topological degree of planar maps avoiding normal cones0 atopological degree of planar maps avoiding normal cones bSISSA3 aThe classical Poincaré–Bohl theorem provides the exis-tence of a zero for a function avoiding external rays. When the do-main is convex, the same holds true when avoiding normal cones. We consider here the possibility of dealing with nonconvex sets having in-ward corners or cusps, in which cases the normal cone vanishes. This allows us to deal with situations where the topological degree may be di˙erent from ±1.1 aFonda, Alessandro1 aKlun, Giuliano uhttp://preprints.sissa.it/handle/1963/3533000414nas a2200109 4500008004100000245010800041210006900149300001100218100002100229700001700250856003700267 2018 eng d00aAccelerating the iterative solution of convection-diffusion problems using singular value decomposition0 aAccelerating the iterative solution of convectiondiffusion probl a1–211 aPitton, Giuseppe1 aHeltai, Luca uhttps://arxiv.org/abs/1807.0946700578nas a2200145 4500008004100000245010500041210006900146300001600215490000700231100001500238700001600253700001700269700001800286856012800304 2018 eng d00aAn authenticated theoretical modeling of electrified fluid jet in core–shell nanofibers production0 aauthenticated theoretical modeling of electrified fluid jet in c a1791–18110 v471 aRafiei, S.1 aNoroozi, B.1 aHeltai, Luca1 aHaghi, A., K. uhttp://www.math.sissa.it/publication/authenticated-theoretical-modeling-electrified-fluid-jet-core%E2%80%93shell-nanofibers00653nas a2200181 4500008004100000245008300041210007100124653001000195653001000205653001000215653001000225653004000235653003600275100001700311700001500328700001800343856011000361 2018 eng d00aThe Baum–Connes conjecture localised at the unit element of a discrete group0 aBaum–Connes conjecture localised at the unit element of a discre10a19K3510a46L8010a46L8510a58J2210aMathematics - K-Theory and Homology10aMathematics - Operator Algebras1 aAntonini, P.1 aAzzali, S.1 aSkandalis, G. uhttp://www.math.sissa.it/publication/baum%E2%80%93connes-conjecture-localised-unit-element-discrete-group00682nas a2200121 4500008004100000245007400041210006600115260001000181520028100191100002100472700001900493856004800512 2018 en d00aOn the Cauchy problem for the wave equation on time-dependent domains0 aCauchy problem for the wave equation on timedependent domains bSISSA3 aWe introduce a notion of solution to the wave equation on a suitable class of time-dependent domains and compare it with a previous de nition. We prove an existence result for the solution of the Cauchy problem and present some additional conditions which imply uniqueness.1 aDal Maso, Gianni1 aToader, Rodica uhttp://preprints.sissa.it/handle/1963/3531400586nas a2200133 4500008004100000245010800041210006900149300001200218490000700230100002200237700002200259700002100281856015000302 2018 eng d00aCertified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models0 aCertified Reduced Basis Approximation for the Coupling of Viscou a197-2190 v741 aMartini, Immanuel1 aHaasdonk, Bernard1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85017156114&doi=10.1007%2fs10915-017-0430-y&partnerID=40&md5=023ef0bb95713f4442d1fa374c92a96401398nas a2200121 4500008004100000245014300041210006900184260001000253520092300263100002301186700001901209856004801228 2018 en d00aCharacteristic boundary layers for mixed hyperbolic systems in one space dimension and applications to the Navier-Stokes and MHD equations0 aCharacteristic boundary layers for mixed hyperbolic systems in o bSISSA3 aWe provide a detailed analysis of the boundary layers for mixed hyperbolic-parabolic systems in one space dimension and small amplitude regimes. As an application of our results, we describe the solution of the so-called boundary Riemann problem recovered as the zero viscosity limit of the physical viscous approximation. In particular, we tackle the so called doubly characteristic case, which is considerably more demanding from the technical viewpoint and occurs when the boundary is characteristic for both the mixed hyperbolic-parabolic system and for the hyperbolic system obtained by neglecting the second order terms. Our analysis applies in particular to the compressible Navier-Stokes and MHD equations in Eulerian coordinates, with both positive and null conductivity. In these cases, the doubly characteristic case occurs when the velocity is close to 0. The analysis extends to non-conservative systems.1 aBianchini, Stefano1 aSpinolo, Laura uhttp://preprints.sissa.it/handle/1963/3532500586nas a2200133 4500008004100000245012400041210006900165260001300234300001400247100001900261700002400280700002100304856012700325 2018 eng d00aCombined parameter and model reduction of cardiovascular problems by means of active subspaces and POD-Galerkin methods0 aCombined parameter and model reduction of cardiovascular problem bSpringer a185–2071 aTezzele, Marco1 aBallarin, Francesco1 aRozza, Gianluigi uhttp://www.math.sissa.it/publication/combined-parameter-and-model-reduction-cardiovascular-problems-means-active-subspaces01813nas a2200205 4500008004100000245005400041210005400095260001400149300000700163520117300170100002601343700001901369700002001388700002101408700002201429700002101451700002601472700002501498856008401523 2018 eng d00aComputational methods in cardiovascular mechanics0 aComputational methods in cardiovascular mechanics bCRC Press a543 aThe introduction of computational models in cardiovascular sciences has been progressively bringing new and unique tools for the investigation of the physiopathology. Together with the dramatic improvement of imaging and measuring devices on one side, and of computational architectures on the other one, mathematical and numerical models have provided a new, clearly noninvasive, approach for understanding not only basic mechanisms but also patient-specific conditions, and for supporting the design and the development of new therapeutic options. The terminology in silico is, nowadays, commonly accepted for indicating this new source of knowledge added to traditional in vitro and in vivo investigations. The advantages of in silico methodologies are basically the low cost in terms of infrastructures and facilities, the reduced invasiveness and, in general, the intrinsic predictive capabilities based on the use of mathematical models. The disadvantages are generally identified in the distance between the real cases and their virtual counterpart required by the conceptual modeling that can be detrimental for the reliability of numerical simulations.

1 aAuricchio, Ferdinando1 aConti, Michele1 aLefieux, Adrian1 aMorganti, Simone1 aReali, Alessandro1 aRozza, Gianluigi1 aVeneziani, Alessandro1 aLabrosse, Michel, F. uhttps://www.taylorfrancis.com/books/e/9781315280288/chapters/10.1201%2Fb21917-500773nas a2200097 4500008004100000245007100041210006000112520043500172100002000607856004800627 2018 en d00aOn the continuity of the trace operator in GSBV (Ω) and GSBD (Ω)0 acontinuity of the trace operator in GSBV Ω and GSBD Ω3 aIn this paper we present a new result of continuity for the trace operator acting on functions that might jump on a prescribed (n−1)-dimensional set Г, with the only hypothesis of being rectifiable and of finite measure. We also show an application of our result in relation to the variational model of elasticity with cracks, when the associated minimum problems are coupled with Dirichlet and Neumann boundary conditions.1 aTasso, Emanuele uhttp://preprints.sissa.it/handle/1963/3532400539nas a2200145 4500008004100000245007700041210006900118300001400187490000600201100002100207700002100228700002200249700001700271856010500288 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 uhttp://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-2018-005402306nas a2200169 4500008004100000245011900041210006900160260000800229300000700237490000600244520167500250100001901925700002501944700001701969700002101986856012902007 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 uhttp://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/1712.02545v101281nas a2200109 4500008004100000245007800041210006900119520088200188100002901070700002401099856004801123 2018 en d00aEffective non-linear spinor dynamics in a spin-1 Bose-Einstein condensate0 aEffective nonlinear spinor dynamics in a spin1 BoseEinstein cond3 aWe derive from first principles the experimentally observed effective dynamics of a spinor Bose gas initially prepared as a Bose–Einstein condensate and then left free to expand ballistically. In spinor condensates, which represent one of the recent frontiers in the manipulation of ultra-cold atoms, particles interact with a two-body spatial interaction and a spin–spin interaction. The effective dynamics is well-known to be governed by a system of coupled semi-linear Schrödinger equations: we recover this system, in the sense of marginals in the limit of infinitely many particles, with a mean-field re-scaling of the manybody Hamiltonian. When the resulting control of the dynamical persistence of condensation is quantified with the parameters of modern observations, we obtain a bound that remains quite accurate for the whole typical duration of the experiment.1 aMichelangeli, Alessandro1 aOlgiati, Alessandro uhttp://preprints.sissa.it/handle/1963/3531102869nas a2200241 4500008004100000022002200041245016200063210006900225260007400294520193000368653002102298653002802319653003102347653003202378653002602410653003002436653002602466100001702492700001902509700001702528700002102545856006102566 2018 eng d a978-1-880653-87-600aAn efficient shape parametrisation by free-form deformation enhanced by active subspace for hull hydrodynamic ship design problems in open source environment0 aefficient shape parametrisation by freeform deformation enhanced aSapporo, JapanbInternational Society of Offshore and Polar Engineers3 aIn this contribution, we present the results of the application of a parameter space reduction methodology based on active subspaces to the hull hydrodynamic design problem. Several parametric deformations of an initial hull shape are considered to assess the influence of the shape parameters considered on the hull total drag. The hull resistance is typically computed by means of numerical simulations of the hydrodynamic flow past the ship. Given the high number of parameters involved - which might result in a high number of time consuming hydrodynamic simulations - assessing whether the parameters space can be reduced would lead to considerable computational cost reduction. Thus, the main idea of this work is to employ the active subspaces to identify possible lower dimensional structures in the parameter space, or to verify the parameter distribution in the position of the control points. To this end, a fully automated procedure has been implemented to produce several small shape perturbations of an original hull CAD geometry which are then used to carry out high-fidelity flow simulations and collect data for the active subspaces analysis. To achieve full automation of the open source pipeline described, both the free form deformation methodology employed for the hull perturbations and the solver based on unsteady potential flow theory, with fully nonlinear free surface treatment, are directly interfaced with CAD data structures and operate using IGES vendor-neutral file formats as input files. The computational cost of the fluid dynamic simulations is further reduced through the application of dynamic mode decomposition to reconstruct the steady state total drag value given only few initial snapshots of the simulation. The active subspaces analysis is here applied to the geometry of the DTMB-5415 naval combatant hull, which is which is a common benchmark in ship hydrodynamics simulations.10aActive subspaces10aBoundary element method10aDynamic mode decomposition10aFluid structure interaction10aFree form deformation10aFully nonlinear potential10aNumerical towing tank1 aDemo, Nicola1 aTezzele, Marco1 aMola, Andrea1 aRozza, Gianluigi uhttps://www.onepetro.org/conference-paper/ISOPE-I-18-48100589nas a2200133 4500008004100000245012000041210006900161100001900230700001700249700002200266700002400288700002100312856012200333 2018 eng d00aThe Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: from Laminar to Turbulent Flows0 aEffort of Increasing Reynolds Number in ProjectionBased Reduced 1 aHijazi, Saddam1 aAli, Shafqat1 aStabile, Giovanni1 aBallarin, Francesco1 aRozza, Gianluigi uhttp://www.math.sissa.it/publication/effort-increasing-reynolds-number-projection-based-reduced-order-methods-laminar00754nas a2200121 4500008004100000245005600041210005500097520037100152100001900523700002200542700002000564856004800584 2018 en d00aEnergy-dissipation balance of a smooth moving crack0 aEnergydissipation balance of a smooth moving crack3 aIn this paper we provide necessary and sufficient conditions in order to guarantee the energy-dissipation balance of a Mode III crack, growing on a prescribed smooth path. Moreover, we characterize the singularity of the displacement near the crack tip, generalizing the result in [S. Nicaise, A.M. Sandig - J. Math. Anal. Appl., 2007] valid for straight fractures.1 aCaponi, Maicol1 aLucardesi, Ilaria1 aTasso, Emanuele uhttp://preprints.sissa.it/handle/1963/3532000939nas a2200109 4500008004100000245010200041210006900143520053000212100002100742700001800763856004800781 2018 en d00aExistence and uniqueness of dynamic evolutions for a one dimensional debonding model with damping0 aExistence and uniqueness of dynamic evolutions for a one dimensi3 aIn this paper we analyse a one-dimensional debonding model for a thin film peeled from a substrate when friction is taken into account. It is described by the weakly damped wave equation whose domain, the debonded region, grows according to a Griffth's criterion. Firstly we prove that the equation admits a unique solution when the evolution of the debonding front is assigned. Finally we provide an existence and uniqueness result for the coupled problem given by the wave equation together with Griffth's criterion.

1 aNardini, Lorenzo1 aRiva, Filippo uhttp://preprints.sissa.it/handle/1963/3531900762nas a2200121 4500008004100000245009200041210006900133520032400202100002100526700002600547700001900573856004800592 2018 en d00aExistence for elastodynamic Griffith fracture with a weak maximal dissipation condition0 aExistence for elastodynamic Griffith fracture with a weak maxima3 aWe consider a model of elastodynamics with fracture evolution, based on energy-dissipation balance and a maximal dissipation condition. We prove an existence result in the case of planar elasticity with a free crack path, where the maximal dissipation condition is satisfied among suitably regular competitor cracks.1 aDal Maso, Gianni1 aLarsen, Cristopher J.1 aToader, Rodica uhttp://preprints.sissa.it/handle/1963/3530800904nas a2200097 4500008004100000245010500041210006900146520052400215100001900739856004800758 2018 en d00aExistence of solutions to a phase field model of dynamic fracture with a crack dependent dissipation0 aExistence of solutions to a phase field model of dynamic fractur3 aWe propose a phase-field model of dynamic crack propagation based on the Ambrosio-Tortorelli approximation, which takes in account dissipative effects due to the speed of the crack tips. In particular, adapting the time discretization scheme contained in [Bourdin et al., Int. J. Fracture 168 (2011), 133-143] and [Larsen et al., Math. Models Methods Appl. Sci. 20 (2010), 1021-1048], we show the existence of a dynamic crack evolution satisfying an energy dissipation balance, according to Griffith's criterion.1 aCaponi, Maicol uhttp://preprints.sissa.it/handle/1963/3530700373nas a2200133 4500008004100000245003700041210003600078300000800114490000600122100001700128700001900145700002100164856005400185 2018 eng d00aEZyRB: Easy Reduced Basis method0 aEZyRB Easy Reduced Basis method a6610 v31 aDemo, Nicola1 aTezzele, Marco1 aRozza, Gianluigi uhttps://joss.theoj.org/papers/10.21105/joss.0066100462nas a2200109 4500008004100000245012400041210006900165260002300234100002200257700002100279856005200300 2018 eng d00aFinite volume POD-Galerkin stabilised reduced order methods for the parametrised incompressible Navier-Stokes equations0 aFinite volume PODGalerkin stabilised reduced order methods for t bElsevier {BV}cfeb1 aStabile, Giovanni1 aRozza, Gianluigi uhttps://doi.org/10.1016/j.compfluid.2018.01.03500956nas a2200133 4500008004100000245008600041210006900127260001000196520049500206100002900701700002100730700002300751856004800774 2018 en d00aFractional powers and singular perturbations of quantum differential Hamiltonians0 aFractional powers and singular perturbations of quantum differen bSISSA3 aWe consider the fractional powers of singular (point-like) perturbations of the Laplacian, and the singular perturbations of fractional powers of the Laplacian, and we compare such two constructions focusing on their perturbative structure for resolvents and on the local singularity structure of their domains. In application to the linear and non-linear Schrödinger equations for the corresponding operators we outline a programme of relevant questions that deserve being investigated.1 aMichelangeli, Alessandro1 aOttolini, Andrea1 aScandone, Raffaele uhttp://preprints.sissa.it/handle/1963/3530501596nas a2200169 4500008004100000245012200041210006900163260002100232300001200253490000700265520094600272100002501218700002201243700001801265700002101283856012201304 2018 eng d00aFree-form deformation, mesh morphing and reduced-order methods: enablers for efficient aerodynamic shape optimisation0 aFreeform deformation mesh morphing and reducedorder methods enab bTaylor & Francis a233-2470 v323 aIn this work, we provide an integrated pipeline for the model-order reduction of turbulent flows around parametrised geometries in aerodynamics. In particular, free-form deformation is applied for geometry parametrisation, whereas two different reduced-order models based on proper orthogonal decomposition (POD) are employed in order to speed-up the full-order simulations: the first method exploits POD with interpolation, while the second one is based on domain decomposition. For the sampling of the parameter space, we adopt a Greedy strategy coupled with Constrained Centroidal Voronoi Tessellations, in order to guarantee a good compromise between space exploration and exploitation. The proposed framework is tested on an industrially relevant application, i.e. the front-bumper morphing of the DrivAer car model, using the finite-volume method for the full-order resolution of the Reynolds-Averaged Navier–Stokes equations.

1 aSalmoiraghi, Filippo1 aScardigli, Angela1 aTelib, Haysam1 aRozza, Gianluigi uhttp://www.math.sissa.it/publication/free-form-deformation-mesh-morphing-and-reduced-order-methods-enablers-efficient00800nas a2200121 4500008004100000245006300041210005900104520039700163100002000560700002900580700002100609856004800630 2018 en d00aOn Geometric Quantum Confinement in Grushin-Like Manifolds0 aGeometric Quantum Confinement in GrushinLike Manifolds3 aWe study the problem of so-called geometric quantum confinement in a class of two-dimensional incomplete Riemannian manifold with metric of Grushin type. We employ a constant-fibre direct integral scheme, in combination with Weyl's analysis in each fibre, thus fully characterising the regimes of presence and absence of essential self-adjointness of the associated Laplace-Beltrami operator.1 aGallone, Matteo1 aMichelangeli, Alessandro1 aPozzoli, Eugenio uhttp://preprints.sissa.it/handle/1963/3532201241nas a2200121 4500008004100000245004900041210004900090520085800139100002900997700002101026700002401047856004801071 2018 en d00aGround state energy of mixture of Bose gases0 aGround state energy of mixture of Bose gases3 aWe consider the asymptotic behavior of a system of multi-component trapped bosons, when the total particle number N becomes large. In the dilute regime, when the interaction potentials have the length scale of order O(N-1), we show that the leading order of the ground state energy is captured correctly by the Gross-Pitaevskii energy functional and that the many-body ground state fully condensates on the Gross- Pitaevskii minimizers. In the mean-field regime, when the interaction length scale is O(1), we are able to verify Bogoliubov's approximation and obtain the second order expansion of the ground state energy. While such asymptotic results have several precursors in the literature on one-component condensates, the adaption to the multi-component setting is non-trivial in various respects and the analysis will be presented in details1 aMichelangeli, Alessandro1 aNam, Phan, Thanh1 aOlgiati, Alessandro uhttp://preprints.sissa.it/handle/1963/3531201340nas a2200109 4500008004100000245005100041210005100092520099000143100002001133700002901153856004801182 2018 en d00aHydrogenoid Spectra with Central Perturbations0 aHydrogenoid Spectra with Central Perturbations3 aThrough the Kreĭn-Višik-Birman extension scheme, unlike the previous classical analysis based on von Neumann's theory, we reproduce the construction and classification of all self-adjoint realisations of two intimately related models: the three-dimensional hydrogenoid-like Hamiltonians with singular perturbation supported at the centre (the nucleus), and the Schördinger operators on the halfline with Coulomb potentials centred at the origin. These two problems are technically equivalent, albeit sometimes treated by their own in the the literature. Based on such scheme, we then recover the formula to determine the eigenvalues of each self-adjoint extension, which are corrections to the non-relativistic hydrogenoid energy levels.We discuss in which respect the Kreĭn-Višik-Birman scheme is somehow more natural in yielding the typical boundary condition of self-adjointness at the centre of the perturbation and in identifying the eigenvalues of each extension.1 aGallone, Matteo1 aMichelangeli, Alessandro uhttp://preprints.sissa.it/handle/1963/3532100612nas a2200169 4500008004100000245015500041210006900196300001100265490000800276100002200284700002000306700002000326700002300346700001700369700001900386856003700405 2018 eng d00aIterative map-making with two-level preconditioning for polarized cosmic microwave background data sets. A worked example for ground-based experiments0 aIterative mapmaking with twolevel preconditioning for polarized a1–140 v6181 aPuglisi, Giuseppe1 aPoletti, Davide1 aFabbian, Giulio1 aBaccigalupi, Carlo1 aHeltai, Luca1 aStompor, Radek uhttps://arxiv.org/abs/1801.0893700840nas a2200133 4500008004100000245007200041210006800113260001000181520040400191100001600595700002900611700001800640856004800658 2018 en d00aOn Krylov solutions to infinite-dimensional inverse linear problems0 aKrylov solutions to infinitedimensional inverse linear problems bSISSA3 aWe discuss, in the context of inverse linear problems in Hilbert space, the notion of the associated infinite-dimensional Krylov subspace and we produce necessary and sufficient conditions for the Krylov-solvability of the considered inverse problem. The presentation is based on theoretical results together with a series of model examples, and it is corroborated by specific numerical experiments.1 aCaruso, Noe1 aMichelangeli, Alessandro1 aNovati, Paolo uhttp://preprints.sissa.it/handle/1963/3532701251nas a2200133 4500008004100000245006300041210006300104260001000167520083100177100002001008700002001028700002101048856004801069 2018 en d00aLocal moduli of semisimple Frobenius coalescent structures0 aLocal moduli of semisimple Frobenius coalescent structures bSISSA3 aThere is a conjectural relation, formulated by the second author, between the enumerative geometry of a wide class of smooth projective varieties and their derived category of coherent sheaves. In particular, there is an increasing interest for an explicit description of certain local invariants, called monodromy data, of semisimple quantum cohomologies in terms of characteristic classes of exceptional collections in the derived categories. Being intentioned to address this problem, which, to our opinion, is still not well understood, we have realized that some issues in the theory of Frobenius manifolds need to be preliminarily clarified, and that an extension of the theory itself is necessary, in view of the fact that quantum cohomologies of certain classes of homogeneous spaces may show a coalescence phenomenon.1 aCotti, Giordano1 aDubrovin, Boris1 aGuzzetti, Davide uhttp://preprints.sissa.it/handle/1963/3530400582nas a2200145 4500008004100000245008400041210006900125653003700194100002100231700001300252700002100265700002100286700001900307856011000326 2018 eng d00aA Localized Reduced-Order Modeling Approach for PDEs with Bifurcating Solutions0 aLocalized ReducedOrder Modeling Approach for PDEs with Bifurcati10aMathematics - Numerical Analysis1 aHess, Martin, W.1 aAlla, A.1 aQuaini, Annalisa1 aRozza, Gianluigi1 aGunzburger, M. uhttp://www.math.sissa.it/publication/localized-reduced-order-modeling-approach-pdes-bifurcating-solutions00694nas a2200121 4500008004100000245007500041210006900116260001000185520028900195100002100484700001900505856004800524 2018 en d00aA minimization approach to the wave equation on time-dependent domains0 aminimization approach to the wave equation on timedependent doma bSISSA3 aWe prove the existence of weak solutions to the homogeneous wave equation on a suitable class of time-dependent domains. Using the approach suggested by De Giorgi and developed by Serra and Tilli, such solutions are approximated by minimizers of suitable functionals in space-time.1 aDal Maso, Gianni1 aDe Luca, Lucia uhttp://preprints.sissa.it/handle/1963/3531801777nas a2200157 4500008004100000245013300041210006900174260003000243520120300273100001901476700001701495700002101512700001701533700002101550856004801571 2018 eng d00aModel Order Reduction by means of Active Subspaces and Dynamic Mode Decomposition for Parametric Hull Shape Design Hydrodynamics0 aModel Order Reduction by means of Active Subspaces and Dynamic M aTrieste, ItalybIOS Press3 aWe present the results of the application of a parameter space reduction methodology based on active subspaces (AS) to the hull hydrodynamic design problem. Several parametric deformations of an initial hull shape are considered to assess the influence of the shape parameters on the hull wave resistance. Such problem is relevant at the preliminary stages of the ship design, when several flow simulations are carried out by the engineers to establish a certain sensibility with respect to the parameters, which might result in a high number of time consuming hydrodynamic simulations. The main idea of this work is to employ the AS to identify possible lower dimensional structures in the parameter space. The complete pipeline involves the use of free form deformation to parametrize and deform the hull shape, the full order solver based on unsteady potential flow theory with fully nonlinear free surface treatment directly interfaced with CAD, the use of dynamic mode decomposition to reconstruct the final steady state given only few snapshots of the simulation, and the reduction of the parameter space by AS, and shared subspace. Response surface method is used to minimize the total drag.1 aTezzele, Marco1 aDemo, Nicola1 aGadalla, Mahmoud1 aMola, Andrea1 aRozza, Gianluigi uhttp://ebooks.iospress.nl/publication/4927000512nas a2200145 4500008004100000245011100041210006900152300001600221490000700237100002200244700002400266700001600290700002100306856003900327 2018 eng d00aModel Reduction for Parametrized Optimal Control Problems in Environmental Marine Sciences and Engineering0 aModel Reduction for Parametrized Optimal Control Problems in Env aB1055-B10790 v401 aStrazzullo, Maria1 aBallarin, Francesco1 aMosetti, R.1 aRozza, Gianluigi uhttps://doi.org/10.1137/17M115059100448nas a2200109 4500008004100000245006800041210006800109100001900177700002000196700001600216856010600232 2018 eng d00aNoncommutative Painlevé Equations and Systems of Calogero Type0 aNoncommutative Painlevé Equations and Systems of Calogero Type1 aBertola, Marco1 aCafasso, Mattia1 aRubtsov, V. uhttp://www.math.sissa.it/publication/noncommutative-painlev%C3%A9-equations-and-systems-calogero-type00730nas a2200109 4500008004100000245008900041210006900130520032300199100002900522700002100551856004800572 2018 en d00aNon-linear Gross-Pitaevskii dynamics of a 2D binary condensate: a numerical analysis0 aNonlinear GrossPitaevskii dynamics of a 2D binary condensate a n3 aWe present a numerical study of the two-dimensional Gross-Pitaevskii systems in a wide range of relevant regimes of population ratios and intra-species and inter-species interactions. Our numerical method is based on a Fourier collocation scheme in space combined with a fourth order integrating factor scheme in time.1 aMichelangeli, Alessandro1 aPitton, Giuseppe uhttp://preprints.sissa.it/handle/1963/3532300508nas a2200145 4500008004100000245008900041210006900130260002300199300001400222490000800236100002200244700002600266700001900292856005100311 2018 eng d00aA novel reduced order model for vortex induced vibrations of long flexible cylinders0 anovel reduced order model for vortex induced vibrations of long bElsevier {BV}cmay a191–2070 v1561 aStabile, Giovanni1 aMatthies, Hermann, G.1 aBorri, Claudio uhttps://doi.org/10.1016/j.oceaneng.2018.02.06400437nas a2200121 4500008004100000245010800041210006900149300001400218490000800232100002100240700001700261856003700278 2018 eng d00aNURBS-SEM: A hybrid spectral element method on NURBS maps for the solution of elliptic PDEs on surfaces0 aNURBSSEM A hybrid spectral element method on NURBS maps for the a440–4620 v3381 aPitton, Giuseppe1 aHeltai, Luca uhttps://arxiv.org/abs/1804.0827102225nas a2200253 4500008004100000022001400041245007200055210006900127260001200196490000600208520146100214653002201675653002201697653002501719653002101744653001701765653001601782653002001798653001801818100002501836700002301861700002201884856006501906 2018 eng d a2296-914400aPeristaltic Waves as Optimal Gaits in Metameric Bio-Inspired Robots0 aPeristaltic Waves as Optimal Gaits in Metameric BioInspired Robo c09/20180 v53 a*Peristalsis*, i.e., a motion pattern arising from the propagation of muscle contraction and expansion waves along the body, is a common locomotion strategy for limbless animals. Mimicking peristalsis in bio-inspired robots has attracted considerable attention in the literature. It has recently been observed that maximal velocity in a metameric earthworm-like robot is achieved by actuating the segments using a “phase coordination” principle. This paper shows that, in fact, peristalsis (which requires not only phase coordination, but also that all segments oscillate at same frequency and amplitude) emerges from optimization principles. More precisely, basing our analysis on the assumption of small deformations, we show that peristaltic waves provide the optimal actuation solution in the ideal case of a periodic infinite system, and that this is approximately true, modulo edge effects, for the real, finite length system. Therefore, this paper confirms the effectiveness of mimicking peristalsis in bio-inspired robots, at least in the small-deformation regime. Further research will be required to test the effectiveness of this strategy if large deformations are allowed.

Motivated by a debonding model for a thin film peeled from a substrate, we analyse the one-dimensional wave equation, in a time-dependent domain which is degenerate at the initial time. In the first part of the paper we prove existence for the wave equation when the evolution of the domain is given; in the second part of the paper, the evolution of the domain is unknown and is governed by an energy criterion coupled with the wave equation. Our existence result for such coupled problem is a contribution to the study of crack initiation in dynamic fracture.

1 aLazzaroni, Giuliano1 aNardini, Lorenzo uhttp://preprints.sissa.it/handle/1963/3530201821nas a2200181 4500008004100000024003700041245012000078210006900198520118600267653002301453653002601476100002201502700001901524700002101543700001701564700002101581856003701602 2017 eng d ahttps://arxiv.org/abs/1701.0342400aAdvances in Reduced order modelling for CFD: vortex shedding around a circular cylinder using a POD-Galerkin method0 aAdvances in Reduced order modelling for CFD vortex shedding arou3 aVortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. In this work a Reduced Order Model (ROM) of the incompressible flow around a circular cylinder, built performing a Galerkin projection of the governing equations onto a lower dimensional space is presented. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pressure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) for this purpose the projection of the Governing equations (momentum equation and Poisson equation for pressure) is performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework are presented. The accuracy of the reduced order model is assessed against full order results.

10afinite volume, CFD10aReduced order methods1 aStabile, Giovanni1 aHijazi, Saddam1 aLorenzi, Stefano1 aMola, Andrea1 aRozza, Gianluigi uhttps://arxiv.org/abs/1701.0342402169nas a2200109 4500008004100000245012900041210006900170520172600239100002401965700002201989856004802011 2017 en d00aAlmost global existence of solutions for capillarity-gravity water waves equations with periodic spatial boundary conditions0 aAlmost global existence of solutions for capillaritygravity wate3 aThe goal of this monograph is to prove that any solution of the Cauchy problem for the capillarity-gravity water waves equations, in one space dimension, with periodic, even in space, initial data of small size ϵ, is almost globally defined in time on Sobolev spaces, i.e. it exists on a time interval of length of magnitude ϵ−N for any N, as soon as the initial data are smooth enough, and the gravity-capillarity parameters are taken outside an exceptional subset of zero measure. In contrast to the many results known for these equations on the real line, with decaying Cauchy data, one cannot make use of dispersive properties of the linear flow. Instead, our method is based on a normal forms procedure, in order to eliminate those contributions to the Sobolev energy that are of lower degree of homogeneity in the solution. Since the water waves equations are a quasi-linear system, usual normal forms approaches would face the well known problem of losses of derivatives in the unbounded transformations. In this monograph, to overcome such a difficulty, after a paralinearization of the capillarity-gravity water waves equations, necessary to obtain energy estimates, and thus local existence of the solutions, we first perform several paradifferential reductions of the equations to obtain a diagonal system with constant coefficients symbols, up to smoothing remainders. Then we may start with a normal form procedure where the small divisors are compensated by the previous paradifferential regularization.The reversible structure of the water waves equations, and the fact that we look for solutions even in x, guarantees a key cancellation which prevents the growth of the Sobolev norms of the solutions.1 aBerti, Massimiliano1 aDelort, Jean-Marc uhttp://preprints.sissa.it/handle/1963/3528501010nas a2200109 4500008004100000245007000041210006900111520062700180100002400807700002100831856004800852 2017 en d00aAnalysis of a dynamic peeling test with speed-dependent toughness0 aAnalysis of a dynamic peeling test with speeddependent toughness3 aWe analyse a one-dimensional model of dynamic debonding for a thin film, where the local toughness of the glue between the film and the substrate also depends on the debonding speed. The wave equation on the debonded region is strongly coupled with Griffth's criterion for the evolution of the debonding front. We provide an existence and uniqueness result and find explicitly the solution in some concrete examples. We study the limit of solutions as inertia tends to zero, observing phases of unstable propagation, as well as time discontinuities, even though the toughness diverges at a limiting debonding speed.

1 aLazzaroni, Giuliano1 aNardini, Lorenzo uhttp://preprints.sissa.it/handle/1963/3529201211nas a2200109 4500008004100000245010500041210006900146520071800215100002100933700002100954856012600975 2017 eng d00aOn the Application of Reduced Basis Methods to Bifurcation Problems in Incompressible Fluid Dynamics0 aApplication of Reduced Basis Methods to Bifurcation Problems in 3 aIn this paper we apply a reduced basis framework for the computation of flow bifurcation (and stability) problems in fluid dynamics. The proposed method aims at reducing the complexity and the computational time required for the construction of bifurcation and stability diagrams. The method is quite general since it can in principle be specialized to a wide class of nonlinear problems, but in this work we focus on an application in incompressible fluid dynamics at low Reynolds numbers. The validation of the reduced order model with the full order computation for a benchmark cavity flow problem is promising.

1 aPitton, Giuseppe1 aRozza, Gianluigi uhttp://www.math.sissa.it/publication/application-reduced-basis-methods-bifurcation-problems-incompressible-fluid-dynamics02453nas a2200169 4500008004100000020002200041024003400063245010200097210006900199250004300268260002500311490000900336520177800345100001802123700002102141856012102162 2017 eng d a978-3-319-65869-8 aDOI 10.1007/978-3-319-65870-400aCertified Reduced Basis Method for Affinely Parametric Isogeometric Analysis NURBS Approximation0 aCerti fied Reduced Basis Method for Affinely Parametric Isogeome aBittencourt, Dumont, Hesthaven. (Eds). aHeildebergbSpringer0 v 1193 aIn this work we apply reduced basis methods for parametric PDEs to an isogeometric formulation based on

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

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

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

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

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

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

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

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

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

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

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

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

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

1 aDevaud, Denis1 aRozza, Gianluigi uhttp://www.math.sissa.it/publication/certi-fied-reduced-basis-method-affinely-parametric-isogeometric-analysis-nurbs00579nas a2200157 4500008004100000245006200041210005700103300001400160490000700174100001800181700001700199700001700216700002400233700002100257856014300278 2017 eng d00aOn a certified smagorinsky reduced basis turbulence model0 acertified smagorinsky reduced basis turbulence model a3047-30670 v551 aRebollo, T.C.1 aÁvila, E.D.1 aMarmol, M.G.1 aBallarin, Francesco1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85039928218&doi=10.1137%2f17M1118233&partnerID=40&md5=221d9cd2bcc74121fcef93efd9d3d76c01282nas a2200133 4500008004100000245004800041210004800089520088200137100002001019700002301039700001801062700001701080856005101097 2017 en d00aComplex Friedrichs systems and applications0 aComplex Friedrichs systems and applications3 aWe provide a suitable extension of the theory of abstract Friedrichs systems from real Hilbert spaces to the complex Hilbert space setting, which allows for applications to partial differential equations with complex coeffcients. We also provide examples where the involved Hilbert space is not the space of square integrable functions, as it was the case in previous works, but rather its closed subspace or the space Hs(Rd;Cr), for real s. This setting appears to be suitable for particular systems of partial differential equations, such as the Dirac system, the Dirac-Klein-Gordon system, the Dirac-Maxwell system, and the time-harmonic Maxwell system, which are all addressed in the paper. Moreover, for the time-harmonic Maxwell system we also applied a suitable version of the two-field theory with partial coercivity assumption which is developed in the paper.1 aAntonić, Nenad1 aBurazin, Krešimir1 aCrnjac, Ivana1 aErceg, Marko uhttp://urania.sissa.it/xmlui/handle/1963/3527002412nas a2200205 4500008004100000245015800041210006900199260001200268300000800280490000800288520159500296653004301891653002501934653002301959653003401982100002102016700002102037700002102058856012702079 2017 eng d00aComputational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: Applications to Coanda effect in cardiology0 aComputational reduction strategies for the detection of steady b c09/2017 a5570 v3443 aWe focus on reducing the computational costs associated with the hydrodynamic stability of solutions of the incompressible Navier–Stokes equations for a Newtonian and viscous fluid in contraction–expansion channels. In particular, we are interested in studying steady bifurcations, occurring when non-unique stable solutions appear as physical and/or geometric control parameters are varied. The formulation of the stability problem requires solving an eigenvalue problem for a partial differential operator. An alternative to this approach is the direct simulation of the flow to characterize the asymptotic behavior of the solution. Both approaches can be extremely expensive in terms of computational time. We propose to apply Reduced Order Modeling (ROM) techniques to reduce the demanding computational costs associated with the detection of a type of steady bifurcations in fluid dynamics. The application that motivated the present study is the onset of asymmetries (i.e., symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the regurgitant mitral valve orifice shape.

We present a novel quasi-Newton continuation procedure that efficiently solves the system of nonlinear equations arising from the discretization of a phase field model for wetting phenomena. We perform a comparative numerical analysis that shows the improved speed of convergence gained with respect to other numerical schemes. Moreover, we discuss the conditions that, on a theoretical level, guarantee the convergence of this method. At each iterative step, a suitable continuation procedure develops and passes to the nonlinear solver an accurate initial guess. Discretization performs through cell-centered finite differences. The resulting system of equations is solved on a composite grid that uses dynamic mesh refinement and multi-grid techniques. The final code achieves three-dimensional, realistic computer experiments comparable to those produced in laboratory settings. This code offers not only new insights into the phenomenology of super-hydrophobicity, but also serves as a reliable predictive tool for the study of hydrophobic surfaces.

10aMultigrid10aPhase field10aQuasi-Newton10aSuper-hydrophobicity1 aFedeli, Livio uhttp://www.sciencedirect.com/science/article/pii/S002199911730356X00871nas a2200109 4500008004100000245005900041210005600100520051100156100001700667700002900684856004800713 2017 en d00aOn contact interactions realised as Friedrichs systems0 acontact interactions realised as Friedrichs systems3 aWe realise the Hamiltonians of contact interactions in quantum mechanics within the framework of abstract Friedrichs systems. In particular, we show that the construction of the self-adjoint (or even only closed) operators of contact interaction supported at a fixed point can be associated with the construction of the bijective realisations of a suitable pair of abstract Friedrich operators. In this respect, the Hamiltonians of contact interaction provide novel examples of abstract Friedrich systems.1 aErceg, Marko1 aMichelangeli, Alessandro uhttp://preprints.sissa.it/handle/1963/3529800424nas a2200145 4500008004100000245005000041210004700091260002500138300001400163490000700177100001800184700001700202700001300219856004600232 2017 eng d00aCurvature-adapted remeshing of {CAD} surfaces0 aCurvatureadapted remeshing of CAD surfaces bSpringer Naturecdec a565–5760 v341 aDassi, Franco1 aMola, Andrea1 aSi, Hang uhttps://doi.org/10.1007/s00366-017-0558-200585nas 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/1963/3530001196nas a2200109 4500008004100000245008200041210007000123520080200193100002000995700002301015856004801038 2017 en d00aDispersive estimates for Schrödinger operators with point interactions in R30 aDispersive estimates for Schrödinger operators with point intera3 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 R3, the perturbed Laplacian satisfies the same Lp -Lq estimates of the free Laplacian in the smaller regime q ∈ 2 [2;3). These estimates are implied by a recent result concerning the Lp boundedness 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 ≥ 3.1 aIandoli, Felice1 aScandone, Raffaele uhttp://preprints.sissa.it/handle/1963/3527701090nas a2200121 4500008004100000245009000041210006900131520064600200100002300846700002400869700002400893856005100917 2017 en d00aOn the effect of interactions beyond nearest neighbours on non-convex lattice systems0 aeffect of interactions beyond nearest neighbours on nonconvex la3 aWe analyse the rigidity of non-convex discrete energies where at least nearest and next-to-nearest neighbour interactions are taken into account. Our purpose is to show that interactions beyond nearest neighbours have the role of penalising changes of orientation and, to some extent, they may replace the positive-determinant constraint that is usually required when only nearest neighbours are accounted for. In a discrete to continuum setting, we prove a compactness result for a family of surface-scaled energies and we give bounds on its possible Gamma-limit in terms of interfacial energies that penalise changes of orientation.1 aAlicandro, Roberto1 aLazzaroni, Giuliano1 aPalombaro, Mariapia uhttp://urania.sissa.it/xmlui/handle/1963/3526800962nas a2200133 4500008004100000245012600041210006900167260002600236300001400262490000700276520044200283100001800725856008500743 2017 eng d00aEnergy release rate and quasi-static evolution via vanishing viscosity in a fracture model depending on the crack opening0 aEnergy release rate and quasistatic evolution via vanishing visc bEDP Sciencesc05/2017 a791–8260 v233 aIn the setting of planar linearized elasticity, we study a fracture model depending on the crack opening. Assuming that the crack path is known a priori and sufficiently smooth, we prove that the energy release rate is well defined. Then, we consider the problem of quasi-static evolution for our model. Thanks to a vanishing viscosity approach, we show the existence of such an evolution satisfying a weak Griffith’s criterion.

1 aAlmi, Stefano uhttps://www.esaim-cocv.org/component/article?access=doi&doi=10.1051/cocv/201601400952nas a2200121 4500008004100000245006800041210006500109520053300174100002300707700002900730700002300759856004800782 2017 en d00aOn fractional powers of singular perturbations of the Laplacian0 afractional powers of singular perturbations of the Laplacian3 aWe qualify a relevant range of fractional powers of the so-called Hamiltonian of point interaction in three dimensions, namely the singular perturbation of the negative Laplacian with a contact interaction supported at the origin. In particular we provide an explicit control of the domain of such a fractional operator and of its decomposition into regular and singular parts. We also qualify the norms of the resulting singular fractional Sobolev spaces and their mutual control with the corresponding classical Sobolev norms.1 aGeorgiev, Vladimir1 aMichelangeli, Alessandro1 aScandone, Raffaele uhttp://preprints.sissa.it/handle/1963/3529301281nas a2200121 4500008004100000245008200041210006900123520085300192100002001045700001701065700002901082856004801111 2017 en d00aFriedrichs systems in a Hilbert space framework: solvability and multiplicity0 aFriedrichs systems in a Hilbert space framework solvability and 3 aThe Friedrichs (1958) theory of positive symmetric systems of first order partial differential equations encompasses many standard equations of mathematical physics, irrespective of their type. This theory was recast in an abstract Hilbert space setting by Ern, Guermond and Caplain (2007), and by Antonić and Burazin (2010). In this work we make a further step, presenting a purely operator-theoretic description of abstract Friedrichs systems, and proving that any pair of abstract Friedrichs operators admits bijective extensions with a signed boundary map. Moreover, we provide suffcient and necessary conditions for existence of infinitely many such pairs of spaces, and by the universal operator extension theory (Grubb, 1968) we get a complete identification of all such pairs, which we illustrate on two concrete one-dimensional examples.1 aAntonić, Nenad1 aErceg, Marko1 aMichelangeli, Alessandro uhttp://preprints.sissa.it/handle/1963/3528001393nas a2200145 4500008004100000245005300041210005100094260001000145520095500155100002201110700002101132700001901153700002701172856004801199 2017 en d00aGamma-Convergence of Free-discontinuity problems0 aGammaConvergence of Freediscontinuity problems bSISSA3 aWe study the Gamma-convergence of sequences of free-discontinuity functionals depending on vector-valued functions u which can be discontinuous across hypersurfaces whose shape and location are not known a priori. The main novelty of our result is that we work under very general assumptions on the integrands which, in particular, are not required to be periodic in the space variable. Further, we consider the case of surface integrands which are not bounded from below by the amplitude of the jump of u. We obtain three main results: compactness with respect to Gamma-convergence, representation of the Gamma-limit in an integral form and identification of its integrands, and homogenisation formulas without periodicity assumptions. In particular, the classical case of periodic homogenisation follows as a by-product of our analysis. Moreover, our result covers also the case of stochastic homogenisation, as we will show in a forthcoming paper.1 aCagnetti, Filippo1 aDal Maso, Gianni1 aScardia, Lucia1 aZeppieri, Caterina Ida uhttp://preprints.sissa.it/handle/1963/3527601194nas a2200121 4500008004100000245010100041210006900142520074000211100002100951700002900972700002301001856004801024 2017 en d00aGlobal, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials0 aGlobal finite energy weak solutions for the NLS with rough timed3 aWe prove the existence of weak solutions in the space of energy for a class of nonlinear Schrödinger equations in the presence of a external, rough, time-dependent magnetic potential. Under our assumptions, it is not possible to study the problem by means of usual arguments like resolvent techniques or Fourier integral operators, for example. We use a parabolic regularisation, and we solve the approximating Cauchy problem. This is achieved by obtaining suitable smoothing estimates for the dissipative evolution. The total mass and energy bounds allow to extend the solution globally in time. We then infer sufficient compactness properties in order to produce a global-in-time finite energy weak solution to our original problem.1 aAntonelli, Paolo1 aMichelangeli, Alessandro1 aScandone, Raffaele uhttp://preprints.sissa.it/handle/1963/3529401865nas a2200109 4500008004100000245007100041210006800112520147400180100002901654700002401683856004801707 2017 en d00aGross-Pitaevskii non-linear dynamics for pseudo-spinor condensates0 aGrossPitaevskii nonlinear dynamics for pseudospinor condensates3 aWe derive the equations for the non-linear effective dynamics of a so called pseudo-spinor Bose-Einstein condensate, which emerges from the linear many-body Schrödinger equation at the leading order in the number of particles. The considered system is a three-dimensional diluted gas of identical bosons with spin, possibly confined in space, and coupled with an external time-dependent magnetic field; particles also interact among themselves through a short-scale repulsive interaction. The limit of infinitely many particles is monitored in the physically relevant Gross-Pitaevskii scaling. In our main theorem, if at time zero the system is in a phase of complete condensation (at the level of the reduced one-body marginal) and with energy per particle fixed by the Gross-Pitaevskii functional, then such conditions persist also at later times, with the one-body orbital of the condensate evolving according to a system of non-linear cubic Schrödinger equations coupled among themselves through linear (Rabi) terms. The proof relies on an adaptation to the spinor setting of Pickl’s projection counting method developed for the scalar case. Quantitative rates of convergence are available, but not made explicit because evidently non-optimal. In order to substantiate the formalism and the assumptions made in the main theorem, in an introductory section we review the mathematical formalisation of modern typical experiments with pseudo-spinor condensates.1 aMichelangeli, Alessandro1 aOlgiati, Alessandro uhttp://preprints.sissa.it/handle/1963/3527900707nas a2200157 4500008004100000245004400041210004000085520026500125653001200390653001000402653004000412100001700452700002100469700001800490856004100508 2017 eng d00aThe injectivity radius of Lie manifolds0 ainjectivity radius of Lie manifolds3 aWe prove in a direct, geometric way that for any compatible Riemannian metric on a Lie manifold the injectivity radius is positive

10a(58J40)10a53C2110aMathematics - Differential Geometry1 aAntonini, P.1 aDe Philippis, G.1 aGigli, Nicola uhttps://arxiv.org/pdf/1707.07595.pdf01296nas a2200145 4500008004100000245005100041210005100092520086700143653001001010653001001020653004001030100002201070700001701092856004101109 2017 eng d00aIntegrable lifts for transitive Lie algebroids0 aIntegrable lifts for transitive Lie algebroids3 aInspired by the work of Molino, we show that the integrability obstruction for transitive Lie algebroids can be made to vanish by adding extra dimensions. In particular, we prove that the Weinstein groupoid of a non-integrable transitive and abelian Lie algebroid, is the quotient of a finite dimensional Lie groupoid. Two constructions as such are given: First, explaining the counterexample to integrability given by Almeida and Molino, we see that it can be generalized to the construction of an "Almeida-Molino" integrable lift when the base manifold is simply connected. On the other hand, we notice that the classical de Rham isomorphism provides a universal integrable algebroid. Using it we construct a "de Rham" integrable lift for any given transitive Abelian Lie algebroid.

10a14F4010a58H0510aMathematics - Differential Geometry1 aAndroulidakis, I.1 aAntonini, P. uhttps://arxiv.org/pdf/1707.04855.pdf02050nas a2200121 4500008004100000245008600041210006900127520162300196100002001819700002001839700002101859856004801880 2017 en d00aIsomonodromy Deformations at an Irregular Singularity with Coalescing Eigenvalues0 aIsomonodromy Deformations at an Irregular Singularity with Coale3 aWe consider an n×n linear system of ODEs with an irregular singularity of Poincar\'e rank 1 at z=∞, holomorphically depending on parameter t within a polydisc in Cn centred at t=0. The eigenvalues of the leading matrix at z=∞ coalesce along a locus Δ contained in the polydisc, passing through t=0. Namely, z=∞ is a resonant irregular singularity for t∈Δ. We analyse the case when the leading matrix remains diagonalisable at Δ. We discuss the existence of fundamental matrix solutions, their asymptotics, Stokes phenomenon and monodromy data as t varies in the polydisc, and their limits for t tending to points of Δ. When the deformation is isomonodromic away from Δ, it is well known that a fundamental matrix solution has singularities at Δ. When the system also has a Fuchsian singularity at z=0, we show under minimal vanishing conditions on the residue matrix at z=0 that isomonodromic deformations can be extended to the whole polydisc, including Δ, in such a way that the fundamental matrix solutions and the constant monodromy data are well defined in the whole polydisc. These data can be computed just by considering the system at fixed t=0. Conversely, if the t-dependent system is isomonodromic in a small domain contained in the polydisc not intersecting Δ, if the entries of the Stokes matrices with indices corresponding to coalescing eigenvalues vanish, then we show that Δ is not a branching locus for the fundamental matrix solutions. The importance of these results for the analytic theory of Frobenius Manifolds is explained. An application to Painlev\'e equations is discussed.1 aCotti, Giordano1 aDubrovin, Boris1 aGuzzetti, Davide uhttp://preprints.sissa.it/handle/1963/3528900428nas a2200109 4500008004100000245009800041210007000139490003400209100001900243700002000262856003600282 2017 eng d00aThe Kontsevich matrix integral: convergence to the Painlevé hierarchy and Stokes' phenomenon0 aKontsevich matrix integral convergence to the Painlevé hierarchy0 vDOI 10.1007/s00220-017-2856-31 aBertola, Marco1 aCafasso, Mattia uhttp://arxiv.org/abs/1603.0642000742nas a2200121 4500008004100000245006300041210006000104520033800164100002000502700002900522700002100551856004800572 2017 en d00aKrein-Visik-Birman self-adjoint extension theory revisited0 aKreinVisikBirman selfadjoint extension theory revisited3 aThe core results of the so-called KreIn-Visik-Birman theory of self-adjoint extensions of semi-bounded symmetric operators are reproduced, both in their original and in a more modern formulation, within a comprehensive discussion that includes missing details, elucidative steps, and intermediate results of independent interest.1 aGallone, Matteo1 aMichelangeli, Alessandro1 aOttolini, Andrea uhttp://preprints.sissa.it/handle/1963/3528600384nas a2200109 4500008004100000245006300041210006000104100002300164700002100187700001800208856004800226 2017 en d00aA Lagrangian approach for scalar multi-d conservation laws0 aLagrangian approach for scalar multid conservation laws1 aBianchini, Stefano1 aBonicatto, Paolo1 aMarconi, Elio uhttp://preprints.sissa.it/handle/1963/3529001226nas a2200097 4500008004100000245006100041210006100102520089500163100001901058856005101077 2017 en d00aLinear hyperbolic systems in domains with growing cracks0 aLinear hyperbolic systems in domains with growing cracks3 aWe consider the hyperbolic system $\ddot u-{\rm div}\,(\mathbb A\nabla u)=f$ in the time varying cracked domain $\Omega\setminus\Gamma_t$, where the set $\Omega\subset\mathbb R^d$ is open, bounded, and with Lipschitz boundary, the cracks $\Gamma_t$, $t\in[0,T]$, are closed subsets of $\overline\Omega$, increasing with respect to inclusion, and $u(t):\Omega\setminus\Gamma_t\to\mathbb R^d$ for every $t\in[0,T]$. We assume the existence of suitable regular changes of variables, which reduce our problem to the transformed system $\ddot v-{\rm div}\,(\mathbb B\nabla v)+\mathbf a\nabla v -2\nabla\dot vb=g$ on the fixed domain $\Omega\setminus\Gamma_0$. Under these assumptions, we obtain existence and uniqueness of weak solutions for these two problems. Moreover, we show an energy equality for the functions $v$, which allows us to prove a continuous dependence result for both systems.1 aCaponi, Maicol uhttp://urania.sissa.it/xmlui/handle/1963/3527101406nas a2200133 4500008004100000245004000041210004000081520101100121100002301132700002101155700002401176700002401200856004801224 2017 en d00aLinearisation of multiwell energies0 aLinearisation of multiwell energies3 aLinear elasticity can be rigorously derived from finite elasticity under the assumption of small loadings in terms of Gamma-convergence. This was first done in the case of one-well energies with super-quadratic growth and later generalised to different settings, in particular to the case of multi-well energies where the distance between the wells is very small (comparable to the size of the load). In this paper we study the case when the distance between the wells is independent of the size of the load. In this context linear elasticity can be derived by adding to the multi-well energy a singular higher order term which penalises jumps from one well to another. The size of the singular term has to satisfy certain scaling assumptions whose optimality is shown in most of the cases. Finally, the derivation of linear elasticty from a two-well discrete model is provided, showing that the role of the singular perturbation term is played in this setting by interactions beyond nearest neighbours.1 aAlicandro, Roberto1 aDal Maso, Gianni1 aLazzaroni, Giuliano1 aPalombaro, Mariapia uhttp://preprints.sissa.it/handle/1963/3528801104nas a2200145 4500008004100000245009100041210006900132300001200201490000800213520063400221100001800855700002100873700001900894856004500913 2017 en d00aA lower semicontinuity result for a free discontinuity functional with a boundary term0 alower semicontinuity result for a free discontinuity functional a952-9900 v1083 aWe study the lower semicontinuity in $GSBV^{p}(\Omega;\mathbb{R}^{m})$ of a free discontinuity functional $\mathcal{F}(u)$ that can be written as the sum of a crack term, depending only on the jump set $S_{u}$, and of a boundary term, depending on the trace of $u$ on $\partial\Omega$. We give sufficient conditions on the integrands for the lower semicontinuity of $\mathcal{F}$. Moreover, we prove a relaxation result, which shows that, if these conditions are not satisfied, the lower semicontinuous envelope of $\mathcal{F}$ can be represented by the sum of two integrals on $S_{u}$ and $\partial\Omega$, respectively.

1 aAlmi, Stefano1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/20.500.11767/1597900711nas a2200133 4500008004100000245009400041210006900135520022600204100002900430700002900459700002300488700001800511856004800529 2017 en d00aLp-boundedness of wave operators for the three-dimensional multi-centre point interaction0 aLpboundedness of wave operators for the threedimensional multice3 aWe prove that, for arbitrary centres and strengths, the wave operators for three dimensional Schrödinger operators with multi-centre local point interactions are bounded in Lp(R3) for 1 < p < 3 and unbounded otherwise.1 aDell'Antonio, Gianfausto1 aMichelangeli, Alessandro1 aScandone, Raffaele1 aYajima, Kenji uhttp://preprints.sissa.it/handle/1963/3528300364nas a2200121 4500008004100000022001400041245004900055210004500104300002200149490000700171100001900178856004500197 2017 eng d a1815-065900aThe Malgrange form and Fredholm determinants0 aMalgrange form and Fredholm determinants aPaper No. 046, 120 v131 aBertola, Marco uhttp://dx.doi.org/10.3842/SIGMA.2017.04600465nas a2200133 4500008004100000022001400041245009600055210006900151300001400220490000800234100001900242700002200261856004800283 2017 eng d a0010-361600aMaximal amplitudes of finite-gap solutions for the focusing Nonlinear Schrödinger Equation0 aMaximal amplitudes of finitegap solutions for the focusing Nonli a525–5470 v3541 aBertola, Marco1 aTovbis, Alexander uhttp://dx.doi.org/10.1007/s00220-017-2895-901990nas a2200157 4500008004100000245002800041210002800069260002200097300000900119520158000128100002401708700002001732700002101752700001901773856004001792 2017 eng d00aModel Reduction Methods0 aModel Reduction Methods bJohn Wiley & Sons a1-363 aThis chapter presents an overview of model order reduction – a new paradigm in the field of simulation-based engineering sciences, and one that can tackle the challenges and leverage the opportunities of modern ICT technologies. Despite the impressive progress attained by simulation capabilities and techniques, a number of challenging problems remain intractable. These problems are of different nature, but are common to many branches of science and engineering. Among them are those related to high-dimensional problems, problems involving very different time scales, models defined in degenerate domains with at least one of the characteristic dimensions much smaller than the others, model requiring real-time simulation, and parametric models. All these problems represent a challenge for standard mesh-based discretization techniques; yet the ability to solve these problems efficiently would open unexplored routes for real-time simulation, inverse analysis, uncertainty quantification and propagation, real-time optimization, and simulation-based control – critical needs in many branches of science and engineering. Model order reduction offers new simulation alternatives by circumventing, or at least alleviating, otherwise intractable computational challenges. In the present chapter, we revisit three of these model reduction techniques: proper orthogonal decomposition, proper generalized decomposition, and reduced basis methodologies.} preprint = {http://preprints.sissa.it/xmlui/bitstream/handle/1963/35194/ECM_MOR.pdf?sequence=1&isAllowed=y

1 aChinesta, Francisco1 aHuerta, Antonio1 aRozza, Gianluigi1 aWillcox, Karen uhttp://www.math.sissa.it/node/1294900506nas a2200145 4500008004100000245009700041210006900138300001400207490000800221100001700229700001500246700002200261700002200283856005500305 2017 eng d00aA natural framework for isogeometric fluid-structure interaction based on BEM-shell coupling0 anatural framework for isogeometric fluidstructure interaction ba a522–5460 v3161 aHeltai, Luca1 aKiendl, J.1 aDeSimone, Antonio1 aReali, Alessandro uhttp://cdsads.u-strasbg.fr/abs/2017CMAME.316..522H00711nas a2200181 4500008004100000245009900041210006900140300001400209490000700223100002400230700002000254700002000274700002200294700002100316700002000337700002200357856015000379 2017 eng d00aNumerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts0 aNumerical modeling of hemodynamics scenarios of patientspecific a1373-13990 v161 aBallarin, Francesco1 aFaggiano, Elena1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi1 aIppolito, Sonia1 aScrofani, Roberto uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85015065851&doi=10.1007%2fs10237-017-0893-7&partnerID=40&md5=c388f20bd5de14187bad9ed7d9affbd000603nas a2200169 4500008004100000245012600041210006900167260003400236300001400270490000600284100002200290700001900312700001700331700002100348700002100369856004300390 2017 eng d00aPOD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder0 aPODGalerkin reduced order methods for CFD using Finite Volume Di bWalter de Gruyter {GmbH}cdec a210–2360 v81 aStabile, Giovanni1 aHijazi, Saddam1 aMola, Andrea1 aLorenzi, Stefano1 aRozza, Gianluigi uhttps://doi.org/10.1515/caim-2017-001102503nas a2200157 4500008004100000245005700041210005700098260001200155300000800167490000600175520201600181100001502197700002202212700002102234856009002255 2017 eng d00aReduced Basis Methods for Uncertainty Quantification0 aReduced Basis Methods for Uncertainty Quantification c08/2017 a8690 v53 aIn this work we review a reduced basis method for the solution of uncertainty quantification problems. Based on the basic setting of an elliptic partial differential equation with random input, we introduce the key ingredients of the reduced basis method, including proper orthogonal decomposition and greedy algorithms for the construction of the reduced basis functions, a priori and a posteriori error estimates for the reduced basis approximations, as well as its computational advantages and weaknesses in comparison with a stochastic collocation method [I. Babuška, F. Nobile, and R. Tempone, *SIAM Rev.*, 52 (2010), pp. 317--355]. We demonstrate its computational efficiency and accuracy for a benchmark problem with parameters ranging from a few to a few hundred dimensions. Generalizations to more complex models and applications to uncertainty quantification problems in risk prediction, evaluation of statistical moments, Bayesian inversion, and optimal control under uncertainty are also presented to illustrate how to use the reduced basis method in practice. Further challenges, advancements, and research opportunities are outlined.

Read More: http://epubs.siam.org/doi/abs/10.1137/151004550

POD–Galerkin reduced-order models (ROMs) for fluid-structure interaction problems (incompressible fluid and thin structure) are proposed in this paper. Both the high-fidelity and reduced-order methods are based on a Chorin-Temam operator-splitting approach. Two different reduced-order methods are proposed, which differ on velocity continuity condition, imposed weakly or strongly, respectively. The resulting ROMs are tested and compared on a representative haemodynamics test case characterized by wave propagation, in order to assess the capabilities of the proposed strategies.

1 aBallarin, Francesco1 aRozza, Gianluigi1 aMaday, Yvon1 aBenner, Peter1 aOhlberger, Mario1 aPatera, Anthony1 aRozza, Gianluigi1 aUrban, Karsten uhttp://www.math.sissa.it/node/1294801221nas a2200097 4500008004100000245007700041210006900118520087000187100001801057856004801075 2017 en d00aRegularity estimates for scalar conservation laws in one space dimension0 aRegularity estimates for scalar conservation laws in one space d3 aIn this paper we deal with the regularizing effect that, in a scalar conservation laws in one space dimension, the nonlinearity of the flux function ƒ has on the entropy solution. More precisely, if the set ⟨w : ƒ " (w) ≠ 0⟩ is dense, the regularity of the solution can be expressed in terms of BV Ф spaces, where Ф depends on the nonlinearity of ƒ. If moreover the set ⟨w : ƒ " (w) = 0⟩ is finite, under the additional polynomial degeneracy condition at the inflection points, we prove that ƒ' 0 u(t) ∈ BVloc (R) for every t > 0 and that this can be improved to SBVloc (R) regularity except an at most countable set of singular times. Finally we present some examples that shows the sharpness of these results and counterexamples to related questions, namely regularity in the kinetic formulation and a property of the fractional BV spaces.1 aMarconi, Elio uhttp://preprints.sissa.it/handle/1963/3529100941nas a2200109 4500008004100000245006900041210006800110260001000178520057200188100002000760856005100780 2017 en d00aSelf-Adjoint Extensions of Dirac Operator with Coulomb Potential0 aSelfAdjoint Extensions of Dirac Operator with Coulomb Potential bSISSA3 aIn this note we give a concise review of the present state-of-art for the problem of self-adjoint realisations for the Dirac operator with a Coulomb-like singular scalar potential V(x) = Ø(x)I4. We try to follow the historical and conceptual path that leads to the present understanding of the problem and to highlight the techniques employed and the main ideas. In the final part we outline a few major open questions that concern the topical problem of the multiplicity of self-adjoint realisations of the model, and which are worth addressing in the future.1 aGallone, Matteo uhttp://urania.sissa.it/xmlui/handle/1963/3527301120nas a2200109 4500008004100000245008000041210006900121520072300190100002000913700002900933856004800962 2017 en d00aSelf-adjoint realisations of the Dirac-Coulomb Hamiltonian for heavy nuclei0 aSelfadjoint realisations of the DiracCoulomb Hamiltonian for hea3 aWe derive a classification of the self-adjoint extensions of the three-dimensional Dirac-Coulomb operator in the critical regime of the Coulomb coupling. Our approach is solely based upon the KreĬn-Višik- Birman extension scheme, or also on Grubb's universal classification theory, as opposite to previous works within the standard von Neu- mann framework. This let the boundary condition of self-adjointness emerge, neatly and intrinsically, as a multiplicative constraint between regular and singular part of the functions in the domain of the exten- sion, the multiplicative constant giving also immediate information on the invertibility property and on the resolvent and spectral gap of the extension.1 aGallone, Matteo1 aMichelangeli, Alessandro uhttp://preprints.sissa.it/handle/1963/3528700688nas a2200121 4500008004100000245005300041210005200094520031100146100001600457700002100473700002400494856004800518 2017 en d00aSemistable Higgs Bundles on Calabi-Yau Manifolds0 aSemistable Higgs Bundles on CalabiYau Manifolds3 aWe provide a partial classification of semistable Higgs bundles over a simply connected Calabi-Yau manifold. Applications to a conjecture about a special class of semistable Higgs bundles are given. In particular, the conjecture is proved for K3 and Enriques surfaces, and some related classes of surfaces.1 aBruzzo, Ugo1 aLanza, Valeriano1 aLo Giudice, Alessio uhttp://preprints.sissa.it/handle/1963/3529501216nas a2200121 4500008004100000245006900041210006900110520079100179100002900970700002400999700002301023856004801046 2017 en d00aSingular Hartree equation in fractional perturbed Sobolev spaces0 aSingular Hartree equation in fractional perturbed Sobolev spaces3 aWe establish the local and global theory for the Cauchy problem of the singular Hartree equation in three dimensions, that is, the modification of the non-linear Schrödinger equation with Hartree non-linearity, where the linear part is now given by the Hamiltonian of point interaction. The latter is a singular, self-adjoint perturbation of the free Laplacian, modelling a contact interaction at a fixed point. The resulting non-linear equation is the typical effective equation for the dynamics of condensed Bose gases with fixed pointlike impurities. We control the local solution theory in the perturbed Sobolev spaces of fractional order between the mass space and the operator domain. We then control the global solution theory both in the mass and in the energy space.1 aMichelangeli, Alessandro1 aOlgiati, Alessandro1 aScandone, Raffaele uhttp://preprints.sissa.it/handle/1963/3530101206nas a2200133 4500008004100000245006200041210006000103260001300163490000800176520080600184100002100990700002101011856004001032 2017 eng d00aA Spectral Element Reduced Basis Method in Parametric CFD0 aSpectral Element Reduced Basis Method in Parametric CFD bSpringer0 v1263 aWe consider the Navier-Stokes equations in a channel with varying Reynolds numbers. The model is discretized with high-order spectral element ansatz functions, resulting in 14 259 degrees of freedom. The steady-state snapshot solu- tions define a reduced order space, which allows to accurately evaluate the steady- state solutions for varying Reynolds number with a reduced order model within a fixed-point iteration. In particular, we compare different aspects of implementing the reduced order model with respect to the use of a spectral element discretization. It is shown, how a multilevel static condensation in the pressure and velocity boundary degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios.

1 aHess, Martin, W.1 aRozza, Gianluigi uhttp://www.math.sissa.it/node/1294600399nas a2200097 4500008004100000245006400041210006000105100002100165700002100186856009400207 2017 eng d00aA Spectral Element Reduced Basis Method in Parametric {CFD}0 aSpectral Element Reduced Basis Method in Parametric CFD1 aHess, Martin, W.1 aRozza, Gianluigi uhttp://www.math.sissa.it/publication/spectral-element-reduced-basis-method-parametric-cfd01253nas a2200133 4500008004100000245007800041210006900119260001000188520080500198100001801003700002901021700002101050856004801071 2017 en d00aSpectral Properties of the 2+1 Fermionic Trimer with Contact Interactions0 aSpectral Properties of the 21 Fermionic Trimer with Contact Inte bSISSA3 aWe qualify the main features of the spectrum of the Hamiltonian of point interaction for a three-dimensional quantum system consisting of three point-like particles, two identical fermions, plus a third particle of different species, with two-body interaction of zero range. For arbitrary magnitude of the interaction, and arbitrary value of the mass parameter (the ratio between the mass of the third particle and that of each fermion) above the stability threshold, we identify the essential spectrum, localise and prove the finiteness of the discrete spectrum, qualify the angular symmetry of the eigenfunctions, and prove the monotonicity of the eigenvalues with respect to the mass parameter. We also demonstrate the existence of bound states in a physically relevant regime of masses.1 aBecker, Simon1 aMichelangeli, Alessandro1 aOttolini, Andrea uhttp://preprints.sissa.it/handle/1963/3530300453nas a2200133 4500008004100000245009600041210006900137260000700206300001100213100001900224700002100243700001800264856003700282 2017 eng d00aSymplectic geometry of the moduli space of projective structures in homological coordinates0 aSymplectic geometry of the moduli space of projective structures c06 a1–561 aBertola, Marco1 aKorotkin, Dmitry1 aNorton, Chaya uhttps://arxiv.org/abs/1506.0791801540nas a2200133 4500008004100000245006000041210005900101520111900160100001301279700002401292700001901316700002301335856004801358 2017 en d00aTime quasi-periodic gravity water waves in finite depth0 aTime quasiperiodic gravity water waves in finite depth3 aWe prove the existence and the linear stability of Cantor families of small amplitude time quasi-periodic standing water wave solutions - namely periodic and even in the space variable x - of a bi-dimensional ocean with finite depth under the action of pure gravity. Such a result holds for all the values of the depth parameter in a Borel set of asymptotically full measure. This is a small divisor problem. The main difficulties are the quasi-linear nature of the gravity water waves equations and the fact that the linear frequencies grow just in a sublinear way at infinity. We overcome these problems by first reducing the linearized operators obtained at each approximate quasi-periodic solution along the Nash-Moser iteration to constant coefficients up to smoothing operators, using pseudo-differential changes of variables that are quasi-periodic in time. Then we apply a KAM reducibility scheme which requires very weak Melnikov non-resonance conditions (losing derivatives both in time and space), which we are able to verify for most values of the depth parameter using degenerate KAM theory arguments.1 aBaldi, P1 aBerti, Massimiliano1 aHaus, Emanuele1 aMontalto, Riccardo uhttp://preprints.sissa.it/handle/1963/3529601457nas a2200121 4500008004100000245006900041210006700110260001000177520105600187100002301243700002101266856004801287 2017 en d00aA uniqueness result for the decomposition of vector fields in Rd0 auniqueness result for the decomposition of vector fields in Rd bSISSA3 aGiven a vector field $\rho (1,\b) \in L^1_\loc(\R^+\times \R^{d},\R^{d+1})$ such that $\dive_{t,x} (\rho (1,\b))$ is a measure, we consider the problem of uniqueness of the representation $\eta$ of $\rho (1,\b) \mathcal L^{d+1}$ as a superposition of characteristics $\gamma : (t^-_\gamma,t^+_\gamma) \to \R^d$, $\dot \gamma (t)= \b(t,\gamma(t))$. We give conditions in terms of a local structure of the representation $\eta$ on suitable sets in order to prove that there is a partition of $\R^{d+1}$ into disjoint trajectories $\wp_\a$, $\a \in \A$, such that the PDE \begin{equation*} \dive_{t,x} \big( u \rho (1,\b) \big) \in \mathcal M(\R^{d+1}), \qquad u \in L^\infty(\R^+\times \R^{d}), \end{equation*} can be disintegrated into a family of ODEs along $\wp_\a$ with measure r.h.s.. The decomposition $\wp_\a$ is essentially unique. We finally show that $\b \in L^1_t(\BV_x)_\loc$ satisfies this local structural assumption and this yields, in particular, the renormalization property for nearly incompressible $\BV$ vector fields.1 aBianchini, Stefano1 aBonicatto, Paolo uhttp://preprints.sissa.it/handle/1963/3527400463nas a2200133 4500008004100000022001400041245009600055210006900151300001600220490000600236100001900242700002000261856004800281 2017 eng d a2010-326300aUniversality of the matrix Airy and Bessel functions at spectral edges of unitary ensembles0 aUniversality of the matrix Airy and Bessel functions at spectral a1750010, 220 v61 aBertola, Marco1 aCafasso, Mattia uhttp://dx.doi.org/10.1142/S201032631750010100795nas a2200241 4500008004100000245011200041210006900153260003500222300001100257490000800268100001800276700001800294700001600312700002200328700001900350700002300369700002200392700002200414700001800436700001800454700002100472856006000493 2017 eng d00aUniversality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schrödinger Equation0 aUniversality of the Peregrine Soliton in the Focusing Dynamics o bAmerican Physical SocietycJul a0339010 v1191 aTikan, Alexey1 aBillet, Cyril1 aEl, Gennady1 aTovbis, Alexander1 aBertola, Marco1 aSylvestre, Thibaut1 aGustave, Francois1 aRandoux, Stephane1 aGenty, Goëry1 aSuret, Pierre1 aDudley, John, M. uhttps://link.aps.org/doi/10.1103/PhysRevLett.119.03390102561nas a2200145 4500008004100000245012400041210006900165300001100234490000700245520198000252100001702232700001702249700002202266856012702288 2017 eng d00aWet and Dry Transom Stern Treatment for Unsteady and Nonlinear Potential Flow Model for Naval Hydrodynamics Simulations0 aWet and Dry Transom Stern Treatment for Unsteady and Nonlinear P a1–140 v613 aWe present a model for the fast evaluation of the total drag of ship hulls operating in both wet and dry transom stern conditions, in calm or wavy water, based on the combination of an unsteady semi-Lagrangian potential flow formulation with fully nonlinear free-surface treatment, experimental correlations, and simplified viscous drag modeling. The implementation is entirely based on open source libraries. The spatial discretization is solved using a streamline upwind Petrov‐Galerkin stabilization of an iso-parametric, collocation based, boundary element method, implemented using the open source library deal.II. The resulting nonlinear differential-algebraic system is integrated in time using implicit backward differentiation formulas, implemented in the open source library SUNDIALS. The Open CASCADE library is used to interface the model directly with computer-aided design data structures. The model accounts automatically for hulls with a transom stern, both in wet and dry regimes, by using a specific treatment of the free-surface nodes on the stern edge that automatically detects when the hull advances at low speeds. In this case, the transom stern is partially immersed, and a pressure patch is applied on the water surface detaching from the transom stern, to recover the gravity effect of the recirculating water on the underlying irrotational flow domain. The parameters of the model used to impose the pressure patch are approximated from experimental relations found in the literature. The test cases considered are those of the U.S. Navy Combatant DTMB-5415 and the National Physical Laboratory hull. Comparisons with experimental data on quasi-steady test cases for both water elevation and total hull drag are presented and discussed. The quality of the results obtained on quasi-steady simulations suggests that this model can represent a promising alternative to current unsteady solvers for simulations with Froude numbers below 0.35.

1 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio uhttp://www.math.sissa.it/publication/wet-and-dry-transom-stern-treatment-unsteady-and-nonlinear-potential-flow-model-naval02111nas a2200217 4500008004100000245018600041210006900227260003600296520123100332100002501563700002401588700002001612700001701632700001901649700002101668700002101689700002101710700001701731700001601748856012901764 2016 en d00aAdvances in geometrical parametrization and reduced order models and methods for computational fluid dynamics problems in applied sciences and engineering: overview and perspectives0 aAdvances in geometrical parametrization and reduced order models aCrete, GreecebECCOMASc06/20163 aSeveral problems in applied sciences and engineering require reduction techniques in order to allow computational tools to be employed in the daily practice, especially in iterative procedures such as optimization or sensitivity analysis. Reduced order methods need to face increasingly complex problems in computational mechanics, especially into a multiphysics setting. Several issues should be faced: stability of the approximation, efficient treatment of nonlinearities, uniqueness or possible bifurcations of the state solutions, proper coupling between fields, as well as offline-online computing, computational savings and certification of errors as measure of accuracy. Moreover, efficient geometrical parametrization techniques should be devised to efficiently face shape optimization problems, as well as shape reconstruction and shape assimilation problems. A related aspect deals with the management of parametrized interfaces in multiphysics problems, such as fluid-structure interaction problems, and also a domain decomposition based approach for complex parametrized networks. We present some illustrative industrial and biomedical problems as examples of recent advances on methodological developments.

1 aSalmoiraghi, Filippo1 aBallarin, Francesco1 aCorsi, Giovanni1 aMola, Andrea1 aTezzele, Marco1 aRozza, Gianluigi1 aPapadrakakis, M.1 aPapadopoulos, V.1 aStefanou, G.1 aPlevris, V. uhttp://www.math.sissa.it/publication/advances-geometrical-parametrization-and-reduced-order-models-and-methods-computational00479nas a2200133 4500008004100000022001400041245010000055210006900155300002800224490000700252100001900259700002200278856004500300 2016 eng d a1815-065900aOn asymptotic regimes of orthogonal polynomials with complex varying quartic exponential weight0 aasymptotic regimes of orthogonal polynomials with complex varyin aPaper No. 118, 50 pages0 v121 aBertola, Marco1 aTovbis, Alexander uhttp://dx.doi.org/10.3842/SIGMA.2016.11801557nas a2200133 4500008004100000245009700041210006900138260001000207520109000217100001901307700002401326700002201350856005101372 2016 en d00aCohesive fracture with irreversibility: quasistatic evolution for a model subject to fatigue0 aCohesive fracture with irreversibility quasistatic evolution for bSISSA3 aIn this paper we prove the existence of quasistatic evolutions for a cohesive fracture on a prescribed crack surface, in small-strain antiplane elasticity. The main feature of the model is that the density of the energy dissipated in the fracture process depends on the total variation of the amplitude of the jump. Thus, any change in the crack opening entails a loss of energy, until the crack is complete. In particular this implies a fatigue phenomenon, i.e., a complete fracture may be produced by oscillation of small jumps. The rst step of the existence proof is the construction of approximate evolutions obtained by solving discrete-time incremental minimum problems. The main di culty in the passage to the continuous-time limit is that we lack of controls on the variations of the jump of the approximate evolutions. Therefore we resort to a weak formulation where the variation of the jump is replaced by a Young measure. Eventually, after proving the existence in this weak formulation, we improve the result by showing that the Young measure is concentrated1 aCrismale, Vito1 aLazzaroni, Giuliano1 aOrlando, Gianluca uhttp://urania.sissa.it/xmlui/handle/1963/3520501304nas a2200133 4500008004100000245008300041210006900124520084400193100002201037700002201059700002001081700001801101856005101119 2016 en d00aConfinement of dislocations inside a crystal with a prescribed external strain0 aConfinement of dislocations inside a crystal with a prescribed e3 aWe study screw dislocations in an isotropic crystal undergoing antiplane shear. In the framework of linear elasticity, by fixing a suitable boundary condition for the strain (prescribed non-vanishing boundary integral), we manage to confine the dislocations inside the material. More precisely, in the presence of an external strain with circulation equal to n times the lattice spacing, it is energetically convenient to have n distinct dislocations lying inside the crystal. The novelty of introducing a Dirichlet boundary condition for the tangential strain is crucial to the confinement: it is well known that, if Neumann boundary conditions are imposed, the dislocations tend to migrate to the boundary. The results are achieved using PDE techniques and Ƭ-convergence theory, in the framework of the so-called core radius approach.1 aLucardesi, Ilaria1 aMorandotti, Marco1 aScala, Riccardo1 aZucco, Davide uhttp://urania.sissa.it/xmlui/handle/1963/3524700506nas a2200145 4500008004100000022001400041245011400055210006900169300001200238490000800250100001900258700002000277700001300297856005000310 2016 eng d a0167-278900aCorrelation functions of the KdV hierarchy and applications to intersection numbers over $\overline\CalM_g,n$0 aCorrelation functions of the KdV hierarchy and applications to i a30–570 v3271 aBertola, Marco1 aDubrovin, Boris1 aYang, Di uhttp://dx.doi.org/10.1016/j.physd.2016.04.00800358nas a2200097 4500008004100000245008800041210006900129260000700198100001900205856003600224 2016 eng d00aCORRIGENDUM: The dependence on the monodromy data of the isomonodromic tau function0 aCORRIGENDUM The dependence on the monodromy data of the isomonod c011 aBertola, Marco uhttp://arxiv.org/abs/1601.0479000494nas 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.pdf00589nas a2200157 4500008004100000245009800041210006900139300001400208490000700222100001600229700001700245700001400262700001700276700001400293856012400307 2016 eng d00aError Estimates of B-spline based finite-element method for the wind-driven ocean circulation0 aError Estimates of Bspline based finiteelement method for the wi a430–4590 v691 aRotundo, N.1 aKim, T., -Y.1 aJiang, W.1 aHeltai, Luca1 aFried, E. uhttp://www.math.sissa.it/publication/error-estimates-b-spline-based-finite-element-method-wind-driven-ocean-circulation00434nas a2200109 4500008004100000245009700041210006900138100002200207700002300229700002100252856005100273 2016 en d00aEulerian, Lagrangian and Broad continuous solutions to a balance law with non convex flux II0 aEulerian Lagrangian and Broad continuous solutions to a balance 1 aAlberti, Giovanni1 aBianchini, Stefano1 aCaravenna, Laura uhttp://urania.sissa.it/xmlui/handle/1963/3519700458nas a2200121 4500008004100000245009600041210006900137260001300206100002200219700002300241700002100264856005100285 2016 en d00aEulerian, Lagrangian and Broad continuous solutions to a balance law with non-convex flux I0 aEulerian Lagrangian and Broad continuous solutions to a balance bElsevier1 aAlberti, Giovanni1 aBianchini, Stefano1 aCaravenna, Laura uhttp://urania.sissa.it/xmlui/handle/1963/3520700798nas a2200133 4500008004100000245008700041210006900128260001000197520034000207100002100547700002400568700002100592856005100613 2016 en d00aExistence and uniqueness of dynamic evolutions for a peeling test in dimension one0 aExistence and uniqueness of dynamic evolutions for a peeling tes bSISSA3 aIn this paper we present a one-dimensional model of a dynamic peeling test for a thin film, where the wave equation is coupled with a Griffith criterion for the propagation of the debonding front. Our main results provide existence and uniqueness for the solution to this coupled problem under different assumptions on the data.

1 aDal Maso, Gianni1 aLazzaroni, Giuliano1 aNardini, Lorenzo uhttp://urania.sissa.it/xmlui/handle/1963/3516801717nas a2200193 4500008004100000245011900041210006900160260001400229520106200243100002401305700002001329700002001349700002101369700002201390700002001412700002201432700001801454856005101472 2016 en d00aA fast virtual surgery platform for many scenarios haemodynamics of patient-specific coronary artery bypass grafts0 afast virtual surgery platform for many scenarios haemodynamics o bSubmitted3 aA fast computational framework is devised to the study of several configurations of patient-specific coronary artery bypass grafts. This is especially useful to perform a sensitivity analysis of the haemodynamics for different flow conditions occurring in native coronary arteries and bypass grafts, the investigation of the progression of the coronary artery disease and the choice of the most appropriate surgical procedure. A complete pipeline, from the acquisition of patientspecific medical images to fast parametrized computational simulations, is proposed. Complex surgical configurations employed in the clinical practice, such as Y-grafts and sequential grafts, are studied. A virtual surgery platform based on model reduction of unsteady Navier Stokes equations for blood dynamics is proposed to carry out sensitivity analyses in a very rapid and reliable way. A specialized geometrical parametrization is employed to compare the effect of stenosis and anastomosis variation on the outcome of the surgery in several relevant cases.1 aBallarin, Francesco1 aFaggiano, Elena1 aManzoni, Andrea1 aRozza, Gianluigi1 aQuarteroni, Alfio1 aIppolito, Sonia1 aScrofani, Roberto1 aAntona, Carlo uhttp://urania.sissa.it/xmlui/handle/1963/3524001113nas a2200121 4500008004100000245006200041210006200103260001000165520067200175653001800847100003000865856009600895 2016 en d00aFrames symplectic sheaves on surfaces and their ADHM data0 aFrames symplectic sheaves on surfaces and their ADHM data bSISSA3 aThis dissertation is centered on the moduli space of what we call framed symplectic sheaves on a surface, compactifying the corresponding moduli space of framed principal SP−bundles. It contains the construction of the moduli space, which is carried out for every smooth projective surface X with a big and nef framing divisor, and a study of its deformation theory. We also develop an in-depth analysis of the examples X = P2 and X = Blp (P2 ), showing that the corresponding moduli spaces enjoy an ADHM-type description. In the former case, we prove irreducibility of the space and exhibit a relation with the space of framed ideal instantons on S4 in type C.10amoduli spaces1 aScalise, Jacopo, Vittorio uhttp://www.math.sissa.it/publication/frames-symplectic-sheaves-surfaces-and-their-adhm-data00491nas a2200145 4500008004100000022001400041245009400055210006900149300001400218490000700232100001900239700001900258700002000277856004800297 2016 eng d a0176-427600aHankel determinant approach to generalized Vorob'ev-Yablonski polynomials and their roots0 aHankel determinant approach to generalized VorobevYablonski poly a417–4530 v441 aBalogh, Ferenc1 aBertola, Marco1 aBothner, Thomas uhttp://dx.doi.org/10.1007/s00365-016-9328-402791nas a2200121 4500008004100000245004400041210004400085260001000129520243500139653001802574100002602592856005102618 2016 en d00aInstanton counting on compact manifolds0 aInstanton counting on compact manifolds bSISSA3 aIn this thesis we analyze supersymmetric gauge theories on compact manifolds and their relation with representation theory of infinite Lie algebras associated to conformal field theories, and with the computation of geometric invariants and superconformal indices. The thesis contains the work done by the candidate during the doctorate programme at SISSA under the supervision of A. Tanzini and G. Bonelli. • in Chapter 2, we consider N = 2 supersymmetric gauge theories on four manifolds admitting an isometry. Generalized Killing spinor equations are derived from the consistency of supersymmetry algebrae and solved in the case of four manifolds admitting a U(1) isometry. This is used to explicitly compute the supersymmetric path integral on S2 × S2 via equivariant localization. The building blocks of the resulting partition function are shown to contain the three point functions and the conformal blocks of Liouville Gravity. • in Chapter 3, we provide a contour integral formula for the exact partition function of N = 2 supersymmetric U(N) gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the contour integral for U(2) N = 2∗ theory on P2 for all instanton numbers. In the zero mass case, corresponding to the N = 4 supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of mock-modular forms. In the decoupling limit of infinite mass we find that the generating function of local and surface observables computes equivariant Donaldson invariants, thus proving in this case a long-standing conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new. • in Chapter 4, we explore N = (1, 0) superconformal six-dimensional theories arising from M5 branes probing a transverse Ak singularity. Upon circle compactification to five dimensions, we describe this system with a dual pq-web of five-branes and propose the spectrum of basic five-dimensional in- stanton operators driving global symmetry enhancement. For a single M5 brane, we find that the exact partition function of the 5d quiver gauge theory matches the 6d (1, 0) index, which we compute by letter counting. We finally show which relations among vertex correlators of qW algebrae are implied by the S-duality of the pq-web.10aSupersymmetry1 aRonzani, Massimiliano uhttp://urania.sissa.it/xmlui/handle/1963/3521900538nas a2200109 4500008004100000245007800041210006900119260001000188520009700198100002400295856010900319 2016 en d00aIntegrability of continuous bundles and applications to dynamical systems0 aIntegrability of continuous bundles and applications to dynamica bSISSA3 aIn this dissertation we study the problem of integrability of bundles with low regularities.1 aWar, Khadim, Mbacke uhttp://www.math.sissa.it/publication/integrability-continuous-bundles-and-applications-dynamical-systems01409nas a2200145 4500008004100000245011900041210006900160260007700229520081900306100002501125700002401150700001701174700002101191856005101212 2016 en d00aIsogeometric analysis-based reduced order modelling for incompressible linear viscous flows in parametrized shapes0 aIsogeometric analysisbased reduced order modelling for incompres bSpringer, AMOS Advanced Modelling and Simulation in Engineering Sciences3 aIn this work we provide a combination of isogeometric analysis with reduced order modelling techniques, based on proper orthogonal decomposition, to guarantee computational reduction for the numerical model, and with free-form deformation, for versatile geometrical parametrization. We apply it to computational fluid dynamics problems considering a Stokes flow model. The proposed reduced order model combines efficient shape deformation and accurate and stable velocity and pressure approximation for incompressible viscous flows, computed with a reduced order method. Efficient offine-online computational decomposition is guaranteed in view of repetitive calculations for parametric design and optimization problems. Numerical test cases show the efficiency and accuracy of the proposed reduced order model.1 aSalmoiraghi, Filippo1 aBallarin, Francesco1 aHeltai, Luca1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3519901362nas a2200121 4500008004100000245005800041210005800099520096700157100002401124700002101148700002301169856004801192 2016 en d00aLarge KAM tori for perturbations of the dNLS equation0 aLarge KAM tori for perturbations of the dNLS equation3 aWe prove that small, semi-linear Hamiltonian perturbations of the defocusing nonlinear Schr\"odinger (dNLS) equation on the circle have an abundance of invariant tori of any size and (finite) dimension which support quasi-periodic solutions. When compared with previous results the novelty consists in considering perturbations which do not satisfy any symmetry condition (they may depend on x in an arbitrary way) and need not be analytic. The main difficulty is posed by pairs of almost resonant dNLS frequencies. The proof is based on the integrability of the dNLS equation, in particular the fact that the nonlinear part of the Birkhoff coordinates is one smoothing. We implement a Newton-Nash-Moser iteration scheme to construct the invariant tori. The key point is the reduction of linearized operators, coming up in the iteration scheme, to 2×2 block diagonal ones with constant coefficients together with sharp asymptotic estimates of their eigenvalues.1 aBerti, Massimiliano1 aKappeler, Thomas1 aMontalto, Riccardo uhttp://preprints.sissa.it/handle/1963/3528400521nas a2200133 4500008004100000245008200041210006900123300001100192490000700203100002000210700002200230700001700252856011800269 2016 eng d00aLinearOperator – a generic, high-level expression syntax for linear algebra0 aLinearOperator a generic highlevel expression syntax for linear a1–240 v721 aMaier, Matthias1 aBardelloni, Mauro1 aHeltai, Luca uhttp://www.math.sissa.it/publication/linearoperator-%E2%80%93-generic-high-level-expression-syntax-linear-algebra00865nas a2200109 4500008004100000245007500041210006900116520046600185100002900651700002400680856005100704 2016 en d00aMean-field quantum dynamics for a mixture of Bose-Einstein condensates0 aMeanfield quantum dynamics for a mixture of BoseEinstein condens3 aWe study the effective time evolution of a large quantum system consisting of a mixture of different species of identical bosons in interaction. If the system is initially prepared so as to exhibit condensation in each component, we prove that condensation persists at later times and we show quantitatively that the many-body Schrödinger dynamics is effectively described by a system of coupled cubic non-linear Schrödinger equations, one for each component.1 aMichelangeli, Alessandro1 aOlgiati, Alessandro uhttp://urania.sissa.it/xmlui/handle/1963/3517200690nas a2200109 4500008004100000245007500041210006900116520030100185100002100486700002200507856005100529 2016 en d00aA model for the quasistatic growth of cracks with fractional dimension0 amodel for the quasistatic growth of cracks with fractional dimen3 aWe study a variational model for the quasistatic growth of cracks with fractional dimension in brittle materials. We give a minimal set of properties of the collection of admissible cracks which ensure the existence of a quasistatic evolution. Both the antiplane and the planar cases are treated.1 aDal Maso, Gianni1 aMorandotti, Marco uhttp://urania.sissa.it/xmlui/handle/1963/3517500391nas a2200133 4500008004100000245003600041210003500077260001000112100002400122700002000146700002100166700001900187856005100206 2016 en d00aModel Order Reduction: a survey0 aModel Order Reduction a survey bWiley1 aChinesta, Francisco1 aHuerta, Antonio1 aRozza, Gianluigi1 aWillcox, Karen uhttp://urania.sissa.it/xmlui/handle/1963/3519401951nas a2200169 4500008004100000245009300041210006900134260001300203300000800216490000700224520142100231100002101652700001901673700001701692700002101709856005101730 2016 en d00aA multi-physics reduced order model for the analysis of Lead Fast Reactor single channel0 amultiphysics reduced order model for the analysis of Lead Fast R bElsevier a2080 v873 aIn this work, a Reduced Basis method, with basis functions sampled by a Proper Orthogonal Decomposition technique, has been employed to develop a reduced order model of a multi-physics parametrized Lead-cooled Fast Reactor single-channel. Being the first time that a reduced order model is developed in this context, the work focused on a methodological approach and the coupling between the neutronics and the heat transfer, where the thermal feedbacks on neutronics are explicitly taken into account, in time-invariant settings. In order to address the potential of such approach, two different kinds of varying parameters have been considered, namely one related to a geometric quantity (i.e., the inner radius of the fuel pellet) and one related to a physical quantity (i.e., the inlet lead velocity). The capabilities of the presented reduced order model (ROM) have been tested and compared with a high-fidelity finite element model (upon which the ROM has been constructed) on different aspects. In particular, the comparison focused on the system reactivity prediction (with and without thermal feedbacks on neutronics), the neutron flux and temperature field reconstruction, and on the computational time. The outcomes provided by the reduced order model are in good agreement with the high-fidelity finite element ones, and a computational speed-up of at least three orders of magnitude is achieved as well.1 aSartori, Alberto1 aCammi, Antonio1 aLuzzi, Lelio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3519101319nas a2200109 4500008004100000245011100041210006900152520088700221100002901108700002101137856005101158 2016 en d00aMultiplicity of self-adjoint realisations of the (2+1)-fermionic model of Ter-Martirosyan--Skornyakov type0 aMultiplicity of selfadjoint realisations of the 21fermionic mode3 aWe reconstruct the whole family of self-adjoint Hamiltonians of Ter-Martirosyan- Skornyakov type for a system of two identical fermions coupled with a third particle of different nature through an interaction of zero range. We proceed through an operator-theoretic approach based on the self-adjoint extension theory of Kreĭn, Višiik, and Birman. We identify the explicit `Kreĭn-Višik-Birman extension param- eter' as an operator on the `space of charges' for this model (the `Kreĭn space') and we come to formulate a sharp conjecture on the dimensionality of its kernel. Based on our conjecture, for which we also discuss an amount of evidence, we explain the emergence of a multiplicity of extensions in a suitable regime of masses and we re- produce for the first time the previous partial constructions obtained by means of an alternative quadratic form approach.1 aMichelangeli, Alessandro1 aOttolini, Andrea uhttp://urania.sissa.it/xmlui/handle/1963/3526701002nas a2200109 4500008004100000245009900041210007000140520058100210100002900791700002100820856005100841 2016 en d00aNon-linear Schrödinger system for the dynamics of a binary condensate: theory and 2D numerics0 aNonlinear Schrödinger system for the dynamics of a binary conden3 aWe present a comprehensive discussion of the mathematical framework for binary Bose-Einstein condensates and for the rigorous derivation of their effective dynamics, governed by a system of coupled non-linear Gross-Pitaevskii equations. We also develop in the 2D case a systematic numerical study of the Gross-Pitaevskii systems in a wide range of relevant regimes of population ratios and intra-species and inter-species interactions. Our numerical method is based on a Fourier collocation scheme in space combined with a fourth order integrating factor scheme in time.1 aMichelangeli, Alessandro1 aPitton, Giuseppe uhttp://urania.sissa.it/xmlui/handle/1963/3526600965nas a2200133 4500008004100000245014200041210006900183260003100252520043200283100002300715700002300738700001900761856005100780 2016 en d00aPairs of positive periodic solutions of nonlinear ODEs with indefinite weight: a topological degree approach for the super-sublinear case0 aPairs of positive periodic solutions of nonlinear ODEs with inde bCambridge University Press3 aWe study the periodic and Neumann boundary value problems associated with the second order nonlinear differential equation u''+cu'+λa(t)g(u)=0, where g:[0,+∞[→[0,+∞[ is a sublinear function at infinity having superlinear growth at zero. We prove the existence of two positive solutions when ∫a(t)dt<0 and λ > 0 is sufficiently large. Our approach is based on Mawhin's coincidence degree theory and index computations.1 aBoscaggin, Alberto1 aFeltrin, Guglielmo1 aZanolin, Fabio uhttp://urania.sissa.it/xmlui/handle/1963/3526202274nas a2200145 4500008004100000245009200041210006900133260006800202520165800270100002101928700001901949700001701968700002101985856012202006 2016 en d00aPOD-Galerkin Method for Finite Volume Approximation of Navier-Stokes and RANS Equations0 aPODGalerkin Method for Finite Volume Approximation of NavierStok bComputer Methods in Applied Mechanics and Engineering, Elsevier3 aNumerical simulation of fluid flows requires important computational efforts but it is essential in engineering applications. Reduced Order Model (ROM) can be employed whenever fast simulations are required, or in general, whenever a trade-off between computational cost and solution accuracy is a preeminent issue as in process optimization and control. In this work, the efforts have been put to develop a ROM for Computational Fluid Dynamics (CFD) application based on Finite Volume approximation, starting from the results available in turbulent Reynold-Averaged Navier Stokes simulations in order to enlarge the application field of Proper Orthogonal Decomposition – Reduced Order Model (POD – ROM) technique to more industrial fields. The approach is tested in the classic benchmark of the numerical simulation of the 2D lid-driven cavity. In particular, two simulations at Re = 103 and Re = 105 have been considered in order to assess both a laminar and turbulent case. Some quantities have been compared with the Full Order Model in order to assess the performance of the proposed ROM procedure i.e., the kinetic energy of the system and the reconstructed quantities of interest (velocity, pressure and turbulent viscosity). In addition, for the laminar case, the comparison between the ROM steady-state solution and the data available in literature has been presented. The results have turned out to be very satisfactory both for the accuracy and the computational times. As a major outcome, the approach turns out not to be affected by the energy blow up issue characterizing the results obtained by classic turbulent POD-Galerkin methods.1 aLorenzi, Stefano1 aCammi, Antonio1 aLuzzi, Lelio1 aRozza, Gianluigi uhttp://www.math.sissa.it/publication/pod-galerkin-method-finite-volume-approximation-navier-stokes-and-rans-equations01501nas a2200121 4500008004100000245010500041210007100146260001000217520097200227100002401199700002101223856013501244 2016 en d00aPOD–Galerkin monolithic reduced order models for parametrized fluid-structure interaction problems0 aPOD–Galerkin monolithic reduced order models for parametrized fl bWiley3 aIn this paper we propose a monolithic approach for reduced order modelling of parametrized fluid-structure interaction problems based on a proper orthogonal decomposition (POD)–Galerkin method. Parameters of the problem are related to constitutive properties of the fluid or structural problem, or to geometrical parameters related to the domain configuration at the initial time. We provide a detailed description of the parametrized formulation of the multiphysics problem in its components, together with some insights on how to obtain an offline-online efficient computational procedure through the approximation of parametrized nonlinear tensors. Then, we present the monolithic POD–Galerkin method for the online computation of the global structural displacement, fluid velocity and pressure of the coupled problem. Finally, we show some numerical results to highlight the capabilities of the proposed reduced order method and its computational performances1 aBallarin, Francesco1 aRozza, Gianluigi uhttp://www.math.sissa.it/publication/pod%E2%80%93galerkin-monolithic-reduced-order-models-parametrized-fluid-structure-interaction01116nas a2200109 4500008004100000245007800041210006900119520071700188100002900905700002100934856005100955 2016 en d00aOn point interactions realised as Ter-Martirosyan-Skornyakov Hamiltonians0 apoint interactions realised as TerMartirosyanSkornyakov Hamilton3 aFor quantum systems of zero-range interaction we discuss the mathematical scheme within which modelling the two-body interaction by means of the physically relevant ultra-violet asymptotics known as the ``Ter-Martirosyan--Skornyakov condition'' gives rise to a self-adjoint realisation of the corresponding Hamiltonian. This is done within the self-adjoint extension scheme of Krein, Visik, and Birman. We show that the Ter-Martirosyan--Skornyakov asymptotics is a condition of self-adjointness only when is imposed in suitable functional spaces, and not just as a point-wise asymptotics, and we discuss the consequences of this fact on a model of two identical fermions and a third particle of different nature.1 aMichelangeli, Alessandro1 aOttolini, Andrea uhttp://urania.sissa.it/xmlui/handle/1963/3519502864nas a2200121 4500008004100000245007000041210006900111260001000180520240500190653002302595100002302618856010102641 2016 en d00aPositive solutions to indefinite problems: a topological approach0 aPositive solutions to indefinite problems a topological approach bSISSA3 aThe present Ph.D. thesis is devoted to the study of positive solutions to indefinite problems. In particular, we deal with the second order nonlinear differential equation u'' + a(t) g(u) = 0, where g : [0,+∞[→[0,+∞[ is a continuous nonlinearity and a : [0,T]→R is a Lebesgue integrable sign-changing weight. We analyze the Dirichlet, Neumann and periodic boundary value problems on [0,T] associated with the equation and we provide existence, nonexistence and multiplicity results for positive solutions. In the first part of the manuscript, we investigate nonlinearities g(u) with a superlinear growth at zero and at infinity (including the classical superlinear case g(u)=u^p, with p>1). In particular, we prove that there exist 2^m-1 positive solutions when a(t) has m positive humps separated by negative ones and the negative part of a(t) is sufficiently large. Then, for the Dirichlet problem, we solve a conjecture by Gómez‐Reñasco and López‐Gómez (JDE, 2000) and, for the periodic problem, we give a complete answer to a question raised by Butler (JDE, 1976). In the second part, we study the super-sublinear case (i.e. g(u) is superlinear at zero and sublinear at infinity). If a(t) has m positive humps separated by negative ones, we obtain the existence of 3^m-1 positive solutions of the boundary value problems associated with the parameter-dependent equation u'' + λ a(t) g(u) = 0, when both λ>0 and the negative part of a(t) are sufficiently large. We propose a new approach based on topological degree theory for locally compact operators on open possibly unbounded sets, which applies for Dirichlet, Neumann and periodic boundary conditions. As a byproduct of our method, we obtain infinitely many subharmonic solutions and globally defined positive solutions with complex behavior, and we deal with chaotic dynamics. Moreover, we study positive radially symmetric solutions to the Dirichlet and Neumann problems associated with elliptic PDEs on annular domains. Furthermore, this innovative technique has the potential and the generality needed to deal with indefinite problems with more general differential operators. Indeed, our approach apply also for the non-Hamiltonian equation u'' + cu' + a(t) g(u) = 0. Meanwhile, more general operators in the one-dimensional case and problems involving PDEs will be subjects of future investigations.10apositive solutions1 aFeltrin, Guglielmo uhttp://www.math.sissa.it/publication/positive-solutions-indefinite-problems-topological-approach00971nas a2200121 4500008004100000245009000041210006900131260001000200520038100210653011700591100001800708856012300726 2016 en d00aQualitative properties and construction of solutions to some semilinear elliptic PDEs0 aQualitative properties and construction of solutions to some sem bSISSA3 aThis thesis is devoted to the study of elliptic equations. On the one hand, we study some qualitative properties, such as symmetry of solutions, on the other hand we explicitly construct some solutions vanishing near some fixed manifold. The main techniques are the moving planes method, in order to investigate the qualitative properties and the Lyapunov-Schmidt reduction.10amoving planes method, maximum principle, Lyapunov-Schmidt reduction, Willmore surfaces, Otha-Kawasaki functional1 aRizzi, Matteo uhttp://www.math.sissa.it/publication/qualitative-properties-and-construction-solutions-some-semilinear-elliptic-pdes-001140nas a2200097 4500008004100000245007200041210006900113520073300182100002200915856010500937 2016 en d00aQuasi-periodic solutions for quasi-linear generalized KdV equations0 aQuasiperiodic solutions for quasilinear generalized KdV equation3 aWe prove the existence of Cantor families of small amplitude, linearly stable, quasi-periodic solutions of quasi-linear autonomous Hamiltonian generalized KdV equations. We consider the most general quasi-linear quadratic nonlinearity. The proof is based on an iterative Nash-Moser algorithm. To initialize this scheme, we need to perform a bifurcation analysis taking into account the strongly perturbative effects of the nonlinearity near the origin. In particular, we implement a weak version of the Birkhoff normal form method. The inversion of the linearized operators at each step of the iteration is achieved by pseudo-differential techniques, linear Birkhoff normal form algorithms and a linear KAM reducibility scheme.1 aGiuliani, Filippo uhttp://www.math.sissa.it/publication/quasi-periodic-solutions-quasi-linear-generalized-kdv-equations00739nas a2200109 4500008004100000245009600041210006900137520032900206100001900535700002400554856005100578 2016 en d00aQuasistatic crack growth based on viscous approximation: a model with branching and kinking0 aQuasistatic crack growth based on viscous approximation a model 3 aEmploying the technique of vanishing viscosity and time rescaling, we show the existence of quasistatic evolutions of cracks in brittle materials in the setting of antiplane shear. The crack path is not prescribed a priori and is chosen in an admissible class of piecewise regular sets that allows for branching and kinking.1 aCrismale, Vito1 aLazzaroni, Giuliano uhttp://urania.sissa.it/xmlui/handle/1963/3519301110nas a2200097 4500008004100000245006200041210006000103520078000163100001800943856005100961 2016 en d00aQuasi-static hydraulic crack growth driven by Darcy's law0 aQuasistatic hydraulic crack growth driven by Darcys law3 aIn the framework of rate independent processes, we present a variational model of quasi-static crack growth in hydraulic fracture. We first introduce the energy functional and study the equilibrium conditions of an unbounded linearly elastic body subject to a remote strain ε ∈ R and with a sufficiently regular crack Γ filled by a volume V of incompressible fluid. In particular, we are able to find the pressure p of the fluid inside the crack as a function of Γ, V , and ε. Then, we study the problem of quasi-static evolution for our model, imposing that the fluid volume V and the fluid pressure p are related by Darcy’s law. We show the existence of such an evolution, and we prove that it satisfies a weak notion of the so-called Griffith’s criterion.

1 aAlmi, Stefano uhttp://urania.sissa.it/xmlui/handle/1963/3519800933nas a2200109 4500008004100000245008700041210006900128520053000197100002400727700002100751856005100772 2016 en d00aOn the quasistatic limit of dynamic evolutions for a peeling test in dimension one0 aquasistatic limit of dynamic evolutions for a peeling test in di3 aThe aim of this paper is to study the quasistatic limit of a one-dimensional model of dynamic debonding. We start from a dynamic problem that strongly couples the wave equation in a time-dependent domain with Griffith's criterion for the evolution of the domain. Passing to the limit as inertia tends to zero, we find that the limit evolution satisfies a stability condition; however, the activation rule in Griffith's (quasistatic) criterion does not hold in general, thus the limit evolution is not rate-independent.

1 aLazzaroni, Giuliano1 aNardini, Lorenzo uhttp://urania.sissa.it/xmlui/handle/1963/3526001691nas a2200169 4500008004100000245008700041210006900128260001800197300000600215490000600221520116500227100002101392700001901413700001701432700002101449856005101470 2016 en d00aA Reduced Basis Approach for Modeling the Movement of Nuclear Reactor Control Rods0 aReduced Basis Approach for Modeling the Movement of Nuclear Reac bASMEc02/2016 a80 v23 aThis work presents a reduced order model (ROM) aimed at simulating nuclear reactor control rods movement and featuring fast-running prediction of reactivity and neutron flux distribution as well. In particular, the reduced basis (RB) method (built upon a high-fidelity finite element (FE) approximation) has been employed. The neutronics has been modeled according to a parametrized stationary version of the multigroup neutron diffusion equation, which can be formulated as a generalized eigenvalue problem. Within the RB framework, the centroidal Voronoi tessellation is employed as a sampling technique due to the possibility of a hierarchical parameter space exploration, without relying on a “classical” a posteriori error estimation, and saving an important amount of computational time in the offline phase. Here, the proposed ROM is capable of correctly predicting, with respect to the high-fidelity FE approximation, both the reactivity and neutron flux shape. In this way, a computational speedup of at least three orders of magnitude is achieved. If a higher precision is required, the number of employed basis functions (BFs) must be increased.1 aSartori, Alberto1 aCammi, Antonio1 aLuzzi, Lelio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3519201826nas a2200145 4500008004100000245012700041210006900168260001600237520129800253100002101551700001901572700001701591700002101608856005101629 2016 en d00aReduced basis approaches in time-dependent noncoercive settings for modelling the movement of nuclear reactor control rods0 aReduced basis approaches in timedependent noncoercive settings f bSISSAc20163 aIn this work, two approaches, based on the certified Reduced Basis method, have been developed for simulating the movement of nuclear reactor control rods, in time-dependent non-coercive settings featuring a 3D geometrical framework. In particular, in a first approach, a piece-wise affine transformation based on subdomains division has been implemented for modelling the movement of one control rod. In the second approach, a “staircase” strategy has been adopted for simulating the movement of all the three rods featured by the nuclear reactor chosen as case study. The neutron kinetics has been modelled according to the so-called multi-group neutron diffusion, which, in the present case, is a set of ten coupled parametrized parabolic equations (two energy groups for the neutron flux, and eight for the precursors). Both the reduced order models, developed according to the two approaches, provided a very good accuracy compared with high-fidelity results, assumed as “truth” solutions. At the same time, the computational speed-up in the Online phase, with respect to the fine “truth” finite element discretization, achievable by both the proposed approaches is at least of three orders of magnitude, allowing a real-time simulation of the rod movement and control.

1 aSartori, Alberto1 aCammi, Antonio1 aLuzzi, Lelio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3496301904nas a2200157 4500008004100000245012000041210006900161260002200230300000800252490000700260520128900267100002101556700002201577700002101599856012601620 2016 en d00aReduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries0 aReduced basis method and domain decomposition for elliptic probl bElsevierc01/2016 a4300 v713 aThe aim of this work is to solve parametrized partial differential equations in computational domains represented by networks of repetitive geometries by combining reduced basis and domain decomposition techniques. The main idea behind this approach is to compute once, locally and for few reference shapes, some representative finite element solutions for different values of the parameters and with a set of different suitable boundary conditions on the boundaries: these functions will represent the basis of a reduced space where the global solution is sought for. The continuity of the latter is assured by a classical domain decomposition approach. Test results on Poisson problem show the flexibility of the proposed method in which accuracy and computational time may be tuned by varying the number of reduced basis functions employed, or the set of boundary conditions used for defining locally the basis functions. The proposed approach simplifies the pre-computation of the reduced basis space by splitting the global problem into smaller local subproblems. Thanks to this feature, it allows dealing with arbitrarily complex network and features more flexibility than a classical global reduced basis approximation where the topology of the geometry is fixed.1 aIapichino, Laura1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://www.math.sissa.it/publication/reduced-basis-method-and-domain-decomposition-elliptic-problems-networks-and-complex00485nas a2200145 4500008004100000022001400041245008800055210006900143300001700212490000800229100001900237700001600256700002200272856004500294 2016 eng d a1364-502100aRogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation0 aRogue waves in multiphase solutions of the focusing nonlinear Sc a20160340, 120 v4721 aBertola, Marco1 aEl, Gennady1 aTovbis, Alexander uhttp://dx.doi.org/10.1098/rspa.2016.034000430nas a2200133 4500008004100000245004100041210004000082260001000122100002700132700001700159700002200176700002000198856007800218 2016 en d00aSecond-order structured deformations0 aSecondorder structured deformations bSISSA1 aBarroso, Ana, Cristina1 aMatias, Jose1 aMorandotti, Marco1 aOwen, David, R. uhttp://www.math.sissa.it/publication/second-order-structured-deformations00650nas a2200157 4500008004100000245009600041210006900137260005800206300001400264490000600278100001700284700001700301700002200318700002400340856012800364 2016 eng d00aShip Sinkage and Trim Predictions Based on a CAD Interfaced Fully Nonlinear Potential Model0 aShip Sinkage and Trim Predictions Based on a CAD Interfaced Full bInternational Society of Offshore and Polar Engineers a511–5180 v31 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio1 aBerti, Massimiliano uhttp://www.math.sissa.it/publication/ship-sinkage-and-trim-predictions-based-cad-interfaced-fully-nonlinear-potential-model00396nas a2200121 4500008004100000245004500041210004500086490000900131100001900140700002000159700001300179856008200192 2016 eng d00aSimple Lie Algebras and Topological ODEs0 aSimple Lie Algebras and Topological ODEs0 v20161 aBertola, Marco1 aDubrovin, Boris1 aYang, Di uhttp://www.math.sissa.it/publication/simple-lie-algebras-and-topological-odes00433nas a2200109 4500008004100000245006500041210006200106100001900168700002500187700002200212856008900234 2016 eng d00aOn Sobolev instability of the interior problem of tomography0 aSobolev instability of the interior problem of tomography1 aBertola, Marco1 aKatsevich, Alexander1 aTovbis, Alexander uhttp://www.math.sissa.it/publication/sobolev-instability-interior-problem-tomography00427nas a2200097 4500008004100000245008000041210006900121260001000190100001900200856011000219 2016 en d00aSome results on quasistatic evolution problems for unidirectional processes0 aSome results on quasistatic evolution problems for unidirectiona bSISSA1 aCrismale, Vito uhttp://www.math.sissa.it/publication/some-results-quasistatic-evolution-problems-unidirectional-processes01438nas a2200121 4500008004100000245010500041210006900146260001000215520093000225653002301155100001801178856012001196 2016 en d00aSome results on the mathematical analysis of crack problems with forces applied on the fracture lips0 aSome results on the mathematical analysis of crack problems with bSISSA3 aThis thesis is devoted to the study of some models of fracture growth in elastic materials, characterized by the presence of forces acting on the crack lips. Working in the general framework of rate-independent processes, we first discuss a variational formulation of the problem of quasi-static crack evolution in hydraulic fracture. Then, we investigate the crack growth process in a cohesive fracture model, showing the existence of an evolution satisfying a weak Griffith's criterion. Finally, in the last chapter of this work we investigate, in the static case, the interaction between the energy spent in order to create a new fracture and the energy spent by the applied surface forces. This leads us to study the lower semicontinuity properties of a free discontinuity functional F(u) that can be written as the sum of a crack term, depending on the jump set of u, and of a boundary term, depending on the trace of u.10aFracture mechanics1 aAlmi, Stefano uhttp://www.math.sissa.it/publication/some-results-mathematical-analysis-crack-problems-forces-applied-fracture-lips01088nas a2200121 4500008004100000245010400041210006900145260001000214520065000224100002300874700001800897856005100915 2016 en d00aOn the structure of $L^\infty$-entropy solutions to scalar conservation laws in one-space dimension0 astructure of Linftyentropy solutions to scalar conservation laws bSISSA3 aWe prove that if $u$ is the entropy solution to a scalar conservation law in one space dimension, then the entropy dissipation is a measure concentrated on countably many Lipschitz curves. This result is a consequence of a detailed analysis of the structure of the characteristics. In particular the characteristic curves are segments outside a countably 1-rectifiable set and the left and right traces of the solution exist in a $C^0$-sense up to the degeneracy due to the segments where $f''=0$. We prove also that the initial data is taken in a suitably strong sense and we give some counterexamples which show that these results are sharp.1 aBianchini, Stefano1 aMarconi, Elio uhttp://urania.sissa.it/xmlui/handle/1963/3520901183nas a2200121 4500008004100000245007100041210006300112260001800175520077400193100002100967700002200988856005101010 2016 en d00aOn the third critical speed for rotating Bose-Einstein condensates0 athird critical speed for rotating BoseEinstein condensates bAIP Publisher3 aWe study a two-dimensional rotating Bose-Einstein condensate confined by an anharmonic trap in the framework of the Gross-Pitaevskii theory. We consider a rapid rotation regime close to the transition to a giant vortex state. It was proven in Correggi et al. [J. Math. Phys. 53, 095203 (2012)] that such a transition occurs when the angular velocity is of order ε−4, with ε−2 denoting the coefficient of the nonlinear term in the Gross-Pitaevskii functional and ε ≪ 1 (Thomas-Fermi regime). In this paper, we identify a finite value Ωc such that if Ω = Ω0/ε4 with Ω0 > Ωc, the condensate is in the giant vortex phase. Under the same condition, we prove a refined energy asymptotics and an estimate of the winding number of any Gross-Pitaevskii minimizer.1 aDimonte, Daniele1 aCorreggi, Michele uhttp://urania.sissa.it/xmlui/handle/1963/3524601189nas a2200121 4500008004100000245005100041210004600092260001000138520072900148653011900877100002000996856005101016 2016 en d00at-structures on stable (infinity,1)-categories0 atstructures on stable infinity1categories bSISSA3 aThe present work re-enacts the classical theory of t-structures reducing the classical definition coming from Algebraic Geometry to a rather primitive categorical gadget: suitable reflective factorization systems (defined in the work of Rosický, Tholen, and Cassidy-Hébert-Kelly), which we call "normal torsion theories" following. A relation between these two objects has previously been noticed by other authors, on the level of the triangulated homotopy categories of stable (infinity,1)-categories. The main achievement of the present thesis is to observe and prove that this relation exists genuinely when the definition is lifted to the higher-dimensional world where the notion of triangulated category comes from.10acategory theory, higher category theory, factorization system, torsion theory, homological algebra, higher algebra1 aLoregian, Fosco uhttp://urania.sissa.it/xmlui/handle/1963/3520200744nas a2200121 4500008004100000245005600041210005600097260001000153520032000163653003100483100001800514856009000532 2016 en d00aTwo explorations in Dynamical Systems and Mechanics0 aTwo explorations in Dynamical Systems and Mechanics bSISSA3 aThis thesis contains the work done by Paolo Gidoni during the doctorate programme in Matematical Analysis at SISSA, under the supervision of A. Fonda and A. DeSimone. The thesis is composed of two parts: "Avoiding cones conditions and higher dimensional twist" and "Directional friction in bio-inspired locomotion".10aPoincaré-Birkhoff Theorem1 aGidoni, Paolo uhttp://www.math.sissa.it/publication/two-explorations-dynamical-systems-and-mechanics01389nas a2200133 4500008004300000245007200043210006900115260001500184520094300199100001901142700001801161700002501179856005101204 2015 en_Ud 00aAnisotropic mean curvature on facets and relations with capillarity0 aAnisotropic mean curvature on facets and relations with capillar bde Gruyter3 aWe discuss the relations between the anisotropic calibrability of a facet F of a solid crystal E, and the capillary problem on a capillary tube with base F. When F is parallel to a facet of the Wulff shape, calibrability is equivalent to show the existence of an anisotropic subunitary vector field in $F, with suitable normal trace on the boundary of the facet, and with constant divergence equal to the anisotropic mean curvature of F. When the Wulff shape is a cylynder, assuming E convex at F, and F (strictly) calibrable, such a vector field is obtained by solving the capillary problem on F in absence of gravity and with zero contact angle. We show some examples of facets for which it is possible, even without the strict calibrability assumption, to build one of these vector fields. The construction provides, at least for convex facets of class C^{1,1}, the solution of the total variation flow starting at 1_F.1 aAmato, Stefano1 aTealdi, Lucia1 aBellettini, Giovanni uhttp://urania.sissa.it/xmlui/handle/1963/3448100522nas a2200133 4500008004100000022001400041245015400055210006900209300001400278490000700292100001900299700002200318856004800340 2015 eng d a0176-427600aAsymptotics of orthogonal polynomials with complex varying quartic weight: global structure, critical point behavior and the first Painlevé equation0 aAsymptotics of orthogonal polynomials with complex varying quart a529–5870 v411 aBertola, Marco1 aTovbis, Alexander uhttp://dx.doi.org/10.1007/s00365-015-9288-001509nas a2200121 4500008004100000245009300041210006900134520100200203100001701205700001701222700002401239856012401263 2015 en d00aBenchmarking the Immersed Finite Element Method for Fluid-Structure Interaction Problems0 aBenchmarking the Immersed Finite Element Method for FluidStructu3 aWe present an implementation of a fully variational formulation of an immersed methods for fluid-structure interaction problems based on the finite element method. While typical implementation of immersed methods are characterized by the use of approximate Dirac delta distributions, fully variational formulations of the method do not require the use of said distributions. In our implementation the immersed solid is general in the sense that it is not required to have the same mass density and the same viscous response as the surrounding fluid. We assume that the immersed solid can be either viscoelastic of differential type or hyperelastic. Here we focus on the validation of the method via various benchmarks for fluid-structure interaction numerical schemes. This is the first time that the interaction of purely elastic compressible solids and an incompressible fluid is approached via an immersed method allowing a direct comparison with established benchmarks.1 aSaswati, Roy1 aHeltai, Luca1 aCostanzo, Francesco uhttp://www.math.sissa.it/publication/benchmarking-immersed-finite-element-method-fluid-structure-interaction-problems-000903nas a2200133 4500008004100000245009000041210006900131260001000200520043700210100002100647700002400668700002700692856005000719 2015 en d00aA bridging mechanism in the homogenisation of brittle composites with soft inclusions0 abridging mechanism in the homogenisation of brittle composites w bSISSA3 aWe provide a homogenisation result for the energy-functional associated with a purely brittle composite whose microstructure is characterised by soft periodic inclusions embedded in a stiffer matrix. We show that the two constituents as above can be suitably arranged on a microscopic scale ε to obtain, in the limit as ε tends to zero, a homogeneous macroscopic energy-functional explicitly depending on the opening of the crack.1 aBarchiesi, Marco1 aLazzaroni, Giuliano1 aZeppieri, Caterina Ida uhttp://urania.sissa.it/xmlui/handle/1963/749201367nam a2200229 4500008004100000020002200041022001400063245008400077210006900161250000600230260002600236300000800262520053600270653003000806653002800836653004800864653004500912100002200957700002100979700002001000856011701020 2015 eng d a978-3-319-22469-5 a2191-820100aCertified Reduced Basis Methods for Parametrized Partial Differential Equations0 aCertified Reduced Basis Methods for Parametrized Partial Differe a1 aSwitzerlandbSpringer a1353 aThis book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.

10aa posteriori error bounds10aempirical interpolation10aparametrized partial differential equations10areduced basis methods, greedy algorithms1 aHesthaven, Jan, S1 aRozza, Gianluigi1 aStamm, Benjamin uhttp://www.math.sissa.it/publication/certified-reduced-basis-methods-parametrized-partial-differential-equations01837nas a2200145 4500008004100000245007900041210006900120520133000189100002201519700002901541700002001570700002901590700002101619856005101640 2015 en d00aA class of Hamiltonians for a three-particle fermionic system at unitarity0 aclass of Hamiltonians for a threeparticle fermionic system at un3 aWe consider a quantum mechanical three-particle system made of two identical fermions of mass one and a different particle of mass $m$, where each fermion interacts via a zero-range force with the different particle. In particular we study the unitary regime, i.e., the case of infinite two-body scattering length. The Hamiltonians describing the system are, by definition, self-adjoint extensions of the free Hamiltonian restricted on smooth functions vanishing at the two-body coincidence planes, i.e., where the positions of two interacting particles coincide. It is known that for $m$ larger than a critical value $m^* \simeq (13.607)^{-1}$ a self-adjoint and lower bounded Hamiltonian $H_0$ can be constructed, whose domain is characterized in terms of the standard point-interaction boundary condition at each coincidence plane. Here we prove that for $m\in(m^*,m^{**})$, where $m^{**}\simeq (8.62)^{-1}$, there is a further family of self-adjoint and lower bounded Hamiltonians $H_{0,\beta}$, $\beta \in \mathbb{R}$, describing the system. Using a quadratic form method, we give a rigorous construction of such Hamiltonians and we show that the elements of their domains satisfy a further boundary condition, characterizing the singular behavior when the positions of all the three particles coincide.1 aCorreggi, Michele1 aDell'Antonio, Gianfausto1 aFinco, Domenico1 aMichelangeli, Alessandro1 aTeta, Alessandro uhttp://urania.sissa.it/xmlui/handle/1963/3446901185nas a2200121 4500008004100000245008500041210006900126260001000195520076800205100002100973700001800994856005101012 2015 en d00aConvex combinations of low eigenvalues, Fraenkel asymmetries and attainable sets0 aConvex combinations of low eigenvalues Fraenkel asymmetries and bSISSA3 aWe consider the problem of minimizing convex combinations of the first two eigenvalues of the Dirichlet-Laplacian among open set of $R^N$ of fixed measure. We show that, by purely elementary arguments, based on the minimality condition, it is possible to obtain informations on the geometry of the minimizers of convex combinations: we study, in particular, when these minimizers are no longer convex, and the optimality of balls. As an application of our results we study the boundary of the attainable set for the Dirichlet spectrum. Our techniques involve symmetry results à la Serrin, explicit constants in quantitative inequalities, as well as a purely geometrical problem: the minimization of the Fraenkel 2-asymmetry among convex sets of fixed measure.1 aMazzoleni, Dario1 aZucco, Davide uhttp://urania.sissa.it/xmlui/handle/1963/3514001640nas 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/1963/3446400480nas 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/10.1063/1.492236201005nas a2200097 4500008004100000245007800041210006900119520059600188100001900784856010400803 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 uhttp://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/1963/3449501267nas a2200121 4500008004100000245009800041210006900139520082000208100002101028700002601049700001901075856005101094 2015 en d00aExistence for constrained dynamic Griffith fracture with a weak maximal dissipation condition0 aExistence for constrained dynamic Griffith fracture with a weak 3 aThere are very few existence results for fracture evolution, outside of globally minimizing quasi-static evolutions. Dynamic evolutions are particularly problematic, due to the difficulty of showing energy balance, as well as of showing that solutions obey a maximal dissipation condition, or some similar condition that prevents stationary cracks from always being solutions. Here we introduce a new weak maximal dissipation condition and show that it is compatible with cracks constrained to grow smoothly on a smooth curve. In particular, we show existence of dynamic fracture evolutions satisfying this maximal dissipation condition, subject to the above smoothness constraints, and exhibit explicit examples to show that this maximal dissipation principle can indeed rule out stationary cracks as solutions.1 aDal Maso, Gianni1 aLarsen, Cristopher J.1 aToader, Rodica uhttp://urania.sissa.it/xmlui/handle/1963/3504501077nas a2200121 4500008004100000245013700041210006900178260002300247520059200270100002300862700001900885856005100904 2015 en d00aExistence of positive solutions in the superlinear case via coincidence degree: the Neumann and the periodic boundary value problems0 aExistence of positive solutions in the superlinear case via coin bKhayyam Publishing3 aWe prove the existence of positive periodic solutions for the second order nonlinear equation u'' + a(x) g(u) = 0, where g(u) has superlinear growth at zero and at infinity. The weight function a(x) is allowed to change its sign. Necessary and sufficient conditions for the existence of nontrivial solutions are obtained. The proof is based on Mawhin's coincidence degree and applies also to Neumann boundary conditions. Applications are given to the search of positive solutions for a nonlinear PDE in annular domains and for a periodic problem associated to a non-Hamiltonian equation.1 aFeltrin, Guglielmo1 aZanolin, Fabio uhttp://projecteuclid.org/euclid.ade/143506451800593nas a2200145 4500008004100000245009400041210006900135260001300204300001200217100001900229700001700248700003200265700002600297856012400323 2015 eng d00aExperience on vectorizing lattice Boltzmann kernels for multi-and many-core architectures0 aExperience on vectorizing lattice Boltzmann kernels for multiand bSpringer a53–621 aCalore, Enrico1 aDemo, Nicola1 aSchifano, Sebastiano, Fabio1 aTripiccione, Raffaele uhttp://www.math.sissa.it/publication/experience-vectorizing-lattice-boltzmann-kernels-multi-and-many-core-architectures02252nas a2200145 4500008004100000245009600041210006900137260001000206520175300216100002701969700001701996700002202013700002002035856005102055 2015 en d00aExplicit formulas for relaxed disarrangement densities arising from structured deformations0 aExplicit formulas for relaxed disarrangement densities arising f bSISSA3 aStructured deformations provide a multiscale geometry that captures the contributions at the macrolevel of both smooth geometrical changes and non-smooth geometrical changes (disarrangements) at submacroscopic levels. For each (first-order) structured deformation (g,G) of a continuous body, the tensor field G is known to be a measure of deformations without disarrangements, and M:=∇g−G is known to be a measure of deformations due to disarrangements. The tensor fields G and M together deliver not only standard notions of plastic deformation, but M and its curl deliver the Burgers vector field associated with closed curves in the body and the dislocation density field used in describing geometrical changes in bodies with defects. Recently, Owen and Paroni [13] evaluated explicitly some relaxed energy densities arising in Choksi and Fonseca’s energetics of structured deformations [4] and thereby showed: (1) (trM)+ , the positive part of trM, is a volume density of disarrangements due to submacroscopic separations, (2) (trM)−, the negative part of trM, is a volume density of disarrangements due to submacroscopic switches and interpenetrations, and (3) trM, the absolute value of trM, is a volume density of all three of these non-tangential disarrangements: separations, switches, and interpenetrations. The main contribution of the present research is to show that a different approach to the energetics of structured deformations, that due to Ba\'{i}a, Matias, and Santos [1], confirms the roles of (trM)+, (trM)−, and trM established by Owen and Paroni. In doing so, we give an alternative, shorter proof of Owen and Paroni’s results, and we establish additional explicit formulas for other measures of disarrangements.1 aBarroso, Ana, Cristina1 aMatias, Jose1 aMorandotti, Marco1 aOwen, David, R. uhttp://urania.sissa.it/xmlui/handle/1963/3449200912nas a2200145 4500008004100000245010700041210006900148260001000217520041300227100002000640700002400660700001800684700001600702856004800718 2015 en d00aExtended affine Weyl groups of BCD type, Frobenius manifolds and their Landau-Ginzburg superpotentials0 aExtended affine Weyl groups of BCD type Frobenius manifolds and bSISSA3 aFor the root systems of type Bl, Cl and Dl, we generalize the result of [7] by showing the existence of Frobenius manifold structures on the orbit spaces of the extended affine Weyl groups that correspond to any vertex of the Dynkin diagram instead of a particular choice made in [7]. It also depends on certain additional data. We also construct LG superpotentials for these Frobenius manifold structures.1 aDubrovin, Boris1 aStrachan, Ian, A.B.1 aZhang, Youjin1 aZuo, Dafeng uhttp://preprints.sissa.it/handle/1963/3531601820nas a2200169 4500008004100000245015600041210006900197520118400266100002401450700002001474700002001494700002001514700002201534700002101556700002201577856005101599 2015 en d00aFast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization0 aFast simulations of patientspecific haemodynamics of coronary ar3 aIn this work a reduced-order computational framework for the study of haemodynamics in three-dimensional patient-specific configurations of coronary artery bypass grafts dealing with a wide range of scenarios is proposed. We combine several efficient algorithms to face at the same time both the geometrical complexity involved in the description of the vascular network and the huge computational cost entailed by time dependent patient-specific flow simulations. Medical imaging procedures allow to reconstruct patient-specific configurations from clinical data. A centerlines-based parametrization is proposed to efficiently handle geometrical variations. POD–Galerkin reduced-order models are employed to cut down large computational costs. This computational framework allows to characterize blood flows for different physical and geometrical variations relevant in the clinical practice, such as stenosis factors and anastomosis variations, in a rapid and reliable way. Several numerical results are discussed, highlighting the computational performance of the proposed framework, as well as its capability to perform sensitivity analysis studies, so far out of reach.1 aBallarin, Francesco1 aFaggiano, Elena1 aIppolito, Sonia1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi1 aScrofani, Roberto uhttp://urania.sissa.it/xmlui/handle/1963/3462301899nas a2200133 4500008004300000245010100043210006900144520142800213100002101641700001701662700001701679700001801696856005101714 2015 en_Ud 00aFEM SUPG stabilisation of mixed isoparametric BEMs: application to linearised free surface flows0 aFEM SUPG stabilisation of mixed isoparametric BEMs application t3 aIn finite element formulations, transport dominated problems are often stabilised through the Streamline-Upwind-Petrov–Galerkin (SUPG) method. Its application is straightforward when the problem at hand is solved using Galerkin methods. Applications of boundary integral formulations often resort to collocation techniques which are computationally more tractable. In this framework, the Galerkin method and the stabilisation may still be used to successfully apply boundary conditions and resolve instabilities that are frequently observed in transport dominated problems. We apply this technique to an adaptive collocation boundary element method for the solution of stationary potential flows, where we solve a mixed Poisson problem in boundary integral form, with the addition of linearised free surface boundary conditions. We use a mixed boundary element formulation to allow for different finite dimensional spaces describing the flow potential and its normal derivative, and we validate our method simulating the flow around both a submerged body and a surface piercing body. The coupling of mixed surface finite elements and strongly consistent stabilisation techniques with boundary elements opens up the possibility to use non conformal unstructured grids with local refinement, without introducing the inconsistencies of other stabilisation techniques based on up-winding and finite difference schemes.

1 aGiuliani, Nicola1 aMola, Andrea1 aHeltai, Luca1 aFormaggia, L. uhttp://urania.sissa.it/xmlui/handle/1963/3446600845nas a2200121 4500008004100000245007700041210007000118260001300188520043100201100002200632700001800654856005100672 2015 en d00aGeneralizing the Poincaré-Miranda theorem: the avoiding cones condition0 aGeneralizing the PoincaréMiranda theorem the avoiding cones cond bSpringer3 aAfter proposing a variant of the Poincaré-Bohl theorem, we extend the Poincaré-Miranda theorem in several directions, by introducing an avoiding cones condition. We are thus able to deal with functions defined on various types of convex domains, and situations where the topological degree may be different from ±1. An illustrative application is provided for the study of functionals having degenerate multi-saddle points.1 aFonda, Alessandro1 aGidoni, Paolo uhttp://urania.sissa.it/xmlui/handle/1963/3517302042nas a2200121 4500008004100000245006000041210006000101260001000161520154600171653008801717100002101805856009401826 2015 en d00aGeometric phases in graphene and topological insulators0 aGeometric phases in graphene and topological insulators bSISSA3 aThis thesis collects three of the publications that the candidate produced during his Ph.D. studies. They all focus on geometric phases in solid state physics. We first study topological phases of 2-dimensional periodic quantum systems, in absence of a spectral gap, like e.g. (multilayer) graphene. A topological invariant n_v in Z, baptized eigenspace vorticity, is attached to any intersection of the energy bands, and characterizes the local topology of the eigenprojectors around that intersection. With the help of explicit models, each associated to a value of n_v in Z, we are able to extract the decay at infinity of the single-band Wannier function w in mono- and bilayer graphene, obtaining |w(x)| <= const |x|^{-2} as |x| tends to infinity. Next, we investigate gapped periodic quantum systems, in presence of time-reversal symmetry. When the time-reversal operator Theta is of bosonic type, i.e. it satisfies Theta^2 = 1, we provide an explicit algorithm to construct a frame of smooth, periodic and time-reversal symmetric (quasi-)Bloch functions, or equivalently a frame of almost-exponentially localized, real-valued (composite) Wannier functions, in dimension d <= 3. In the case instead of a fermionic time-reversal operator, satisfying Theta^2 = -1, we show that the existence of such a Bloch frame is in general topologically obstructed in dimension d=2 and d=3. This obstruction is encoded in Z_2-valued topological invariants, which agree with the ones proposed in the solid state literature by Fu, Kane and Mele.10aGeometric phases, graphene, topological insulators, Wannier functions, Bloch frames1 aMonaco, Domenico uhttp://www.math.sissa.it/publication/geometric-phases-graphene-and-topological-insulators01835nas a2200121 4500008004100000245006000041210005800101260001000159520139100169653003901560100002001599856009401619 2015 en d00aGibbs-Markov-Young Structures and Decay of Correlations0 aGibbsMarkovYoung Structures and Decay of Correlations bSISSA3 aIn this work we study mixing properties of discrete dynamical systems and related to them geometric structure. In the first chapter we show that the direct product of maps with Young towers admits a Young tower whose return times decay at a rate which is bounded above by the slowest of the rates of decay of the return times of the component maps. An application of this result, together with other results in the literature, yields various statistical properties for the direct product of various classes of systems, including Lorenz-like maps, multimodal maps, piecewise $C^2$ interval maps with critical points and singularities, H\'enon maps and partially hyperbolic systems. The second chapter is dedicated to the problem of decay of correlations for continuous observables. First we show that if the underlying system admits Young tower then the rate of decay of correlations for continuous observables can be estimated in terms of modulus of continuity and the decay rate of tail of Young tower. In the rest of the second chapter we study the relations between the rates of decay of correlations for smooth observables and continuous observables. We show that if the rates of decay of correlations is known for $C^r,$ observables ($r\ge 1$) then it is possible to obtain decay of correlations for continuous observables in terms of modulus of continuity.10aDecay of Correlations, GMY-towers1 aRuziboev, Marks uhttp://www.math.sissa.it/publication/gibbs-markov-young-structures-and-decay-correlations00332nas a2200085 4500008004100000245007900041210006900120100001900189856003800208 2015 eng d00aGli abachi: antichi strumenti precursori delle moderne macchine da calcolo0 aGli abachi antichi strumenti precursori delle moderne macchine d1 aKlun, Giuliano uhttp://hdl.handle.net/10077/1088400723nas a2200109 4500008004100000245009500041210006900136260001000205520031800215100002900533856005100562 2015 en d00aGlobal well-posedness of the magnetic Hartree equation with non-Strichartz external fields0 aGlobal wellposedness of the magnetic Hartree equation with nonSt bSISSA3 aWe study the magnetic Hartree equation with external fields to which magnetic Strichartz estimates are not necessarily applicable. We characterise the appropriate notion of energy space and in such a space we prove the global well-posedness of the associated initial value problem by means of energy methods only.1 aMichelangeli, Alessandro uhttp://urania.sissa.it/xmlui/handle/1963/3444001304nas a2200097 4500008004300000245009400043210006900137520085900206100001901065856012201084 2015 en_Ud 00aGlobally stable quasi static evolution for strain gradient plasticity coupled with damage0 aGlobally stable quasi static evolution for strain gradient plast3 aAbstract. Weconsiderevolutionsforamaterialmodelwhichcouplesscalardamage with strain gradient plasticity, in small strain assumptions. For strain gradient plasticity, we follow the Gurtin-Anand formulation [Gurtin-Anand 2005]. The aim of the present model is to account for different phenomena: on the one hand the elastic stiffness reduces and the plastic yield surface shrinks due to material’s degradation, on the other hand the dislocation density affects the damage growth. The main result of this paper is the existence of a globally stable quasistatic evolution (in the so- called energetic formulation). Furthermore we study the limit model as the strain gradient terms tend to zero. Under stronger regularity assumptions, we show that the evolutions converge to the ones for the coupled elastoplastic–damage model studied in [Crismale, 2014].1 aCrismale, Vito uhttp://www.math.sissa.it/publication/globally-stable-quasi-static-evolution-strain-gradient-plasticity-coupled-damage00692nas a2200109 4500008004100000245006100041210005800102260003100160520032400191100001600515856005100531 2015 en d00aHilbert schemes of points of OP1(-n) as quiver varieties0 aHilbert schemes of points of OP1n as quiver varieties barXiv:1504.02987 [math.AG]3 aRelying on a representation of framed torsion-free sheaves on Hirzebruch surfaces in terms of monads, we construct ADHM data for the Hilbert scheme of points of the total space of the line bundle $\mathcal O(-n)$ on $\mathbb P^1$. This ADHM description is then used to realize these Hilbert schemes as quiver varieties.1 aBruzzo, Ugo uhttp://urania.sissa.it/xmlui/handle/1963/3448700685nas a2200121 4500008004100000245007200041210006900113260001000182520028100192100001700473700002200490856005100512 2015 en d00aHomogenization problems in the Calculus of Variations: an overview0 aHomogenization problems in the Calculus of Variations an overvie bSISSA3 aIn this note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundamental theoretical tools, both classical and modern. We conclude by mentioning some open problems.1 aMatias, Jose1 aMorandotti, Marco uhttp://urania.sissa.it/xmlui/handle/1963/3445501023nas a2200121 4500008004100000245005200041210005100093260001000144520060600154653007300760100001700833856005100850 2015 en d00aIntegrability of Continuous Tangent Sub-bundles0 aIntegrability of Continuous Tangent Subbundles bSISSA3 aIn this thesis, the main aim is to study the integrability properties of continuous tangent sub-bundles, especially those that arise in the study of dynamical systems. After the introduction and examples part we start by studying integrability of such sub-bundles under different regularity and dynamical assumptions. Then we formulate a continuous version of the classical Frobenius theorem and state some applications to such bundles, to ODE and PDE. Finally we close of by stating some ongoing work related to interactions between integrability, sub-Riemannian geometry and contact geometry.10aDynamical Systems, Global Analysis, Frobenius Theorem, Integrability1 aTureli, Sina uhttp://urania.sissa.it/xmlui/handle/1963/3463003404nas a2200121 4500008004100000245013600041210006900177260001000246520292200256653003303178100002003211856005103231 2015 en d00aInteraction functionals, Glimm approximations and Lagrangian structure of BV solutions for Hyperbolic Systems of Conservations Laws0 aInteraction functionals Glimm approximations and Lagrangian stru bSISSA3 aThis thesis is a contribution to the mathematical theory of Hyperbolic Conservation Laws. Three are the main results which we collect in this work. The first and the second result (denoted in the thesis by Theorem A and Theorem B respectively) deal with the following problem. The most comprehensive result about existence, uniqueness and stability of the solution to the Cauchy problem \begin{equation}\tag{$\mathcal C$} \label{E:abstract} \begin{cases} u_t + F(u)_x = 0, \\u(0, x) = \bar u(x), \end{cases} \end{equation} where $F: \R^N \to \R^N$ is strictly hyperbolic, $u = u(t,x) \in \R^N$, $t \geq 0$, $x \in \R$, $\TV(\bar u) \ll 1$, can be found in [Bianchini, Bressan 2005], where the well-posedness of \eqref{E:abstract} is proved by means of vanishing viscosity approximations. After the paper [Bianchini, Bressan 2005], however, it seemed worthwhile to develop a \emph{purely hyperbolic} theory (based, as in the genuinely nonlinear case, on Glimm or wavefront tracking approximations, and not on vanishing viscosity parabolic approximations) to prove existence, uniqueness and stability results. The reason of this interest can be mainly found in the fact that hyperbolic approximate solutions are much easier to study and to visualize than parabolic ones. Theorems A and B in this thesis are a contribution to this line of research. In particular, Theorem A proves an estimate on the change of the speed of the wavefronts present in a Glimm approximate solution when two of them interact; Theorem B proves the convergence of the Glimm approximate solutions to the weak admissible solution of \eqref{E:abstract} and provides also an estimate on the rate of convergence. Both theorems are proved in the most general setting when no assumption on $F$ is made except the strict hyperbolicity. The third result of the thesis, denoted by Theorem C, deals with the Lagrangian structure of the solution to \eqref{E:abstract}. The notion of Lagrangian flow is a well-established concept in the theory of the transport equation and in the study of some particular system of conservation laws, like the Euler equation. However, as far as we know, the general system of conservations laws \eqref{E:abstract} has never been studied from a Lagrangian point of view. This is exactly the subject of Theorem C, where a Lagrangian representation for the solution to the system \eqref{E:abstract} is explicitly constructed. The main reasons which led us to look for a Lagrangian representation of the solution of \eqref{E:abstract} are two: on one side, this Lagrangian representation provides the continuous counterpart in the exact solution of \eqref{E:abstract} to the well established theory of wavefront approximations; on the other side, it can lead to a deeper understanding of the behavior of the solutions in the general setting, when the characteristic field are not genuinely nonlinear or linearly degenerate.10aHyperbolic conservation laws1 aModena, Stefano uhttp://urania.sissa.it/xmlui/handle/1963/3454201496nas a2200133 4500008004100000245005300041210005300094260001300147520108900160100002201249700001801271700002201289856005101311 2015 en d00aLiquid crystal elastomer strips as soft crawlers0 aLiquid crystal elastomer strips as soft crawlers bElsevier3 aIn this paper, we speculate on a possible application of Liquid Crystal Elastomers to the field of soft robotics. In particular, we study a concept for limbless locomotion that is amenable to miniaturisation. For this purpose, we formulate and solve the evolution equations for a strip of nematic elastomer, subject to directional frictional interactions with a flat solid substrate, and cyclically actuated by a spatially uniform, time-periodic stimulus (e.g., temperature change). The presence of frictional forces that are sensitive to the direction of sliding transforms reciprocal, 'breathing-like' deformations into directed forward motion. We derive formulas quantifying this motion in the case of distributed friction, by solving a differential inclusion for the displacement field. The simpler case of concentrated frictional interactions at the two ends of the strip is also solved, in order to provide a benchmark to compare the continuously distributed case with a finite-dimensional benchmark. We also provide explicit formulas for the axial force along the crawler body.1 aDeSimone, Antonio1 aGidoni, Paolo1 aNoselli, Giovanni uhttp://urania.sissa.it/xmlui/handle/1963/3464300631nas a2200133 4500008004100000245010900041210006900150260001000219520015500229100002100384700002200405700001900427856005100446 2015 en d00aLower semicontinuity of a class of integral functionals on the space of functions of bounded deformation0 aLower semicontinuity of a class of integral functionals on the s bSISSA3 aWe study the lower semicontinuity of some free discontinuity functionals, whose volume term depends on the Euclidean norm of the symmetrized gradient.1 aDal Maso, Gianni1 aOrlando, Gianluca1 aToader, Rodica uhttp://urania.sissa.it/xmlui/handle/1963/3453300495nas a2200109 4500008004100000245010000041210006900141260001000210653001300220100002600233856012600259 2015 en d00aMathematical Models of Locomotion: Legged Crawling, Snake-like Motility, and Flagellar Swimming0 aMathematical Models of Locomotion Legged Crawling Snakelike Moti bSISSA10aMotility1 aCicconofri, Giancarlo uhttp://www.math.sissa.it/publication/mathematical-models-locomotion-legged-crawling-snake-motility-and-flagellar-swimming00454nas a2200133 4500008004100000022001400041245009000055210006900145300001100214490000600225100001900231700002200250856004800272 2015 eng d a1664-236800aMeromorphic differentials with imaginary periods on degenerating hyperelliptic curves0 aMeromorphic differentials with imaginary periods on degenerating a1–220 v51 aBertola, Marco1 aTovbis, Alexander uhttp://dx.doi.org/10.1007/s13324-014-0088-700677nas a2200169 4500008004100000245013400041210006900175300001400244490000700258100001800265700002100283700002000304700002100324700001900345700001900364856012400383 2015 eng d00aModel order reduction of parameterized systems ({MoRePaS}): Preface to the special issue of advances in computational mathematics0 aModel order reduction of parameterized systems MoRePaS Preface t a955–9600 v411 aBenner, Peter1 aOhlberger, Mario1 aPatera, Anthony1 aRozza, Gianluigi1 aSorensen, D.C.1 aUrban, Karsten uhttp://www.math.sissa.it/publication/model-order-reduction-parameterized-systems-morepas-preface-special-issue-advances01807nas a2200121 4500008004100000245011400041210006900155260001000224520121600234653008901450100001901539856012701558 2015 en d00aMultidimensional Poisson Vertex Algebras and Poisson cohomology of Hamiltonian operators of hydrodynamic type0 aMultidimensional Poisson Vertex Algebras and Poisson cohomology bSISSA3 aThe Poisson brackets of hydrodynamic type, also called Dubrovin-Novikov brackets, constitute the Hamiltonian structure of a broad class of evolutionary PDEs, that are ubiquitous in the theory of Integrable Systems, ranging from Hopf equation to the principal hierarchy of a Frobenius manifold. They can be regarded as an analogue of the classical Poisson brackets, defined on an infinite dimensional space of maps Σ → M between two manifolds. Our main problem is the study of Poisson-Lichnerowicz cohomology of such space when dim Σ > 1. We introduce the notion of multidimensional Poisson Vertex Algebras, generalizing and adapting the theory by A. Barakat, A. De Sole, and V. Kac [Poisson Vertex Algebras in the theory of Hamiltonian equations, 2009]; within this framework we explicitly compute the first nontrivial cohomology groups for an arbitrary Poisson bracket of hydrodynamic type, in the case dim Σ = dim M = 2. For the case of the so-called scalar brackets, namely the ones for which dim M = 1, we give a complete description on their Poisson–Lichnerowicz cohomology. From this computations it follows, already in the particular case dim Σ = 2, that the cohomology is infinite dimensional.10aPoisson Vertex Algebras, Poisson brackets, Hamiltonian operators, Integrable Systems1 aCasati, Matteo uhttp://www.math.sissa.it/publication/multidimensional-poisson-vertex-algebras-and-poisson-cohomology-hamiltonian-operators01516nas a2200133 4500008004100000245012100041210006900162260001300231520102900244100002101273700001501294700002201309856005101331 2015 en d00aMultilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations0 aMultilevel and weighted reduced basis method for stochastic opti bSpringer3 aIn this paper we develop and analyze a multilevel weighted reduced basis method for solving stochastic optimal control problems constrained by Stokes equations. We prove the analytic regularity of the optimal solution in the probability space under certain assumptions on the random input data. The finite element method and the stochastic collocation method are employed for the numerical approximation of the problem in the deterministic space and the probability space, respectively, resulting in many large-scale optimality systems to solve. In order to reduce the unaffordable computational effort, we propose a reduced basis method using a multilevel greedy algorithm in combination with isotropic and anisotropic sparse-grid techniques. A weighted a posteriori error bound highlights the contribution stemming from each method. Numerical tests on stochastic dimensions ranging from 10 to 100 demonstrate that our method is very efficient, especially for solving high-dimensional and large-scale optimization problems.1 aRozza, Gianluigi1 aChen, Peng1 aQuarteroni, Alfio uhttp://urania.sissa.it/xmlui/handle/1963/3449101188nas a2200121 4500008004100000245008200041210006900123260001300192520076800205100002300973700001900996856005101015 2015 en d00aMultiple positive solutions for a superlinear problem: a topological approach0 aMultiple positive solutions for a superlinear problem a topologi bElsevier3 aWe study the multiplicity of positive solutions for a two-point boundary value problem associated to the nonlinear second order equation u''+f(x,u)=0. We allow x ↦ f(x,s) to change its sign in order to cover the case of scalar equations with indefinite weight. Roughly speaking, our main assumptions require that f(x,s)/s is below λ_1 as s→0^+ and above λ_1 as s→+∞. In particular, we can deal with the situation in which f(x,s) has a superlinear growth at zero and at infinity. We propose a new approach based on the topological degree which provides the multiplicity of solutions. Applications are given for u'' + a(x) g(u) = 0, where we prove the existence of 2^n-1 positive solutions when a(x) has n positive humps and a^-(x) is sufficiently large.1 aFeltrin, Guglielmo1 aZanolin, Fabio uhttp://urania.sissa.it/xmlui/handle/1963/3514701698nas a2200121 4500008004100000245011400041210006900155260001000224520117400234653002501408100001701433856012601450 2015 en d00aNormal matrix models and orthogonal polynomials for a class of potentials with discrete rotational symmetries0 aNormal matrix models and orthogonal polynomials for a class of p bSISSA3 aIn this thesis we are going to study normal random matrix models which generalize naturally the polynomially perturbed Ginibre ensamble, focusing in particular on their eigenvalue distribution and on the asymptotics of the associated orthogonal polynomials. \\ The main result we are going to present are the following: \begin{itemize} \item we describe the explicit derivation of the equilibrium measure for a class of potentials with discrete rotational symmetries, namely of the form \[V(z)=|z|^{2n}-t(z^{d}+\bar{z}^{d})\qquad n,d\in\mathbb{N},\ \ d\leq2n\ \ t>0 .\] \item We obtain the strong asymptotics for the orthogonal polynomials associated to the weight \[ e^{-NV(z)},\quad V(z)=|z|^{2s}-t(z^s+\bar{z}^{s}) \qquad z \in \mathbb{C},\;s\in \mathbb{N},\quad t>0,\] and we will show how the density of their zeroes is related to the eigenvalue distribution of the corresponding matrix model; \item We show how the conformal maps used to describe the support of the equilibrium measure for polynomial perturbation of the potential $V(z)=|z|^{2n}$ lead to a natural generalization of the concept of polynomial curves introduced in by Elbau. \end{itemize}10aMathematical Physics1 aMerzi, Dario uhttp://www.math.sissa.it/publication/normal-matrix-models-and-orthogonal-polynomials-class-potentials-discrete-rotational00685nas a2200109 4500008004100000245006500041210006300106520031300169100002000482700002200502856005100524 2015 en d00aA note on compactness properties of the singular Toda system0 anote on compactness properties of the singular Toda system3 aIn this note, we consider blow-up for solutions of the SU(3) Toda system on compact surfaces. In particular, we give a complete proof of a compactness result stated by Jost, Lin and Wang and we extend it to the case of singular systems. This is a necessary tool to find solutions through variational methods.1 aBattaglia, Luca1 aMancini, Gabriele uhttp://urania.sissa.it/xmlui/handle/1963/3448400383nas a2200097 4500008004100000245009300041210006900134260001000203100002100213856005100234 2015 en d00aA note on the convergence of a singularly perturbed second order potential-type equation0 anote on the convergence of a singularly perturbed second order p bSISSA1 aNardini, Lorenzo uhttp://urania.sissa.it/xmlui/handle/1963/3445300761nas a2200109 4500008004100000245006200041210006100103260001600164520035400180100002200534856009500556 2015 en d00aOnofri-Type Inequalities for Singular Liouville Equations0 aOnofriType Inequalities for Singular Liouville Equations bSpringer US3 aWe study the blow-up behavior of minimizing sequences for the singular Moser–Trudinger functional on compact surfaces. Assuming non-existence of minimum points, we give an estimate for the infimum value of the functional. This result can be applied to give sharp Onofri-type inequalities on the sphere in the presence of at most two singularities.1 aMancini, Gabriele uhttp://www.math.sissa.it/publication/onofri-type-inequalities-singular-liouville-equations00453nas a2200133 4500008004100000022001400041245008800055210006900143300001500212490000700227100001900234700001300253856005300266 2015 eng d a1751-811300aThe partition function of the extended $r$-reduced Kadomtsev-Petviashvili hierarchy0 apartition function of the extended rreduced KadomtsevPetviashvil a195205, 200 v481 aBertola, Marco1 aYang, Di uhttp://dx.doi.org/10.1088/1751-8113/48/19/19520500719nas a2200217 4500008004100000245009200041210006900133260003300202100002200235700002400257700001600281700002300297700001500320700001400335700002200349700002600371700002100397700001300418700001900431856005100450 2015 en d00aThe phototransduction machinery in the rod outer segment has a strong efficacy gradient0 aphototransduction machinery in the rod outer segment has a stron bNational Academy of Sciences1 aMazzolini, Monica1 aFacchetti, Giuseppe1 aAndolfi, L.1 aZaccaria, Proietti1 aTuccio, S.1 aTreud, J.1 aAltafini, Claudio1 aDi Fabrizio, Enzo, M.1 aLazzarino, Marco1 aRapp, G.1 aTorre, Vincent uhttp://urania.sissa.it/xmlui/handle/1963/3515700789nas a2200121 4500008004100000245007600041210006900117520031400186100001800500700001900518700002000537856011000557 2015 en d00aPoisson cohomology of scalar multidimensional Dubrovin-Novikov brackets0 aPoisson cohomology of scalar multidimensional DubrovinNovikov br3 aWe compute the Poisson cohomology of a scalar Poisson bracket of Dubrovin-Novikov type with D independent variables. We find that the second and third cohomology groups are generically non-vanishing in D>1. Hence, in contrast with the D=1 case, the deformation theory in the multivariable case is non-trivial.1 aCarlet, Guido1 aCasati, Matteo1 aShadrin, Sergey uhttp://www.math.sissa.it/publication/poisson-cohomology-scalar-multidimensional-dubrovin-novikov-brackets01306nas a2200109 4500008004100000245006700041210006600108260001000174520088800184100002101072856010301093 2015 en d00aPrincipal circle bundles, Pimsner algebras and Gysin sequences0 aPrincipal circle bundles Pimsner algebras and Gysin sequences bSISSA3 aPrincipal circle bundles and Gysin sequences play a crucial role in mathematical physics, in particular in Chern-Simons theories and T-duality. This works focuses on the noncommutative topology of principal circle bundles: we investigate the connections between noncommutative principal circle bundles, Pimsner algebras and strongly graded algebras. At the C*-algebraic level, we start from a self-Morita equivalence bimodule E for a C*-algebra B which we think of as a non commutative line bundle over the `base space’ algebra B. The corresponding Pimsner algebra O_E, is then the total space algebra of an associated circle bundle. A natural six term exact sequence, an analogue of the Gysin sequence for circle bundles, relates the KK-theories of O_E and of the base space B. We illustrate several results with the examples of quantum weighted projective and lens spaces.1 aArici, Francesca uhttp://www.math.sissa.it/publication/principal-circle-bundles-pimsner-algebras-and-gysin-sequences00962nas a2200097 4500008004100000245010000041210006900141520051200210100002000722856012200742 2015 en d00aQuadratic interaction estimate for conservation laws: motivations, techniques and open problems0 aQuadratic interaction estimate for conservation laws motivations3 aIn a series joint works with S. Bianchini [3, 4, 5], we proved a quadratic interaction estimate for general systems of conservation laws. Aim of this article is to present the results obtained in the three cited papers, setting them in the context of the theory of Hyperbolic Conservation Laws. To this purpose, first we explain why we considered this quadratic estimate interesting, then we give a brief overview of the techniques we used to prove it and finally we present some related open problems.1 aModena, Stefano uhttp://www.math.sissa.it/publication/quadratic-interaction-estimate-conservation-laws-motivations-techniques-and-open02041nas a2200217 4500008004100000022001400041245010200055210006900157490003500226520122900261653002501490653002101515653002501536653002701561653002501588653001601613100002201629700002101651700002201672856012901694 2015 eng d a1019-716800aReduced basis approximation and a-posteriori error estimation for the coupled Stokes-Darcy system0 aReduced basis approximation and aposteriori error estimation for0 vspecial issue for MoRePaS 20123 aThe coupling of a free flow with a flow through porous media has many potential applications in several fields related with computational science and engineering, such as blood flows, environmental problems or food technologies. We present a reduced basis method for such coupled problems. The reduced basis method is a model order reduction method applied in the context of parametrized systems. Our approach is based on a heterogeneous domain decomposition formulation, namely the Stokes-Darcy problem. Thanks to an offline/online-decomposition, computational times can be drastically reduced. At the same time the induced error can be bounded by fast evaluable a-posteriori error bounds. In the offline-phase the proposed algorithms make use of the decomposed problem structure. Rigorous a-posteriori error bounds are developed, indicating the accuracy of certain lifting operators used in the offline-phase as well as the accuracy of the reduced coupled system. Also, a strategy separately bounding pressure and velocity errors is extended. Numerical experiments dealing with groundwater flow scenarios demonstrate the efficiency of the approach as well as the limitations regarding a-posteriori error estimation.

10aDomain decomposition10aError estimation10aNon-coercive problem10aPorous medium equation10aReduced basis method10aStokes flow1 aMartini, Immanuel1 aRozza, Gianluigi1 aHaasdonk, Bernard uhttp://www.math.sissa.it/publication/reduced-basis-approximation-and-posteriori-error-estimation-coupled-stokes-darcy-system01085nas a2200133 4500008004100000245009800041210006900139300001400208490000800222520055000230100001900780700002100799856013100820 2015 eng d00aReduced basis approximation of parametrized advection-diffusion PDEs with high Péclet number0 aReduced basis approximation of parametrized advectiondiffusion P a419–4260 v1033 aIn this work we show some results about the reduced basis approximation of advection dominated parametrized problems, i.e. advection-diffusion problems with high Péclet number. These problems are of great importance in several engineering applications and it is well known that their numerical approximation can be affected by instability phenomena. In this work we compare two possible stabilization strategies in the framework of the reduced basis method, by showing numerical results obtained for a steady advection-diffusion problem.

1 aPacciarini, P.1 aRozza, Gianluigi uhttp://www.math.sissa.it/publication/reduced-basis-approximation-parametrized-advection-diffusion-pdes-high-p%C3%A9clet-number01234nas a2200145 4500008004100000245010300041210006900144300001400213490000700227520066400234100002000898700002000918700002100938856012900959 2015 eng d00aReduced basis approximation of parametrized optimal flow control problems for the Stokes equations0 aReduced basis approximation of parametrized optimal flow control a319–3360 v693 aThis paper extends the reduced basis method for the solution of parametrized optimal control problems presented in Negri et al. (2013) to the case of noncoercive (elliptic) equations, such as the Stokes equations. We discuss both the theoretical properties-with particular emphasis on the stability of the resulting double nested saddle-point problems and on aggregated error estimates-and the computational aspects of the method. Then, we apply it to solve a benchmark vorticity minimization problem for a parametrized bluff body immersed in a two or a three-dimensional flow through boundary control, demonstrating the effectivity of the methodology.

1 aNegri, Federico1 aManzoni, Andrea1 aRozza, Gianluigi uhttp://www.math.sissa.it/publication/reduced-basis-approximation-parametrized-optimal-flow-control-problems-stokes-equations02448nas a2200121 4500008004100000245012900041210006900170520189900239100002002138700002502158700001702183856012602200 2015 en d00aReduced Basis Isogeometric Methods (RB-IGA) for the real-time simulation of potential flows about parametrized NACA airfoils0 aReduced Basis Isogeometric Methods RBIGA for the realtime simula3 aWe present a Reduced Basis (RB) method based on Isogeometric Analysis (IGA) for the rapid and reliable evaluation of PDE systems characterized by complex geometrical features. At the current state of the art, this is the first case of coupling between RB and IGA methods. The construction of the RB method relies on an Isogeometric Boundary Element Method (IGA-BEM) as the high-fidelity technique, allowing a direct interface with Computer Aided Design (CAD) tools. A suitable Empirical Interpolation Method (EIM) ensures an efficient offline/online decomposition between the construction and the evaluation of the RB method. We consider the real-time simulation of potential flows past airfoils, parametrized with respect to the angle of attack and the NACA number identifying their shape, and we provide a validation of our methodology with respect to experimental data and reference numerical codes, showing in both cases a very good agreement.We present a Reduced Basis (RB) method based on Isogeometric Analysis (IGA) for the rapid and reliable evaluation of PDE systems characterized by complex geometrical features. At the current state of the art, this is the first case of coupling between RB and IGA methods. The construction of the RB method relies on an Isogeometric Boundary Element Method (IGA-BEM) as the high-fidelity technique, allowing a direct interface with Computer Aided Design (CAD) tools. A suitable Empirical Interpolation Method (EIM) ensures an efficient offline/online decomposition between the construction and the evaluation of the RB method. We consider the real-time simulation of potential flows past airfoils, parametrized with respect to the angle of attack and the NACA number identifying their shape, and we provide a validation of our methodology with respect to experimental data and reference numerical codes, showing in both cases a very good agreement.1 aManzoni, Andrea1 aSalmoiraghi, Filippo1 aHeltai, Luca uhttp://www.math.sissa.it/publication/reduced-basis-isogeometric-methods-rb-iga-real-time-simulation-potential-flows-about01508nas a2200121 4500008004100000245012400041210006900165260001000234520098200244653002001226100001801246856012201264 2015 en d00aThe relaxed area of maps from the plane to the plane with a line discontinuity, and the role of semicartesian surfaces.0 arelaxed area of maps from the plane to the plane with a line dis bSISSA3 aIn this thesis we study the relaxation of the area functional w.r.t. the L^1 topology of a map from a bounded planar domain with values in the plane and jumping on a segment. We estimate from above the singular contribution of this functional due to the presence of the jump in terms of the infimum of the area among a suitable family of surfaces that we call semicartesian surfaces. In our analysis, we also introduce a different notion of area, namely the relaxation of the area w.r.t. a convergence stronger than the L^1 convergence, whose singular contribution is completely characterized in terms of suitable semicartesian area minimizing problems. We propose also some examples of maps for which the two notions of relaxation are different: these examples underline the highly non-local behaviour of the L^1-relaxation, and justify the introduction of the other functional. Some result about the existence of a semicartesian area-minimizing surface is also provided.10aArea functional1 aTealdi, Lucia uhttp://www.math.sissa.it/publication/relaxed-area-maps-plane-plane-line-discontinuity-and-role-semicartesian-surfaces00947nas a2200121 4500008004100000245009700041210006900138520050200207100001800709700002500727700002200752856005100774 2015 en d00aResults on the minimization of the Dirichlet functional among semicartesian parametrizations0 aResults on the minimization of the Dirichlet functional among se3 aWe start to investigate the existence of conformal minimizers for the Dirichlet functional in the setting of the so-called semicartesian parametrizations, adapting to this context some techniques used in solving the classical Plateau's problem. The final goal is to find area minimizing semicartesian parametrizations spanning a Jordan curve obtained as union of two graphs; this problem appeared in the study of the relaxed area functional for maps from the plane to the plane jumping on a line.1 aTealdi, Lucia1 aBellettini, Giovanni1 aPaolini, Maurizio uhttp://urania.sissa.it/xmlui/handle/1963/3448801420nas a2200133 4500008004100000245009400041210006900135260001000204520094900214100002401163700002401187700002501211856005001236 2015 en d00aRigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires0 aRigidity of threedimensional lattices and dimension reduction in bSISSA3 aIn the context of nanowire heterostructures we perform a discrete to continuum limit of the corresponding free energy by means of Γ-convergence techniques. Nearest neighbours are identified by employing the notions of Voronoi diagrams and Delaunay triangulations. The scaling of the nanowire is done in such a way that we perform not only a continuum limit but a dimension reduction simultaneously. The main part of the proof is a discrete geometric rigidity result that we announced in an earlier work and show here in detail for a variety of three-dimensional lattices. We perform the passage from discrete to continuum twice: once for a system that compensates a lattice mismatch between two parts of the heterogeneous nanowire without defects and once for a system that creates dislocations. It turns out that we can verify the experimentally observed fact that the nanowires show dislocations when the radius of the specimen is large1 aLazzaroni, Giuliano1 aPalombaro, Mariapia1 aSchlomerkemper, Anja uhttp://urania.sissa.it/xmlui/handle/1963/749401018nas a2200121 4500008004100000245007900041210007000120260001000190520058700200100002900787700002900816856005100845 2015 en d00aSchödinger operators on half-line with shrinking potentials at the origin0 aSchödinger operators on halfline with shrinking potentials at th bSISSA3 aWe discuss the general model of a Schrödinger quantum particle constrained on a straight half-line with given self-adjoint boundary condition at the origin and an interaction potential supported around the origin. We study the limit when the range of the potential scales to zero and its magnitude blows up. We show that in the limit the dynamics is generated by a self-adjoint negative Laplacian on the half-line, with a possible preservation or modification of the boundary condition at the origin, depending on the magnitude of the scaling and of the strength of the potential.1 aDell'Antonio, Gianfausto1 aMichelangeli, Alessandro uhttp://urania.sissa.it/xmlui/handle/1963/3443901475nas a2200121 4500008004100000245011300041210006900154520101400223100001801237700002501255700002201280856005101302 2015 en d00aSemicartesian surfaces and the relaxed area of maps from the plane to the plane with a line discontinuity0 aSemicartesian surfaces and the relaxed area of maps from the pla3 aWe address the problem of estimating the area of the graph of a map u, defined on a bounded planar domain O and taking values in the plane, jumping on a segment J, either compactly contained in O or having both the end points on the boundary of O. We define the relaxation of the area functional w.r.t. a sort of uniform convergence, and we characterize it in terms of the infimum of the area among those surfaces in the space spanning the graphs of the traces of u on the two side of J and having what we have called a semicartesian structure. We exhibit examples showing that the relaxed area functional w.r.t the L^1 convergence may depend also on the values of u far from J, and on the relative position of J w.r.t. the boundary of O; these examples confirm the non-local behaviour of the L^1 relaxed area functional, and justify the interest in studying the relaxation w.r.t. a stronger convergence. We prove also that the L^1 relaxed area functional in non-subadditive for a rather class of maps.1 aTealdi, Lucia1 aBellettini, Giovanni1 aPaolini, Maurizio uhttp://urania.sissa.it/xmlui/handle/1963/3448301018nas a2200121 4500008004100000245008500041210006900126260001000195520053500205653002000740100002200760856011400782 2015 en d00aSharp Inequalities and Blow-up Analysis for Singular Moser-Trudinger Embeddings.0 aSharp Inequalities and Blowup Analysis for Singular MoserTruding bSISSA3 aWe investigate existence of solutions for a singular Liouville equation on S^2 and prove sharp Onofri-type inequalities for a Moser-Trudinger functional in the presence of singular potentials. As a consequence we obtain existence of extremal functions for the Moser-Trudinger embedding on compact surfaces with conical singularities. Finally we study the blow-up behavior for sequences of solutions Liouville-type systems and prove a compactness condition which plays an important role in the variational analysis of Toda systems.10aMoser-Trudinger1 aMancini, Gabriele uhttp://www.math.sissa.it/publication/sharp-inequalities-and-blow-analysis-singular-moser-trudinger-embeddings00678nas a2200097 4500008004100000245008200041210006900123520031500192100002200507856005100529 2015 en d00aSingular Liouville Equations on S^2: Sharp Inequalities and Existence Results0 aSingular Liouville Equations on S2 Sharp Inequalities and Existe3 aWe prove a sharp Onofri-type inequality and non-existence of extremals for a Moser-Tudinger functional on S^2 in the presence of potentials having positive order singularities. We also investigate the existence of critical points and give some sufficient conditions under symmetry or nondegeneracy assumptions.1 aMancini, Gabriele uhttp://urania.sissa.it/xmlui/handle/1963/3448900980nas a2200121 4500008004100000245008300041210006900124260001000193520048800203653003100691100001900722856011700741 2015 en d00aSome results on anisotropic mean curvature and other phase-transition problems0 aSome results on anisotropic mean curvature and other phasetransi bSISSA3 aThe present thesis is divided into three parts. In the first part, we analyze a suitable regularization — which we call nonlinear multidomain model — of the motion of a hypersurface under smooth anisotropic mean curvature flow. The second part of the thesis deals with crystalline mean curvature of facets of a solid set of R^3 . Finally, in the third part we study a phase-transition model for Plateau’s type problems based on the theory of coverings and of BV functions.10aAnisotropic mean curvature1 aAmato, Stefano uhttp://www.math.sissa.it/publication/some-results-anisotropic-mean-curvature-and-other-phase-transition-problems01282nas a2200121 4500008004100000245007500041210006900116260001000185520086400195100002901059700002101088856005101109 2015 en d00aStability of closed gaps for the alternating Kronig-Penney Hamiltonian0 aStability of closed gaps for the alternating KronigPenney Hamilt bSISSA3 aWe consider the Kronig-Penney model for a quantum crystal with equispaced periodic delta-interactions of alternating strength. For this model all spectral gaps at the centre of the Brillouin zone are known to vanish, although so far this noticeable property has only been proved through a very delicate analysis of the discriminant of the corresponding ODE and the associated monodromy matrix. We provide a new, alternative proof by showing that this model can be approximated, in the norm resolvent sense, by a model of regular periodic interactions with finite range for which all gaps at the centre of the Brillouin zone are still vanishing. In particular this shows that the vanishing gap property is stable in the sense that it is present also for the "physical" approximants and is not only a feature of the idealised model of zero-range interactions.1 aMichelangeli, Alessandro1 aMonaco, Domenico uhttp://urania.sissa.it/xmlui/handle/1963/3446001228nas a2200109 4500008004100000245007200041210006700113520083900180100002901019700001901048856005101067 2015 en d00aStability of the (2+2)-fermionic system with zero-range interaction0 aStability of the 22fermionic system with zerorange interaction3 aWe introduce a 3D model, and we study its stability, consisting of two distinct pairs of identical fermions coupled with a two-body interaction between fermions of different species, whose effective range is essentially zero (a so called (2+2)-fermionic system with zero-range interaction). The interaction is modelled by implementing the the celebrated (and ubiquitous, in the literature of this field) Bethe-Peierls contact condition with given two-body scattering length within the Krein-Visik-Birman theory of extensions of semi-bounded symmetric operators, in order to make the Hamiltonian a well-defined (self-adjoint) physical observable. After deriving the expression for the associated energy quadratic form, we show analytically and numerically that the energy of the model is bounded below, thus describing a stable system.1 aMichelangeli, Alessandro1 aPfeiffer, Paul uhttp://urania.sissa.it/xmlui/handle/1963/3447400527nas a2200157 4500008004100000022001400041245010200055210006900157300001400226490000700240100001900247700001900266700002000285700002400305856004000329 2015 eng d a0010-364000aStrong asymptotics of the orthogonal polynomials with respect to a measure supported on the plane0 aStrong asymptotics of the orthogonal polynomials with respect to a112–1720 v681 aBalogh, Ferenc1 aBertola, Marco1 aLee, Seung-Yeop1 aMcLaughlin, Kenneth uhttp://dx.doi.org/10.1002/cpa.2154100689nas a2200145 4500008004100000245009900041210006900140260001000209520018600219100002400405700002000429700002200449700002100471856005100492 2015 en d00aSupremizer stabilization of POD-Galerkin approximation of parametrized Navier-Stokes equations0 aSupremizer stabilization of PODGalerkin approximation of paramet bWiley3 aIn this work, we present a stable proper orthogonal decomposition–Galerkin approximation for parametrized steady incompressible Navier–Stokes equations with low Reynolds number.1 aBallarin, Francesco1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3470101551nas a2200121 4500008004100000245012000041210006900161260001300230520109300243100002101336700002101357856005101378 2015 en d00aSymmetry and localization in periodic crystals: triviality of Bloch bundles with a fermionic time-reversal symmetry0 aSymmetry and localization in periodic crystals triviality of Blo bSpringer3 aWe describe some applications of group- and bundle-theoretic methods in solid state physics, showing how symmetries lead to a proof of the localization of electrons in gapped crystalline solids, as e.g. insulators and semiconductors. We shortly review the Bloch-Floquet decomposition of periodic operators, and the related concepts of Bloch frames and composite Wannier functions. We show that the latter are almost-exponentially localized if and only if there exists a smooth periodic Bloch frame, and that the obstruction to the latter condition is the triviality of a Hermitian vector bundle, called the Bloch bundle. The rôle of additional Z_2-symmetries, as time-reversal and space-reflection symmetry, is discussed, showing how time-reversal symmetry implies the triviality of the Bloch bundle, both in the bosonic and in the fermionic case. Moreover, the same Z_2-symmetry allows to define a finer notion of isomorphism and, consequently, to define new topological invariants, which agree with the indices introduced by Fu, Kane and Mele in the context of topological insulators.1 aMonaco, Domenico1 aPanati, Gianluca uhttp://urania.sissa.it/xmlui/handle/1963/3446801401nas a2200121 4500008004100000245007200041210006900113260001300182520098700195100002401182700002201206856005101228 2015 en d00aThree-sphere low-Reynolds-number swimmer with a passive elastic arm0 aThreesphere lowReynoldsnumber swimmer with a passive elastic arm bSpringer3 aOne of the simplest model swimmers at low Reynolds number is the three-sphere swimmer by Najafi and Golestanian. It consists of three spheres connected by two rods which change their lengths periodically in non-reciprocal fashion. Here we investigate a variant of this model in which one rod is periodically actuated while the other is replaced by an elastic spring. We show that the competition between the elastic restoring force and the hydrodynamic drag produces a delay in the response of the passive elastic arm with respect to the active one. This leads to non-reciprocal shape changes and self-propulsion. After formulating the equations of motion, we study their solutions qualitatively and numerically. The leading-order term of the solution is computed analytically. We then address questions of optimization with respect to both actuation frequency and swimmer's geometry. Our results can provide valuable conceptual guidance in the engineering of robotic microswimmers.1 aMontino, Alessandro1 aDeSimone, Antonio uhttp://urania.sissa.it/xmlui/handle/1963/3453000787nas a2200121 4500008004100000245013000041210006900171260001000240520031200250100002300562700002900585856005100614 2015 en d00aTranslation and adaptation of Birman's paper "On the theory of self-adjoint extensions of positive definite operators" (1956)0 aTranslation and adaptation of Birmans paper On the theory of sel bSISSA3 aThis is an accurate translation from Russian and adaptation to the modern mathematical jargon of a classical paper by M. Sh. Birman published in 1956, which is still today central in the theory of self-adjoint extensions of semi-bounded operators, and for which yet no English version was available so far.1 aKhotyakov, Mikhail1 aMichelangeli, Alessandro uhttp://urania.sissa.it/xmlui/handle/1963/3444300475nas a2200133 4500008004100000245009800041210006900139260000700208300001600215490000800231100001900239700002000258856006300278 2015 eng d00aUniversality Conjecture and Results for a Model of Several Coupled Positive-Definite Matrices0 aUniversality Conjecture and Results for a Model of Several Coupl c08 a1077–11410 v3371 aBertola, Marco1 aBothner, Thomas uhttp://link.springer.com/article/10.1007/s00220-015-2327-700408nas a2200109 4500008004100000245005900041210005900100260001000159653001600169100002000185856009300205 2015 en d00aVariational aspects of Liouville equations and systems0 aVariational aspects of Liouville equations and systems bSISSA10aToda system1 aJevnikar, Aleks uhttp://www.math.sissa.it/publication/variational-aspects-liouville-equations-and-systems00778nas a2200121 4500008004100000245005400041210005400095260001000149520029900159653009000458100002000548856008800568 2015 en d00aVariational aspects of singular Liouville systems0 aVariational aspects of singular Liouville systems bSISSA3 aI studied singular Liouville systems on compact surfaces from a variational point of view. I gave sufficient and necessary conditions for the existence of globally minimizing solutions, then I found min-max solutions for some particular systems. Finally, I also gave some non-existence results.10aVariational methods, Liouville systems, Moser-Trudinger inequalities, min-max methods1 aBattaglia, Luca uhttp://www.math.sissa.it/publication/variational-aspects-singular-liouville-systems00796nas a2200121 4500008004300000245009300043210006900136260001000205520029500215100001900510700002400529856012100553 2015 en_Ud 00aViscous approximation of quasistatic evolutions for a coupled elastoplastic-damage model0 aViscous approximation of quasistatic evolutions for a coupled el bSISSA3 aEmploying the technique of vanishing viscosity and time rescaling, we show the exis- tence of quasistatic evolutions for elastoplastic materials with incomplete damage affecting both the elastic tensor and the plastic yield surface, in a softening framework and in small strain assumptions.1 aCrismale, Vito1 aLazzaroni, Giuliano uhttp://www.math.sissa.it/publication/viscous-approximation-quasistatic-evolutions-coupled-elastoplastic-damage-model02045nas a2200121 4500008004100000245006500041210006500106260001000171520159900181653002801780100001701808856009801825 2015 en d00aVolume variation and heat kernel for affine control problems0 aVolume variation and heat kernel for affine control problems bSISSA3 aIn this thesis we study two main problems. The first one is the small-time heat kernel expansion on the diagonal for second order hypoelliptic opeartors. We consider operators that can depend on a drift field and that satisfy only the weak Hörmander condition. In a first work we use perturbation techniques to determine the exact order of decay of the heat kernel, that depends on the Lie algebra generated by the fields involved in the hypoelliptic operator. We generalize in particular some results already obtained in the sub-Riemannian setting. In a second work we consider a model class of hypoelliptic operators and we characterize geometrically all the coefficients in the on-the diagonal asymptotics at the equilibrium points of the drift field. The class of operators that we consider contains the linear hypoelliptic operators with constant second order part on the Euclidean space. We describe the coefficients in terms only of the divergence of the drift field and of curvature-like invariants, related to the minimal cost of geodesics of the associated optimal control problem. In the second part of the thesis we consider the variation of a smooth volume along a geodesic. The structure of the manifold is induced by a quadratic Hamiltonian and the geodesic in described as the projection of the Hamiltonian flow. We find an expansion similar to the classical Riemannian one. It depends on the curvature operator associated to the Hamiltonian, on the symbol of the geodesic and on a new metric-measure invariant determined by the symbol of the geodesic and by the given volume.10aHeat kernel asymptotics1 aPaoli, Elisa uhttp://www.math.sissa.it/publication/volume-variation-and-heat-kernel-affine-control-problems01514nas a2200109 4500008004100000245013600041210006900177520106400246100002101310700002201331856005101353 2015 en d00aThe wave equation on domains with cracks growing on a prescribed path: existence, uniqueness, and continuous dependence on the data0 awave equation on domains with cracks growing on a prescribed pat3 aGiven a bounded open set $\Omega \subset \mathbb R^d$ with Lipschitz boundary and an increasing family $\Gamma_t$, $t\in [0,T]$, of closed subsets of $\Omega$, we analyze the scalar wave equation $\ddot{u} - div (A \nabla u) = f$ in the time varying cracked domains $\Omega\setminus\Gamma_t$. Here we assume that the sets $\Gamma_t$ are contained into a prescribed $(d-1)$-manifold of class $C^2$. Our approach relies on a change of variables: recasting the problem on the reference configuration $\Omega\setminus \Gamma_0$, we are led to consider a hyperbolic problem of the form $\ddot{v} - div (B\nabla v) + a \cdot \nabla v - 2 b \cdot \nabla \dot{v} = g$ in $\Omega \setminus \Gamma_0$. Under suitable assumptions on the regularity of the change of variables that transforms $\Omega\setminus \Gamma_t$ into $\Omega\setminus \Gamma_0$, we prove existence and uniqueness of weak solutions for both formulations. Moreover, we provide an energy equality, which gives, as a by-product, the continuous dependence of the solutions with respect to the cracks.1 aDal Maso, Gianni1 aLucardesi, Ilaria uhttp://urania.sissa.it/xmlui/handle/1963/3462901482nas a2200133 4500008004100000245013000041210007100171260001300242520098000255100002401235700001701259700002101276856005101297 2014 en d00aAn Abstract Nash–Moser Theorem and Quasi-Periodic Solutions for NLW and NLS on Compact Lie Groups and Homogeneous Manifolds0 aAbstract Nash–Moser Theorem and QuasiPeriodic Solutions for NLW bSpringer3 aWe prove an abstract implicit function theorem with parameters for smooth operators defined on scales of sequence spaces, modeled for the search of quasi-periodic solutions of PDEs. The tame estimates required for the inverse linearised operators at each step of the iterative scheme are deduced via a multiscale inductive argument. The Cantor-like set of parameters where the solution exists is defined in a non inductive way. This formulation completely decouples the iterative scheme from the measure theoretical analysis of the parameters where the small divisors non-resonance conditions are verified. As an application, we deduce the existence of quasi-periodic solutions for forced NLW and NLS equations on any compact Lie group or manifold which is homogeneous with respect to a compact Lie group, extending previous results valid only for tori. A basic tool of harmonic analysis is the highest weight theory for the irreducible representations of compact Lie groups.1 aBerti, Massimiliano1 aCorsi, Livia1 aProcesi, Michela uhttp://urania.sissa.it/xmlui/handle/1963/3465101483nas a2200121 4500008004100000245005900041210005900100260005900159520105100218100002201269700001901291856005101310 2014 en d00aAchieving unanimous opinions in signed social networks0 aAchieving unanimous opinions in signed social networks bInstitute of Electrical and Electronics Engineers Inc.3 aBeing able to predict the outcome of an opinion forming process is an important problem in social network theory. However, even for linear dynamics, this becomes a difficult task as soon as non-cooperative interactions are taken into account. Such interactions are naturally modeled as negative weights on the adjacency matrix of the social network. In this paper we show how the Perron-Frobenius theorem can be used for this task also beyond its standard formulation for cooperative systems. In particular we show how it is possible to associate the achievement of unanimous opinions with the existence of invariant cones properly contained in the positive orthant. These cases correspond to signed adjacency matrices having the eventual positivity property, i.e., such that in sufficiently high powers all negative entries have disappeared. More generally, we show how for social networks the achievement of a, possibily non-unanimous, opinion can be associated to the existence of an invariant cone fully contained in one of the orthants of n.1 aAltafini, Claudio1 aLini, Gabriele uhttp://urania.sissa.it/xmlui/handle/1963/3493501209nas a2200133 4500008004100000245010300041210006900144260001000213520075500223100002100978700002000999700002001019856003601039 2014 eng d00aAdler-Gelfand-Dickey approach to classical W-algebras within the theory of Poisson vertex algebras0 aAdlerGelfandDickey approach to classical Walgebras within the th bSISSA3 aWe put the Adler-Gelfand-Dickey approach to classical W-algebras in the framework of Poisson vertex algebras. We show how to recover the bi-Poisson structure of the KP hierarchy, together with its generalizations and reduction to the N-th KdV hierarchy, using the formal distribution calculus and the lambda-bracket formalism. We apply the Lenard-Magri scheme to prove integrability of the corresponding hierarchies. We also give a simple proof of a theorem of Kupershmidt and Wilson in this framework. Based on this approach, we generalize all these results to the matrix case. In particular, we find (non-local) bi-Poisson structures of the matrix KP and the matrix N-th KdV hierarchies, and we prove integrability of the N-th matrix KdV hierarchy.1 aDe Sole, Alberto1 aKac, Victor, G.1 aValeri, Daniele uhttp://hdl.handle.net/1963/724200836nas a2200121 4500008004100000245009000041210007300131260001300204520040500217100001600622700002500638856005100663 2014 en d00aApproximate Hermitian–Yang–Mills structures on semistable principal Higgs bundles0 aApproximate Hermitian–Yang–Mills structures on semistable princi bSpringer3 aWe generalize the Hitchin-Kobayashi correspondence between semistability and the existence of approximate Hermitian-Yang-Mills structures to the case of principal Higgs bundles. We prove that a principal Higgs bundle on a compact Kaehler manifold, with structure group a connected linear algebraic reductive group, is semistable if and only if it admits an approximate Hermitian-Yang-Mills structure.1 aBruzzo, Ugo1 aGrana-Otero, Beatriz uhttp://urania.sissa.it/xmlui/handle/1963/3464500747nas a2200121 4500008004100000245006900041210006700110260003200177520032200209100001600531700002700547856005100574 2014 en d00aApproximate Hitchin-Kobayashi correspondence for Higgs G-bundles0 aApproximate HitchinKobayashi correspondence for Higgs Gbundles bWorld Scientific Publishing3 aWe announce a result about the extension of the Hitchin-Kobayashi correspondence to principal Higgs bundles. A principal Higgs bundle on a compact Kähler manifold, with structure group a connected linear algebraic reductive group, is semistable if and only if it admits an approximate Hermitian-Yang-Mills structure.1 aBruzzo, Ugo1 aOtero, Beatriz, Graña uhttp://urania.sissa.it/xmlui/handle/1963/3509501081nas a2200145 4500008004100000245007400041210006900115260003100184520057600215100002700791700002100818700002300839700002200862856005100884 2014 en d00aBuckling dynamics of a solvent-stimulated stretched elastomeric sheet0 aBuckling dynamics of a solventstimulated stretched elastomeric s bRoyal Society of Chemistry3 aWhen stretched uniaxially, a thin elastic sheet may exhibit buckling. The occurrence of buckling depends on the geometrical properties of the sheet and the magnitude of the applied strain. Here we show that an elastomeric sheet initially stable under uniaxial stretching can destabilize when exposed to a solvent that swells the elastomer. We demonstrate experimentally and computationally that the features of the buckling pattern depend on the magnitude of stretching, and this observation offers a new way for controlling the shape of a swollen homogeneous thin sheet.1 aLucantonio, Alessandro1 aRoché, Matthieu1 aNardinocchi, Paola1 aStone, Howard, A. uhttp://urania.sissa.it/xmlui/handle/1963/3496700469nas a2200145 4500008004100000022001400041245007300055210006900128300001400197490000800211100001900219700001700238700002000255856004800275 2014 eng d a0010-361600aCauchy-Laguerre two-matrix model and the Meijer-G random point field0 aCauchyLaguerre twomatrix model and the MeijerG random point fiel a111–1440 v3261 aBertola, Marco1 aGekhtman, M.1 aSzmigielski, J. uhttp://dx.doi.org/10.1007/s00220-013-1833-801294nas a2200133 4500008004100000245010400041210006900145260001000214520083900224100002101063700002001084700002001104856003601124 2014 en d00aClassical W-algebras and generalized Drinfeld-Sokolov hierarchies for minimal and short nilpotents0 aClassical Walgebras and generalized DrinfeldSokolov hierarchies bSISSA3 aWe derive explicit formulas for lambda-brackets of the affine classical W-algebras attached to the minimal and short nilpotent elements of any simple Lie algebra g. This is used to compute explicitly the first non-trivial PDE of the corresponding intgerable generalized Drinfeld-Sokolov hierarchies. It turns out that a reduction of the equation corresponding to a short nilpotent is Svinolupov's equation attached to a simple Jordan algebra, while a reduction of the equation corresponding to a minimal nilpotent is an integrable Hamiltonian equation on 2h-3 functions, where h is the dual Coxeter number of g. In the case when g is sl_2 both these equations coincide with the KdV equation. In the case when g is not of type C_n, we associate to the minimal nilpotent element of g yet another generalized Drinfeld-Sokolov hierarchy.1 aDe Sole, Alberto1 aKac, Victor, G.1 aValeri, Daniele uhttp://hdl.handle.net/1963/697902162nas a2200133 4500008004100000245009400041210006900135260001300204520170200217100001501919700002201934700002101956856005101977 2014 en d00aComparison between reduced basis and stochastic collocation methods for elliptic problems0 aComparison between reduced basis and stochastic collocation meth bSpringer3 aThe stochastic collocation method (Babuška et al. in SIAM J Numer Anal 45(3):1005-1034, 2007; Nobile et al. in SIAM J Numer Anal 46(5):2411-2442, 2008a; SIAM J Numer Anal 46(5):2309-2345, 2008b; Xiu and Hesthaven in SIAM J Sci Comput 27(3):1118-1139, 2005) has recently been applied to stochastic problems that can be transformed into parametric systems. Meanwhile, the reduced basis method (Maday et al. in Comptes Rendus Mathematique 335(3):289-294, 2002; Patera and Rozza in Reduced basis approximation and a posteriori error estimation for parametrized partial differential equations Version 1.0. Copyright MIT, http://augustine.mit.edu, 2007; Rozza et al. in Arch Comput Methods Eng 15(3):229-275, 2008), primarily developed for solving parametric systems, has been recently used to deal with stochastic problems (Boyaval et al. in Comput Methods Appl Mech Eng 198(41-44):3187-3206, 2009; Arch Comput Methods Eng 17:435-454, 2010). In this work, we aim at comparing the performance of the two methods when applied to the solution of linear stochastic elliptic problems. Two important comparison criteria are considered: (1), convergence results of the approximation error; (2), computational costs for both offline construction and online evaluation. Numerical experiments are performed for problems from low dimensions O (1) to moderate dimensions O (10) and to high dimensions O (100). The main result stemming from our comparison is that the reduced basis method converges better in theory and faster in practice than the stochastic collocation method for smooth problems, and is more suitable for large scale and high dimensional stochastic problems when considering computational costs.1 aChen, Peng1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3472702011nas a2200241 4500008004100000245013600041210006900177260002200246300000800268490000700276520123100283100002101514700001901535700001901554700001901573700001701592700002701609700002001636700002301656700002101679700001801700856005101718 2014 en d00aComparison of a Modal Method and a Proper Orthogonal Decomposition approach for multi-group time-dependent reactor spatial kinetics0 aComparison of a Modal Method and a Proper Orthogonal Decompositi bElsevierc09/2014 a2290 v713 aIn this paper, two modelling approaches based on a Modal Method (MM) and on the Proper Orthogonal Decomposition (POD) technique, for developing a control-oriented model of nuclear reactor spatial kinetics, are presented and compared. Both these methods allow developing neutronics description by means of a set of ordinary differential equations. The comparison of the outcomes provided by the two approaches focuses on the capability of evaluating the reactivity and the neutron flux shape in different reactor configurations, with reference to a TRIGA Mark II reactor. The results given by the POD-based approach are higher-fidelity with respect to the reference solution than those computed according to the MM-based approach, in particular when the perturbation concerns a reduced region of the core. If the perturbation is homogeneous throughout the core, the two approaches allow obtaining comparable accuracy results on the quantities of interest. As far as the computational burden is concerned, the POD approach ensures a better efficiency rather than direct Modal Method, thanks to the ability of performing a longer computation in the preprocessing that leads to a faster evaluation during the on-line phase.

1 aSartori, Alberto1 aBaroli, Davide1 aCammi, Antonio1 aChiesa, Davide1 aLuzzi, Lelio1 aPonciroli, Roberto, R.1 aPrevitali, Ezio1 aRicotti, Marco, E.1 aRozza, Gianluigi1 aSisti, Monica uhttp://urania.sissa.it/xmlui/handle/1963/3503901580nas a2200157 4500008004100000245009300041210006900134260002800203520103900231100001901270700001901289700002101308700002001329700002201349856005101371 2014 en d00aConformal invariants from nodal sets. I. negative eigenvalues and curvature prescription0 aConformal invariants from nodal sets I negative eigenvalues and bOxford University Press3 aIn this paper, we study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators; more specifically, the Graham, Jenne, Mason, and Sparling (GJMS) operators, which include the Yamabe and Paneitz operators. We give several applications to curvature prescription problems. We establish a version in conformal geometry of Courant's Nodal Domain Theorem. We also show that on any manifold of dimension n≥3, there exist many metrics for which our invariants are nontrivial. We prove that the Yamabe operator can have an arbitrarily large number of negative eigenvalues on any manifold of dimension n≥3. We obtain similar results for some higher order GJMS operators on some Einstein and Heisenberg manifolds. We describe the invariants arising from the Yamabe and Paneitz operators associated to left-invariant metrics on Heisenberg manifolds. Finally, in Appendix, the second named author and Andrea Malchiodi study the Q-curvature prescription problems for noncritical Q-curvatures.1 aGover, Rod, R.1 aCanzani, Yaiza1 aJakobson, Dmitry1 aPonge, Raphaël1 aMalchiodi, Andrea uhttp://urania.sissa.it/xmlui/handle/1963/3512801122nas a2200145 4500008004100000245005400041210005100095260001300146520066000159653006000819100002500879700001600904700002000920856003600940 2014 en d00aOn conjugate times of LQ optimal control problems0 aconjugate times of LQ optimal control problems bSpringer3 aMotivated by the study of linear quadratic optimal control problems, we consider a dynamical system with a constant, quadratic Hamiltonian, and we characterize the number of conjugate times in terms of the spectrum of the Hamiltonian vector field $\vec{H}$. We prove the following dichotomy: the number of conjugate times is identically zero or grows to infinity. The latter case occurs if and only if $\vec{H}$ has at least one Jordan block of odd dimension corresponding to a purely imaginary eigenvalue. As a byproduct, we obtain bounds from below on the number of conjugate times contained in an interval in terms of the spectrum of $\vec{H}$.10aOptimal control, Lagrange Grassmannian, Conjugate point1 aAgrachev, Andrei, A.1 aRizzi, Luca1 aSilveira, Pavel uhttp://hdl.handle.net/1963/722701209nas a2200121 4500008004300000245007700043210006900120520072600189100001900915700002500934700002200959856010600981 2014 en_Ud 00aConstrained BV functions on double coverings for Plateau's type problems0 aConstrained BV functions on double coverings for Plateaus type p3 aWe link Brakke's "soap films" covering construction with the theory of finite perimeter sets, in order to study Plateau's problem without fixing a priori the topology of the solution. The minimization is set up in the class of $BV$ functions defined on a double covering space of the complement of an $(n − 2)$-dimensional smooth compact manifold $S$ without boundary. The main novelty of our approach stands in the presence of a suitable constraint on the fibers, which couples together the covering sheets. The model allows to avoid all issues concerning the presence of the boundary $S$. The constraint is lifted in a natural way to Sobolev spaces, allowing also an approach based on $Γ$-convergence theory.1 aAmato, Stefano1 aBellettini, Giovanni1 aPaolini, Maurizio uhttp://www.math.sissa.it/publication/constrained-bv-functions-double-coverings-plateaus-type-problems00720nas a2200109 4500008004100000245007700041210006900118260003100187520031700218100002400535856005100559 2014 en d00aA correction and an extension of Stampacchia's work on the geometric BVP0 acorrection and an extension of Stampacchias work on the geometri bAdvanced Nonlinear Studies3 aG. Stampacchia introduced the geometric boundary value problem for ODEs in his doctoral thesis and published four papers related to it. Here we point out that the proof of his last theorem on the subject is incorrect and we provide a substitute for it as well as a generalizations of some of his earlier results.1 aVidossich, Giovanni uhttp://urania.sissa.it/xmlui/handle/1963/3502301487nas a2200133 4500008004100000245003700041210003700078260001300115520111200128100001801240700002201258700002201280856005101302 2014 en d00aCrawling on directional surfaces0 aCrawling on directional surfaces bElsevier3 aIn this paper we study crawling locomotion based on directional frictional interactions, namely, frictional forces that are sensitive to the sign of the sliding velocity. Surface interactions of this type are common in biology, where they arise from the presence of inclined hairs or scales at the crawler/substrate interface, leading to low resistance when sliding ‘along the grain’, and high resistance when sliding ‘against the grain’. This asymmetry can be exploited for locomotion, in a way analogous to what is done in cross-country skiing (classic style, diagonal stride). We focus on a model system, namely, a continuous one-dimensional crawler and provide a detailed study of the motion resulting from several strategies of shape change. In particular, we provide explicit formulae for the displacements attainable with reciprocal extensions and contractions (breathing), or through the propagation of extension or contraction waves. We believe that our results will prove particularly helpful for the study of biological crawling motility and for the design of bio-mimetic crawling robots.1 aGidoni, Paolo1 aNoselli, Giovanni1 aDeSimone, Antonio uhttp://urania.sissa.it/xmlui/handle/1963/3445001111nas a2200121 4500008004100000245006400041210006300105260003400168520070800202100002200910700002100932856003600953 2014 en d00aCritical points of the Moser-Trudinger functional on a disk0 aCritical points of the MoserTrudinger functional on a disk bEuropean Mathematical Society3 aOn the 2-dimensional unit disk $B_1$ we study the Moser-Trudinger functional $$E(u)=\int_{B_1}(e^{u^2}-1)dx, u\in H^1_0(B_1)$$ and its restrictions to $M_\Lambda:=\{u \in H^1_0(B_1):\|u\|^2_{H^1_0}=\Lambda\}$ for $\Lambda>0$. We prove that if a sequence $u_k$ of positive critical points of $E|_{M_{\Lambda_k}}$ (for some $\Lambda_k>0$) blows up as $k\to\infty$, then $\Lambda_k\to 4\pi$, and $u_k\to 0$ weakly in $H^1_0(B_1)$ and strongly in $C^1_{\loc}(\bar B_1\setminus\{0\})$. Using this we also prove that when $\Lambda$ is large enough, then $E|_{M_\Lambda}$ has no positive critical point, complementing previous existence results by Carleson-Chang, M. Struwe and Lamm-Robert-Struwe.1 aMalchiodi, Andrea1 aMartinazzi, Luca uhttp://hdl.handle.net/1963/656001220nas a2200121 4500008004100000245009100041210006900132260001000201520080700211653002801018100001601046856003601062 2014 en d00aThe curvature of optimal control problems with applications to sub-Riemannian geometry0 acurvature of optimal control problems with applications to subRi bSISSA3 aOptimal control theory is an extension of the calculus of variations, and deals with the optimal behaviour of a system under a very general class of constraints. This field has been pioneered by the group of mathematicians led by Lev Pontryagin in the second half of the 50s and nowadays has countless applications to the real worlds (robotics, trains, aerospace, models for human behaviour, human vision, image reconstruction, quantum control, motion of self-propulsed micro-organism). In this thesis we introduce a novel definition of curvature for an optimal control problem. In particular it works for any sub-Riemannian and sub-Finsler structure. Related problems, such as comparison theorems for sub-Riemannian manifolds, LQ optimal control problem and Popp's volume and are also investigated.10aSub-Riemannian geometry1 aRizzi, Luca uhttp://hdl.handle.net/1963/732101482nas a2200157 4500008004100000245004800041210004700089260001300136300001400149490000700163520105700170100001801227700001701245700001301262856004901275 2014 en d00aCurvature-adapted remeshing of CAD surfaces0 aCurvatureadapted remeshing of CAD surfaces bElsevier a253–2650 v823 aA common representation of surfaces with complicated topology and geometry is through composite parametric surfaces as is the case for most CAD modelers. A challenging problem is how to generate a mesh of such a surface that well approximates the geometry of the surface, preserves its topology and important geometric features, and contains nicely shaped elements. In this work, we present an optimization-based surface remeshing method that is able to satisfy many of these requirements simultaneously. This method is inspired by the recent work of Lévy and Bonneel (Proc. 21th International Meshing Roundtable, October 2012), which embeds a smooth surface into a high-dimensional space and remesh it uniformly in that embedding space. Our method works directly in the 3d spaces and uses an embedding space in R6 to evaluate mesh size and mesh quality. It generates a curvatureadapted anisotropic surface mesh that well represents the geometry of the surface with a low number of elements. We illustrate our approach through various examples.

1 aDassi, Franco1 aMola, Andrea1 aSi, Hang uhttps://doi.org/10.1016/j.proeng.2014.10.38800422nas a2200121 4500008004100000245005500041210005500096300000700151490001100158100001900169700002000188856009200208 2014 eng d00aDarboux Transformations and Random Point Processes0 aDarboux Transformations and Random Point Processes a560 vrnu1221 aBertola, Marco1 aCafasso, Mattia uhttp://www.math.sissa.it/publication/darboux-transformations-and-random-point-processes00387nas 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/1963/743300403nas 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/1963/747500914nas a2200109 4500008004100000245010000041210006900141260001300210520050800223100002200731856005100753 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/1963/3444900943nas 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/1963/748500316nas a2200121 4500008004100000245001400041210001400055260001300069100002000082700002100102700002000123856005100143 2014 en d00aEditorial0 aEditorial bSpringer1 aCiliberto, Ciro1 aDal Maso, Gianni1 aVetro, Pasquale uhttp://urania.sissa.it/xmlui/handle/1963/3471201955nas a2200145 4500008004100000245009100041210006900132260006400201520139800265100002701663700002201690700002101712700002501733856005101758 2014 en d00aAn effective model for nematic liquid crystal composites with ferromagnetic inclusions0 aeffective model for nematic liquid crystal composites with ferro bSociety for Industrial and Applied Mathematics Publications3 aMolecules of a nematic liquid crystal respond to an applied magnetic field by reorienting themselves in the direction of the field. Since the dielectric anisotropy of a nematic is small, it takes relatively large fields to elicit a significant liquid crystal response. The interaction may be enhanced in colloidal suspensions of ferromagnetic particles in a liquid crystalline matrix- ferronematics-as proposed by Brochard and de Gennes in 1970. The ability of these particles to align with the field and simultaneously cause reorientation of the nematic molecules greatly increases the magnetic response of the mixture. Essentially the particles provide an easy axis of magnetization that interacts with the liquid crystal via surface anchoring. We derive an expression for the effective energy of ferronematic in the dilute limit, that is, when the number of particles tends to infinity while their total volume fraction tends to zero. The total energy of the mixture is assumed to be the sum of the bulk elastic liquid crystal contribution, the anchoring energy of the liquid crystal on the surfaces of the particles, and the magnetic energy of interaction between the particles and the applied magnetic field. The homogenized limiting ferronematic energy is obtained rigorously using a variational approach. It generalizes formal expressions previously reported in the physical literature.1 aCalderer, Maria, Carme1 aDeSimone, Antonio1 aGolovaty, Dmitry1 aPanchenko, Alexander uhttp://urania.sissa.it/xmlui/handle/1963/3494001996nas a2200109 4500008004100000245014300041210006900184520134000253653014901593100002001742856012401762 2014 en d00aAn efficient computational framework for reduced basis approximation and a posteriori error estimation of parametrized Navier-Stokes flows0 aefficient computational framework for reduced basis approximatio3 aWe present the current Reduced Basis framework for the efficient numerical approximation of parametrized steady Navier-Stokes equations. We have extended the existing setting developed in the last decade (see e.g. [Deparis, Veroy & Patera, Quarteroni & Rozza] to more general affine and nonaffine parametrizations (such as volume-based techniques), to a simultaneous velocity-pressure error estimates and to a fully decoupled Offline/Online procedure in order to speedup the solution of the reduced-order problem. This is particularly suitable for real-time and many-query contexts, which are both part of our final goal. Furthermore, we present an efficient numerical implementation for treating nonlinear advection terms in a convenient way. A residual-based a posteriori error estimation with respect to a truth, full-order Finite Element approximation is provided for joint pressure/velocity errors, according to the Brezzi-Rappaz-Raviart stability theory. To do this, we take advantage of an extension of the Successive Constraint Method for the estimation of stability factors and of a suitable fixed-point algorithm for the approximation of Sobolev embedding constants. Finally, we present some numerical test cases, in order to show both the approximation properties and the computational efficiency of the derived framework.10aReduced Basis Method, parametrized Navier-Stokes equations, steady incompressible fluids, a posteriori error estimation, approximation stability1 aManzoni, Andrea uhttp://www.math.sissa.it/publication/efficient-computational-framework-reduced-basis-approximation-and-posteriori-error01442nas a2200133 4500008004100000245015900041210006900200300001400269490000700283520085800290100001401148700002101162856012501183 2014 eng d00aEfficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems0 aEfficient geometrical parametrisation techniques of interfaces f a158–1690 v283 aWe present some recent advances and improvements in shape parametrisation techniques of interfaces for reduced-order modelling with special attention to fluid–structure interaction problems and the management of structural deformations, namely, to represent them into a low-dimensional space (by control points). This allows to reduce the computational effort, and to significantly simplify the (geometrical) deformation procedure, leading to more efficient and fast reduced-order modelling applications in this kind of problems. We propose an efficient methodology to select the geometrical control points for the radial basis functions based on a modal greedy algorithm to improve the computational efficiency in view of more complex fluid–structure applications in several fields. The examples provided deal with aeronautics and wind engineering.1 aForti, D.1 aRozza, Gianluigi uhttp://www.math.sissa.it/publication/efficient-geometrical-parametrisation-techniques-interfaces-reduced-order-modelling00833nas a2200121 4500008004100000245010200041210006900143260003900212520036100251100002300612700002500635856005100660 2014 en d00aExistence and uniqueness of the gradient flow of the Entropy in the space of probability measures0 aExistence and uniqueness of the gradient flow of the Entropy in bEUT Edizioni Universita di Trieste3 aAfter a brief introduction on gradient flows in metric spaces and on geodesically convex functionals, we give an account of the proof (following the outline of [3, 7]) of the existence and uniqueness of the gradient flow of the Entropy in the space of Borel probability measures over a compact geodesic metric space with Ricci curvature bounded from below.1 aBianchini, Stefano1 aDabrowski, Alexander uhttp://urania.sissa.it/xmlui/handle/1963/3469301351nas a2200133 4500008004100000245008400041210007000125260003900195520087300234100001901107700001901126700002101145856005101166 2014 en d00aFinite dimensional Kadomtsev-Petviashvili τ-functions. I. Finite Grassmannians0 aFinite dimensional KadomtsevPetviashvili τfunctions I Finite Gra bAmerican Institute of Physics Inc.3 aWe study τ-functions of the Kadomtsev-Petviashvili hierarchy in terms of abelian group actions on finite dimensional Grassmannians, viewed as subquotients of the Hilbert space Grassmannians of Sato, Segal, and Wilson. A determinantal formula of Gekhtman and Kasman involving exponentials of finite dimensional matrices is shown to follow naturally from such reductions. All reduced flows of exponential type generated by matrices with arbitrary nondegenerate Jordan forms are derived, both in the Grassmannian setting and within the fermionic operator formalism. A slightly more general determinantal formula involving resolvents of the matrices generating the flow, valid on the big cell of the Grassmannian, is also derived. An explicit expression is deduced for the Plücker coordinates appearing as coefficients in the Schur function expansion of the τ-function.1 aBalogh, Ferenc1 aFonseca, Tiago1 aHarnad, John, P. uhttp://urania.sissa.it/xmlui/handle/1963/3495201201nas a2200145 4500008004100000245010600041210006900147260001000216520062900226653002300855100001700878700001700895700002200912856012100934 2014 en d00aA fully nonlinear potential model for ship hydrodynamics directly interfaced with CAD data structures0 afully nonlinear potential model for ship hydrodynamics directly bSISSA3 aWe present a model for ship hydrodynamics simulations currently under development at SISSA. The model employs potential flow theory and fully nonlinear free surface boundary conditions. The spatial discretization of the equations is performed by means of a collocation BEM. This gives rise to a Differential Algbraic Equations (DAE) system, solved using an implicit BDF scheme to time advance the solution. The model has been implemented into a C++ software able to automatically generate the computational grids from the CAD geometry of the hull. Numerical results on Kriso KCS and KVLCC2 hulls are presented and discussed.10aship hydrodynamics1 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio uhttp://www.math.sissa.it/publication/fully-nonlinear-potential-model-ship-hydrodynamics-directly-interfaced-cad-data01603nas a2200133 4500008004100000245010100041210006900142260001900211490000800230520099000238653009201228100002101320856012801341 2014 eng d00aFundamentals of Reduced Basis Method for problems governed by parametrized PDEs and applications0 aFundamentals of Reduced Basis Method for problems governed by pa aWienbSpringer0 v5543 aIn this chapter we consider Reduced Basis (RB) approximations of parametrized Partial Differential Equations (PDEs). The the idea behind RB is to decouple the generation and projection stages (Offline/Online computational procedures) of the approximation process in order to solve parametrized PDEs in a fast, inexpensive and reliable way. The RB method, especially applied to 3D problems, allows great computational savings with respect to the classical Galerkin Finite Element (FE) Method. The standard FE method is typically ill suited to (i) iterative contexts like optimization, sensitivity analysis and many-queries in general, and (ii) real time evaluation. We consider for simplicity coercive PDEs. We discuss all the steps to set up a RB approximation, either from an analytical and a numerical point of view. Then we present an application of the RB method to a steady thermal conductivity problem in heat transfer with emphasis on geometrical and physical parameters.

10areduced basis method, linear elasticity, heat transfer, error bounds, parametrized PDEs1 aRozza, Gianluigi uhttp://www.math.sissa.it/publication/fundamentals-reduced-basis-method-problems-governed-parametrized-pdes-and-applications01517nas a2200121 4500008004100000245010200041210006900143260001000212520108600222653001901308100001801327856005001345 2014 en d00aGeometry and analysis of control-affine systems: motion planning, heat and Schrödinger evolution0 aGeometry and analysis of controlaffine systems motion planning h bSISSA3 aThis thesis is dedicated to two problems arising from geometric control theory, regarding control-affine systems $\dot q= f_0(q)+\sum_{j=1}^m u_j f_j(q)$, where $f_0$ is called the drift. In the first part we extend the concept of complexity of non-admissible trajectories, well understood for sub-Riemannian systems, to this more general case, and find asymptotic estimates. In order to do this, we also prove a result in the same spirit as the Ball-Box theorem for sub-Riemannian systems, in the context of control-affine systems equipped with the L1 cost. Then, in the second part of the thesis, we consider a family of 2-dimensional driftless control systems. For these, we study how the set where the control vector fields become collinear affects the diffusion dynamics. More precisely, we study whether solutions to the heat and Schrödinger equations associated with this Laplace-Beltrami operator are able to cross this singularity, and how its the presence affects the spectral properties of the operator, in particular under a magnetic Aharonov–Bohm-type perturbation.10acontrol theory1 aPrandi, Dario uhttp://urania.sissa.it/xmlui/handle/1963/747401325nas a2200121 4500008004100000245014300041210006900184260002100253520084300274100002301117700001201140856005101152 2014 en d00aGlobal Structure of Admissible BV Solutions to Piecewise Genuinely Nonlinear, Strictly Hyperbolic Conservation Laws in One Space Dimension0 aGlobal Structure of Admissible BV Solutions to Piecewise Genuine bTaylor & Francis3 aThe paper describes the qualitative structure of an admissible BV solution to a strictly hyperbolic system of conservation laws whose characteristic families are piecewise genuinely nonlinear. More precisely, we prove that there are a countable set of points Θ and a countable family of Lipschitz curves T{script} such that outside T{script} ∪ Θ the solution is continuous, and for all points in T{script}{set minus}Θ the solution has left and right limit. This extends the corresponding structural result in [7] for genuinely nonlinear systems. An application of this result is the stability of the wave structure of solution w.r.t. -convergence. The proof is based on the introduction of subdiscontinuities of a shock, whose behavior is qualitatively analogous to the discontinuities of the solution to genuinely nonlinear systems.1 aBianchini, Stefano1 aYu, Lei uhttp://urania.sissa.it/xmlui/handle/1963/3469400855nas a2200121 4500008004100000245008300041210006900124260001000193520045200203653002300655100001900678856003600697 2014 en d00aGlobally stable quasistatic evolution for a coupled elastoplastic-damage model0 aGlobally stable quasistatic evolution for a coupled elastoplasti bSISSA3 aWe show the existence of globally stable quasistatic evolutions for a material model with elastoplasticity and incomplete damage, in small strain assumptions. The main feature of our model is that the scalar internal variable which describes the damage a ects both the elastic tensor and the plastic yield surface. It is also possible to require that the history of plastic strain up to the current state influences the future evolution of damage.10aVariational models1 aCrismale, Vito uhttp://hdl.handle.net/1963/732400950nas a2200121 4500008004100000245004700041210004300088520060300131100002100734700001700755700002000772856003600792 2014 en d00aThe Gysin Sequence for Quantum Lens Spaces0 aGysin Sequence for Quantum Lens Spaces3 aWe define quantum lens spaces as `direct sums of line bundles' and exhibit them as `total spaces' of certain principal bundles over quantum projective spaces. For each of these quantum lens spaces we construct an analogue of the classical Gysin sequence in K-theory. We use the sequence to compute the K-theory of the quantum lens spaces, in particular to give explicit geometric representatives of their K-theory classes. These representatives are interpreted as `line bundles' over quantum lens spaces and generically define `torsion classes'. We work out explicit examples of these classes.1 aArici, Francesca1 aBrain, Simon1 aLandi, Giovanni uhttp://hdl.handle.net/1963/724601342nas a2200121 4500008004100000245007300041210006900114260001000183520091400193653004101107100002201148856005001170 2014 en d00aHolomorphically symplectic varieties with Prym Lagrangian fibrations0 aHolomorphically symplectic varieties with Prym Lagrangian fibrat bSISSA3 aThe thesis presents a construction of singular holomorphically symplectic varieties as Lagrangian fibrations. They are relative compactified Prym varieties associated to curves on symplectic surfaces with an antisymplectic involution. They are identified with the fixed locus of a symplectic involution on singular moduli spaces of sheaves of dimension 1. An explicit example, giving a singular irreducible symplectic 6-fold without symplectic resolutions, is described for a K3 surface which is the double cover of a cubic surface. In the case of abelian surfaces, a variation of this construction is studied to get irreducible symplectic varieties: relative compactified 0-Prym varieties. A partial classification result is obtained for involutions without fixed points: either the 0-Prym variety is birational to an irreducible symplectic variety of K3[n]-type, or it does not admit symplectic resolutions.10aHolomorphically symplectic varieties1 aMatteini, Tommaso uhttp://urania.sissa.it/xmlui/handle/1963/743400862nas a2200133 4500008004100000245008700041210006900128260001000197520041000207100001700617700002200634700002200656856005000678 2014 en d00aHomogenization of functional with linear growth in the context of A-quasiconvexity0 aHomogenization of functional with linear growth in the context o bSISSA3 aThis work deals with the homogenization of functionals with linear growth in the context of A-quasiconvexity. A representation theorem is proved, where the new integrand function is obtained by solving a cell problem where the coupling between homogenization and the A-free condition plays a crucial role. This result extends some previous work to the linear case, thus allowing for concentration effects.1 aMatias, Jose1 aMorandotti, Marco1 aSantos, Pedro, M. uhttp://urania.sissa.it/xmlui/handle/1963/743600620nas a2200121 4500008004100000245006500041210006500106260001300171520022300184100001800407700002200425856005100447 2014 en d00aHomology computation for a class of contact structures on T30 aHomology computation for a class of contact structures on T3 bSpringer3 aWe consider a family of tight contact forms on the three-dimensional torus and we compute the relative Contact Homology by using the variational theory of critical points at infinity. We will also show local stability.1 aMaalaoui, Ali1 aMartino, Vittorio uhttp://urania.sissa.it/xmlui/handle/1963/3464901081nas a2200145 4500008004100000245007200041210006900113300001400182490000800196520057300204100001600777700002100793700002100814856010000835 2014 eng d00aAn improvement on geometrical parameterizations by transfinite maps0 aimprovement on geometrical parameterizations by transfinite maps a263–2680 v3523 aWe present a method to generate a non-affine transfinite map from a given reference domain to a family of deformed domains. The map is a generalization of the Gordon-Hall transfinite interpolation approach. It is defined globally over the reference domain. Once we have computed some functions over the reference domain, the map can be generated by knowing the parametric expressions of the boundaries of the deformed domain. Being able to define a suitable map from a reference domain to a desired deformation is useful for the management of parameterized geometries.1 aJäggli, C.1 aIapichino, Laura1 aRozza, Gianluigi uhttp://www.math.sissa.it/publication/improvement-geometrical-parameterizations-transfinite-maps00921nas a2200121 4500008004100000245008300041210006900124260001300193520050800206100001800714700001600732856005100748 2014 en d00aInfinite-dimensional Frobenius manifolds underlying the Toda lattice hierarchy0 aInfinitedimensional Frobenius manifolds underlying the Toda latt bElsevier3 aFollowing the approach of Carlet et al. (2011) [9], we construct a class of infinite-dimensional Frobenius manifolds underlying the Toda lattice hierarchy, which are defined on the space of pairs of meromorphic functions with possibly higher-order poles at the origin and at infinity. We also show a connection between these infinite-dimensional Frobenius manifolds and the finite-dimensional Frobenius manifolds on the orbit space of extended affine Weyl groups of type A defined by Dubrovin and Zhang.1 aWu, Chaozhong1 aZuo, Dafeng uhttp://urania.sissa.it/xmlui/handle/1963/3502600754nas a2200133 4500008004100000245006000041210005900101260001000160520035300170100002100523700002000544700002000564856003600584 2014 en d00aIntegrability of Dirac reduced bi-Hamiltonian equations0 aIntegrability of Dirac reduced biHamiltonian equations bSISSA3 aFirst, we give a brief review of the theory of the Lenard-Magri scheme for a non-local bi-Poisson structure and of the theory of Dirac reduction. These theories are used in the remainder of the paper to prove integrability of three hierarchies of bi-Hamiltonian PDE's, obtained by Dirac reduction from some generalized Drinfeld-Sokolov hierarchies.1 aDe Sole, Alberto1 aKac, Victor, G.1 aValeri, Daniele uhttp://hdl.handle.net/1963/724700973nas a2200109 4500008004100000245008800041210006900129520042300198653010900621100002200730856011100752 2014 en d00aAn irreducible symplectic orbifold of dimension 6 with a Lagrangian Prym fibration0 airreducible symplectic orbifold of dimension 6 with a Lagrangian3 aA new example of an irreducible symplectic variety of dimension 6, with only finite quotient singularities, is described as a relative compactified Prymian of a family of genus 4 curves with involution. It is associated to a K3 surface which is a double cover of a cubic surface. It has a natural Lagrangian fibration in abelian 3-folds with polarization type (1,1,2). It does not admit any symplectic resolution.10aIrreducible symplectic variety, Lagrangian fibration, Prym variety, automorphism of symplectic varieties1 aMatteini, Tommaso uhttp://www.math.sissa.it/publication/irreducible-symplectic-orbifold-dimension-6-lagrangian-prym-fibration00957nas a2200121 4500008004100000245007500041210006900116260004100185520053400226100002000760700001900780856003600799 2014 en d00aOn an isomonodromy deformation equation without the Painlevé property0 aisomonodromy deformation equation without the Painlevé property bMaik Nauka-Interperiodica Publishing3 aWe show that the fourth order nonlinear ODE which controls the pole dynamics in the general solution of equation $P_I^2$ compatible with the KdV equation exhibits two remarkable properties: 1) it governs the isomonodromy deformations of a $2\times2$ matrix linear ODE with polynomial coefficients, and 2) it does not possesses the Painlev\'e property. We also study the properties of the Riemann--Hilbert problem associated to this ODE and find its large $t$ asymptotic solution for the physically interesting initial data.1 aDubrovin, Boris1 aKapaev, Andrey uhttp://hdl.handle.net/1963/646601518nas a2200145 4500008004100000022001300041245008300054210006900137300000900206520098400215100001301199700002401212700002301236856011301259 2014 eng d a0025583100aKAM for quasi-linear and fully nonlinear forced perturbations of Airy equation0 aKAM for quasilinear and fully nonlinear forced perturbations of a1-663 aWe prove the existence of small amplitude quasi-periodic solutions for quasi-linear and fully nonlinear forced perturbations of the linear Airy equation. For Hamiltonian or reversible nonlinearities we also prove their linear stability. The key analysis concerns the reducibility of the linearized operator at an approximate solution, which provides a sharp asymptotic expansion of its eigenvalues. For quasi-linear perturbations this cannot be directly obtained by a KAM iteration. Hence we first perform a regularization procedure, which conjugates the linearized operator to an operator with constant coefficients plus a bounded remainder. These transformations are obtained by changes of variables induced by diffeomorphisms of the torus and pseudo-differential operators. At this point we implement a Nash-Moser iteration (with second order Melnikov non-resonance conditions) which completes the reduction to constant coefficients. © 2014 Springer-Verlag Berlin Heidelberg.1 aBaldi, P1 aBerti, Massimiliano1 aMontalto, Riccardo uhttp://www.math.sissa.it/publication/kam-quasi-linear-and-fully-nonlinear-forced-perturbations-airy-equation00376nas a2200097 4500008004100000245008500041210006900126260001000195100002300205856005000228 2014 en d00aKAM for quasi-linear and fully nonlinear perturbations of Airy and KdV equations0 aKAM for quasilinear and fully nonlinear perturbations of Airy an bSISSA1 aMontalto, Riccardo uhttp://urania.sissa.it/xmlui/handle/1963/747600573nas a2200157 4500008004100000245002900041210002800070260001300098300001200111490000800123520017300131100001300304700002400317700002300341856005100364 2014 en d00aKAM for quasi-linear KdV0 aKAM for quasilinear KdV bElsevier a603-6070 v3523 aWe prove the existence and stability of Cantor families of quasi-periodic, small-amplitude solutions of quasi-linear autonomous Hamiltonian perturbations of KdV.

1 aBaldi, P1 aBerti, Massimiliano1 aMontalto, Riccardo uhttp://urania.sissa.it/xmlui/handle/1963/3506700608nas a2200157 4500008004100000245004900041210004900090260001300139300001200152490000800164520016500172100002400337700001700361700002100378856005100399 2014 en d00aKAM for Reversible Derivative Wave Equations0 aKAM for Reversible Derivative Wave Equations bSpringer a905-9550 v2123 aWe prove the existence of Cantor families of small amplitude, analytic, linearly stable quasi-periodic solutions of reversible derivative wave equations.

1 aBerti, Massimiliano1 aBiasco, Luca1 aProcesi, Michela uhttp://urania.sissa.it/xmlui/handle/1963/3464601112nas a2200145 4500008004100000245013100041210006900172260001000241520051500251653010200766100002100868700002200889700001900911856003600930 2014 en d00aLaplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length0 aLaplace equation in a domain with a rectilinear crack higher ord bSISSA3 aWe consider the weak solution of the Laplace equation in a planar domain with a straight crack, prescribing a homogeneous Neumann condition on the crack and a nonhomogeneous Dirichlet condition on the rest of the boundary. For every k we express the k-th derivative of the energy with respect to the crack length in terms of a finite number of coefficients of the asymptotic expansion of the solution near the crack tip and of a finite number of other parameters, which only depend on the shape of the domain.10acracked domains, energy release rate, higher order derivatives, asymptotic expansion of solutions1 aDal Maso, Gianni1 aOrlando, Gianluca1 aToader, Rodica uhttp://hdl.handle.net/1963/727100830nas a2200121 4500008004100000245005800041210005800099260003100157520043000188100001700618700002200635856005100657 2014 en d00aLecture notes on gradient flows and optimal transport0 aLecture notes on gradient flows and optimal transport bCambridge University Press3 aWe present a short overview on the strongest variational formulation for gradient flows of geodesically λ-convex functionals in metric spaces, with applications to diffusion equations in Wasserstein spaces of probability measures. These notes are based on a series of lectures given by the second author for the Summer School "Optimal transportation: Theory and applications" in Grenoble during the week of June 22-26, 2009.1 aDaneri, Sara1 aSavarè, Giuseppe uhttp://urania.sissa.it/xmlui/handle/1963/3509300818nas a2200109 4500008004100000245005900041210005900100260003000159520044600189100002200635856005100657 2014 en d00aLegendre duality on hypersurfaces in Kähler manifolds0 aLegendre duality on hypersurfaces in Kähler manifolds bWalter de Gruyter and Co.3 aWe give a sufficient condition on real strictly Levi-convex hypersurfaces M, embedded in four-dimensional Kähler manifolds V , such that Legendre duality can be performed. We consider the contact form onM whose kernel is the restriction of the holomorphic tangent space of V and show that if there exists a Legendrian Killing vector field v, then the dual form β(̇) := d(v, ̇) is a contact form on M with the same orientation than theta.1 aMartino, Vittorio uhttp://urania.sissa.it/xmlui/handle/1963/3477700762nas a2200121 4500008004100000245010000041210006900141260001300210520031900223100002200542700002500564856005100589 2014 en d00aLipschitz continuous viscosity solutions for a class of fully nonlinear equations on lie groups0 aLipschitz continuous viscosity solutions for a class of fully no bSpringer3 aIn this paper, we prove existence and uniqueness of Lipschitz continuous viscosity solutions for Dirichlet problems involving a class a fully non-linear operators on Lie groups. In particular, we consider the elementary symmetric functions of the eigenvalues of the Hessian built with left-invariant vector fields.1 aMartino, Vittorio1 aMontanari, Annamaria uhttp://urania.sissa.it/xmlui/handle/1963/3469901008nas a2200133 4500008004100000245008400041210006900125260002200194520054200216653003500758100002000793700002500813856003600838 2014 en d00aLocal and global minimality results for a nonlocal isoperimetric problem on R^N0 aLocal and global minimality results for a nonlocal isoperimetric bSIAM Publications3 aWe consider a nonlocal isoperimetric problem defined in the whole space R^N, whose nonlocal part is given by a Riesz potential with exponent $\alpha\in(0, N-1)$. We show that critical configurations with positive second variation are local minimizers and satisfy a quantitative inequality with respect to the L^1-norm. This criterion provides the existence of a (explicitly determined) critical threshold determining the interval of volumes for which the ball is a local minimizer, and allows to address several global minimality issues.10aNonlocal isoperimetric problem1 aBonacini, Marco1 aCristoferi, Riccardo uhttp://hdl.handle.net/1963/698400577nas a2200145 4500008004100000245004600041210004500087260001000132520011500142653003000257100002200287700001700309700002500326856008000351 2014 en d00aLocal behavior of fractional p-minimizers0 aLocal behavior of fractional pminimizers bSISSA3 aWe extend the De Giorgi-Nash Moser theory to nonlocal, possibly degerate integro-differential operators

10afractional Sobolev spaces1 aDi Castro, Agnese1 aKuusi, Tuomo1 aPalatucci, Giampiero uhttp://www.math.sissa.it/publication/local-behavior-fractional-p-minimizers00800nas a2200133 4500008004100000245006400041210005600105260003400161520035400195100002200549700002300571700002100594856005100615 2014 en d00aOn the Lp-differentiability of certain classes of functions0 aLpdifferentiability of certain classes of functions bEuropean Mathematical Society3 aWe prove the Lp-differentiability at almost every point for convolution products on ℝd of the form K*μ, where μ is bounded measure and K is a homogeneous kernel of degree 1-d. From this result we derive the Lp-differentiability for vector fields on R d whose curl and divergence are measures, and also for vector fields with bounded deformation.1 aAlberti, Giovanni1 aBianchini, Stefano1 aCrippa, Gianluca uhttp://urania.sissa.it/xmlui/handle/1963/3469500683nas a2200109 4500008004100000245005300041210005300094260001300147520034200160100002000502856005100522 2014 en d00aMaximal generalized solution of eikonal equation0 aMaximal generalized solution of eikonal equation bElsevier3 aWe study the Dirichlet problem for the eikonal equation: 1/2 |∇u(x)|^2-a(x)=0 in Ω u(x)=(x) on Ω, without continuity assumptions on the map a(.). We find a class of maps a(.) contained in the space L∞(Ω) for which the problem admits a (maximal) generalized solution, providing a generalization of the notion of viscosity solution.1 aZagatti, Sandro uhttp://urania.sissa.it/xmlui/handle/1963/3464201625nas a2200133 4500008004100000245007900041210006900120260001300189520117000202100002301372700002001395700002501415856005101440 2014 en d00aMinimal Liouville gravity correlation numbers from Douglas string equation0 aMinimal Liouville gravity correlation numbers from Douglas strin bSpringer3 aWe continue the study of $(q,p)$ Minimal Liouville Gravity with the help of Douglas string equation. We generalize the results of \cite{Moore:1991ir}, \cite{Belavin:2008kv}, where Lee-Yang series $(2,2s+1)$ was studied, to $(3,3s+p_0)$ Minimal Liouville Gravity, where $p_0=1,2$. We demonstrate that there exist such coordinates $\tau_{m,n}$ on the space of the perturbed Minimal Liouville Gravity theories, in which the partition function of the theory is determined by the Douglas string equation. The coordinates $\tau_{m,n}$ are related in a non-linear fashion to the natural coupling constants $\lambda_{m,n}$ of the perturbations of Minimal Lioville Gravity by the physical operators $O_{m,n}$. We find this relation from the requirement that the correlation numbers in Minimal Liouville Gravity must satisfy the conformal and fusion selection rules. After fixing this relation we compute three- and four-point correlation numbers when they are not zero. The results are in agreement with the direct calculations in Minimal Liouville Gravity available in the literature \cite{Goulian:1990qr}, \cite{Zamolodchikov:2005sj}, \cite{Belavin:2006ex}.1 aBelavin, Alexander1 aDubrovin, Boris1 aMukhametzhanov, Baur uhttp://urania.sissa.it/xmlui/handle/1963/3458801649nas a2200145 4500008004100000245007300041210006900114260001300183520112000196100001801316700002001334700002201354700002101376856010601397 2014 en d00aModel Order Reduction in Fluid Dynamics: Challenges and Perspectives0 aModel Order Reduction in Fluid Dynamics Challenges and Perspecti bSpringer3 aThis chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities - which are mainly related either to nonlinear convection terms and/or some geometric variability - that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration. We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of inf-sup stability, certification through error estimation, computational issues and-in the unsteady case - long-time stability of the reduced model. Moreover, we provide an extensive list of literature references.1 aLassila, Toni1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://www.math.sissa.it/publication/model-order-reduction-fluid-dynamics-challenges-and-perspectives01391nas a2200109 4500008004100000245005300041210005000094260001300144520105400157100001901211856005101230 2014 en d00aA modular spectral triple for κ-Minkowski space0 amodular spectral triple for κMinkowski space bElsevier3 aWe present a spectral triple for κ-Minkowski space in two dimensions. Starting from an algebra naturally associated to this space, a Hilbert space is built using a weight which is invariant under the κ-Poincaré algebra. The weight satisfies a KMS condition and its associated modular operator plays an important role in the construction. This forces us to introduce two ingredients which have a modular flavour: the first is a twisted commutator, used to obtain a boundedness condition for the Dirac operator, and the second is a weight replacing the usual operator trace, used to measure the growth of the resolvent of the Dirac operator. We show that, under some assumptions related to the symmetries and the classical limit, there is a unique Dirac operator and automorphism such that the twisted commutator is bounded. Then, using the weight mentioned above, we compute the spectral dimension associated to the spectral triple and find that is equal to the classical dimension. Finally we briefly discuss the introduction of a real structure.1 aMatassa, Marco uhttp://urania.sissa.it/xmlui/handle/1963/3489501400nas a2200121 4500008004100000245006100041210005800102260001000160520101000170100002601180700002201206856005001228 2014 en d00aMotility of a Model Bristle-Bot: a Theoretical Analysis.0 aMotility of a Model BristleBot a Theoretical Analysis bSISSA3 aBristle-bots are legged robots that can be easily made out of a toothbrush head and a small vibrating engine. Despite their simple appearance, the mechanism enabling them to propel themselves by exploiting friction with the substrate is far from trivial. Numerical experiments on a model bristle-bot have been able to reproduce such a mechanism revealing, in addition, the ability to switch direction of motion by varying the vibration frequency. This paper provides a detailed account of these phenomena through a fully analytical treatment of the model. The equations of motion are solved through an expansion in terms of a properly chosen small parameter. The convergence of the expansion is rigorously proven. In addition, the analysis delivers formulas for the average velocity of the robot and for the frequency at which the direction switch takes place. A quantitative description of the mechanism for the friction modulation underlying the motility of the bristle-bot is also provided.1 aCicconofri, Giancarlo1 aDeSimone, Antonio uhttp://urania.sissa.it/xmlui/handle/1963/746501308nas a2200133 4500008004100000245005300041210005000094260001300144520090800157100001601065700002001081700002201101856005101123 2014 en d00aN = 2 Quiver Gauge Theories on A-type ALE Spaces0 aN 2 Quiver Gauge Theories on Atype ALE Spaces bSpringer3 aWe survey and compare recent approaches to the computation of the partition functions and correlators of chiral BPS observables in N = 2 gauge theories on ALE spaces based on quiver varieties and the minimal resolution Xk of the Ak-1 toric singularity C2/Zk, in light of their recently conjectured duality with two-dimensional coset conformal field theories. We review and elucidate the rigorous constructions of gauge theories for a particular family of ALE spaces, using their relation to the cohomology of moduli spaces of framed torsion-free sheaves on a suitable orbifold compactification of Xk. We extend these computations to generic N = 2 superconformal quiver gauge theories, obtaining in these instances new constraints on fractional instanton charges, a rigorous proof of the Nekrasov master formula, and new quantizations of Hitchin systems based on the underlying Seiberg–Witten geometry.1 aBruzzo, Ugo1 aSala, Francesco1 aSzabo, Richard J. uhttp://urania.sissa.it/xmlui/handle/1963/3471900423nas a2200133 4500008004100000245005600041210005500097260001300152653002200165100001800187700002100205700002700226856003600253 2014 en d00aNew results on Gamma-limits of integral functionals0 aNew results on Gammalimits of integral functionals bElsevier10aGamma-convergence1 aAnsini, Nadia1 aDal Maso, Gianni1 aZeppieri, Caterina Ida uhttp://hdl.handle.net/1963/588000655nas a2200121 4500008004100000245008200041210006900123260001000192520017100202653002900373100001900402856011200421 2014 en d00aNon-commutative integration for spectral triples associated to quantum groups0 aNoncommutative integration for spectral triples associated to qu bSISSA3 aThis thesis is dedicated to the study of non-commutative integration, in the sense of spectral triples, for some non-commutative spaces associated to quantum groups.10aNon-commutative geometry1 aMatassa, Marco uhttp://www.math.sissa.it/publication/non-commutative-integration-spectral-triples-associated-quantum-groups02051nas a2200145 4500008004100000245007600041210006900117260001300186520158600199653002601785100001701811700001901828700002201847856003601869 2014 en d00aNonsingular Isogeometric Boundary Element Method for Stokes Flows in 3D0 aNonsingular Isogeometric Boundary Element Method for Stokes Flow bElsevier3 aIsogeometric analysis (IGA) is emerging as a technology bridging Computer Aided Geometric Design (CAGD), most commonly based on Non-Uniform Rational B-Splines (NURBS) surfaces, and engineering analysis. In finite element and boundary element isogeometric methods (FE-IGA and IGA-BEM), the NURBS basis functions that de- scribe the geometry define also the approximation spaces. In the FE-IGA approach, the surfaces generated by the CAGD tools need to be extended to volumetric descriptions, a major open problem in 3D. This additional passage can be avoided in principle when the partial differential equations to be solved admit a formulation in terms of bound- ary integral equations, leading to Boundary Element Isogeometric Analysis (IGA-BEM). The main advantages of such an approach are given by the dimensionality reduction of the problem (from volumetric-based to surface-based), by the fact that the interface with CAGD tools is direct, and by the possibility to treat exterior problems, where the computational domain is infinite. By contrast, these methods produce system matrices which are full, and require the integration of singular kernels. In this paper we address the second point and propose a nonsingular formulation of IGA-BEM for 3D Stokes flows, whose convergence is carefully tested numerically. Standard Gaussian quadrature rules suffice to integrate the boundary integral equations, and carefully chosen known exact solutions of the interior Stokes problem are used to correct the resulting matrices, extending the work by Klaseboer et al. [27] to IGA-BEM.10aIsogeometric Analysis1 aHeltai, Luca1 aArroyo, Marino1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/632600908nas a2200109 4500008004100000245004700041210004700088260001300135520057900148100002000727856005100747 2014 en d00aPfaffian representations of cubic surfaces0 aPfaffian representations of cubic surfaces bSpringer3 aLet K be a field of characteristic zero. We describe an algorithm which requires a homogeneous polynomial F of degree three in K[x0,x1,x2,x3] and a zero a of F in P3 K and ensures a linear Pfaffian representation of V(F) with entries in K[x0,x1,x2,x3], under mild assumptions on F and a. We use this result to give an explicit construction of (and to prove the existence of) a linear Pfaffian representation of V (F), with entries in K′[x0,x1,x2,x3], being K′ an algebraic extension of K of degree at most six. An explicit example of such a construction is given.

1 aTanturri, Fabio uhttp://urania.sissa.it/xmlui/handle/1963/3468800929nas a2200121 4500008003900000245007100039210006900110520052100179100002100700700001500721700002000736856005100756 2014 d00aPimsner algebras and Gysin sequences from principal circle actions0 aPimsner algebras and Gysin sequences from principal circle actio3 aA self Morita equivalence over an algebra B, given by a B-bimodule E, is thought of as a line bundle over B. The corresponding Pimsner algebra O_E is then the total space algebra of a noncommutative principal circle bundle over B. A natural Gysin-like sequence relates the KK-theories of O_E and of B. Interesting examples come from O_E a quantum lens space over B a quantum weighted projective line (with arbitrary weights). The KK-theory of these spaces is explicitly computed and natural generators are exhibited.1 aArici, Francesca1 aKaad, Jens1 aLandi, Giovanni uhttp://urania.sissa.it/xmlui/handle/1963/3446100654nas a2200157 4500008004100000245010000041210006900141260005800210300001400268490000600282100001700288700001700305700002200322700002400344856012800368 2014 eng d00aPotential Model for Ship Hydrodynamics Simulations Directly Interfaced with CAD Data Structures0 aPotential Model for Ship Hydrodynamics Simulations Directly Inte bInternational Society of Offshore and Polar Engineers a815–8220 v41 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio1 aBerti, Massimiliano uhttp://www.math.sissa.it/publication/potential-model-ship-hydrodynamics-simulations-directly-interfaced-cad-data-structures00851nas a2200121 4500008004100000245009300041210006900134260001300203520042700216100001900643700001600662856005100678 2014 en d00aPseudo-automorphisms of positive entropy on the blowups of products of projective spaces0 aPseudoautomorphisms of positive entropy on the blowups of produc bSpringer3 aWe use a concise method to construct pseudo-automorphisms fn of the first dynamical degree d1(fn) > 1 on the blowups of the projective n-space for all n ≥ 2 and more generally on the blowups of products of projective spaces. These fn, for n=3 have positive entropy, and for n≥ 4 seem to be the first examples of pseudo-automorphisms with d1(fn) > 1 (and of non-product type) on rational varieties of higher dimensions.1 aPerroni, Fabio1 aZhang, Deqi uhttp://urania.sissa.it/xmlui/handle/1963/3471400679nas a2200121 4500008004100000245005900041210005400100260003200154520027700186100002300463700002000486856005100506 2014 en d00aOn a quadratic functional for scalar conservation laws0 aquadratic functional for scalar conservation laws bWorld Scientific Publishing3 aWe prove a quadratic interaction estimate for approximate solutions to scalar conservation laws obtained by the wavefront tracking approximation or the Glimm scheme. This quadratic estimate has been used in the literature to prove the convergence rate of the Glimm scheme.1 aBianchini, Stefano1 aModena, Stefano uhttp://urania.sissa.it/xmlui/handle/1963/3469001648nas a2200121 4500008004100000245007800041210006900119260001000188520123500198100002301433700002001456856005001476 2014 en d00aQuadratic interaction functional for general systems of conservation laws0 aQuadratic interaction functional for general systems of conserva bSISSA3 aFor the Glimm scheme approximation u" to the solution of the system of conservation laws in one space dimension ut + f(u)x = 0; u(0; x) = u0(x) 2 Rn; with initial data u0 with small total variation, we prove a quadratic (w.r.t. Tot.Var.(u0)) interaction estimate, which has been used in the literature for stability and convergence results. No assumptions on the structure of the ux f are made (apart smoothness), and this estimate is the natural extension of the Glimm type interaction estimate for genuinely nonlinear systems. More precisely we obtain the following results: a new analysis of the interaction estimates of simple waves; a Lagrangian representation of the derivative of the solution, i.e. a map x(t;w) which follows the trajectory of each wave w from its creation to its cancellation; the introduction of the characteristic interval and partition for couples of waves, representing the common history of the two waves; a new functional Q controlling the variation in speed of the waves w.r.t. time. This last functional is the natural extension of the Glimm functional for genuinely nonlinear systems. The main result is that the distribution Dttx(t;w) is a measure with total mass O(1)Tot.Var.(u0)2.1 aBianchini, Stefano1 aModena, Stefano uhttp://urania.sissa.it/xmlui/handle/1963/744000844nas a2200109 4500008004100000245005200041210005200093260002900145520049000174100001900664856005100683 2014 en d00aQuantum dimension and quantum projective spaces0 aQuantum dimension and quantum projective spaces bInstitute of Mathematics3 aWe show that the family of spectral triples for quantum projective spaces introduced by D'Andrea and Dbrowski, which have spectral dimension equal to zero, can be reconsidered as modular spectral triples by taking into account the action of the element K2por its inverse. The spectral dimension computed in this sense coincides with the dimension of the classical projective spaces. The connection with the well known notion of quantum dimension of quantum group theory is pointed out.1 aMatassa, Marco uhttp://urania.sissa.it/xmlui/handle/1963/3476401462nas a2200145 4500008004100000245005600041210005600097260005100153520096300204100002501167700002401192700002701216700002201243856005101265 2014 en d00aQuantum gauge symmetries in noncommutative geometry0 aQuantum gauge symmetries in noncommutative geometry bEuropean Mathematical Society Publishing House3 aWe discuss generalizations of the notion of i) the group of unitary elements of a (real or complex) finite-dimensional C*-algebra, ii) gauge transformations and iii) (real) automorphisms in the framework of compact quantum group theory and spectral triples. The quantum analogue of these groups are defined as universal (initial) objects in some natural categories. After proving the existence of the universal objects, we discuss several examples that are of interest to physics, as they appear in the noncommutative geometry approach to particle physics: in particular, the C*-algebras M n(R), Mn(C) and Mn(H), describing the finite noncommutative space of the Einstein-Yang-Mills systems, and the algebras A F = C H M3 (C) and Aev = H H M4(C), that appear in Chamseddine-Connes derivation of the Standard Model of particle physics coupled to gravity. As a byproduct, we identify a "free" version of the symplectic group Sp.n/ (quaternionic unitary group).1 aBhowmick, Jyotishman1 aD'Andrea, Francesco1 aDas, Biswarup, Krishna1 aDabrowski, Ludwik uhttp://urania.sissa.it/xmlui/handle/1963/3489700712nas a2200157 4500008004100000245005200041210005100093260001300144300001200157490000800169520027400177100001800451700002100469700001900490856004500509 2014 en d00aQuasi-static crack growth in hydraulic fracture0 aQuasistatic crack growth in hydraulic fracture bElsevier a301-3180 v1093 aWe present a variational model for the quasi-static crack growth in hydraulic fracture in the framework of the energy formulation of rate-independent processes. The cracks are assumed to lie on a prescribed plane and to satisfy a very weak regularity assumption.

1 aAlmi, Stefano1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/20.500.11767/1735000777nas a2200133 4500008004100000245007800041210006900119260001000188520034000198653002800538100002100566700002000587856003600607 2014 en d00aQuasistatic evolution in perfect plasticity as limit of dynamic processes0 aQuasistatic evolution in perfect plasticity as limit of dynamic bSISSA3 aWe introduce a model of dynamic visco-elasto-plastic evolution in the linearly elastic regime and we prove an existence and uniqueness result. Then we study the limit of (a rescaled version of) the solutions when the data vary slowly. We prove that they converge, up to a subsequence, to a quasistatic evolution in perfect plasticity.10avisco-elasto-plasticity1 aDal Maso, Gianni1 aScala, Riccardo uhttp://hdl.handle.net/1963/698201353nas a2200145 4500008004100000245007400041210006900115260001000184520088100194100002401075700002001099700001901119700001901138856005001157 2014 en d00aRate-independent damage in thermo-viscoelastic materials with inertia0 aRateindependent damage in thermoviscoelastic materials with iner bSISSA3 aWe present a model for rate-independent, unidirectional, partial damage in visco-elastic materials with inertia and thermal effects. The damage process is modeled by means of an internal variable, governed by a rate-independent flow rule. The heat equation and the momentum balance for the displacements are coupled in a highly nonlinear way. Our assumptions on the corresponding energy functional also comprise the case of the Ambrosio-Tortorelli phase-field model (without passage to the brittle limit). We discuss a suitable weak formulation and prove an existence theorem obtained with the aid of a (partially) decoupled time-discrete scheme and variational convergence methods. We also carry out the asymptotic analysis for vanishing viscosity and inertia and obtain a fully rate-independent limit model for displacements and damage, which is Independent of temperature.1 aLazzaroni, Giuliano1 aRossi, Riccarda1 aThomas, Marita1 aToader, Rodica uhttp://urania.sissa.it/xmlui/handle/1963/744401330nas a2200121 4500008004100000245006100041210006000102260001900162520091900181653003501100100002301135856005001158 2014 en d00aRational curves and instantons on the Fano threefold Y_50 aRational curves and instantons on the Fano threefold Y5 barXiv preprint3 aThis thesis is an investigation of the moduli spaces of instanton bundles on the Fano threefold Y_5 (a linear section of Gr(2,5)). It contains new proofs of classical facts about lines, conics and cubics on Y_5, and about linear sections of Y_5. The main original results are a Grauert-Mülich theorem for the splitting type of instantons on conics, a bound to the splitting type of instantons on lines and an SL_2-equivariant description of the moduli space in charge 2 and 3. Using these results we prove the existence of a unique SL_2-equivariant instanton of minimal charge and we show that for all instantons of charge 2 the divisor of jumping lines is smooth. In charge 3, we provide examples of instantons with reducible divisor of jumping lines. Finally, we construct a natural compactification for the moduli space of instantons of charge 3, together with a small resolution of singularities for it.10aModuli space of vector bundles1 aSanna, Giangiacomo uhttp://urania.sissa.it/xmlui/handle/1963/748200565nas a2200133 4500008004100000245010000041210006900141300001000210100002100220700002200241700002100263700002100284856012600305 2014 eng d00aReduced basis method for the Stokes equations in decomposable domains using greedy optimization0 aReduced basis method for the Stokes equations in decomposable do a1–71 aIapichino, Laura1 aQuarteroni, Alfio1 aRozza, Gianluigi1 aVolkwein, Stefan uhttp://www.math.sissa.it/publication/reduced-basis-method-stokes-equations-decomposable-domains-using-greedy-optimization01877nam a2200181 4500008004100000022002200041245006700063210006700130250000600197260002100203300000800224490000600232520123600238653007801474100002201552700002101574856010001595 2014 eng d a978-3-319-02089-100aReduced Order Methods for Modeling and Computational Reduction0 aReduced Order Methods for Modeling and Computational Reduction a1 aMilanobSpringer a3340 v93 aThis monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics.

Several topics are covered, including: design, optimization, and control theory in real-time with applications in engineering; data assimilation, geometry registration, and parameter estimation with special attention to real-time computing in biomedical engineering and computational physics; real-time visualization of physics-based simulations in computer science; the treatment of high-dimensional problems in state space, physical space, or parameter space; the interactions between different model reduction and dimensionality reduction approaches; the development of general error estimation frameworks which take into account both model and discretization effects.

This book is primarily addressed to computational scientists interested in computational reduction techniques for large scale differential problems.

10areduced order methods, MOR, ROM, POD, RB, greedy, CFD, Numerical Analysis1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://www.math.sissa.it/publication/reduced-order-methods-modeling-and-computational-reduction01688nas a2200193 4500008004100000020002000041245009500061210006900156250004400225260008500269300002800354520096400382100002101346700001901367700001901386700001701405700002101422856005101443 2014 en d a978-079184595-000aA reduced order model for multi-group time-dependent parametrized reactor spatial kinetics0 areduced order model for multigroup timedependent parametrized re aAmerican Society Mechanical Engineering aPrague, Czech RepublicbAmerican Society of Mechanical Engineers (ASME)c07/2014 aV005T17A048-V005T17A0483 a

In this work, a Reduced Order Model (ROM) for multigroup time-dependent parametrized reactor spatial kinetics is presented. The Reduced Basis method (built upon a high-fidelity "truth" finite element approximation) has been applied to model the neutronics behavior of a parametrized system composed by a control rod surrounded by fissile material. The neutron kinetics has been described by means of a parametrized multi-group diffusion equation where the height of the control rod (i.e., how much the rod is inserted) plays the role of the varying parameter. In order to model a continuous movement of the rod, a piecewise affine transformation based on subdomain division has been implemented. The proposed ROM is capable to efficiently reproduce the neutron flux distribution allowing to take into account the spatial effects induced by the movement of the control rod with a computational speed-up of 30000 times, with respect to the "truth" model.

1 aSartori, Alberto1 aBaroli, Davide1 aCammi, Antonio1 aLuzzi, Lelio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3512300458nas a2200133 4500008004100000245007200041210006900113260001000182653003000192100002200222700002300244700002100267856003600288 2014 en d00aReduction on characteristics for continuous of a scalar balance law0 aReduction on characteristics for continuous of a scalar balance bSISSA10aMethod of characteristics1 aAlberti, Giovanni1 aBianchini, Stefano1 aCaravenna, Laura uhttp://hdl.handle.net/1963/656201325nas a2200133 4500008004100000245008000041210006900121260001000190520088100200100002301081700002101104700001601125856005001141 2014 en d00aRenormalization for autonomous nearly incompressible BV vector fields in 2D0 aRenormalization for autonomous nearly incompressible BV vector f bSISSA3 aGiven a bounded autonomous vector field $b \colon \R^d \to \R^d$, we study the uniqueness of bounded solutions to the initial value problem for the related transport equation \begin{equation*} \partial_t u + b \cdot \nabla u= 0. \end{equation*} We are interested in the case where $b$ is of class BV and it is nearly incompressible. Assuming that the ambient space has dimension $d=2$, we prove uniqueness of weak solutions to the transport equation. The starting point of the present work is the result which has been obtained in [7] (where the steady case is treated). Our proof is based on splitting the equation onto a suitable partition of the plane: this technique was introduced in [3], using the results on the structure of level sets of Lipschitz maps obtained in [1]. Furthermore, in order to construct the partition, we use Ambrosio's superposition principle [4].1 aBianchini, Stefano1 aBonicatto, Paolo1 aGusev, N.A. uhttp://urania.sissa.it/xmlui/handle/1963/748300545nas a2200109 4500008004100000245004500041210004300086260001300129520022100142100002100363856005100384 2014 en d00aA Review of the Sixth Painlevé Equation0 aReview of the Sixth Painlevé Equation bSpringer3 aFor the Painlevé VI transcendents, we provide a unitary description of the critical behaviours, the connection formulae, their complete tabulation, and the asymptotic distribution of poles close to a critical point.1 aGuzzetti, Davide uhttp://urania.sissa.it/xmlui/handle/1963/3465801082nas a2200121 4500008004100000245012700041210006900168260002900237520052100266100002200787700002200809856012900831 2014 en d00aA robotic crawler exploiting directional frictional interactions: experiments, numerics, and derivation of a reduced model0 arobotic crawler exploiting directional frictional interactions e bRoyal Society Publishing3 aWe present experimental and numerical results for a model crawler which is able to extract net positional changes from reciprocal shape changes, i.e. ‘breathing-like’ deformations, thanks to directional, frictional interactions with a textured solid substrate, mediated by flexible inclined feet. We also present a simple reduced model that captures the essential features of the kinematics and energetics of the gait, and compare its predictions with the results from experiments and from numerical simulations.1 aNoselli, Giovanni1 aDeSimone, Antonio uhttp://www.math.sissa.it/publication/robotic-crawler-exploiting-directional-frictional-interactions-experiments-numerics-and00632nas a2200109 4500008004100000245008300041210007100124260001300195520024000208100002300448856005100471 2014 en d00aSBV Regularity of Systems of Conservation Laws and Hamilton–Jacobi Equations0 aSBV Regularity of Systems of Conservation Laws and Hamilton–Jaco bSpringer3 aWe review the SBV regularity for solutions to hyperbolic systems of conservation laws and Hamilton-Jacobi equations. We give an overview of the techniques involved in the proof, and a collection of related problems concludes the paper.1 aBianchini, Stefano uhttp://urania.sissa.it/xmlui/handle/1963/3469101169nas a2200145 4500008004100000245008500041210006900126260001000195520065500205653006700860100002100927700001900948700002000967856003600987 2014 en d00aSecond Order Asymptotic Development for the Anisotropic Cahn-Hilliard Functional0 aSecond Order Asymptotic Development for the Anisotropic CahnHill bSISSA3 aThe asymptotic behavior of an anisotropic Cahn-Hilliard functional with prescribed mass and Dirichlet boundary condition is studied when the parameter $\varepsilon$ that determines the width of the transition layers tends to zero. The double-well potential is assumed to be even and equal to $|s-1|^\beta$ near $s=1$, with $1<\beta<2$. The first order term in the asymptotic development by $\Gamma$-convergence is well-known, and is related to a suitable anisotropic perimeter of the interface. Here it is shown that, under these assumptions, the second order term is zero, which gives an estimate on the rate of convergence of the minimum values.10aGamma-convergence, Cahn-Hilliard functional, phase transitions1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni uhttp://hdl.handle.net/1963/739001605nas a2200121 4500008004100000245008400041210006900125260002200194520117200216100002001388700002401408856005101432 2014 en d00aSemiclassical limit of focusing NLS for a family of square barrier initial data0 aSemiclassical limit of focusing NLS for a family of square barri bWiley Periodicals3 aThe small dispersion limit of the focusing nonlinear Schrödinger equation (NLS) exhibits a rich structure of sharply separated regions exhibiting disparate rapid oscillations at microscopic scales. The non-self-adjoint scattering problem and ill-posed limiting Whitham equations associated to focusing NLS make rigorous asymptotic results difficult. Previous studies have focused on special classes of analytic initial data for which the limiting elliptic Whitham equations are wellposed. In this paper we consider another exactly solvable family of initial data,the family of square barriers,ψ 0(x) = qχ[-L,L] for real amplitudes q. Using Riemann-Hilbert techniques, we obtain rigorous pointwise asymptotics for the semiclassical limit of focusing NLS globally in space and up to an O(1) maximal time. In particular, we show that the discontinuities in our initial data regularize by the immediate generation of genus-one oscillations emitted into the support of the initial data. To the best of our knowledge, this is the first case in which the genus structure of the semiclassical asymptotics for focusing NLS have been calculated for nonanalytic initial data.1 aJenkins, Robert1 aMcLaughlin, Kenneth uhttp://urania.sissa.it/xmlui/handle/1963/3506601649nas a2200121 4500008004100000245007500041210006900116260001300185520123700198100001901435700002201454856005101476 2014 en d00aShape control of active surfaces inspired by the movement of euglenids0 aShape control of active surfaces inspired by the movement of eug bElsevier3 aWe examine a novel mechanism for active surface morphing inspired by the cell body deformations of euglenids. Actuation is accomplished through in-plane simple shear along prescribed slip lines decorating the surface. Under general non-uniform actuation, such local deformation produces Gaussian curvature, and therefore leads to shape changes. Geometrically, a deformation that realizes the prescribed local shear is an isometric embedding. We explore the possibilities and limitations of this bio-inspired shape morphing mechanism, by first characterizing isometric embeddings under axisymmetry, understanding the limits of embeddability, and studying in detail the accessibility of surfaces of zero and constant curvature. Modeling mechanically the active surface as a non-Euclidean plate (NEP), we further examine the mechanism beyond the geometric singularities arising from embeddability, where mechanics and buckling play a decisive role. We also propose a non-axisymmetric actuation strategy to accomplish large amplitude bending and twisting motions of elongated cylindrical surfaces. Besides helping understand how euglenids delicately control their shape, our results may provide the background to engineer soft machines.1 aArroyo, Marino1 aDeSimone, Antonio uhttp://urania.sissa.it/xmlui/handle/1963/3511801626nas a2200145 4500008004100000245010700041210006900148260001300217520111600230100002401346700002001370700002101390700001801411856005101429 2014 en d00aShape Optimization by Free-Form Deformation: Existence Results and Numerical Solution for Stokes Flows0 aShape Optimization by FreeForm Deformation Existence Results and bSpringer3 aShape optimization problems governed by PDEs result from many applications in computational fluid dynamics. These problems usually entail very large computational costs and require also a suitable approach for representing and deforming efficiently the shape of the underlying geometry, as well as for computing the shape gradient of the cost functional to be minimized. Several approaches based on the displacement of a set of control points have been developed in the last decades, such as the so-called free-form deformations. In this paper we present a new theoretical result which allows to recast free-form deformations into the general class of perturbation of identity maps, and to guarantee the compactness of the set of admissible shapes. Moreover, we address both a general optimization framework based on the continuous shape gradient and a numerical procedure for solving efficiently three-dimensional optimal design problems. This framework is applied to the optimal design of immersed bodies in Stokes flows, for which we consider the numerical solution of a benchmark case study from literature.1 aBallarin, Francesco1 aManzoni, Andrea1 aRozza, Gianluigi1 aSalsa, Sandro uhttp://urania.sissa.it/xmlui/handle/1963/3469800580nas a2200109 4500008004100000245016900041210006900210100001900279700002500298700002200323856012500345 2014 eng d00aSingular Value Decomposition of a Finite Hilbert Transform Defined on Several Intervals and the Interior Problem of Tomography: The Riemann-Hilbert Problem Approach0 aSingular Value Decomposition of a Finite Hilbert Transform Defin1 aBertola, Marco1 aKatsevich, Alexander1 aTovbis, Alexander uhttp://www.math.sissa.it/publication/singular-value-decomposition-finite-hilbert-transform-defined-several-intervals-and01519nas a2200145 4500008004100000245015300041210006900194260001300263520096300276100002001239700002301259700002401282700001601306856005101322 2014 en d00aSix-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics0 aSixdimensional supersymmetric gauge theories quantum cohomology bSpringer3 aWe show that the exact partition function of U(N) six-dimensional gauge theory with eight supercharges on C^2 x S^2 provides the quantization of the integrable system of hydrodynamic type known as gl(N) periodic Intermediate Long Wave (ILW). We characterize this system as the hydrodynamic limit of elliptic Calogero-Moser integrable system. We compute the Bethe equations from the effective gauged linear sigma model on S^2 with target space the ADHM instanton moduli space, whose mirror computes the Yang-Yang function of gl(N) ILW. The quantum Hamiltonians are given by the local chiral ring observables of the six-dimensional gauge theory. As particular cases, these provide the gl(N) Benjamin-Ono and Korteweg-de Vries quantum Hamiltonians. In the four dimensional limit, we identify the local chiral ring observables with the conserved charges of Heisenberg plus W_N algebrae, thus providing a gauge theoretical proof of AGT correspondence.1 aBonelli, Giulio1 aSciarappa, Antonio1 aTanzini, Alessandro1 aVasko, Petr uhttp://urania.sissa.it/xmlui/handle/1963/3454600987nas a2200145 4500008004100000245008700041210006900128260001000197520050200207100002400709700002000733700001900753700001900772856005000791 2014 en d00aSome remarks on a model for rate-independent damage in thermo-visco-elastodynamics0 aSome remarks on a model for rateindependent damage in thermovisc bSISSA3 aThis note deals with the analysis of a model for partial damage, where the rateindependent, unidirectional flow rule for the damage variable is coupled with the rate-dependent heat equation, and with the momentum balance featuring inertia and viscosity according to Kelvin-Voigt rheology. The results presented here combine the approach from Roubicek [1] with the methods from Lazzaroni/Rossi/Thomas/Toader [2] and extend the analysis to the setting of inhomogeneous time-dependent Dirichlet data.1 aLazzaroni, Giuliano1 aRossi, Riccarda1 aThomas, Marita1 aToader, Rodica uhttp://urania.sissa.it/xmlui/handle/1963/746301769nas a2200133 4500008004100000245008300041210006900124260001900193520130400212100002001516700002101536700002701557856005101584 2014 en d00aSome remarks on the seismic behaviour of embedded cantilevered retaining walls0 aSome remarks on the seismic behaviour of embedded cantilevered r bThomas Telford3 aThis paper is a numerical investigation of the physical phenomena that control the dynamic behaviour of embedded cantilevered retaining walls. Recent experimental observations obtained from centrifuge tests have shown that embedded cantilevered retaining walls experience permanent displacements even before the acceleration reaches its critical value, corresponding to full mobilisation of the soil strength. The motivation for this work stems from the need to incorporate these observations in simplified design procedures. A parametric study was carried out on a pair of embedded cantilevered walls in dry sand, subjected to real earthquakes scaled at different values of the maximum acceleration. The results of these analyses indicate that, for the geotechnical design of the wall, the equivalent acceleration to be used in pseudo-static calculations can be related to the maximum displacement that the structure can sustain, and can be larger than the maximum acceleration expected at the site. For the structural design of the wall, it is suggested that the maximum bending moments of the wall can be computed using a realistic distribution of contact stress and a conservative value of the pseudo-static acceleration, taking into account two-dimensional amplification effects near the walls.1 aConti, Riccardo1 aD'Arezzo, Burali1 aViggiani, Giulia, M.B. uhttp://urania.sissa.it/xmlui/handle/1963/3507300993nas a2200121 4500008004100000245006500041210006500106260003000171520058100201100001600782700002200798856005100820 2014 en d00aSpontaneous division and motility in active nematic droplets0 aSpontaneous division and motility in active nematic droplets bAmerican Physical Society3 aWe investigate the mechanics of an active droplet endowed with internal nematic order and surrounded by an isotropic Newtonian fluid. Using numerical simulations we demonstrate that, due to the interplay between the active stresses and the defective geometry of the nematic director, this system exhibits two of the fundamental functions of living cells: spontaneous division and motility, by means of self-generated hydrodynamic flows. These behaviors can be selectively activated by controlling a single physical parameter, namely, an active variant of the capillary number.1 aGiomi, Luca1 aDeSimone, Antonio uhttp://urania.sissa.it/xmlui/handle/1963/3490201200nas a2200133 4500008004100000245007800041210006900119300001100188490000800199520070800207100001900915700002100934856011100955 2014 eng d00aStabilized reduced basis method for parametrized advection-diffusion PDEs0 aStabilized reduced basis method for parametrized advectiondiffus a1–180 v2743 aIn this work, we propose viable and efficient strategies for the stabilization of the reduced basis approximation of an advection dominated problem. In particular, we investigate the combination of a classic stabilization method (SUPG) with the Offline-Online structure of the RB method. We explain why the stabilization is needed in both stages and we identify, analytically and numerically, which are the drawbacks of a stabilization performed only during the construction of the reduced basis (i.e. only in the Offline stage). We carry out numerical tests to assess the performances of the ``double'' stabilization both in steady and unsteady problems, also related to heat transfer phenomena.

1 aPacciarini, P.1 aRozza, Gianluigi uhttp://www.math.sissa.it/publication/stabilized-reduced-basis-method-parametrized-advection-diffusion-pdes01104nas a2200121 4500008004100000245016100041210006900202300001600271520058500287100001900872700002100891856007000912 2014 eng d00aStabilized reduced basis method for parametrized scalar advection-diffusion problems at higher Péclet number: Roles of the boundary layers and inner fronts0 aStabilized reduced basis method for parametrized scalar advectio a5614–56243 aAdvection-dominated problems, which arise in many engineering situations, often require a fast and reliable approximation of the solution given some parameters as inputs. In this work we want to investigate the coupling of the reduced basis method - which guarantees rapidity and reliability - with some classical stabilization techiques to deal with the advection-dominated condition. We provide a numerical extension of the results presented in [1], focusing in particular on problems with curved boundary layers and inner fronts whose direction depends on the parameter.

1 aPacciarini, P.1 aRozza, Gianluigi uhttps://infoscience.epfl.ch/record/203327/files/ECCOMAS_PP_GR.pdf00469nas a2200109 4500008004100000245008400041210006900125260001000194100002300204700001600227856011600243 2014 en d00aSteady nearly incompressible vector elds in 2D: chain rule and renormalization0 aSteady nearly incompressible vector elds in 2D chain rule and re bSISSA1 aBianchini, Stefano1 aGusev, N.A. uhttp://www.math.sissa.it/publication/steady-nearly-incompressible-vector-elds-2d-chain-rule-and-renormalization01412nas a2200145 4500008004100000245004500041210004100086260001300127520099200140100002001132700002301152700002401175700001601199856005101215 2014 en d00aThe stringy instanton partition function0 astringy instanton partition function bSpringer3 aWe perform an exact computation of the gauged linear sigma model associated to a D1-D5 brane system on a resolved A_1 singularity. This is accomplished via supersymmetric localization on the blown-up two-sphere. We show that in the blow-down limit C^2/Z_2 the partition function reduces to the Nekrasov partition function evaluating the equivariant volume of the instanton moduli space. For finite radius we obtain a tower of world-sheet instanton corrections, that we identify with the equivariant Gromov-Witten invariants of the ADHM moduli space. We show that these corrections can be encoded in a deformation of the Seiberg-Witten prepotential. From the mathematical viewpoint, the D1-D5 system under study displays a twofold nature: the D1-branes viewpoint captures the equivariant quantum cohomology of the ADHM instanton moduli space in the Givental formalism, and the D5-branes viewpoint is related to higher rank equivariant Donaldson-Thomas invariants of P^1 x C^2.1 aBonelli, Giulio1 aSciarappa, Antonio1 aTanzini, Alessandro1 aVasko, Petr uhttp://urania.sissa.it/xmlui/handle/1963/3458901002nas a2200133 4500008004100000245005800041210005500099260001000154520060700164100002100771700002000792700002000812856003600832 2014 en d00aStructure of classical (finite and affine) W-algebras0 aStructure of classical finite and affine Walgebras bSISSA3 aFirst, we derive an explicit formula for the Poisson bracket of the classical finite W-algebra W^{fin}(g,f), the algebra of polynomial functions on the Slodowy slice associated to a simple Lie algebra g and its nilpotent element f. On the other hand, we produce an explicit set of generators and we derive an explicit formula for the Poisson vertex algebra structure of the classical affine W-algebra W(g,f). As an immediate consequence, we obtain a Poisson algebra isomorphism between W^{fin}(g,f) and the Zhu algebra of W(g,f). We also study the generalized Miura map for classical W-algebras.1 aDe Sole, Alberto1 aKac, Victor, G.1 aValeri, Daniele uhttp://hdl.handle.net/1963/731400395nas a2200109 4500008004100000245009400041210006900135260001000204100002300214700001200237856003600249 2014 en d00aStructure of entropy solutions to general scalar conservation laws in one space dimension0 aStructure of entropy solutions to general scalar conservation la bSISSA1 aBianchini, Stefano1 aYu, Lei uhttp://hdl.handle.net/1963/725901169nas a2200133 4500008004100000245007700041210006900118260003400187520069100221100002700912700002300939700002200962856005100984 2014 en d00aSwelling dynamics of a thin elastomeric sheet under uniaxial pre-stretch0 aSwelling dynamics of a thin elastomeric sheet under uniaxial pre bAmerican Institute of Physics3 aIt has been demonstrated experimentally that pre-stretch affects the swelling of an elastomeric membrane when it is exposed to a solvent. We study theoretically the one-dimensional swelling of a pre-stretched thin elastomeric sheet, bonded to an impermeable rigid substrate, to quantify the influence of pre-stretch. We show that the solvent uptake increases when pre-stretch increases, both at equilibrium and during the swelling transient, where it exhibits two different scaling regimes. The coupling between the solvent uptake and pre-stretch may be practically exploited to design soft actuators where the swelling-induced deformations can be controlled by varying the pre-stretch.1 aLucantonio, Alessandro1 aNardinocchi, Paola1 aStone, Howard, A. uhttp://urania.sissa.it/xmlui/handle/1963/3511301394nas a2200133 4500008004100000245006500041210006400106260002800170520094000198100002701138700002301165700002101188856005101209 2014 en d00aSwelling-induced and controlled curving in layered gel beams0 aSwellinginduced and controlled curving in layered gel beams bRoyal Society of London3 aWe describe swelling-driven curving in originally straight and non-homogeneous beams. We present and verify a structural model of swollen beams, based on a new point of view adopted to describe swelling-induced deformation processes in bilayered gel beams, that is based on the split of the swelling-induced deformation of the beam at equilibrium into two components, both depending on the elastic properties of the gel. The method allows us to: (i) determine beam stretching and curving, once assigned the characteristics of the solvent bath and of the non-homogeneous beam, and (ii) estimate the characteristics of non-homogeneous flat gel beams in such a way as to obtain, under free-swelling conditions, three-dimensional shapes. The study was pursued by means of analytical, semi-analytical and numerical tools; excellent agreement of the outcomes of the different techniques was found, thus confirming the strength of the method.1 aLucantonio, Alessandro1 aNardinocchi, Paola1 aPezzulla, Matteo uhttp://urania.sissa.it/xmlui/handle/1963/3498701410nas a2200133 4500008004100000245010100041210006900142260003500211520074000246653011900986100002101105700002101126856012901147 2014 en d00aTopological Invariants of Eigenvalue Intersections and Decrease of Wannier Functions in Graphene0 aTopological Invariants of Eigenvalue Intersections and Decrease bJournal of Statistical Physics3 aWe investigate the asymptotic decrease of the Wannier functions for the valence and conduction band of graphene, both in the monolayer and the multilayer case. Since the decrease of the Wannier functions is characterised by the structure of the Bloch eigenspaces around the Dirac points, we introduce a geometric invariant of the family of eigenspaces, baptised eigenspace vorticity. We compare it with the pseudospin winding number. For every value n∈Z of the eigenspace vorticity, we exhibit a canonical model for the local topology of the eigenspaces. With the help of these canonical models, we show that the single band Wannier function w satisfies |w(x)|≤const |x|^{−2} as |x|→∞, both in monolayer and bilayer graphene.10aWannier functions, Bloch bundles, conical intersections, eigenspace vorticity, pseudospin winding number, graphene1 aMonaco, Domenico1 aPanati, Gianluca uhttp://www.math.sissa.it/publication/topological-invariants-eigenvalue-intersections-and-decrease-wannier-functions-graphene00781nas a2200121 4500008004100000245008700041210006900128260003100197520034000228100001800568700002200586856005100608 2014 en d00aThe topology of a subspace of the Legendrian curves on a closed contact 3-manifold0 atopology of a subspace of the Legendrian curves on a closed cont bAdvanced Nonlinear Studies3 aIn this paper we study a subspace of the space of Legendrian loops and we show that the injection of this space into the full loop space is an S 1-equivariant homotopy equivalence. This space can be also seen as the space of zero Maslov index Legendrian loops and it shows up as a suitable space of variations in contact form geometry.1 aMaalaoui, Ali1 aMartino, Vittorio uhttp://urania.sissa.it/xmlui/handle/1963/3501601084nas a2200133 4500008004100000245014200041210006900183260005100252520053000303100002200833700002300855700002100878856005100899 2014 en d00aA uniqueness result for the continuity equation in two dimensions: dedicated to constantine dafermos on the occasion of his 70th birthday0 auniqueness result for the continuity equation in two dimensions bEuropean Mathematical Society; Springer Verlag3 aWe characterize the autonomous, divergence-free vector fields b on the plane such that the Cauchy problem for the continuity equation ∂tu +div(bu) = 0 admits a unique bounded solution (in the weak sense) for every bounded initial datum; the characterization is given in terms of a property of Sard type for the potential f associated to b. As a corollary we obtain uniqueness under the assumption that the curl of b is a measure. This result can be extended to certain nonautonomous vector fields b with bounded divergence.1 aAlberti, Giovanni1 aBianchini, Stefano1 aCrippa, Gianluca uhttp://urania.sissa.it/xmlui/handle/1963/3469200850nas a2200121 4500008004300000245007700043210006900120260001000189520044200199653001700641100002000658856005000678 2014 en_Ud 00aA variational approach to statics and dynamics of elasto-plastic systems0 avariational approach to statics and dynamics of elastoplastic sy bSISSA3 aWe prove some existence results for dynamic evolutions in elasto-plasticity and delamination. We study the limit as the data vary very slowly and prove convergence results to quasistatic evolutions. We model dislocations by mean of currents, we introduce the space of deformations in the presence of dislocations and study the graphs of these maps. We prove existence results for minimum problems. We study the properties of minimizers.10adelamination1 aScala, Riccardo uhttp://urania.sissa.it/xmlui/handle/1963/747100842nas a2200133 4500008004100000245009600041210006900137260003400206520037200240653002300612100001800635700001900653856003600672 2014 en d00aA variational model for the quasi-static growth of fractional dimensional brittle fractures0 avariational model for the quasistatic growth of fractional dimen bEuropean Mathematical Society3 aWe propose a variational model for the irreversible quasi-static evolution of brittle fractures having fractional Hausdorff dimension in the setting of two-dimensional antiplane and plane elasticity. The evolution along such irregular crack paths can be obtained as $\Gamma$-limit of evolutions along one-dimensional cracks when the fracture toughness tends to zero.10aVariational models1 aRacca, Simone1 aToader, Rodica uhttp://hdl.handle.net/1963/698301601nas a2200145 4500008004100000245008900041210007100130260001300201520110700214100002001321700002301341700002401364700001601388856005101404 2014 en d00aVortex Partition Functions, Wall Crossing and Equivariant Gromov–Witten Invariants0 aVortex Partition Functions Wall Crossing and Equivariant Gromov– bSpringer3 aIn this paper we identify the problem of equivariant vortex counting in a (2,2) supersymmetric two dimensional quiver gauged linear sigma model with that of computing the equivariant Gromov–Witten invariants of the GIT quotient target space determined by the quiver. We provide new contour integral formulae for the I and J-functions encoding the equivariant quantum cohomology of the target space. Its chamber structure is shown to be encoded in the analytical properties of the integrand. This is explained both via general arguments and by checking several key cases. We show how several results in equivariant Gromov–Witten theory follow just by deforming the integration contour. In particular, we apply our formalism to compute Gromov–Witten invariants of the C3/Zn orbifold, of the Uhlembeck (partial) compactification of the moduli space of instantons on C2, and of An and Dn singularities both in the orbifold and resolved phases. Moreover, we analyse dualities of quantum cohomology rings of holomorphic vector bundles over Grassmannians, which are relevant to BPS Wilson loop algebrae.1 aBonelli, Giulio1 aSciarappa, Antonio1 aTanzini, Alessandro1 aVasko, Petr uhttp://urania.sissa.it/xmlui/handle/1963/3465201557nas a2200133 4500008004100000245009400041210006900135260001700204520109300221100001501314700002201329700002101351856005101372 2014 en d00aA weighted empirical interpolation method: A priori convergence analysis and applications0 aweighted empirical interpolation method A priori convergence ana bEDP Sciences3 aWe extend the classical empirical interpolation method [M. Barrault, Y. Maday, N.C. Nguyen and A.T. Patera, An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations. Compt. Rend. Math. Anal. Num. 339 (2004) 667-672] to a weighted empirical interpolation method in order to approximate nonlinear parametric functions with weighted parameters, e.g. random variables obeying various probability distributions. A priori convergence analysis is provided for the proposed method and the error bound by Kolmogorov N-width is improved from the recent work [Y. Maday, N.C. Nguyen, A.T. Patera and G.S.H. Pau, A general, multipurpose interpolation procedure: the magic points. Commun. Pure Appl. Anal. 8 (2009) 383-404]. We apply our method to geometric Brownian motion, exponential Karhunen-Loève expansion and reduced basis approximation of non-affine stochastic elliptic equations. We demonstrate its improved accuracy and efficiency over the empirical interpolation method, as well as sparse grid stochastic collocation method.1 aChen, Peng1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3502100917nas a2200121 4500008004100000245006300041210006300104260002500167520051500192100001900707700001800726856005100744 2014 en d00aWeighted quantile correlation test for the logistic family0 aWeighted quantile correlation test for the logistic family bUniversity of Szeged3 aWe summarize the results of investigating the asymptotic behavior of the weighted quantile correlation tests for the location-scale family associated to the logistic distribution. Explicit representations of the limiting distribution are given in terms of integrals of weighted Brownian bridges or alternatively as infinite series of independent Gaussian random variables. The power of this test and the test for the location logistic family against some alternatives are demonstrated by numerical simulations.1 aBalogh, Ferenc1 aKrauczi, Éva uhttp://urania.sissa.it/xmlui/handle/1963/3502500995nas a2200121 4500008004300000245007400043210006900117260001000186520059200196100001700788700001800805856005000823 2014 en_Ud 00aWhere best to place a Dirichlet condition in an anisotropic membrane?0 aWhere best to place a Dirichlet condition in an anisotropic memb bSISSA3 aWe study a shape optimization problem for the first eigenvalue of an elliptic operator in divergence form, with non constant coefficients, over a fixed domain $\Omega$. Dirichlet conditions are imposed along $\partial\Omega$ and, in addition, along a set $\Sigma$ of prescribed length ($1$-dimensional Hausdorff measure). We look for the best shape and position for the supplementary Dirichlet region $\Sigma$ in order to maximize the first eigenvalue. We characterize the limit distribution of the optimal sets, as their prescribed length tends to infinity, via $\Gamma$-convergence.1 aTilli, Paolo1 aZucco, Davide uhttp://urania.sissa.it/xmlui/handle/1963/748100479nas a2200109 4500008004100000245009100041210006900132490001100201100001900212700002000231856011800251 2014 eng d00aZeros of Large Degree Vorob'ev-Yablonski Polynomials via a Hankel Determinant Identity0 aZeros of Large Degree VorobevYablonski Polynomials via a Hankel 0 vrnu2391 aBertola, Marco1 aBothner, Thomas uhttp://www.math.sissa.it/publication/zeros-large-degree-vorobev-yablonski-polynomials-hankel-determinant-identity01529nas a2200133 4500008004100000245009100041210006900132260001000201520106900211653003701280100002001317700002201337856003601359 2013 en d00aAmbrosio-Tortorelli approximation of cohesive fracture models in linearized elasticity0 aAmbrosioTortorelli approximation of cohesive fracture models in bSISSA3 aWe provide an approximation result in the sense of $\Gamma$-convergence for cohesive fracture energies of the form \[ \int_\Omega \mathscr{Q}_1(e(u))\,dx+a\,\mathcal{H}^{n-1}(J_u)+b\,\int_{J_u}\mathscr{Q}_0^{1/2}([u]\odot\nu_u)\,d\mathcal{H}^{n-1}, \] where $\Omega\subset{\mathbb R}^n$ is a bounded open set with Lipschitz boundary, $\mathscr{Q}_0$ and $\mathscr{Q}_1$ are coercive quadratic forms on ${\mathbb M}^{n\times n}_{sym}$, $a,\,b$ are positive constants, and $u$ runs in the space of fields $SBD^2(\Omega)$ , i.e., it's a special field with bounded deformation such that its symmetric gradient $e(u)$ is square integrable, and its jump set $J_u$ has finite $(n-1)$-Hausdorff measure in ${\mathbb R}^n$. The approximation is performed by means of Ambrosio-Tortorelli type elliptic regularizations, the prototype example being \[ \int_\Omega\Big(v|e(u)|^2+\frac{(1-v)^2}{\varepsilon}+{\gamma\,\varepsilon}|\nabla v|^2\Big)\,dx, \] where $(u,v)\in H^1(\Omega,{\mathbb R}^n){\times} H^1(\Omega)$, $\varepsilon\leq v\leq 1$ and $\gamma>0$.10aFunctions of bounded deformation1 aFocardi, Matteo1 aIurlano, Flaviana uhttp://hdl.handle.net/1963/661501048nas a2200145 4500008004100000245010400041210006900145260001300214520050500227653007400732100002100806700001900827700002000846856003600866 2013 en d00aAnalytical validation of a continuum model for epitaxial growth with elasticity on vicinal surfaces0 aAnalytical validation of a continuum model for epitaxial growth bSpringer3 aIn this paper it is shown existence of weak solutions of a variational inequality derived from the continuum model introduced by Xiang [7, formula (3.62)] (see also the work of Xiang and E [8] and Xu and Xiang [9]) to describe the self-organization of terraces and steps driven by misfit elasticity between a film and a substrate in heteroepitaxial growth. This model is obtained as a continuum limit of discrete theories of Duport, Politi, and Villain [3] and Tersoff, Phang, Zhang, and Lagally[6].10asingular nonlinear parabolic equations, Hilbert transform, thin films1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni uhttp://hdl.handle.net/1963/724500530nas a2200109 4500008004100000245011300041210006900154260001000223653003700233100002200270856012800292 2013 en d00aAn Approximation Result for Generalised Functions of Bounded Deformation and Applications to Damage Problems0 aApproximation Result for Generalised Functions of Bounded Deform bSISSA10aFunctions of bounded deformation1 aIurlano, Flaviana uhttp://www.math.sissa.it/publication/approximation-result-generalised-functions-bounded-deformation-and-applications-damage01509nas a2200133 4500008004100000245011100041210006900152520096400221653002001185100002501205700001801230700002201248856010501270 2013 en d00aOn the area of the graph of a piecewise smooth map from the plane to the plane with a curve discontinuity0 aarea of the graph of a piecewise smooth map from the plane to th3 aIn this paper we provide an estimate from above for the value of the relaxed area functional for a map defined on a bounded domain of the plane with values in the plane and discontinuous on a regular simple curve with two endpoints. We show that, under suitable assumptions, the relaxed area does not exceed the area of the regular part of the map, with the addition of a singular term measuring the area of a disk type solution of the Plateau's problem spanning the two traces of the map on the jump. The result is valid also when the area minimizing surface has self intersections. A key element in our argument is to show the existence of what we call a semicartesian parametrization of this surface, namely a conformal parametrization defined on a suitable parameter space, which is the identity in the first component. To prove our result, various tools of parametric minimal surface theory are used, as well as some result from Morse theory.10aArea functional1 aBellettini, Giovanni1 aTealdi, Lucia1 aPaolini, Maurizio uhttp://www.math.sissa.it/publication/area-graph-piecewise-smooth-map-plane-plane-curve-discontinuity01539nas a2200121 4500008004100000245009200041210006900133260005100202520107800253100001701331700001801348856005101366 2013 en d00aAsymptotics of the first Laplace eigenvalue with Dirichlet regions of prescribed length0 aAsymptotics of the first Laplace eigenvalue with Dirichlet regio bSociety for Industrial and Applied Mathematics3 aWe consider the problem of maximizing the first eigenvalue of the $p$-Laplacian (possibly with nonconstant coefficients) over a fixed domain $\Omega$, with Dirichlet conditions along $\partial\Omega$ and along a supplementary set $\Sigma$, which is the unknown of the optimization problem. The set $\Sigma$, which plays the role of a supplementary stiffening rib for a membrane $\Omega$, is a compact connected set (e.g., a curve or a connected system of curves) that can be placed anywhere in $\overline{\Omega}$ and is subject to the constraint of an upper bound $L$ to its total length (one-dimensional Hausdorff measure). This upper bound prevents $\Sigma$ from spreading throughout $\Omega$ and makes the problem well-posed. We investigate the behavior of optimal sets $\Sigma_L$ as $L\to\infty$ via $\Gamma$-convergence, and we explicitly construct certain asymptotically optimal configurations. We also study the behavior as $p\to\infty$ with $L$ fixed, finding connections with maximum-distance problems related to the principal frequency of the $\infty$-Laplacian.1 aTilli, Paolo1 aZucco, Davide uhttp://urania.sissa.it/xmlui/handle/1963/3514100882nas a2200133 4500008004100000245004600041210004600087260001000133520050000143100002600643700002100669700002200690856003600712 2013 en d00aAttainment results for nematic elastomers0 aAttainment results for nematic elastomers bSISSA3 aWe consider a class of non-quasiconvex frame indifferent energy densities which includes Ogden-type energy densities for nematic elastomers. For the corresponding geometrically linear problem we provide an explicit minimizer of the energy functional satisfying a nontrivial boundary condition. Other attainment results, both for the nonlinear and the linearized model, are obtained by using the theory of convex integration introduced by Mueller and Sverak in the context of crystalline solids.1 aAgostiniani, Virginia1 aDal Maso, Gianni1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/717401443nas a2200121 4500008004100000245006100041210006100102260001000163520093500173653009701108100002101205856009501226 2013 en d00aBiregular and Birational Geometry of Algebraic Varieties0 aBiregular and Birational Geometry of Algebraic Varieties bSISSA3 aEvery area of mathematics is characterized by a guiding problem. In algebraic geometry such problem is the classification of algebraic varieties. In its strongest form it means to classify varieties up to biregular morphisms. However, birationally equivalent varieties share many interesting properties. Therefore for any birational equivalence class it is natural to work out a variety, which is the simplest in a suitable sense, and then study these varieties. This is the aim of birational geometry. In the first part of this thesis we deal with the biregular geometry of moduli spaces of curves, and in particular with their biregular automorphisms. However, in doing this we will consider some aspects of their birational geometry. The second part is devoted to the birational geometry of varieties of sums of powers and to some related problems which will lead us to computational geometry and geometric complexity theory.10aModuli spaces of curves, automorphisms, Hassett's moduli spaces, varieties of sums of powers1 aMassarenti, Alex uhttp://www.math.sissa.it/publication/biregular-and-birational-geometry-algebraic-varieties01065nas a2200133 4500008004100000245012700041210006900168260001300237520058400250100002100834700002000855700002000875856003600895 2013 en d00aClassical W-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras0 aClassical Walgebras and generalized DrinfeldSokolov biHamiltonia bSpringer3 aWe provide a description of the Drinfeld-Sokolov Hamiltonian reduction for the construction of classical W-algebras within the framework of Poisson vertex algebras. In this context, the gauge group action on the phase space is translated in terms of (the exponential of) a Lie conformal algebra action on the space of functions. Following the ideas of Drinfeld and Sokolov, we then establish under certain sufficient conditions the applicability of the Lenard-Magri scheme of integrability and the existence of the corresponding integrable hierarchy of bi-Hamiltonian equations.1 aDe Sole, Alberto1 aKac, Victor, G.1 aValeri, Daniele uhttp://hdl.handle.net/1963/697801890nas a2200145 4500008004100000245011800041210006900159260001300228520137300241653003501614100001801649700002001667700002101687856003601708 2013 en d00aA combination between the reduced basis method and the ANOVA expansion: On the computation of sensitivity indices0 acombination between the reduced basis method and the ANOVA expan bElsevier3 aWe consider a method to efficiently evaluate in a real-time context an output based on the numerical solution of a partial differential equation depending on a large number of parameters. We state a result allowing to improve the computational performance of a three-step RB-ANOVA-RB method. This is a combination of the reduced basis (RB) method and the analysis of variations (ANOVA) expansion, aiming at compressing the parameter space without affecting the accuracy of the output. The idea of this method is to compute a first (coarse) RB approximation of the output of interest involving all the parameter components, but with a large tolerance on the a posteriori error estimate; then, we evaluate the ANOVA expansion of the output and freeze the least important parameter components; finally, considering a restricted model involving just the retained parameter components, we compute a second (fine) RB approximation with a smaller tolerance on the a posteriori error estimate. The fine RB approximation entails lower computational costs than the coarse one, because of the reduction of parameter dimensionality. Our result provides a criterion to avoid the computation of those terms in the ANOVA expansion that are related to the interaction between parameters in the bilinear form, thus making the RB-ANOVA-RB procedure computationally more feasible.

10aPartial differential equations1 aDevaud, Denis1 aManzoni, Andrea1 aRozza, Gianluigi uhttp://hdl.handle.net/1963/738901564nas a2200169 4500008004100000245010100041210006900142260001000211520092400221100002201145700002401167700002201191700001701213700001901230700002201249856012301271 2013 en d00aCommon dynamical features of sensory adaptation in photoreceptors and olfactory sensory neurons.0 aCommon dynamical features of sensory adaptation in photoreceptor bSISSA3 aSensory systems adapt, i.e., they adjust their sensitivity to external stimuli according to the ambient level. In this paper we show that single cell electrophysiological responses of vertebrate olfactory receptors and of photoreceptors to different input protocols exhibit several common features related to adaptation, and that these features can be used to investigate the dynamical structure of the feedback regulation responsible for the adaptation. In particular, we point out that two different forms of adaptation can be observed, in response to steps and to pairs of pulses. These two forms of adaptation appear to be in a dynamical trade-off: the more adaptation to a step is close to perfect, the slower is the recovery in adaptation to pulse pairs and viceversa. Neither of the two forms is explained by the dynamical models currently used to describe adaptation, such as the integral feedback model.

1 aDe Palo, Giovanna1 aFacchetti, Giuseppe1 aMazzolini, Monica1 aMenini, Anna1 aTorre, Vincent1 aAltafini, Claudio uhttp://www.math.sissa.it/publication/common-dynamical-features-sensory-adaptation-photoreceptors-and-olfactory-sensory00784nas a2200121 4500008004100000245005400041210005300095260001300148520042200161100002100583700002200604856003600626 2013 en d00aConnected Sum Construction for σk-Yamabe Metrics0 aConnected Sum Construction for σkYamabe Metrics bSpringer3 aIn this paper we produce families of Riemannian metrics with positive constant $\sigma_k$-curvature equal to $2^{-k} {n \choose k}$ by performing the connected sum of two given compact {\em non degenerate} $n$--dimensional solutions $(M_1,g_1)$ and $(M_2,g_2)$ of the (positive) $\sigma_k$-Yamabe problem, provided $2 \leq 2k < n$. The problem is equivalent to solve a second order fully nonlinear elliptic equation.1 aCatino, Giovanni1 aMazzieri, Lorenzo uhttp://hdl.handle.net/1963/644101070nas a2200145 4500008004100000245006700041210006600108260001300174520054900187100002200736700002400758700002200782700002000804856010000824 2013 en d00aCrawlers in viscous environments: linear vs nonlinear rheology0 aCrawlers in viscous environments linear vs nonlinear rheology bElsevier3 aWe study model self-propelled crawlers which derive their propulsive capabilities from the tangential resistance to motion offered by the environment. Two types of relationships between tangential forces and slip velocities are considered: a linear, Newtonian one and a nonlinear one of Bingham-type. Different behaviors result from the two different rheologies. These differences and their implications in terms of motility performance are discussed. Our aim is to develop new tools and insight for future studies of cell motility by crawling.1 aDeSimone, Antonio1 aGuarnieri, Federica1 aNoselli, Giovanni1 aTatone, Amabile uhttp://www.math.sissa.it/publication/crawlers-viscous-environments-linear-vs-nonlinear-rheology01218nas a2200145 4500008004100000245008300041210006900124260001000193520068100203100002000884700001800904700002100922700001800943856011100961 2013 en d00aOn critical behaviour in systems of Hamiltonian partial differential equations0 acritical behaviour in systems of Hamiltonian partial differentia bSISSA3 aWe study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by particular solutions to the Painlev\'e-I (P$_I$) equation or its fourth order analogue P$_I^2$. As concrete examples we discuss nonlinear Schr\"odinger equations in the semiclassical limit. A numerical study of these cases provides strong evidence in support of the conjecture.

1 aDubrovin, Boris1 aGrava, Tamara1 aKlein, Christian1 aMoro, Antonio uhttp://www.math.sissa.it/publication/critical-behaviour-systems-hamiltonian-partial-differential-equations02036nas a2200133 4500008004100000245005300041210005300094260001000147520152600157653009101683100002001774700002501794856008301819 2013 en d00aCurrents and dislocations at the continuum scale0 aCurrents and dislocations at the continuum scale bSISSA3 aA striking geometric property of elastic bodies with dislocations is their non-Riemannian nature in the sense that the deformation cannot be written as the gradient of a one-to-one immersion, and hence that no displacement field can properly be defined as model variable. In fact, the deformation curl equals to the density of dislocations which is a concentrated Radon measure in the dislocation lines. In this paper we consider a countable family of dislocations, discuss the mathematical properties of such constraint deformations and study a variational problem in finite-strain elasticity. It turns out that both the deformation and the dislocation lines may be modelled by means of the mathematical theory of currents. In particular, Cartesian maps allow one to consider deformations in L^p with 1\leq p<2, which are appropriate for dislocation-induced strain singularities. Moreover, integer-multiplicity currents are perfectly suited to describe either the static or the dynamics of families of dislocations which mutually interact, and possibly form complex structures such as clusters. Though the evolution of dislocations is not considered in this paper, it is the main motivation of our approach. As a matter of fact, this work describes a conservative ground state where dislocations are assumed to obey energy minimization principles, and over which any relevant effect resorting to thermodynamics outside equilibrium might be added in a subsequent step within the proposed mathematical formalism.

10aCartesian maps, integer-valued currents, dislocations, finite elasticity, minimization1 aScala, Riccardo1 aVan Goethem, Nicolas uhttp://www.math.sissa.it/publication/currents-and-dislocations-continuum-scale01043nas a2200145 4500008004100000245004200041210003700083260001000120520060700130653006200737100002500799700002100824700001600845856003600861 2013 en d00aThe curvature: a variational approach0 acurvature a variational approach bSISSA3 aThe curvature discussed in this paper is a rather far going generalization of the Riemannian sectional curvature. We define it for a wide class of optimal control problems: a unified framework including geometric structures such as Riemannian, sub-Riemannian, Finsler and sub-Finsler structures; a special attention is paid to the sub-Riemannian (or Carnot-Caratheodory) metric spaces. Our construction of the curvature is direct and naive, and it is similar to the original approach of Riemann. Surprisingly, it works in a very general setting and, in particular, for all sub-Riemannian spaces.10aCrurvature, subriemannian metric, optimal control problem1 aAgrachev, Andrei, A.1 aBarilari, Davide1 aRizzi, Luca uhttp://hdl.handle.net/1963/722600967nas a2200133 4500008004100000245005000041210004800091260003400139520056900173653001300742100002200755700002000777856003600797 2013 en d00aCurved noncommutative torus and Gauss--Bonnet0 aCurved noncommutative torus and GaussBonnet bAmerican Institute of Physics3 aWe study perturbations of the flat geometry of the noncommutative two-dimensional torus T^2_\theta (with irrational \theta). They are described by spectral triples (A_\theta, \H, D), with the Dirac operator D, which is a differential operator with coefficients in the commutant of the (smooth) algebra A_\theta of T_\theta. We show, up to the second order in perturbation, that the zeta-function at 0 vanishes and so the Gauss-Bonnet theorem holds. We also calculate first two terms of the perturbative expansion of the corresponding local scalar curvature.10aGeometry1 aDabrowski, Ludwik1 aSitarz, Andrzej uhttp://hdl.handle.net/1963/737600604nas 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/1963/723500419nas a2200097 4500008004100000245008000041210006900121260001000190100001900200856010200219 2013 en d00aOn the desingularization of Kahler orbifolds with constant scalar curvature0 adesingularization of Kahler orbifolds with constant scalar curva bSISSA1 aLena, Riccardo uhttp://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/1963/712401988nas a2200133 4500008004100000245010500041210006900146260003000215520151100245100002101756700002201777700001901799856003601818 2013 en d00aEarly phase of plasticity-related gene regulation and SRF dependent transcription in the hippocampus0 aEarly phase of plasticityrelated gene regulation and SRF depende bPublic Library of Science3 aHippocampal organotypic cultures are a highly reliable in vitro model for studying neuroplasticity: in this paper, we analyze the early phase of the transcriptional response induced by a 20 µM gabazine treatment (GabT), a GABA-Ar antagonist, by using Affymetrix oligonucleotide microarray, RT-PCR based time-course and chromatin-immuno-precipitation. The transcriptome profiling revealed that the pool of genes up-regulated by GabT, besides being strongly related to the regulation of growth and synaptic transmission, is also endowed with neuro-protective and pro-survival properties. By using RT-PCR, we quantified a time-course of the transient expression for 33 of the highest up-regulated genes, with an average sampling rate of 10 minutes and covering the time interval [10:90] minutes. The cluster analysis of the time-course disclosed the existence of three different dynamical patterns, one of which proved, in a statistical analysis based on results from previous works, to be significantly related with SRF-dependent regulation (p-value<0.05). The chromatin immunoprecipitation (chip) assay confirmed the rich presence of working CArG boxes in the genes belonging to the latter dynamical pattern and therefore validated the statistical analysis. Furthermore, an in silico analysis of the promoters revealed the presence of additional conserved CArG boxes upstream of the genes Nr4a1 and Rgs2. The chip assay confirmed a significant SRF signal in the Nr4a1 CArG box but not in the Rgs2 CArG box.1 aIacono, Giovanni1 aAltafini, Claudio1 aTorre, Vincent uhttp://hdl.handle.net/1963/728701018nas a2200109 4500008004100000245008100041210006900122260001700191520064400208100002000852856003600872 2013 en d00aEpitaxially strained elastic films: the case of anisotropic surface energies0 aEpitaxially strained elastic films the case of anisotropic surfa bEDP Sciences3 aIn the context of a variational model for the epitaxial growth of strained elastic films, we study the effects of the presence of anisotropic surface energies in the determination of equilibrium configurations. We show that the threshold effect that describes the stability of flat morphologies in the isotropic case remains valid for weak anisotropies, but is no longer present in the case of highly anisotropic surface energies, where we show that the flat configuration is always a local minimizer of the total energy. The main tool used to obtain these results is a minimality criterion based on the positivity of the second variation.1 aBonacini, Marco uhttp://hdl.handle.net/1963/426801024nas a2200121 4500008004100000245008800041210006900129260001000198520062200208100001900830700001700849856003600866 2013 en d00aEquilibrium measures for a class of potentials with discrete rotational symmetries0 aEquilibrium measures for a class of potentials with discrete rot bSISSA3 aIn this note the logarithmic energy problem with external potential $|z|^{2n}+tz^d+\bar{t}\bar{z}^d$ is considered in the complex plane, where $n$ and $d$ are positive integers satisfying $d\leq 2n$. Exploiting the discrete rotational invariance of the potential, a simple symmetry reduction procedure is used to calculate the equilibrium measure for all admissible values of $n,d$ and $t$. It is shown that, for fixed $n$ and $d$, there is a critical value $|t|=t_{cr}$ such that the support of the equilibrium measure is simply connected for $|t|We prove an infinite dimensional KAM theorem which implies the existence of Can- tor families of small-amplitude, reducible, elliptic, analytic, invariant tori of Hamiltonian derivative wave equations. © 2013 Société Mathématique de France.

1 aBerti, Massimiliano1 aBiasco, Luca1 aProcesi, Michela uhttp://www.math.sissa.it/publication/kam-theory-hamiltonian-derivative-wave-equation00619nas a2200157 4500008004100000245011600041210006900157260001700226300001400243490000700257100001500264700001800279700002200297700001800319856012400337 2013 eng d00aMacroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations0 aMacroscopic contact angle and liquid drops on rough solid surfac bEDP Sciences a837–8580 v471 aCacace, S.1 aChambolle, A.1 aDeSimone, Antonio1 aFedeli, Livio uhttp://www.math.sissa.it/publication/macroscopic-contact-angle-and-liquid-drops-rough-solid-surfaces-homogenization-and01676nas a2200145 4500008004100000245009400041210006900135260001000204520112400214653008201338100002001420700002501440700002901465856003601494 2013 en d00aMinimal partitions and image classification using a gradient-free perimeter approximation0 aMinimal partitions and image classification using a gradientfree bSISSA3 aIn this paper a new mathematically-founded method for the optimal partitioning of domains, with applications to the classification of greyscale and color images, is proposed. Since optimal partition problems are in general ill-posed, some regularization strategy is required. Here we regularize by a non-standard approximation of the total interface length, which does not involve the gradient of approximate characteristic functions, in contrast to the classical Modica-Mortola approximation. Instead, it involves a system of uncoupled linear partial differential equations and nevertheless shows $\Gamma$-convergence properties in appropriate function spaces. This approach leads to an alternating algorithm that ensures a decrease of the objective function at each iteration, and which always provides a partition, even during the iterations. The efficiency of this algorithm is illustrated by various numerical examples. Among them we consider binary and multilabel minimal partition problems including supervised or automatic image classification, inpainting, texture pattern identification and deblurring.10aImage classification, deblurring, optimal partitions, perimeter approximation1 aAmstutz, Samuel1 aVan Goethem, Nicolas1 aNovotny, Antonio, André uhttp://hdl.handle.net/1963/697600515nas a2200109 4500008004100000245010700041210006900148260001000217653003200227100002000259856012600279 2013 en d00aMinimality and stability results for a class of free-discontinuity and nonlocal isoperimetric problems0 aMinimality and stability results for a class of freediscontinuit bSISSA10afree-discontinuity problems1 aBonacini, Marco uhttp://www.math.sissa.it/publication/minimality-and-stability-results-class-free-discontinuity-and-nonlocal-isoperimetric01242nas a2200121 4500008004100000245005600041210005400097260001000151520082800161653007700989100001801066856003601084 2013 en d00aA model for crack growth with branching and kinking0 amodel for crack growth with branching and kinking bSISSA3 aWe study an evolution model for fractured elastic materials in the 2-dimensional case, for which the crack path is not assumed to be known a priori. We introduce a topology for the cracks suitable to remove the restrictions on the regularity of the crack set and to allow for kinking and branching to develop. In addition we define the front of the fracture and its velocity at each of its points. By means of a time-discretization approach, we prove the existence of a continuous-time evolution that satisfies an energy inequality and a stability criterion. The energy balance also takes into account the energy dissipated at the front of the fracture. The stability criterion is stated in the framework of Griffith\\\'s theory, in terms of the energy release rate, when the crack grows at least at one point of its front.10aquasistatic crack evolution, branching, kinking, Griffith\\\'s criterion1 aRacca, Simone uhttp://hdl.handle.net/1963/649000732nas a2200133 4500008004100000245005300041210005300094520025800147653004800405100002200453700001600475700002400491856008300515 2013 en d00aMonads for framed sheaves on Hirzebruch surfaces0 aMonads for framed sheaves on Hirzebruch surfaces3 aWe define monads for framed torsion-free sheaves on Hirzebruch surfaces and use them to construct moduli spaces for these objects. These moduli spaces are smooth algebraic varieties, and we show that they are fine by constructing a universal monad.10aMonads, framed sheaves, Hirzebruch surfaces1 aBartocci, Claudio1 aBruzzo, Ugo1 aRava, Claudio, L.S. uhttp://www.math.sissa.it/publication/monads-framed-sheaves-hirzebruch-surfaces00430nas a2200121 4500008004100000245009500041210006900136260001300205653001400218100001800232700002200250856003600272 2013 en d00aMultiplicity result for a nonhomogeneous Yamabe type equation involving the Kohn Laplacian0 aMultiplicity result for a nonhomogeneous Yamabe type equation in bElsevier10aCR-Yamabe1 aMaalaoui, Ali1 aMartino, Vittorio uhttp://hdl.handle.net/1963/737401436nas a2200145 4500008004100000245008000041210006900121260001000190520096800200100002001168700002401188700002401212700001801236856003601254 2013 en d00aN=2 gauge theories on toric singularities, blow-up formulae and W-algebrae0 aN2 gauge theories on toric singularities blowup formulae and Wal bSISSA3 aWe compute the Nekrasov partition function of gauge theories on the\r\n(resolved) toric singularities C^2/\\Gamma in terms of blow-up formulae. We\r\ndiscuss the expansion of the partition function in the \\epsilon_1,\\epsilon_2\r\n\\to 0 limit along with its modular properties and how to derive them from the\r\nM-theory perspective. On the two-dimensional conformal field theory side, our\r\nresults can be interpreted in terms of representations of the direct sum of\r\nHeisenberg plus W_N-algebrae with suitable central charges, which can be\r\ncomputed from the fan of the resolved toric variety.We provide a check of this\r\ncorrespondence by computing the central charge of the two-dimensional theory\r\nfrom the anomaly polynomial of M5-brane theory. Upon using the AGT\r\ncorrespondence our results provide a candidate for the conformal blocks and\r\nthree-point functions of a class of the two-dimensional CFTs which includes\r\nparafermionic theories.1 aBonelli, Giulio1 aMaruyoshi, Kazunobu1 aTanzini, Alessandro1 aYagi, Futoshi uhttp://hdl.handle.net/1963/657700839nas a2200145 4500008004100000245004000041210004000081520035300121653006200474100001600536700002100552700002100573700002200594856007700616 2013 en d00aNonabelian Lie algebroid extensions0 aNonabelian Lie algebroid extensions3 aWe classify nonabelian extensions of Lie algebroids in the holomorphic or algebraic category, and introduce and study a spectral sequence that one can attach to any such extension and generalizes the Hochschild-Serre spectral sequence associated to an ideal in a Lie algebra. We compute the differentials of the spectral sequence up to $d_2$

10aLie algebroids, nonabelian extensions, spectral sequences1 aBruzzo, Ugo1 aMencattini, Igor1 aTortella, Pietro1 aRubtsov, Vladimir uhttp://www.math.sissa.it/publication/nonabelian-lie-algebroid-extensions01090nas a2200133 4500008004100000245005800041210005800099260001300157520067800170653003000848100002200878700002000900856003600920 2013 en d00aNoncommutative circle bundles and new Dirac operators0 aNoncommutative circle bundles and new Dirac operators bSpringer3 aWe study spectral triples over noncommutative principal U(1) bundles. Basing on the classical situation and the abstract algebraic approach, we propose an operatorial definition for a connection and compatibility between the connection and the Dirac operator on the total space and on the base space of the bundle. We analyze in details the example of the noncommutative three-torus viewed as a U(1) bundle over the noncommutative two-torus and find all connections compatible with an admissible Dirac operator. Conversely, we find a family of new Dirac operators on the noncommutative tori, which arise from the base-space Dirac operator and a suitable connection.10aQuantum principal bundles1 aDabrowski, Ludwik1 aSitarz, Andrzej uhttp://hdl.handle.net/1963/738401012nas a2200145 4500008004100000020001500041245007100056210006500127520043600192653007200628100001900700700002500719700002200744856010000766 2013 en d a887642472400aThe nonlinear multidomain model: a new formal asymptotic analysis.0 anonlinear multidomain model a new formal asymptotic analysis3 aWe study the asymptotic analysis of a singularly perturbed weakly parabolic system of m- equations of anisotropic reaction-diffusion type. Our main result formally shows that solutions to the system approximate a geometric motion of a hypersurface by anisotropic mean curvature. The anisotropy, supposed to be uniformly convex, is explicit and turns out to be the dual of the star-shaped combination of the m original anisotropies.10abidomain model, anisotropic mean curvature, star-shaped combination1 aAmato, Stefano1 aBellettini, Giovanni1 aPaolini, Maurizio uhttp://www.math.sissa.it/publication/nonlinear-multidomain-model-new-formal-asymptotic-analysis01375nas a2200145 4500008004100000245007300041210006900114260003400183520083400217653001701051100001301068700002401081700002301105856010101128 2013 en d00aA note on KAM theory for quasi-linear and fully nonlinear forced KdV0 anote on KAM theory for quasilinear and fully nonlinear forced Kd bEuropean Mathematical Society3 aWe present the recent results in [3] concerning quasi-periodic solutions for quasi-linear and fully nonlinear forced perturbations of KdV equations. For Hamiltonian or reversible nonlinearities the solutions are linearly stable. The proofs are based on a combination of di erent ideas and techniques: (i) a Nash-Moser iterative scheme in Sobolev scales. (ii) A regularization procedure, which conjugates the linearized operator to a di erential operator with constant coe cients plus a bounded remainder. These transformations are obtained by changes of variables induced by di eomorphisms of the torus and pseudo-di erential operators. (iii) A reducibility KAM scheme, which completes the reduction to constant coe cients of the linearized operator, providing a sharp asymptotic expansion of the perturbed eigenvalues.10aKAM for PDEs1 aBaldi, P1 aBerti, Massimiliano1 aMontalto, Riccardo uhttp://www.math.sissa.it/publication/note-kam-theory-quasi-linear-and-fully-nonlinear-forced-kdv01597nas a2200133 4500008004100000245010900041210006900150260001000219520113300229100002101362700002201383700002201405856003601427 2013 en d00aOne-dimensional swimmers in viscous fluids: dynamics, controllability, and existence of optimal controls0 aOnedimensional swimmers in viscous fluids dynamics controllabili bSISSA3 aIn this paper we study a mathematical model of one-dimensional swimmers performing a planar motion while fully immersed in a viscous fluid. The swimmers are assumed to be of small size, and all inertial effects are neglected. Hydrodynamic interactions are treated in a simplified way, using the local drag approximation of resistive force theory. We prove existence and uniqueness of the solution of the equations of motion driven by shape changes of the swimmer. Moreover, we prove a controllability result showing that given any pair of initial and final states, there exists a history of shape changes such that the resulting motion takes the swimmer from the initial to the final state. We give a constructive proof, based on the composition of elementary maneuvers (straightening and its inverse, rotation, translation), each of which represents the solution of an interesting motion planning problem. Finally, we prove the existence of solutions for the optimal control problem of finding, among the histories of shape changes taking the swimmer from an initial to a final state, the one of minimal energetic cost.1 aDal Maso, Gianni1 aDeSimone, Antonio1 aMorandotti, Marco uhttp://hdl.handle.net/1963/646700623nas a2200121 4500008004100000245005300041210005100094520026500145653001500410100002200425700001800447856003600465 2013 en d00aA permanence theorem for local dynamical systems0 apermanence theorem for local dynamical systems3 aWe provide a necessary and sufficient condition for permanence related to a local dynamical system on a suitable topological space. We then present an illustrative application to a Lotka–Volterra predator–prey model with intraspecific competition.10apermanence1 aFonda, Alessandro1 aGidoni, Paolo uhttp://hdl.handle.net/1963/697300549nas a2200109 4500008004100000245002500041210002500066260001000091520025100101100002500352856006200377 2013 en d00aQuadratic cohomology0 aQuadratic cohomology bSISSA3 aWe study homological invariants of smooth families of real quadratic forms as\r\na step towards a \"Lagrange multipliers rule in the large\" that intends to\r\ndescribe topology of smooth vector functions in terms of scalar Lagrange\r\nfunctions.1 aAgrachev, Andrei, A. uhttp://www.math.sissa.it/publication/quadratic-cohomology01344nas a2200145 4500008004100000022001300041245009800054210006900152300001200221490000700233520079700240100002401037700002001061856011701081 2013 eng d a1435985500aQuasi-periodic solutions with Sobolev regularity of NLS on Td with a multiplicative potential0 aQuasiperiodic solutions with Sobolev regularity of NLS on Td wit a229-2860 v153 aWe prove the existence of quasi-periodic solutions for Schrödinger equations with a multiplicative potential on Td , d ≥ 1, finitely differentiable nonlinearities, and tangential frequencies constrained along a pre-assigned direction. The solutions have only Sobolev regularity both in time and space. If the nonlinearity and the potential are C∞ then the solutions are C∞. The proofs are based on an improved Nash-Moser iterative scheme, which assumes the weakest tame estimates for the inverse linearized operators ("Green functions") along scales of Sobolev spaces. The key off-diagonal decay estimates of the Green functions are proved via a new multiscale inductive analysis. The main novelty concerns the measure and "complexity" estimates. © European Mathematical Society 2013.1 aBerti, Massimiliano1 aBolle, Philippe uhttp://www.math.sissa.it/publication/quasi-periodic-solutions-sobolev-regularity-nls-td-multiplicative-potential02183nas a2200145 4500008004100000245015300041210006900194260001300263520163200276653003401908100002101942700001801963700002001981856003602001 2013 en d00aReduced basis approximation and a posteriori error estimation for Stokes flows in parametrized geometries: roles of the inf-sup stability constants0 aReduced basis approximation and a posteriori error estimation fo bSpringer3 aIn this paper we review and we extend the reduced basis approximation and a posteriori error estimation for steady Stokes flows in a ffinely parametrized geometries, focusing on the role played by the Brezzi\\\'s and Babu ska\\\'s stability constants. The crucial ingredients of the methodology are a Galerkin projection onto a low-dimensional space of basis functions properly selected, an a ne parametric dependence enabling to perform competitive Off ine-Online splitting in the computational\\r\\nprocedure and a rigorous a posteriori error estimation on eld variables.\\r\\nThe combination of these three factors yields substantial computational savings which are at the basis of an e fficient model order reduction, ideally suited for real-time simulation and many-query contexts (e.g. optimization, control or parameter identi cation). In particular, in this work we focus on i) the stability of the reduced basis approximation based on the Brezzi\\\'s saddle point theory and the introduction of a supremizer operator on the pressure terms, ii) a rigorous a posteriori error estimation procedure for velocity and pressure elds based on the Babu ska\\\'s inf-sup constant (including residuals calculations), iii) the computation of a lower bound of the stability constant, and iv) di erent options for the reduced basis spaces construction. We present some illustrative results for both\\r\\ninterior and external steady Stokes flows in parametrized geometries representing two parametrized classical Poiseuille and Couette \\r\\nflows, a channel contraction and a simple flow control problem around a curved obstacle.10aparametrized Stokes equations1 aRozza, Gianluigi1 aHuynh, Phuong1 aManzoni, Andrea uhttp://hdl.handle.net/1963/633900530nas a2200121 4500008004100000245011700041210006900158300001100227490000700238100001800245700002100263856012400284 2013 eng d00aReduced Basis Approximation for the Structural-Acoustic Design based on Energy Finite Element Analysis (RB-EFEA)0 aReduced Basis Approximation for the StructuralAcoustic Design ba a98-1150 v481 aDevaud, Denis1 aRozza, Gianluigi uhttp://www.math.sissa.it/publication/reduced-basis-approximation-structural-acoustic-design-based-energy-finite-element01700nas a2200157 4500008004100000245007600041210006900117300001800186490000700204520113900211100002001350700002101370700002001391700002201411856010901433 2013 eng d00aReduced basis method for parametrized elliptic optimal control problems0 aReduced basis method for parametrized elliptic optimal control p aA2316–A23400 v353 aWe propose a suitable model reduction paradigm-the certified reduced basis method (RB)-for the rapid and reliable solution of parametrized optimal control problems governed by partial differential equations. In particular, we develop the methodology for parametrized quadratic optimization problems with elliptic equations as a constraint and infinite-dimensional control variable. First, we recast the optimal control problem in the framework of saddle-point problems in order to take advantage of the already developed RB theory for Stokes-type problems. Then, the usual ingredients of the RB methodology are called into play: a Galerkin projection onto a low-dimensional space of basis functions properly selected by an adaptive procedure; an affine parametric dependence enabling one to perform competitive offline-online splitting in the computational procedure; and an efficient and rigorous a posteriori error estimate on the state, control, and adjoint variables as well as on the cost functional. Finally, we address some numerical tests that confirm our theoretical results and show the efficiency of the proposed technique.1 aNegri, Federico1 aRozza, Gianluigi1 aManzoni, Andrea1 aQuarteroni, Alfio uhttp://www.math.sissa.it/publication/reduced-basis-method-parametrized-elliptic-optimal-control-problems00547nas a2200133 4500008004100000245009200041210006900133260001000202100001800212700002000230700002200250700002100272856012000293 2013 en d00aA Reduced Computational and Geometrical Framework for Inverse Problems in Haemodynamics0 aReduced Computational and Geometrical Framework for Inverse Prob bSISSA1 aLassila, Toni1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://www.math.sissa.it/publication/reduced-computational-and-geometrical-framework-inverse-problems-haemodynamics00567nas a2200133 4500008004100000245010500041210006900146260001000215100001800225700002000243700002200263700002100285856012700306 2013 en d00aA reduced-order strategy for solving inverse Bayesian identification problems in physiological flows0 areducedorder strategy for solving inverse Bayesian identificatio bSISSA1 aLassila, Toni1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://www.math.sissa.it/publication/reduced-order-strategy-solving-inverse-bayesian-identification-problems-physiological00489nas a2200121 4500008004100000245007900041210006900120260001000189100001800199700002000217700002100237856010900258 2013 en d00aReduction Strategies for Shape Dependent Inverse Problems in Haemodynamics0 aReduction Strategies for Shape Dependent Inverse Problems in Hae bSISSA1 aLassila, Toni1 aManzoni, Andrea1 aRozza, Gianluigi uhttp://www.math.sissa.it/publication/reduction-strategies-shape-dependent-inverse-problems-haemodynamics00943nas a2200121 4500008004100000245004000041210004000081260001000121520053200131653010100663100002100764856003600785 2013 en d00aSemistability and Decorated Bundles0 aSemistability and Decorated Bundles bSISSA3 aThis thesis is devoted to the study of semistability condition of type t=(a,b,c,N) decorated bundles and sheaves in order to better understand and simplify it. We approach the problem in two different ways: on one side we “enclose” the above semistability condition between a stronger semistability condition (\epsilon-semistability) and a weaker one (k-semistability), on the other side we try, and succeed for the case of a = 2, to bound the length of weighted filtrations on which one checks the semistability condition.10aDecorated sheaves, semistability, moduli space, Mehta-Ramanathan, maximal destabilizing subsheaf1 aPustetto, Andrea uhttp://hdl.handle.net/1963/713001064nas a2200109 4500008004100000245002900041210002900070260001000099520079300109100001600902856003600918 2013 en d00aSoftly Constrained Films0 aSoftly Constrained Films bSISSA3 aThe shape of materials is often subject to a number of geometric constraints\r\nthat limit the size of the system or fix the structure of its boundary. In soft\r\nand biological materials, however, these constraints are not always hard, but\r\nare due to other physical mechanisms that affect the overall force balance. A\r\ncapillary film spanning a flexible piece of wire or a cell anchored to a\r\ncompliant substrate by mean of adhesive contacts are examples of these softly\r\nconstrained systems in the macroscopic and microscopic world. In this article I\r\nreview some of the important mathematical and physical developments that\r\ncontributed to our understanding of shape formation in softly constrained films\r\nand their recent application to the mechanics of adherent cells.1 aGiomi, Luca uhttp://hdl.handle.net/1963/656300402nas a2200109 4500008004100000245005300041210005300094260001000147653003300157100001800190856008400208 2013 en d00aSome models of crack growth in brittle materials0 aSome models of crack growth in brittle materials bSISSA10aQuasi-static crack evolution1 aRacca, Simone uhttp://www.math.sissa.it/publication/some-models-crack-growth-brittle-materials00401nas a2200121 4500008004100000245002300041210002300064260001000087520010800097653001300205100002500218856003600243 2013 en d00aSome open problems0 aSome open problems bSISSA3 aWe discuss some challenging open problems in the geometric control theory and sub-Riemannian geometry.10aGeometry1 aAgrachev, Andrei, A. uhttp://hdl.handle.net/1963/707000835nas a2200145 4500008004100000245006200041210006200103260001000165490000600175520040600181653002300587100002400610700001900634856003600653 2013 en d00aSome remarks on the viscous approximation of crack growth0 aSome remarks on the viscous approximation of crack growth bSISSA0 v63 aWe describe an existence result for quasistatic evolutions of cracks in antiplane elasticity obtained in [16] by a vanishing viscosity approach, with free (but regular enough) crack path. We underline in particular the motivations for the choice of the class of admissible cracks and of the dissipation potential. Moreover, we extend the result to a model with applied forces depending on time.

10aVariational models1 aLazzaroni, Giuliano1 aToader, Rodica uhttp://hdl.handle.net/1963/420601893nas a2200121 4500008004100000245008300041210006900124260001000193520137300203653005401576100002401630856011701654 2013 en d00aSome topics on Higgs bundles over projective varieties and their moduli spaces0 aSome topics on Higgs bundles over projective varieties and their bSISSA3 aIn this thesis we study vector bundles on projective varieties and their moduli spaces. In Chapters 2, 3 and 4 we recall some basic notions as Higgs bundles, decorated bundles and generalized parabolic sheaves and introduce the problem we want to study. In chapter 5, we study Higgs bundles on nodal curves. After moving the problem on the normalization of the curve, starting from a Higgs bundle we obtain a generalized parabolic Higgs bundle. Using decorated bundles we are able to construct a projective moduli space which parametrizes equivalence classes of Higgs bundles on a nodal curve X. This chapter is an extract of a joint work with Andrea Pustetto Later on Chapter 6 is devoted to the study of holomorphic pairs (or twisted Higgs bundles) on elliptic curve. Holomorphic pairs were introduced by Nitsure and they are a natural generalization of the concept of Higgs bundles. In this Chapter we extend a result of E. Franco, O. Garc\'ia-Prada And P.E. Newstead valid for Higgs bundles to holomorphic pairs. Finally the last Chapter describes a joint work with Professor Ugo Bruzzo. We study Higgs bundles over varieties with nef tangent bundle. In particular generalizing a result of Nitsure we prove that if a Higgs bundle $(E,\phi)$ over the variety X with nef tangent remains semisatble when pulled-back to any smooth curve then it discrimiant vanishes.10aAlgebraic Geometry, Moduli spaces, Vector bundles1 aLo Giudice, Alessio uhttp://www.math.sissa.it/publication/some-topics-higgs-bundles-over-projective-varieties-and-their-moduli-spaces00539nas a2200157 4500008004100000022001400041245011800055210006900173300001400242490000800256100001900264700001900283700001600302700001500318856004800333 2013 eng d a0022-471500aSpectra of random Hermitian matrices with a small-rank external source: the supercritical and subcritical regimes0 aSpectra of random Hermitian matrices with a smallrank external s a654–6970 v1531 aBertola, Marco1 aBuckingham, R.1 aLee, S., Y.1 aPierce, V. uhttp://dx.doi.org/10.1007/s10955-013-0845-200744nas a2200097 4500008004100000245004800041210004300089520044800132100001800580856004800598 2013 en d00aThe splitting theorem in non-smooth context0 asplitting theorem in nonsmooth context3 aWe prove that an infinitesimally Hilbertian $CD(0,N)$ space containing a line splits as the product of $R$ and an infinitesimally Hilbertian $CD(0,N −1)$ space. By ‘infinitesimally Hilbertian’ we mean that the Sobolev space $W^{1,2}(X,d,m)$, which in general is a Banach space, is an Hilbert space. When coupled with a curvature-dimension bound, this condition is known to be stable with respect to measured Gromov-Hausdorff convergence.1 aGigli, Nicola uhttp://preprints.sissa.it/handle/1963/3530600898nas a2200121 4500008004100000245009000041210006900131260001000200520039000210653003900600100002000639856011700659 2013 en d00aStability of equilibrium configurations for elastic films in two and three dimensions0 aStability of equilibrium configurations for elastic films in two bSISSA3 aWe establish a local minimality sufficiency criterion, based on the strict positivity of the second variation, in the context of a variational model for the epitaxial growth of elastic films. Our result holds also in the three-dimensional case and for a general class of nonlinear elastic energies. Applications to the study of the local minimality of flat morphologies are also shown.10aEpitaxially strained elastic films1 aBonacini, Marco uhttp://www.math.sissa.it/publication/stability-equilibrium-configurations-elastic-films-two-and-three-dimensions01218nas a2200121 4500008004100000245008200041210006900123520080800192100002201000700002301022700001501045856003601060 2013 en d00aStabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control0 aStabilization of Stochastic Quantum Dynamics via Open and Closed3 aIn this paper, we investigate parametrization-free solutions of the problem of quantum pure state preparation and subspace stabilization by means of Hamiltonian control, continuous measurement, and quantum feedback, in the presence of a Markovian environment. In particular, we show that whenever suitable dissipative effects are induced either by the unmonitored environment, or by non-Hermitian measurements, there is no need for feedback, as open-loop time-invariant control is sufficient to achieve stabilization of the target set in probability. Constructive necessary and sufficient conditions on the form of the control Hamiltonian can be provided in this case. When time-invariant control is not sufficient, state stabilization can be attained by the addition of filtering-based feedback control1 aAltafini, Claudio1 aTicozzi, Francesco1 aNishio, K. uhttp://hdl.handle.net/1963/650301660nas a2200145 4500008004100000245010800041210006900149260001000218520115900228653003501387100001701422700001701439700002201456856003601478 2013 en d00aA stable and adaptive semi-Lagrangian potential model for unsteady and nonlinear ship-wave interactions0 astable and adaptive semiLagrangian potential model for unsteady bSISSA3 aWe present an innovative numerical discretization of the equations of inviscid potential flow for the simulation of three dimensional unsteady and nonlinear water waves generated by a ship hull advancing in water. The equations of motion are written in a semi-Lagrangian framework, and the resulting integro-diff erential equations are discretized in space via an adaptive iso-parametric collocation Boundary Element Method, and in time via adaptive implicit Backward Di erentiation Formulas (BDF) with variable step and variable order. When the velocity of the advancing ship hull is non-negligible, the semi-Lagrangian formulation (also known as Arbitrary Lagrangian Eulerian formulation, or ALE) of the free surface equations contains dominant transport terms which are stabilized with a Streamwise Upwind Petrov-Galerkin (SUPG) method. The SUPG stabilization allows automatic and robust adaptation of the spatial discretization with unstructured quadrilateral grids. Preliminary results are presented where we compare our numerical model with experimental results on the case of a Wigley hull advancing in calm water with fi xed sink and trim.

10aUnsteady ship-wave interaction1 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/566900775nas a2200133 4500008004100000245008700041210006900128260001000197520024400207653002800451100002000479700002500499856011700524 2013 en d00aStable regular critical points of the Mumford-Shah functional are local minimizers0 aStable regular critical points of the MumfordShah functional are bSISSA3 aIn this paper it is shown that any regular critical point of the Mumford-Shah functional, with positive definite second variation, is an isolated local minimizer with respect to competitors which are sufficiently close in the L^1-topology.10aMumford-Shah functional1 aBonacini, Marco1 aMorini, Massimiliano uhttp://www.math.sissa.it/publication/stable-regular-critical-points-mumford-shah-functional-are-local-minimizers01508nas a2200145 4500008004100000245009700041210006900138300001600207490000700223520095300230100001501183700002201198700002101220856012101241 2013 eng d00aStochastic optimal robin boundary control problems of advection-dominated elliptic equations0 aStochastic optimal robin boundary control problems of advectiond a2700–27220 v513 aIn this work we deal with a stochastic optimal Robin boundary control problem constrained by an advection-diffusion-reaction elliptic equation with advection-dominated term. We assume that the uncertainty comes from the advection field and consider a stochastic Robin boundary condition as control function. A stochastic saddle point system is formulated and proved to be equivalent to the first order optimality system for the optimal control problem, based on which we provide the existence and uniqueness of the optimal solution as well as some results on stochastic regularity with respect to the random variables. Stabilized finite element approximations in physical space and collocation approximations in stochastic space are applied to discretize the optimality system. A global error estimate in the product of physical space and stochastic space for the numerical approximation is derived. Illustrative numerical experiments are provided.1 aChen, Peng1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://www.math.sissa.it/publication/stochastic-optimal-robin-boundary-control-problems-advection-dominated-elliptic00583nas a2200145 4500008004100000022001400041245010700055210006900162300001500231490000700246100001900253700001700272700002000289856012800309 2013 eng d a0022-248800aStrong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two-matrix model0 aStrong asymptotics for Cauchy biorthogonal polynomials with appl a043517, 250 v541 aBertola, Marco1 aGekhtman, M.1 aSzmigielski, J. uhttp://www.math.sissa.it/publication/strong-asymptotics-cauchy-biorthogonal-polynomials-application-cauchy-two-matrix-model00931nas a2200109 4500008004100000245011500041210006900156260001000225520044500235100001200680856012900692 2013 en d00aThe structure and regularity of admissible BV solutions to hyperbolic conservation laws in one space dimension0 astructure and regularity of admissible BV solutions to hyperboli bSISSA3 aThis thesis is devoted to the study of the qualitative properties of admissible BV solutions to the strictly hyperbolic conservation laws in one space dimension by using wave-front tracking approximation. This thesis consists of two parts: • SBV-like regularity of vanishing viscosity BV solutions to strict hyperbolic systems of conservation laws. • Global structure of admissible BV solutions to strict hyperbolic conservation laws.1 aYu, Lei uhttp://www.math.sissa.it/publication/structure-and-regularity-admissible-bv-solutions-hyperbolic-conservation-laws-one-space00380nas a2200109 4500008004100000245007400041210006900115260001000184100002300194700001700217856003600234 2013 en d00aOn Sudakov's type decomposition of transference plans with norm costs0 aSudakovs type decomposition of transference plans with norm cost bSISSA1 aBianchini, Stefano1 aDaneri, Sara uhttp://hdl.handle.net/1963/720600812nas a2200133 4500008004100000245006300041210006200104260003000166520036300196100001600559700002600575700002600601856005100627 2013 en d00aSymplectic instanton bundles on P3 and 't Hooft instantons0 aSymplectic instanton bundles on P3 and t Hooft instantons barXiv:1312.5554 [math.AG]3 aWe introduce the notion of tame symplectic instantons by excluding a kind of pathological monads and show that the locus $I^*_{n,r}$ of tame symplectic instantons is irreducible and has the expected dimension, equal to $4n(r+1)-r(2r+1)$. The proof is inherently based on a relation between the spaces $I^*_{n,r}$ and the moduli spaces of 't Hooft instantons.1 aBruzzo, Ugo1 aMarkushevich, Dimitri1 aTikhomirov, Alexander uhttp://urania.sissa.it/xmlui/handle/1963/3448600364nas a2200109 4500008004100000245004800041210004800089260001000137653004600147100002500193856003600218 2013 en d00aTopology of moduli spaces of framed sheaves0 aTopology of moduli spaces of framed sheaves bSISSA10aModuli spaces, framed sheaves, instantons1 aAbdellaoui, Gharchia uhttp://hdl.handle.net/1963/715201014nas a2200133 4500008004100000245004500041210003400086260001000120520062000130100001800750700001900768700002100787856007200808 2013 en d00aOn the tritronquée solutions of P$_I^2$0 atritronquée solutions of PI2 bSISSA3 aFor equation P$_I^2$, the second member in the P$_I$ hierarchy, we prove existence of various degenerate solutions depending on the complex parameter $t$ and evaluate the asymptotics in the complex $x$ plane for $|x|\to\infty$ and $t=o(x^{2/3})$. Using this result, we identify the most degenerate solutions $u^{(m)}(x,t)$, $\hat u^{(m)}(x,t)$, $m=0,\dots,6$, called {\em tritronqu\'ee}, describe the quasi-linear Stokes phenomenon and find the large $n$ asymptotics of the coefficients in a formal expansion of these solutions. We supplement our findings by a numerical study of the tritronqu\'ee solutions.

1 aGrava, Tamara1 aKapaev, Andrey1 aKlein, Christian uhttp://www.math.sissa.it/publication/tritronqu%C3%A9e-solutions-pi200539nas a2200133 4500008004100000022001400041245017800055210007000233300001400303490000700317100001900324700002200343856004000365 2013 eng d a0010-364000aUniversality for the focusing nonlinear Schrödinger equation at the gradient catastrophe point: rational breathers and poles of the \it Tritronquée solution to Painlevé I0 aUniversality for the focusing nonlinear Schrödinger equation at a678–7520 v661 aBertola, Marco1 aTovbis, Alexander uhttp://dx.doi.org/10.1002/cpa.2144500725nas a2200121 4500008004100000245006600041210006400107260001000171520034800181100002200529700001600551856003600567 2013 en d00aA variational Analysis of the Toda System on Compact Surfaces0 avariational Analysis of the Toda System on Compact Surfaces bWiley3 aIn this paper we consider the Toda system of equations on a compact surface. We will give existence results by using variational methods in a non coercive case. A key tool in our analysis is a new Moser-Trudinger type inequality under suitable conditions on the center of mass and the scale of concentration of the two components u_1, u_2.1 aMalchiodi, Andrea1 aRuiz, David uhttp://hdl.handle.net/1963/655801374nas a2200145 4500008004100000245010300041210006900144300001600213490000700229520080500236100001501041700002201056700002101078856012901099 2013 eng d00aA weighted reduced basis method for elliptic partial differential equations with random input data0 aweighted reduced basis method for elliptic partial differential a3163–31850 v513 aIn this work we propose and analyze a weighted reduced basis method to solve elliptic partial differential equations (PDEs) with random input data. The PDEs are first transformed into a weighted parametric elliptic problem depending on a finite number of parameters. Distinctive importance of the solution at different values of the parameters is taken into account by assigning different weights to the samples in the greedy sampling procedure. A priori convergence analysis is carried out by constructive approximation of the exact solution with respect to the weighted parameters. Numerical examples are provided for the assessment of the advantages of the proposed method over the reduced basis method and the stochastic collocation method in both univariate and multivariate stochastic problems.1 aChen, Peng1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://www.math.sissa.it/publication/weighted-reduced-basis-method-elliptic-partial-differential-equations-random-input-data00934nas a2200133 4500008004100000245005700041210005100098260005100149520050200200100002100702700001700723700002400740856003600764 2012 en d00aOn 2-step, corank 2 nilpotent sub-Riemannian metrics0 a2step corank 2 nilpotent subRiemannian metrics bSociety for Industrial and Applied Mathematics3 aIn this paper we study the nilpotent 2-step, corank 2 sub-Riemannian metrics\\r\\nthat are nilpotent approximations of general sub-Riemannian metrics. We exhibit optimal syntheses for these problems. It turns out that in general the cut time is not equal to the first conjugate time but has a simple explicit expression. As a byproduct of this study we get some smoothness properties of the spherical Hausdorff measure in the case of a generic 6 dimensional, 2-step corank 2 sub-Riemannian metric.1 aBarilari, Davide1 aBoscain, Ugo1 aGauthier, Jean-Paul uhttp://hdl.handle.net/1963/606500873nas a2200145 4500008004100000245005400041210004800095260004800143520037100191100002100562700002100583700002500604700002200629856007600651 2012 en d00aAsymptotics of the $s$-perimeter as $s\searrow 0$0 aAsymptotics of the sperimeter as ssearrow 0 bAmerican Institute of Mathematical Sciences3 aWe deal with the asymptotic behavior of the $s$-perimeter of a set $E$ inside a domain $\Omega$ as $s\searrow0$. We prove necessary and sufficient conditions for the existence of such limit, by also providing an explicit formulation in terms of the Lebesgue measure of $E$ and $\Omega$. Moreover, we construct examples of sets for which the limit does not exist.1 aDipierro, Serena1 aFigalli, Alessio1 aPalatucci, Giampiero1 aValdinoci, Enrico uhttp://www.math.sissa.it/publication/asymptotics-s-perimeter-ssearrow-001737nas a2200145 4500008004100000245007100041210006400112260001900176520126500195653002501460100002001485700002301505700002701528856003601555 2012 en d00aOn the behaviour of flexible retaining walls under seismic actions0 abehaviour of flexible retaining walls under seismic actions bICE Publishing3 aThis paper describes an experimental investigation of the behaviour of embedded retaining walls under seismic actions. Nine centrifuge tests were carried out on reduced-scale models of pairs of retaining walls in dry sand, either cantilevered or with one level of props near the top. The experimental data indicate that, for maximum accelerations that are smaller than the critical limit equilibrium value, the retaining walls experience significant permanent displacements under increasing structural loads, whereas for larger accelerations the walls rotate under constant internal forces. The critical acceleration at which the walls start to rotate increases with increasing maximum acceleration. No significant displacements are measured if the current earthquake is less severe than earthquakes previously experienced by the wall. The increase of critical acceleration is explained in terms of redistribution of earth pressures and progressive mobilisation of the passive strength in front of the wall. The experimental data for cantilevered retaining walls indicate that the permanent displacements of the wall can be reasonably predicted adopting a Newmark-type calculation with a critical acceleration that is a fraction of the limit equilibrium value.10aCentrifuge modelling1 aConti, Riccardo1 aMadabhushi, G.S.P.1 aViggiani, Giulia, M.B. uhttp://hdl.handle.net/1963/693301501nas a2200157 4500008004100000245010600041210006900147260003100216520095600247653002301203100001801226700002001244700002201264700002101286856003601307 2012 en d00aBoundary control and shape optimization for the robust design of bypass anastomoses under uncertainty0 aBoundary control and shape optimization for the robust design of bCambridge University Press3 aWe review the optimal design of an arterial bypass graft following either a (i) boundary optimal control approach, or a (ii) shape optimization formulation. The main focus is quantifying and treating the uncertainty in the residual flow when the hosting artery is not completely occluded,\\r\\nfor which the worst-case in terms of recirculation e ffects is inferred to correspond to a strong ori fice flow through near-complete occlusion. A worst-case optimal control approach is applied to the steady\\r\\nNavier-Stokes equations in 2D to identify an anastomosis angle and a cu ed shape that are robust with respect to a possible range of residual \\r\\nflows. We also consider a reduced order modelling framework\\r\\nbased on reduced basis methods in order to make the robust design problem computationally feasible. The results obtained in 2D are compared with simulations in a 3D geometry but without model\\r\\nreduction or the robust framework.10ashape optimization1 aLassila, Toni1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://hdl.handle.net/1963/633701064nas a2200121 4500008004100000245009600041210006900137260001300206520056600219100002000785700002400805856011300829 2012 en d00aOn a class of vector fields with discontinuity of divide-by-zero type and its applications0 aclass of vector fields with discontinuity of dividebyzero type a bSpringer3 aWe study phase portraits and singular points of vector fields of a special type, that is, vector fields whose components are fractions with a common denominator vanishing on a smooth regular hypersurface in the phase space. We assume also some additional conditions, which are fulfilled, for instance, if the vector field is divergence-free. This problem is motivated by a large number of applications. In this paper, we consider three of them in the framework of differential geometry: singularities of geodesic flows in various singular metrics on surfaces.1 aGhezzi, Roberta1 aRemizov, Alexey, O. uhttp://www.math.sissa.it/publication/class-vector-fields-discontinuity-divide-zero-type-and-its-applications01113nas a2200121 4500008004100000245008000041210006900121260001000190520071100200100002000911700002400931856003600955 2012 en d00aClassical double, R-operators, and negative flows of integrable hierarchies0 aClassical double Roperators and negative flows of integrable hie bSISSA3 aUsing the classical double G of a Lie algebra g equipped with the classical R-operator, we define two sets of functions commuting with respect to the initial Lie–Poisson bracket on g and its extensions. We consider examples of Lie algebras g with the “Adler–Kostant–Symes” R-operators and the two corresponding sets of mutually commuting functions in detail. Using the constructed commutative Hamiltonian flows on different extensions of g, we obtain zero-curvature equations with g-valued U–V pairs. The so-called negative flows of soliton hierarchies are among such equations. We illustrate the proposed approach with examples of two-dimensional Abelian and non-Abelian Toda field equations.1 aDubrovin, Boris1 aSkrypnyk, Taras, V. uhttp://hdl.handle.net/1963/646801152nas a2200145 4500008004100000245009700041210006900138260001000207520067600217100002200893700001500915700002000930700002000950856003600970 2012 en d00aA Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group.0 aCodazzilike equation and the singular set for C1 smooth surfaces bSISSA3 aIn this paper, we study the structure of the singular set for a C 1 smooth surface in the 3-dimensional Heisenberg group ℍ 1. We discover a Codazzi-like equation for the p-area element along the characteristic curves on the surface. Information obtained from this ordinary differential equation helps us to analyze the local configuration of the singular set and the characteristic curves. In particular, we can estimate the size and obtain the regularity of the singular set. We understand the global structure of the singular set through a Hopf-type index theorem. We also justify the Codazzi-like equation by proving a fundamental theorem for local surfaces in ℍ 11 aMalchiodi, Andrea1 aYang, Paul1 aCheng, Jih-Hsin1 aHwang, JennFang uhttp://hdl.handle.net/1963/655600824nas a2200169 4500008004100000020001800041245006300059210006300122260001300185520030800198653002400506100002200530700001700552700002300569700002600592856003600618 2012 en d a978146143996700aComputing optimal strokes for low reynolds number swimmers0 aComputing optimal strokes for low reynolds number swimmers bSpringer3 aWe discuss connections between low-Reynolds-number swimming and geometric control theory, and present a general algorithm for the numerical computation of energetically optimal strokes. As an illustration of our approach, we show computed motility maps and optimal strokes for two model swimmers.

10aNumerical analysis.1 aDeSimone, Antonio1 aHeltai, Luca1 aAlouges, François1 aAline, Lefebvre-Lepot uhttp://hdl.handle.net/1963/644500854nas a2200157 4500008004100000245012200041210007200163260002100235300001200256490000700268520031300275100002000588700002300608700001900631856004600650 2012 eng d00aConcentration on circles for nonlinear Schrödinger–Poisson systems with unbounded potentials vanishing at infinity0 aConcentration on circles for nonlinear Schrödinger–Poisson syste bWorld Scientific a12500090 v143 aThe present paper is devoted to weighted nonlinear Schrödinger–Poisson systems with potentials possibly unbounded and vanishing at infinity. Using a purely variational approach, we prove the existence of solutions concentrating on a circle.

1 aBonheure, Denis1 aDi Cosmo, Jonathan1 aMercuri, Carlo uhttps://doi.org/10.1142/S021919971250009500925nas a2200121 4500008004100000245010900041210006900150260001300219520049100232100002500723700001900748856003600767 2012 en d00aConvergence of equilibria of thin elastic plates under physical growth conditions for the energy density0 aConvergence of equilibria of thin elastic plates under physical bElsevier3 aThe asymptotic behaviour of the equilibrium configurations of a thin elastic plate is studied, as the thickness $h$ of the plate goes to zero. More precisely, it is shown that critical points of the nonlinear elastic functional $\mathcal E^h$, whose energies (per unit thickness) are bounded by $Ch^4$, converge to critical points of the $\Gamma$-limit of $h^{-4}\mathcal E^h$. This is proved under the physical assumption that the energy density $W(F)$ blows up as $\det F\to0$.

1 aMora, Maria Giovanna1 aScardia, Lucia uhttp://hdl.handle.net/1963/346601015nas a2200109 4500008004100000245004300041210004300084260001300127520070800140100002100848856003600869 2012 en d00aConvex pencils of real quadratic forms0 aConvex pencils of real quadratic forms bSpringer3 aWe study the topology of the set X of the solutions of a system of two quadratic inequalities in the real projective space RP^n (e.g. X is the intersection of two real quadrics). We give explicit formulae for its Betti numbers and for those of its double cover in the sphere S^n; we also give similar formulae for level sets of homogeneous quadratic maps to the plane. We discuss some applications of these results, especially in classical convexity theory. We prove the sharp bound b(X)\leq 2n for the total Betti number of X; we show that for odd n this bound is attained only by a singular X. In the nondegenerate case we also prove the bound on each specific Betti number b_k(X)\leq 2(k+2).1 aLerario, Antonio uhttp://hdl.handle.net/1963/709901915nas a2200121 4500008004100000245008100041210006900122260001300191520151100204100002201715700002001737856003601757 2012 en d00aCrawling motility through the analysis of model locomotors: two case studies0 aCrawling motility through the analysis of model locomotors two c bSpringer3 aWe study model locomotors on a substrate, which derive their propulsive capabilities from the tangential (viscous or frictional) resistance offered by the substrate. Our aim is to develop new tools and insight for future studies of cellular motility by crawling and of collective bacterial motion. The purely viscous case (worm) is relevant for cellular motility by crawling of individual cells. We re-examine some recent results on snail locomotion in order to assess the role of finely regulated adhesion mechanisms in crawling motility. Our main conclusion is that such regulation, although well documented in several biological systems, is not indispensable to accomplish locomotion driven by internal deformations, provided that the crawler may execute sufficiently large body deformations. Thus, there is no snail theorem. Namely, the crawling analog of the scallop theorem of low Reynolds number hydrodynamics does not hold for snail-like crawlers. The frictional case is obtained by assuming that the viscous coefficient governing tangential resistance forces, which act parallel and in the direction opposite to the velocity of the point to which they are applied, depends on the normal force acting at that point. We combine these surface interactions with inertial effects in order to investigate the mechanisms governing the motility of a bristle-robot. This model locomotor is easily manufactured and has been proposed as an effective tool to replicate and study collective bacterial motility.1 aDeSimone, Antonio1 aTatone, Amabile uhttp://hdl.handle.net/1963/701700864nas a2200121 4500008004100000245008100041210006900122260001000191520046700201100002000668700001800688856003600706 2012 en d00aOn the critical behavior in nonlinear evolutionary PDEs with small viscocity0 acritical behavior in nonlinear evolutionary PDEs with small visc bSISSA3 aWe address the problem of general dissipative regularization of the quasilinear transport equation. We argue that the local behavior of solutions to the regularized equation near the point of gradient catastrophe for the transport equation is described by the logarithmic derivative of the Pearcey function, a statement generalizing the result of A.M.Il\\\'in \\\\cite{ilin}. We provide some analytic arguments supporting such conjecture and test it numerically.1 aDubrovin, Boris1 aElaeva, Maria uhttp://hdl.handle.net/1963/646501414nas 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/1963/522602149nas a2200157 4500008004100000245008500041210006900126260003000195520152900225653003001754100003001784700002301814700001901837700002001856856011501876 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 uhttp://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/1963/605101741nas a2200133 4500008004100000245007700041210006900118260001000187520130700197100002401504700002101528700002201549856003601571 2012 en d00aExploring the low-energy landscape of large-scale signed social networks0 aExploring the lowenergy landscape of largescale signed social ne bSISSA3 aAnalogously to a spin glass, a large-scale signed social network is characterized by the presence of disorder, expressed in this context (and in the social network literature) by the concept of structural balance. If, as we have recently shown, the signed social networks currently available have a limited amount of true disorder (or frustration), it is also interesting to investigate how this frustration is organized, by exploring the landscape of near-optimal structural balance. What we obtain in this paper is that while one of the networks analyzed shows a unique valley of minima, and a funneled landscape that gradually and smoothly worsens as we move away from the optimum, another network shows instead several distinct valleys of optimal or near-optimal structural balance, separated by energy barriers determined by internally balanced subcommunities of users, a phenomenon similar to the replica-symmetry breaking of spin glasses. Multiple, essentially isoenergetic, arrangements of these communities are possible. Passing from one valley to another requires one to destroy the internal arrangement of these balanced subcommunities and then to reform it again. It is essentially this process of breaking the internal balance of the subcommunities which gives rise to the energy barriers.1 aFacchetti, Giuseppe1 aIacono, Giovanni1 aAltafini, Claudio uhttp://hdl.handle.net/1963/650401179nas a2200133 4500008004100000245006000041210005500101260001000156520076500166653004100931100001600972700002100988856003601009 2012 en d00aA formula for Popp\'s volume in sub-Riemannian geometry0 aformula for Popps volume in subRiemannian geometry bSISSA3 aFor an equiregular sub-Riemannian manifold M, Popp\'s volume is a smooth\r\nvolume which is canonically associated with the sub-Riemannian structure, and\r\nit is a natural generalization of the Riemannian one. In this paper we prove a\r\ngeneral formula for Popp\'s volume, written in terms of a frame adapted to the\r\nsub-Riemannian distribution. As a first application of this result, we prove an\r\nexplicit formula for the canonical sub-Laplacian, namely the one associated\r\nwith Popp\'s volume. Finally, we discuss sub-Riemannian isometries, and we prove\r\nthat they preserve Popp\'s volume. We also show that, under some hypotheses on\r\nthe action of the isometry group of M, Popp\'s volume is essentially the unique\r\nvolume with such a property.10asubriemannian, volume, Popp, control1 aRizzi, Luca1 aBarilari, Davide uhttp://hdl.handle.net/1963/650100484nas a2200133 4500008004100000022001400041245009400055210006900149300001400218490000800232100001900240700002000259856007100279 2012 eng d a0010-361600aFredholm determinants and pole-free solutions to the noncommutative Painlevé II equation0 aFredholm determinants and polefree solutions to the noncommutati a793–8330 v3091 aBertola, Marco1 aCafasso, Mattia uhttp://0-dx.doi.org.mercury.concordia.ca/10.1007/s00220-011-1383-x00909nas a2200109 4500008004100000245007800041210006900119260001300188520054100201100002100742856003600763 2012 en d00aFrobenius manifold for the dispersionless Kadomtsev-Petviashvili equation0 aFrobenius manifold for the dispersionless KadomtsevPetviashvili bSpringer3 aWe consider a Frobenius structure associated with the dispersionless\\r\\nKadomtsev-Petviashvili equation. This is done, essentially, by applying a\\r\\ncontinuous analogue of the finite dimensional theory in the space of Schwartz\\r\\nfunctions on the line. The potential of the Frobenius manifold is found to be a\\r\\nlogarithmic potential with quadratic external field. Following the construction\\r\\nof the principal hierarchy, we construct a set of infinitely many commuting\\r\\nflows, which extends the classical dKP hierarchy.1 aRaimondo, Andrea uhttp://hdl.handle.net/1963/604001763nas a2200169 4500008004100000245010700041210006900148260001000217520118200227653002601409653002901435653003501464100001701499700001701516700002401533856003601557 2012 en d00aA Fully Coupled Immersed Finite Element Method for Fluid Structure Interaction via the Deal.II Library0 aFully Coupled Immersed Finite Element Method for Fluid Structure bSISSA3 aWe present the implementation of a solution scheme for fluid-structure\\r\\ninteraction problems via the finite element software library deal.II. The\\r\\nsolution scheme is an immersed finite element method in which two independent discretizations are used for the fluid and immersed deformable body. In this type of formulation the support of the equations of motion of the fluid is extended to cover the union of the solid and fluid domains. The equations of motion over the extended solution domain govern the flow of a fluid under the action of a body force field. This body force field informs the fluid of the presence of the immersed solid. The velocity field of the immersed solid is the restriction over the immersed domain of the velocity field in the extended equations of motion. The focus of this paper is to show how the determination of the motion of the immersed domain is carried out in practice. We show that our implementation is general, that is, it is not dependent on a specific choice of the finite element spaces over the immersed solid and the extended fluid domains. We present some preliminary results concerning the accuracy of the proposed method.10aFinite Element Method10aImmersed Boundary Method10aImmersed Finite Element Method1 aHeltai, Luca1 aRoy, Saswati1 aCostanzo, Francesco uhttp://hdl.handle.net/1963/625500456nas a2200133 4500008004100000245006900041210006700110260001300177653003000190100001800220700002100238700002700259856003600286 2012 en d00aGamma-convergence and H-convergence of linear elliptic operators0 aGammaconvergence and Hconvergence of linear elliptic operators bElsevier10aLinear elliptic operators1 aAnsini, Nadia1 aDal Maso, Gianni1 aZeppieri, Caterina Ida uhttp://hdl.handle.net/1963/587800922nas a2200133 4500008004100000245007400041210006900115260001000184520049000194100002000684700002400704700002400728856003600752 2012 en d00aGauge Theories on ALE Space and Super Liouville Correlation Functions0 aGauge Theories on ALE Space and Super Liouville Correlation Func bSISSA3 aWe present a relation between N=2 quiver gauge theories on the ALE space O_{P^1}(-2) and correlators of N=1 super Liouville conformal field theory, providing checks in the case of punctured spheres and tori. We derive a blow-up formula for the full Nekrasov partition function and show that, up to a U(1) factor, the N=2^* instanton partition function is given by the product of the character of \\\\hat{SU}(2)_2 times the super Virasoro conformal block on the torus with one puncture.1 aBonelli, Giulio1 aMaruyoshi, Kazunobu1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/430501643nas a2200157 4500008004100000245012600041210006900167260001300236520109700249653002201346100001801368700002001386700002201406700002101428856003601449 2012 en d00aGeneralized reduced basis methods and n-width estimates for the approximation of the solution manifold of parametric PDEs0 aGeneralized reduced basis methods and nwidth estimates for the a bSpringer3 aThe set of solutions of a parameter-dependent linear partial di fferential equation with smooth coe fficients typically forms a compact manifold in a Hilbert space. In this paper we review the generalized reduced basis method as a fast computational tool for the uniform approximation of the solution manifold. We focus on operators showing an affi ne parametric dependence, expressed as a linear combination of parameter-independent operators through some smooth, parameter-dependent scalar functions. In the case that the parameter-dependent operator has a dominant term in its affi ne expansion, one can prove the existence of exponentially convergent uniform approximation spaces for the entire solution manifold. These spaces can be constructed without any assumptions on the parametric regularity of the manifold \\r\\nonly spatial regularity of the solutions is required. The exponential convergence rate is then inherited by the generalized reduced basis method. We provide a numerical example related to parametrized elliptic\\r\\nequations con rming the predicted convergence rates.10asolution manifold1 aLassila, Toni1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://hdl.handle.net/1963/634000982nas a2200133 4500008004100000245007000041210006300111260001000174520057500184100002000759700001500779700001800794856003600812 2012 en d00aOn the genus two free energies for semisimple Frobenius manifolds0 agenus two free energies for semisimple Frobenius manifolds bSISSA3 aWe represent the genus two free energy of an arbitrary semisimple Frobenius\\r\\nmanifold as a sum of contributions associated with dual graphs of certain\\r\\nstable algebraic curves of genus two plus the so-called \\\"genus two G-function\\\".\\r\\nConjecturally the genus two G-function vanishes for a series of important\\r\\nexamples of Frobenius manifolds associated with simple singularities as well as\\r\\nfor ${\\\\bf P}^1$-orbifolds with positive Euler characteristics. We explain the\\r\\nreasons for such Conjecture and prove it in certain particular cases.1 aDubrovin, Boris1 aLiu, Si-Qi1 aZhang, Youjin uhttp://hdl.handle.net/1963/646401371nas a2200133 4500008004100000245014300041210006900184260001000253520081800263653008501081100002301166700001201189856003601201 2012 en d00aGlobal structure of admissible BV solutions to piecewise genuinely nonlinear, strictly hyperbolic conservation laws in one space dimension0 aGlobal structure of admissible BV solutions to piecewise genuine bSISSA3 aThe paper gives an accurate description of the qualitative structure of an admissible BV solution to a strictly hyperbolic, piecewise genuinely nonlinear system of conservation laws. We prove that there are a countable set $\\\\Theta$ which contains all interaction points and a family of countably many Lipschitz curves $\\\\T$ such that outside $\\\\T\\\\cup \\\\Theta$ $u$ is continuous, and along the curves in $\\\\T$, u has left and right limit except for points in $\\\\Theta$. This extends the corresponding structural result in \\\\cite{BL,Liu1} for admissible solutions.\\r\\n\\r\\nThe proof is based on approximate wave-front tracking solutions and a proper selection of discontinuity curves in the approximate solutions, which converge to curves covering the discontinuities in the exact solution $u$.10aHyperbolic conservation laws, Wave-front tracking, Global structure of solution.1 aBianchini, Stefano1 aYu, Lei uhttp://hdl.handle.net/1963/631601194nas a2200133 4500008004100000245005500041210004700096260001000143520080800153100002500961700002100986700001701007856003601024 2012 en d00aOn the Hausdorff volume in sub-Riemannian geometry0 aHausdorff volume in subRiemannian geometry bSISSA3 aFor a regular sub-Riemannian manifold we study the Radon-Nikodym derivative\r\nof the spherical Hausdorff measure with respect to a smooth volume. We prove\r\nthat this is the volume of the unit ball in the nilpotent approximation and it\r\nis always a continuous function. We then prove that up to dimension 4 it is\r\nsmooth, while starting from dimension 5, in corank 1 case, it is C^3 (and C^4\r\non every smooth curve) but in general not C^5. These results answer to a\r\nquestion addressed by Montgomery about the relation between two intrinsic\r\nvolumes that can be defined in a sub-Riemannian manifold, namely the Popp and\r\nthe Hausdorff volume. If the nilpotent approximation depends on the point (that\r\nmay happen starting from dimension 5), then they are not proportional, in\r\ngeneral.1 aAgrachev, Andrei, A.1 aBarilari, Davide1 aBoscain, Ugo uhttp://hdl.handle.net/1963/645401970nas a2200169 4500008004100000245009100041210006900132260003100201520131900232100002201551700001701573700002001590700002201610700002201632700002501654856012101679 2012 en d00aHybridization in nanostructured DNA monolayers probed by AFM: theory versus experiment0 aHybridization in nanostructured DNA monolayers probed by AFM the bRoyal Society of Chemistry3 aNanografted monolayers (NAMs) of DNA show novel physico-chemical properties that make them ideally suited for advanced biosensing applications. In comparison with alternative solid-phase techniques for diagnostic DNA detection, NAMs have the advantage of combining a small size with a high homogeneity of the DNA surface coverage. These two properties favour the extreme miniaturization and ultrasensitivity in high-throughput biosensing devices. The systematic use of NAMs for quantitative DNA (and protein) detection has so far suffered from the lack of a control on key fabrication parameters, such as the ss- or ds-DNA surface coverage. Here we report on a combined experimental-computational study that allows us to estimate the surface density of the grafted DNA by analyzing the sample mechanical response, that is the DNA patch height vs. applied tip load curves. It is shown that the same analysis scheme can be used to detect the occurrence of hybridization with complementary strands in solution and estimate its efficiency. Thanks to these quantitative relationships it is possible to use a single AFM-based setup to: (i) fabricate a DNA NAM, (ii) control the DNA surface coverage, and (iii) characterize its level of hybridization helping the design of NAMs with pre-determined fabrication parameters.1 aBosco, Alessandro1 aBano, Fouzia1 aParisse, Pietro1 aCasalis, Loredana1 aDeSimone, Antonio1 aMicheletti, Cristian uhttp://www.math.sissa.it/publication/hybridization-nanostructured-dna-monolayers-probed-afm-theory-versus-experiment00389nas a2200121 4500008004100000245005900041210005800100260001000158100002500168700002100193700001700214856003600231 2012 en d00aIntroduction to Riemannian and sub-Riemannian geometry0 aIntroduction to Riemannian and subRiemannian geometry bSISSA1 aAgrachev, Andrei, A.1 aBarilari, Davide1 aBoscain, Ugo uhttp://hdl.handle.net/1963/587701113nas a2200133 4500008004100000245006400041210005900105260002800164520069000192653002700882100001600909700001800925856003600943 2012 en d00aThe KdV hierarchy: universality and a Painleve transcendent0 aKdV hierarchy universality and a Painleve transcendent bOxford University Press3 aWe study the Cauchy problem for the Korteweg-de Vries (KdV) hierarchy in the small dispersion limit where $\e\to 0$. For negative analytic initial data with a single negative hump, we prove that for small times, the solution is approximated by the solution to the hyperbolic transport equation which corresponds to $\e=0$. Near the time of gradient catastrophe for the transport equation, we show that the solution to the KdV hierarchy is approximated by a particular Painlev\'e transcendent. This supports Dubrovins universality conjecture concerning the critical behavior of Hamiltonian perturbations of hyperbolic equations. We use the Riemann-Hilbert approach to prove our results.10aSmall-Dispersion limit1 aClaeys, Tom1 aGrava, Tamara uhttp://hdl.handle.net/1963/692100659nas a2200145 4500008004100000245011000041210006900151260003000220520013300250653002500383100002600408700002100434700002200455856003600477 2012 en d00aLinear elasticity obtained from finite elasticity by Gamma-convergence under weak coerciveness conditions0 aLinear elasticity obtained from finite elasticity by Gammaconver bGauthier-Villars;Elsevier3 aThe energy functional of linear elasticity is obtained as G-limit of suitable rescalings of the energies of finite elasticity...10aNonlinear elasticity1 aAgostiniani, Virginia1 aDal Maso, Gianni1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/426700646nas a2200133 4500008004100000245005800041210005500099260001300154520025200167653001900419100001600438700002200454856003600476 2012 en d00aOn localization in holomorphic equivariant cohomology0 alocalization in holomorphic equivariant cohomology bSpringer3 aWe prove a localization formula for a "holomorphic equivariant cohomology" attached to the Atiyah algebroid of an equivariant holomorphic vector bundle. This generalizes Feng-Ma, Carrell-Liebermann, Baum-Bott and K. Liu's localization formulas.10aLie algebroids1 aBruzzo, Ugo1 aRubtsov, Vladimir uhttp://hdl.handle.net/1963/658400466nas a2200121 4500008004100000022001400041245010500055210006900160300001600229490000700245100001900252856007300271 2012 eng d a0951-771500aOn the location of poles for the Ablowitz-Segur family of solutions to the second Painlevé equation0 alocation of poles for the AblowitzSegur family of solutions to t a1179–11850 v251 aBertola, Marco uhttp://0-dx.doi.org.mercury.concordia.ca/10.1088/0951-7715/25/4/117901914nas a2200145 4500008004100000020001800041245010100059210006900160260003100229520140500260653002201665100002301687700002201710856003601732 2012 en d a978160511380700aMathematical and numerical modeling of liquid crystal elastomer phase transition and deformation0 aMathematical and numerical modeling of liquid crystal elastomer bCambridge University Press3 aLiquid crystal (in particular, nematic) elastomers consist of cross-linked flexible polymer chains with embedded stiff rod molecules that allow them to behave as a rubber and a liquid crystal. Nematic elastomers are characterized by a phase transition from isotropic to nematic past a temperature threshold. They behave as rubber at high temperature and show nematic behavior below the temperature threshold. Such transition is reversible. While in the nematic phase, the rod molecules are aligned along the direction of the "nematic director". This molecular rearrangement induces a stretch in the polymer chains and hence macroscopic spontaneous deformations. The coupling between nematic order parameter and deformation gives rise to interesting phenomena with a potential for new interesting applications. In the biological field, the ability to considerably change their length makes them very promising as artificial muscles actuators. Their tunable optical properties make them suitable, for example, as lenses for new imaging systems. We present a mathematical model able to describe the behavior of nematic elastomers and numerical simulations reproducing such peculiar behavior. We use a geometrically linear version of the Warner and Terentjev model [1] and consider cooling experiments and stretching experiments in the direction perpendicular to the one of the director at cross-linking.10aArtificial muscle1 aDe Luca, Mariarita1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/702001486nas a2200121 4500008004100000245006100041210006000102260005400162520106700216100002201283700002301305856003601328 2012 en d00aModeling and control of quantum systems: An introduction0 aModeling and control of quantum systems An introduction bInstitute of Electrical and Electronics Engineers3 aThe scope of this work is to provide a self-contained introduction to a selection of basic theoretical aspects in the modeling and control of quantum mechanical systems, as well as a brief survey on the main approaches to control synthesis. While part of the existing theory, especially in the open-loop setting, stems directly from classical control theory (most notably geometric control and optimal control), a number of tools specifically tailored for quantum systems have been developed since the 1980s, in order to take into account their distinctive features: the probabilistic nature of atomic-scale physical systems, the effect of dissipation and the irreversible character of the measurements have all proved to be critical in feedback-design problems. The relevant dynamical models for both closed and open quantum systems are presented, along with the main results on their controllability and stability. A brief review of several currently available control design methods is meant to provide the interested reader with a roadmap for further studies1 aAltafini, Claudio1 aTicozzi, Francesco uhttp://hdl.handle.net/1963/650500979nas a2200133 4500008004100000245010200041210006900143260001000212520051900222100001600741700002600757700002600783856003600809 2012 en d00aModuli of symplectic instanton vector bundles of higher rank on projective space $\\mathbb{P}^3$0 aModuli of symplectic instanton vector bundles of higher rank on bSISSA3 aSymplectic instanton vector bundles on the projective space $\\mathbb{P}^3$ constitute a natural generalization of mathematical instantons of rank 2. We study the moduli space $I_{n,r}$ of rank-$2r$ symplectic instanton vector bundles on $\\mathbb{P}^3$ with $r\\ge2$ and second Chern class $n\\ge r,\\ n\\equiv r({\\rm mod}2)$. We give an explicit construction of an irreducible component $I^*_{n,r}$ of this space for each such value of $n$ and show that $I^*_{n,r}$ has the expected dimension $4n(r+1)-r(2r+1)$.1 aBruzzo, Ugo1 aMarkushevich, Dimitri1 aTikhomirov, Alexander uhttp://hdl.handle.net/1963/465601072nas a2200121 4500008004300000245008700043210006900130260002800199520065000227100001700877700002000894856003600914 2012 en_Ud 00aModuli spaces of noncommutative instantons: gauging away noncommutative parameters0 aModuli spaces of noncommutative instantons gauging away noncommu bOxford University Press3 aUsing the theory of noncommutative geometry in a braided monoidal category, we improve upon a previous construction of noncommutative families of instantons of arbitrary charge on the deformed sphere S^4_\\\\theta. We formulate a notion of noncommutative parameter spaces for families of instantons and we explore what it means for such families to be gauge equivalent, as well as showing how to remove gauge parameters using a noncommutative quotient construction. Although the parameter spaces are a priori noncommutative, we show that one may always recover a classical parameter space by making an appropriate choice of gauge transformation.1 aBrain, Simon1 aLandi, Giovanni uhttp://hdl.handle.net/1963/377700826nas a2200133 4500008004300000245007200043210006900115260002100184520038600205100002000591700002500611700002000636856003600656 2012 en_Ud 00aNonlinear thin-walled beams with a rectangular cross-section-Part I0 aNonlinear thinwalled beams with a rectangular crosssectionPart I bWorld Scientific3 aOur aim is to rigorously derive a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section, starting from three-dimensional nonlinear elasticity. The different limit models are distinguished by the different scaling of the elastic energy and of the ratio between the sides of the cross-section. In this paper we report the first part of our results.1 aFreddi, Lorenzo1 aMora, Maria Giovanna1 aParoni, Roberto uhttp://hdl.handle.net/1963/410401662nas a2200121 4500008004100000245009600041210006900137260001300206520124300219100002001462700002201482856003601504 2012 en d00aNon-uniqueness results for critical metrics of regularized determinants in four dimensions0 aNonuniqueness results for critical metrics of regularized determ bSpringer3 aThe regularized determinant of the Paneitz operator arises in quantum gravity (see Connes 1994, IV.4.$\gamma$). An explicit formula for the relative determinant of two conformally related metrics was computed by Branson in Branson (1996). A similar formula holds for Cheeger's half-torsion, which plays a role in self-dual field theory (see Juhl, 2009), and is defined in terms of regularized determinants of the Hodge laplacian on $p$-forms ($p < n/2$). In this article we show that the corresponding actions are unbounded (above and below) on any conformal four-manifold. We also show that the conformal class of the round sphere admits a second solution which is not given by the pull-back of the round metric by a conformal map, thus violating uniqueness up to gauge equivalence. These results differ from the properties of the determinant of the conformal Laplacian established in Chang and Yang (1995), Branson, Chang, and Yang (1992), and Gursky (1997). We also study entire solutions of the Euler-Lagrange equation of $\log \det P$ and the half-torsion $\tau_h$ on $\mathbb{R}^4 \setminus {0}$, and show the existence of two families of periodic solutions. One of these families includes Delaunay-type solutions.1 aGursky, Matthew1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/655901861nas a2200145 4500008004100000245007600041210006900117260001300186520138500199653002701584100002001611700002101631700002701652856003601679 2012 en d00aNumerical modelling of installation effects for diaphragm walls in sand0 aNumerical modelling of installation effects for diaphragm walls bSpringer3 aThe scopes of this work are to study the mechanisms of load transfer and the deformations of the ground during slurry trenching and concreting in dry sand and to evaluate their effects on service structural loads, wall deflections and ground displacements behind the wall caused by subsequent excavation. A series of three-dimensional finite element analyses was carried out modelling the installation of diaphragm walls consisting of panels of different length. The soil was modelled as either linearly elastic-perfectly plastic or incrementally non-linear (hypoplastic) with elastic strain range. Plane strain analyses of diaphragm walls of identical cross section were also carried out in which wall installation was either modelled or the wall was wished in place (WIP). The analyses predict ground movements consistent with the experimental observations both in magnitude and trend. The results also show that the maximum horizontal wall deflections and structural loads reduce with increasing panel aspect ratio towards a minimum which is about twice the value computed for WIP analyses. Panel aspect ratios should be larger than about three to take advantage of the three-dimensional effects. The pattern and magnitude of surface vertical displacements obtained from linearly elastic-perfectly plastic analyses, no matter whether three- or two-dimensional, are unrealistic.10aConstitutive relations1 aConti, Riccardo1 ade Sanctis, Luca1 aViggiani, Giulia, M.B. uhttp://hdl.handle.net/1963/693400917nas a2200133 4500008004100000245011000041210006900151260001300220520035800233653003100591100001800622700002100640856012200661 2012 en d00aNumerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions0 aNumerical study of the small dispersion limit of the Kortewegde bElsevier3 aWe study numerically the small dispersion limit for the Korteweg-de Vries (KdV) equation $u_t+6uu_x+\epsilon^{2}u_{xxx}=0$ for $\epsilon\ll1$ and give a quantitative comparison of the numerical solution with various asymptotic formulae for small $\epsilon$ in the whole $(x,t)$-plane. The matching of the asymptotic solutions is studied numerically.10aKorteweg-de Vries equation1 aGrava, Tamara1 aKlein, Christian uhttp://www.math.sissa.it/publication/numerical-study-small-dispersion-limit-korteweg-de-vries-equation-and-asymptotic01633nas a2200133 4500008004100000245004700041210004600088260001300134520119900147653002501346100002601371700002201397856008001419 2012 en d00aOgden-type energies for nematic elastomers0 aOgdentype energies for nematic elastomers bElsevier3 aOgden-type extensions of the free-energy densities currently used to model the mechanical behavior of nematic elastomers are proposed and analyzed. Based on a multiplicative decomposition of the deformation gradient into an elastic and a spontaneous or remanent part, they provide a suitable framework to study the stiffening response at high imposed stretches. Geometrically linear versions of the models (Taylor expansions at order two) are provided and discussed. These small strain theories provide a clear illustration of the geometric structure of the underlying energy landscape (the energy grows quadratically with the distance from a non-convex set of spontaneous strains or energy wells). The comparison between small strain and finite deformation theories may also be useful in the opposite direction, inspiring finite deformation generalizations of small strain theories currently used in the mechanics of active and phase-transforming materials. The energy well structure makes the free-energy densities non-convex. Explicit quasi-convex envelopes are provided, and applied to compute the stiffening response of a specimen tested in plane strain extension experiments (pure shear).10aNonlinear elasticity1 aAgostiniani, Virginia1 aDeSimone, Antonio uhttp://www.math.sissa.it/publication/ogden-type-energies-nematic-elastomers00782nas a2200121 4500008004100000245008600041210006900127260001300196520037000209653002400579100002100603856003600624 2012 en d00aPoles Distribution of PVI Transcendents close to a Critical Point (summer 2011)0 aPoles Distribution of PVI Transcendents close to a Critical Poin bElsevier3 aThe distribution of the poles of Painlevé VI transcendents associated to semi-simple Frobenius manifolds is determined close to a critical point. It is shown that the poles accumulate at the critical point,asymptotically along two rays. As an example, the Frobenius manifold given by the quantum cohomology of CP2 is considered. The general PVI is also considered.10aPainleve' equations1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/652602201nas a2200133 4500008004100000245010400041210006900145260001900214520173100233100002401964700002201988700002102010856003602031 2012 en d00aPredicting and characterizing selective multiple drug treatments for metabolic diseases and cancer.0 aPredicting and characterizing selective multiple drug treatments bBioMed Central3 aBackground: In the field of drug discovery, assessing the potential of multidrug therapies is a difficult task because of the combinatorial complexity (both theoretical and experimental) and because of the requirements on the selectivity of the therapy. To cope with this problem, we have developed a novel method for the systematic in silico investigation of synergistic effects of currently available drugs on genome-scale metabolic networks. The algorithm finds the optimal combination of drugs which guarantees the inhibition of an objective function, while minimizing the side effect on the overall network. Results: Two different applications are considered: finding drug synergisms for human metabolic diseases (like diabetes, obesity and hypertension) and finding antitumoral drug combinations with minimal side effect on the normal human metabolism.The results we obtain are consistent with some of the available therapeutic indications and predict some new multiple drug treatments.A cluster analysis on all possible interactions among the currently available drugs indicates a limited variety on the metabolic targets for the approved drugs. Conclusion: The in silico prediction of drug synergism can represent an important tool for the repurposing of drug in a realistic perspective which considers also the selectivty of the therapy. Moreover, for a more profitable exploitation of drug-drug interactions, also drugs which show a too low efficacy but which have a non-common mechanism of action, can be reconsider as potential ingredients of new multicompound therapeutic indications.Needless to say the clues provided by a computational study like ours need in any case to be thoroughly evaluated experimentally.1 aFacchetti, Giuseppe1 aAltafini, Claudio1 aZampieri, Mattia uhttp://hdl.handle.net/1963/651501380nas a2200133 4500008004300000245008800043210006900131260001300200520092800213100002101141700002201162700002601184856003601210 2012 en_Ud 00aQuasistatic evolution for Cam-Clay plasticity: properties of the viscosity solution0 aQuasistatic evolution for CamClay plasticity properties of the v bSpringer3 aCam-Clay plasticity is a well established model for the description of the mechanics of fine grained soils. As solutions can develop discontinuities in time, a weak notion of solution, in terms of a rescaled time s , has been proposed in [8] to give a meaning to this discontinuous evolution. In this paper we first prove that this rescaled evolution satisfies the flow-rule for the rate of plastic strain, in a suitable measure-theoretical sense. In the second part of the paper we consider the behavior of the evolution in terms of the original time variable t . We prove that the unrescaled solution satisfies an energy-dissipation balance and an evolution law for the internal variable, which can be expressed in terms of integrals depending only on the original time. Both these integral identities contain terms concentrated on the jump times, whose size can only be determined by looking at the rescaled formulation.1 aDal Maso, Gianni1 aDeSimone, Antonio1 aSolombrino, Francesco uhttp://hdl.handle.net/1963/390000946nas a2200145 4500008004100000245007300041210006900114260000900183520047100192653002200663100002900685700002500714700002500739856003600764 2012 en d00aQuasistatic evolution in non-associative plasticity - the cap models0 aQuasistatic evolution in nonassociative plasticity the cap model bSIAM3 aNon-associative elasto-plasticity is the working model of plasticity for soil and rocks mechanics. Yet, it is usually viewed as non-variational. In this work, we prove a contrario the existence of a variational evolution for such a model under a natural capping assumption on the hydrostatic stresses and a less natural mollification of the stress admissibility constraint. The obtained elasto-plastic evolution is expressed for times that are conveniently rescaled.10aElasto-plasticity1 aBabadjian, Jean-Francois1 aFrancfort, Gilles A.1 aMora, Maria Giovanna uhttp://hdl.handle.net/1963/413901190nas a2200133 4500008004100000245009200041210006900133260001000202520074300212653002200955100001800977700002500995856003601020 2012 en d00aA Quasistatic evolution model for perfectly plastic plates derived by Gamma-convergence0 aQuasistatic evolution model for perfectly plastic plates derived bSISSA3 aThe subject of this paper is the rigorous derivation of a quasistatic evolution model for a linearly elastic - perfectly plastic thin plate. As the thickness of the plate tends to zero, we prove via Gamma-convergence techniques that solutions to the three-dimensional quasistatic evolution problem of Prandtl-Reuss elastoplasticity converge to a quasistatic evolution of a suitable reduced model. In this limiting model the admissible displacements are of Kirchhoff-Love type and the stretching and bending components of the stress are coupled through a plastic flow rule. Some equivalent formulations of the limiting problem in rate form are derived, together with some two-dimensional characterizations for suitable choices of the data.10aGamma-convergence1 aDavoli, Elisa1 aMora, Maria Giovanna uhttp://hdl.handle.net/1963/567301651nas a2200133 4500008004100000245008400041210006900125520120500194653002101399100002101420700002001441700002001461856003601481 2012 en d00aReduction strategies for PDE-constrained oprimization problems in Haemodynamics0 aReduction strategies for PDEconstrained oprimization problems in3 aSolving optimal control problems for many different scenarios obtained by varying a set of parameters in the state system is a computationally extensive task. In this paper we present a new reduced framework for the formulation, the analysis and the numerical solution of parametrized PDE-constrained optimization problems. This framework is based on a suitable saddle-point formulation of the optimal control problem and exploits the reduced basis method for the rapid and reliable solution of parametrized PDEs, leading to a relevant computational reduction with respect to traditional discretization techniques such as the finite element method. This allows a very efficient evaluation of state solutions and cost functionals, leading to an effective solution of repeated optimal control problems, even on domains of variable shape, for which a further (geometrical) reduction is pursued, relying on flexible shape parametrization techniques. This setting is applied to the solution of two problems arising from haemodynamics, dealing with both data reconstruction and data assimilation over domains of variable shape,\\r\\nwhich can be recast in a common PDE-constrained optimization formulation.10ainverse problems1 aRozza, Gianluigi1 aManzoni, Andrea1 aNegri, Federico uhttp://hdl.handle.net/1963/633802076nas a2200145 4500008004100000245004700041210004700088520166300135653001801798100001901816700001701835700002001852700002201872856003601894 2012 en d00aReverse engineering the euglenoid movement0 aReverse engineering the euglenoid movement3 aEuglenids exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large-amplitude highly concerted deformations of the entire body (euglenoid movement or metaboly). A plastic cell envelope called pellicle mediates these deformations. Unlike ciliary or flagellar motility, the biophysics of this mode is not well understood, including its efficiency and molecular machinery. We quantitatively examine video recordings of four euglenids executing such motions with statistical learning methods. This analysis reveals strokes of high uniformity in shape and pace. We then interpret the observations in the light of a theory for the pellicle kinematics, providing a precise understanding of the link between local actuation by pellicle shear and shape control. We systematically understand common observations, such as the helical conformations of the pellicle, and identify previously unnoticed features of metaboly. While two of our euglenids execute their stroke at constant body volume, the other two exhibit deviations of about 20% from their average volume, challenging current models of low Reynolds number locomotion. We find that the active pellicle shear deformations causing shape changes can reach 340%, and estimate the velocity of the molecular motors. Moreover, we find that metaboly accomplishes locomotion at hydrodynamic efficiencies comparable to those of ciliates and flagellates. Our results suggest new quantitative experiments, provide insight into the evolutionary history of euglenids, and suggest that the pellicle may serve as a model for engineered active surfaces with applications in microfluidics.10amicroswimmers1 aArroyo, Marino1 aHeltai, Luca1 aMillán, Daniel1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/644400581nas a2200121 4500008004100000245004500041210004300086260001000129520024000139653002300379100002100402856003600423 2012 en d00aA Review on The Sixth Painlevé Equation0 aReview on The Sixth Painlevé Equation bSISSA3 aFor the Painlev\\\'e 6 transcendents, we provide a unitary description of the\r\ncritical behaviours, the connection formulae, their complete tabulation, and\r\nthe asymptotic distribution of the poles close to a critical point.

10aPainlevé equation1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/652500516nas a2200145 4500008004100000022001400041245008700055210007100142300001600213490000800229653002300237100001900260700002000279856007100299 2012 eng d a0167-278900aRiemann–Hilbert approach to multi-time processes: The Airy and the Pearcey cases0 aRiemann–Hilbert approach to multitime processes The Airy and the a2237 - 22450 v24110aIntegrable kernels1 aBertola, Marco1 aCafasso, Mattia uhttp://www.sciencedirect.com/science/article/pii/S016727891200011500821nas a2200121 4500008004100000245007700041210006900118520040700187100002500594700002300619700002100642856003600663 2012 en d00aOn robust Lie-algebraic stability conditions for switched linear systems0 arobust Liealgebraic stability conditions for switched linear sys3 aThis paper presents new sufficient conditions for exponential stability of switched linear systems under arbitrary switching, which involve the commutators (Lie brackets) among the given matrices generating the switched system. The main novelty feature of these stability criteria is that, unlike their earlier counterparts, they are robust with respect to small perturbations of the system parameters.1 aAgrachev, Andrei, A.1 aBaryshnikov, Yurij1 aLiberzon, Daniel uhttp://hdl.handle.net/1963/645500431nas a2200109 4500008004300000245011600043210006900159260001300228100002300241700002100264856003600285 2012 en_Ud 00aSBV regularity for genuinely nonlinear, strictly hyperbolic systems of conservation laws in one space dimension0 aSBV regularity for genuinely nonlinear strictly hyperbolic syste bSpringer1 aBianchini, Stefano1 aCaravenna, Laura uhttp://hdl.handle.net/1963/409100447nas a2200133 4500008004100000245008500041210006900126260001000195300001400205490000700219100002300226700001900249856004500268 2012 en d00aSBV regularity for Hamilton-Jacobi equations with Hamiltonian depending on (t,x)0 aSBV regularity for HamiltonJacobi equations with Hamiltonian dep bSISSA a2179-22030 v441 aBianchini, Stefano1 aTonon, Daniela uhttp://hdl.handle.net/20.500.11767/1406600755nas a2200121 4500008004100000245010500041210006900146260001300215520032300228653002300551100002300574856003600597 2012 en d00aSBV regularity of genuinely nonlinear hyperbolic systems of conservation laws in one space dimension0 aSBV regularity of genuinely nonlinear hyperbolic systems of cons bElsevier3 aThe problem of the presence of Cantor part in the derivative of a solution to a hyperbolic system of conservation laws is considered. An overview of the techniques involved in the proof is given, and a collection of related problems concludes the paper. Key words hyperbolic systems; conservation laws; SBV; regularity10aHyperbolic systems1 aBianchini, Stefano uhttp://hdl.handle.net/1963/653500441nas a2200133 4500008004100000245008000041210006900121260001000190300001200200490000800212100002300220700001900243856004500262 2012 en d00aSBV-like regularity for Hamilton-Jacobi equations with a convex Hamiltonian0 aSBVlike regularity for HamiltonJacobi equations with a convex Ha bSISSA a190-2080 v3911 aBianchini, Stefano1 aTonon, Daniela uhttp://hdl.handle.net/20.500.11767/1390901579nas a2200145 4500008004100000245008700041210006900128260001000197520093400207653011301141100001501254700002201269700002101291856012101312 2012 en d00aSimulation-based uncertainty quantification of human arterial network hemodynamics0 aSimulationbased uncertainty quantification of human arterial net bWiley3 aThis work aims at identifying and quantifying uncertainties from various sources in human cardiovascular\r\nsystem based on stochastic simulation of a one dimensional arterial network. A general analysis of\r\ndifferent uncertainties and probability characterization with log-normal distribution of these uncertainties\r\nis introduced. Deriving from a deterministic one dimensional fluid structure interaction model, we establish\r\nthe stochastic model as a coupled hyperbolic system incorporated with parametric uncertainties to describe\r\nthe blood flow and pressure wave propagation in the arterial network. By applying a stochastic collocation\r\nmethod with sparse grid technique, we study systemically the statistics and sensitivity of the solution with\r\nrespect to many different uncertainties in a relatively complete arterial network with potential physiological\r\nand pathological implications for the first time.10auncertainty quantification, mathematical modelling of the cardiovascular system, fluid-structure interaction1 aChen, Peng1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://www.math.sissa.it/publication/simulation-based-uncertainty-quantification-human-arterial-network-hemodynamics01295nas a2200145 4500008004100000022001300041245010400054210006900158300001400227490000700241520073600248100002400984700002001008856012101028 2012 eng d a0951771500aSobolev quasi-periodic solutions of multidimensional wave equations with a multiplicative potential0 aSobolev quasiperiodic solutions of multidimensional wave equatio a2579-26130 v253 aWe prove the existence of quasi-periodic solutions for wave equations with a multiplicative potential on T d , d ≥ 1, and finitely differentiable nonlinearities, quasi-periodically forced in time. The only external parameter is the length of the frequency vector. The solutions have Sobolev regularity both in time and space. The proof is based on a Nash-Moser iterative scheme as in [5]. The key tame estimates for the inverse linearized operators are obtained by a multiscale inductive argument, which is more difficult than for NLS due to the dispersion relation of the wave equation. We prove the 'separation properties' of the small divisors assuming weaker non-resonance conditions than in [11]. © 2012 IOP Publishing Ltd.1 aBerti, Massimiliano1 aBolle, Philippe uhttp://www.math.sissa.it/publication/sobolev-quasi-periodic-solutions-multidimensional-wave-equations-multiplicative01270nas a2200109 4500008004100000245012700041210007000168260002800238520083700266100002101103856003601124 2012 en d00aSolving the Sixth Painlevé Equation: Towards the Classification of all the Critical Behaviors and the Connection Formulae0 aSolving the Sixth Painlevé Equation Towards the Classification o bOxford University Press3 aThe critical behavior of a three real parameter class of solutions of the\\r\\nsixth Painlev\\\\\\\'e equation is computed, and parametrized in terms of monodromy\\r\\ndata of the associated $2\\\\times 2$ matrix linear Fuchsian system of ODE. The\\r\\nclass may contain solutions with poles accumulating at the critical point. The\\r\\nstudy of this class closes a gap in the description of the transcendents in one\\r\\nto one correspondence with the monodromy data. These transcendents are reviewed in the paper. Some formulas that relate the monodromy data to the critical behaviors of the four real (two complex) parameter class of solutions are\\r\\nmissing in the literature, so they are computed here. A computational procedure to write the full expansion of the four and three real parameter class of solutions is proposed.1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/609300790nas a2200121 4500008004100000245014600041210006900187300001400256490000600270520032300276100001900599856005000618 2012 eng d00aSome applications of the SBV Regularity Theorem for entropy solutions of 1D scalar conservation laws to ConvectionTheory and sticky particles0 aSome applications of the SBV Regularity Theorem for entropy solu a163–1750 v33 aWe show how it is possible to apply the SBV Regularity Theorem for entropy solutions of one-dimensional scalar conservation laws, proved by Ambrosio and De Lellis, to Convection Theory and sticky particles. In the multi-dimensional case we present a counterexample which prevent us from using the same approach.

1 aTonon, Daniela uhttps://hal.archives-ouvertes.fr/hal-0091840900324nas a2200097 4500008004100000245006100041210005700102260001000159100002100169856003600190 2012 en d00aSome aspects of spinors – classical and noncommutative0 aSome aspects of spinors classical and noncommutative bSISSA1 aDossena, Giacomo uhttp://hdl.handle.net/1963/631700568nas a2200121 4500008004100000245003800041210003800079260003200117520021000149653002200359100002900381856003600410 2012 en d00aSome remarks on quantum mechanics0 aSome remarks on quantum mechanics bWorld Scientific Publishing3 aWe discuss the similarities and differences between the formalism of Hamiltonian Classical Mechanics and of Quantum Mechanics and exemplify the differences through an analysis of tracks in a cloud chamber.10aQuantum mechanics1 aDell'Antonio, Gianfausto uhttp://hdl.handle.net/1963/701800559nas a2200157 4500008004100000022001400041245011500055210006900170300001400239490000800253100001900261700001900280700001600299700001500315856007100330 2012 eng d a0022-471500aSpectra of random Hermitian matrices with a small-rank external source: the critical and near-critical regimes0 aSpectra of random Hermitian matrices with a smallrank external s a475–5180 v1461 aBertola, Marco1 aBuckingham, R.1 aLee, S., Y.1 aPierce, V. uhttp://0-dx.doi.org.mercury.concordia.ca/10.1007/s10955-011-0409-201607nas a2200157 4500008004100000245009600041210006900137260002100206520106500227100002201292700002901314700002001343700002901363700002101392856003601413 2012 en d00aStability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions0 aStability for a System of N Fermions Plus a Different Particle w bWorld Scientific3 aWe study the stability problem for a non-relativistic quantum system in\\r\\ndimension three composed by $ N \\\\geq 2 $ identical fermions, with unit mass,\\r\\ninteracting with a different particle, with mass $ m $, via a zero-range\\r\\ninteraction of strength $ \\\\alpha \\\\in \\\\R $. We construct the corresponding\\r\\nrenormalised quadratic (or energy) form $ \\\\form $ and the so-called\\r\\nSkornyakov-Ter-Martirosyan symmetric extension $ H_{\\\\alpha} $, which is the\\r\\nnatural candidate as Hamiltonian of the system. We find a value of the mass $\\r\\nm^*(N) $ such that for $ m > m^*(N)$ the form $ \\\\form $ is closed and bounded from below. As a consequence, $ \\\\form $ defines a unique self-adjoint and bounded from below extension of $ H_{\\\\alpha}$ and therefore the system is stable. On the other hand, we also show that the form $ \\\\form $ is unbounded from below for $ m < m^*(2)$. In analogy with the well-known bosonic case, this suggests that the system is unstable for $ m < m^*(2)$ and the so-called Thomas effect occurs.1 aCorreggi, Michele1 aDell'Antonio, Gianfausto1 aFinco, Domenico1 aMichelangeli, Alessandro1 aTeta, Alessandro uhttp://hdl.handle.net/1963/606900517nas a2200109 4500008004100000245011900041210006900160100001700229700001700246700002200263856012200285 2012 eng d00aA stable semi-lagrangian potential method for the simulation of ship interaction with unsteady and nonlinear waves0 astable semilagrangian potential method for the simulation of shi1 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio uhttp://www.math.sissa.it/publication/stable-semi-lagrangian-potential-method-simulation-ship-interaction-unsteady-and00752nas a2200121 4500008004100000245004700041210004600088260001000134520040400144100002500548700002100573856003600594 2012 en d00aSub-Riemannian structures on 3D Lie groups0 aSubRiemannian structures on 3D Lie groups bSISSA3 aWe give a complete classification of left-invariant sub-Riemannian structures on three dimensional Lie groups in terms of the basic differential invariants. As a corollary we explicitly find a sub-Riemannian isometry between the nonisomorphic Lie groups $SL(2)$ and $A^+(\mathbb{R})\times S^1$, where $A^+(\mathbb{R})$ denotes the group of orientation preserving affine maps on the real line.

1 aAgrachev, Andrei, A.1 aBarilari, Davide uhttp://hdl.handle.net/1963/645300723nas a2200121 4500008004100000245003800041210003800079260001000117520039200127100002500519700002100544856003600565 2012 en d00aSystems of Quadratic Inequalities0 aSystems of Quadratic Inequalities bSISSA3 aWe present a spectral sequence which efficiently computes Betti numbers of a closed semi-algebraic subset of RP^n defined by a system of quadratic inequalities and the image of the homology homomorphism induced by the inclusion of this subset in RP^n. We do not restrict ourselves to the term E_2 of the spectral sequence and give a simple explicit formula for the differential d_2.1 aAgrachev, Andrei, A.1 aLerario, Antonio uhttp://hdl.handle.net/1963/707200562nas a2200109 4500008004100000245004400041210004400085260001900129520024700148100002100395856003600416 2012 en d00aTabulation of Painlevé 6 transcendents0 aTabulation of Painlevé 6 transcendents bIOP Publishing3 aThe critical and asymptotic behaviors of solutions of the sixth Painlev'e equation PVI, obtained in the framework of the monodromy preserving deformation method, and their explicit parametrization in terms of monodromy data, are tabulated.1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/652000948nas a2200121 4500008004100000245006000041210006000101260002200161520056500183100002400748700001800772856003600790 2012 en d00aThermodynamic phase transitions and shock singularities0 aThermodynamic phase transitions and shock singularities bThe Royal Society3 aWe show that under rather general assumptions on the form of the entropy\\r\\nfunction, the energy balance equation for a system in thermodynamic equilibrium is equivalent to a set of nonlinear equations of hydrodynamic type. This set of equations is integrable via the method of the characteristics and it provides the equation of state for the gas. The shock wave catastrophe set identifies the phase transition. A family of explicitly solvable models of\\r\\nnon-hydrodynamic type such as the classical plasma and the ideal Bose gas are\\r\\nalso discussed.1 aDe Nittis, Giuseppe1 aMoro, Antonio uhttp://hdl.handle.net/1963/609001511nas a2200145 4500008004100000245007100041210006900112260001000181520099600191653006801187100002001255700002901275700002501304856003601329 2012 en d00aTopological sensitivity analysis for high order elliptic operators0 aTopological sensitivity analysis for high order elliptic operato bSISSA3 aThe topological derivative is defined as the first term of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of a singular domain perturbation. It has applications in many different fields such as shape and topology optimization, inverse problems, image processing and mechanical modeling including synthesis and/or optimal design of microstructures, fracture mechanics sensitivity analysis and damage evolution modeling. The topological derivative has been fully developed for a wide range of second order differential operators. In this paper we deal with the topological asymptotic expansion of a class of shape functionals associated with elliptic differential operators of order 2m, m>=1. The general structure of the polarization tensor is derived and the concept of degenerate polarization tensor is introduced. We provide full mathematical justifications for the derived formulas, including precise estimates of remainders.10aTopological derivative, Elliptic operators, Polarization tensor1 aAmstutz, Samuel1 aNovotny, Antonio, André1 aVan Goethem, Nicolas uhttp://hdl.handle.net/1963/634302171nas a2200133 4500008004100000245006600041210006600107260001300173520175500186653001901941100001701960700002401977856003602001 2012 en d00aVariational implementation of immersed finite element methods0 aVariational implementation of immersed finite element methods bElsevier3 aDirac-delta distributions are often crucial components of the solid-fluid coupling operators in immersed solution methods for fluid-structure interaction (FSI) problems. This is certainly so for methods like the Immersed Boundary Method (IBM) or the Immersed Finite Element Method (IFEM), where Dirac-delta distributions are approximated via smooth functions. By contrast, a truly variational formulation of immersed methods does not require the use of Dirac-delta distributions, either formally or practically. This has been shown in the Finite Element Immersed Boundary Method (FEIBM), where the variational structure of the problem is exploited to avoid Dirac-delta distributions at both the continuous and the discrete level. In this paper, we generalize the FEIBM to the case where an incompressible Newtonian fluid interacts with a general hyperelastic solid. Specifically, we allow (i) the mass density to be different in the solid and the fluid, (ii) the solid to be either viscoelastic of differential type or purely elastic, and (iii) the solid to be and either compressible or incompressible. At the continuous level, our variational formulation combines the natural stability estimates of the fluid and elasticity problems. In immersed methods, such stability estimates do not transfer to the discrete level automatically due to the non- matching nature of the finite dimensional spaces involved in the discretization. After presenting our general mathematical framework for the solution of FSI problems, we focus in detail on the construction of natural interpolation operators between the fluid and the solid discrete spaces, which guarantee semi-discrete stability estimates and strong consistency of our spatial discretization.

10aTurbulent flow1 aHeltai, Luca1 aCostanzo, Francesco uhttp://hdl.handle.net/1963/646201295nas a2200133 4500008004100000245005500041210005200096260001000148520090800158100002001066700002401086700001501110856003601125 2012 en d00aVertices, vortices & interacting surface operators0 aVertices vortices interacting surface operators bSISSA3 aWe show that the vortex moduli space in non-abelian supersymmetric N=(2,2) gauge theories on the two dimensional plane with adjoint and anti-fundamental matter can be described as an holomorphic submanifold of the instanton moduli space in four dimensions. The vortex partition functions for these theories are computed via equivariant localization. We show that these coincide with the field theory limit of the topological vertex on the strip with boundary conditions corresponding to column diagrams. Moreover, we resum the field theory limit of the vertex partition functions in terms of generalized hypergeometric functions formulating their AGT dual description as interacting surface operators of simple type. Analogously we resum the topological open string amplitudes in terms of q-deformed generalized hypergeometric functions proving that they satisfy appropriate finite difference equations.1 aBonelli, Giulio1 aTanzini, Alessandro1 aJian, Zhao uhttp://hdl.handle.net/1963/413401103nas a2200109 4500008004100000245003900041210003600080260001000116520081300126100001800939856003600957 2012 en d00aA Viscosity-driven crack evolution0 aViscositydriven crack evolution bSISSA3 aWe present a model of crack growth in brittle materials which couples dissipative effects on the crack tip and viscous effects. We consider the 2 -dimensional antiplane case with pre-assigned crack path, and firstly prove an existence result for a rate-dependent evolution problem by means of time-discretization. The next goal is to describe the rate-independent evolution as limit of the rate-dependent ones when the dissipative and viscous effects vanish. The rate-independent evolution satisfies a Griffith’s criterion for the crack growth, but, in general, it does not fulfil a global minimality condition; its fracture set may exhibit jump discontinuities with respect to time. Under suitable regularity assumptions, the quasi-static crack growth is described by solving a finite-dimensional problem.1 aRacca, Simone uhttp://hdl.handle.net/1963/513001567nas a2200121 4500008004100000245008300041210006900124260001300193520115600206100002501362700002201387856003601409 2012 en d00aWeighted barycentric sets and singular Liouville equations on compact surfaces0 aWeighted barycentric sets and singular Liouville equations on co bElsevier3 aGiven a closed two dimensional manifold, we prove a general existence result\\r\\nfor a class of elliptic PDEs with exponential nonlinearities and negative Dirac\\r\\ndeltas on the right-hand side, extending a theory recently obtained for the\\r\\nregular case. This is done by global methods: since the associated Euler\\r\\nfunctional is in general unbounded from below, we need to define a new model\\r\\nspace, generalizing the so-called space of formal barycenters and\\r\\ncharacterizing (up to homotopy equivalence) its very low sublevels. As a\\r\\nresult, the analytic problem is reduced to a topological one concerning the\\r\\ncontractibility of this model space. To this aim, we prove a new functional\\r\\ninequality in the spirit of [16] and then we employ a min-max scheme based on a cone-style construction, jointly with the blow-up analysis given in [5] (after\\r\\n[6] and [8]). This study is motivated by abelian Chern- Simons theory in\\r\\nself-dual regime, or from the problem of prescribing the Gaussian curvature in\\r\\npresence of conical singularities (hence generalizing a problem raised by\\r\\nKazdan and Warner in [26]).1 aCarlotto, Alessandro1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/521800994nas a2200133 4500008004100000245003100041210003100072260001000103520064300113100002000756700002400776700002400800856003600824 2012 en d00aWild quiver gauge theories0 aWild quiver gauge theories bSISSA3 aWe study $N=2$ supersymmetric $SU(2)$ gauge theories coupled to non-Lagrangian superconformal field theories induced by compactifying the six dimensional $A_1 (2,0)$ theory on Riemann surfaces with irregular punctures. These are naturally associated to Hitchin systems with wild ramification whose spectral curves provide the relevant Seiberg-Witten geometries. We propose that the prepotential of these gauge theories on the Omega-background can be obtained from the corresponding irregular conformal blocks on the Riemann surfaces via a generalization of the coherent state construction to the case of higher order singularities.

1 aBonelli, Giulio1 aMaruyoshi, Kazunobu1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/518401400nas a2200169 4500008004100000245009000041210006900131260005000200520083200250100001401082700001801096700001501114700002201129700002201151700002101173856003601194 2011 en d00aAdaptation as a genome-wide autoregulatory principle in the stress response of yeast.0 aAdaptation as a genomewide autoregulatory principle in the stres bThe Institution of Engineering and Technology3 aThe gene expression response of yeast to various types of stresses/perturbations shows a common functional and dynamical pattern for the vast majority of genes, characterised by a quick transient peak (affecting primarily short genes) followed by a return to the pre-stimulus level. Kinetically, this process of adaptation following the transient excursion can be modelled using a genome-wide autoregulatory mechanism by means of which yeast aims at maintaining a preferential concentration in its mRNA levels. The resulting feedback system explains well the different time constants observable in the transient response, while being in agreement with all the known experimental dynamical features. For example, it suggests that a very rapid transient can be induced also by a slowly varying concentration of the gene products.1 aEduati, F1 aDi Camillo, B1 aToffolo, G1 aAltafini, Claudio1 aDe Palo, Giovanna1 aZampieri, Mattia uhttp://hdl.handle.net/1963/510600665nas a2200109 4500008004100000245007400041210007100115260001900186520029300205100002100498856003600519 2011 en d00aAn asymptotic reduction of a Painlevé VI equation to a Painlevé III0 aasymptotic reduction of a Painlevé VI equation to a Painlevé III bIOP Publishing3 aWhen the independent variable is close to a critical point, it is shown that\\r\\nPVI can be asymptotically reduced to PIII. In this way, it is possible to\\r\\ncompute the leading term of the critical behaviors of PVI transcendents\\r\\nstarting from the behaviors of PIII transcendents.1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/512400772nas a2200157 4500008004300000245008600043210007000129260003400199520023700233653003600470100001900506700002200525700001600547700001500563856003600578 2011 en_Ud 00aAxial symmetry of some steady state solutions to nonlinear Schrödinger equations0 aAxial symmetry of some steady state solutions to nonlinear Schrö bAmerican Mathematical Society3 aIn this note, we show the axial symmetry of steady state solutions of nonlinear Schrodinger equations when the exponent of the nonlinearity is between the critical Sobolev exponent of n dimensional space and n - 1 dimensional space.10aNonlinear Schrödinger equation1 aGui, Changfeng1 aMalchiodi, Andrea1 aXu, Haoyuan1 aYang, Paul uhttp://hdl.handle.net/1963/410000585nas a2200121 4500008004100000245011300041210006900154260001000223520015500233100002500388700001400413856003600427 2011 en d00aBishop and Laplacian Comparison Theorems on Three Dimensional Contact Subriemannian Manifolds with Symmetry0 aBishop and Laplacian Comparison Theorems on Three Dimensional Co bSISSA3 aWe prove a Bishop volume comparison theorem and a Laplacian comparison\r\ntheorem for three dimensional contact subriemannian manifolds with symmetry.1 aAgrachev, Andrei, A.1 aLee, Paul uhttp://hdl.handle.net/1963/650800425nas a2200121 4500008004100000022001400041245009200055210006900147300001400216490000600230100001900236856004800255 2011 eng d a1664-236800aBoutroux curves with external field: equilibrium measures without a variational problem0 aBoutroux curves with external field equilibrium measures without a167–2110 v11 aBertola, Marco uhttp://dx.doi.org/10.1007/s13324-011-0012-301305nas a2200145 4500008004100000022001300041245007600054210006900130300001200199490000800211520079500219100002401014700001701038856010401055 2011 eng d a0010361600aBranching of Cantor Manifolds of Elliptic Tori and Applications to PDEs0 aBranching of Cantor Manifolds of Elliptic Tori and Applications a741-7960 v3053 aWe consider infinite dimensional Hamiltonian systems. We prove the existence of "Cantor manifolds" of elliptic tori-of any finite higher dimension-accumulating on a given elliptic KAM torus. Then, close to an elliptic equilibrium, we show the existence of Cantor manifolds of elliptic tori which are "branching" points of other Cantor manifolds of higher dimensional tori. We also answer to a conjecture of Bourgain, proving the existence of invariant elliptic tori with tangential frequency along a pre-assigned direction. The proofs are based on an improved KAM theorem. Its main advantages are an explicit characterization of the Cantor set of parameters and weaker smallness conditions on the perturbation. We apply these results to the nonlinear wave equation. © 2011 Springer-Verlag.1 aBerti, Massimiliano1 aBiasco, Luca uhttp://www.math.sissa.it/publication/branching-cantor-manifolds-elliptic-tori-and-applications-pdes00981nas a2200121 4500008004100000245006900041210006700110260001300177520058600190100002500776700002200801856003600823 2011 en d00aA class of existence results for the singular Liouville equation0 aclass of existence results for the singular Liouville equation bElsevier3 aWe consider a class of elliptic PDEs on closed surfaces with exponential nonlinearities and Dirac deltas on the right-hand side. The study arises from abelian Chern–Simons theory in self-dual regime, or from the problem of prescribing the Gaussian curvature in presence of conical singularities. A general existence result is proved using global variational methods: the analytic problem is reduced to a topological problem concerning the contractibility of a model space, the so-called space of formal barycenters, characterizing the very low sublevels of a suitable functional.1 aCarlotto, Alessandro1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/579300613nas a2200097 4500008004100000245003000041210003000071520034600101100002000447856004800467 2011 en d00aCompactness by maximality0 aCompactness by maximality3 aWe derive a compactness property in the Sobolev space $W^{1,1}(\O)$ in order to study the Dirichlet problem for the eikonal equation \begin{displaymath} \begin{cases} \ha |\n u(x)|^2 - a(x) = 0 & \ \textrm{in} \ \O\cr u(x)=\varphi(x) & \ \textrm{on} \ \partial \O, \end{cases} \end{displaymath} without continuity assumptions on the map $a$.1 aZagatti, Sandro uhttp://preprints.sissa.it/handle/1963/3531701286nas a2200145 4500008004100000245007900041210006900120260003300189520078400222653003101006100002401037700002101061700002201082856003601104 2011 en d00aComputing global structural balance in large-scale signed social networks.0 aComputing global structural balance in largescale signed social bNational Academy of Sciences3 aStructural balance theory affirms that signed social networks (i.e., graphs whose signed edges represent friendly/hostile interactions among individuals) tend to be organized so as to avoid conflictual situations, corresponding to cycles of negative parity. Using an algorithm for ground-state calculation in large-scale Ising spin glasses, in this paper we compute the global level of balance of very large online social networks and verify that currently available networks are indeed extremely balanced. This property is explainable in terms of the high degree of skewness of the sign distributions on the nodes of the graph. In particular, individuals linked by a large majority of negative edges create mostly \\\"apparent disorder,\\\" rather than true \\\"frustration.\\\"10aCombinatorial optimization1 aFacchetti, Giuseppe1 aIacono, Giovanni1 aAltafini, Claudio uhttp://hdl.handle.net/1963/642601012nas a2200169 4500008004100000245005500041210005400096260006700150520046800217653002100685100002400706700002400730700002000754700001900774700001300793856003600806 2011 en d00aCones of divisors of blow-ups of projective spaces0 aCones of divisors of blowups of projective spaces bUniversità degli Studi di Catania. Dipartimento di matematica3 aWe investigate Mori dream spaces obtained by blowing-up the n-dimensional complex projective space at n+1, n+2 or n+3 points in very general position. Using toric techniques we study the movable cone of the blow-up of Pn at n+1 points, its decomposition into nef chambers and the action of theWeyl group on the set of chambers. Moreover, using different methods, we explicitly write down the equations of the movable cone also for Pn blown-up at n+2 points.10aMori dream space1 aLo Giudice, Alessio1 aCacciola, Salvatore1 aDonten-Bury, M.1 aDumitrescu, O.1 aPark, J. uhttp://hdl.handle.net/1963/661300920nas a2200133 4500008004100000245005100041210005100092260007200143520047100215100002100686700002100707700002200728856003600750 2011 en d00aCovered by lines and Conic connected varieties0 aCovered by lines and Conic connected varieties bUniversita\\\' di Catania, Dipartimento di Matematica e Informatica3 aWe study some properties of an embedded variety covered by lines and give a\\r\\nnumerical criterion ensuring the existence of a singular conic through two of\\r\\nits general points. We show that our criterion is sharp. Conic-connected,\\r\\ncovered by lines, QEL, LQEL, prime Fano, defective, and dual defective\\r\\nvarieties are closely related. We study some relations between the above\\r\\nmentioned classes of objects using celebrated results by Ein and Zak.1 aMarchesi, Simone1 aMassarenti, Alex1 aTafazolian, Saeed uhttp://hdl.handle.net/1963/578800974nas a2200121 4500008004300000245009300043210006900136260004800205520051800253100002100771700002400792856003600816 2011 en_Ud 00aCrack growth with non-interpenetration : a simplified proof for the pure Neumann problem0 aCrack growth with noninterpenetration a simplified proof for the bAmerican Institute of Mathematical Sciences3 aWe present a recent existence result concerning the quasi-static evolution of cracks in hyperelastic brittle materials, in the frame-work of finite elasticity with non-interpenetration. In particular, here we consider the problem where no Dirichlet conditions are imposed, the boundary is traction-free, and the body is subject only to time-dependent volume forces. This allows us to present the main ideas of the proof in a simpler way, avoiding some of the technicalities needed in the general case, studied in.1 aDal Maso, Gianni1 aLazzaroni, Giuliano uhttp://hdl.handle.net/1963/380100934nas a2200133 4500008004100000245007900041210006900120260001000189520050600199100002200705700001800727700001900745856003600764 2011 en d00aCrepant resolutions of weighted projective spaces and quantum deformations0 aCrepant resolutions of weighted projective spaces and quantum de bSISSA3 aWe compare the Chen-Ruan cohomology ring of the weighted projective spaces\r\n$\\IP(1,3,4,4)$ and $\\IP(1,...,1,n)$ with the cohomology ring of their crepant\r\nresolutions. In both cases, we prove that the Chen-Ruan cohomology ring is\r\nisomorphic to the quantum corrected cohomology ring of the crepant resolution\r\nafter suitable evaluation of the quantum parameters. For this, we prove a\r\nformula for the Gromov-Witten invariants of the resolution of a transversal\r\n${\\rm A}_3$ singularity.1 aBoissiere, Samuel1 aMann, Etienne1 aPerroni, Fabio uhttp://hdl.handle.net/1963/651400428nas a2200133 4500008004100000245005400041210005300095260001000148653003100158100002600189700002200215700002100237856003600258 2011 en d00aCritical points of the Moser-Trudinger functional0 aCritical points of the MoserTrudinger functional bSISSA10aMoser-Trudinger inequality1 aDe Marchis, Francesca1 aMalchiodi, Andrea1 aMartinazzi, Luca uhttp://hdl.handle.net/1963/459200524nas a2200133 4500008004100000245012600041210006900167260003300236100002000269700002100289700002200310700002200332856003600354 2011 en d00aCytoskeletal actin networks in motile cells are critically self-organized systems synchronized by mechanical interactions0 aCytoskeletal actin networks in motile cells are critically selfo bNational Academy of Sciences1 aCardamone, Luca1 aLaio, Alessandro1 aShahapure, Rajesh1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/435801229nas 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/20.500.11767/1459900918nas a2200157 4500008004100000022001300041245006100054210006100115300001400176490000800190520040200198100001900600700002400619700002300643856009400666 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 uhttp://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/1963/534801116nas a2200145 4500008004100000245013000041210007000171260001300241300001600254490000800270520060700278100002000885700001900905856004600924 2011 eng d00aEmbedding theorems and existence results for nonlinear Schrödinger–Poisson systems with unbounded and vanishing potentials0 aEmbedding theorems and existence results for nonlinear Schröding bElsevier a1056–10850 v2513 aMotivated by existence results for positive solutions of non-autonomous nonlinear Schrödinger–Poisson systems with potentials possibly unbounded or vanishing at infinity, we prove embedding theorems for weighted Sobolev spaces. We both consider a general framework and spaces of radially symmetric functions when assuming radial symmetry of the potentials.

1 aBonheure, Denis1 aMercuri, Carlo uhttps://doi.org/10.1016/j.jde.2011.04.01000728nas a2200121 4500008004300000245007600043210006900119260001300188520032600201100002400527700001900551856003600570 2011 en_Ud 00aEnergy release rate and stress intensity factor in antiplane elasticity0 aEnergy release rate and stress intensity factor in antiplane ela bElsevier3 aIn the setting of antiplane linearized elasticity, we show the existence of the stress intensity factor and its relation with the energy release rate when the crack path is a C1,1 curve. Finally, we show that the energy release rate is continuous with respect to the Hausdorff convergence in a class of admissible cracks.1 aLazzaroni, Giuliano1 aToader, Rodica uhttp://hdl.handle.net/1963/378000628nas a2200109 4500008004100000245003900041210003800080260004800118520029500166100002100461856003600482 2011 en d00aEnnio De Giorgi and Γ-convergence0 aEnnio De Giorgi and Γconvergence bAmerican Institute of Mathematical Sciences3 aΓ-convergence was introduced by Ennio De Giorgi in a series of papers published between 1975 and 1983. In the same years he developed many applications of this tool to a great variety of asymptotic problems in the calculus of variations and in the theory of partial differential equations.1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/530800369nas a2200109 4500008004300000245006000043210005700103260002100160100002300181700001900204856003600223 2011 en_Ud 00aAn Estimate on the Flow Generated by Monotone Operators0 aEstimate on the Flow Generated by Monotone Operators bTaylor & Francis1 aBianchini, Stefano1 aGloyer, Matteo uhttp://hdl.handle.net/1963/364601495nas a2200133 4500008004300000245008600043210006900129260005100198520101100249100002101260700002201281700002201303856003601325 2011 en_Ud 00aAn Existence and Uniqueness Result for the Motion of Self-Propelled Microswimmers0 aExistence and Uniqueness Result for the Motion of SelfPropelled bSociety for Industrial and Applied Mathematics3 aWe present an analytical framework to study the motion of micro-swimmers in a viscous fluid. Our main result is that, under very mild regularity assumptions, the change of shape determines uniquely the motion of the swimmer. We assume that the Reynolds number is very small, so that the velocity field of the surrounding, infinite fluid is governed by the Stokes system and all inertial effects can be neglected. Moreover, we enforce the self propulsion constraint (no external forces and torques). Therefore, Newton\\\'s equations of motion reduce to the vanishing of the viscous drag force and torque acting on the body. By exploiting an integral representation of viscous force and torque, the equations of motion can be reduced to a system of six ordinary differential equations. Variational techniques are used to prove the boundedness and measurability of its coefficients, so that classical results on ordinary differential equations can be invoked to prove existence and uniqueness of the solution.1 aDal Maso, Gianni1 aDeSimone, Antonio1 aMorandotti, Marco uhttp://hdl.handle.net/1963/389401004nas a2200133 4500008004100000245007400041210006900115260003400184520055100218653001800769100002100787700002600808856003600834 2011 en d00aExistence for wave equations on domains with arbitrary growing cracks0 aExistence for wave equations on domains with arbitrary growing c bEuropean Mathematical Society3 aIn this paper we formulate and study scalar wave equations on domains with arbitrary growing cracks. This includes a zero Neumann condition on the crack sets, and the only assumptions on these sets are that they have bounded surface measure and are growing in the sense of set inclusion. In particular, they may be dense, so the weak formulations must fall outside of the usual weak formulations using Sobolev spaces. We study both damped and undamped equations, showing existence and, for the damped equation, uniqueness and energy conservation.10aWave equation1 aDal Maso, Gianni1 aLarsen, Cristopher J. uhttp://hdl.handle.net/1963/428400878nas a2200109 4500008004100000245008900041210006900130260002200199520048900221100002200710856003600732 2011 en d00aFracture and plastic models as Gamma-limits of damage models under different regimes0 aFracture and plastic models as Gammalimits of damage models unde bWalter de Gruyter3 aWe consider a variational model for damaged elastic materials. This model depends on three small parameters, which are related to the cost of the damage, to the width of the damaged regions, and to the minimum elasticity constant attained in the damaged regions. As these parameters tend to zero, our models Gamma-converge to a model for brittle fracture, for fracture with a cohesive zone, or for perfect plasticity, depending on the asymptotic ratios of the three parameters.

1 aIurlano, Flaviana uhttp://hdl.handle.net/1963/506900871nas a2200133 4500008004100000245008300041210006900124260001300193520042700206653002000633100002600653700002200679856003600701 2011 en d00aGamma-convergence of energies for nematic elastomers in the small strain limit0 aGammaconvergence of energies for nematic elastomers in the small bSpringer3 aWe study two variational models recently proposed in the literature to describe the mechanical behaviour of nematic elastomers either in the fully nonlinear regime or in the framework of a geometrically linear theory. We show that, in the small strain limit, the energy functional of the first one I\\\"-converges to the relaxation of the second one, a functional for which an explicit representation formula is available.10aLiquid crystals1 aAgostiniani, Virginia1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/414101081nas a2200121 4500008004100000245004900041210004900090260001000139520061100149653014200760100002100902856003600923 2011 en d00aGeneralised functions of bounded deformation0 aGeneralised functions of bounded deformation bSISSA3 aWe introduce the space GBD of generalized functions of bounded deformation and study the structure properties of these functions: the rectifiability and the slicing properties of their jump sets, and the existence of their approximate symmetric gradients. We conclude by proving a compactness results for GBD, which leads to a compactness result for the space GSBD of generalized special functions of bounded deformation. The latter is connected to the existence of solutions to a weak formulation of some variational problems arising in fracture mechanics in the framework of linearized elasticity.

10afree discontinuity problems, special functions of bounded deformation, jump set, rec- tifiability, slicing, approximate differentiability1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/637401134nas a2200145 4500008004100000245006700041210006700108260001000175520068000185100002000865700002400885700002400909700001900933856003600952 2011 en d00aGeneralized matrix models and AGT correspondence at all genera0 aGeneralized matrix models and AGT correspondence at all genera bSISSA3 aWe study generalized matrix models corresponding to n-point Virasoro\r\nconformal blocks on Riemann surfaces with arbitrary genus g. Upon AGT\r\ncorrespondence, these describe four dimensional N=2 SU(2)^{n+3g-3} gauge\r\ntheories with generalized quiver diagrams. We obtain the generalized matrix\r\nmodels from the perturbative evaluation of the Liouville correlation functions\r\nand verify the consistency of the description with respect to degenerations of\r\nthe Riemann surface. Moreover, we derive the Seiberg-Witten curve for the N=2\r\ngauge theory as the spectral curve of the generalized matrix model, thus\r\nproviding a check of AGT correspondence at all genera.1 aBonelli, Giulio1 aMaruyoshi, Kazunobu1 aTanzini, Alessandro1 aYagib, Futoshi uhttp://hdl.handle.net/1963/656800398nas a2200109 4500008004100000245009300041210006900134260001000203100002500213700001400238856003600252 2011 en d00aGeneralized Ricci Curvature Bounds for Three Dimensional Contact Subriemannian manifolds0 aGeneralized Ricci Curvature Bounds for Three Dimensional Contact bSISSA1 aAgrachev, Andrei, A.1 aLee, Paul uhttp://hdl.handle.net/1963/650700442nas a2200109 4500008004100000245003800041210003400079520013500113100002500248700002300273856003600296 2011 en d00aThe geometry of Maximum Principle0 ageometry of Maximum Principle3 aAn invariant formulation of the maximum principle in optimal control is presented, and some second-order invariants are discussed.1 aAgrachev, Andrei, A.1 aGamkrelidze, Revaz uhttp://hdl.handle.net/1963/645600395nas a2200109 4500008004300000245008700043210006900130260001300199100002100212700001600233856003600249 2011 en_Ud 00aHolomorphic Cartan geometry on manifolds with numerically effective tangent bundle0 aHolomorphic Cartan geometry on manifolds with numerically effect bElsevier1 aBiswas, Indranil1 aBruzzo, Ugo uhttp://hdl.handle.net/1963/383001189nas a2200109 4500008004100000245004200041210004200083260001000125520088700135100002101022856003601043 2011 en d00aHomology invariants of quadratic maps0 aHomology invariants of quadratic maps bSISSA3 aGiven a real projective algebraic set X we could hope that the equations describing it can give some information on its topology, e.g. on the number of its connected components. Unfortunately in the general case this hope is too vague and there is no direct way to extract such information from the algebraic description of X: Even the problem to decide whether X is empty or not is far from an easy visualization and requires some complicated algebraic machinery. A fi rst step observation is that as long as we are interested only in the topology of X, we can replace, using some Veronese embedding, the original ambient space with a much bigger RPn and assume that X is cut by quadratic equations. The price for this is the increase of the number of equations de ning our set; the advantage is that quadratic polynomials are easier to handle and our hope becomes more concrete...1 aLerario, Antonio uhttp://hdl.handle.net/1963/624500770nas a2200133 4500008004300000245007400043210006900117260001300186520033600199100001800535700002000553700002700573856003600600 2011 en_Ud 00aInfinite-dimensional Frobenius manifolds for 2 + 1 integrable systems0 aInfinitedimensional Frobenius manifolds for 2 1 integrable syste bSpringer3 aWe introduce a structure of an infinite-dimensional Frobenius manifold on a subspace in the space of pairs of functions analytic inside/outside the unit circle with simple poles at 0/infinity respectively. The dispersionless 2D Toda equations are embedded into a bigger integrable hierarchy associated with this Frobenius manifold.1 aCarlet, Guido1 aDubrovin, Boris1 aMertens, Luca Philippe uhttp://hdl.handle.net/1963/358400632nas a2200133 4500008004100000245007400041210006900115260001000184520020000194100002000394700002400414700002400438856003600462 2011 en d00aInstantons on ALE spaces and Super Liouville Conformal Field Theories0 aInstantons on ALE spaces and Super Liouville Conformal Field The bSISSA3 aWe provide evidence that the conformal blocks of N=1 super Liouville\\r\\nconformal field theory are described in terms of the SU(2) Nekrasov partition\\r\\nfunction on the ALE space O_{P^1}(-2).1 aBonelli, Giulio1 aMaruyoshi, Kazunobu1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/426201512nas a2200109 4500008004100000245009500041210006900136260002200205520111900227100002001346856003601366 2011 en d00aAn Integro-Extremization Approach for Non Coercive and Evolution Hamilton-Jacobi Equations0 aIntegroExtremization Approach for Non Coercive and Evolution Ham bHeldermann Verlag3 aWe devote the \\\\textit{integro-extremization} method to the study of the Dirichlet problem for homogeneous Hamilton-Jacobi equations \\\\begin{displaymath} \\\\begin{cases} F(Du)=0 & \\\\quad \\\\textrm{in} \\\\quad\\\\O\\\\cr u(x)=\\\\varphi(x) & \\\\quad \\\\textrm{for} \\\\quad x\\\\in \\\\partial \\\\O, \\\\end{cases} \\\\end{displaymath} with a particular interest for non coercive hamiltonians $F$, and to the Cauchy-Dirichlet problem for the corresponding homogeneous time-dependent equations \\\\begin{displaymath} \\\\begin{cases} \\\\frac{\\\\partial u}{\\\\partial t}+ F(\\\\nabla u)=0 & \\\\quad \\\\textrm{in} \\\\quad ]0,T[\\\\times \\\\O\\\\cr u(0,x)=\\\\eta(x) & \\\\quad \\\\textrm{for} \\\\quad x\\\\in\\\\O \\\\cr u(t,x)=\\\\psi(x) & \\\\quad \\\\textrm{for} \\\\quad (t,x)\\\\in[0,T]\\\\times \\\\partial \\\\O. \\\\end{cases} \\\\end{displaymath} We prove existence and some qualitative results for viscosity and almost everywhere solutions, under suitably convexity conditions on the hamiltonian $F$, on the domain $\\\\O$ and on the boundary datum, without any growth assumptions on $F$.1 aZagatti, Sandro uhttp://hdl.handle.net/1963/553800383nas a2200109 4500008004300000245007000043210006900113260001300182100002300195700001900218856003600237 2011 en_Ud 00aInvariant manifolds for a singular ordinary differential equation0 aInvariant manifolds for a singular ordinary differential equatio bElsevier1 aBianchini, Stefano1 aSpinolo, Laura uhttp://hdl.handle.net/1963/255401397nas a2200121 4500008004100000245006800041210006600109260001000175520100500185653002801190100002101218856003601239 2011 en d00aInvariants, volumes and heat kernels in sub-Riemannian geometry0 aInvariants volumes and heat kernels in subRiemannian geometry bSISSA3 aSub-Riemannian geometry can be seen as a generalization of Riemannian geometry under non-holonomic constraints. From the theoretical point of view, sub-Riemannian geometry is the geometry underlying the theory of hypoelliptic operators (see [32, 57, 70, 92] and references therein) and many problems of geometric measure theory (see for instance [18, 79]). In applications it appears in the study of many mechanical problems (robotics, cars with trailers, etc.) and recently in modern elds of research such as mathematical models of human behaviour, quantum control or motion of self-propulsed micro-organism (see for instance [15, 29, 34])\\r\\nVery recently, it appeared in the eld of cognitive neuroscience to model the\\r\\nfunctional architecture of the area V1 of the primary visual cortex, as proposed by Petitot in [87, 86], and then by Citti and Sarti in [51]. In this context, the sub-Riemannian heat equation has been used as basis to new applications in image reconstruction (see [35]).10aSub-Riemannian geometry1 aBarilari, Davide uhttp://hdl.handle.net/1963/612401000nas a2200133 4500008004300000245005100043210005100094260002100145520060100166100001800767700002500785700002000810856003600830 2011 en_Ud 00aLarge Time Existence for Thin Vibrating Plates0 aLarge Time Existence for Thin Vibrating Plates bTaylor & Francis3 aWe construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence of strong solutions for large\\r\\ntimes under appropriate scaling of the initial values such that the limit system as h --> 0 is either the nonlinear von Karman plate equation or the linear fourth order Germain-Lagrange equation. In the case of the\\r\\nlinear Germain-Lagrange equation we even obtain a convergence rate of the three-dimensional solution to the solution of the two-dimensional linear plate equation.1 aAbels, Helmut1 aMora, Maria Giovanna1 aMüller, Stefan uhttp://hdl.handle.net/1963/375500923nas a2200145 4500008004100000245010600041210006900147260001300216520043000229653002300659100002000682700001700702700002200719856003600741 2011 en d00aLinearly degenerate Hamiltonian PDEs and a new class of solutions to the WDVV associativity equations0 aLinearly degenerate Hamiltonian PDEs and a new class of solution bSpringer3 aWe define a new class of solutions to the WDVV associativity equations. This class is determined by the property that one of the commuting PDEs associated with such a WDVV solution is linearly degenerate. We reduce the problem of classifying such solutions of the WDVV equations to the particular case of the so-called algebraic Riccati equation and, in this way, arrive at a complete classification of irreducible solutions.10aFrobenius manifold1 aDubrovin, Boris1 aPavlov, M.V.1 aZykov, Sergei, A. uhttp://hdl.handle.net/1963/643000818nas a2200133 4500008004100000245003700041210003300078260001000111520046800121100002000589700002400609700001500633856003600648 2011 en d00aThe Liouville side of the vortex0 aLiouville side of the vortex bSISSA3 aWe analyze conformal blocks with multiple (semi-)degenerate field insertions in Liouville/Toda conformal field theories an show that their vector space is fully reproduced by the four-dimensional limit of open topological string amplitudes on the strip with generic boundary conditions associated to a suitable quiver gauge theory. As a byproduct we identify the non-abelian vortex partition function with a specific fusion channel of degenerate conformal blocks.1 aBonelli, Giulio1 aTanzini, Alessandro1 aZhao, Jian uhttp://hdl.handle.net/1963/430401120nas a2200133 4500008004300000245010500043210006900148260001300217520065000230100001900880700002500899700002600924856003600950 2011 en_Ud 00aThe matching property of infinitesimal isometries on elliptic surfaces and elasticity on thin shells0 amatching property of infinitesimal isometries on elliptic surfac bSpringer3 aUsing the notion of Γ-convergence, we discuss the limiting behavior of the three-dimensional nonlinear elastic energy for thin elliptic shells, as their thickness h converges to zero, under the assumption that the elastic energy of deformations scales like h β with 2 < β < 4. We establish that, for the given scaling regime, the limiting theory reduces to linear pure bending. Two major ingredients of the proofs are the density of smooth infinitesimal isometries in the space of W 2,2 first order infinitesimal isometries, and a result on matching smooth infinitesimal isometries with exact isometric immersions on smooth elliptic surfaces.1 aLewicka, Marta1 aMora, Maria Giovanna1 aPakzad, Mohammad Reza uhttp://hdl.handle.net/1963/339201329nas a2200169 4500008004100000022001400041245008700055210006900142260000800211300001400219490000700233520081100240100001801051700002201069700002201091856004601113 2011 eng d a1432-095900aMetastable equilibria of capillary drops on solid surfaces: a phase field approach0 aMetastable equilibria of capillary drops on solid surfaces a pha cSep a453–4710 v233 aWe discuss a phase field model for the numerical simulation of metastable equilibria of capillary drops resting on rough solid surfaces and for the description of contact angle hysteresis phenomena in wetting. The model is able to reproduce observed transitions of drops on micropillars from Cassie–Baxter to Wenzel states. When supplemented with a dissipation potential which describes energy losses due to frictional forces resisting the motion of the contact line, the model can describe metastable states such as drops in equilibrium on vertical glass plates. The reliability of the model is assessed by a detailed comparison of its predictions with experimental data on the maximal size of water drops that can stick on vertical glass plates which have undergone different surface treatments.

1 aFedeli, Livio1 aTurco, Alessandro1 aDeSimone, Antonio uhttps://doi.org/10.1007/s00161-011-0189-601531nas a2200277 4500008004100000022001600041245006500057210006300122260009400185300001600279490000900295520056700304653002100871653002200892653002200914653002400936653003200960653002500992653002101017653002901038653002401067653002401091100002401115700001901139856009501158 2011 eng d a{0218-2025}00aA MODEL FOR CRACK PROPAGATION BASED ON VISCOUS APPROXIMATION0 aMODEL FOR CRACK PROPAGATION BASED ON VISCOUS APPROXIMATION a{5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE}b{WORLD SCIENTIFIC PUBL CO PTE LTD}c{OCT} a{2019-2047}0 v{21}3 a{In the setting of antiplane linearized elasticity, we show the existence of quasistatic evolutions of cracks in brittle materials by using a vanishing viscosity approach, thus taking into account local minimization. The main feature of our model is that the path followed by the crack need not be prescribed a priori: indeed, it is found as the limit (in the sense of Hausdorff convergence) of curves obtained by an incremental procedure. The result is based on a continuity property for the energy release rate in a suitable class of admissible cracks.}

10aBrittle fracture10aCrack propagation10aenergy derivative10aenergy release rate10afree-discontinuity problems10aGriffith's criterion10alocal minimizers10astress intensity factor}10avanishing viscosity10a{Variational models1 aLazzaroni, Giuliano1 aToader, Rodica uhttp://www.math.sissa.it/publication/model-crack-propagation-based-viscous-approximation-000841nas a2200121 4500008004100000245005200041210005200093260002600145520047000171100001600641700002600657856003600683 2011 en d00aModuli of framed sheaves on projective surfaces0 aModuli of framed sheaves on projective surfaces bDocumenta Mathematica3 aWe show that there exists a fine moduli space for torsion-free sheaves on a\\r\\nprojective surface, which have a \\\"good framing\\\" on a big and nef divisor. This\\r\\nmoduli space is a quasi-projective scheme. This is accomplished by showing that such framed sheaves may be considered as stable pairs in the sense of\\r\\nHuybrechts and Lehn. We characterize the obstruction to the smoothness of the moduli space, and discuss some examples on rational surfaces.1 aBruzzo, Ugo1 aMarkushevich, Dimitri uhttp://hdl.handle.net/1963/512600490nas a2200145 4500008004100000245008500041210006900126260002500195300001200220490000700232100001700239700001900256700002300275856004600298 2011 eng d00aMulti-physics modelling and sensitivity analysis of olympic rowing boat dynamics0 aMultiphysics modelling and sensitivity analysis of olympic rowin bSpringer Naturecnov a85–940 v141 aMola, Andrea1 aGhommem, Mehdi1 aHajj, Muhammad, R. uhttps://doi.org/10.1007/s12283-011-0075-200729nas a2200121 4500008004300000245009900043210006900142260001300211520030900224100002200533700001600555856003600571 2011 en_Ud 00aNew improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces0 aNew improved MoserTrudinger inequalities and singular Liouville bSpringer3 aWe consider a singular Liouville equation on a compact surface, arising from the study of Chern-Simons vortices in a self dual regime. Using new improved versions of the Moser-Trudinger inequalities (whose main feature is to be scaling invariant) and a variational scheme, we prove new existence results.1 aMalchiodi, Andrea1 aRuiz, David uhttp://hdl.handle.net/1963/409900668nas a2200145 4500008004100000245007500041210006900116260001000185520019000195653003600385100002000421700002500441700002000466856003600486 2011 en d00aNonlinear thin-walled beams with a rectangular cross-section - Part II0 aNonlinear thinwalled beams with a rectangular crosssection Part bSISSA3 aIn this paper we report the second part of our results concerning the rigorous derivation of a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section..10aThin-walled cross-section beams1 aFreddi, Lorenzo1 aMora, Maria Giovanna1 aParoni, Roberto uhttp://hdl.handle.net/1963/416901453nas a2200145 4500008004100000022001400041245009100055210007000146260000900216490000800225520090000233100002401133700002101157856012901178 2011 eng d a0012-709400aNonlinear wave and Schrödinger equations on compact Lie groups and homogeneous spaces0 aNonlinear wave and Schrödinger equations on compact Lie groups a c20110 v1593 aWe develop linear and nonlinear harmonic analysis on compact Lie groups and homogeneous spaces relevant for the theory of evolutionary Hamiltonian PDEs. A basic tool is the theory of the highest weight for irreducible representations of compact Lie groups. This theory provides an accurate description of the eigenvalues of the Laplace-Beltrami operator as well as the multiplication rules of its eigenfunctions. As an application, we prove the existence of Cantor families of small amplitude time-periodic solutions for wave and Schr¨odinger equations with differentiable nonlinearities. We apply an abstract Nash-Moser implicit function theorem to overcome the small divisors problem produced by the degenerate eigenvalues of the Laplace operator. We provide a new algebraic framework to prove the key tame estimates for the inverse linearized operators on Banach scales of Sobolev functions.1 aBerti, Massimiliano1 aProcesi, Michela uhttp://www.math.sissa.it/publication/nonlinear-wave-and-schr%C3%B6dinger-equations-compact-lie-groups-and-homogeneous-spaces00467nas a2200121 4500008004100000245010400041210006900145260001900214100002900233700002600262700002100288856003600309 2011 en d00aOn the number of eigenvalues of a model operator related to a system of three particles on lattices0 anumber of eigenvalues of a model operator related to a system of bIOP Publishing1 aDell'Antonio, Gianfausto1 aMuminov, Zahriddin I.1 aShermatova, Y.M. uhttp://hdl.handle.net/1963/549600977nas a2200145 4500008004300000245007900043210006900122260002100191520050000212653002100712100002300733700002200756700001700778856003600795 2011 en_Ud 00aNumerical Strategies for Stroke Optimization of Axisymmetric Microswimmers0 aNumerical Strategies for Stroke Optimization of Axisymmetric Mic bWorld Scientific3 aWe propose a computational method to solve optimal swimming problems, based on the boundary integral formulation of the hydrodynamic interaction between swimmer and surrounding fluid and direct constrained minimization of the energy consumed by the swimmer. We apply our method to axisymmetric model examples. We consider a classical model swimmer (the three-sphere swimmer of Golestanian et al.) as well as a novel axisymmetric swimmer inspired by the observation of biological micro-organisms.10aOptimal swimming1 aAlouges, François1 aDeSimone, Antonio1 aHeltai, Luca uhttp://hdl.handle.net/1963/365701547nas a2200133 4500008004100000245008700041210006900128260000900197520111200206100002001318700001801338700002101356856003601377 2011 en d00aNumerical Study of breakup in generalized Korteweg-de Vries and Kawahara equations0 aNumerical Study of breakup in generalized Kortewegde Vries and K bSIAM3 aThis article is concerned with a conjecture in [B. Dubrovin, Comm. Math. Phys., 267 (2006), pp. 117–139] on the formation of dispersive shocks in a class of Hamiltonian dispersive regularizations of the quasi-linear transport equation. The regularizations are characterized by two arbitrary functions of one variable, where the condition of integrability implies that one of these functions must not vanish. It is shown numerically for a large class of equations that the local behavior of their solution near the point of gradient catastrophe for the transport equation is described by a special solution of a Painlevé-type equation. This local description holds also for solutions to equations where blowup can occur in finite time. Furthermore, it is shown that a solution of the dispersive equations away from the point of gradient catastrophe is approximated by a solution of the transport equation with the same initial data, modulo terms of order $\\\\epsilon^2$, where $\\\\epsilon^2$ is the small dispersion parameter. Corrections up to order $\\\\epsilon^4$ are obtained and tested numerically.1 aDubrovin, Boris1 aGrava, Tamara1 aKlein, Christian uhttp://hdl.handle.net/1963/495100449nas a2200109 4500008004300000245005100043210005100094260003400145520010000179100002400279856003600303 2011 en_Ud 00aOsservazioni sui teoremi di inversione globale0 aOsservazioni sui teoremi di inversione globale bEuropean Mathematical Society3 aSome global inversion theorems with applications to semilinear elliptic equation are discussed.1 aAmbrosetti, Antonio uhttp://hdl.handle.net/1963/406800420nas a2200109 4500008004300000245009100043210006900134260003400203653001700237100002000254856003600274 2011 en_Ud 00aPlanar loops with prescribed curvature: existence, multiplicity and uniqueness results0 aPlanar loops with prescribed curvature existence multiplicity an bAmerican Mathematical Society10aPlane curves1 aMusina, Roberta uhttp://hdl.handle.net/1963/384200961nas a2200121 4500008004300000245005200043210005100095260001300146520059700159100002200756700002500778856003600803 2011 en_Ud 00aPoincaré covariance and κ-Minkowski spacetime0 aPoincaré covariance and κMinkowski spacetime bElsevier3 aA fully Poincaré covariant model is constructed out of the k-Minkowski spacetime. Covariance is implemented by a unitary representation of the Poincaré group, and thus complies with the original Wigner approach to quantum symmetries. This provides yet another example (besides the DFR model), where Poincaré covariance is realised á la Wigner in the presence of two characteristic dimensionful parameters: the light speed and the Planck length. In other words, a Doubly Special Relativity (DSR) framework may well be realised without deforming the meaning of \\\"Poincaré covariance\\\".1 aDabrowski, Ludwik1 aPiacitelli, Gherardo uhttp://hdl.handle.net/1963/389301388nas a2200157 4500008004300000245009200043210007000135260002200205300001200227490000800239520088500247100001601132700002201148700002401170856003601194 2011 en_Ud 00aPoincaré polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces0 aPoincaré polynomial of moduli spaces of framed sheaves on stacky bSpringerc06/2011 a395-4090 v3043 aWe perform a study of the moduli space of framed torsion-free sheaves on Hirzebruch surfaces by using localization techniques. We discuss some general properties of this moduli space by studying it in the framework of Huybrechts-Lehn theory of framed modules. We classify the fixed points under a toric action on the moduli space, and use this to compute the Poincare polynomial of the latter. This will imply that the moduli spaces we are considering are irreducible. We also consider fractional first Chern classes, which means that we are extending our computation to a stacky deformation of a Hirzebruch surface. From the physical viewpoint, our results provide the partition function of N=4 Vafa-Witten theory on total spaces of line bundles on P1, which is relevant in black hole entropy counting problems according to a conjecture due to Ooguri, Strominger and Vafa.

1 aBruzzo, Ugo1 aPoghossian, Rubik1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/373800741nas a2200121 4500008004100000245003700041210003700078260002100115520040400136100002200540700002100562856003600583 2011 en d00aProduct of real spectral triples0 aProduct of real spectral triples bWorld Scientific3 aWe construct the product of real spectral triples of arbitrary finite dimension (and arbitrary parity) taking into account the fact that in the even case there are two possible real structures, in the odd case there are two inequivalent representations of the gamma matrices (Clifford algebra), and in the even-even case there are two natural candidates for the Dirac operator of the product triple.1 aDabrowski, Ludwik1 aDossena, Giacomo uhttp://hdl.handle.net/1963/551000842nas a2200109 4500008004300000245005800043210005600101260001300157520050500170100002100675856003600696 2011 en_Ud 00aA proof of Sudakov theorem with strictly convex norms0 aproof of Sudakov theorem with strictly convex norms bSpringer3 aWe establish a solution to the Monge problem in Rn, with an asymmetric, strictly convex norm cost function, when the initial measure is absolutely continuous. We focus on the strategy, based on disintegration of measures, initially proposed by Sudakov. As known, there is a gap to fill. The missing step is completed when the unit ball is strictly convex, but not necessarily differentiable nor uniformly convex. The key disintegration is achieved following a similar proof for a variational problem.1 aCaravenna, Laura uhttp://hdl.handle.net/1963/296700609nas a2200121 4500008004100000245003000041210002900071260001000100520030300110100001600413700002200429856003600451 2011 en d00aQ-factorial Laurent rings0 aQfactorial Laurent rings bSISSA3 aDolgachev proved that, for any field k, the ring naturally associated to a\\r\\ngeneric Laurent polynomial in d variables, $d \\\\geq 4$, is factorial. We prove a\\r\\nsufficient condition for the ring associated to a very general complex Laurent\\r\\npolynomial in d=3 variables to be Q-factorial.1 aBruzzo, Ugo1 aGrassi, Antonella uhttp://hdl.handle.net/1963/418302121nas a2200145 4500008004100000245007900041210006900120260001300189520164700202100002001849700002201869700002301891700002501914856003601939 2011 en d00aQuantum Geometry on Quantum Spacetime: Distance, Area and Volume Operators0 aQuantum Geometry on Quantum Spacetime Distance Area and Volume O bSpringer3 aWe develop the first steps towards an analysis of geometry on the quantum\\r\\nspacetime proposed in Doplicher et al. (Commun Math Phys 172:187–220, 1995). The homogeneous elements of the universal differential algebra are naturally identified with operators living in tensor powers of Quantum Spacetime; this allows us to compute their spectra. In particular, we consider operators that can be interpreted as distances, areas, 3- and 4-volumes. The Minkowski distance operator between two independent events is shown to have pure Lebesgue spectrum with infinite multiplicity. The Euclidean distance operator is shown to have spectrum bounded below by a constant of the order of the Planck length. The corresponding statement is proved also for both the space-space and space-time area operators, as well as for the Euclidean length of the vector representing the 3-volume operators. However, the space 3-volume operator (the time component of that vector) is shown to have spectrum equal to the whole complex plane. All these operators are normal, while the distance operators are also selfadjoint. The Lorentz invariant spacetime volume operator, representing the 4- volume spanned by five\\r\\nindependent events, is shown to be normal. Its spectrum is pure point with a\\r\\nfinite distance (of the order of the fourth power of the Planck length) away\\r\\nfrom the origin. The mathematical formalism apt to these problems is developed and its relation to a general formulation of Gauge Theories on Quantum Spaces is outlined. As a byproduct, a Hodge Duality between the absolute differential and the Hochschild boundary is pointed out.1 aBahns, Dorothea1 aDoplicher, Sergio1 aFredenhagen, Klaus1 aPiacitelli, Gherardo uhttp://hdl.handle.net/1963/520301134nas a2200133 4500008004100000245006000041210005900101260001000160520072600170100002000896700002400916700002400940856003600964 2011 en d00aQuantum Hitchin Systems via beta-deformed Matrix Models0 aQuantum Hitchin Systems via betadeformed Matrix Models bSISSA3 aWe study the quantization of Hitchin systems in terms of beta-deformations of generalized matrix models related to conformal blocks of Liouville theory on punctured Riemann surfaces. We show that in a suitable limit, corresponding to the Nekrasov-Shatashvili one, the loop equations of the matrix model reproduce the Hamiltonians of the quantum Hitchin system on the sphere and the torus with marked points. The eigenvalues of these Hamiltonians are shown to be the epsilon1-deformation of the chiral observables of the corresponding N=2 four ndimensional gauge theory. Moreover, we find the exact wave-functions in terms of the matrix model representation of the conformal blocks with degenerate field insertions.

1 aBonelli, Giulio1 aMaruyoshi, Kazunobu1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/418100860nas a2200133 4500008004100000245008400041210006900125260001300194520041200207100002500619700002400644700002200668856003600690 2011 en d00aQuantum Isometries of the finite noncommutative geometry of the Standard Model0 aQuantum Isometries of the finite noncommutative geometry of the bSpringer3 aWe compute the quantum isometry group of the finite noncommutative geometry F describing the internal degrees of freedom in the Standard Model of particle physics. We show that this provides genuine quantum symmetries of the spectral triple corresponding to M x F where M is a compact spin manifold. We also prove that the bosonic and fermionic part of the spectral action are preserved by these symmetries.1 aBhowmick, Jyotishman1 aD'Andrea, Francesco1 aDabrowski, Ludwik uhttp://hdl.handle.net/1963/490600673nas a2200109 4500008004300000245010600043210006900149520026500218100002200483700002200505856003600527 2011 en_Ud 00aQuasiconvex envelopes of energies for nematic elastomers in the small strain regime and applications0 aQuasiconvex envelopes of energies for nematic elastomers in the 3 aWe provide some explicit formulas for the quasiconvex envelope of energy densities for nematic elastomers in the small strain regime and plane strain conditions. We then demonstrate their use as a powerful tool for the interpretation of mechanical experiments.1 aCesana, Pierluigi1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/406500919nas a2200121 4500008004300000245013400043210006900177260004600246520042800292100002200720700001900742856003600761 2011 en_Ud 00aQuasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a Young measures approach0 aQuasistatic crack evolution for a cohesive zone model with diffe bCambridge University Press / EDP Sciences3 aA new approach to irreversible quasistatic fracture growth is given, by means of Young measures. The study concerns a cohesive zone model with prescribed crack path, when the material gives different responses to loading and unloading phases. In the particular situation of constant unloading response, the result contained in [6] is recovered. In this case, the convergence of the discrete time approximations is improved.1 aCagnetti, Filippo1 aToader, Rodica uhttp://hdl.handle.net/1963/235501262nas a2200277 4500008004100000022001600041245007000057210006900127260008600196300001400282490001000296520028400306653002100590653002200611653002400633653002200657653003200679653002500711653002600736653001800762653002600780653003100806653002400837100002400861856009900885 2011 eng d a{0373-3114}00aQuasistatic crack growth in finite elasticity with Lipschitz data0 aQuasistatic crack growth in finite elasticity with Lipschitz dat a{TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY}b{SPRINGER HEIDELBERG}c{JAN} a{165-194}0 v{190}3 a{We extend the recent existence result of Dal Maso and Lazzaroni (Ann Inst H Poincare Anal Non Lineaire 27:257-290, 2010) for quasistatic evolutions of cracks in finite elasticity, allowing for boundary conditions and external forces with discontinuous first derivatives.}

10aBrittle fracture10aCrack propagation10aEnergy minimization10aFinite elasticity10afree-discontinuity problems10aGriffith's criterion10aNon-interpenetration}10aPolyconvexity10aQuasistatic evolution10aRate-independent processes10a{Variational models1 aLazzaroni, Giuliano uhttp://www.math.sissa.it/publication/quasistatic-crack-growth-finite-elasticity-lipschitz-data01420nas a2200145 4500008004300000245012100043210006900164260001300233520089900246653002401145100002101169700002201190700002601212856003601238 2011 en_Ud 00aQuasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling0 aQuasistatic evolution for CamClay plasticity a weak formulation bSpringer3 aCam-Clay nonassociative plasticity exhibits both hardening and softening behaviour, depending on the loading. For many initial data the classical formulation of the quasistatic evolution problem has no smooth solution. We propose here a notion of generalized solution, based on a viscoplastic approximation. To study the limit of the viscoplastic evolutions we rescale time, in such a way that the plastic strain is uniformly Lipschitz with respect to the rescaled time. The limit of these rescaled solutions, as the viscosity parameter tends to zero, is characterized through an energy-dissipation balance, that can be written in a natural way using the rescaled time. As shown in [4] and [6], the proposed solution may be discontinuous with respect to the original time. Our formulation allows to compute the amount of viscous dissipation occurring instantaneously at each discontinuity time.10aCam-Clay plasticity1 aDal Maso, Gianni1 aDeSimone, Antonio1 aSolombrino, Francesco uhttp://hdl.handle.net/1963/367000823nas a2200121 4500008004100000245007200041210006900113260001300182520042600195100002200621700002200643856003600665 2011 en d00aQuasistatic evolution of sessile drops and contact angle hysteresis0 aQuasistatic evolution of sessile drops and contact angle hystere bSpringer3 aWe consider the classical model of capillarity coupled with a rate-independent dissipation mechanism due to frictional forces acting on the contact line, and prove the existence of quasistatic evolutions with prescribed initial configuration. We also discuss in detail some explicit solutions to show that the model does account for contact angle hysteresis, and to compare its predictions with experimental observations.1 aAlberti, Giovanni1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/491200804nas a2200133 4500008004100000245005600041210005400097260001300151520040700164100002300571700002300594700001700617856003600634 2011 en d00aSBV regularity for Hamilton-Jacobi equations in R^n0 aSBV regularity for HamiltonJacobi equations in Rn bSpringer3 aIn this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$ \partial_t u + H(D_{x} u)=0 \qquad \textrm{in}\quad \Omega\subset \mathbb{R}\times \mathbb{R}^{n} . $$ In particular, under the assumption that the Hamiltonian $H\in C^2(\mathbb{R}^n)$ is uniformly convex, we prove that $D_{x}u$ and $\partial_t u$ belong to the class $SBV_{loc}(\Omega)$.

1 aBianchini, Stefano1 aDe Lellis, Camillo1 aRobyr, Roger uhttp://hdl.handle.net/1963/491101465nas a2200121 4500008004300000245006700043210006500110260001300175520107800188100001601266700002501282856003601307 2011 en_Ud 00aSemistable and numerically effective principal (Higgs) bundles0 aSemistable and numerically effective principal Higgs bundles bElsevier3 aWe study Miyaoka-type semistability criteria for principal Higgs G-bundles E on complex projective manifolds of any dimension. We prove that E has the property of being semistable after pullback to any projective curve if and only if certain line bundles, obtained from some characters of the parabolic subgroups of G, are numerically effective. One also proves that these conditions are met for semistable principal Higgs bundles whose adjoint bundle has vanishing second Chern class.\\r\\n\\r\\nIn a second part of the paper, we introduce notions of numerical effectiveness and numerical flatness for principal (Higgs) bundles, discussing their main properties. For (non-Higgs) principal bundles, we show that a numerically flat principal bundle admits a reduction to a Levi factor which has a flat Hermitian–Yang–Mills connection, and, as a consequence, that the cohomology ring of a numerically flat principal bundle with coefficients in R is trivial. To our knowledge this notion of numerical effectiveness is new even in the case of (non-Higgs) principal bundles.1 aBruzzo, Ugo1 aGrana-Otero, Beatriz uhttp://hdl.handle.net/1963/363801135nas a2200145 4500008004300000245008100043210006900124260002300193520065600216100002100872700002100893700001900914700002000933856003600953 2011 en_Ud 00aSingular perturbation models in phase transitions for second order materials0 aSingular perturbation models in phase transitions for second ord bIndiana University3 aA variational model proposed in the physics literature to describe the onset of pattern formation in two-component bilayer membranes and amphiphilic monolayers leads to the analysis of a Ginzburg-Landau type energy with a negative term depending on the first derivative of the phase function. Scaling arguments motivate the study of the family of second order singular perturbed energies Fe having a negative term depending on the first derivative of the phase function. Here, the asymptotic behavior of {Fe} is studied using G-convergence techniques. In particular, compactness results and an integral representation of the limit energy are obtained.1 aChermisi, Milena1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni uhttp://hdl.handle.net/1963/385801019nas a2200133 4500008004100000020001800041245004500059210004500104260001000149520064400159653002500803100002100828856003600849 2011 en d a978311027558200aSolving PVI by Isomonodromy Deformations0 aSolving PVI by Isomonodromy Deformations bSISSA3 aThe critical and asymptotic behaviors of solutions of the sixth Painlev\\\'e\r\nequation, an their parametrization in terms of monodromy data, are\r\nsynthetically reviewed. The explicit formulas are given. This paper has been\r\nwithdrawn by the author himself, because some improvements are necessary.\r\nThis is a proceedings of the international conference \"Painlevé Equations and Related Topics\" which was taking place at the Euler International Mathematical Institute, a branch of the Saint Petersburg Department of the SteklovInstitute of Mathematicsof theRussian Academy of Sciences, in Saint Petersburg on June 17 to 23, 2011.10aPainlevé Equations1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/652200674nas a2200121 4500008004100000245006800041210006100109260001000170520028700180653002400467100002500491856003600516 2011 en d00aOn the Space of Symmetric Operators with Multiple Ground States0 aSpace of Symmetric Operators with Multiple Ground States bSISSA3 aWe study homological structure of the filtrations of the spaces of self-adjoint operators by the multiplicity of the ground state. We consider only operators acting in a finite dimensional complex or real Hilbert space but infinite dimensional generalizations are easily guessed.10aMultiple eigenvalue1 aAgrachev, Andrei, A. uhttp://hdl.handle.net/1963/706900940nas a2200145 4500008004100000245009900041210006900140260001300209520045300222100002100675700002300696700002000719700001900739856003600758 2011 en d00aThe sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry0 asphere and the cut locus at a tangency point in twodimensional a bSpringer3 aWe study the tangential case in 2-dimensional almost-Riemannian geometry. We\\r\\nanalyse the connection with the Martinet case in sub-Riemannian geometry. We\\r\\ncompute estimations of the exponential map which allow us to describe the\\r\\nconjugate locus and the cut locus at a tangency point. We prove that this last\\r\\none generically accumulates at the tangency point as an asymmetric cusp whose branches are separated by the singular set.1 aBonnard, Bernard1 aCharlot, Grégoire1 aGhezzi, Roberta1 aJanin, Gabriel uhttp://hdl.handle.net/1963/491400415nas a2200121 4500008004100000245007100041210006900112260001000181100002200191700002300213700002100236856003600257 2011 en d00aStructure of level sets and Sard-type properties of Lipschitz maps0 aStructure of level sets and Sardtype properties of Lipschitz map bSISSA1 aAlberti, Giovanni1 aBianchini, Stefano1 aCrippa, Gianluca uhttp://hdl.handle.net/1963/465700724nas a2200133 4500008004300000245007500043210006900118260002800187520026900215100002200484700002600506700002200532856003600554 2011 en_Ud 00aSupercritical conformal metrics on surfaces with conical singularities0 aSupercritical conformal metrics on surfaces with conical singula bOxford University Press3 aWe study the problem of prescribing the Gaussian curvature on surfaces with conical singularities in supercritical regimes. Using a Morse-theoretical approach we prove a general existence theorem on surfaces with positive genus, with a generic multiplicity result.1 aBardelloni, Mauro1 aDe Marchis, Francesca1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/409501822nas a2200145 4500008004100000245009200041210006900133260002800202520132600230100002101556700002201577700001901599700002201618856003601640 2011 en d00aA system-level approach for deciphering the transcriptional response to prion infection0 asystemlevel approach for deciphering the transcriptional respons bOxford University Press3 aMOTIVATION: Deciphering the response of a complex biological system to an insulting event, at the gene expression level, requires adopting theoretical models that are more sophisticated than a one-to-one comparison (i.e. t-test). Here, we investigate the ability of a novel reverse engineering approach (System Response Inference) to unveil non-obvious transcriptional signatures of the system response induced by prion infection.\\r\\nRESULTS: To this end, we analyze previously published gene expression data, from which we extrapolate a putative full-scale model of transcriptional gene-gene dependencies in the mouse central nervous system. Then, we use this nominal model to interpret the gene expression changes caused by prion replication, aiming at selecting the genes primarily influenced by this perturbation. Our method sheds light on the mode of action of prions by identifying key transcripts that are the most likely to be responsible for the overall transcriptional rearrangement from a nominal regulatory network. As a first result of our inference, we have been able to predict known targets of prions (i.e. PrP(C)) and to unveil the potential role of previously unsuspected genes.\\r\\nCONTACT: altafini@sissa.it\\r\\nSUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.1 aZampieri, Mattia1 aLegname, Giuseppe1 aSegrè, Daniel1 aAltafini, Claudio uhttp://hdl.handle.net/1963/574500881nas a2200133 4500008004300000245008900043210007100132260001300203520043200216100001800648700002500666700002000691856003600711 2011 en_Ud 00aThe time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity0 atimedependent von Kármán plate equation as a limit of 3d nonline bSpringer3 aThe asymptotic behaviour of the solutions of three-dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness $h$ of the plate tends to zero. Under appropriate scalings of the applied force and of the initial values in terms of $h$, it is shown that three-dimensional solutions of the nonlinear elastodynamic equation converge to solutions of the time-dependent von K\\\\\\\'arm\\\\\\\'an plate equation.1 aAbels, Helmut1 aMora, Maria Giovanna1 aMüller, Stefan uhttp://hdl.handle.net/1963/383500557nas a2200121 4500008004100000245011500041210006900156300000900225490002900234100001900263700002000282856013300302 2011 eng d00aThe Transition between the Gap Probabilities from the Pearcey to the Airy Process–a Riemann-Hilbert Approach0 aTransition between the Gap Probabilities from the Pearcey to the a1-500 vdoi: 10.1093/imrn/rnr0661 aBertola, Marco1 aCafasso, Mattia uhttp://www.math.sissa.it/publication/transition-between-gap-probabilities-pearcey-airy-process%E2%80%93-riemann-hilbert-approach00843nas a2200169 4500008004100000022001400041245011600055210006900171300001600240490000700256520022700263653002300490653003700513653002500550100002700575856007100602 2011 eng d a0362-546X00aUniqueness and nondegeneracy of the ground state for a quasilinear Schrödinger equation with a small parameter0 aUniqueness and nondegeneracy of the ground state for a quasiline a1731 - 17370 v743 aWe study least energy solutions of a quasilinear Schrödinger equation with a small parameter. We prove that the ground state is nondegenerate and unique up to translations and phase shifts using bifurcation theory.

10aBifurcation theory10aNonlinear Schrödinger equations10aStationary solutions1 aSelvitella, Alessandro uhttp://www.sciencedirect.com/science/article/pii/S0362546X1000761300413nas a2200121 4500008004100000245007000041210006800111260001000179100002200189700002300211700002100234856003600255 2011 en d00aA uniqueness result for the continuity equation in two dimensions0 auniqueness result for the continuity equation in two dimensions bSISSA1 aAlberti, Giovanni1 aBianchini, Stefano1 aCrippa, Gianluca uhttp://hdl.handle.net/1963/466302009nas a2200385 4500008004100000022001300041245007600054210006900130300001200199490000700211520082800218653001601046653002101062653002301083653002101106653003001127653001901157653002201176653002501198653002701223653001801250653001801268653002401286653002801310653002201338653002201360653002401382653001901406653001201425653001901437100002401456700002001480700002101500856010201521 2010 eng d a0294144900aAn abstract Nash-Moser theorem with parameters and applications to PDEs0 aabstract NashMoser theorem with parameters and applications to P a377-3990 v273 aWe prove an abstract Nash-Moser implicit function theorem with parameters which covers the applications to the existence of finite dimensional, differentiable, invariant tori of Hamiltonian PDEs with merely differentiable nonlinearities. The main new feature of the abstract iterative scheme is that the linearized operators, in a neighborhood of the expected solution, are invertible, and satisfy the "tame" estimates, only for proper subsets of the parameters. As an application we show the existence of periodic solutions of nonlinear wave equations on Riemannian Zoll manifolds. A point of interest is that, in presence of possibly very large "clusters of small divisors", due to resonance phenomena, it is more natural to expect solutions with only Sobolev regularity. © 2009 Elsevier Masson SAS. All rights reserved.10aAbstracting10aAircraft engines10aFinite dimensional10aHamiltonian PDEs10aImplicit function theorem10aInvariant tori10aIterative schemes10aLinearized operators10aMathematical operators10aMoser theorem10aNon-Linearity10aNonlinear equations10aNonlinear wave equation10aPeriodic solution10aPoint of interest10aResonance phenomena10aSmall divisors10aSobolev10aWave equations1 aBerti, Massimiliano1 aBolle, Philippe1 aProcesi, Michela uhttp://www.math.sissa.it/publication/abstract-nash-moser-theorem-parameters-and-applications-pdes00340nas a2200097 4500008004100000245006800041210006700109260001000176100002000186856003600206 2010 en d00aAlmost-Riemannian Geometry from a Control Theoretical Viewpoint0 aAlmostRiemannian Geometry from a Control Theoretical Viewpoint bSISSA1 aGhezzi, Roberta uhttp://hdl.handle.net/1963/470500564nas a2200109 4500008004100000245005700041210005700098260001000155520022800165100002500393856003600418 2010 en d00aAspects of Quantum Field Theory on Quantum Spacetime0 aAspects of Quantum Field Theory on Quantum Spacetime bSISSA3 aWe provide a minimal, self-contained introduction to the covariant DFR flat\\r\\nquantum spacetime, and to some partial results for the corresponding quantum field theory. Explicit equations are given in the Dirac notation.1 aPiacitelli, Gherardo uhttp://hdl.handle.net/1963/417101351nas a2200109 4500008004300000245003600043210003500079520104400114100002501158700002201183856003601205 2010 en_Ud 00aCanonical k-Minkowski Spacetime0 aCanonical kMinkowski Spacetime3 aA complete classification of the regular representations of the relations [T,X_j] = (i/k)X_j, j=1,...,d, is given. The quantisation of RxR^d canonically (in the sense of Weyl) associated with the universal representation of the above relations is intrinsically \\\"radial\\\", this meaning that it only involves the time variable and the distance from the origin; angle variables remain classical. The time axis through the origin is a spectral singularity of the model: in the large scale limit it is topologically disjoint from the rest. The symbolic calculus is developed; in particular there is a trace functional on symbols. For suitable choices of states localised very close to the origin, the uncertainties of all spacetime coordinates can be made simultaneously small at wish. On the contrary, uncertainty relations become important at \\\"large\\\" distances: Planck scale effects should be visible at LHC energies, if processes are spread in a region of size 1mm (order of peak nominal beam size) around the origin of spacetime.1 aPiacitelli, Gherardo1 aDabrowski, Ludwik uhttp://hdl.handle.net/1963/386300422nas a2200145 4500008004100000022001400041245003600055210003600091300001400127490000800141100001900149700001700168700002000185856007100205 2010 eng d a0021-904500aCauchy biorthogonal polynomials0 aCauchy biorthogonal polynomials a832–8670 v1621 aBertola, Marco1 aGekhtman, M.1 aSzmigielski, J. uhttp://0-dx.doi.org.mercury.concordia.ca/10.1016/j.jat.2009.09.00801271nas a2200133 4500008004300000245007300043210006800116520083300184100001801017700001901035700002301054700002401077856003601101 2010 en_Ud 00aChern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality0 aChernSimons theory on Lpq lens spaces and GopakumarVafa duality3 aWe consider aspects of Chern-Simons theory on L(p,q) lens spaces and its relation with matrix models and topological string theory on Calabi-Yau threefolds, searching for possible new large N dualities via geometric transition for non-SU(2) cyclic quotients of the conifold. To this aim we find, on one hand, some novel matrix integral representations of the SU(N) CS partition function in a generic flat background for the whole L(p,q) family and provide a solution for its large N dynamics; on the other, we perform in full detail the construction of a family of would-be dual closed string backgrounds via conifold geometric transition from T^*L(p,q). We can then explicitly prove that Gopakumar-Vafa duality in a fixed vacuum fails in the case q>1, and briefly discuss how it could be restored in a non-perturbative setting.1 aBrini, Andrea1 aGriguolo, Luca1 aSeminara, Domenico1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/293800560nas a2200109 4500008004300000245005000043210004900093520023400142100001600376700002200392856003600414 2010 en_Ud 00aCohomology of Skew-holomorphic lie algebroids0 aCohomology of Skewholomorphic lie algebroids3 aWe introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.1 aBruzzo, Ugo1 aRubtsov, Vladimir uhttp://hdl.handle.net/1963/385300912nas a2200133 4500008004300000245011700043210006900160520042800229100002600657700002200683700001900705700001800724856003600742 2010 en_Ud 00aConcentration of solutions for some singularly perturbed mixed problems: Asymptotics of minimal energy solutions0 aConcentration of solutions for some singularly perturbed mixed p3 aIn this paper we carry on the study of asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions, started in the first paper. Here we are mainly interested in the analysis of the location and shape of least energy solutions when the singular perturbation parameter tends to zero. We show that in many cases they coincide with the new solutions produced in.1 aGarcia Azorero, Jesus1 aMalchiodi, Andrea1 aMontoro, Luigi1 aPeral, Ireneo uhttp://hdl.handle.net/1963/340900856nas a2200133 4500008004300000245010300043210006900146520038600215100002600601700002200627700001900649700001800668856003600686 2010 en_Ud 00aConcentration of solutions for some singularly perturbed mixed problems. Part I: existence results0 aConcentration of solutions for some singularly perturbed mixed p3 aIn this paper we study the asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions. We prove that, under suitable geometric conditions on the boundary of the domain, there exist solutions which approach the intersection of the Neumann and the Dirichlet parts as the singular perturbation parameter tends to zero.1 aGarcia Azorero, Jesus1 aMalchiodi, Andrea1 aMontoro, Luigi1 aPeral, Ireneo uhttp://hdl.handle.net/1963/340600703nas a2200121 4500008004100000245007900041210006900120260001000189520030700199100002500506700001400531856003600545 2010 en d00aContinuity of optimal control costs and its application to weak KAM theory0 aContinuity of optimal control costs and its application to weak bSISSA3 aWe prove continuity of certain cost functions arising from optimal control of\\r\\naffine control systems. We give sharp sufficient conditions for this\\r\\ncontinuity. As an application, we prove a version of weak KAM theorem and\\r\\nconsider the Aubry-Mather problems corresponding to these systems.1 aAgrachev, Andrei, A.1 aLee, Paul uhttp://hdl.handle.net/1963/645900908nas a2200109 4500008004300000245010700043210006900150520050000219100001800719700002500737856003600762 2010 en_Ud 00aConvergence of equilibria of thin elastic rods under physical growth conditions for the energy density0 aConvergence of equilibria of thin elastic rods under physical gr3 aThe subject of this paper is the study of the asymptotic behaviour of the equilibrium configurations of a nonlinearly elastic thin rod, as the diameter of the cross-section tends to zero. Convergence results are established assuming physical growth conditions for the elastic energy density and suitable scalings of the applied loads, that correspond at the limit to different rod models: the constrained linear theory, the analogous of von Kármán plate theory for rods, and the linear theory.1 aDavoli, Elisa1 aMora, Maria Giovanna uhttp://hdl.handle.net/1963/408600433nas 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 0\\\\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/1963/646100702nas a2200121 4500008004300000245011200043210007000155260001900225520025100244100002900495700002000524856003600544 2010 en_Ud 00aEffective Schroedinger dynamics on $ ε$-thin Dirichlet waveguides via Quantum Graphs I: star-shaped graphs0 aEffective Schroedinger dynamics on εthin Dirichlet waveguides vi bIOP Publishing3 aWe describe the boundary conditions at the vertex that one must choose to obtain a dynamical system that best describes the low-energy part of the evolution of a quantum system confined to a very small neighbourhood of a star-shaped metric graph.1 aDell'Antonio, Gianfausto1 aCosta, Emanuele uhttp://hdl.handle.net/1963/410601221nas a2200109 4500008004300000245005800043210005800101520086900159100002301028700002401051856003601075 2010 en_Ud 00aEstimates on path functionals over Wasserstein Spaces0 aEstimates on path functionals over Wasserstein Spaces3 aIn this paper we consider the class a functionals (introduced in [Brancolini, Buttazzo, and Santambrogio, J. Eur. Math. Soc. (JEMS), 8 (2006), pp. 415-434] $\\\\mathcal{G}_{r,p}$ defined on Lipschitz curves $\\\\gamma$ valued in the $p$-Wasserstein space. The problem considered is the following: given a measure $\\\\mu$, give conditions in order to assure the existence of a curve $\\\\gamma$ such that $\\\\gamma(0)=\\\\mu$, $\\\\gamma(1)=\\\\delta_{x_0}$, and $\\\\mathcal{G}_{r,p}(\\\\gamma)<+\\\\infty$. To this end, new estimates on $\\\\mathcal{G}_{r,p}(\\\\mu)$ are given, and a notion of dimension of a measure (called path dimension) is introduced: the path dimension specifies the values of the parameters $(r,p)$ for which the answer to the previous reachability problem is positive. Finally, we compare the path dimension with other known dimensions.1 aBianchini, Stefano1 aBrancolini, Alessio uhttp://hdl.handle.net/1963/358300371nas a2200097 4500008004300000245008300043210006900126100002300195700001900218856003600237 2010 en_Ud 00aOn the Euler-Lagrange equation for a variational problem : the general case II0 aEulerLagrange equation for a variational problem the general cas1 aBianchini, Stefano1 aGloyer, Matteo uhttp://hdl.handle.net/1963/255100773nas a2200145 4500008004300000245007900043210006900122260001300191520030200204100001900506700002000525700002100545700002500566856003600591 2010 en_Ud 00aExact reconstruction of damaged color images using a total variation model0 aExact reconstruction of damaged color images using a total varia bElsevier3 aIn this paper the reconstruction of damaged piecewice constant color images is studied using a RGB total variation based model for colorization/inpainting. In particular, it is shown that when color is known in a uniformly distributed region, then reconstruction is possible with maximal fidelity.1 aFonseca, Irene1 aLeoni, Giovanni1 aMaggi, Francesco1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/403901347nas a2200133 4500008004300000245006300043210006300106260001300169520093400182100001701116700002301133700002101156856003601177 2010 en_Ud 00aExistence of planar curves minimizing length and curvature0 aExistence of planar curves minimizing length and curvature bSpringer3 aIn this paper we consider the problem of reconstructing a curve that is partially hidden or corrupted by minimizing the functional $\\\\int \\\\sqrt{1+K_\\\\gamma^2} ds$, depending both on length and curvature $K$. We fix starting and ending points as well as initial and final directions.\\nFor this functional we discuss the problem of existence of minimizers on various functional spaces. We find non-existence of minimizers in cases in which initial and final directions are considered with orientation. In this case, minimizing sequences of trajectories can converge to curves with angles.\\nWe instead prove existence of minimizers for the \\\"time-reparameterized\\\" functional $$\\\\int \\\\| \\\\dot\\\\gamma(t) \\\\|\\\\sqrt{1+K_\\\\ga^2} dt$$ for all boundary conditions if initial and final directions are considered regardless to orientation. In this case, minimizers can present cusps (at most two) but not angles.1 aBoscain, Ugo1 aCharlot, Grégoire1 aRossi, Francesco uhttp://hdl.handle.net/1963/410701148nas a2200133 4500008004100000245009700041210006900138260001300207520069800220100002200918700002200940700001600962856003600978 2010 en d00aFeedback schemes for radiation damping suppression in NMR: a control-theoretical perspective0 aFeedback schemes for radiation damping suppression in NMR a cont bElsevier3 aIn NMR spectroscopy, the collective measurement is weakly invasive and its back-action is called radiation damping. The aim of this paper is to provide a control-theoretical analysis of the problem of suppressing this radiation damping. It is shown that the two feedback schemes commonly used in the NMR practice correspond one to a high gain oputput feedback for the simple case of maintaining the spin 1/2 in its inverted state, and the second to a 2-degree of freedom control design with a prefeedback that exactly cancels the radiation damping field. A general high gain feedback stabilization design not requiring the knowledge of the radiation damping time constant is also investigated.1 aAltafini, Claudio1 aCappellaro, Paola1 aCory, David uhttp://hdl.handle.net/1963/438400439nas a2200133 4500008004100000022001400041245006200055210006100117300001400178490000700192100001900199700001600218856007100234 2010 eng d a0176-427600aFirst colonization of a hard-edge in random matrix theory0 aFirst colonization of a hardedge in random matrix theory a231–2570 v311 aBertola, Marco1 aLee, S., Y. uhttp://0-dx.doi.org.mercury.concordia.ca/10.1007/s00365-009-9052-400792nas a2200109 4500008004300000245004300043210004200086260005400128520044800182100001600630856003600646 2010 en_Ud 00aGauge theory: from physics to geometry0 aGauge theory from physics to geometry bIstituto di matematica. Universita\\\' di Trieste3 aMaxwell theory may be regarded as a prototype of gauge theory and generalized to nonabelian gauge theory. We briey sketch the history of the gauge theories, from Maxwell to Yang-Mills theory, and the identification of gauge fields with connections on fibre bundles. We introduce the notion of instanton and consider the moduli spaces of such objects. Finally, we discuss some modern techniques for studying the topology of these moduli spaces.1 aBruzzo, Ugo uhttp://hdl.handle.net/1963/410502590nas a2200265 4500008004100000245013200041210006900173260001000242520175000252100001702002700002402019700002002043700001902063700002102082700001802103700003002121700001802151700001702169700001702186700002002203700002202223700002402245700001902269856003602288 2010 en d00aGene expression analysis of the emergence of epileptiform activity after focal injection of kainic acid into mouse hippocampus.0 aGene expression analysis of the emergence of epileptiform activi bWiley3 aWe report gene profiling data on genomic processes underlying the progression towards recurrent seizures after injection of kainic acid (KA) into the mouse hippocampus. Focal injection enabled us to separate the effects of proepileptic stimuli initiated by KA injection. Both the injected and contralateral hippocampus participated in the status epilepticus. However, neuronal death induced by KA treatment was restricted to the injected hippocampus, although there was some contralateral axonal degeneration. We profiled gene expression changes in dorsal and ventral regions of both the injected and contralateral hippocampus. Changes were detected in the expression of 1526 transcripts in samples from three time-points: (i) during the KA-induced status epilepticus, (ii) at 2 weeks, before recurrent seizures emerged, and (iii) at 6 months after seizures emerged. Grouping genes with similar spatio-temporal changes revealed an early transcriptional response, strong immune, cell death and growth responses at 2 weeks and an activation of immune and extracellular matrix genes persisting at 6 months. Immunostaining for proteins coded by genes identified from array studies provided evidence for gliogenesis and suggested that the proteoglycan biglycan is synthesized by astrocytes and contributes to a glial scar. Gene changes at 6 months after KA injection were largely restricted to tissue from the injection site. This suggests that either recurrent seizures might depend on maintained processes including immune responses and changes in extracellular matrix proteins near the injection site or alternatively might result from processes, such as growth, distant from the injection site and terminated while seizures are maintained.

1 aMotti, Dario1 aLe Duigou, Caroline1 aChemaly, Nicole1 aWittner, Lucia1 aLazarevic, Dejan1 aKrmac, Helena1 aMarstrand, Troels, Torben1 aValen, Eivind1 aSanges, Remo1 aStupka, Elia1 aSandelin, Albin1 aCherubini, Enrico1 aGustincich, Stefano1 aMiles, Richard uhttp://hdl.handle.net/1963/448000807nas a2200157 4500008004300000245008900043210006900132260002800201520027900229100002200508700002100530700002100551700002200572700001900594856003600613 2010 en_Ud 00aOn the geometric origin of the bi-Hamiltonian structure of the Calogero-Moser system0 ageometric origin of the biHamiltonian structure of the CalogeroM bOxford University Press3 aWe show that the bi-Hamiltonian structure of the rational n-particle (attractive) Calogero-Moser system can be obtained by means of a double projection from a very simple Poisson pair on the cotangent bundle of gl(n,R). The relation with the Lax formalism is also discussed.1 aBartocci, Claudio1 aFalqui, Gregorio1 aMencattini, Igor1 aOrtenzi, Giovanni1 aPedroni, Marco uhttp://hdl.handle.net/1963/380001140nas a2200109 4500008004300000245006600043210006200109520077800171100002400949700002100973856003600994 2010 en_Ud 00aThe geometry emerging from the symmetries of a quantum system0 ageometry emerging from the symmetries of a quantum system3 aWe investigate the relation between the symmetries of a quantum system and its topological quantum numbers, in a general C*-algebraic framework. We prove that, under suitable assumptions on the symmetry algebra, there exists a generalization of the Bloch-Floquet transform which induces a direct-integral decomposition of the algebra of observables. Such generalized transform selects uniquely the set of \\\"continuous sections\\\" in the direct integral, thus yielding a Hilbert bundle. The emerging geometric structure provides some topological invariants of the quantum system. Two running examples provide an Ariadne\\\'s thread through the paper. For the sake of completeness, we review two related theorems by von Neumann and Maurin and compare them with our result.1 aDe Nittis, Giuseppe1 aPanati, Gianluca uhttp://hdl.handle.net/1963/383400848nas a2200133 4500008004100000245008600041210006900127300001400196490000700210520038600217100001900603700001900622856007300641 2010 eng d00aA global compactness result for the p-Laplacian involving critical nonlinearities0 aglobal compactness result for the pLaplacian involving critical a469–4930 v283 aWe prove a representation theorem for Palais-Smale sequences involving the p-Laplacian and critical nonlinearities. Applications are given to a critical problem.1 aMercuri, Carlo1 aWillem, Michel uhttp://www.aimsciences.org/journals/displayArticles.jsp?paperID=509700685nas a2200109 4500008004100000245006100041210005800102260001000160520034900170100002000519856003600539 2010 en d00aHamiltonian PDEs: deformations, integrability, solutions0 aHamiltonian PDEs deformations integrability solutions bSISSA3 aWe review recent classification results on the theory of systems of nonlinear\\r\\nHamiltonian partial differential equations with one spatial dimension, including\\r\\na perturbative approach to the integrability theory of such systems, and discuss\\r\\nuniversality conjectures describing critical behaviour of solutions to such\\r\\nsystems.1 aDubrovin, Boris uhttp://hdl.handle.net/1963/646900979nas a2200109 4500008004300000245005400043210005100097520064100148100002000789700002400809856003600833 2010 en_Ud 00aHitchin systems, N=2 gauge theories and W-gravity0 aHitchin systems N2 gauge theories and Wgravity3 aWe propose some arguments supporting an M-theory derivation of the duality recently discovered by Alday, Gaiotto and Tachikawa between two-dimensional conformal field theories and N=2 superconformal gauge theories in four dimensions. We find that A_{N-1} Toda field theory is the simplest two-dimensional conformal field theory quantizing the moduli of N M5-branes wrapped on a Riemann surface. This leads us to identify chiral operators of the N=2 gauge theories with W-algebra currents. As a check of this correspondence we study some relevant OPE\\\'s obtaining that Nekrasov\\\'s partition function satisfies W-geometry constraints.1 aBonelli, Giulio1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/383101044nas a2200169 4500008004300000245007900043210006900122260003000191520049100221100001800712700002600730700002300756700001800779700002200797700001900819856003600838 2010 en_Ud 00aHomogeneous binary trees as ground states of quantum critical Hamiltonians0 aHomogeneous binary trees as ground states of quantum critical Ha bAmerican Physical Society3 aMany-body states whose wave-function admits a representation in terms of a uniform binary-tree tensor decomposition are shown to obey to power-law two-body correlations functions. Any such state can be associated with the ground state of a translational invariant Hamiltonian which, depending on the dimension of the systems sites, involve at most couplings between third-neighboring sites. A detailed analysis of their spectra shows that they admit an exponentially large ground space.1 aSilvi, Pietro1 aGiovannetti, Vittorio1 aMontangero, Simone1 aRizzi, Matteo1 aCirac, J. Ignacio1 aFazio, Rosario uhttp://hdl.handle.net/1963/390901181nas a2200157 4500008004300000245010800043210006900151260001900220520064400239100001800883700002300901700001800924700002600942700001900968856003600987 2010 en_Ud 00aHomogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems0 aHomogeneous multiscale entanglement renormalization ansatz tenso bIOP Publishing3 aIn this paper, we review the properties of homogeneous multiscale entanglement renormalization ansatz (MERA) to describe quantum critical systems.We discuss in more detail our results for one-dimensional (1D) systems (the Ising and Heisenberg models) and present new data for the 2D Ising model. Together with the results for the critical exponents, we provide a detailed description of the numerical algorithm and a discussion of new optimization\\nstrategies. The relation between the critical properties of the system and the tensor structure of the MERA is expressed using the formalism of quantum channels, which we review and extend.1 aRizzi, Matteo1 aMontangero, Simone1 aSilvi, Pietro1 aGiovannetti, Vittorio1 aFazio, Rosario uhttp://hdl.handle.net/1963/406700629nas a2200121 4500008004300000245007900043210006900122260002200191520021000213100002100423700002700444856003600471 2010 en_Ud 00aHomogenization of fiber reinforced brittle material: the intermediate case0 aHomogenization of fiber reinforced brittle material the intermed bWalter de Gruyter3 aWe derive a cohesive fracture model by homogenizing a periodic composite material whose microstructure is characterized by the presence of brittle inclusions in a reticulated unbreakable elastic structure.1 aDal Maso, Gianni1 aZeppieri, Caterina Ida uhttp://hdl.handle.net/1963/360700468nas a2200109 4500008004100000245005900041210005900100260001000159520012800169100002500297856003600322 2010 en d00aInvariant Lagrange submanifolds of dissipative systems0 aInvariant Lagrange submanifolds of dissipative systems bSISSA3 aWe study solutions of modified Hamilton-Jacobi equations H(du/dq,q) + cu(q) =\\r\\n0, q \\\\in M, on a compact manifold M .1 aAgrachev, Andrei, A. uhttp://hdl.handle.net/1963/645700781nas a2200121 4500008004300000245008400043210006900127260004800196520033500244100002200579700002200601856003600623 2010 en_Ud 00aA kinetic mechanism inducing oscillations in simple chemical reactions networks0 akinetic mechanism inducing oscillations in simple chemical react bAmerican Institute of Mathematical Sciences3 aIt is known that a kinetic reaction network in which one or more secondary substrates are acting as cofactors may exhibit an oscillatory behavior. The aim of this work is to provide a description of the functional form of such a cofactor action guaranteeing the\\r\\nonset of oscillations in sufficiently simple reaction networks.1 aCoatleven, Julien1 aAltafini, Claudio uhttp://hdl.handle.net/1963/239300901nas a2200121 4500008004300000245004400043210004300087520054400130100002200674700002200696700002500718856003600743 2010 en_Ud 00aLorentz Covariant k-Minkowski Spacetime0 aLorentz Covariant kMinkowski Spacetime3 aIn recent years, different views on the interpretation of Lorentz covariance of non commuting coordinates were discussed. Here, by a general procedure, we construct the minimal canonical central covariantisation of the k-Minkowski spacetime. We then show that, though the usual k-Minkowski spacetime is covariant under deformed (or twisted) Lorentz action, the resulting framework is equivalent to taking a non covariant restriction of the covariantised model. We conclude with some general comments on the approach of deformed covariance.1 aDabrowski, Ludwik1 aGodlinski, Michal1 aPiacitelli, Gherardo uhttp://hdl.handle.net/1963/382900300nas a2200097 4500008004300000245004100043210003700084100002300121700002200144856003600166 2010 en_Ud 00aThe Monge problem in geodesic spaces0 aMonge problem in geodesic spaces1 aBianchini, Stefano1 aCavalletti, Fabio uhttp://hdl.handle.net/1963/387302106nas a2200121 4500008004300000245013400043210006900177260001900246520164000265100002101905700002201926856003601948 2010 en_Ud 00aMonotonicity, frustration, and ordered response: an analysis of the energy landscape of perturbed large-scale biological networks0 aMonotonicity frustration and ordered response an analysis of the bBioMed Central3 aBackground. \\nFor large-scale biological networks represented as signed graphs, the index of frustration measures how far a network is from a monotone system, i.e., how incoherently the system responds to perturbations.\\nResults. \\nIn this paper we find that the frustration is systematically lower in transcriptional networks (modeled at functional level) than in signaling and metabolic networks (modeled at stoichiometric level). A possible interpretation of this result is in terms of energetic cost of an interaction: an erroneous or contradictory transcriptional action costs much more than a signaling/metabolic error, and therefore must be avoided as much as possible. Averaging over all possible perturbations, however, we also find that unlike for transcriptional networks, in the signaling/metabolic networks the probability of finding the system in its least frustrated configuration tends to be high also in correspondence of a moderate energetic regime, meaning that, in spite of the higher frustration, these networks can achieve a globally ordered response to perturbations even for moderate values of the strength of the interactions. Furthermore, an analysis of the energy landscape shows that signaling and metabolic networks lack energetic barriers around their global optima, a property also favouring global order.\\nConclusion. \\nIn conclusion, transcriptional and signaling/metabolic networks appear to have systematic differences in both the index of frustration and the transition to global order. These differences are interpretable in terms of the different functions of the various classes of networks.1 aIacono, Giovanni1 aAltafini, Claudio uhttp://hdl.handle.net/1963/405500928nas a2200109 4500008004300000245008500043210006900128520053800197100002300735700002400758856003600782 2010 en_Ud 00aMoore-Read Fractional Quantum Hall wavefunctions and SU(2) quiver gauge theories0 aMooreRead Fractional Quantum Hall wavefunctions and SU2 quiver g3 aWe identify Moore-Read wavefunctions, describing non-abelian statistics in fractional quantum Hall systems, with the instanton partition of N=2 superconformal quiver gauge theories at suitable values of masses and \\\\Omega-background parameters. This is obtained by extending to rational conformal field theories the SU(2) gauge quiver/Liouville field theory duality recently found by Alday-Gaiotto-Tachikawa. A direct link between the Moore-Read Hall $n$-body wavefunctions and Z_n-equivariant Donaldson polynomials is pointed out.1 aSantachiara, Raoul1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/385200409nas a2200109 4500008004300000245009100043210006900134100002100203700001900224700002000243856003600263 2010 en_Ud 00aNonlocal character of the reduced theory of thin films with higher order perturbations0 aNonlocal character of the reduced theory of thin films with high1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni uhttp://hdl.handle.net/1963/375400335nas a2200085 4500008004300000245007700043210006900120100002400189856003600213 2010 en_Ud 00aOn the number of positive solutions of some semilinear elliptic problems0 anumber of positive solutions of some semilinear elliptic problem1 aAmbrosetti, Antonio uhttp://hdl.handle.net/1963/408301048nas a2200121 4500008004300000245012100043210006900164520059600233100002200829700001800851700002100869856003600890 2010 en_Ud 00aNumerical Solution of the Small Dispersion Limit of the Camassa-Holm and Whitham Equations and Multiscale Expansions0 aNumerical Solution of the Small Dispersion Limit of the CamassaH3 aThe small dispersion limit of solutions to the Camassa-Holm (CH) equation is characterized by the appearance of a zone of rapid modulated oscillations. An asymptotic description of these oscillations is given, for short times, by the one-phase solution to the CH equation, where the branch points of the corresponding elliptic curve depend on the physical coordinates via the Whitham equations. We present a conjecture for the phase of the asymptotic solution. A numerical study of this limit for smooth hump-like initial data provides strong evidence for the validity of this conjecture....1 aAbenda, Simonetta1 aGrava, Tamara1 aKlein, Christian uhttp://hdl.handle.net/1963/384001159nas a2200121 4500008004300000245006200043210005800105260001300163520078100176100002300957700002100980856003601001 2010 en_Ud 00aOn optimality of c-cyclically monotone transference plans0 aoptimality of ccyclically monotone transference plans bElsevier3 aAbstract. This note deals with the equivalence between the optimality of a transport plan for the Monge-Kantorovich problem and the condition of c-cyclical monotonicity, as an outcome of the construction in [7]. We emphasize the measurability assumption on the hidden structure of linear preorder, applied also to extremality and uniqueness problems. Resume. Dans la presente note nous decrivons brievement la construction introduite dans [7] a propos de l\\\'equivalence entre l\\\'optimalite d\\\'un plan de transport pour le probleme de Monge-Kantorovich et la condition de monotonie c-cyclique ainsi que d\\\'autres sujets que cela nous amene a aborder. Nous souhaitons mettre en evidence l\\\'hypothese de mesurabilite sur la structure sous-jacente de pre-ordre lineaire.1 aBianchini, Stefano1 aCaravenna, Laura uhttp://hdl.handle.net/1963/402301187nas a2200145 4500008004300000245004000043210004000083520078100123100002300904700002200927700001700949700002000966700001900986856003601005 2010 en_Ud 00aOptimally swimming Stokesian Robots0 aOptimally swimming Stokesian Robots3 aWe study self propelled stokesian robots composed of assemblies of balls, in dimen-\\nsions 2 and 3, and prove that they are able to control their position and orientation. This is a result of controllability, and its proof relies on applying Chow\\\'s theorem in an analytic framework, similarly to what has been done in [3] for an axisymmetric system swimming along the axis of symmetry. However, we simplify drastically\\nthe analyticity result given in [3] and apply it to a situation where more complex swimmers move either in a plane or in three-dimensional space, hence experiencing also rotations. We then focus our attention on energetically optimal strokes, which we are able to compute numerically. Some examples of computed optimal strokes are discussed in detail.1 aAlouges, François1 aDeSimone, Antonio1 aHeltai, Luca1 aLefebvre, Aline1 aMerlet, Benoit uhttp://hdl.handle.net/1963/392900900nas a2200121 4500008004300000245014000043210007000183260001000253520044500263100001600708700001800724856003600742 2010 en_Ud 00aPainlevé II asymptotics near the leading edge of the oscillatory zone for the Korteweg-de Vries equation in the small-dispersion limit0 aPainlevé II asymptotics near the leading edge of the oscillatory bWiley3 aIn the small dispersion limit, solutions to the Korteweg-de Vries equation develop an interval of fast oscillations after a certain time. We obtain a universal asymptotic expansion for the Korteweg-de Vries solution near the leading edge of the oscillatory zone up to second order corrections. This expansion involves the Hastings-McLeod solution of the Painlev\\\\\\\'e II equation. We prove our results using the Riemann-Hilbert approach.1 aClaeys, Tom1 aGrava, Tamara uhttp://hdl.handle.net/1963/379900901nas a2200169 4500008004100000020002200041245007700063210006900140260003600209300001200245520028600257100002200543700001800565700002200583700001700605856010900622 2010 eng d a978-90-481-9195-600aA Phase Field Approach to Wetting and Contact Angle Hysteresis Phenomena0 aPhase Field Approach to Wetting and Contact Angle Hysteresis Phe aDordrechtbSpringer Netherlands a51–633 a

We discuss a phase field model for the numerical simulation of contact angle hysteresis phenomena in wetting. The performance of the model is assessed by comparing its predictions with experimental data on the critical size of drops that can stick on a vertical glass plate.

1 aDeSimone, Antonio1 aFedeli, Livio1 aTurco, Alessandro1 aHackl, Klaus uhttp://www.math.sissa.it/publication/phase-field-approach-wetting-and-contact-angle-hysteresis-phenomena00671nas a2200109 4500008004300000245005300043210005300096520033800149100001600487700002200503856003600525 2010 en_Ud 00aPicard group of hypersurfaces in toric varieties0 aPicard group of hypersurfaces in toric varieties3 aWe show that the usual sufficient criterion for a generic hypersurface in a smooth projective manifold to have the same Picard number as the ambient variety can be generalized to hypersurfaces in complete simplicial toric varieties. This sufficient condition is always satisfied by generic K3 surfaces embedded in Fano toric 3-folds.1 aBruzzo, Ugo1 aGrassi, Antonella uhttp://hdl.handle.net/1963/410300784nas a2200097 4500008004300000245010500043210006900148520041300217100002000630856003600650 2010 en_Ud 00aPoles of Integrale Tritronquee and Anharmonic Oscillators. Asymptotic localization from WKB analysis0 aPoles of Integrale Tritronquee and Anharmonic Oscillators Asympt3 aPoles of integrale tritronquee are in bijection with cubic oscillators that admit the simultaneous solutions of two quantization conditions. We show that the poles lie near the solutions of a pair of Bohr-Sommerfeld quantization conditions (the Bohr-Sommerfeld-Boutroux system): the distance between a pole and the corresponding solution of the Bohr-Sommerfeld-Boutroux system vanishes asymptotically.

1 aMasoero, Davide uhttp://hdl.handle.net/1963/384101299nas a2200109 4500008004300000245006000043210005600103520095600159100001701115700002101132856003601153 2010 en_Ud 00aProjective Reeds-Shepp car on $S^2$ with quadratic cost0 aProjective ReedsShepp car on S2 with quadratic cost3 aFix two points $x,\\\\bar{x}\\\\in S^2$ and two directions (without orientation) $\\\\eta,\\\\bar\\\\eta$ of the velocities in these points. In this paper we are interested to the problem of minimizing the cost $$ J[\\\\gamma]=\\\\int_0^T g_{\\\\gamma(t)}(\\\\dot\\\\gamma(t),\\\\dot\\\\gamma(t))+\\nK^2_{\\\\gamma(t)}g_{\\\\gamma(t)}(\\\\dot\\\\gamma(t),\\\\dot\\\\gamma(t)) ~dt$$ along all smooth curves starting from $x$ with direction $\\\\eta$ and ending in $\\\\bar{x}$ with direction $\\\\bar\\\\eta$. Here $g$ is the standard Riemannian metric on $S^2$ and $K_\\\\gamma$ is the corresponding geodesic curvature.\\nThe interest of this problem comes from mechanics and geometry of vision. It can be formulated as a sub-Riemannian problem on the lens space L(4,1).\\nWe compute the global solution for this problem: an interesting feature is that some optimal geodesics present cusps. The cut locus is a stratification with non trivial topology.1 aBoscain, Ugo1 aRossi, Francesco uhttp://hdl.handle.net/1963/266801210nas a2200097 4500008004300000245004000043210003900083520092900122100002501051856003601076 2010 en_Ud 00aQuantum Spacetime: a Disambiguation0 aQuantum Spacetime a Disambiguation3 aWe review an approach to non-commutative geometry, where models are constructed by quantisation of the coordinates. In particular we focus on the full DFR model and its irreducible components; the (arbitrary) restriction to a particular irreducible component is often referred to as the \\\"canonical quantum spacetime\\\". The aim is to distinguish and compare the approaches under various points of view, including motivations, prescriptions for quantisation, the choice of mathematical objects and concepts, approaches to dynamics and to covariance. Some incorrect statements as \\\"universality of Planck scale conflicts with Lorentz-Fitzgerald contraction and requires a modification of covariance\\\", or \\\"stability of the geometric background requires an absolute lower bound of (\\\\Delta x^\\\\mu)\\\", or \\\"violations of unitarity are due to time/space non-commutativity\\\" are put in context, and discussed.1 aPiacitelli, Gherardo uhttp://hdl.handle.net/1963/386400550nas a2200109 4500008004300000245008300043210006900126520016900195100002100364700001900385856003600404 2010 en_Ud 00aQuasistatic crack growth in elasto-plastic materials: the two-dimensional case0 aQuasistatic crack growth in elastoplastic materials the twodimen3 aWe study a variational model for the quasistatic evolution of elasto-plastic materials with cracks in the case of planar small strain associative elasto-plasticity.1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/1963/296400595nas a2200109 4500008004300000245007600043210006900119520021600188100002100404700002400425856003600449 2010 en_Ud 00aQuasistatic crack growth in finite elasticity with non-interpenetration0 aQuasistatic crack growth in finite elasticity with noninterpenet3 aWe present a variational model to study the quasistatic growth of brittle cracks in hyperelastic materials, in the framework of finite elasticity, taking\\ninto account the non-interpenetration condition.

1 aDal Maso, Gianni1 aLazzaroni, Giuliano uhttp://hdl.handle.net/1963/339701304nas a2200121 4500008004300000245008200043210006900125520088100194653002401075100002101099700002601120856003601146 2010 en_Ud 00aQuasistatic evolution for Cam-Clay plasticity: the spatially homogeneous case0 aQuasistatic evolution for CamClay plasticity the spatially homog3 aWe study the spatially uniform case of the problem of quasistatic evolution in small strain nonassociative elastoplasticity (Cam-Clay model). Through the introdution of a viscous approximation, the problem reduces to determine the limit behavior of the solutions of a singularly perturbed system of ODE\\\'s in a finite dimensional Banach space. Depending on the sign of two explicit scalar indicators, we see that the limit dynamics presents, under quite generic assumptions, the alternation of three possible regimes: the elastic regime, when the limit equation is just the equation of linearized elasticity, the slow dynamics, when the strain evolves smoothly on the yield surface and plastic flow is produced, and the fast dynamics, which may happen only in the softening regime, where\\nviscous solutions exhibit a jump across a heteroclinic orbit of an auxiliary system.10aCam-Clay plasticity1 aDal Maso, Gianni1 aSolombrino, Francesco uhttp://hdl.handle.net/1963/367100741nas a2200133 4500008004300000245009200043210006900135260001900204520028800223100001800511700002100529700002100550856003600571 2010 en_Ud 00aThe reductions of the dispersionless 2D Toda hierarchy and their Hamiltonian structures0 areductions of the dispersionless 2D Toda hierarchy and their Ham bIOP Publishing3 aWe study finite-dimensional reductions of the dispersionless 2D Toda hierarchy showing that the consistency conditions for such reductions are given by a system of radial Loewner equations. We then construct their Hamiltonian structures, following an approach proposed by Ferapontov.1 aCarlet, Guido1 aLorenzoni, Paolo1 aRaimondo, Andrea uhttp://hdl.handle.net/1963/384601121nas a2200121 4500008004300000245007400043210006900117260003700186520069600223100002200919700002200941856003600963 2010 en_Ud 00aRiemann-Roch theorems and elliptic genus for virtually smooth schemes0 aRiemannRoch theorems and elliptic genus for virtually smooth sch bMathematical Sciences Publishers3 aFor a proper scheme X with a fixed 1-perfect obstruction theory, we define virtual versions of holomorphic Euler characteristic, chi y-genus, and elliptic genus; they are deformation invariant, and extend the usual definition in the smooth case. We prove virtual versions of the Grothendieck-Riemann-Roch and Hirzebruch-Riemann-Roch theorems. We show that the virtual chi y-genus is a polynomial, and use this to define a virtual topological Euler characteristic. We prove that the virtual elliptic genus satisfies a Jacobi modularity property; we state and prove a localization theorem in the toric equivariant case. We show how some of our results apply to moduli spaces of stable sheaves.1 aFantechi, Barbara1 aGöttsche, Lothar uhttp://hdl.handle.net/1963/388801810nas a2200121 4500008004300000245007000043210006600113520141500179100001901594700002201613700001701635856003601652 2010 en_Ud 00aThe role of membrane viscosity in the dynamics of fluid membranes0 arole of membrane viscosity in the dynamics of fluid membranes3 aFluid membranes made out of lipid bilayers are the fundamental separation structure in eukaryotic cells. Many physiological processes rely on dramatic shape and topological changes (e.g. fusion, fission) of fluid membrane systems. Fluidity is key to the versatility and constant reorganization of lipid bilayers. Here, we study the role of the membrane intrinsic viscosity, arising from the friction of the lipid molecules as they rearrange to accommodate shape changes, in the dynamics of morphological changes of fluid vesicles. In particular, we analyze the competition between the membrane viscosity and the viscosity of the bulk fluid surrounding the vesicle as the dominant dissipative mechanism. We consider the relaxation dynamics of fluid vesicles put in an out-of-equilibrium state, but conclusions can be drawn regarding the kinetics or power consumption in regulated shape changes in the cell. On the basis of numerical calculations, we find that the dynamics arising from the membrane viscosity are qualitatively different from the dynamics arising from the bulk viscosity. When these two dissipation mechanisms are put in competition, we find that for small vesicles the membrane dissipation dominates, with a relaxation time that scales as the size of the vesicle to the power 2. For large vesicles, the bulk dissipation dominates, and the exponent in the relaxation time vs. size relation is 3.1 aArroyo, Marino1 aDeSimone, Antonio1 aHeltai, Luca uhttp://hdl.handle.net/1963/393000486nas a2200121 4500008004100000245011700041210006900158260003300227300001400260490000700274100002700281856005600308 2010 eng d00aSemiclassical evolution of two rotating solitons for the Nonlinear Schrödinger Equation with electric potential0 aSemiclassical evolution of two rotating solitons for the Nonline bKhayyam Publishing, Inc.c03 a315–3480 v151 aSelvitella, Alessandro uhttps://projecteuclid.org:443/euclid.ade/135585475201102nas a2200109 4500008004300000245007400043210006900117520073300186100002100919700001600940856003600956 2010 en_Ud 00aOn semistable principal bundles over complex projective manifolds, II0 asemistable principal bundles over complex projective manifolds I3 aLet (X, \\\\omega) be a compact connected Kaehler manifold of complex dimension d and E_G a holomorphic principal G-bundle on X, where G is a connected reductive linear algebraic group defined over C. Let Z (G) denote the center of G. We prove that the following three statements are equivalent: (1) There is a parabolic subgroup P of G and a holomorphic reduction of the structure group of E_G to P (say, E_P) such that the bundle obtained by extending the structure group of E_P to L(P)/Z(G) (where L(P) is the Levi quotient of P) admits a flat connection; (2) The adjoint vector bundle ad(E_G) is numerically flat; (3) The principal G-bundle E_G is pseudostable, and the degree of the charateristic class c_2(ad(E_G) is zero.1 aBiswas, Indranil1 aBruzzo, Ugo uhttp://hdl.handle.net/1963/340400622nas a2200109 4500008004300000245010100043210006900144520021400213100002900427700002000456856003600476 2010 en_Ud 00aSharp nonexistence results for a linear elliptic inequality involving Hardy and Leray potentials0 aSharp nonexistence results for a linear elliptic inequality invo3 aIn this paper we deal with nonnegative distributional supersolutions for a class of linear\\nelliptic equations involving inverse-square potentials and logarithmic weights. We prove sharp nonexistence results.1 aFall, Mouhamed Moustapha1 aMusina, Roberta uhttp://hdl.handle.net/1963/386900794nas a2200121 4500008004300000245008000043210006900123520037400192100001900566700002500585700002600610856003600636 2010 en_Ud 00aShell theories arising as low energy Gamma-limit of 3d nonlinear elasticity0 aShell theories arising as low energy Gammalimit of 3d nonlinear 3 aWe discuss the limiting behavior (using the notion of gamma-limit) of the 3d nonlinear elasticity for thin shells around an arbitrary smooth 2d surface. In particular, under the assumption that the elastic energy of deformations scales like h4, h being the thickness of a shell, we derive a limiting theory which is a generalization of the von Karman theory for plates.1 aLewicka, Marta1 aMora, Maria Giovanna1 aPakzad, Mohammad Reza uhttp://hdl.handle.net/1963/260101244nas a2200145 4500008004100000022001300041245008800054210006900142300001200211490000800223520070400231100002400935700002000959856011900979 2010 eng d a0003952700aSobolev periodic solutions of nonlinear wave equations in higher spatial dimensions0 aSobolev periodic solutions of nonlinear wave equations in higher a609-6420 v1953 aWe prove the existence of Cantor families of periodic solutions for nonlinear wave equations in higher spatial dimensions with periodic boundary conditions. We study both forced and autonomous PDEs. In the latter case our theorems generalize previous results of Bourgain to more general nonlinearities of class C k and assuming weaker non-resonance conditions. Our solutions have Sobolev regularity both in time and space. The proofs are based on a differentiable Nash-Moser iteration scheme, where it is sufficient to get estimates of interpolation-type for the inverse linearized operators. Our approach works also in presence of very large "clusters of small divisors". © Springer-Verlag (2009).1 aBerti, Massimiliano1 aBolle, Philippe uhttp://www.math.sissa.it/publication/sobolev-periodic-solutions-nonlinear-wave-equations-higher-spatial-dimensions00906nas a2200109 4500008004300000245009100043210006900134520052300203100001800726700001600744856003600760 2010 en_Ud 00aSolitonic asymptotics for the Korteweg-de Vries equation in the small dispersion limit0 aSolitonic asymptotics for the Kortewegde Vries equation in the s3 aWe study the small dispersion limit for the Korteweg-de Vries (KdV) equation $u_t+6uu_x+\\\\epsilon^{2}u_{xxx}=0$ in a critical scaling regime where $x$ approaches the trailing edge of the region where the KdV solution shows oscillatory behavior. Using the Riemann-Hilbert approach, we obtain an asymptotic expansion for the KdV solution in a double scaling limit, which shows that the oscillations degenerate to sharp pulses near the trailing edge. Locally those pulses resemble soliton solutions of the KdV equation.1 aGrava, Tamara1 aClaeys, Tom uhttp://hdl.handle.net/1963/383901005nas a2200121 4500008004300000245005700043210005600100520062300156100002000779700002400799700002400823856003600847 2010 en_Ud 00aTaming open/closed string duality with a Losev trick0 aTaming openclosed string duality with a Losev trick3 aA target space string field theory formulation for open and closed B-model is provided by giving a Batalin-Vilkovisky quantization of the holomorphic Chern-Simons theory with off-shell gravity background. The target space expression for the coefficients of the holomorphic anomaly equation for open strings are obtained. Furthermore, open/closed string duality is proved from a judicious integration over the open string fields. In particular, by restriction to the case of independence on continuous open moduli, the shift formulas of [7] are reproduced and shown therefore to encode the data of a closed string dual.1 aBonelli, Giulio1 aPrudenziati, Andrea1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/385501029nas a2200157 4500008004100000245008100041210006900122300001000191490000800201520055000209100001800759700001700777700001600794700001800810856004300828 2010 eng d00aA three-dimensional model for the dynamics and hydrodynamics of rowing boats0 athreedimensional model for the dynamics and hydrodynamics of row a51-610 v2243 aThis paper proposes a new model describing the dynamics of a rowing boat for general three-dimensional motions. The complex interaction between the different components of the rowers–-oars–-boat system is analysed and reduced to a set of ordinary differential equations governing the rigid motion along the six degrees of freedom. To treat the unstable nature of the physical problem, a rather simple (but effective) control model is included, which mimics the main active control techniques adopted by the rowers during their action.

1 aFormaggia, L.1 aMola, Andrea1 aParolini, N1 aPischiutta, M uhttps://doi.org/10.1243/17543371jset4601175nas a2200133 4500008004300000245008500043210006900128260001300197520072500210100002900935700002000964700002100984856003601005 2010 en_Ud 00aA time-dependent perturbative analysis for a quantum particle in a cloud chamber0 atimedependent perturbative analysis for a quantum particle in a bSpringer3 aWe consider a simple model of a cloud chamber consisting of a test particle (the alpha-particle) interacting with two other particles (the atoms of the vapour) subject to attractive potentials centered in $a_1, a_2 \\\\in \\\\mathbb{R}^3$. At time zero the alpha-particle is described by an outgoing spherical wave centered in the origin and the atoms are in their ground state. We show that, under suitable assumptions on the physical parameters of the system and up to second order in perturbation theory, the probability that both atoms are ionized is negligible unless $a_2$ lies on the line joining the origin with $a_1$. The work is a fully time-dependent version of the original analysis proposed by Mott in 1929.1 aDell'Antonio, Gianfausto1 aFigari, Rodolfo1 aTeta, Alessandro uhttp://hdl.handle.net/1963/396901480nas a2200097 4500008004300000245008700043210006900130520112200199100002501321856003601346 2010 en_Ud 00aTwisted Covariance as a Non Invariant Restriction of the Fully Covariant DFR Model0 aTwisted Covariance as a Non Invariant Restriction of the Fully C3 aWe discuss twisted covariance over the noncommutative spacetime algebra generated by the relations [q_theta^mu,q_theta^nu]=i theta^{mu nu}, where the matrix theta is treated as fixed (not a tensor), and we refrain from using the asymptotic Moyal expansion of the twists. We show that the tensor nature of theta is only hidden in the formalism: in particular if theta fulfils the DFR conditions, the twisted Lorentz covariant model of the flat quantum spacetime may be equivalently described in terms of the DFR model, if we agree to discard a huge non invariant set of localisation states; it is only this last step which, if taken as a basic assumption, severely breaks the relativity principle. We also will show that the above mentioned, relativity breaking, ad hoc rejection of localisation states is an independent, unnecessary assumption, as far as some popular approaches to quantum field theory on the quantum Minkowski spacetime are concerned. The above should raise some concerns about speculations on possible observable consequences of arbitrary choices of theta in arbitrarily selected privileged frames.1 aPiacitelli, Gherardo uhttp://hdl.handle.net/1963/360501396nas a2200157 4500008004300000245007000043210006800113260001300181520090200194100002501096700001701121700002301138700002001161700002101181856003601202 2010 en_Ud 00aTwo-dimensional almost-Riemannian structures with tangency points0 aTwodimensional almostRiemannian structures with tangency points bElsevier3 aTwo-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We study the relation between the topological invariants of an almost-Riemannian structure on a compact oriented surface and the rank-two vector bundle over the surface which defines the structure. We analyse the generic case including the presence of tangency points, i.e. points where two generators of the distribution and their Lie bracket are linearly dependent. The main result of the paper provides a classification of oriented almost-Riemannian structures on compact oriented surfaces in terms of the Euler number of the vector bundle corresponding to the structure. Moreover, we present a Gauss-Bonnet formula for almost-Riemannian structures with tangency points.

1 aAgrachev, Andrei, A.1 aBoscain, Ugo1 aCharlot, Grégoire1 aGhezzi, Roberta1 aSigalotti, Mario uhttp://hdl.handle.net/1963/387001011nas a2200121 4500008004300000245008300043210006900126520059000195100001600785700002600801700002600827856003600853 2010 en_Ud 00aUhlenbeck-Donaldson compactification for framed sheaves on projective surfaces0 aUhlenbeckDonaldson compactification for framed sheaves on projec3 aWe construct a compactification $M^{\\\\mu ss}$ of the Uhlenbeck-Donaldson type for the moduli space of slope stable framed bundles. This is a kind of a moduli space of slope semistable framed sheaves. We show that there exists a projective morphism $\\\\gamma \\\\colon M^s \\\\to M^{\\\\mu ss}$, where $M^s$ is the moduli space of S-equivalence classes of Gieseker-semistable framed sheaves. The space $M^{\\\\mu ss}$ has a natural set-theoretic stratification which allows one, via a Hitchin-Kobayashi correspondence, to compare it with the moduli spaces of framed ideal instantons.1 aBruzzo, Ugo1 aMarkushevich, Dimitri1 aTikhomirov, Alexander uhttp://hdl.handle.net/1963/404900513nas a2200121 4500008004100000022001400041245014500055210006900200300001600269100001900285700002200304856006500326 2010 eng d a1073-792800aUniversality in the profile of the semiclassical limit solutions to the focusing nonlinear Schrödinger equation at the first breaking curve0 aUniversality in the profile of the semiclassical limit solutions a2119–21671 aBertola, Marco1 aTovbis, Alexander uhttp://0-dx.doi.org.mercury.concordia.ca/10.1093/imrn/rnp19600894nas a2200109 4500008004100000245007500041210006900116260001000185520052800195100002500723856003600748 2010 en d00aWell-posed infinite horizon variational problems on a compact manifold0 aWellposed infinite horizon variational problems on a compact man bSISSA3 aWe give an effective sufficient condition for a variational problem with infinite horizon on a compact Riemannian manifold M to admit a smooth optimal synthesis, i. e., a smooth dynamical system on M whose positive semi-trajectories are solutions to the problem. To realize the synthesis, we construct an invariant Lagrangian submanifold (well-projected to M) of the flow of extremals in the cotangent bundle T*M. The construction uses the curvature of the flow in the cotangent bundle and some ideas of hyperbolic dynamics1 aAgrachev, Andrei, A. uhttp://hdl.handle.net/1963/645801174nas a2200109 4500008004300000245005400043210005300097520082800150100002900978700002101007856003601028 2009 en_Ud 00a1D periodic potentials with gaps vanishing at k=00 a1D periodic potentials with gaps vanishing at k03 aAppearance of energy bands and gaps in the dispersion relations of a periodic potential is a standard feature of Quantum Mechanics. We investigate the class of one-dimensional periodic potentials for which all gaps vanish at the center of the Brillouin zone. We characterise themthrough a necessary and sufficient condition. Potentials of the form we focus on arise in different fields of Physics, from supersymmetric Quantum Mechanics, to Korteweg-de Vries equation theory and classical diffusion problems. The O.D.E. counterpart to this problem is the characterisation of periodic potentials for which coexistence occurs of linearly independent solutions of the corresponding Schrödinger equation (Hill\\\'s equation). This result is placed in the perspective of the previous related results available in the literature.1 aMichelangeli, Alessandro1 aZagordi, Osvaldo uhttp://hdl.handle.net/1963/181800396nas a2200109 4500008004300000245007300043210006900116100002200185700002300207700002000230856003600250 2009 en_Ud 00aBiological Fluid Dynamics, Non-linear Partial Differential Equations0 aBiological Fluid Dynamics Nonlinear Partial Differential Equatio1 aDeSimone, Antonio1 aAlouges, François1 aLefebvre, Aline uhttp://hdl.handle.net/1963/263002193nas a2200109 4500008004300000245008700043210006900130520180600199100002302005700001902028856003602047 2009 en_Ud 00aThe boundary Riemann solver coming from the real vanishing viscosity approximation0 aboundary Riemann solver coming from the real vanishing viscosity3 aWe study the limit of the hyperbolic-parabolic approximation $$ \\\\begin{array}{lll} v_t + \\\\tilde{A} ( v, \\\\, \\\\varepsilon v_x ) v_x = \\\\varepsilon \\\\tilde{B}(v ) v_{xx} \\\\qquad v \\\\in R^N\\\\\\\\ \\\\tilde \\\\beta (v (t, \\\\, 0)) = \\\\bar g \\\\\\\\ v (0, \\\\, x) = \\\\bar v_0. \\\\\\\\ \\\\end{array} \\\\right. $$\\nThe function $\\\\tilde \\\\beta$ is defined in such a way to guarantee that the initial boundary value problem is well posed even if $\\\\tilde \\\\beta$ is not invertible.\\nThe data $\\\\bar g$ and $\\\\bar v_0$ are constant. When $\\\\tilde B$ is invertible, the previous problem takes the simpler form $$ \\\\left\\\\{ \\\\begin{array}{lll} v_t + \\\\tilde{A} \\\\big( v, \\\\, \\\\varepsilon v_x \\\\big) v_x = \\\\varepsilon \\\\tilde{B}(v ) v_{xx} \\\\qquad v \\\\in \\\\mathbb{R}^N\\\\\\\\ v (t, \\\\, 0) \\\\equiv \\\\bar v_b \\\\\\\\ v (0, \\\\, x) \\\\equiv \\\\bar{v}_0. \\\\\\\\ \\\\end{array} \\\\right. $$\\nAgain, the data $\\\\bar v_b$ and $\\\\bar v_0$ are constant. The conservative case is included in the previous formulations. It is assumed convergence of the v, smallness of the total variation and other technical hypotheses and it is provided a complete characterization of the limit. The most interesting points are the following two. First, the boundary characteristic case is considered, i.e. one eigenvalue of $\\\\tilde A$ can be 0.\\n Second, as pointed out before we take into account the possibility that $\\\\tilde B$ is not invertible. To deal with this case, we take as hypotheses conditions that were introduced by Kawashima and Shizuta relying on physically meaningful examples. We also introduce a new condition of block linear degeneracy. We prove that, if it is not satisfied, then pathological behaviours may occur.1 aBianchini, Stefano1 aSpinolo, Laura uhttp://hdl.handle.net/1963/183100355nas a2200097 4500008004300000245006900043210006800112100002100180700002000201856003600221 2009 en_Ud 00aBubbles with prescribed mean curvature: the variational approach0 aBubbles with prescribed mean curvature the variational approach1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/365900389nas a2200133 4500008004100000245003400041210003000075300001500105490000800120100001900128700001600147700001900163856007300182 2009 eng d00aThe Cauchy two–matrix model0 aCauchy two–matrix model a983–10140 v2871 aBertola, Marco1 aGekhtman, M1 aSzmigielski, J uhttp://www.math.sissa.it/publication/cauchy-two%E2%80%93matrix-model02219nas a2200157 4500008004300000245014000043210006900183260001900252520163800271100002601909700002101935700002801956700002201984700001902006856003602025 2009 en_Ud 00aCharacterization of the time course of changes of the evoked electrical activity in a model of a chemically-induced neuronal plasticity0 aCharacterization of the time course of changes of the evoked ele bBioMed Central3 aBACKGROUND: Neuronal plasticity is initiated by transient elevations of neuronal networks activity leading to changes of synaptic properties and providing the basis for memory and learning 1. An increase of electrical activity can be caused by electrical stimulation 2 or by pharmacological manipulations: elevation of extracellular K+ 3, blockage of inhibitory pathways 4 or by an increase of second messengers intracellular concentrations 5. Neuronal plasticity is mediated by several biochemical pathways leading to the modulation of synaptic strength, density of ionic channels and morphological changes of neuronal arborisation 6. On a time scale of a few minutes, neuronal plasticity is mediated by local protein trafficking 7 while, in order to sustain modifications beyond 2-3 h, changes of gene expression are required 8. FINDINGS: In the present manuscript we analysed the time course of changes of the evoked electrical activity during neuronal plasticity and we correlated it with a transcriptional analysis of the underlying changes of gene expression. Our investigation shows that treatment for 30 min. with the GABAA receptor antagonist gabazine (GabT) causes a potentiation of the evoked electrical activity occurring 2-4 hours after GabT and the concomitant up-regulation of 342 genes. Inhibition of the ERK1/2 pathway reduced but did not abolish the potentiation of the evoked response caused by GabT. In fact not all the genes analysed were blocked by ERK1/2 inhibitors. CONCLUSION: These results are in agreement with the notion that neuronal plasticity is mediated by several distinct pathways working in unison.1 aBroccard, Frederic D.1 aPegoraro, Silvia1 aRuaro, Maria Elisabetta1 aAltafini, Claudio1 aTorre, Vincent uhttp://hdl.handle.net/1963/370600577nas a2200133 4500008004100000022001400041245013700055210006900192300001400261490000800275100001900283700001500302856012600317 2009 eng d a0001-870800aCommuting difference operators, spinor bundles and the asymptotics of orthogonal polynomials with respect to varying complex weights0 aCommuting difference operators spinor bundles and the asymptotic a154–2180 v2201 aBertola, Marco1 aMo, M., Y. uhttp://www.math.sissa.it/publication/commuting-difference-operators-spinor-bundles-and-asymptotics-orthogonal-polynomials00337nas a2200097 4500008004300000245006000043210005800103100002300161700001900184856003600203 2009 en_Ud 00aA connection between viscous profiles and singular ODEs0 aconnection between viscous profiles and singular ODEs1 aBianchini, Stefano1 aSpinolo, Laura uhttp://hdl.handle.net/1963/255500997nas a2200109 4500008004300000245011900043210006900162260001300231520058500244100002200829856003600851 2009 en_Ud 00aControllability and simultaneous controllability of isospectral bilinear control systems on complex flag manifolds0 aControllability and simultaneous controllability of isospectral bElsevier3 aFor isospectral bilinear control systems evolving on the so-called complex flag manifolds (i.e., on the orbits of the Hermitian matrices under unitary conjugation action) it is shown that controllability is almost always verified. Easy and generic sufficient conditions are provided. The result applies to the problem of density operator controllability of finite dimensional quantum mechanical systems. In addition, we show that systems having different drifts (corresponding for example to different Larmor frequencies) are simultaneously controllable by the same control field.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/352301061nas a2200133 4500008004300000245009500043210006900138520060700207100002200814700001700836700002100853700001700874856003600891 2009 en_Ud 00aControllability of the discrete-spectrum Schrodinger equation driven by an external field0 aControllability of the discretespectrum Schrodinger equation dri3 aWe prove approximate controllability of the bilinear Schrodinger equation in the case in which the uncontrolled Hamiltonian has discrete nonresonant\\nspectrum. The results that are obtained apply both to bounded or unbounded domains and to the case in which the control potential is bounded or unbounded. The method relies on finite-dimensional techniques applied to the\\nGalerkin approximations and permits, in addition, to get some controllability properties for the density matrix. Two examples are presented: the harmonic oscillator and the 3D well of potential controlled by suitable potentials.1 aChambrion, Thomas1 aMason, Paolo1 aSigalotti, Mario1 aBoscain, Ugo uhttp://hdl.handle.net/1963/254700583nas a2200109 4500008004300000245005200043210005200095520024400147100002500391700002100416856003600437 2009 en_Ud 00aControllability on the group of diffeomorphisms0 aControllability on the group of diffeomorphisms3 aGiven a compact manifold M, we prove that any bracket generating family of vector fields on M, which is invariant under multiplication by smooth functions, generates the connected component of identity of the group of diffeomorphisms of M.1 aAgrachev, Andrei, A.1 aCaponigro, Marco uhttp://hdl.handle.net/1963/339600806nas a2200121 4500008004300000245007400043210006700117260004800184520037100232100002100603700002400624856003600648 2009 en_Ud 00aOn the convergence of viscous approximations after shock interactions0 aconvergence of viscous approximations after shock interactions bAmerican Institute of Mathematical Sciences3 aWe consider a piecewise smooth solution to a scalar conservation law, with possibly interacting shocks. We show that, after the interactions have taken place, vanishing viscosity approximations can still be represented by a regular expansion on smooth regions and by a singular perturbation expansion near the shocks, in terms of powers of the viscosity coefficient.1 aBressan, Alberto1 aDonadello, Carlotta uhttp://hdl.handle.net/1963/341200501nas a2200145 4500008004100000022001400041245007700055210006900132300001500201490000700216100001900223700001700242700002000259856007600279 2009 eng d a1751-811300aCubic string boundary value problems and Cauchy biorthogonal polynomials0 aCubic string boundary value problems and Cauchy biorthogonal pol a454006, 130 v421 aBertola, Marco1 aGekhtman, M.1 aSzmigielski, J. uhttp://0-dx.doi.org.mercury.concordia.ca/10.1088/1751-8113/42/45/45400601270nas 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/1963/590000760nas a2200145 4500008004300000020002200043245006300065210006300128520031500191100001600506700001700522700001700539700002200556856003600578 2009 en_Ud a978-981-270-377-400aEquivariant cohomology and localization for Lie algebroids0 aEquivariant cohomology and localization for Lie algebroids3 aLet M be a manifold carrying the action of a Lie group G, and A a Lie algebroid on M equipped with a compatible infinitesimal G-action. Out of these data we construct an equivariant Lie algebroid cohomology and prove for compact G a related localization formula. As an application we prove a Bott-type formula.1 aBruzzo, Ugo1 aCirio, Lucio1 aRossi, Paolo1 aRubtsov, Vladimir uhttp://hdl.handle.net/1963/172400980nas a2200121 4500008004300000245005900043210005800102260002800160520059200188100002000780700002200800856003600822 2009 en_Ud 00aERNEST: a toolbox for chemical reaction network theory0 aERNEST a toolbox for chemical reaction network theory bOxford University Press3 aSummary: ERNEST Reaction Network Equilibria Study Toolbox is a MATLAB package which, by checking various different criteria on the structure of a chemical reaction network, can exclude the multistationarity of the corresponding reaction system. The results obtained are independent of the rate constants of the reactions, and can be used for model discrimination.\\nAvailability and Implementation: The software, implemented in MATLAB, is available under the GNU GPL free software license from http://people.sissa.it/~altafini/papers/SoAl09/. It requires the MATLAB Optimization Toolbox.1 aSoranzo, Nicola1 aAltafini, Claudio uhttp://hdl.handle.net/1963/382600361nas a2200097 4500008004300000245007300043210006900116100001800185700002400203856003600227 2009 en_Ud 00aExact results for topological strings on resolved Yp,q singularities0 aExact results for topological strings on resolved Ypq singularit1 aBrini, Andrea1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/263100512nas a2200097 4500008004300000245009600043210006900139520015000208100002000358856003600378 2009 en_Ud 00aExistence of extremals for the Maz\\\'ya and for the Caffarelli-Kohn-Nirenberg inequalities0 aExistence of extremals for the Mazya and for the CaffarelliKohnN3 aThis paper deals with some Sobolev-type inequalities with weights that were proved by Maz\\\'ya in 1980 and by Caffarelli-Kohn-Nirenberg in 1984.1 aMusina, Roberta uhttp://hdl.handle.net/1963/273900318nas a2200085 4500008004300000245006800043210006400111100002100175856003600196 2009 en_Ud 00aAn existence result for the Monge problem in R^n with norm cost0 aexistence result for the Monge problem in Rn with norm cost1 aCaravenna, Laura uhttp://hdl.handle.net/1963/364700624nas a2200109 4500008004300000245007200043210006400115520025500179100002300434700002100457856003600478 2009 en_Ud 00aOn the extremality, uniqueness and optimality of transference plans0 aextremality uniqueness and optimality of transference plans3 aWe consider the following standard problems appearing in optimal mass transportation theory: when a transference plan is extremal; when a transference plan is the unique transference plan concentrated on a set A,; when a transference plan is optimal.1 aBianchini, Stefano1 aCaravenna, Laura uhttp://hdl.handle.net/1963/369200938nas a2200109 4500008004300000245007800043210006900121520056500190100001700755700002000772856003600792 2009 en_Ud 00aFamilies of Monads and Instantons from a Noncommutative ADHM Construction0 aFamilies of Monads and Instantons from a Noncommutative ADHM Con3 aWe give a \\\\theta-deformed version of the ADHM construction of SU(2) instantons with arbitrary topological charge on the sphere S^4. Classically the instanton gauge fields are constructed from suitable monad data; we show that in the deformed case the set of monads is itself a noncommutative space. We use these monads to construct noncommutative `families\\\' of SU(2) instantons on the deformed sphere S^4_\\\\theta. We also compute the topological charge of each of the families. Finally we discuss what it means for such families to be gauge equivalent.1 aBrain, Simon1 aLandi, Giovanni uhttp://hdl.handle.net/1963/347800454nas a2200133 4500008004100000022001400041245006900055210006900124300001400193490000700207100001900214700001600233856007100249 2009 eng d a0176-427600aFirst colonization of a spectral outpost in random matrix theory0 aFirst colonization of a spectral outpost in random matrix theory a225–2630 v301 aBertola, Marco1 aLee, S., Y. uhttp://0-dx.doi.org.mercury.concordia.ca/10.1007/s00365-008-9026-y08321nas a2200145 4500008004100000245008100041210006900122260001300191300001600204490000700220520785400227100003008081700001908111856004508130 2009 eng d00aFoliations of small tubes in Riemannian manifolds by capillary minimal discs0 aFoliations of small tubes in Riemannian manifolds by capillary m bElsevier a4422–44400 v703 aLetting be an embedded curve in a Riemannian manifold , we prove the existence of minimal disc-type surfaces centered at inside the surface of revolution of around , having small radius, and intersecting it with constant angles. In particular we obtain that small tubular neighborhoods can be foliated by minimal discs.

1 aFall, Mouhamed, Moustapha1 aMercuri, Carlo uhttps://doi.org/10.1016/j.na.2008.10.02400873nas a2200133 4500008004300000245004600043210004600089260001300135520049300148100002000641700001800661700002400679856003600703 2009 en_Ud 00aGauged Laplacians on quantum Hopf bundles0 aGauged Laplacians on quantum Hopf bundles bSpringer3 aWe study gauged Laplacian operators on line bundles on a quantum 2-dimensional sphere. Symmetry under the (co)-action of a quantum group allows for their complete diagonalization. These operators describe `excitations moving on the quantum sphere\\\' in the field of a magnetic monopole. The energies are not invariant under the exchange monopole/antimonopole, that is under inverting the direction of the magnetic field. There are potential applications to models of quantum Hall effect.1 aLandi, Giovanni1 aReina, Cesare1 aZampini, Alessandro uhttp://hdl.handle.net/1963/354001528nas a2200121 4500008004100000020002200041245010900063210006900172260001000241520109900251100002001350856003601370 2009 en d a978-90-481-2810-500aHamiltonian perturbations of hyperbolic PDEs: from classification results to the properties of solutions0 aHamiltonian perturbations of hyperbolic PDEs from classification bSISSA3 aWe begin with presentation of classi cation results in the theory of Hamiltonian\\r\\nPDEs with one spatial dimension depending on a small parameter. Special\\r\\nattention is paid to the deformation theory of integrable hierarchies, including an\\r\\nimportant subclass of the so-called integrable hierarchies of the topological type\\r\\nassociated with semisimple Frobenius manifolds. Many well known equations of\\r\\nmathematical physics, such as KdV, NLS, Toda, Boussinesq etc., belong to this\\r\\nsubclass, but there are many new integrable PDEs, some of them being of interest\\r\\nfor applications. Connections with the theory of Gromov{Witten invariants\\r\\nand random matrices are outlined. We then address the problem of comparative\\r\\nstudy of singularities of solutions to the systems of first order quasilinear\\r\\nPDEs and their Hamiltonian perturbations containing higher derivatives. We\\r\\nformulate Universality Conjectures describing different types of critical behavior\\r\\nof perturbed solutions near the point of gradient catastrophe of the unperturbed\\r\\none.1 aDubrovin, Boris uhttp://hdl.handle.net/1963/647000381nas a2200097 4500008004300000245009500043210006900138100002000207700002000227856003600247 2009 en_Ud 00aHardy-Sobolev-Maz\\\'ja inequalities: symmetry and breaking symmetry of extremal functions0 aHardySobolevMazja inequalities symmetry and breaking symmetry of1 aGazzini, Marita1 aMusina, Roberta uhttp://hdl.handle.net/1963/256900927nas a2200133 4500008004300000245007300043210006900116520048700185100002100672700001900693700002000712700002500732856003600757 2009 en_Ud 00aA higher order model for image restoration: the one dimensional case0 ahigher order model for image restoration the one dimensional cas3 aThe higher order total variation-based model for image restoration proposed by Chan, Marquina, and Mulet in [6] is analyzed in one dimension. A suitable functional framework in which the minimization problem is well posed is being proposed and it is proved analytically that the\\nhigher order regularizing term prevents the occurrence of the staircase effect. The generalized version of the model considered here includes, as particular cases, some curvature dependent functionals.1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/317400361nas a2200097 4500008004300000245007700043210006900120100001600189700002200205856003600227 2009 en_Ud 00aHolomorphic equivariant cohomology of Atiyah algebroids and localization0 aHolomorphic equivariant cohomology of Atiyah algebroids and loca1 aBruzzo, Ugo1 aRubtsov, Vladimir uhttp://hdl.handle.net/1963/377401152nas a2200121 4500008004300000245007700043210006900120260000900189520075400198100002100952700002100973856003600994 2009 en_Ud 00aHomogenization of fiber reinforced brittle materials: the extremal cases0 aHomogenization of fiber reinforced brittle materials the extrema bSIAM3 aWe analyze the behavior of a fragile material reinforced by a reticulated elastic unbreakable structure in the case of antiplane shear. The microscopic geometry of this material is described by means of two small parameters: the period $\\\\varepsilon$ of the grid and the ratio $\\\\delta$ between the thickness of the fibers and the period $\\\\varepsilon$. We show that the asymptotic behavior as $\\\\varepsilon\\\\to0^+$ and $\\\\delta\\\\to0^+$ depends dramatically on the relative size of these parameters. Indeed, in the two cases considered, i.e., $\\\\varepsilon\\\\ll\\\\delta$ and $\\\\varepsilon\\\\gg\\\\delta$, we obtain two different limit models: a perfectly elastic model and an elastic model with macroscopic cracks, respectively.1 aBarchiesi, Marco1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/270500963nas a2200133 4500008004300000245008100043210006900124260001300193520052900206100001800735700002200753700001800775856003600793 2009 en_Ud 00aInitial value problem of the Whitham equations for the Camassa-Holm equation0 aInitial value problem of the Whitham equations for the CamassaHo bElsevier3 aWe study the Whitham equations for the Camassa-Holm equation. The equations are neither strictly hyperbolic nor genuinely nonlinear. We are interested in the initial value problem of the Whitham equations. When the initial values are given by a step function, the Whitham solution is self-similar. When the initial values are given by a smooth function, the Whitham solution exists within a cusp in the x-t plane. On the boundary of the cusp, the Whitham equation matches the Burgers solution, which exists outside the cusp.1 aGrava, Tamara1 aPierce, Virgil U.1 aTian, Fei-Ran uhttp://hdl.handle.net/1963/342901520nas a2200133 4500008004300000245008600043210006900129520106500198100002501263700001701288700002401305700002101329856003601350 2009 en_Ud 00aThe intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups0 aintrinsic hypoelliptic Laplacian and its heat kernel on unimodul3 aWe present an invariant definition of the hypoelliptic Laplacian on sub-Riemannian structures with constant growth vector, using the Popp\\\'s volume form introduced by Montgomery. This definition generalizes the one of the Laplace-Beltrami operator in Riemannian geometry. In the case of left-invariant problems on unimodular Lie groups we prove that it coincides with the usual sum of squares.\\nWe then extend a method (first used by Hulanicki on the Heisenberg group) to compute explicitly the kernel of the hypoelliptic heat equation on any unimodular Lie group of type I. The main tool is the noncommutative Fourier transform. We then study some relevant cases: SU(2), SO(3), SL(2) (with the metrics inherited by the Killing form), and the group SE(2) of rototranslations of the plane.\\nOur study is motivated by some recent results about the cut and conjugate loci on these sub-Riemannian manifolds. The perspective is to understand how singularities of the sub-Riemannian distance reflect on the kernel of the corresponding hypoelliptic heat equation.1 aAgrachev, Andrei, A.1 aBoscain, Ugo1 aGauthier, Jean-Paul1 aRossi, Francesco uhttp://hdl.handle.net/1963/266901588nas a2200133 4500008004300000245010000043210006900143260000900212520113200221100002101353700002201374700002201396856003601418 2009 en_Ud 00aInvestigating the Conformational Stability of Prion Strains through a Kinetic Replication Model0 aInvestigating the Conformational Stability of Prion Strains thro bPLoS3 aPrion proteins are known to misfold into a range of different aggregated forms, showing different phenotypic and pathological states. Understanding strain specificities is an important problem in the field of prion disease. Little is known about which PrPSc structural properties and molecular mechanisms determine prion replication, disease progression and strain phenotype. The aim of this work is to investigate, through a mathematical model, how the structural stability of different aggregated forms can influence the kinetics of prion replication. The model-based results suggest that prion strains with different conformational stability undergoing in vivo replication are characterizable in primis by means of different rates of breakage. A further role seems to be played by the aggregation rate (i.e. the rate at which a prion fibril grows). The kinetic variability introduced in the model by these two parameters allows us to reproduce the different characteristic features of the various strains (e.g., fibrils\\\' mean length) and is coherent with all experimental observations concerning strain-specific behavior.1 aZampieri, Mattia1 aLegname, Giuseppe1 aAltafini, Claudio uhttp://hdl.handle.net/1963/398902238nas a2200109 4500008004300000245010000043210006900143520184600212100001602058700001802074856003602092 2009 en_Ud 00aJacobi Equations and Comparison Theorems for Corank 1 Sub-Riemannian structures with symmetries0 aJacobi Equations and Comparison Theorems for Corank 1 SubRiemann3 aThe Jacobi curve of an extremal of optimal control problem is a curve in a Lagrangian Grassmannian defined up to a symplectic transformation and containing all information about the solutions of the Jacobi equations along this extremal. In our previous works we constructed the canonical\\nbundle of moving frames and the complete system of symplectic invariants, called curvature maps, for\\nparametrized curves in Lagrange Grassmannians satisfying very general assumptions. The structural\\nequation for a canonical moving frame of the Jacobi curve of an extremal can be interpreted as the\\nnormal form for the Jacobi equation along this extremal and the curvature maps can be seen as the\\n\\\"coefficients\\\"of this normal form. In the case of a Riemannian metric there is only one curvature map and it is naturally related to the Riemannian sectional curvature. In the present paper we study the curvature maps for a sub-Riemannian structure on a corank 1 distribution having an additional transversal infinitesimal symmetry. After the factorization by the integral foliation of this symmetry, such sub-Riemannian structure can be reduced to a Riemannian manifold equipped with a closed 2-form(a magnetic field). We obtain explicit expressions for the curvature maps of the original sub-Riemannian structure in terms of the curvature tensor of this Riemannian manifold and the magnetic field. We also estimate the number of conjugate points along the sub-Riemannian extremals in terms of the bounds for the curvature tensor of this Riemannian manifold and the magnetic field in the case of an uniform magnetic field. The language developed for the calculation of the curvature maps can be applied to more general sub-Riemannian structures with symmetries, including sub-Riemmannian structures appearing naturally in Yang-Mills fields.1 aChengbo, Li1 aZelenko, Igor uhttp://hdl.handle.net/1963/373600554nas a2200145 4500008004100000245010200041210006900143260005400212300001400266490000800280100001700288700002500305700002300330856005500353 2009 eng d00aLow-Frequency Variations of Force Coefficients on Square Cylinders with Sharp and Rounded Corners0 aLowFrequency Variations of Force Coefficients on Square Cylinder bAmerican Society of Civil Engineers ({ASCE})cjul a828–8350 v1351 aMola, Andrea1 aBordonaro, Giancarlo1 aHajj, Muhammad, R. uhttps://doi.org/10.1061/(asce)st.1943-541x.000003400443nas a2200145 4500008004100000022001400041245004700055210004700102300001500149490000700164100001900171700001600190700001500206856007600221 2009 eng d a1751-811300aMesoscopic colonization in a spectral band0 aMesoscopic colonization in a spectral band a415204, 170 v421 aBertola, Marco1 aLee, S., Y.1 aMo, M., Y. uhttp://0-dx.doi.org.mercury.concordia.ca/10.1088/1751-8113/42/41/41520400903nas a2200145 4500008004100000245006400041210006300105260002900168300001600197490000700213520043600220100003000656700001900686856005200705 2009 eng d00aMinimal disc-type surfaces embedded in a perturbed cylinder0 aMinimal disctype surfaces embedded in a perturbed cylinder bKhayyam Publishing, Inc. a1115–11240 v223 aIn the present note we deal with small perturbations of an infinite cylinder in the 3D euclidian space. We find minimal disc-type surfaces embedded in the cylinder and intersecting its boundary perpendicularly. The existence and localization of those minimal discs is a consequence of a non-degeneracy condition for the critical points of a functional related to the oscillations of the cylinder from the flat configuration.

1 aFall, Mouhamed, Moustapha1 aMercuri, Carlo uhttps://projecteuclid.org/euclid.die/135601940700433nas a2200157 4500008004100000245004500041210004300086260001500129300001400144490000700158100001800165700001700183700001700200700002100217856003700238 2009 eng d00aA model for the dynamics of rowing boats0 amodel for the dynamics of rowing boats bWileycsep a119–1430 v611 aFormaggia, L.1 aMiglio, Edie1 aMola, Andrea1 aMontano, Antonio uhttps://doi.org/10.1002/fld.194000606nas a2200133 4500008004300000245006900043210006700112260002300179520017500202100002200377700001800399700001900417856003600436 2009 en_Ud 00aA model for the orbifold Chow ring of weighted projective spaces0 amodel for the orbifold Chow ring of weighted projective spaces bTaylor and Francis3 aWe construct an isomorphism of graded Frobenius algebras between the orbifold Chow ring of weighted projective spaces and graded algebras of groups of roots of the unity.1 aBoissiere, Samuel1 aMann, Etienne1 aPerroni, Fabio uhttp://hdl.handle.net/1963/358900388nas a2200109 4500008004100000245005500041210005500096300001200151490000700163100001900170856008900189 2009 eng d00aMoment determinants as isomonodromic tau functions0 aMoment determinants as isomonodromic tau functions a29–500 v221 aBertola, Marco uhttp://www.math.sissa.it/publication/moment-determinants-isomonodromic-tau-functions00336nas a2200097 4500008004300000245005900043210005500102100002300157700002200180856003600202 2009 en_Ud 00aThe Monge problem for distance cost in geodesic spaces0 aMonge problem for distance cost in geodesic spaces1 aBianchini, Stefano1 aCavalletti, Fabio uhttp://hdl.handle.net/1963/370301344nas a2200145 4500008004300000245009700043210006900140260001900209520085100228100002001079700002101099700002001120700002201140856003601162 2009 en_Ud 00amRNA stability and the unfolding of gene expression in the long-period yeast metabolic cycle0 amRNA stability and the unfolding of gene expression in the longp bBioMed Central3 aBackground: In yeast, genome-wide periodic patterns associated with energy-metabolic oscillations have been shown recently for both short (approx. 40 min) and long (approx. 300 min) periods.\\nResults: The dynamical regulation due to mRNA stability is found to be an important aspect of the genome-wide coordination of the long-period yeast metabolic cycle. It is shown that for periodic genes, arranged in classes according either to expression profile or to function, the pulses of mRNA abundance have phase and width which are directly proportional to the corresponding turnover rates.\\nConclusion: The cascade of events occurring during the yeast metabolic cycle (and their correlation with mRNA turnover) reflects to a large extent the gene expression program observable in other dynamical contexts such as the response to stresses/stimuli.1 aSoranzo, Nicola1 aZampieri, Mattia1 aFarina, Lorenzo1 aAltafini, Claudio uhttp://hdl.handle.net/1963/363000530nas a2200121 4500008004300000245006400043210006200107520013300169100001900302700002500321700002600346856003600372 2009 en_Ud 00aA nonlinear theory for shells with slowly varying thickness0 anonlinear theory for shells with slowly varying thickness3 aWe study the Γ-limit of 3d nonlinear elasticity for shells of small, variable thickness, around an arbitrary smooth 2d surface.1 aLewicka, Marta1 aMora, Maria Giovanna1 aPakzad, Mohammad Reza uhttp://hdl.handle.net/1963/263200356nas a2200085 4500008004300000245010200043210006900145100002000214856003600234 2009 en_Ud 00aA note on the paper \\\"Optimizing improved Hardy inequalities\\\" by S. Filippas and A. Tertikas0 anote on the paper Optimizing improved Hardy inequalities by S Fi1 aMusina, Roberta uhttp://hdl.handle.net/1963/269801018nas a2200109 4500008004300000245005800043210005800101520067400159100002500833700001400858856003600872 2009 en_Ud 00aOptimal transportation under nonholonomic constraints0 aOptimal transportation under nonholonomic constraints3 aWe study the Monge\\\'s optimal transportation problem where the cost is given by optimal control cost. We prove the existence and uniqueness of optimal map under certain regularity conditions on the Lagrangian, absolute continuity of the measures and most importantly the absent of sharp abnormal minimizers. In particular, this result is applicable in the case of subriemannian manifolds with a 2-generating distribution and cost given by d2, where d is the subriemannian distance. Also, we discuss some properties of the optimal plan when abnormal minimizers are present. Finally, we consider some examples of displacement interpolation in the case of Grushin plane.1 aAgrachev, Andrei, A.1 aLee, Paul uhttp://hdl.handle.net/1963/217600462nas a2200133 4500008004100000022001400041245008300055210007000138300001500208490000700223100001900230700001600249856006300265 2009 eng d a0022-248800aThe partition function of the two-matrix model as an isomonodromic τ function0 apartition function of the twomatrix model as an isomonodromic τ a013529, 170 v501 aBertola, Marco1 aMarchal, O. uhttp://0-dx.doi.org.mercury.concordia.ca/10.1063/1.305486500735nas a2200109 4500008004300000245009500043210006900138520033900207100002100546700002200567856003600589 2009 en_Ud 00aQuasistatic evolution for Cam-Clay plasticity: examples of spatially homogeneous solutions0 aQuasistatic evolution for CamClay plasticity examples of spatial3 aWe study a quasistatic evolution problem for Cam-Clay plasticity under a special loading program which leads to spatially homogeneous solutions. Under some initial conditions, the solutions exhibit a softening behaviour and time discontinuities.\\nThe behavior of the solutions at the jump times is studied by a viscous approximation.1 aDal Maso, Gianni1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/339500456nas a2200133 4500008004100000022001400041245006800055210006800123300001400191490000800205100001900213700001900232856007100251 2009 eng d a0021-904500aRegularity of a vector potential problem and its spectral curve0 aRegularity of a vector potential problem and its spectral curve a353–3700 v1611 aBalogh, Ferenc1 aBertola, Marco uhttp://0-dx.doi.org.mercury.concordia.ca/10.1016/j.jat.2008.10.01001411nas a2200121 4500008004300000245004300043210004300086260003000129520105300159100001901212700002201231856003601253 2009 en_Ud 00aRelaxation dynamics of fluid membranes0 aRelaxation dynamics of fluid membranes bAmerican Physical Society3 aWe study the effect of membrane viscosity in the dynamics of liquid membranes-possibly with free or internal boundaries-driven by conservative forces (curvature elasticity and line tension) and dragged by the bulk dissipation of the ambient fluid and the friction occurring when the amphiphilic molecules move relative to each other. To this end, we formulate a continuum model which includes a form of the governing equations for a two-dimensional viscous fluid moving on a curved, time-evolving surface. The effect of membrane viscosity has received very limited attention in previous continuum studies of the dynamics of fluid membranes, although recent coarse-grained discrete simulations suggest its importance. By applying our model to the study of vesiculation and membrane fusion in a simplified geometry, we conclude that membrane viscosity plays a dominant role in the relaxation dynamics of fluid membranes of sizes comparable to those found in eukaryotic cells, and is not negligible in many large synthetic systems of current interest.1 aArroyo, Marino1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/361800362nas a2200097 4500008004300000245007600043210006900119100002000188700002000208856003600228 2009 en_Ud 00aOn a Sobolev type inequality related to the weighted p-Laplace operator0 aSobolev type inequality related to the weighted pLaplace operato1 aGazzini, Marita1 aMusina, Roberta uhttp://hdl.handle.net/1963/261300350nas a2200097 4500008004300000245006900043210006900112260001300181100002200194856003600216 2009 en_Ud 00aSome new entire solutions of semilinear elliptic equations on Rn0 aSome new entire solutions of semilinear elliptic equations on Rn bElsevier1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/364500893nas a2200109 4500008004300000245007600043210006900119520051500188100002200703700002200725856003600747 2009 en_Ud 00aStrain-order coupling in nematic elastomers: equilibrium configurations0 aStrainorder coupling in nematic elastomers equilibrium configura3 aWe consider models that describe liquid crystal elastomers either in a biaxial or in a uniaxial phase and in the framework of Frank\\\'s director theory. We prove existence of static equilibrium solutions in the presence of frustrations due to electro-mechanical boundary conditions and to applied loads and fields. We find explicit solutions arising in connection with special boundary conditions and the corresponding phase diagrams, leading to significant implications on possible experimental observations.1 aCesana, Pierluigi1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/270000754nas a2200121 4500008004300000245007200043210006900115520035700184100002200541700001600563700001700579856003600596 2009 en_Ud 00aStratos: a code for 3D free surface flows with floating constraints0 aStratos a code for 3D free surface flows with floating constrain3 aThis report presents a brief discussion of the theoretical aspects and practical implementation of STRATOS . STRATOS is a 3D code for the simulation\\nof hydrodynamic flows for incompressible fluids, in the presence of a free surface, capable of simulating the interaction between the free surface and a\\nfloating object via Lagrange multipliers......1 aDeSimone, Antonio1 aBianchi, B.1 aHeltai, Luca uhttp://hdl.handle.net/1963/370100841nas a2200121 4500008004300000245007600043210006900119520043200188100002200620700001700642700002400659856003600683 2009 en_Ud 00aTools for the Solution of PDEs Defined on Curved Manifolds with deal.II0 aTools for the Solution of PDEs Defined on Curved Manifolds with 3 aThe deal.II finite element library was originally designed to solve partial differential equations defined on one, two or three space dimensions, mostly\\nvia the Finite Element Method. In its versions prior to version 6.2, the user could not solve problems defined on curved manifolds embedded in two or\\nthree spacial dimensions. This infrastructure is needed if one wants to solve, for example, Boundary Integral Equations.1 aDeSimone, Antonio1 aHeltai, Luca1 aManigrasso, Cataldo uhttp://hdl.handle.net/1963/370001000nas a2200121 4500008004300000245006600043210006400109520060600173100002000779700002400799700001900823856003600842 2009 en_Ud 00aTopological branes, p-algebras and generalized Nahm equations0 aTopological branes palgebras and generalized Nahm equations3 aInspired by the recent advances in multiple M2-brane theory, we consider the generalizations of Nahm equations for arbitrary p-algebras. We construct the topological p-algebra quantum mechanics associated to them and we show that this can be obtained as a truncation of the topological p-brane theory previously studied by the authors. The resulting topological p-algebra quantum mechanics is discussed in detail and the relation with the M2-M5 system is pointed out in the p=3 case, providing a geometrical argument for the emergence of the 3-algebra structure in the Bagger-Lambert-Gustavsson theory1 aBonelli, Giulio1 aTanzini, Alessandro1 aZabzine, Maxim uhttp://hdl.handle.net/1963/270200416nas a2200133 4500008004100000022001400041245005800055210005700113300001500170490000700185100001900192700001800211856005300229 2009 eng d a1751-811300aTopological expansion for the Cauchy two-matrix model0 aTopological expansion for the Cauchy twomatrix model a335201, 280 v421 aBertola, Marco1 aFerrer, Prats uhttp://dx.doi.org/10.1088/1751-8113/42/33/33520100591nas a2200097 4500008004300000245004400043210004400087520030100131100002500432856003600457 2009 en_Ud 00aTwisted Covariance vs Weyl Quantisation0 aTwisted Covariance vs Weyl Quantisation3 aIn this letter we wish to clarify in which sense the tensor nature of the commutation relations [x^mu,x^nu]=i theta ^{mu nu} underlying Minkowski spacetime quantisation cannot be suppressed even in the twisted approach to Lorentz covariance. We then address the vexata quaestio \\\"why theta\\\"?1 aPiacitelli, Gherardo uhttp://hdl.handle.net/1963/345100978nas a2200121 4500008004300000245018700043210006900230520046200299100002000761700001800781700002100799856003600820 2009 en_Ud 00aOn universality of critical behaviour in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the {\\\\it tritronquée} solution to the Painlevé-I equation0 auniversality of critical behaviour in the focusing nonlinear Sch3 aWe argue that the critical behaviour near the point of ``gradient catastrophe\\\" of the solution to the Cauchy problem for the focusing nonlinear Schr\\\\\\\"odinger equation $ i\\\\epsilon \\\\psi_t +\\\\frac{\\\\epsilon^2}2\\\\psi_{xx}+ |\\\\psi|^2 \\\\psi =0$ with analytic initial data of the form $\\\\psi(x,0;\\\\epsilon) =A(x) e^{\\\\frac{i}{\\\\epsilon} S(x)}$ is approximately described by a particular solution to the Painlev\\\\\\\'e-I equation.1 aDubrovin, Boris1 aGrava, Tamara1 aKlein, Christian uhttp://hdl.handle.net/1963/252501175nas a2200109 4500008004300000245012700043210006900170520075600239100001800995700001601013856003601029 2009 en_Ud 00aUniversality of the break-up profile for the KdV equation in the small dispersion limit using the Riemann-Hilbert approach0 aUniversality of the breakup profile for the KdV equation in the 3 aWe obtain an asymptotic expansion for the solution of the Cauchy problem for the Korteweg-de Vries (KdV) equation in the small dispersion limit near the point of gradient catastrophe (x_c,t_c) for the solution of the dispersionless equation.\\nThe sub-leading term in this expansion is described by the smooth solution of a fourth order ODE, which is a higher order analogue to the Painleve I equation. This is in accordance with a conjecture of Dubrovin, suggesting that this is a universal phenomenon for any Hamiltonian perturbation of a hyperbolic equation. Using the Deift/Zhou steepest descent method applied on the Riemann-Hilbert problem for the KdV equation, we are able to prove the asymptotic expansion rigorously in a double scaling limit.1 aGrava, Tamara1 aClaeys, Tom uhttp://hdl.handle.net/1963/263600454nas a2200109 4500008004300000245012300043210006900166100002100235700002600256700002600282856003600308 2009 en_Ud 00aA variational model for quasistatic crack growth in nonlinear elasticity: some qualitative properties of the solutions0 avariational model for quasistatic crack growth in nonlinear elas1 aDal Maso, Gianni1 aGiacomini, Alessandro1 aPonsiglione, Marcello uhttp://hdl.handle.net/1963/267500547nas a2200109 4500008004300000245005600043210005200099260003400151520019600185100002000381856003600401 2009 en_Ud 00aOn viscosity solutions of Hamilton-Jacobi equations0 aviscosity solutions of HamiltonJacobi equations bAmerican Mathematical Society3 aWe consider the Dirichlet problem for Hamilton-Jacobi equations and prove existence, uniqueness and continuous dependence on boundary data of Lipschitz continuous maximal viscosity solutions.1 aZagatti, Sandro uhttp://hdl.handle.net/1963/342000988nas a2200133 4500008004100000022001400041245012300055210007000178300001600248490000800264520048400272100002700756856007100783 2008 eng d a0022-039600aAsymptotic evolution for the semiclassical nonlinear Schrödinger equation in presence of electric and magnetic fields0 aAsymptotic evolution for the semiclassical nonlinear Schrödinger a2566 - 25840 v2453 aIn this paper we study the semiclassical limit for the solutions of a subcritical focusing NLS with electric and magnetic potentials. We consider in particular the Cauchy problem for initial data close to solitons and show that, when the Planck constant goes to zero, the motion shadows that of a classical particle. Several works were devoted to the case of standing waves: differently from these we show that, in the dynamic version, the Lorentz force appears crucially.

1 aSelvitella, Alessandro uhttp://www.sciencedirect.com/science/article/pii/S002203960800243X00786nas a2200145 4500008004100000022001300041245008100054210006900135300001200204490000600216520026300222100002400485700002000509856011100529 2008 eng d a1673345200aCantor families of periodic solutions for completely resonant wave equations0 aCantor families of periodic solutions for completely resonant wa a151-1650 v33 aWe present recent existence results of Cantor families of small amplitude periodic solutions for completely resonant nonlinear wave equations. The proofs rely on the Nash-Moser implicit function theory and variational methods. © 2008 Higher Education Press.1 aBerti, Massimiliano1 aBolle, Philippe uhttp://www.math.sissa.it/publication/cantor-families-periodic-solutions-completely-resonant-wave-equations01283nas a2200145 4500008004100000022001300041245008900054210006900143300001400212490000800226520074600234100002400980700002001004856011301024 2008 eng d a0001870800aCantor families of periodic solutions for wave equations via a variational principle0 aCantor families of periodic solutions for wave equations via a v a1671-17270 v2173 aWe prove existence of small amplitude periodic solutions of completely resonant wave equations with frequencies in a Cantor set of asymptotically full measure, via a variational principle. A Lyapunov-Schmidt decomposition reduces the problem to a finite dimensional bifurcation equation-variational in nature-defined on a Cantor set of non-resonant parameters. The Cantor gaps are due to "small divisors" phenomena. To solve the bifurcation equation we develop a suitable variational method. In particular, we do not require the typical "Arnold non-degeneracy condition" of the known theory on the nonlinear terms. As a consequence our existence results hold for new generic sets of nonlinearities. © 2007 Elsevier Inc. All rights reserved.1 aBerti, Massimiliano1 aBolle, Philippe uhttp://www.math.sissa.it/publication/cantor-families-periodic-solutions-wave-equations-variational-principle00826nas a2200145 4500008004100000022001300041245008400054210006900138300001200207490000700219520030000226100002400526700002000550856011000570 2008 eng d a1021972200aCantor families of periodic solutions of wave equations with C k nonlinearities0 aCantor families of periodic solutions of wave equations with C k a247-2760 v153 aWe prove bifurcation of Cantor families of periodic solutions for wave equations with nonlinearities of class C k . It requires a modified Nash-Moser iteration scheme with interpolation estimates for the inverse of the linearized operators and for the composition operators. © 2008 Birkhaueser.1 aBerti, Massimiliano1 aBolle, Philippe uhttp://www.math.sissa.it/publication/cantor-families-periodic-solutions-wave-equations-c-k-nonlinearities00588nas a2200097 4500008004300000245007600043210006900119520024400188100002200432856003600454 2008 en_Ud 00aConcentrating solutions of some singularly perturbed elliptic equations0 aConcentrating solutions of some singularly perturbed elliptic eq3 aWe study singularly perturbed elliptic equations arising from models in physics or biology, and investigate the asymptotic behavior of some special solutions. We also discuss some connections with problems arising in differential geometry.1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/265701160nas a2200109 4500008004300000245007000043210006900113520078700182100002500969700002000994856003601014 2008 en_Ud 00aConvergence of equilibria of three-dimensional thin elastic beams0 aConvergence of equilibria of threedimensional thin elastic beams3 aA convergence result is proved for the equilibrium configurations of a three-dimensional thin elastic beam, as the diameter $h$ of the cross-section tends to zero. More precisely, we show that stationary points of the nonlinear elastic functional $E^h$, whose energies (per unit cross-section) are bounded by $Ch^2$, converge to stationary points of the $\\\\varGamma$-limit of $E^h/h^2$. This corresponds to a nonlinear one-dimensional model for inextensible rods, describing bending and torsion effects. The proof is based on the rigidity estimate for low-energy deformations by Friesecke, James and Müller and on a compensated compactness argument in a singular geometry. In addition, possible concentration effects of the strain are controlled by a careful truncation argument.1 aMora, Maria Giovanna1 aMüller, Stefan uhttp://hdl.handle.net/1963/189600386nas 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/1963/275700657nas a2200097 4500008004300000245007900043210006900122520031000191100002200501856003600523 2008 en_Ud 00aEntire solutions of autonomous equations on Rn with nontrivial asymptotics0 aEntire solutions of autonomous equations on Rn with nontrivial a3 aWe prove existence of a new type of solutions for the semilinear equation $- \\\\D u + u = u^p$ on $\\\\R^n$, with $1 < p < \\\\frac{n+2}{n-2}$. These solutions are positive, bounded, decay exponentially to zero away from three half-lines with a common origin, and at infinity are asymptotically periodic.1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/264000301nas a2200097 4500008004300000245004300043210003900086260002100125100002100146856003600167 2008 en_Ud 00aAn entropy based Glimm-type functional0 aentropy based Glimmtype functional bWorld Scientific1 aCaravenna, Laura uhttp://hdl.handle.net/1963/405100767nas a2200097 4500008004300000245005300043210004900096520045900145100002900604856003600633 2008 en_Ud 00aEquivalent definitions of asymptotic 100% B.E.C.0 aEquivalent definitions of asymptotic 100 BEC3 aIn the mathematical analysis Bose-Einstein condensates, in particular in the study of the quantum dynamics, some kind of factorisation property has been recently proposed as a convenient technical assumption of condensation. After having surveyed both the standard definition of complete Bose-Einstein condensation in the limit of infinitely many particles and some forms of asymptotic factorisation, we prove that these characterisations are equivalent.1 aMichelangeli, Alessandro uhttp://hdl.handle.net/1963/254600962nas a2200121 4500008004300000245008100043210006900124260000900193520056300202100001700765700002200782856003600804 2008 en_Ud 00aEulerian calculus for the displacement convexity in the Wasserstein distance0 aEulerian calculus for the displacement convexity in the Wasserst bSIAM3 aIn this paper we give a new proof of the (strong) displacement convexity of a class of integral functionals defined on a compact Riemannian manifold satisfying a lower Ricci curvature bound. Our approach does not rely on existence and regularity results for optimal transport maps on Riemannian manifolds, but it is based on the Eulerian point of view recently introduced by Otto and Westdickenberg [SIAM J. Math. Anal., 37 (2005), pp. 1227-1255] and on the metric characterization of the gradient flows generated by the functionals in the Wasserstein space.1 aDaneri, Sara1 aSavarè, Giuseppe uhttp://hdl.handle.net/1963/341300797nas a2200109 4500008004300000245006300043210006000106520044300166100002000609700002200629856003600651 2008 en_Ud 00aExistence of conformal metrics with constant $Q$-curvature0 aExistence of conformal metrics with constant Qcurvature3 aGiven a compact four dimensional manifold, we prove existence of conformal metrics with constant $Q$-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure. Since the corresponding Euler functional is in general unbounded from above and from below, we employ topological methods and minimax schemes, jointly with a compactness result by the second author.1 aDjadli, Zindine1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/230800501nas a2200157 4500008004100000245009500041210007100136260001000207300001400217490000700231100001800238700001700256700001700273700001600290856003700306 2008 eng d00aFluid–structure interaction problems in free surface flows: Application to boat dynamics0 aFluid–structure interaction problems in free surface flows Appli bWiley a965–9780 v561 aFormaggia, L.1 aMiglio, Edie1 aMola, Andrea1 aParolini, N uhttps://doi.org/10.1002/fld.158300637nas a2200109 4500008004300000245004900043210004900092520031300141100001300454700002400467856003600491 2008 en_Ud 00aForced Vibrations of a Nonhomogeneous String0 aForced Vibrations of a Nonhomogeneous String3 aWe prove existence of vibrations of a nonhomogeneous string under a nonlinear time periodic forcing term in the case in which the forcing frequency avoids resonances with the vibration modes of the string (nonresonant case). The proof relies on a Lyapunov-Schmidt reduction and a Nash-Moser iteration scheme.1 aBaldi, P1 aBerti, Massimiliano uhttp://hdl.handle.net/1963/264300701nas a2200121 4500008004300000245009900043210006900142520027900211100002000490700001500510700001800525856003600543 2008 en_Ud 00aFrobenius Manifolds and Central Invariants for the Drinfeld - Sokolov Bihamiltonian Structures0 aFrobenius Manifolds and Central Invariants for the Drinfeld Soko3 aThe Drinfeld - Sokolov construction associates a hierarchy of bihamiltonian integrable systems with every untwisted affine Lie algebra. We compute the complete set of invariants of the related bihamiltonian structures with respect to the group of Miura type transformations.1 aDubrovin, Boris1 aSi-Qi, Liu1 aYoujin, Zhang uhttp://hdl.handle.net/1963/252301552nas a2200157 4500008004300000245008100043210006900124520104600193100001801239700001801257700002501275700002001300700001901320700001901339856003601358 2008 en_Ud 00aFulde-Ferrell-Larkin-Ovchinnikov pairing in one-dimensional optical lattices0 aFuldeFerrellLarkinOvchinnikov pairing in onedimensional optical 3 aSpin-polarized attractive Fermi gases in one-dimensional (1D) optical lattices are expected to be remarkably good candidates for the observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We model these systems with an attractive Hubbard model with population imbalance. By means of the density-matrix renormalization-group method we compute the pairing correlations as well as the static spin and charge structure factors in the whole range from weak to strong coupling. We demonstrate that pairing correlations exhibit quasi-long range order and oscillations at the wave number expected from FFLO theory. However, we also show by numerically computing the mixed spin-charge static structure factor that charge and spin degrees of freedom appear to be coupled already for small imbalance. We discuss the consequences of this coupling for the observation of the FFLO phase, as well as for the stabilization of the quasi-long range order into long-range order by coupling many identical 1D systems, as in quasi-1D optical lattices.1 aRizzi, Matteo1 aPolini, Marco1 aCazalilla, Miguel A.1 aBakhtiari, M.R.1 aTosi, Mario P.1 aFazio, Rosario uhttp://hdl.handle.net/1963/269401551nas a2200121 4500008004300000245007900043210006900122520113900191100002501330700001701355700002101372856003601393 2008 en_Ud 00aA Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds0 aGaussBonnetlike formula on twodimensional almostRiemannian manif3 aWe consider a generalization of Riemannian geometry that naturally arises in the framework of control theory. Let $X$ and $Y$ be two smooth vector fields on a two-dimensional manifold $M$. If $X$ and $Y$ are everywhere linearly independent, then they define a classical Riemannian metric on $M$ (the metric for which they are orthonormal) and they give to $M$ the structure of metric space. If $X$ and $Y$ become linearly dependent somewhere on $M$, then the corresponding Riemannian metric has singularities, but under generic conditions the metric structure is still well defined. Metric structures that can be defined locally in this way are called almost-Riemannian structures. They are special cases of rank-varying sub-Riemannian structures, which are naturally defined in terms of submodules of the space of smooth vector fields on $M$. Almost-Riemannian structures show interesting phenomena, in particular for what concerns the relation between curvature, presence of conjugate points, and topology of the manifold. The main result of the paper is a generalization to almost-Riemannian structures of the Gauss-Bonnet formula.1 aAgrachev, Andrei, A.1 aBoscain, Ugo1 aSigalotti, Mario uhttp://hdl.handle.net/1963/186901036nas a2200133 4500008004300000245007100043210006900114520059000183100002100773700002200794700002500816700002500841856003600866 2008 en_Ud 00aGlobally stable quasistatic evolution in plasticity with softening0 aGlobally stable quasistatic evolution in plasticity with softeni3 aWe study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is characterized by the following properties: global stability at each time and energy balance on each\\ntime interval. An example developed in detail compares the solutions obtained by this method with the ones provided by a vanishing viscosity approximation, and shows that only the latter capture a decreasing branch in the stress-strain response.1 aDal Maso, Gianni1 aDeSimone, Antonio1 aMora, Maria Giovanna1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/196500681nas a2200109 4500008004300000245012000043210006900163520026100232100002100493700002100514856003600535 2008 en_Ud 00aGradient bounds for minimizers of free discontinuity problems related to cohesive zone models in fracture mechanics0 aGradient bounds for minimizers of free discontinuity problems re3 aIn this note we consider a free discontinuity problem for a scalar function, whose energy depends also on the size of the jump. We prove that the gradient of every smooth local minimizer never exceeds a constant, determined only by the data of the problem.1 aDal Maso, Gianni1 aGarroni, Adriana uhttp://hdl.handle.net/1963/172301495nas a2200109 4500008004100000245007100041210006900112260001000181520113800191100002001329856003601349 2008 en d00aHamiltonian partial differential equations and Frobenius manifolds0 aHamiltonian partial differential equations and Frobenius manifol bSISSA3 aIn the first part of this paper the theory of Frobenius manifolds\\r\\nis applied to the problem of classification of Hamiltonian systems of partial\\r\\ndifferential equations depending on a small parameter. Also developed is\\r\\na deformation theory of integrable hierarchies including the subclass of\\r\\nintegrable hierarchies of topological type. Many well-known examples\\r\\nof integrable hierarchies, such as the Korteweg–de Vries, non-linear\\r\\nSchr¨odinger, Toda, Boussinesq equations, and so on, belong to this\\r\\nsubclass that also contains new integrable hierarchies. Some of these new\\r\\nintegrable hierarchies may be important for applications. Properties of the\\r\\nsolutions to these equations are studied in the second part. Consideration\\r\\nis given to the comparative study of the local properties of perturbed and\\r\\nunperturbed solutions near a point of gradient catastrophe. A Universality\\r\\nConjecture is formulated describing the various types of critical behaviour\\r\\nof solutions to perturbed Hamiltonian systems near the point of gradient\\r\\ncatastrophe of the unperturbed solution.1 aDubrovin, Boris uhttp://hdl.handle.net/1963/647100433nas a2200121 4500008004100000022001400041245005200055210005100107300002300158100001900181700002500200856008600225 2008 eng d a1073-792800aHarish-Chandra integrals as nilpotent integrals0 aHarishChandra integrals as nilpotent integrals aArt. ID rnn062, 151 aBertola, Marco1 aFerrer, Aleix, Prats uhttp://www.math.sissa.it/publication/harish-chandra-integrals-nilpotent-integrals00891nas a2200121 4500008004300000245004600043210004600089520053600135100001600671700002200687700002400709856003600733 2008 en_Ud 00aInstanton counting on Hirzebruch surfaces0 aInstanton counting on Hirzebruch surfaces3 aWe perform a study of the moduli space of framed torsion free sheaves on Hirzebruch surfaces by using localization techniques. After discussing general properties of this moduli space, we classify its fixed points under the appropriate toric action and compute its Poincare\\\' polynomial. From the physical viewpoint, our results provide the partition function of N=4 Vafa-Witten theory on Hirzebruch surfaces, which is relevant in black hole entropy counting problems according to a conjecture due to Ooguri, Strominger and Vafa.1 aBruzzo, Ugo1 aPoghossian, Rubik1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/285200870nas a2200109 4500008004300000245007800043210006900121520049600190100001700686700002100703856003600724 2008 en_Ud 00aInvariant Carnot-Caratheodory metrics on S3, SO(3), SL(2) and Lens Spaces0 aInvariant CarnotCaratheodory metrics on S3 SO3 SL2 and Lens Spac3 aIn this paper we study the invariant Carnot-Caratheodory metrics on SU(2) \\\' S3,\\nSO(3) and SL(2) induced by their Cartan decomposition. Beside computing explicitly geodesics and conjugate loci, we compute the cut loci (globally) and we give the expression of the Carnot-Caratheodory distance as the inverse of an elementary function. We then prove that the metric\\ngiven on SU(2) projects on the so called Lens Spaces L(p; q). Also for Lens Spaces, we compute\\nthe cut loci (globally).1 aBoscain, Ugo1 aRossi, Francesco uhttp://hdl.handle.net/1963/214400382nas a2200097 4500008004300000245009400043210006900137100002300206700001900229856003600248 2008 en_Ud 00aInvariant Manifolds for Viscous Profiles of a Class of Mixed Hyperbolic-Parabolic Systems0 aInvariant Manifolds for Viscous Profiles of a Class of Mixed Hyp1 aBianchini, Stefano1 aSpinolo, Laura uhttp://hdl.handle.net/1963/340001110nas a2200121 4500008004300000245008200043210006900125520069200194100002400886700002200910700002000932856003600952 2008 en_Ud 00aThe Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere0 aIsospectral Dirac Operator on the 4dimensional Orthogonal Quantu3 aEquivariance under the action of Uq(so(5)) is used to compute the left regular and (chiral) spinorial representations of the algebra of the quantum Euclidean 4-sphere S^4_q. These representations are the constituents of a spectral triple on this sphere with a Dirac operator which is isospectral to the canonical one of the spin structure of the round undeformed four-sphere and which gives metric dimension four for the noncommutative geometry. Non-triviality of the geometry is proved by pairing the associated Fredholm module with an `instanton\\\' projection. A real structure which satisfies all required properties modulo a suitable ideal of `infinitesimals\\\' is also introduced.1 aD'Andrea, Francesco1 aDabrowski, Ludwik1 aLandi, Giovanni uhttp://hdl.handle.net/1963/256701845nas a2200133 4500008004300000245006800043210006700111520142200178100001701600700002101617700001701638700002001655856003601675 2008 en_Ud 00aLimit Time Optimal Syntheses for a control-affine system on S²0 aLimit Time Optimal Syntheses for a controlaffine system on S²3 aFor $\\\\alpha \\\\in ]0,\\\\pi/2[$, let $(\\\\Sigma)_\\\\alpha$ be the control system $\\\\dot{x}=(F+uG)x$, where $x$ belongs to the two-dimensional unit sphere $S^2$, $u\\\\in [-1,1]$, and $F,G$ are $3\\\\times3$ skew-symmetric matrices generating rotations with perpendicular axes and of respective norms $\\\\cos(\\\\alpha)$ and $\\\\sin(\\\\alpha)$. In this paper, we study the time optimal synthesis (TOS) from the north pole $(0,0,1)^T$ associated to $(\\\\Sigma)_\\\\alpha$, as the parameter $\\\\alpha$ tends to zero; this problem is motivated by specific issues in the control of quantum systems. We first prove that the TOS is characterized by a \\\"two-snakes\\\" configuration on the whole $S^2$, except for a neighborhood $U_\\\\alpha$ of the south pole $(0,0,-1)^T$ of diameter at most ${\\\\cal O}(\\\\alpha)$. We next show that, inside $U_\\\\alpha$, the TOS depends on the relationship between $r(\\\\alpha):=\\\\pi/2\\\\alpha-[\\\\pi/2\\\\alpha]$ and $\\\\alpha$. More precisely, we characterize three main relationships by considering sequences $(\\\\alpha_k)_{k\\\\geq 0}$ satisfying (a) $r(\\\\alpha_k)=\\\\bar{r}$, (b) $r(\\\\alpha_k)=C\\\\alpha_k$, and (c) $r(\\\\alpha_k)=0$, where $\\\\bar{r}\\\\in (0,1)$ and $C>0$. In each case, we describe the TOS and provide, after a suitable rescaling, the limiting behavior, as $\\\\alpha$ tends to zero, of the corresponding TOS inside $U_\\\\alpha$.1 aMason, Paolo1 aSalmoni, Rebecca1 aBoscain, Ugo1 aChitour, Yacine uhttp://hdl.handle.net/1963/186200688nas a2200109 4500008004100000245008400041210006900125260001000194520031700204100002100521856003600542 2008 en d00aOn the Logarithmic Asymptotics of the Sixth Painleve\' Equation (Summer 2007)0 aLogarithmic Asymptotics of the Sixth Painleve Equation Summer 20 bSISSA3 aWe study the solutions of the sixth Painlev\'e equation with a logarithmic\r\nasymptotic behavior at a critical point. We compute the monodromy group\r\nassociated to the solutions by the method of monodromy preserving deformations\r\nand we characterize the asymptotic behavior in terms of the monodromy itself.1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/652100334nas a2200085 4500008004300000245008000043210006900123100002000192856003600212 2008 en_Ud 00aMinimization of non quasiconvex functionals by integro-extremization method0 aMinimization of non quasiconvex functionals by integroextremizat1 aZagatti, Sandro uhttp://hdl.handle.net/1963/276100355nas a2200085 4500008004300000245010100043210006900144100002000213856003600233 2008 en_Ud 00aMinimizers of non convex scalar functionals and viscosity solutions of Hamilton-Jacobi equations0 aMinimizers of non convex scalar functionals and viscosity soluti1 aZagatti, Sandro uhttp://hdl.handle.net/1963/276000352nas a2200097 4500008004300000245006500043210006500108260002300173100002200196856003600218 2008 en_Ud 00aMorse theory and a scalar field equation on compact surfaces0 aMorse theory and a scalar field equation on compact surfaces bKhayyam Publishing1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/353100342nas a2200097 4500008004300000245006300043210006200106100002400168700001600192856003600208 2008 en_Ud 00aMultiple bound states for the Schroedinger-Poisson problem0 aMultiple bound states for the SchroedingerPoisson problem1 aAmbrosetti, Antonio1 aRuiz, David uhttp://hdl.handle.net/1963/267900746nas a2200145 4500008004300000245004200043210004200085260002800127520032600155100002000481700001900501700001800520700002600538856003600564 2008 en_Ud 00aNoncommutative families of instantons0 aNoncommutative families of instantons bOxford University Press3 aWe construct $\\\\theta$-deformations of the classical groups SL(2,H) and Sp(2). Coacting on the basic instanton on a noncommutative four-sphere $S^4_\\\\theta$, we construct a noncommutative family of instantons of charge 1. The family is parametrized by the quantum quotient of $SL_\\\\theta(2,H)$ by $Sp_\\\\theta(2)$.1 aLandi, Giovanni1 aPagani, Chiara1 aReina, Cesare1 avan Suijlekom, Walter uhttp://hdl.handle.net/1963/341700576nas a2200121 4500008004300000245006400043210006000107520018500167100002400352700002200376700002000398856003600418 2008 en_Ud 00aThe Noncommutative Geometry of the Quantum Projective Plane0 aNoncommutative Geometry of the Quantum Projective Plane3 aWe study the spectral geometry of the quantum projective plane CP^2_q. In particular, we construct a Dirac operator which gives a 0^+ summable triple, equivariant under U_q(su(3)).1 aD'Andrea, Francesco1 aDabrowski, Ludwik1 aLandi, Giovanni uhttp://hdl.handle.net/1963/254800355nas a2200085 4500008004300000245009600043210006900139100002500208856003600233 2008 en_Ud 00aA note on the differentiability of Lipschitz functions and the chain rule in Sobolev spaces0 anote on the differentiability of Lipschitz functions and the cha1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/265401399nas a2200109 4500008004300000245010600043210006900149520099600218100001801214700002101232856003601253 2008 en_Ud 00aNumerical study of a multiscale expansion of the Korteweg-de Vries equation and Painlevé-II equation0 aNumerical study of a multiscale expansion of the Kortewegde Vrie3 aThe Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion of order $\\\\e^2$, $\\\\e\\\\ll 1$, is characterized by the appearance of a zone of rapid modulated oscillations. These oscillations are approximately described by the elliptic solution of KdV where the amplitude, wave-number and frequency are not constant but evolve according to the Whitham equations. Whereas the difference between the KdV and the asymptotic solution decreases as $\\\\epsilon$ in the interior of the Whitham oscillatory zone, it is known to be only of order $\\\\epsilon^{1/3}$ near the leading edge of this zone. To obtain a more accurate description near the leading edge of the oscillatory zone we present a multiscale expansion of the solution of KdV in terms of the Hastings-McLeod solution of the Painlev\\\\\\\'e-II equation. We show numerically that the resulting multiscale solution approximates the KdV solution, in the small dispersion limit, to the order $\\\\epsilon^{2/3}$.1 aGrava, Tamara1 aKlein, Christian uhttp://hdl.handle.net/1963/259201131nas a2200133 4500008004300000245006500043210006400108260001300172520071100185100002300896700002200919700002000941856003600961 2008 en_Ud 00aOptimal Strokes for Low Reynolds Number Swimmers: An Example0 aOptimal Strokes for Low Reynolds Number Swimmers An Example bSpringer3 aSwimming, i.e., being able to advance in the absence of external forces by performing cyclic shape changes, is particularly demanding at low Reynolds numbers. This is the regime of interest for micro-organisms and micro- or nano-robots. We focus in this paper on a simple yet representative example: the three-sphere swimmer of Najafi and Golestanian (Phys. Rev. E, 69, 062901-062904, 2004). For this system, we show how to cast the problem of swimming in the language of control theory, prove global controllability (which implies that the three-sphere swimmer can indeed swim), and propose a numerical algorithm to compute optimal strokes (which turn out to be suitably defined sub-Riemannian geodesics).1 aAlouges, François1 aDeSimone, Antonio1 aLefebvre, Aline uhttp://hdl.handle.net/1963/400602183nas a2200133 4500008004300000245010900043210006900152520170600221100002101927700002001948700002301968700002201991856003602013 2008 en_Ud 00aOrigin of Co-Expression Patterns in E.coli and S.cerevisiae Emerging from Reverse Engineering Algorithms0 aOrigin of CoExpression Patterns in Ecoli and Scerevisiae Emergin3 aBackground: The concept of reverse engineering a gene network, i.e., of inferring a genome-wide graph of putative genegene interactions from compendia of high throughput microarray data has been extensively used in the last few years to deduce/integrate/validate various types of \\\"physical\\\" networks of interactions among genes or gene products. Results: This paper gives a comprehensive overview of which of these networks emerge significantly when reverse engineering large collections of gene expression data for two model organisms, E.coli and S.cerevisiae, without any prior information. For the first organism the pattern of co-expression is shown to reflect in fine detail both the operonal structure of the DNA and the regulatory effects exerted by the gene products when co-participating in a protein complex. For the second organism we find that direct transcriptional control (e.g., transcription factor-binding site interactions) has little statistical significance in comparison to the other regulatory mechanisms (such as co-sharing a protein complex, colocalization on a metabolic pathway or compartment), which are however resolved at a lower level of detail than in E.coli. Conclusion: The gene co-expression patterns deduced from compendia of profiling experiments tend to unveil functional categories that are mainly associated to stable bindings rather than transient interactions. The inference power of this systematic analysis is substantially reduced when passing from E.coli to S.cerevisiae. This extensive analysis provides a way to describe the different complexity between the two organisms and discusses the critical limitations affecting this type of methodologies.1 aZampieri, Mattia1 aSoranzo, Nicola1 aBianchini, Daniele1 aAltafini, Claudio uhttp://hdl.handle.net/1963/272200665nas a2200157 4500008004100000022001300041245006000054210005700114300001200171490000600183520016900189100002400358700001400382700002200396856008900418 2008 eng d a1534039200aOn periodic elliptic equations with gradient dependence0 aperiodic elliptic equations with gradient dependence a601-6150 v73 aWe construct entire solutions of Δu = f(x, u, ∇u) which are superpositions of odd, periodic functions and linear ones, with prescribed integer or rational slope.1 aBerti, Massimiliano1 aMatzeu, M1 aValdinoci, Enrico uhttp://www.math.sissa.it/publication/periodic-elliptic-equations-gradient-dependence00618nas a2200133 4500008004100000245011000041210007000151260001300221300001400234490000700248520012200255100001900377856008800396 2008 eng d00aPositive solutions of nonlinear Schrödinger-Poisson systems with radial potentials vanishing at infinity0 aPositive solutions of nonlinear SchrödingerPoisson systems with bCiteseer a211–2270 v193 aWe deal with a weighted nonlinear Schr¨odinger-Poisson system, allowing the potentials to vanish at infinity.

1 aMercuri, Carlo uhttp://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.510.3635&rep=rep1&type=pdf00444nas a2200121 4500008004300000245009700043210006900140100001700209700001800226700002200244700002000266856003600286 2008 en_Ud 00aRelaxation of some transversally isotropic energies and applications to smectic A elastomers0 aRelaxation of some transversally isotropic energies and applicat1 aAdams, James1 aConti, Sergio1 aDeSimone, Antonio1 aDolzmann, Georg uhttp://hdl.handle.net/1963/191201111nas a2200121 4500008004300000245007200043210006900115520069700184100002200881700002500903700002500928856003600953 2008 en_Ud 00aA second order minimality condition for the Mumford-Shah functional0 asecond order minimality condition for the MumfordShah functional3 aA new necessary minimality condition for the Mumford-Shah functional is derived by means of second order variations. It is expressed in terms of a sign condition for a nonlocal quadratic form on $H^1_0(\\\\Gamma)$, $\\\\Gamma$ being a submanifold of the regular part of the discontinuity set of the critical point. Two equivalent formulations are provided: one in terms of the first eigenvalue of a suitable compact operator, the other involving a sort of nonlocal capacity of $\\\\Gamma$. A sufficient condition for minimality is also deduced. Finally, an explicit example is discussed, where a complete characterization of the domains where the second variation is nonnegative can be given.1 aCagnetti, Filippo1 aMora, Maria Giovanna1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/195501262nas a2200121 4500008004300000245007100043210006800114260002800182520085700210100002101067700001601088856003601104 2008 en_Ud 00aOn semistable principal bundles over a complex projective manifold0 asemistable principal bundles over a complex projective manifold bOxford University Press3 aLet G be a simple linear algebraic group defined over the complex numbers. Fix a proper parabolic subgroup P of G and a nontrivial antidominant character \\\\chi of P. We prove that a holomorphic principal G-bundle E over a connected complex projective manifold M is semistable and the second Chern class of its adjoint bundle vanishes in rational cohomology if and only if the line bundle over E/P defined by \\\\chi is numerically effective. Similar results remain valid for principal bundles with a reductive linear algebraic group as the structure group. These generalize an earlier work of Y. Miyaoka where he gave a characterization of semistable vector bundles over a smooth projective curve. Using these characterizations one can also produce similar criteria for the semistability of parabolic principal bundles over a compact Riemann surface.1 aBiswas, Indranil1 aBruzzo, Ugo uhttp://hdl.handle.net/1963/341800611nas a2200121 4500008004300000245008600043210006900129520019400198100002400392700002100416700001600437856003600453 2008 en_Ud 00aSolitons of linearly coupled systems of semilinear non-autonomous equations on Rn0 aSolitons of linearly coupled systems of semilinear nonautonomous3 aUsing concentration compactness type arguments, we prove some results about the existence of positive ground and bound state of linearly coupled systems of nonlinear Schrödinger equations.1 aAmbrosetti, Antonio1 aCerami, Giovanna1 aRuiz, David uhttp://hdl.handle.net/1963/217500349nas a2200097 4500008004300000245006900043210006800112100001700180700001800197856003600215 2008 en_Ud 00aStability of planar switched systems: the nondiagonalizable case0 aStability of planar switched systems the nondiagonalizable case1 aBoscain, Ugo1 aBalde, Moussa uhttp://hdl.handle.net/1963/185701518nas a2200109 4500008004300000245007900043210006900122520114200191100001701333700002201350856003601372 2008 en_Ud 00aSymmetric obstruction theories and Hilbert schemes of points on threefolds0 aSymmetric obstruction theories and Hilbert schemes of points on 3 aIn an earlier paper by one of us (Behrend), Donaldson-Thomas type invariants were expressed as certain weighted Euler characteristics of the moduli space. The Euler characteristic is weighted by a certain canonical\\nZ-valued constructible function on the moduli space. This constructible function associates to\\nany point of the moduli space a certain invariant of the singularity of the space at the point. Here we evaluate this invariant for the case of a singularity that is an isolated point of a C∗-action and that admits a symmetric obstruction theory compatible with the C∗-action. The answer is (-1)d, where d\\nis the dimension of the Zariski tangent space. We use this result to prove that for any threefold, proper or not, the weighted Euler characteristic of the Hilbert scheme of n points on the threefold is, up to sign, equal to the usual Euler characteristic. For the case of a projective Calabi-Yau threefold, we deduce that the Donaldson-Thomas invariant of the Hilbert scheme of n points is, up to sign, equal to the Euler characteristic. This proves a conjecture of Maulik, Nekrasov, Okounkov and Pandharipande.1 aBehrend, Kai1 aFantechi, Barbara uhttp://hdl.handle.net/1963/270900905nas a2200121 4500008004100000245006700041210006700108260001000175520051900185653002600704100001700730856003600747 2008 en d00aSymmetries of noncommutative spaces and equivariant cohomology0 aSymmetries of noncommutative spaces and equivariant cohomology bSISSA3 aAs the title suggests, the main subject of this thesis is the study of symmetries of noncommutative spaces and related equivariant cohomologies. We focus on deformations of classical geometries coming from the action of some symmetry. A close relation between the deformation of the symmetry and the deformation of the space on which it acts is at the heart of our approach; we will use this idea to generate noncommutative geometries, and to de¯ne algebraic models for the equivariant cohomology of such actions.10aNoncommutative spaces1 aCirio, Lucio uhttp://hdl.handle.net/1963/525401205nas a2200109 4500008004300000245008000043210006900123520082300192100002001015700002401035856003601059 2008 en_Ud 00aTopological Gauge Theories on Local Spaces and Black Hole Entropy Countings0 aTopological Gauge Theories on Local Spaces and Black Hole Entrop3 aWe study cohomological gauge theories on total spaces of holomorphic line bundles over complex manifolds and obtain their reduction to the base manifold by U(1) equivariant localization of the path integral. We exemplify this general mechanism by proving via exact path integral localization a reduction for local curves conjectured in hep-th/0411280, relevant to the calculation of black hole entropy/Gromov-Witten invariants. Agreement with the four-dimensional gauge theory is recovered by taking into account in the latter non-trivial contributions coming from one-loop fluctuations determinants at the boundary of the total space. We also study a class of abelian gauge theories on Calabi-Yau local surfaces, describing the quantum foam for the A-model, relevant to the calculation of Donaldson-Thomas invariants.1 aBonelli, Giulio1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/199200725nas a2200097 4500008004300000245008100043210006900124520037600193100002200569856003600591 2008 en_Ud 00aTopological methods for an elliptic equation with exponential nonlinearities0 aTopological methods for an elliptic equation with exponential no3 aWe consider a class of variational equations with exponential nonlinearities on compact surfaces. From considerations involving the Moser-Trudinger inequality, we characterize some sublevels of the Euler-Lagrange functional in terms of the topology of the surface and of the data of the equation. This is used together with a min-max argument to obtain existence results.1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/259401148nas a2200121 4500008004300000245006300043210006200106520076200168100002000930700002200950700001800972856003600990 2008 en_Ud 00aTransition layer for the heterogeneous Allen-Cahn equation0 aTransition layer for the heterogeneous AllenCahn equation3 aWe consider the equation $\\\\e^{2}\\\\Delta u=(u-a(x))(u^2-1)$ in $\\\\Omega$, $\\\\frac{\\\\partial u}{\\\\partial \\\\nu} =0$ on $\\\\partial \\\\Omega$, where $\\\\Omega$ is a smooth and bounded domain in $\\\\R^n$, $\\\\nu$ the outer unit normal to $\\\\pa\\\\Omega$, and $a$ a smooth function satisfying $-10} and {a<0}. Assuming $\\\\nabla a \\\\neq 0$ on $K$ and $a\\\\ne 0$ on $\\\\partial \\\\Omega$, we show that there exists a sequence $\\\\e_j \\\\to 0$ such that the above equation has a solution $u_{\\\\e_j}$ which converges uniformly to $\\\\pm 1$ on the compact sets of $\\\\O_{\\\\pm}$ as $j \\\\to + \\\\infty$.1 aMahmoudi, Fethi1 aMalchiodi, Andrea1 aWei, Juncheng uhttp://hdl.handle.net/1963/265600781nas a2200133 4500008004100000020002200041245006700063210006700130260001300197520035900210100002300569700001900592856003600611 2008 en d a978-3-642-21718-000aTransport Rays and Applications to Hamilton–Jacobi Equations0 aTransport Rays and Applications to Hamilton–Jacobi Equations bSpringer3 aThe aim of these notes is to introduce the readers to the use of the Disintegration Theorem for measures as an effective tool for reducing problems in transport equations to simpler ones. The basic idea is to partition Rd into one dimensional sets, on which the problem under consideration becomes one space dimensional (and thus much easier, hopefully).1 aBianchini, Stefano1 aGloyer, Matteo uhttp://hdl.handle.net/1963/546301276nas a2200133 4500008004300000245008900043210006900132520081200201100002101013700002201034700002501056700002501081856003601106 2008 en_Ud 00aA vanishing viscosity approach to quasistatic evolution in plasticity with softening0 avanishing viscosity approach to quasistatic evolution in plastic3 aWe deal with quasistatic evolution problems in plasticity with softening, in the framework of small strain associative elastoplasticity. The presence of a nonconvex term due to the softening phenomenon requires a nontrivial extension of the variational framework for rate-independent problems to the case of a nonconvex energy functional. We argue that, in this case, the use of global minimizers in the corresponding incremental problems is not justified from the mechanical point of view. Thus, we analize a different selection criterion for the solutions of the quasistatic evolution problem, based on a viscous approximation. This leads to a generalized formulation in terms of Young measures, developed in the first part of the paper. In the second part we apply our approach to some concrete examples.1 aDal Maso, Gianni1 aDeSimone, Antonio1 aMora, Maria Giovanna1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/184401562nas a2200133 4500008004100000020001800041022001300059245004500072210004500117300001200162520115200174100002401326856007801350 2008 eng d a9781402069628 a1874650000aVariational methods for Hamiltonian PDEs0 aVariational methods for Hamiltonian PDEs a391-4203 aWe present recent existence results of periodic solutions for completely resonant nonlinear wave equations in which both "small divisor" difficulties and infinite dimensional bifurcation phenomena occur. These results can be seen as generalizations of the classical finite-dimensional resonant center theorems of Weinstein-Moser and Fadell-Rabinowitz. The proofs are based on variational bifurcation theory: after a Lyapunov-Schmidt reduction, the small divisor problem in the range equation is overcome with a Nash-Moser implicit function theorem for a Cantor set of non-resonant parameters. Next, the infinite dimensional bifurcation equation, variational in nature, possesses minimax mountain-pass critical points. The big difficulty is to ensure that they are not in the "Cantor gaps". This is proved under weak non-degeneracy conditions. Finally, we also discuss the existence of forced vibrations with rational frequency. This problem requires variational methods of a completely different nature, such as constrained minimization and a priori estimates derivable from variational inequalities. © 2008 Springer Science + Business Media B.V.1 aBerti, Massimiliano uhttp://www.math.sissa.it/publication/variational-methods-hamiltonian-pdes00645nas a2200121 4500008004300000245011200043210006900155520019600224100002300420700002200443700002200465856003600487 2007 en_Ud 00aAsymptotic behaviour of smooth solutions for partially dissipative hyperbolic systems with a convex entropy0 aAsymptotic behaviour of smooth solutions for partially dissipati3 aWe study the asymptotic time behavior of global smooth solutions to general entropy dissipative hyperbolic systems of balance law in m space dimensions, under the Shizuta-Kawashima condition.1 aBianchini, Stefano1 aHanouzet, Bernard1 aNatalini, Roberto uhttp://hdl.handle.net/1963/178000924nas a2200121 4500008004100000245012500041210006900166260004700235520035300282100002100635700002100656856012500677 2007 en d00aThe Asymptotic Behaviour of the Fourier Transforms of Orthogonal Polynomials II: L.I.F.S. Measures and Quantum Mechanics0 aAsymptotic Behaviour of the Fourier Transforms of Orthogonal Pol b2007 Birkh¨auser Verlag Basel/Switzerland3 aWe study measures generated by systems of linear iterated functions,\r\ntheir Fourier transforms, and those of their orthogonal polynomials. We\r\ncharacterize the asymptotic behaviours of their discrete and continuous averages.\r\nFurther related quantities are analyzed, and relevance of this analysis\r\nto quantum mechanics is briefly discussed1 aGuzzetti, Davide1 aMantica, Giorgio uhttp://www.math.sissa.it/publication/asymptotic-behaviour-fourier-transforms-orthogonal-polynomials-ii-lifs-measures-and01700nas a2200121 4500008004300000245004200043210004200085520136200127100002101489700001601510700001601526856003601542 2007 en_Ud 00aAsymptotic variational wave equations0 aAsymptotic variational wave equations3 aWe investigate the equation $(u_t + (f(u))_x)_x = f\\\'\\\'(u) (u_x)^2/2$ where $f(u)$ is a given smooth function. Typically $f(u)= u^2/2$ or $u^3/3$. This equation models unidirectional and weakly nonlinear waves for the variational wave equation $u_{tt} - c(u) (c(u)u_x)_x =0$ which models some liquid crystals with a natural sinusoidal $c$. The equation itself is also the Euler-Lagrange equation of a variational problem. Two natural classes of solutions can be associated with this equation. A conservative solution will preserve its energy in time, while a dissipative weak solution loses energy at the time when singularities appear. Conservative solutions are globally defined, forward and backward in time, and preserve interesting geometric features, such as the Hamiltonian structure. On the other hand, dissipative solutions appear to be more natural from the physical point of view.\\nWe establish the well-posedness of the Cauchy problem within the class of conservative solutions, for initial data having finite energy and assuming that the flux function $f$ has Lipschitz continuous second-order derivative. In the case where $f$ is convex, the Cauchy problem is well-posed also within the class of dissipative solutions. However, when $f$ is not convex, we show that the dissipative solutions do not depend continuously on the initial data.1 aBressan, Alberto1 aPing, Zhang1 aYuxi, Zheng uhttp://hdl.handle.net/1963/218200553nas a2200133 4500008004100000022001400041245011300055210007000168300001400238490000700252100001900259700001700278856012400295 2007 eng d a0176-427600aBiorthogonal Laurent polynomials, Töplitz determinants, minimal Toda orbits and isomonodromic tau functions0 aBiorthogonal Laurent polynomials Töplitz determinants minimal To a383–4300 v261 aBertola, Marco1 aGekhtman, M. uhttp://www.math.sissa.it/publication/biorthogonal-laurent-polynomials-t%C3%B6plitz-determinants-minimal-toda-orbits-and00477nas a2200121 4500008004100000022001400041245008100055210006900136300001400205490000800219100001900227856010900246 2007 eng d a0021-904500aBiorthogonal polynomials for two-matrix models with semiclassical potentials0 aBiorthogonal polynomials for twomatrix models with semiclassical a162–2120 v1441 aBertola, Marco uhttp://www.math.sissa.it/publication/biorthogonal-polynomials-two-matrix-models-semiclassical-potentials01457nas a2200133 4500008004300000245010800043210006900151520097900220100001901199700002301218700002201241700002401263856003601287 2007 en_Ud 00aBlack Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory0 aBlack Holes Instanton Counting on Toric Singularities and qDefor3 aWe study the relationship between instanton counting in N=4 Yang-Mills theory on a generic four-dimensional toric orbifold and the semi-classical expansion of q-deformed Yang-Mills theory on the blowups of the minimal resolution of the orbifold singularity, with an eye to clarifying the recent proposal of using two-dimensional gauge theories to count microstates of black holes in four dimensions. We describe explicitly the instanton contributions to the counting of D-brane bound states which are captured by the two-dimensional gauge theory. We derive an intimate relationship between the two-dimensional Yang-Mills theory and Chern-Simons theory on generic Lens spaces, and use it to show that the correct instanton counting is only reproduced when the Chern-Simons contributions are treated as non-dynamical boundary conditions in the D4-brane gauge theory. We also use this correspondence to discuss the counting of instantons on higher genus ruled Riemann surfaces.1 aGriguolo, Luca1 aSeminara, Domenico1 aSzabo, Richard J.1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/188800337nas a2200085 4500008004300000245007400043210006900117100002900186856003600215 2007 en_Ud 00aBose-Einstein condensation: analysis of problems and rigorous results0 aBoseEinstein condensation analysis of problems and rigorous resu1 aMichelangeli, Alessandro uhttp://hdl.handle.net/1963/218900318nas a2200097 4500008004300000245005100043210005000094100002200144700001800166856003600184 2007 en_Ud 00aBoundary interface for the Allen-Cahn equation0 aBoundary interface for the AllenCahn equation1 aMalchiodi, Andrea1 aWei, Juncheng uhttp://hdl.handle.net/1963/202700420nas a2200121 4500008004100000245006400041210006300105260003700168100002200205700001700227700001800244856003600262 2007 en d00aBoundary-clustered interfaces for the Allen–Cahn equation0 aBoundaryclustered interfaces for the Allen–Cahn equation bMathematical Sciences Publishers1 aMalchiodi, Andrea1 aNi, Wei-Ming1 aWei, Juncheng uhttp://hdl.handle.net/1963/508900820nas a2200121 4500008004300000245004900043210004800092520045600140100001700596700002100613700002800634856003600662 2007 en_Ud 00aBV instability for the Lax-Friedrichs scheme0 aBV instability for the LaxFriedrichs scheme3 aIt is proved that discrete shock profiles (DSPs) for the Lax-Friedrichs scheme for a system of conservation laws do not necessarily depend continuously in BV on their speed. We construct examples of $2 \\\\times 2$-systems for which there are sequences of DSPs with speeds converging to a rational number. Due to a resonance phenomenon, the difference between the limiting DSP and any DSP in the sequence will contain an order-one amount of variation.1 aBaiti, Paolo1 aBressan, Alberto1 aJenssen, Helge Kristian uhttp://hdl.handle.net/1963/233500899nas a2200109 4500008004300000245006800043210006800111520053400179100002000713700002000733856003600753 2007 en_Ud 00aCanonical structure and symmetries of the Schlesinger equations0 aCanonical structure and symmetries of the Schlesinger equations3 aThe Schlesinger equations S (n,m) describe monodromy preserving deformations of order m Fuchsian systems with n+1 poles. They can be considered as a family of commuting time-dependent Hamiltonian systems on the direct product of n copies of m×m matrix algebras equipped with the standard linear Poisson bracket. In this paper we present a new canonical Hamiltonian formulation ofthe general Schlesinger equations S (n,m) for all n, m and we compute the action of the symmetries of the Schlesinger equations in these coordinates.1 aDubrovin, Boris1 aMazzocco, Marta uhttp://hdl.handle.net/1963/199701185nas a2200121 4500008004100000245004600041210004500087260001000132520079900142653006700941100001901008856003601027 2007 en d00aChen-Ruan cohomology of ADE singularities0 aChenRuan cohomology of ADE singularities bSISSA3 aWe study Ruan\'s \\textit{cohomological crepant resolution conjecture} for\r\norbifolds with transversal ADE singularities. In the $A_n$-case we compute both\r\nthe Chen-Ruan cohomology ring $H^*_{\\rm CR}([Y])$ and the quantum corrected\r\ncohomology ring $H^*(Z)(q_1,...,q_n)$. The former is achieved in general, the\r\nlater up to some additional, technical assumptions. We construct an explicit\r\nisomorphism between $H^*_{\\rm CR}([Y])$ and $H^*(Z)(-1)$ in the $A_1$-case,\r\nverifying Ruan\'s conjecture. In the $A_n$-case, the family\r\n$H^*(Z)(q_1,...,q_n)$ is not defined for $q_1=...=q_n=-1$. This implies that\r\nthe conjecture should be slightly modified. We propose a new conjecture in the\r\n$A_n$-case which we prove in the $A_2$-case by constructing an explicit\r\nisomorphism.10aChen-Ruan cohomology, Ruan\'s conjecture, McKay correspondence1 aPerroni, Fabio uhttp://hdl.handle.net/1963/650200671nas a2200133 4500008004100000245006700041210005800108260001000166520026600176100002200442700001900464700001800483856003600501 2007 en d00aThe cohomological crepant resolution conjecture for P(1,3,4,4)0 acohomological crepant resolution conjecture for P1344 bSISSA3 aWe prove the cohomological crepant resolution conjecture of Ruan for the\r\nweighted projective space P(1,3,4,4). To compute the quantum corrected\r\ncohomology ring we combine the results of Coates-Corti-Iritani-Tseng on\r\nP(1,1,1,3) and our previous results.1 aBoissiere, Samuel1 aPerroni, Fabio1 aMann, Etienne uhttp://hdl.handle.net/1963/651302020nas a2200121 4500008004300000245013300043210006900176520155200245100002001797700002301817700002201840856003601862 2007 en_Ud 00aComparing association network algorithms for reverse engineering of large scale gene regulatory networks: synthetic vs real data0 aComparing association network algorithms for reverse engineering3 aMotivation: Inferring a gene regulatory network exclusively from microarray expression profiles is a difficult but important task. The aim of this work is to compare the predictive power of some of the most popular algorithms in different conditions (like data taken at equilibrium or time courses) and on both synthetic and real microarray data. We are in particular interested in comparing similarity measures both of linear type (like correlations and partial correlations) and of nonlinear type (mutual information and conditional mutual information), and in investigating the underdetermined case (less samples than genes). Results: In our simulations we see that all network inference algorithms obtain better performances from data produced with \\\"structural\\\" perturbations, like gene knockouts at steady state, than with any dynamical perturbation. The predictive power of all algorithms is confirmed on a reverse engineering problem from E. coli gene profiling data: the edges of the \\\"physical\\\" network of transcription factor-binding sites are significantly overrepresented among the highest weighting edges of the graph that we infer directly from the data without any structure supervision. Comparing synthetic and in vivo data on the same network graph allows us to give an indication of how much more complex a real transcriptional regulation program is with respect to an artificial model. Availability: Software and supplementary material are freely available at the URL http://people.sissa.it/~altafini/papers/SoBiAl07/1 aSoranzo, Nicola1 aBianconi, Ginestra1 aAltafini, Claudio uhttp://hdl.handle.net/1963/202800643nas a2200109 4500008004300000245006200043210005400105520029200159100002200451700002400473856003600497 2007 en_Ud 00aThe complete one-loop spin chain for N=2 Super-Yang-Mills0 acomplete oneloop spin chain for N2 SuperYangMills3 aWe show that the complete planar one-loop mixing matrix of the N=2 Super Yang--Mills theory can be obtained from a reduction of that of the N=4 theory. For composite operators of scalar fields, this yields an anisotropic XXZ spin chain, whose spectrum of excitations displays a mass gap.1 aDi Vecchia, Paolo1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/230901000nas a2200121 4500008004300000245004900043210004800092520063900140100002000779700002400799700001900823856003600842 2007 en_Ud 00aComputing Amplitudes in topological M-theory0 aComputing Amplitudes in topological Mtheory3 aWe define a topological quantum membrane theory on a seven dimensional manifold of $G_2$ holonomy. We describe in detail the path integral evaluation for membrane geometries given by circle bundles over Riemann surfaces. We show that when the target space is $CY_3\\\\times S^1$ quantum amplitudes of non-local observables of membranes wrapping the circle reduce to the A-model amplitudes. \\nIn particular for genus zero we show that our model computes the Gopakumar-Vafa invariants. Moreover, for membranes wrapping calibrated homology spheres in the $CY_3$, we find that the amplitudes of our model are related to Joyce invariants.1 aBonelli, Giulio1 aTanzini, Alessandro1 aZabzine, Maxim uhttp://hdl.handle.net/1963/190100919nas a2200109 4500008004300000245008500043210006900128520053400197100002000731700002200751856003600773 2007 en_Ud 00aConcentration on minimal submanifolds for a singularly perturbed Neumann problem0 aConcentration on minimal submanifolds for a singularly perturbed3 aWe consider the equation $- \\\\e^2 \\\\D u + u= u^p$ in $\\\\Omega \\\\subseteq \\\\R^N$, where $\\\\Omega$ is open, smooth and bounded, and we prove concentration of solutions along $k$-dimensional minimal submanifolds of $\\\\partial \\\\O$, for $N \\\\geq 3$ and for $k \\\\in \\\\{1, ..., N-2\\\\}$. We impose Neumann boundary conditions, assuming $13 or with two inputs for n=4 and n=5, up to state-feedback transformations, preserving the affine structure. First using the Poincare series of moduli numbers we introduce the intrinsic numbers of functional moduli of each prescribed number of variables on which a classification problem depends. In order to classify affine systems with scalar input we associate with such a system the canonical frame by normalizing some structural functions in a commutative relation of the vector fields, which define our control system. Then, using this canonical frame, we introduce the canonical coordinates and find a complete system of state-feedback invariants of the system. It also gives automatically the micro-local (i.e. local in state-input space) classification of the generic non-affine n-dimensional control system with scalar input for n>2. Further we show how the problem of feedback-equivalence of affine systems with two-dimensional input in state space of dimensions 4 and 5 can be reduced to the same problem for affine systems with scalar input. In order to make this reduction we distinguish the subsystem of our control system, consisting of the directions of all extremals in dimension 4 and all abnormal extremals in dimension 5 of the time optimal problem, defined by the original control system. In each classification problem under consideration we find the intrinsic numbers of functional moduli of each prescribed number of variables according to its Poincare series.1 aAgrachev, Andrei, A.1 aZelenko, Igor uhttp://hdl.handle.net/1963/218600760nas a2200097 4500008004300000245003700043210003700080520048700117100002200604856003600626 2007 en_Ud 00aFeedback control of spin systems0 aFeedback control of spin systems3 aThe feedback stabilization problem for ensembles of coupled spin 1/2 systems is discussed from a control theoretic perspective. The noninvasive nature of the bulk measurement allows for a fully unitary and deterministic closed loop. The Lyapunov-based feedback design presented does not require spins that are selectively addressable. With this method, it is possible to obtain control inputs also for difficult tasks, like suppressing undesired couplings in identical spin systems.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/180801194nas a2200097 4500008004300000245010500043210006900148520082100217100002201038856003601060 2007 en_Ud 00aFeedback stabilization of quantum ensembles: a global convergence analysis on complex flag manifolds0 aFeedback stabilization of quantum ensembles a global convergence3 aIn an N-level quantum mechanical system, the problem of unitary feedback stabilization of mixed density operators to periodic orbits admits a natural Lyapunov-based time-varying feedback design. A global description of the domain of attraction of the closed-loop system can be provided based on a \\\"root-space\\\"-like structure of the space of density operators. This convex set foliates as a complex flag manifold where each leaf is identified with the coadjoint orbit of the eigenvalues of the density operator. The converging conditions are time-independent but depend from the topology of the flag manifold: it is shown that the closed loop must have a number of equilibria at least equal to the Euler characteristic of the manifold, thus imposing obstructions of topological nature to global stabilizability.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/172900873nas a2200133 4500008004300000245009700043210006900140520040800209100002500617700001900642700002100661700002100682856003600703 2007 en_Ud 00aOn finite-dimensional projections of distributions for solutions of randomly forced PDE\\\'s0 afinitedimensional projections of distributions for solutions of 3 aThe paper is devoted to studying the image of probability measures on a Hilbert space under finite-dimensional analytic maps. We establish sufficient conditions under which the image of a measure has a density with respect to the Lebesgue measure and continuously depends on the map. The results obtained are applied to the 2D Navier-Stokes equations perturbed by various random forces of low dimension.1 aAgrachev, Andrei, A.1 aKuksin, Sergei1 aSarychev, Andrey1 aShirikyan, Armen uhttp://hdl.handle.net/1963/201200617nas a2200109 4500008004300000245007000043210006900113520025100182100001700433700002100450856003600471 2007 en_Ud 00aGaussian estimates for hypoelliptic operators via optimal control0 aGaussian estimates for hypoelliptic operators via optimal contro3 aWe obtain Gaussian lower bounds for the fundamental solution of a class of hypoelliptic equations, by using repeatedly an invariant Harnack inequality. Our main result is given in terms of the value function of a suitable optimal control problem.1 aBoscain, Ugo1 aPolidoro, Sergio uhttp://hdl.handle.net/1963/199401180nas a2200109 4500008004300000245005200043210005000095520085100145100001700996700002101013856003601034 2007 en_Ud 00aHigh-order angles in almost-Riemannian geometry0 aHighorder angles in almostRiemannian geometry3 aLet X and Y be two smooth vector fields on a two-dimensional manifold M. If X and Y are everywhere linearly independent, then they define a Riemannian metric on M (the metric for which they are orthonormal) and they give to M the structure of metric space. If X and Y become linearly dependent somewhere on M, then the corresponding Riemannian metric has singularities, but under generic conditions the metric structure is still well defined. Metric structures that can be defined locally in this way are called almost-Riemannian structures. The main result of the paper is a generalization to almost-Riemannian structures of the Gauss-Bonnet formula for domains with piecewise-C2 boundary. The main feature of such formula is the presence of terms that play the role of high-order angles at the intersection points with the set of singularities.1 aBoscain, Ugo1 aSigalotti, Mario uhttp://hdl.handle.net/1963/199500967nas a2200109 4500008004300000245005100043210004700094520063600141100002000777700002400797856003600821 2007 en_Ud 00aThe holomorphic anomaly for open string moduli0 aholomorphic anomaly for open string moduli3 aWe complete the holomorphic anomaly equations for topological strings with their dependence on open moduli. We obtain the complete system by standard path integral arguments generalizing the analysis of BCOV (Commun. Math. Phys. 165 (1994) 311) to strings with boundaries. We study both the anti-holomorphic dependence on open moduli and on closed moduli in presence of Wilson lines. By providing the compactification a\\\' la Deligne-Mumford of the moduli space of Riemann surfaces with boundaries, we show that the open holomorphic anomaly equations are structured on the (real codimension one) boundary components of this space.1 aBonelli, Giulio1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/211301443nas a2200169 4500008004300000245007300043210006900116520091500185100001801100700001801118700001801136700001901154700001901173700002601192700001901218856003601237 2007 en_Ud 00aLuther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas0 aLutherEmery Phase and AtomicDensity Waves in a Trapped Fermion G3 aThe Luther-Emery liquid is a state of matter that is predicted to occur in one-dimensional systems of interacting fermions and is characterized by a gapless charge spectrum and a gapped spin spectrum. In this Letter we discuss a realization of the Luther-Emery phase in a trapped cold-atom gas. We study by means of the density-matrix renormalization-group technique a two-component atomic Fermi gas with attractive interactions subject to parabolic trapping inside an optical lattice. We demonstrate how this system exhibits compound phases characterized by the coexistence of spin pairing and atomic-density waves. A smooth crossover occurs with increasing magnitude of the atom-atom attraction to a state in which tightly bound spin-singlet dimers occupy the center of the trap. The existence of atomic-density waves could be detected in the elastic contribution to the light-scattering diffraction pattern.1 aXianlong, Gao1 aRizzi, Matteo1 aPolini, Marco1 aFazio, Rosario1 aTosi, Mario P.1 aCampo, Vivaldo L. Jr.1 aCapelle, Klaus uhttp://hdl.handle.net/1963/205600521nas a2200145 4500008004100000245006600041210006500107260002300172300001200195490000800207100001900215700002400234700001900258856009800277 2007 eng d00aMassless scalar field in a two-dimensional de Sitter universe0 aMassless scalar field in a twodimensional de Sitter universe aBaselbBirkhäuser a27–380 v2511 aBertola, Marco1 aCorbetta, Francesco1 aMoschella, Ugo uhttp://www.math.sissa.it/publication/massless-scalar-field-two-dimensional-de-sitter-universe00410nas a2200097 4500008004300000245012400043210006900167100002000236700002000256856003600276 2007 en_Ud 00aOn the Maz\\\'ya inequalities: existence and multiplicity results for an elliptic problem involving cylindrical weights0 aMazya inequalities existence and multiplicity results for an ell1 aGazzini, Marita1 aMusina, Roberta uhttp://hdl.handle.net/1963/252201055nas a2200109 4500008004300000245006600043210006600109520069300175100001600868700002500884856003600909 2007 en_Ud 00aMetrics on semistable and numerically effective Higgs bundles0 aMetrics on semistable and numerically effective Higgs bundles3 aWe consider fibre metrics on Higgs vector bundles on compact K\\\\\\\"ahler manifolds, providing notions of numerical effectiveness and numerical flatness in terms of such metrics. We prove several properties of bundles satisfying such conditions and in particular we show that numerically flat Higgs bundles have vanishing Chern classes, and that they admit filtrations whose quotients are stable flat Higgs bundles. We compare these definitions with those previously given in the case of projective varieties. Finally we study the relations between numerically effectiveness and semistability, providing semistability criteria for Higgs bundles on projective manifolds of any dimension.1 aBruzzo, Ugo1 aGrana-Otero, Beatriz uhttp://hdl.handle.net/1963/184000408nas a2200109 4500008004300000245008800043210006900131100002400200700002200224700001600246856003600262 2007 en_Ud 00aMulti-bump solitons to linearly coupled systems of nonlinear Schrödinger equations0 aMultibump solitons to linearly coupled systems of nonlinear Schr1 aAmbrosetti, Antonio1 aColorado, Eduardo1 aRuiz, David uhttp://hdl.handle.net/1963/183500894nas a2200109 4500008004300000245005300043210005300096520056000149100001800709700002100727856003600748 2007 en_Ud 00aNearly time optimal stabilizing patchy feedbacks0 aNearly time optimal stabilizing patchy feedbacks3 aWe consider the time optimal stabilization problem for a nonlinear control system $\\\\dot x=f(x,u)$. Let $\\\\tau(y)$ be the minimum time needed to steer the system from the state $y\\\\in\\\\R^n$ to the origin, and call $\\\\A(T)$ the set of initial states that can be steered to the origin in time $\\\\tau(y)\\\\leq T$. Given any $\\\\ve>0$, in this paper we construct a patchy feedback $u=U(x)$ such that every solution of $\\\\dot x=f(x, U(x))$, $x(0)=y\\\\in \\\\A(T)$ reaches an $\\\\ve$-neighborhood of the origin within time $\\\\tau(y)+\\\\ve$.1 aAncona, Fabio1 aBressan, Alberto uhttp://hdl.handle.net/1963/218500581nas a2200109 4500008004300000245009300043210006900136520018500205100002000390700002500410856003600435 2007 en_Ud 00aNecessary and sufficient conditions for the chainrule in W1,1loc(RN;Rd) and BVloc(RN;Rd)0 aNecessary and sufficient conditions for the chainrule in W11locR3 a

In this paper we prove necessary and sufficient conditions for the validity of the classical chain rule in Sobolev spaces and in the space of functions of bounded variation.

1 aLeoni, Giovanni1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/203701154nas a2200121 4500008004300000245004500043210004300088520080300131100002200934700002400956700001600980856003600996 2007 en_Ud 00aA new model for contact angle hysteresis0 anew model for contact angle hysteresis3 aWe present a model which explains several experimental observations relating contact angle hysteresis with surface roughness. The model is based on the balance between released energy and dissipation, and it describes the stick-slip behavior of drops on a rough surface using ideas similar to those employed in dry friction, elasto-plasticity and fracture mechanics. The main results of our analysis are formulas giving the interval of stable contact angles as a function of the surface roughness. These formulas show that the difference between advancing and receding angles is much larger for a drop in complete contact with the substrate (Wenzel drop) than for one whose cavities are filled with air (Cassie-Baxter drop). This fact is used as the key tool to interpret the experimental evidence.1 aDeSimone, Antonio1 aGruenewald, Natalie1 aOtto, Felix uhttp://hdl.handle.net/1963/184801143nas a2200121 4500008004100000245005700041210005700098260001000155520076800165653002800933100002400961856003600985 2007 en d00aNoncommutative geometry and quantum group symmetries0 aNoncommutative geometry and quantum group symmetries bSISSA3 aIt is a widespread belief that mathematics originates from the desire to understand (and eventually to formalize) some aspects of the real world. Quoting [Man07], «we are doing mathematics in order to understand, create, and handle things, and perhaps this understanding is mathematics» . Let me thus begin with a brief discussion of the physical ideas that motivated the development of Noncommutative Geometry and Quantum Group Theory - the areas of mathematics to which this dissertation belongs. Some physicists believe, and Einstein himself expressed this view in [Ein98a], that physics progresses in stages: there is no `final\\\' theory of Nature, but simply a sequence of theories which provide more and more accurate descriptions of the real world...10aNoncommutative geometry1 aD'Andrea, Francesco uhttp://hdl.handle.net/1963/526900613nas a2200109 4500008004300000245006800043210006200111520025400173100002100427700001900448856003600467 2007 en_Ud 00aOn a notion of unilateral slope for the Mumford-Shah functional0 anotion of unilateral slope for the MumfordShah functional3 aIn this paper we introduce a notion of unilateral slope for the Mumford-Shah functional, and provide an explicit formula in the case of smooth cracks. We show that the slope is not lower semicontinuous and study the corresponding relaxed functional.1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/1963/205901687nas a2200121 4500008004300000245008300043210007000126520125600196100002201452700002901474700002601503856003601529 2007 en_Ud 00aThe number of eigenvalues of three-particle Schrödinger operators on lattices0 anumber of eigenvalues of threeparticle Schrödinger operators on 3 aWe consider the Hamiltonian of a system of three quantum mechanical particles (two identical fermions and boson)on the three-dimensional lattice $\\\\Z^3$ and interacting by means of zero-range attractive potentials. We describe the location and structure of the essential spectrum of the three-particle discrete Schr\\\\\\\"{o}dinger operator $H_{\\\\gamma}(K),$ $K$ being the total quasi-momentum and $\\\\gamma>0$ the ratio of the mass of fermion and boson.\\nWe choose for $\\\\gamma>0$ the interaction $v(\\\\gamma)$ in such a way the system consisting of one fermion and one boson has a zero energy resonance.\\nWe prove for any $\\\\gamma> 0$ the existence infinitely many eigenvalues of the operator $H_{\\\\gamma}(0).$ We establish for the number $N(0,\\\\gamma; z;)$ of eigenvalues lying below $z<0$ the following asymptotics $$ \\\\lim_{z\\\\to 0-}\\\\frac{N(0,\\\\gamma;z)}{\\\\mid \\\\log \\\\mid z\\\\mid \\\\mid}={U} (\\\\gamma) .$$ Moreover, for all nonzero values of the quasi-momentum $K \\\\in T^3 $ we establish the finiteness of the number $ N(K,\\\\gamma;\\\\tau_{ess}(K))$ of eigenvalues of $H(K)$ below the bottom of the essential spectrum and we give an asymptotics for the number $N(K,\\\\gamma;0)$ of eigenvalues below zero.1 aAlbeverio, Sergio1 aDell'Antonio, Gianfausto1 aLakaev, Saidakhmat N. uhttp://hdl.handle.net/1963/257601358nas a2200109 4500008004300000245009600043210006900139520096500208100001801173700002101191856003601212 2007 en_Ud 00aNumerical solution of the small dispersion limit of Korteweg de Vries and Whitham equations0 aNumerical solution of the small dispersion limit of Korteweg de 3 aThe Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion of order $\\\\epsilon^2$, is characterized by the appearance of a zone of rapid modulated oscillations of wave-length of order $\\\\epsilon$. These oscillations are approximately described by the elliptic solution of KdV where the amplitude, wave-number and frequency are not constant but evolve according to the Whitham equations. In this manuscript we give a quantitative analysis of the discrepancy between the numerical solution of the KdV equation in the small dispersion limit and the corresponding approximate solution for values of $\\\\epsilon$ between $10^{-1}$ and $10^{-3}$. The numerical results are compatible with a difference of order $\\\\epsilon$ within the `interior\\\' of the Whitham oscillatory zone, of order $\\\\epsilon^{1/3}$ at the left boundary outside the Whitham zone and of order $\\\\epsilon^{1/2}$ at the right boundary outside the Whitham zone.1 aGrava, Tamara1 aKlein, Christian uhttp://hdl.handle.net/1963/178801084nas a2200109 4500008004300000245007900043210006900122520070800191100001800899700002100917856003600938 2007 en_Ud 00aNumerical study of a multiscale expansion of KdV and Camassa-Holm equation0 aNumerical study of a multiscale expansion of KdV and CamassaHolm3 aWe study numerically solutions to the Korteweg-de Vries and Camassa-Holm equation close to the breakup of the corresponding solution to the dispersionless equation. The solutions are compared with the properly rescaled numerical solution to a fourth order ordinary differential equation, the second member of the Painlev\\\\\\\'e I hierarchy. It is shown that this solution gives a valid asymptotic description of the solutions close to breakup. We present a detailed analysis of the situation and compare the Korteweg-de Vries solution quantitatively with asymptotic solutions obtained via the solution of the Hopf and the Whitham equations. We give a qualitative analysis for the Camassa-Holm equation1 aGrava, Tamara1 aKlein, Christian uhttp://hdl.handle.net/1963/252700810nas a2200109 4500008004300000245004200043210004200085520049600127100001600623700002500639856003600664 2007 en_Ud 00aNumerically flat Higgs vector bundles0 aNumerically flat Higgs vector bundles3 aAfter providing a suitable definition of numerical effectiveness for Higgs bundles, and a related notion of numerical flatness, in this paper we prove, together with some side results, that all Chern classes of a Higgs-numerically flat Higgs bundle vanish, and that a Higgs bundle is Higgs-numerically flat if and only if it is has a filtration whose quotients are flat stable Higgs bundles. We also study the relation between these numerical properties of Higgs bundles and (semi)stability.1 aBruzzo, Ugo1 aGrana-Otero, Beatriz uhttp://hdl.handle.net/1963/175700311nas a2200097 4500008004300000245005000043210005000093100001800143700001600161856003600177 2007 en_Ud 00aParametrized curves in Lagrange Grassmannians0 aParametrized curves in Lagrange Grassmannians1 aZelenko, Igor1 aChengbo, Li uhttp://hdl.handle.net/1963/256000408nas a2200097 4500008004100000245011900041210006900160260001000229100002300239856004800262 2007 en d00aPerturbation techniques applied to the real vanishing viscosity approximation of an initial boundary value problem0 aPerturbation techniques applied to the real vanishing viscosity bSISSA1 aBianchini, Stefano uhttp://preprints.sissa.it/handle/1963/3531500626nas a2200109 4500008004300000245008200043210006900125520024600194100002100440700001900461856003600480 2007 en_Ud 00aQuasistatic crack growth for a cohesive zone model with prescribed crack path0 aQuasistatic crack growth for a cohesive zone model with prescrib3 aIn this paper we study the quasistatic crack growth for a cohesive zone model. We assume that the crack path is prescribed and we study the time evolution of the crack in the framework of the variational theory of rate-independent processes.1 aDal Maso, Gianni1 aZanini, Chiara uhttp://hdl.handle.net/1963/168600558nas a2200121 4500008004300000245007600043210006900119520014800188100002100336700002100357700002200378856003600400 2007 en_Ud 00aQuasistatic evolution problems for pressure-sensitive plastic materials0 aQuasistatic evolution problems for pressuresensitive plastic mat3 aWe study quasistatic evolution problems for pressure-sensitive plastic materials in the context of small strain associative perfect plasticity.1 aDal Maso, Gianni1 aDemyanov, Alexey1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/196200973nas a2200109 4500008004300000245006600043210006600109520061200175100002200787700001800809856003600827 2007 en_Ud 00aReciprocal transformations and flat metrics on Hurwitz spaces0 aReciprocal transformations and flat metrics on Hurwitz spaces3 aWe consider hydrodynamic systems which possess a local Hamiltonian structure of Dubrovin-Novikov type. To such a system there are also associated an infinite number of nonlocal Hamiltonian structures. We give necessary and sufficient conditions so that, after a nonlinear transformation of the independent variables, the reciprocal system still possesses a local Hamiltonian structure of Dubrovin-Novikov type. We show that, under our hypotheses, bi-hamiltonicity is preserved by the reciprocal transformation. Finally we apply such results to reciprocal systems of genus g Whitham-KdV modulation equations.1 aAbenda, Simonetta1 aGrava, Tamara uhttp://hdl.handle.net/1963/221001299nas a2200097 4500008004300000245006000043210005900103520097400162100002901136856003601165 2007 en_Ud 00aReduced density matrices and Bose-Einstein condensation0 aReduced density matrices and BoseEinstein condensation3 aEmergence and applications of the ubiquitous tool of reduced density matrices in the rigorous analysis of Bose Einstein condensation is reviewed, and new related results are added. The need and the nature of scaling limits of infinitely many particles is discussed, which imposes that a physically meaningful and mathematically well-posed definition of asymptotic condensation is placed at the level of marginals.\\nThe topic of correlations in the condensed state is addressed in order to show their influence at this level of marginals, both in the true condensed state and in the suitable trial functions one introduces to approximate the many-body structure and energy. Complete condensation is shown to be equivalently defined at any fixed k-body level, both for pure and mixed states. Further, it is proven to be equivalent to some other characterizations in terms of asymptotic factorization of the many-body state, which are currently present in the literature.1 aMichelangeli, Alessandro uhttp://hdl.handle.net/1963/198600931nas a2200121 4500008004100000245007500041210006800116260001000184520053900194100002000733700002000753856003600773 2007 en d00aOn the reductions and classical solutions of the Schlesinger equations0 areductions and classical solutions of the Schlesinger equations bSISSA3 aThe Schlesinger equations S(n,m) describe monodromy preserving\\r\\ndeformations of order m Fuchsian systems with n+1 poles. They\\r\\ncan be considered as a family of commuting time-dependent Hamiltonian\\r\\nsystems on the direct product of n copies of m×m matrix algebras\\r\\nequipped with the standard linear Poisson bracket. In this paper we address\\r\\nthe problem of reduction of particular solutions of “more complicated”\\r\\nSchlesinger equations S(n,m) to “simpler” S(n′,m′) having n′ < n\\r\\nor m′ < m.1 aDubrovin, Boris1 aMazzocco, Marta uhttp://hdl.handle.net/1963/647200600nas a2200097 4500008004300000245005300043210004500096520030500141100002000446856003600466 2007 en_Ud 00aOn the regularity of weak solutions to H-systems0 aregularity of weak solutions to Hsystems3 aAbstract. In this paper we prove that every weak solution to the H-surface equation is locally bounded, provided the prescibed mean curvatore H is asymptotic to a constant at infinity (with a suitable decay rate). No smoothness ssumptions are required on H. We consider also the Dirichlet problem....1 aMusina, Roberta uhttp://hdl.handle.net/1963/175300981nas a2200097 4500008004300000245008200043210006900125520062400194100002900818856003600847 2007 en_Ud 00aRole of scaling limits in the rigorous analysis of Bose-Einstein condensation0 aRole of scaling limits in the rigorous analysis of BoseEinstein 3 aIn the context of the rigorous analysis of Bose-Einstein condensation, recent achievements have been obtained in the form of asymptotic results when some appropriate scaling is performed in the Hamiltonian, and the limit of infinite number of particles is taken. In particular, two modified thermodynamic limits of infinite dilution turned out to provide an insight in this analysis, the so-\\ncalled Gross-Pitaevskii limit and the related Tomas-Fermi limit. Here such scalings are discussed with respect to their physical and mathematical motivations, and to the currently known results obtained within this framework.1 aMichelangeli, Alessandro uhttp://hdl.handle.net/1963/198400296nas a2200097 4500008004300000245003900043210003900082100001600121700002500137856003600162 2007 en_Ud 00aSemistable principal Higgs bundles0 aSemistable principal Higgs bundles1 aBruzzo, Ugo1 aGrana-Otero, Beatriz uhttp://hdl.handle.net/1963/253300729nas a2200121 4500008004300000245002700043210002700070520041600097100002200513700001800535700001800553856003600571 2007 en_Ud 00aSmooth toric DM stacks0 aSmooth toric DM stacks3 aWe give a new definition of smooth toric DM stacks in the same spirit of toric varieties. We show that our definition is equivalent to the one of Borisov, Chen and Smith in terms of stacky fans. In particular, we give a geometric interpretation of the combinatorial data contained in a stacky fan. We also give a bottom up classification in terms of simplicial toric varieties and fiber products of root stacks.1 aFantechi, Barbara1 aMann, Etienne1 aNironi, Fabio uhttp://hdl.handle.net/1963/212000945nas a2200121 4500008004300000245006300043210006300106520056100169100002200730700001700752700001800769856003600787 2007 en_Ud 00aSoft elasticity and microstructure in smectic C elastomers0 aSoft elasticity and microstructure in smectic C elastomers3 aSmectic C elastomers are layered materials exhibiting a solid-like elastic response along the layer normal and a rubbery one in the plane. The set of strains minimizing the elastic energy contains a one-parameter family of simple stretches associated with an internal degree of freedom, coming from the in-plane component of the director. We investigate soft elasticity and the corresponding microstructure by determining the quasiconvex hull of the set , and use this to propose experimental tests that should make the predicted soft response observable.1 aDeSimone, Antonio1 aAdams, James1 aConti, Sergio uhttp://hdl.handle.net/1963/181100726nas a2200097 4500008004300000245009800043210006900141520036200210100002000572856003600592 2007 en_Ud 00aSolutions of vectorial Hamilton-Jacobi equations and minimizers of nonquasiconvex functionals0 aSolutions of vectorial HamiltonJacobi equations and minimizers o3 aWe provide a unified approach to prove existence results for the Dirichlet problem for Hamilton-Jacobi equations and for the minimum problem for nonquasiconvex functionals of the Calculus of Variations with affine boundary data. The idea relies on the definition of integro-extremal solutions introduced in the study of nonconvex scalar variational problem.1 aZagatti, Sandro uhttp://hdl.handle.net/1963/276301499nas a2200121 4500008004300000245014300043210006900186520102000255100002001275700002201295700002401317856003601341 2007 en_Ud 00aSolutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part I: study of the limit set and approximate solutions0 aSolutions to the nonlinear Schroedinger equation carrying moment3 aWe prove existence of a special class of solutions to the (elliptic) Nonlinear Schroeodinger Equation $- \\\\epsilon^2 \\\\Delta \\\\psi + V(x) \\\\psi = |\\\\psi|^{p-1} \\\\psi$, on a manifold or in the Euclidean space. Here V represents the potential, p an exponent greater than 1 and $\\\\epsilon$ a small parameter corresponding to the Planck constant. As $\\\\epsilon$ tends to zero (namely in the semiclassical limit) we prove existence of complex-valued solutions which concentrate along closed curves, and whose phase is highly oscillatory. Physically, these solutions carry quantum-mechanical momentum along the limit curves. In this first part we provide the characterization of the limit set, with natural stationarity and non-degeneracy conditions. We then construct an approximate solution up to order $\\\\epsilon^2$, showing that these conditions appear naturally in a Taylor expansion of the equation in powers of $\\\\epsilon$. Based on these, an existence result will be proved in the second part.1 aMahmoudi, Fethi1 aMalchiodi, Andrea1 aMontenegro, Marcelo uhttp://hdl.handle.net/1963/211201231nas a2200109 4500008004300000245012500043210006900168520080600237100002001043700002201063856003601085 2007 en_Ud 00aSolutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part II: proof of the existence result0 aSolutions to the nonlinear Schroedinger equation carrying moment3 aWe prove existence of a special class of solutions to the (elliptic) Nonlinear Schroedinger Equation $- \\\\epsilon^2 \\\\Delta \\\\psi + V(x) \\\\psi = |\\\\psi|^{p-1} \\\\psi$ on a manifold or in the Euclidean space. Here V represents the potential, p is an exponent greater than 1 and $\\\\epsilon$ a small parameter corresponding to the Planck constant. As $\\\\epsilon$ tends to zero (namely in the semiclassical limit) we prove existence of complex-valued solutions which concentrate along closed curves, and whose phase in highly oscillatory. Physically, these solutions carry quantum-mechanical momentum along the limit curves. In the first part of this work we identified the limit set and constructed approximate solutions, while here we give the complete proof of our main existence result.1 aMahmoudi, Fethi1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/211100914nas a2200109 4500008004300000245006600043210006600109520054400175100002200719700002700741856003600768 2007 en_Ud 00aSome existence results for the Toda system on closed surfaces0 aSome existence results for the Toda system on closed surfaces3 aGiven a compact closed surface $\\\\Sig$, we consider the {\\\\em generalized Toda} system of equations on $\\\\Sig$: $- \\\\D u_i = \\\\sum_{j=1}^2 \\\\rho_j a_{ij} \\\\left( \\\\frac{h_j e^{u_j}}{\\\\int_\\\\Sig h_j e^{u_j} dV_g} - 1 \\\\right)$ for $i = 1, 2$, where $\\\\rho_1, \\\\rho_2$ are real parameters and $h_1, h_2$ are smooth positive functions. Exploiting the variational structure of the problem and using a new minimax scheme we prove existence of solutions for generic values of $\\\\rho_1$ and for $\\\\rho_2 < 4 \\\\pi$.1 aMalchiodi, Andrea1 aNdiaye, Cheikh Birahim uhttp://hdl.handle.net/1963/177500406nas a2200097 4500008004300000245011700043210006900160100001900229700002400248856003600272 2007 en_Ud 00aStability of front tracking solutions to the initial and boundary value problem for systems of conservation laws0 aStability of front tracking solutions to the initial and boundar1 aMarson, Andrea1 aDonadello, Carlotta uhttp://hdl.handle.net/1963/176900537nas a2200109 4500008004300000245006800043210006800111520016600179100002400345700002200369856003600391 2007 en_Ud 00aStanding waves of some coupled Nonlinear Schrödinger Equations0 aStanding waves of some coupled Nonlinear Schrödinger Equations3 aWe deal with a class of systems of NLS equations, proving the existence of bound and ground states provided the coupling parameter is small, respectively, large.1 aAmbrosetti, Antonio1 aColorado, Eduardo uhttp://hdl.handle.net/1963/182100738nas a2200097 4500008004300000245008700043210006900130520037600199100002900575856003600604 2007 en_Ud 00aStrengthened convergence of marginals to the cubic nonlinear Schroedinger equation0 aStrengthened convergence of marginals to the cubic nonlinear Sch3 aWe rewrite a recent derivation of the cubic non-linear Schroedinger equation by Adami, Golse, and Teta in the more natural formof the asymptotic factorisation of marginals at any fixed time and in the trace norm. This is the standard form in which the emergence of the\\nnon-linear effective dynamics of a large system of interacting bosons is\\nproved in the literature.1 aMichelangeli, Alessandro uhttp://hdl.handle.net/1963/197700907nas a2200121 4500008004300000245005500043210005300098520053100151100001900682700002500701700002300726856003600749 2007 en_Ud 00aSurfactants in Foam Stability: A Phase-Field Model0 aSurfactants in Foam Stability A PhaseField Model3 aThe role of surfactants in stabilizing the formation of bubbles in foams is studied using a phase-field model. The analysis is centered on a van der Walls-Cahn-Hilliard-type energy with an added term accounting for the interplay between the presence of a surfactant density and the creation of interfaces. In particular, it is concluded that the surfactant segregates to the interfaces, and that the prescriptionof the distribution of surfactant will dictate the locus of interfaces, what is in agreement with experimentation.1 aFonseca, Irene1 aMorini, Massimiliano1 aSlastikov, Valeriy uhttp://hdl.handle.net/1963/203500512nas a2200121 4500008004300000245004900043210004800092520014900140100002500289700001700314700002300331856003600354 2007 en_Ud 00aTime optimal swing-up of the planar pendulum0 aTime optimal swingup of the planar pendulum3 aThis paper presents qualitative and numerical results on the global structure of the time optimal trajectories of the planar pendulum on a cart.1 aBroucke, Mireille E.1 aMason, Paolo1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/186700987nas a2200133 4500008004300000245005700043210005600100520056800156100002100724700002200745700002500767700002500792856003600817 2007 en_Ud 00aTime-dependent systems of generalized Young measures0 aTimedependent systems of generalized Young measures3 aIn this paper some new tools for the study of evolution problems in the framework of Young measures are introduced. A suitable notion of time-dependent system of generalized Young measures is defined, which allows to extend the classical notions of total variation and absolute continuity with respect to time, as well as the notion of time derivative. The main results are a Helly type theorem for sequences of systems of generalized Young measures and a theorem about the existence of the time derivative for systems with bounded variation with respect to time.1 aDal Maso, Gianni1 aDeSimone, Antonio1 aMora, Maria Giovanna1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/179500630nas a2200097 4500008004300000245003900043210003900082520035800121100001700479856003600496 2007 en_Ud 00aTwisted noncommutative equivariant0 aTwisted noncommutative equivariant3 aWe propose Weil and Cartan models for the equivariant cohomology of covariant actions on toric deformation manifolds. The construction is based on the noncommutative Weil algebra of Alekseev and Meinrenken; we show that one can implement a Drinfeld twist of their models in order to take into account the noncommutativity of the spaces we are acting on.1 aCirio, Lucio uhttp://hdl.handle.net/1963/199100718nas a2200097 4500008004300000245012400043210006900167520032800236100002000564856003600584 2007 en_Ud 00aUniqueness and continuous dependence on boundary data for integro-extremal minimizers of the functional of the gradient0 aUniqueness and continuous dependence on boundary data for integr3 aWe study some qualitative properties of the integro-extremal minimizers of the functional of the gradient defined on Sobolev spaces with Dirichlet boundary conditions. We discuss their use in the non-convex case via viscosity methods and give conditions under which they are unique and depend continuously on boundary data.1 aZagatti, Sandro uhttp://hdl.handle.net/1963/276201073nas a2200121 4500008004300000245008500043210006900128260002100197520064400218100002800862700002500890856003600915 2007 en_Ud 00aViscosity solutions of Hamilton-Jacobi equations with discontinuous coefficients0 aViscosity solutions of HamiltonJacobi equations with discontinuo bWorld Scientific3 aWe consider Hamilton--Jacobi equations, where the Hamiltonian depends discontinuously on both the spatial and temporal location. Our main results are the existence and well--posedness of a viscosity solution to the Cauchy problem. We define a viscosity solution by treating the discontinuities in the coefficients analogously to \\\"internal boundaries\\\". By defining an appropriate penalization function, we prove that viscosity solutions are unique. The existence of viscosity solutions is established by showing that a sequence of front tracking approximations is compact in $L^\\\\infty$, and that the limits are viscosity solutions.1 aCoclite, Giuseppe Maria1 aRisebro, Nils Henrik uhttp://hdl.handle.net/1963/290700572nas a2200121 4500008004300000245003600043210003500079520024300114100002200357700001900379700001600398856003600414 2006 en_Ud 00a2-d stability of the Néel wall0 a2d stability of the Néel wall3 aWe are interested in thin-film samples in micromagnetism, where the magnetization m is a 2-d unit-length vector field. More precisely we are interested in transition layers which connect two opposite magnetizations, so called Néel walls.1 aDeSimone, Antonio1 aKnuepfer, Hans1 aOtto, Felix uhttp://hdl.handle.net/1963/219401024nas a2200121 4500008004300000245007500043210006900118520061700187100001800804700002500822700001900847856003600866 2006 en_Ud 00a4e-condensation in a fully frustrated Josephson junction diamond chain0 a4econdensation in a fully frustrated Josephson junction diamond 3 aFully frustrated one-dimensional diamond Josephson chains have been shown [B. Dou\\\\c{c}ot and J. Vidal, Phys. Rev. Lett. {\\\\bf 88}, 227005 (2002)] to posses a remarkable property: The superfluid phase occurs through the condensation of pairs of Cooper pairs. By means of Monte Carlo simulations we analyze quantitatively the Insulator to $4e$-Superfluid transition. We determine the location of the critical point and discuss the behaviour of the phase-phase correlators. For comparison we also present the case of a diamond chain at zero and 1/3 frustration where the standard $2e$-condensation is observed.1 aRizzi, Matteo1 aCataudella, Vittorio1 aFazio, Rosario uhttp://hdl.handle.net/1963/240000859nas a2200109 4500008004300000245008400043210006900127520047200196100002200668700002300690856003600713 2006 en_Ud 00aAlmost Global Stochastic Feedback Stabilization of Conditional Quantum Dynamics0 aAlmost Global Stochastic Feedback Stabilization of Conditional Q3 aWe propose several parametrization-free solutions to the problem of quantum state reduction control by means of continuous measurement and smooth quantum feedback. In particular, we design a feedback law for which almost global stochastic feedback stabilization can be proved analytically by means of Lyapunov techinques. This synthesis arises very naturally from the physics of the problem, as it relies on the variance associated with the quantum filtering process.1 aAltafini, Claudio1 aTicozzi, Francesco uhttp://hdl.handle.net/1963/172700611nas a2200109 4500008004300000245006500043210006200108520025700170100001900427700001900446856003600465 2006 en_Ud 00aAn artificial viscosity approach to quasistatic crack growth0 aartificial viscosity approach to quasistatic crack growth3 aWe introduce a new model of irreversible quasistatic crack growth in which the evolution of cracks is the limit of a suitably modified $\\\\epsilon$-gradient flow of the energy functional, as the \\\"viscosity\\\" parameter $\\\\epsilon$ tends to zero.1 aToader, Rodica1 aZanini, Chiara uhttp://hdl.handle.net/1963/185000957nas a2200109 4500008004300000245006000043210005600103520060900159100001900768700002400787856003600811 2006 en_Ud 00aA Birkhoff-Lewis-Type Theorem for Some Hamiltonian PDEs0 aBirkhoffLewisType Theorem for Some Hamiltonian PDEs3 aIn this paper we give an extension of the Birkhoff--Lewis theorem to some semilinear PDEs. Accordingly we prove existence of infinitely many periodic orbits with large period accumulating at the origin. Such periodic orbits bifurcate from resonant finite dimensional invariant tori of the fourth order normal form of the system. Besides standard nonresonance and nondegeneracy assumptions, our main result is obtained assuming a regularizing property of the nonlinearity. We apply our main theorem to a semilinear beam equation and to a nonlinear Schr\\\\\\\"odinger equation with smoothing nonlinearity.1 aBambusi, Dario1 aBerti, Massimiliano uhttp://hdl.handle.net/1963/215901209nas a2200097 4500008004300000245009800043210006900141520083600210100002901046856003601075 2006 en_Ud 00aBorn approximation in the problem of the rigorous derivation of the Gross-Pitaevskii equation0 aBorn approximation in the problem of the rigorous derivation of 3 a\\\"It has a flavour of Mathematical Physics...\\\"With these words, just few years ago, prof. Di Giacomo\\nused to introduce the topic of the Born approximation within a nonrelativistic potential theory, in his `oversize\\\' course of Theoretical Physics in Pisa. Something maybe too fictitious inside the formal theory of the scattering he was teaching us at that point of the course. Now that I\\\'m (studying to become) a Mathematical Physicist indeed, dealing with such an `exotic tasting\\\' topic, those words come back to the mind, into a new perspective. Here the very recent problem of the rigorous derivation of\\nthe cubic nonlinear Schrödinger equation (the Gross-Pitaevskiî equation) is reviewed and discussed, with respect to the role of the Born approximation that one ends up with in an appropriate scaling limit1 aMichelangeli, Alessandro uhttp://hdl.handle.net/1963/181900487nas a2200109 4500008004300000245007200043210007000115520011000185100002400295700002200319856003600341 2006 en_Ud 00aBound and ground states of coupled nonlinear Schrödinger equations0 aBound and ground states of coupled nonlinear Schrödinger equatio3 aWe prove existence of bound and ground states of some systems of coupled nonlinear Schrodinger equations.1 aAmbrosetti, Antonio1 aColorado, Eduardo uhttp://hdl.handle.net/1963/214900412nas a2200109 4500008004300000245009200043210006900135100002400204700002200228700001600250856003600266 2006 en_Ud 00aBound states of Nonlinear Schroedinger Equations with Potentials Vanishing at Infinity0 aBound states of Nonlinear Schroedinger Equations with Potentials1 aAmbrosetti, Antonio1 aMalchiodi, Andrea1 aRuiz, David uhttp://hdl.handle.net/1963/175600319nas a2200085 4500008004300000245006900043210006200112100002300174856003600197 2006 en_Ud 00aOn Bressan\\\'s conjecture on mixing properties of vector fields0 aBressans conjecture on mixing properties of vector fields1 aBianchini, Stefano uhttp://hdl.handle.net/1963/180601054nas a2200097 4500008004300000245006500043210005900108520073200167100002100899856003600920 2006 en_Ud 00aOn a Camassa-Holm type equation with two dependent variables0 aCamassaHolm type equation with two dependent variables3 aWe consider a generalization of the Camassa Holm (CH) equation with two dependent variables, called CH2, introduced in [16]. We briefly provide an alternative derivation of it based on the theory of Hamiltonian structures\\non (the dual of) a Lie Algebra. The Lie Algebra here involved is the same algebra underlying the NLS hierarchy. We study the structural properties of the CH2 hierarchy within the bihamiltonian theory of integrable PDEs, and\\nprovide its Lax representation. Then we explicitly discuss how to construct classes of solutions, both of peakon and of algebro-geometrical type. We finally sketch the construction of a class of singular solutions, defined by setting to zero one of the two dependent variables.1 aFalqui, Gregorio uhttp://hdl.handle.net/1963/172100728nas a2200109 4500008004300000245007900043210006900122520035400191100001900545700001800564856003600582 2006 en_Ud 00aA Canonical Frame for Nonholonomic Rank Two Distributions of Maximal Class0 aCanonical Frame for Nonholonomic Rank Two Distributions of Maxim3 aIn 1910 E. Cartan constructed the canonical frame and found the most symmetric case for maximally nonholonomic rank 2 distributions in R5. We solve the analogous problems for rank 2 distributions in Rn for arbitrary n > 5. Our method is a kind of symplectification of the problem and it is completely different from the Cartan method of equivalence.1 aDoubrov, Boris1 aZelenko, Igor uhttp://hdl.handle.net/1963/171201190nas a2200109 4500008004300000245009100043210006900134520079700203100002401000700002001024856003601044 2006 en_Ud 00aCantor families of periodic solutions for completely resonant nonlinear wave equations0 aCantor families of periodic solutions for completely resonant no3 aWe prove the existence of small amplitude, $2\\\\pi \\\\slash \\\\om$-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions, for any frequency $ \\\\om $ belonging to a Cantor-like set of positive measure and for a new set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem. In spite of the complete resonance of the equation we show that we can still reduce the problem to a {\\\\it finite} dimensional bifurcation equation. Moreover, a new simple approach for the inversion of the linearized operators required by the Nash-Moser scheme is developed. It allows to deal also with nonlinearities which are not odd and with finite spatial regularity.1 aBerti, Massimiliano1 aBolle, Philippe uhttp://hdl.handle.net/1963/216100378nas a2200109 4500008004300000245006600043210006400109100001700173700001900190700002300209856003600232 2006 en_Ud 00aClassification of stable time-optimal controls on 2-manifolds0 aClassification of stable timeoptimal controls on 2manifolds1 aBoscain, Ugo1 aNikolaev, Igor1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/219601052nas a2200121 4500008004300000245006900043210006900112520065900181100001700840700001700857700002000874856003600894 2006 en_Ud 00aCommon Polynomial Lyapunov Functions for Linear Switched Systems0 aCommon Polynomial Lyapunov Functions for Linear Switched Systems3 aIn this paper, we consider linear switched systems $\\\\dot x(t)=A_{u(t)} x(t)$, $x\\\\in\\\\R^n$, $u\\\\in U$, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching ({\\\\bf UAS} for short). We first prove that, given a {\\\\bf UAS} system, it is always possible to build a common polynomial Lyapunov function. Then our main result is that the degree of that common polynomial Lyapunov function is not uniformly bounded over all the {\\\\bf UAS} systems. This result answers a question raised by Dayawansa and Martin. A generalization to a class of piecewise-polynomial Lyapunov functions is given.1 aMason, Paolo1 aBoscain, Ugo1 aChitour, Yacine uhttp://hdl.handle.net/1963/218100823nas a2200097 4500008004300000245007000043210006900113520048500182100002200667856003600689 2006 en_Ud 00aCompactness of solutions to some geometric fourth-order equations0 aCompactness of solutions to some geometric fourthorder equations3 aWe prove compactness of solutions to some fourth order equations with exponential nonlinearities on four manifolds. The proof is based on a refined bubbling analysis, for which the main estimates are given in integral form. Our result is used in a subsequent paper to find critical points (via minimax arguments) of some geometric functional, which give rise to conformal metrics of constant $Q$-curvature. As a byproduct of our method, we also obtain compactness of such metrics.1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/212600921nas a2200109 4500008004300000245009700043210006900140520052400209100002000733700002200753856003600775 2006 en_Ud 00aConcentration at manifolds of arbitrary dimension for a singularly perturbed Neumann problem0 aConcentration at manifolds of arbitrary dimension for a singular3 aWe consider the equation $- \\\\e^2 \\\\D u + u = u^p$ in $\\\\O \\\\subseteq \\\\R^N$, where $\\\\O$ is open, smooth and bounded, and we prove concentration of solutions along $k$-dimensional minimal submanifolds of $\\\\pa \\\\O$, for $N \\\\geq 3$ and for $k \\\\in \\\\{1, \\\\dots, N-2\\\\}$. We impose Neumann boundary conditions, assuming $1<\\\\frac{N-k+2}{N-k-2}$ and $\\\\e \\\\to 0^+$. This result settles in full generality a phenomenon previously considered only in the particular case $N = 3$ and $k = 1$.1 aMahmoudi, Fethi1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/217000638nas a2200109 4500008004300000245006800043210006800111520027600179100002100455700001600476856003600492 2006 en_Ud 00aConservative Solutions to a Nonlinear Variational Wave Equation0 aConservative Solutions to a Nonlinear Variational Wave Equation3 aWe establish the existence of a conservative weak solution to the Cauchy problem for the nonlinear variational wave equation $u_{tt} - c(u)(c(u)u_x)_x=0$, for initial data of finite energy. Here $c(\\\\cdot)$ is any smooth function with uniformly positive bounded values.1 aBressan, Alberto1 aYuxi, Zheng uhttp://hdl.handle.net/1963/218401941nas a2200133 4500008004300000245006300043210005900106520150700165100002501672700003001697700002001727700002401747856003601771 2006 en_Ud 00aA cyclic integral on k-Minkowski noncommutative space-time0 acyclic integral on kMinkowski noncommutative spacetime3 aWe examine some alternative possibilities for an action functional for $\\\\kappa$-Minkowski noncommutative spacetime, with an approach which should be applicable to other spacetimes with coordinate-dependent commutators of the spacetime coordinates ($[x_\\\\mu,x_\\\\nu]=f_{\\\\mu,\\\\nu}(x)$). Early works on $\\\\kappa$-Minkowski focused on $\\\\kappa$-Poincar\\\\\\\'e covariance and the dependence of the action functional on the choice of Weyl map, renouncing to invariance under cyclic permutations of the factors composing the argument of the action functional. A recent paper (hep-th/0307149), by Dimitrijevic, Jonke, Moller, Tsouchnika, Wess and Wohlgenannt, focused on a specific choice of Weyl map and, setting aside the issue of $\\\\kappa$-Poincar\\\\\\\'e covariance of the action functional, introduced in implicit form a cyclicity-inducing measure. We provide an explicit formula for (and derivation of) a choice of measure which indeed ensures cyclicity of the action functional, and we show that the same choice of measure is applicable to all the most used choices of Weyl map. We find that this ``cyclicity-inducing measure\\\'\\\' is not covariant under $\\\\kappa$-Poincar\\\\\\\'e transformations. We also notice that the cyclicity-inducing measure can be straightforwardly derived using a map which connects the $\\\\kappa$-Minkowski spacetime coordinates and the spacetime coordinates of a ``canonical\\\'\\\' noncommutative spacetime, with coordinate-independent commutators.1 aAgostini, Alessandra1 aAmelino-Camelia, Giovanni1 aArzano, Michele1 aD'Andrea, Francesco uhttp://hdl.handle.net/1963/215800395nas 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/1963/225200974nas a2200109 4500008004300000245009300043210006900136520057600205100002500781700002200806856003600828 2006 en_Ud 00aAn estimation of the controllability time for single-input systems on compact Lie Groups0 aestimation of the controllability time for singleinput systems o3 aGeometric control theory and Riemannian techniques are used to describe the reachable set at time t of left invariant single-input control systems on semi-simple compact Lie groups and to estimate the minimal time needed to reach any point from identity. This method provides an effective way to give an upper and a lower bound for the minimal time needed to transfer a controlled quantum system with a drift from a given initial position to a given final position. The bounds include diameters of the flag manifolds; the latter are also explicitly computed in the paper.1 aAgrachev, Andrei, A.1 aChambrion, Thomas uhttp://hdl.handle.net/1963/213502436nas a2200169 4500008004100000245007600041210006900117260007200186520184400258100002002102700002202122700001802144700002502162700001902187700002402206856003602230 2006 en d00aExperimental and modeling studies of desensitization of P2X3 receptors.0 aExperimental and modeling studies of desensitization of P2X3 rec bthe American Society for Pharmacology and Experimental Therapeutics3 aThe function of ATP-activated P2X3 receptors involved in pain sensation is modulated by desensitization, a phenomenon poorly understood. The present study used patch-clamp recording from cultured rat or mouse sensory neurons and kinetic modeling to clarify the properties of P2X3 receptor desensitization. Two types of desensitization were observed, a fast process (t1/2 = 50 ms; 10 microM ATP) following the inward current evoked by micromolar agonist concentrations, and a slow process (t1/2 = 35 s; 10 nM ATP) that inhibited receptors without activating them. We termed the latter high-affinity desensitization (HAD). Recovery from fast desensitization or HAD was slow and agonist-dependent. When comparing several agonists, there was analogous ranking order for agonist potency, rate of desensitization and HAD effectiveness, with 2-methylthioadenosine triphosphate the strongest and beta,gamma-methylene-ATP the weakest. HAD was less developed with recombinant (ATP IC50 = 390 nM) than native P2X3 receptors (IC50 = 2.3 nM). HAD could also be induced by nanomolar ATP when receptors seemed to be nondesensitized, indicating that resting receptors could express high-affinity binding sites. Desensitization properties were well accounted for by a cyclic model in which receptors could be desensitized from either open or closed states. Recovery was assumed to be a multistate process with distinct kinetics dependent on the agonist-dependent dissociation rate from desensitized receptors. Thus, the combination of agonist-specific mechanisms such as desensitization onset, HAD, and resensitization could shape responsiveness of sensory neurons to P2X3 receptor agonists. By using subthreshold concentrations of an HAD-potent agonist, it might be possible to generate sustained inhibition of P2X3 receptors for controlling chronic pain.1 aSokolova, Elena1 aSkorinkin, Andrei1 aMoiseev, Igor1 aAgrachev, Andrei, A.1 aNistri, Andrea1 aGiniatullin, Rashid uhttp://hdl.handle.net/1963/497400687nas a2200121 4500008004300000245006200043210005900105520031100164100002000475700001800495700001600513856003600529 2006 en_Ud 00aExtended affine Weyl groups and Frobenius manifolds -- II0 aExtended affine Weyl groups and Frobenius manifolds II3 aFor the root system of type $B_l$ and $C_l$, we generalize the result of \\\\cite{DZ1998} by showing the existence of a Frobenius manifold structure on the orbit space of the extended affine Weyl group that corresponds to any vertex of the Dynkin diagram instead of a particular choice of \\\\cite{DZ1998}.1 aDubrovin, Boris1 aYoujin, Zhang1 aDafeng, Zuo uhttp://hdl.handle.net/1963/178700868nas a2200109 4500008004300000245007300043210006900116520049600185100002400681700001700705856003600722 2006 en_Ud 00aForced vibrations of wave equations with non-monotone nonlinearities0 aForced vibrations of wave equations with nonmonotone nonlinearit3 aWe prove existence and regularity of periodic in time solutions of completely resonant nonlinear forced wave equations with Dirichlet boundary conditions for a large class of non-monotone forcing terms. Our approach is based on a variational Lyapunov-Schmidt reduction. It turns out that the infinite dimensional bifurcation equation exhibits an intrinsic lack of compactness. We solve it via a minimization argument and a-priori estimate methods inspired to regularity theory of Rabinowitz.1 aBerti, Massimiliano1 aBiasco, Luca uhttp://hdl.handle.net/1963/216001285nas a2200097 4500008004300000245007100043210006700114520095200181100001801133856003601151 2006 en_Ud 00aFundamental form and Cartan tensor of (2,5)-distributions coincide0 aFundamental form and Cartan tensor of 25distributions coincide3 aIn our previous paper for generic rank 2 vector distributions on n-dimensional manifold (n greater or equal to 5) we constructed a special differential invariant, the fundamental form. In the case n=5 this differential invariant has the same algebraic nature, as the covariant binary biquadratic form, constructed by E.Cartan in 1910, using his ``reduction- prolongation\\\'\\\' procedure (we call this form Cartan\\\'s tensor). In the present paper we prove that our fundamental form coincides (up to constant factor -35) with Cartan\\\'s tensor. This result explains geometric reason for existence of Cartan\\\'s tensor (originally this tensor was obtained by very sophisticated algebraic manipulations) and gives the true analogs of this tensor in Riemannian geometry. In addition, as a part of the proof, we obtain a new useful formula for Cartan\\\'s tensor in terms of structural functions of any frame naturally adapted to the distribution.1 aZelenko, Igor uhttp://hdl.handle.net/1963/218701442nas a2200097 4500008004300000245010600043210006900149520107200218100001801290856003601308 2006 en_Ud 00aOn geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on distributions of corank 10 ageodesic equivalence of Riemannian metrics and subRiemannian met3 aThe present paper is devoted to the problem of (local) geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on generic corank 1 distributions. Using Pontryagin Maximum Principle, we treat Riemannian and sub-Riemannian cases in an unified way and obtain some algebraic necessary conditions for the geodesic equivalence of (sub-)Riemannian metrics. In this way first we obtain a new elementary proof of classical Levi-Civita\\\'s Theorem about the classification of all Riemannian geodesically equivalent metrics in a neighborhood of so-called regular (stable) point w.r.t. these metrics. Secondly we prove that sub-Riemannian metrics on contact distributions are geodesically equivalent iff they are constantly proportional. Then we describe all geodesically equivalent sub-Riemannian metrics on quasi-contact distributions. Finally we make the classification of all pairs of geodesically equivalent Riemannian metrics on a surface, which proportional in an isolated point. This is the simplest case, which was not covered by Levi-Civita\\\'s Theorem.1 aZelenko, Igor uhttp://hdl.handle.net/1963/220500286nas a2200085 4500008004300000245004900043210004900092100002300141856003600164 2006 en_Ud 00aGlimm interaction functional for BGK schemes0 aGlimm interaction functional for BGK schemes1 aBianchini, Stefano uhttp://hdl.handle.net/1963/177000819nas a2200097 4500008004300000245011600043210006900159520043700228100002000665856003600685 2006 en_Ud 00aOn Hamiltonian perturbations of hyperbolic systems of conservation laws, II: universality of critical behaviour0 aHamiltonian perturbations of hyperbolic systems of conservation 3 aHamiltonian perturbations of the simplest hyperbolic equation $u_t + a(u) u_x=0$ are studied. We argue that the behaviour of solutions to the perturbed equation near the point of gradient catastrophe of the unperturbed one should be essentially independent on the choice of generic perturbation neither on the choice of generic solution. Moreover, this behaviour is described by a special solution to an integrable fourth order ODE.1 aDubrovin, Boris uhttp://hdl.handle.net/1963/178601265nas a2200121 4500008004300000245012600043210006900169520081600238100002001054700001501074700001801089856003601107 2006 en_Ud 00aOn Hamiltonian perturbations of hyperbolic systems of conservation laws I: quasitriviality of bihamiltonian perturbations0 aHamiltonian perturbations of hyperbolic systems of conservation 3 aWe study the general structure of formal perturbative solutions to the Hamiltonian perturbations of spatially one-dimensional systems of hyperbolic PDEs. Under certain genericity assumptions it is proved that any bihamiltonian perturbation can be eliminated in all orders of the perturbative expansion by a change of coordinates on the infinite jet space depending rationally on the derivatives. The main tools is in constructing of the so-called quasi-Miura transformation of jet coordinates eliminating an arbitrary deformation of a semisimple bihamiltonian structure of hydrodynamic type (the quasitriviality theorem). We also describe, following \\\\cite{LZ1}, the invariants of such bihamiltonian structures with respect to the group of Miura-type transformations depending polynomially on the derivatives.1 aDubrovin, Boris1 aSi-Qi, Liu1 aYoujin, Zhang uhttp://hdl.handle.net/1963/253500866nas a2200097 4500008004300000245013100043210006900174520046700243100002200710856003600732 2006 en_Ud 00aHomogeneous polynomial forms for simultaneous stabilizability of families of linear control systems: a tensor product approach0 aHomogeneous polynomial forms for simultaneous stabilizability of3 aThe paper uses the formalism of tensor products in order to deal with the problem of simultaneous\\nstabilizability of a family of linear control systems by means of Lyapunov functions which are homogeneous polynomial forms. While the feedback synthesis seems to be nonconvex, the simultaneous stability by means of homogeneous polynomial forms of the uncontrollable modes yields (convex) necessary but not sufficient conditions for simultaneous stabilizability.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/222601156nas a2200121 4500008004300000245007100043210006800114520075900182100002000941700001900961700001800980856003600998 2006 en_Ud 00aA Hopf bundle over a quantum four-sphere from the symplectic group0 aHopf bundle over a quantum foursphere from the symplectic group3 aWe construct a quantum version of the SU(2) Hopf bundle $S^7 \\\\to S^4$. The quantum sphere $S^7_q$ arises from the symplectic group $Sp_q(2)$ and a quantum 4-sphere $S^4_q$ is obtained via a suitable self-adjoint idempotent $p$ whose entries generate the algebra $A(S^4_q)$ of polynomial functions over it. This projection determines a deformation of an (anti-)instanton bundle over the classical sphere $S^4$. We compute the fundamental $K$-homology class of $S^4_q$ and pair it with the class of $p$ in the $K$-theory getting the value -1 for the topological charge. There is a right coaction of $SU_q(2)$ on $S^7_q$ such that the algebra $A(S^7_q)$ is a non trivial quantum principal bundle over $A(S^4_q)$ with structure quantum group $A(SU_q(2))$.1 aLandi, Giovanni1 aPagani, Chiara1 aReina, Cesare uhttp://hdl.handle.net/1963/217900794nas a2200109 4500008004300000245005500043210005500098520044900153100002100602700002500623856003600648 2006 en_Ud 00aInfinite Horizon Noncooperative Differential Games0 aInfinite Horizon Noncooperative Differential Games3 aFor a non-cooperative differential game, the value functions of the various players satisfy a system of Hamilton-Jacobi equations. In the present paper, we consider a class of infinite-horizon games with nonlinear costs exponentially discounted in time. By the analysis of the value\\nfunctions, we establish the existence of Nash equilibrium solutions in feedback form and provide results and counterexamples on their uniqueness and stability.1 aBressan, Alberto1 aPriuli, Fabio Simone uhttp://hdl.handle.net/1963/172000891nas a2200121 4500008004300000245004100043210003800084520054500122100002100667700002800688700001700716856003600733 2006 en_Ud 00aAn instability of the Godunov scheme0 ainstability of the Godunov scheme3 aWe construct a solution to a $2\\\\times 2$ strictly hyperbolic system of conservation laws, showing that the Godunov scheme \\\\cite{Godunov59} can produce an arbitrarily large amount of oscillations. This happens when the speed of a shock is close to rational, inducing a resonance with the grid. Differently from the Glimm scheme or the vanishing viscosity method, for systems of conservation laws our counterexample indicates that no a priori BV bounds or $L^1$ stability estimates can in general be valid for finite difference schemes.1 aBressan, Alberto1 aJenssen, Helge Kristian1 aBaiti, Paolo uhttp://hdl.handle.net/1963/218300940nas a2200109 4500008004300000245005300043210005300096520060900149100001800758700001800776856003600794 2006 en_Ud 00aLarge Parameter Behavior of Equilibrium Measures0 aLarge Parameter Behavior of Equilibrium Measures3 aWe study the equilibrium measure for a logarithmic potential in the presence of an external field V*(x) + tp(x), where t is a parameter, V*(x) is a smooth function and p(x) a monic polynomial. When p(x) is of an odd degree, the equilibrium measure is shown to be supported on a single interval as |t| is sufficiently large. When p(x) is of an even degree, the equilibrium measure is supported on two disjoint intervals as t is negatively large; it is supported on a single interval for convex p(x) as t is positively large and is likely to be supported on multiple disjoint intervals for non-convex p(x).1 aGrava, Tamara1 aTian, Fei-Ran uhttp://hdl.handle.net/1963/178900649nas a2200109 4500008004300000245005600043210005600099520030200155100002400457700002200481856003600503 2006 en_Ud 00aLocal Index Formula on the Equatorial Podles Sphere0 aLocal Index Formula on the Equatorial Podles Sphere3 aWe discuss spectral properties of the equatorial Podles sphere. As a preparation we also study the `degenerate\\\' (i.e. $q=0$) case (related to the quantum disk). We consider two different spectral triples: one related to the Fock representation of the Toeplitz algebra and the isopectral one....1 aD'Andrea, Francesco1 aDabrowski, Ludwik uhttp://hdl.handle.net/1963/178200691nas a2200109 4500008004100000245006700041210006500108260001000173520034100183100002100524856003600545 2006 en d00aMatching Procedure for the Sixth Painlevé Equation (May 2006)0 aMatching Procedure for the Sixth Painlevé Equation May 2006 bSISSA3 aWe present a constructive procedure to obtain the critical behavior of\r\nPainleve\' VI transcendents and solve the connection problem. This procedure\r\nyields two and one parameter families of solutions, including trigonometric and\r\nlogarithmic behaviors, and three classes of solutions with Taylor expansion at\r\na critical point.1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/652400790nas a2200133 4500008004300000245005400043210005200097520038200149100002200531700002100553700002200574700002400596856003600620 2006 en_Ud 00aN=1 superpotentials from multi-instanton calculus0 aN1 superpotentials from multiinstanton calculus3 aIn this paper we compute gaugino and scalar condensates in N = 1 supersymmetric gauge\\ntheories with and without massive adjoint matter, using localization formulae over the multi-instanton moduli space. Furthermore we compute the chiral ring relations among the correlators of the N = 1* theory and check this result against the multi-instanton computation finding agreement.1 aFucito, Francesco1 aMorales, Jose F.1 aPoghossian, Rubik1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/177300736nas a2200109 4500008004300000245007600043210006900119520036700188100001600555700001900571856003600590 2006 en_Ud 00aNormal bundles to Laufer rational curves in local Calabi-Yau threefolds0 aNormal bundles to Laufer rational curves in local CalabiYau thre3 aWe prove a conjecture by F. Ferrari. Let X be the total space of a nonlinear deformation of a rank 2 holomorphic vector bundle on a smooth rational curve, such that X has trivial canonical bundle and has sections. Then the normal bundle to such sections is computed in terms of the rank of the Hessian of a suitably defined superpotential at its critical points.1 aBruzzo, Ugo1 aRicco, Antonio uhttp://hdl.handle.net/1963/178500673nas a2200109 4500008004300000245005900043210005300102520033100155100002100486700002000507856003600527 2006 en_Ud 00aOn Palais-Smale sequences for H-systems: some examples0 aPalaisSmale sequences for Hsystems some examples3 aWe exhibit a series of examples of Palais-Smale sequences for the Dirichlet problem associated to the mean curvature equation with null boundary condition, and we show that in the case of nonconstant mean curvature functions different kinds of blow up phenomena appear and Palais-Smale sequences may have quite wild behaviour.1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/215700484nas a2200133 4500008004100000022001400041245007300055210006800128300001200196490000600208100001900214700002100233856009600254 2006 eng d a1385-017200aThe PDEs of biorthogonal polynomials arising in the two-matrix model0 aPDEs of biorthogonal polynomials arising in the twomatrix model a23–520 v91 aBertola, Marco1 aEynard, Bertrand uhttp://www.math.sissa.it/publication/pdes-biorthogonal-polynomials-arising-two-matrix-model00833nas a2200145 4500008004100000022001300041245010300054210006900157300001200226490000700238520027500245100001300520700002400533856013000557 2006 eng d a1120633000aPeriodic solutions of nonlinear wave equations for asymptotically full measure sets of frequencies0 aPeriodic solutions of nonlinear wave equations for asymptoticall a257-2770 v173 aWe prove existence and multiplicity of small amplitude periodic solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for asymptotically full measure sets of frequencies, extending the results of [7] to new types of nonlinearities.1 aBaldi, P1 aBerti, Massimiliano uhttp://www.math.sissa.it/publication/periodic-solutions-nonlinear-wave-equations-asymptotically-full-measure-sets-frequenci-000273nas a2200097 4500008004300000245002800043210002600071100002200097700002000119856003600139 2006 en_Ud 00aQ-curvature flow on S^40 aQcurvature flow on S41 aMalchiodi, Andrea1 aStruwe, Michael uhttp://hdl.handle.net/1963/219300738nas a2200109 4500008004300000245003400043210003400077520044300111100002100554700001700575856003600592 2006 en_Ud 00aQuantisation of bending flows0 aQuantisation of bending flows3 aWe briefly review the Kapovich-Millson notion of Bending flows as an integrable system on the space of polygons in ${\\\\bf R}^3$, its connection with a specific Gaudin XXX system, as well as the generalisation to $su(r), r>2$. Then we consider the quantisation problem of the set of Hamiltonians pertaining to the problem, quite naturally called Bending Hamiltonians, and prove that their commutativity is preserved at the quantum level.1 aFalqui, Gregorio1 aMusso, Fabio uhttp://hdl.handle.net/1963/253700676nas a2200109 4500008004300000245007400043210006900117520029900186100002400485700002100509856003600530 2006 en_Ud 00aQuasi-periodic solutions of completely resonant forced wave equations0 aQuasiperiodic solutions of completely resonant forced wave equat3 aWe prove existence of quasi-periodic solutions with two frequencies of completely resonant, periodically forced nonlinear wave equations with periodic spatial boundary conditions. We consider both the cases the forcing frequency is: (Case A) a rational number and (Case B) an irrational number.1 aBerti, Massimiliano1 aProcesi, Michela uhttp://hdl.handle.net/1963/223401091nas a2200121 4500008004300000245008400043210006900127520066900196100002100865700002200886700002500908856003600933 2006 en_Ud 00aQuasistatic evolution problems for linearly elastic-perfectly plastic materials0 aQuasistatic evolution problems for linearly elasticperfectly pla3 aThe problem of quasistatic evolution in small strain associative elastoplasticity is studied in the framework of the variational theory for rate-independent processes. Existence of solutions is proved through the use of incremental variational problems in spaces of functions with bounded deformation. This provides a new approximation result for the solutions of the quasistatic evolution problem, which are shown to be absolutely continuous in time. Four equivalent formulations of the problem in rate form are derived. A strong formulation of the flow rule is obtained by introducing a precise definition of the stress on the singular set of the plastic strain.1 aDal Maso, Gianni1 aDeSimone, Antonio1 aMora, Maria Giovanna uhttp://hdl.handle.net/1963/212900669nas a2200109 4500008004300000245010800043210007000151520026200221100002400483700001600507856003600523 2006 en_Ud 00aRadial solutions concentrating on spheres of nonlinear Schrödinger equations with vanishing potentials0 aRadial solutions concentrating on spheres of nonlinear Schröding3 aWe prove the existence of radial solutions of 1.2) concentrating at a sphere for potentials which might be zero and might decay to zero at\\r\\ninfinity. The proofs use a perturbation technique in a variational setting, through a Lyapunov-Schmidt reduction.1 aAmbrosetti, Antonio1 aRuiz, David uhttp://hdl.handle.net/1963/175500420nas a2200133 4500008004300000020002200043245005300065210005300118100002200171700002100193700002000214700001600234856003600250 2006 en_Ud a978-0-12-480874-400aRecent analytical developments in micromagnetics0 aRecent analytical developments in micromagnetics1 aDeSimone, Antonio1 aKohn, Robert, V.1 aMüller, Stefan1 aOtto, Felix uhttp://hdl.handle.net/1963/223001165nas a2200109 4500008004300000245005900043210005900102520081400161100002200975700002200997856003601019 2006 en_Ud 00aReflection symmetries for multiqubit density operators0 aReflection symmetries for multiqubit density operators3 aFor multiqubit density operators in a suitable tensorial basis, we show that a number of nonunitary operations used in the detection and synthesis of entanglement are classifiable as reflection symmetries, i.e., orientation changing rotations. While one-qubit reflections correspond to antiunitary symmetries, as is known for example from the partial transposition criterion, reflections on the joint density of two or more qubits are not accounted for by the Wigner Theorem and are well-posed only for sufficiently mixed states. One example of such nonlocal reflections is the unconditional NOT operation on a multiparty density, i.e., an operation yelding another density and such that the sum of the two is the identity operator. This nonphysical operation is admissible only for sufficiently mixed states.1 aAltafini, Claudio1 aHavel, Timothy F. uhttp://hdl.handle.net/1963/212100553nas a2200145 4500008004100000022001400041245008800055210006900143300001400212490000800226100001900234700001500253700001500268856012400283 2006 eng d a0010-361600aSemiclassical orthogonal polynomials, matrix models and isomonodromic tau functions0 aSemiclassical orthogonal polynomials matrix models and isomonodr a401–4370 v2631 aBertola, Marco1 aEynard, B.1 aHarnad, J. uhttp://www.math.sissa.it/publication/semiclassical-orthogonal-polynomials-matrix-models-and-isomonodromic-tau-functions01043nas a2200109 4500008004300000245005700043210005400100520069600154100001600850700003100866856003600897 2006 en_Ud 00aSemistability vs. nefness for (Higgs) vector bundles0 aSemistability vs nefness for Higgs vector bundles3 aAccording to Miyaoka, a vector bundle E on a smooth projective curve is semistable if and only if a certain numerical class in the projectivized bundle PE is nef. We establish a similar criterion for the semistability of Higgs bundles: namely, such a bundle is semistable if and only if for every integer s between 0 and the rank of E, a suitable numerical class in the scheme parametrizing the rank s locally-free Higgs quotients of E is nef. We also extend this result to higher-dimensional complex projective varieties by showing that the nefness of the above mentioned classes is equivalent to the semistability of the Higgs bundle E together with the vanishing of the discriminant of E.1 aBruzzo, Ugo1 aHernandez Ruiperez, Daniel uhttp://hdl.handle.net/1963/223700519nas a2200109 4500008004300000245006800043210006300111520016100174100002100335700001700356856003600373 2006 en_Ud 00aOn Separation of Variables for Homogeneous SL(r) Gaudin Systems0 aSeparation of Variables for Homogeneous SLr Gaudin Systems3 aBy means of a recently introduced bihamiltonian structure for the homogeneous Gaudin models, we find a new set of Separation Coordinates for the sl(r) case.1 aFalqui, Gregorio1 aMusso, Fabio uhttp://hdl.handle.net/1963/253801217nas a2200097 4500008004300000245004300043210004200086520093100128100002401059856003601083 2006 en_Ud 00aSpectral geometry of k-Minkowski space0 aSpectral geometry of kMinkowski space3 aAfter recalling Snyder's idea of using vector fields over a smooth manifold as "coordinates on a noncommutative space", we discuss a two dimensional toy-model whose "dual" noncommutative coordinates form a Lie algebra: this is the well known $\kappa$-Minkowski space. We show how to improve Snyder's idea using the tools of quantum groups and noncommutative geometry. We find a natural representation of the coordinate algebra of $\kappa$-Minkowski as linear operators on an Hilbert space study its "spectral properties" and discuss how to obtain a Dirac operator for this space. We describe two Dirac operators. The first is associated with a spectral triple. We prove that the cyclic integral of M. Dimitrijevic et al. can be obtained as Dixmier trace associated to this triple. The second Dirac operator is equivariant for the action of the quantum Euclidean group, but it has unbounded commutators with the algebra.

1 aD'Andrea, Francesco uhttp://hdl.handle.net/1963/213100968nas a2200121 4500008004300000245005100043210005100094520060400145100001700749700002300766700002100789856003600810 2006 en_Ud 00aStability of planar nonlinear switched systems0 aStability of planar nonlinear switched systems3 aWe consider the time-dependent nonlinear system ˙ q(t) = u(t)X(q(t)) + (1 − u(t))Y (q(t)), where q ∈ R2, X and Y are two smooth vector fields, globally asymptotically stable at the origin and u : [0,∞) → {0, 1} is an arbitrary measurable function. Analysing the topology of the set where X and Y are parallel, we give some sufficient and some necessary conditions for global asymptotic stability, uniform with respect to u(.). Such conditions can be verified without any integration or construction of a Lyapunov function, and they are robust under small perturbations of the vector fields.1 aBoscain, Ugo1 aCharlot, Grégoire1 aSigalotti, Mario uhttp://hdl.handle.net/1963/171000778nas a2200109 4500008004300000245004900043210004800092520045100140100002300591700001800614856003600632 2006 en_Ud 00aThomae type formulae for singular Z_N curves0 aThomae type formulae for singular ZN curves3 aWe give an elementary and rigorous proof of the Thomae type formula for singular $Z_N$ curves. To derive the Thomae formula we use the traditional variational method which goes back to Riemann, Thomae and Fuchs. An important step of the proof is the use of the Szego kernel computed explicitly in algebraic form for non-singular 1/N-periods. The proof inherits principal points of Nakayashiki\\\'s proof [31], obtained for non-singular ZN curves.1 aEnolski, Victor Z.1 aGrava, Tamara uhttp://hdl.handle.net/1963/212502083nas a2200109 4500008004300000245007400043210006900117520171700186100001701903700001701920856003601937 2006 en_Ud 00aTime Minimal Trajectories for a Spin 1/2 Particle in a Magnetic field0 aTime Minimal Trajectories for a Spin 12 Particle in a Magnetic f3 aIn this paper we consider the minimum time population transfer problem for the z-component\\nof the spin of a (spin 1/2) particle driven by a magnetic field, controlled along the x axis, with bounded amplitude. On the Bloch sphere (i.e. after a suitable Hopf projection), this problem can be attacked with techniques of optimal syntheses on 2-D manifolds. Let (-E,E) be the two energy levels, and |omega (t)| ≤ M the bound on the field amplitude. For each couple of values E and M, we determine the time optimal synthesis starting from the level -E and we provide the explicit expression of the time optimal trajectories steering the state one to the state two, in terms of a parameter that can be computed solving numerically a suitable equation. For M/E << 1, every time optimal trajectory is bang-bang and in particular the corresponding control is periodic with frequency of the order of the resonance frequency wR = 2E. On the other side, for M/E > 1, the time optimal trajectory steering the state one to the state two is bang-bang with exactly one switching. Fixed E we also prove that for M → ∞ the time needed to reach the state two tends to zero. In the case M/E > 1 there are time optimal trajectories containing a singular arc. Finally we compare these results with some known results of Khaneja, Brockett and Glaser and with those obtained by controlling the magnetic field both on the x and y directions (or with one external field, but in the rotating wave approximation). As byproduct we prove that the qualitative shape of the time optimal synthesis presents different patterns, that cyclically alternate as M/E → 0, giving a partial proof of a conjecture formulated in a previous paper.1 aBoscain, Ugo1 aMason, Paolo uhttp://hdl.handle.net/1963/173400584nas a2200121 4500008004300000245002800043210002400071520026800095100002000363700002400383700001900407856003600426 2006 en_Ud 00aOn topological M-theory0 atopological Mtheory3 aWe construct a gauge fixed action for topological membranes on G2-manifolds such that its bosonic part is the standard membrane theory in a particular gauge. We prove that quantum mechanically the path-integral in this gauge localizes on associative submanifolds.1 aBonelli, Giulio1 aTanzini, Alessandro1 aZabzine, Maxim uhttp://hdl.handle.net/1963/176501554nas a2200109 4500008004300000245008800043210006900131520116300200100002101363700002401384856003601408 2006 en_Ud 00aTopological symmetry of forms, N=1 supersymmetry and S-duality on special manifolds0 aTopological symmetry of forms N1 supersymmetry and Sduality on s3 aWe study the quantization of a holomorphic two-form coupled to a Yang-Mills field on special manifolds in various dimensions, and we show that it yields twisted supersymmetric theories. The construction determines ATQFT\\\'s (Almost Topological Quantum Field Theories), that is, theories with observables that are invariant under changes of metrics belonging to restricted classes. For Kahler manifolds in four dimensions, our topological model is related to N=1 Super Yang-Mills theory. Extended supersymmetries are recovered by considering the coupling with chiral multiplets. We also analyse Calabi-Yau manifolds in six and eight dimensions, and seven dimensional G_2 manifolds of the kind recently discussed by Hitchin. We argue that the two-form field could play an interesting role for the study of the conjectured S-duality in topological string. We finally show that in the case of real forms in six dimensions the partition function of our topological model is related to the square of that of the holomorphic Chern-Simons theory, and we discuss the uplift to seven dimensions and its relation with the recent proposals for the topological M-theory.1 aBaulieu, Laurent1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/216800484nas a2200121 4500008004100000022001400041245008200055210006900137300001600206490000700222100001900229856011400248 2006 eng d a0305-447000aTwo-matrix model with semiclassical potentials and extended Whitham hierarchy0 aTwomatrix model with semiclassical potentials and extended Whith a8823–88550 v391 aBertola, Marco uhttp://www.math.sissa.it/publication/two-matrix-model-semiclassical-potentials-and-extended-whitham-hierarchy01070nas a2200121 4500008004100000020002200041245006200063210005900125260003400184520067400218100002000892856003600912 2006 en d a978-0-8218-4674-200aOn universality of critical behaviour in Hamiltonian PDEs0 auniversality of critical behaviour in Hamiltonian PDEs bAmerican Mathematical Society3 aOur main goal is the comparative study of singularities of solutions to\\r\\nthe systems of rst order quasilinear PDEs and their perturbations containing higher\\r\\nderivatives. The study is focused on the subclass of Hamiltonian PDEs with one\\r\\nspatial dimension. For the systems of order one or two we describe the local structure\\r\\nof singularities of a generic solution to the unperturbed system near the point of\\r\\n\\\\gradient catastrophe\\\" in terms of standard objects of the classical singularity theory;\\r\\nwe argue that their perturbed companions must be given by certain special solutions\\r\\nof Painlev e equations and their generalizations.1 aDubrovin, Boris uhttp://hdl.handle.net/1963/649101764nas a2200097 4500008004300000245008100043210006900124520141900193100001801612856003601630 2006 en_Ud 00aOn variational approach to differential invariants of rank two distributions0 avariational approach to differential invariants of rank two dist3 an the present paper we construct differential invariants for generic rank 2 vector distributions on n-dimensional manifold. In the case n=5 (the first case containing functional parameters) E. Cartan found in 1910 the covariant fourth-order tensor invariant for such distributions, using his \\\"reduction-prolongation\\\" procedure. After Cartan\\\'s work the following questions remained open: first the geometric reason for existence of Cartan\\\'s tensor was not clear; secondly it was not clear how to generalize this tensor to other classes of distributions; finally there were no explicit formulas for computation of Cartan\\\'s tensor. Our paper is the first in the series of papers, where we develop an alternative approach, which gives the answers to the questions mentioned above. It is based on the investigation of dynamics of the field of so-called abnormal extremals (singular curves) of rank 2 distribution and on the general theory of unparametrized curves in the Lagrange Grassmannian, developed in our previous works with A. Agrachev . In this way we construct the fundamental form and the projective Ricci curvature of rank 2 vector distributions for arbitrary n greater than 4.\\nFor n=5 we give an explicit method for computation of these invariants and demonstrate it on several examples. In our next paper we show that in the case n=5 our fundamental form coincides with Cartan\\\'s tensor.1 aZelenko, Igor uhttp://hdl.handle.net/1963/218800654nas a2200097 4500008004300000245004700043210004700090520036200137100002100499856003600520 2006 en_Ud 00aVariational problems in fracture mechanics0 aVariational problems in fracture mechanics3 aWe present some recent existence results for the variational model of crack growth in brittle materials proposed by Francfort and Marigo in 1998. These results, obtained in collaboration with Francfort and Toader, cover the case of arbitrary space dimension with a general quasiconvex bulk energy and with prescribed boundary deformations and applied loads.1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/181600318nas a2200109 4500008004100000020001500041245004300056210004300099260001000142100002000152856003600172 2006 en d a012512661100aWDVV equations and Frobenius manifolds0 aWDVV equations and Frobenius manifolds bSISSA1 aDubrovin, Boris uhttp://hdl.handle.net/1963/647300897nas a2200121 4500008004300000245008900043210006900132260002400201520047200225100002000697700002200717856003600739 2005 en_Ud 00aAsymptotic Morse theory for the equation $\\\\Delta v=2v\\\\sb x\\\\wedge v\\\\sb y$0 aAsymptotic Morse theory for the equation Delta v2vsb xwedge vsb bInternational Press3 aGiven a smooth bounded domain ${\\\\O}\\\\subseteq \\\\R^2$, we consider the equation $\\\\D v = 2 v_x \\\\wedge v_y$ in $\\\\O$, where $v: {\\\\O}\\\\to \\\\R^3$. We prescribe Dirichlet boundary datum, and consider the case in which this datum converges to zero. An asymptotic study of the corresponding Euler functional is performed, analyzing multiple-bubbling phenomena. This allows us to settle a particular case of a question raised by H. Brezis and J.M. Coron.1 aChanillo, Sagun1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/353301579nas a2200121 4500008004100000245007400041210006700115260001800182520117500200100001801375700002801393856003601421 2005 en d00aOn the attainable set for Temple class systems with boundary controls0 aattainable set for Temple class systems with boundary controls bSISSA Library3 aConsider the initial-boundary value problem for a strictly hyperbolic, genuinely nonlinear, Temple class system of conservation laws % $$ u_t+f(u)_x=0, \\\\qquad u(0,x)=\\\\ov u(x), \\\\qquad {{array}{ll} &u(t,a)=\\\\widetilde u_a(t), \\\\noalign{\\\\smallskip} &u(t,b)=\\\\widetilde u_b(t), {array}. \\\\eqno(1) $$ on the domain $\\\\Omega =\\\\{(t,x)\\\\in\\\\R^2 : t\\\\geq 0, a \\\\le x\\\\leq b\\\\}.$ We study the mixed problem (1) from the point of view of control theory, taking the initial data $\\\\bar u$ fixed, and regarding the boundary data $\\\\widetilde u_a, \\\\widetilde u_b$ as control functions that vary in prescribed sets $\\\\U_a, \\\\U_b$, of $\\\\li$ boundary controls. In particular, we consider the family of configurations $$ \\\\A(T) \\\\doteq \\\\big\\\\{u(T,\\\\cdot); ~ u {\\\\rm is a sol. to} (1), \\\\quad \\\\widetilde u_a\\\\in \\\\U_a, \\\\widetilde u_b \\\\in \\\\U_b \\\\big\\\\} $$ that can be attained by the system at a given time $T>0$, and we give a description of the attainable set $\\\\A(T)$ in terms of suitable Oleinik-type conditions. We also establish closure and compactness of the set $\\\\A(T)$ in the $lu$ topology.1 aAncona, Fabio1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/158100648nas a2200109 4500008004300000245006600043210005800109520029500167100002100462700001900483856003600502 2005 en_Ud 00aOn the Blow-up for a Discrete Boltzmann Equation in the Plane0 aBlowup for a Discrete Boltzmann Equation in the Plane3 aWe study the possibility of finite-time blow-up for a two dimensional Broadwell model. In a set of rescaled variables, we prove that no self-similar blow-up solution exists, and derive some a priori bounds on the blow-up rate. In the final section, a possible blow-up scenario is discussed.1 aBressan, Alberto1 aFonte, Massimo uhttp://hdl.handle.net/1963/224401041nas a2200097 4500008004300000245006900043210006900112520070400181100002200885856003600907 2005 en_Ud 00aCommuting multiparty quantum observables and local compatibility0 aCommuting multiparty quantum observables and local compatibility3 aA formula for the commutator of tensor product matrices is used to shows that, for qubits, compatibility of quantum multiparty observables almost never implies local compatibility at each site and to predict when this happens/does not happen in a concise manner. In particular, it is shown that two ``fully nontrivial\\\'\\\' $n$-qubit observables are compatible locally and globally if and only if they are equal up to sign. In addition, the formula gives insight into the construction of new paradoxes of the type of the Kochen-Specker Theorem, which can then be easily rephrased into proposals for new no hidden variable experiments of the type of the ``Bell Theorem without inequalities\\\'\\\'.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/222801949nas a2200097 4500008004300000245007900043210006900122520160600191100001801797856003601815 2005 en_Ud 00aComplete systems of invariants for rank 1 curves in Lagrange Grassmannians0 aComplete systems of invariants for rank 1 curves in Lagrange Gra3 aCurves in Lagrange Grassmannians naturally appear when one studies intrinsically \\\"the Jacobi equations for extremals\\\", associated with control systems and geometric structures. In this way one reduces the problem of construction of the curvature-type invariants for these objects to the much more concrete problem of finding of invariants of curves in Lagrange Grassmannians w.r.t. the action of the linear Symplectic group. In the present paper we develop a new approach to differential geometry of so-called rank 1 curves in Lagrange Grassmannian, i.e., the curves with velocities being rank one linear mappings (under the standard identification of the tangent space to a point of the Lagrange Grassmannian with an appropriate space of linear mappings). The curves of this class are associated with \\\"the Jacobi equations for extremals\\\", corresponding to control systems with scalar control and to rank 2 vector distributions. In particular, we construct the tuple of m principal invariants, where m is equal to half of dimension of the ambient linear symplectic space, such that for a given tuple of arbitrary m smooth functions there exists the unique, up to a symplectic transformation, rank 1 curve having this tuple, as the tuple of the principal invariants. This approach extends and essentially simplifies some results of our previous paper (J. Dynamical and Control Systems, 8, 2002, No. 1, 93-140), where only the uniqueness part was proved and in rather cumbersome way. It is based on the construction of the new canonical moving frame with the most simple structural equation.1 aZelenko, Igor uhttp://hdl.handle.net/1963/231000658nas a2200109 4500008004100000245010000041210006900141260001300210520026700223100002200490856003600512 2005 en d00aConcentration at curves for a singularly perturbed Neumann problem in three-dimensional domains0 aConcentration at curves for a singularly perturbed Neumann probl bSpringer3 aWe prove new concentration phenomena for the equation −ɛ2 Δu + u = up in a smooth bounded domain R3 and with Neumann boundary conditions. Here p > 1 and ɛ > 0 is small. We show that concentration of solutions occurs at some geodesics of ∂Ω when ɛ → 0.1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/486600982nas a2200121 4500008004100000245006900041210006900110260001800179520057400197100002800771700002500799856003600824 2005 en d00aConservation laws with time dependent discontinuous coefficients0 aConservation laws with time dependent discontinuous coefficients bSISSA Library3 aWe consider scalar conservation laws where the flux function depends discontinuously on both the spatial and temporal location. Our main results are the existence and well-posedness of an entropy solution to the Cauchy problem. The existence is established by showing that a sequence of front tracking approximations is compact in L1, and that the limits are entropy solutions. Then, using the definition of an entropy solution taken form [11], we show that the solution operator is L1 contractive. These results generalize the corresponding results from [16] and [11].1 aCoclite, Giuseppe Maria1 aRisebro, Nils Henrik uhttp://hdl.handle.net/1963/166602094nas a2200121 4500008004300000245013000043210006900173520162100242100002501863700003001888700001801918856003601936 2005 en_Ud 00aOn curvatures and focal points of distributions of dynamical Lagrangian distributions and their reductions by first integrals0 acurvatures and focal points of distributions of dynamical Lagran3 aPairs (Hamiltonian system, Lagrangian distribution), called dynamical Lagrangian distributions, appear naturally in Differential Geometry, Calculus of Variations and Rational Mechanics. The basic differential invariants of a dynamical Lagrangian distribution w.r.t. the action of the group of symplectomorphisms of the ambient symplectic manifold are the curvature operator and the curvature form. These invariants can be seen as generalizations of the classical curvature tensor in Riemannian Geometry. In particular, in terms of these invariants one can localize the focal points along extremals of the corresponding variational problems. In the present paper we study the behavior of the curvature operator, the curvature form and the focal points of a dynamical Lagrangian distribution after its reduction by arbitrary first integrals in involution. The interesting phenomenon is that the curvature form of so-called monotone increasing Lagrangian dynamical distributions, which appear naturally in mechanical systems, does not decrease after reduction. It also turns out that the set of focal points to the given point w.r.t. the monotone increasing dynamical Lagrangian distribution and the corresponding set of focal points w.r.t. its reduction by one integral are alternating sets on the corresponding integral curve of the Hamiltonian system of the considered dynamical distributions. Moreover, the first focal point corresponding to the reduced Lagrangian distribution comes before any focal point related to the original dynamical distribution. We illustrate our results on the classical $N$-body problem.1 aAgrachev, Andrei, A.1 aChtcherbakova, Natalia N.1 aZelenko, Igor uhttp://hdl.handle.net/1963/225400818nas 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/1963/442500739nas a2200109 4500008004100000245008000041210007100121260001300192520036600205100002200571856003600593 2005 en d00aExplicit Wei–Norman formulae for matrix Lie groups via Putzer\\\'s method0 aExplicit Wei–Norman formulae for matrix Lie groups via Putzers m bElsevier3 aThe Wei–Norman formula locally relates the Magnus solution of a system of linear time-varying ODEs with the solution expressed in terms of products of exponentials by means of a set of nonlinear differential equations in the parameters of the two types of solutions. A closed form expression of such formula is proposed based on the use of Putzer\\\'s method.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/453800716nas a2200121 4500008004100000245009400041210006900135260001300204520029900217100002000516700002200536856003600558 2005 en d00aA fourth order uniformization theorem on some four manifolds with large total Q-curvature0 afourth order uniformization theorem on some four manifolds with bElsevier3 aGiven a four-dimensional manifold (M,g), we study the existence of a conformal metric for which the Q-curvature, associated to a conformally invariant fourth-order operator (the Paneitz operator), is constant. Using a topological argument, we obtain a new result in cases which were still open.1 aDjadli, Zindine1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/486800711nas a2200109 4500008004300000245009600043210006900139520031700208100002100525700001900546856003600565 2005 en_Ud 00aGel\\\'fand-Zakharevich Systems and Algebraic Integrability: the Volterra Lattice Revisited0 aGelfandZakharevich Systems and Algebraic Integrability the Volte3 aIn this paper we will discuss some features of the bi-Hamiltonian method for solving the Hamilton-Jacobi (H-J) equations by Separation of Variables, and make contact with the theory of Algebraic Complete Integrability and, specifically, with the Veselov-Novikov notion of algebro-geometric (AG) Poisson brackets.1 aFalqui, Gregorio1 aPedroni, Marco uhttp://hdl.handle.net/1963/168900651nas a2200109 4500008004300000245005100043210005000094520031700144100002100461700002300482856003600505 2005 en_Ud 00aGlobal solutions of the Hunter-Saxton equation0 aGlobal solutions of the HunterSaxton equation3 aWe construct a continuous semigroup of weak, dissipative solutions to a nonlinear partial differential equations modeling nematic liquid crystals. A new distance functional, determined by a problem of optimal transportation, yields sharp estimates on the continuity of solutions with respect to the initial data.1 aBressan, Alberto1 aConstantin, Adrian uhttp://hdl.handle.net/1963/225600958nas a2200121 4500008004300000245009200043210006900135520053000204100002400734700002000758700002200778856003600800 2005 en_Ud 00aGround states of nonlinear Schroedinger equations with potentials vanishing at infinity0 aGround states of nonlinear Schroedinger equations with potential3 aWe deal with a class on nonlinear Schr\\\\\\\"odinger equations \\\\eqref{eq:1} with potentials $V(x)\\\\sim |x|^{-\\\\a}$, $0<\\\\a<2$, and $K(x)\\\\sim |x|^{-\\\\b}$, $\\\\b>0$. Working in weighted Sobolev spaces, the existence of ground states $v_{\\\\e}$ belonging to $W^{1,2}(\\\\Rn)$ is proved under the assumption that $p$ satisfies \\\\eqref{eq:p}. Furthermore, it is shown that $v_{\\\\e}$ are {\\\\em spikes} concentrating at a minimum of ${\\\\cal A}=V^{\\\\theta}K^{-2/(p-1)}$, where $\\\\theta= (p+1)/(p-1)-1/2$.1 aAmbrosetti, Antonio1 aFelli, Veronica1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/235200679nas a2200121 4500008004100000245003100041210003100072260000900103520036500112100002100477700002300498856003600521 2005 en d00aHybrid necessary principle0 aHybrid necessary principle bSIAM3 aWe consider a hybrid control system and general optimal control problems for this system. We suppose that the switching strategy imposes restrictions on control sets and we provide necessary conditions for an optimal hybrid trajectory, stating a hybrid necessary principle (HNP). Our result generalizes various necessary principles available in the literature.1 aGaravello, Mauro1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/164101006nas a2200133 4500008004300000245007100043210006900114520056200183100002200745700002900767700002000796700002000816856003600836 2005 en_Ud 00aIonization for Three Dimensional Time-dependent Point Interactions0 aIonization for Three Dimensional Timedependent Point Interaction3 aWe study the time evolution of a three dimensional quantum particle under the action of a time-dependent point interaction fixed at the origin. We assume that the ``strength\\\'\\\' of the interaction (\\\\alpha(t)) is a periodic function with an arbitrary mean. Under very weak conditions on the Fourier coefficients of (\\\\alpha(t)), we prove that there is complete ionization as (t \\\\to \\\\infty), starting from a bound state at time (t = 0). Moreover we prove also that, under the same conditions, all the states of the system are scattering states.1 aCorreggi, Michele1 aDell'Antonio, Gianfausto1 aFigari, Rodolfo1 aMantile, Andrea uhttp://hdl.handle.net/1963/229700448nas a2200121 4500008004100000022001400041245006300055210006300118300001400181100001900195700001500214856009700229 2005 eng d a1687-301700aIsomonodromic deformation of resonant rational connections0 aIsomonodromic deformation of resonant rational connections a565–6351 aBertola, Marco1 aMo, M., Y. uhttp://www.math.sissa.it/publication/isomonodromic-deformation-resonant-rational-connections00687nas a2200145 4500008004300000245003900043210003300082520027900115100002600394700002200420700002000442700002000462700002300482856003600505 2005 en_Ud 00aThe local index formula for SUq(2)0 alocal index formula for SUq23 aWe discuss the local index formula of Connes-Moscovici for the isospectral noncommutative geometry that we have recently constructed on quantum SU(2). We work out the cosphere bundle and the dimension spectrum as well as the local cyclic cocycles yielding the index formula.1 avan Suijlekom, Walter1 aDabrowski, Ludwik1 aLandi, Giovanni1 aSitarz, Andrzej1 aVarilly, Joseph C. uhttp://hdl.handle.net/1963/171301933nas a2200145 4500008004100000245004900041210004900090260002900139520150600168100002001674700002001694700002201714700001501736856003601751 2005 en d00aMinimal surfaces in pseudohermitian geometry0 aMinimal surfaces in pseudohermitian geometry bScuola Normale Superiore3 aWe consider surfaces immersed in three-dimensional pseudohermitian manifolds. We define the notion of (p-)mean curvature and of the associated (p-)minimal surfaces, extending some concepts previously given for the (flat) Heisenberg group. We interpret the p-mean curvature not only as the tangential sublaplacian of a defining function, but also as the curvature of a characteristic curve, and as a quantity in terms of calibration geometry. As a differential equation, the p-minimal surface equation is degenerate (hyperbolic and elliptic). To analyze the singular set, we formulate some {\em extension} theorems, which describe how the characteristic curves meet the singular set. This allows us to classify the entire solutions to this equation and to solve a Bernstein-type problem (for graphs over the $xy$-plane) in the Heisenberg group $H_1$. In $H_{1}$, identified with the Euclidean space $R^{3}$, the p-minimal surfaces are classical ruled surfaces with the rulings generated by Legendrian lines. We also prove a uniqueness theorem for the Dirichlet problem under a condition on the size of the singular set in two dimensions, and generalize to higher dimensions without any size control condition. We also show that there are no closed, connected, $C^{2}$ smoothly immersed constant p-mean curvature or p-minimal surfaces of genus greater than one in the standard $S^{3}.$ This fact continues to hold when $S^{3}$ is replaced by a general spherical pseudohermitian 3-manifold.1 aCheng, Jih-Hsin1 aHwang, JennFang1 aMalchiodi, Andrea1 aYang, Paul uhttp://hdl.handle.net/1963/457900521nas a2200097 4500008004300000245006000043210005300103520021100156100002000367856003600387 2005 en_Ud 00aOn the Minimum Problem for Nonconvex Scalar Functionals0 aMinimum Problem for Nonconvex Scalar Functionals3 aWe study the minimum problem for scalar nonconvex functionals defined on Sobolev maps satisfying a Dirichlet boundary condition and refine well-known existence results under standard regularity assumptions.1 aZagatti, Sandro uhttp://hdl.handle.net/1963/276401078nas a2200109 4500008004300000245007500043210006900118520070500187100002200892700001800914856003600932 2005 en_Ud 00aModulation of the Camassa-Holm equation and reciprocal transformations0 aModulation of the CamassaHolm equation and reciprocal transforma3 aWe derive the modulation equations or Whitham equations for the Camassa-Holm (CH) equation. We show that the modulation equations are hyperbolic and admit bi-Hamiltonian structure. Furthermore they are connected by a reciprocal transformation to the modulation equations of the first negative flow of the Korteweg de Vries (KdV) equation. The reciprocal transformation is generated by the Casimir of the second Poisson bracket of the KdV averaged flow. We show that the geometry of the bi-Hamiltonian structure of the KdV and CH modulation equations is quite different: indeed the KdV averaged bi-Hamiltonian structure can always be related to a semisimple Frobenius manifold while the CH one cannot.1 aAbenda, Simonetta1 aGrava, Tamara uhttp://hdl.handle.net/1963/230500421nas a2200121 4500008004300000245008100043210006900124260001300193100002200206700001700228700001800245856003600263 2005 en_Ud 00aMultiple clustered layer solutions for semilinear Neumann problems on a ball0 aMultiple clustered layer solutions for semilinear Neumann proble bElsevier1 aMalchiodi, Andrea1 aNi, Wei-Ming1 aWei, Juncheng uhttp://hdl.handle.net/1963/353201293nas a2200121 4500008004300000245009700043210006900140520086400209100001701073700002201090700002301112856003601135 2005 en_Ud 00aNonisotropic 3-level quantum systems: complete solutions for minimum time and minimum energy0 aNonisotropic 3level quantum systems complete solutions for minim3 aWe apply techniques of subriemannian geometry on Lie groups and of optimal synthesis on 2-D manifolds to the population transfer problem in a three-level quantum system driven by two laser pulses, of arbitrary shape and frequency. In the rotating wave approximation, we consider a nonisotropic model i.e. a model in which the two coupling constants of the lasers are different. The aim is to induce transitions from the first to the third level, minimizing 1) the time of the transition (with bounded laser amplitudes),\\n2) the energy of lasers (with fixed final time). After reducing the problem to real variables, for the purpose 1) we develop a theory of time optimal syntheses for distributional problem on 2-D-manifolds, while for the purpose 2) we use techniques of subriemannian geometry on 3-D Lie groups. The complete optimal syntheses are computed.1 aBoscain, Ugo1 aChambrion, Thomas1 aCharlot, Grégoire uhttp://hdl.handle.net/1963/225900367nas a2200097 4500008004300000245007600043210007000119100002400189700002000213856003600233 2005 en_Ud 00aNonlinear Schrödinger Equations with vanishing and decaying potentials0 aNonlinear Schrödinger Equations with vanishing and decaying pote1 aAmbrosetti, Antonio1 aZhi-Qiang, Wang uhttp://hdl.handle.net/1963/176000982nas a2200109 4500008004300000245008000043210006900123520060400192100002100796700001900817856003600836 2005 en_Ud 00aAn Optimal Transportation Metric for Solutions of the Camassa-Holm Equation0 aOptimal Transportation Metric for Solutions of the CamassaHolm E3 aIn this paper we construct a global, continuous flow of solutions to the Camassa-Holm equation on the entire space H1. Our solutions are conservative, in the sense that the total energy int[(u2 + u2x) dx] remains a.e. constant in time. Our new approach is based on a distance functional J(u, v), defined in terms of an optimal transportation problem, which satisfies d dtJ(u(t), v(t)) ≤ κ · J(u(t), v(t)) for every couple of solutions. Using this new distance functional, we can construct arbitrary solutions as the uniform limit of multi-peakon solutions, and prove a general uniqueness result.1 aBressan, Alberto1 aFonte, Massimo uhttp://hdl.handle.net/1963/171900319nas a2200109 4500008004100000245004500041210004400086260001000130653001400140100001900154856003600173 2005 en d00aOrbifold Cohomology of ADE-singularities0 aOrbifold Cohomology of ADEsingularities bSISSA10aOrbifolds1 aPerroni, Fabio uhttp://hdl.handle.net/1963/529800415nas a2200109 4500008004100000245008300041210006900124260003500193100002400228700001700252856003600269 2005 en d00aPeriodic solutions of nonlinear wave equations with non-monotone forcing terms0 aPeriodic solutions of nonlinear wave equations with nonmonotone bAccademia Nazionale dei Lincei1 aBerti, Massimiliano1 aBiasco, Luca uhttp://hdl.handle.net/1963/458100942nas a2200109 4500008004300000245005300043210005300096520060100149100002000750700002600770856003600796 2005 en_Ud 00aPrincipal fibrations from noncommutative spheres0 aPrincipal fibrations from noncommutative spheres3 aWe construct noncommutative principal fibrations S_\\\\theta^7 \\\\to S_\\\\theta^4 which are deformations of the classical SU(2) Hopf fibration over the four sphere. We realize the noncommutative vector bundles associated to the irreducible representations of SU(2) as modules of coequivariant maps and construct corresponding projections. The index of Dirac operators with coefficients in the associated bundles is computed with the Connes-Moscovici local index formula. The algebra inclusion $A(S_\\\\theta^4) \\\\into A(S_\\\\theta^7)$ is an example of a not trivial quantum principal bundle.1 aLandi, Giovanni1 avan Suijlekom, Walter uhttp://hdl.handle.net/1963/228400410nas a2200109 4500008004100000245007400041210006900115260003500184100002400219700002100243856003600264 2005 en d00aQuasi-periodic oscillations for wave equations under periodic forcing0 aQuasiperiodic oscillations for wave equations under periodic for bAccademia Nazionale dei Lincei1 aBerti, Massimiliano1 aProcesi, Michela uhttp://hdl.handle.net/1963/458300706nas a2200121 4500008004300000245005300043210005300096520033400149100002100483700002500504700001900529856003600548 2005 en_Ud 00aQuasistatic Crack Growth in Nonlinear Elasticity0 aQuasistatic Crack Growth in Nonlinear Elasticity3 aIn this paper, we prove a new existence result for a variational model of crack growth in brittle materials proposed in [15]. We consider the case of $n$-dimensional finite elasticity, for an arbitrary $n\\\\ge1$, with a quasiconvex bulk energy and with prescribed boundary deformations and applied loads, both depending on time.1 aDal Maso, Gianni1 aFrancfort, Gilles A.1 aToader, Rodica uhttp://hdl.handle.net/1963/229301167nas a2200109 4500008004100000245010100041210006900142260001300211520077600224100002101000856003601021 2005 en d00aRegularity properties of optimal trajectories of single-input control systems in dimension three0 aRegularity properties of optimal trajectories of singleinput con bSpringer3 aLet q=f(q)+ug(q) be a smooth control system on a three-dimensional manifold. Given a point q 0 of the manifold at which the iterated Lie brackets of f and g satisfy some prescribed independence condition, we analyze the structure of a control function u(t) corresponding to a time-optimal trajectory lying in a neighborhood of q 0. The control turns out to be the concatenation of some bang-bang and some singular arcs. More general optimality criteria than time-optimality are considered. The paper is a step toward to the analysis of generic single-input systems affine in the control in dimension 3. The main techniques used are second-order optimality conditions and, in particular, the index of the second variation of the switching times for bang-bang trajectories.1 aSigalotti, Mario uhttp://hdl.handle.net/1963/479401313nas a2200133 4500008004300000245008200043210006900125260001300194520087600207100001801083700002201101700002001123856003601143 2005 en_Ud 00aSelf-similar folding patterns and energy scaling in compressed elastic sheets0 aSelfsimilar folding patterns and energy scaling in compressed el bElsevier3 aThin elastic sheets under isotropic compression, such as for example blisters formed by thin films which debonded from the substrate, can exhibit remarkably complex folding patterns. We discuss the scaling of the elastic energy with respect to the film thickness, and show that in certain regimes the optimal energy scaling can be reached\\nby self-similar folding patterns that refine towards the boundary, in agreement with experimental observations. We then extend the analysis\\nto anisotropic compression, and discuss a simplified scalar model which suggests the presence of a transition between a regime where\\nthe deformation is governed by global properties of the domain and another one where the direction of maximal compression dominates and the scale of the folds is mainly determined by the distance to the boundary in the direction of the folds themselves.1 aConti, Sergio1 aDeSimone, Antonio1 aMüller, Stefan uhttp://hdl.handle.net/1963/300000333nas a2200109 4500008004300000020001800043245004400061210004200105100001700147700002300164856003600187 2005 en_Ud a2 7056 6511 000aA short introduction to optimal control0 ashort introduction to optimal control1 aBoscain, Ugo1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/225700351nas a2200085 4500008004300000245009600043210006900139100002100208856003600229 2005 en_Ud 00aSolutions of Neumann problems in domains with cracks and applications to fracture mechanics0 aSolutions of Neumann problems in domains with cracks and applica1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/168400730nas a2200133 4500008004300000245005800043210005400101520032400155100002200479700002000501700001900521700002000540856003600560 2005 en_Ud 00aThe spectral geometry of the equatorial Podles sphere0 aspectral geometry of the equatorial Podles sphere3 aWe propose a slight modification of the properties of a spectral geometry a la Connes, which allows for some of the algebraic relations to be satisfied only modulo compact operators. On the equatorial Podles sphere we construct suq2-equivariant Dirac operator and real structure which satisfy these modified properties.1 aDabrowski, Ludwik1 aLandi, Giovanni1 aPaschke, Mario1 aSitarz, Andrzej uhttp://hdl.handle.net/1963/227501445nas a2200121 4500008004300000245006200043210006200105260001300167520106100180100002801241700001801269856003601287 2005 en_Ud 00aStability of solutions of quasilinear parabolic equations0 aStability of solutions of quasilinear parabolic equations bElsevier3 aWe bound the difference between solutions $u$ and $v$ of $u_t = a\\\\Delta u+\\\\Div_x f+h$ and $v_t = b\\\\Delta v+\\\\Div_x g+k$ with initial data $\\\\phi$ and $ \\\\psi$, respectively, by $\\\\Vert u(t,\\\\cdot)-v(t,\\\\cdot)\\\\Vert_{L^p(E)}\\\\le A_E(t)\\\\Vert \\\\phi-\\\\psi\\\\Vert_{L^\\\\infty(\\\\R^n)}^{2\\\\rho_p}+ B(t)(\\\\Vert a-b\\\\Vert_{\\\\infty}+ \\\\Vert \\\\nabla_x\\\\cdot f-\\\\nabla_x\\\\cdot g\\\\Vert_{\\\\infty}+ \\\\Vert f_u-g_u\\\\Vert_{\\\\infty} + \\\\Vert h-k\\\\Vert_{\\\\infty})^{\\\\rho_p} \\\\abs{E}^{\\\\eta_p}$. Here all functions $a$, $f$, and $h$ are smooth and bounded, and may depend on $u$, $x\\\\in\\\\R^n$, and $t$. The functions $a$ and $h$ may in addition depend on $\\\\nabla u$. Identical assumptions hold for the functions that determine the solutions $v$. Furthermore, $E\\\\subset\\\\R^n$ is assumed to be a bounded set, and $\\\\rho_p$ and $\\\\eta_p$ are fractions that depend on $n$ and $p$. The diffusion coefficients $a$ and $b$ are assumed to be strictly positive and the initial data are smooth.1 aCoclite, Giuseppe Maria1 aHolden, Helge uhttp://hdl.handle.net/1963/289201246nas a2200109 4500008004300000245010500043210006900148520083800217100002201055700002301077856003601100 2005 en_Ud 00aStress-dilatancy based modelling of granular materials and extensions to soils with crushable grains0 aStressdilatancy based modelling of granular materials and extens3 aStress-dilatancy relations have played a crucial role in the understanding of the mechanical behaviour of soils and in the development of realistic constitutive models for their response. Recent investigations on the mechanical behaviour of materials with crushable grains have called into question the validity of classical relations such as those used in critical state soil mechanics.\\nIn this paper, a method to construct thermodynamically consistent (isotropic, three-invariant) elasto-plastic models based on a given stress-dilatancy relation is discussed. Extensions to cover the case of granular materials with crushable grains are also presented, based on the interpretation of some classical model parameters (e.g. the stress ratio at critical state) as internal variables that evolve according to suitable hardening laws.1 aDeSimone, Antonio1 aTamagnini, Claudio uhttp://hdl.handle.net/1963/216500714nas a2200109 4500008004300000245007100043210006900114520035100183100001700534700001700551856003600568 2005 en_Ud 00aTime minimal trajectories for two-level quantum systems with drift0 aTime minimal trajectories for twolevel quantum systems with drif3 aOn a two-level quantum system driven by an external field, we consider the population transfer problem from the first to the second level, minimizing the time of transfer, with bounded field amplitude. On the Bloch sphere (i.e. after a suitable Hopf projection), this problem can be attacked with techniques of optimal syntheses on 2-D manifolds.1 aBoscain, Ugo1 aMason, Paolo uhttp://hdl.handle.net/1963/168801372nas a2200109 4500008004300000245007100043210006800114520100700182100001701189700002001206856003601226 2005 en_Ud 00aTime Optimal Synthesis for Left-Invariant Control Systems on SO(3)0 aTime Optimal Synthesis for LeftInvariant Control Systems on SO33 aConsider the control system given by $\\\\dot x=x(f+ug)$, where $x\\\\in SO(3)$, $|u|\\\\leq 1$ and $f,g\\\\in so(3)$ define two perpendicular left-invariant vector fields normalized so that $\\\\|f\\\\|=\\\\cos(\\\\al)$ and $\\\\|g\\\\|=\\\\sin(\\\\al)$, $\\\\al\\\\in ]0,\\\\pi/4[$. In this paper, we provide an upper bound and a lower bound for $N(\\\\alpha)$, the maximum number of switchings for time-optimal trajectories. More precisely, we show that $N_S(\\\\al)\\\\leq N(\\\\al)\\\\leq N_S(\\\\al)+4$, where $N_S(\\\\al)$ is a suitable integer function of $\\\\al$ which for $\\\\al\\\\to 0$ is of order $\\\\pi/(4\\\\alpha).$ The result is obtained by studying the time optimal synthesis of a projected control problem on $R P^2$, where the projection is defined by an appropriate Hopf fibration. Finally, we study the projected control problem on the unit sphere $S^2$. It exhibits interesting features which will be partly rigorously derived and partially described by numerical simulations.1 aBoscain, Ugo1 aChitour, Yacine uhttp://hdl.handle.net/1963/225801557nas a2200121 4500008004300000245011100043210006900154520110800223100002101331700002301352700002401375856003601399 2005 en_Ud 00aTopological vector symmetry, topological gauge fixing of BRSTQFT and construction of maximal supersymmetry0 aTopological vector symmetry topological gauge fixing of BRSTQFT 3 aThe scalar and vector topological Yang-Mills symmetries determine a closed and consistent sector of Yang-Mills supersymmetry. We provide a geometrical construction of these symmetries, based on a horizontality condition on reducible manifolds. This yields globally well-defined scalar and vector topological BRST operators. These operators generate a subalgebra of maximally supersymmetric Yang-Mills theory, which is small enough to be closed off-shell with a finite set of auxiliary fields and large enough to determine the Yang-Mills supersymmetric theory. Poincaré supersymmetry is reached in the limit of flat manifolds. The arbitrariness of the gauge functions in BRSTQFTs is thus removed by the requirement of scalar and vector topological symmetry, which also determines the complete supersymmetry transformations in a twisted way. Provided additional Killing vectors exist on the manifold, an equivariant extension of our geometrical framework is provided, and the resulting \\\"equivariant topological field theory\\\" corresponds to the twist of super Yang-Mills theory on omega backgrounds.1 aBaulieu, Laurent1 aBossard, Guillaume1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/174101069nas a2200133 4500008004100000245003500041210003500076260001800111520069800129100002800827700002300855700002100878856003600899 2005 en d00aTraffic flow on a road network0 aTraffic flow on a road network bSISSA Library3 aThis paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from conservation of the number of cars,\\ndefined on a road network that is a collection of roads with junctions. The evolution problem is underdetermined at junctions, hence we choose to have some fixed rules for the distribution of traffic plus an optimization criteria for the flux. We prove existence, uniqueness and stability of solutions to the Cauchy problem. Our method is based on wave front tracking approach, see [6], and works also for boundary data and time dependent coefficients of traffic distribution at junctions, so including traffic lights.1 aCoclite, Giuseppe Maria1 aPiccoli, Benedetto1 aGaravello, Mauro uhttp://hdl.handle.net/1963/158401264nas a2200121 4500008004300000245006600043210006600109260002600175520086100201100002301062700002101085856003601106 2005 en_Ud 00aVanishing viscosity solutions of nonlinear hyperbolic systems0 aVanishing viscosity solutions of nonlinear hyperbolic systems bAnnals of Mathematics3 aWe consider the Cauchy problem for a strictly hyperbolic, $n\\\\times n$ system in one space dimension: $u_t+A(u)u_x=0$, assuming that the initial data has small total variation.\\nWe show that the solutions of the viscous approximations $u_t+A(u)u_x=\\\\ve u_{xx}$ are defined globally in time and satisfy uniform BV estimates, independent of $\\\\ve$. Moreover, they depend continuously on the initial data in the $\\\\L^1$ distance, with a Lipschitz constant independent of $t,\\\\ve$. Letting $\\\\ve\\\\to 0$, these viscous solutions converge to a unique limit, depending Lipschitz continuously on the initial data. In the conservative case where $A=Df$ is the Jacobian of some flux function $f:\\\\R^n\\\\mapsto\\\\R^n$, the vanishing viscosity limits are precisely the unique entropy weak solutions to the system of conservation laws $u_t+f(u)_x=0$.1 aBianchini, Stefano1 aBressan, Alberto uhttp://hdl.handle.net/1963/307401324nas a2200109 4500008004300000245005700043210005600100520097800156100002201134700002201156856003601178 2005 en_Ud 00aWetting of rough surfaces: a homogenization approach0 aWetting of rough surfaces a homogenization approach3 aThe contact angle of a drop in equilibrium on a solid is strongly affected by the roughness of the surface on which it rests. We study the roughness-induced enhancement of the hydrophobic or hydrophilic properties of a solid surface through homogenization theory. By relying on a variational formulation of the problem, we show that the macroscopic contact angle is associated with the solution of two cell problems, giving the minimal energy per unit macroscopic area for a transition layer between the rough solid surface and a liquid or vapor phase. Our results are valid for both chemically heterogeneous and homogeneous surfaces. In the latter case, a very transparent structure emerges from the variational\\napproach: the classical laws of Wenzel and Cassie-Baxter give bounds for the optimal energy, and configurations of minimal energy are those leading to the smallest macroscopic contact angle in the hydrophobic case, to the largest one in the hydrophilic case.1 aDeSimone, Antonio1 aAlberti, Giovanni uhttp://hdl.handle.net/1963/225300665nas a2200097 4500008004300000245004600043210004300089520037900132100002000511856003600531 2004 en_Ud 00aOn almost duality for Frobenius manifolds0 aalmost duality for Frobenius manifolds3 aWe present a universal construction of almost duality for Frobenius manifolds. The analytic setup of this construction is described in details for the case of semisimple Frobenius manifolds. We illustrate the general considerations by examples from the singularity theory, mirror symmetry, the theory of Coxeter groups and Shephard groups, from the Seiberg - Witten duality.1 aDubrovin, Boris uhttp://hdl.handle.net/1963/254301230nas a2200109 4500008004100000245005200041210004900093260001000142520091200152100002001064856003601084 2004 en d00aOn analytic families of invariant tori for PDEs0 aanalytic families of invariant tori for PDEs bSISSA3 aWe propose to apply a version of the classical Stokes\\r\\nexpansion method to the perturbative construction of invariant tori for\\r\\nPDEs corresponding to solutions quasiperiodic in space and time variables.\\r\\nWe argue that, for integrable PDEs all but finite number of the\\r\\nsmall divisors arising in the perturbative analysis cancel. As an illustrative\\r\\nexample we establish such cancellations for the case of KP equation.\\r\\nIt is proved that, under mild assumptions about decay of the magnitude\\r\\nof the Fourier modes all analytic families of finite-dimensional invariant\\r\\ntori for KP are given by the Krichever construction in terms of thetafunctions\\r\\nof Riemann surfaces. We also present an explicit construction\\r\\nof infinite dimensional real theta-functions and corresponding quasiperiodic\\r\\nsolutions to KP as sums of infinite number of interacting plane\\r\\nwaves.1 aDubrovin, Boris uhttp://hdl.handle.net/1963/647401188nas a2200121 4500008004100000245012000041210006900161260001800230520074100248100002100989700002001010856003601030 2004 en d00aAsymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains0 aAsymptotic behaviour and correctors for linear Dirichlet problem bSISSA Library3 aWe consider a sequence of Dirichlet problems in varying domains (or, more generally, of relaxed Dirichlet problems involving measures in M_0) for second order linear elliptic operators in divergence form with varying matrices of coefficients. When the matrices H-converge to a matrix A^0, we prove that there exist a subsequence and a measure mu^0 in M_0 such that the limit problem is the relaxed Dirichlet problem corresponding to A^0 and mu^0. We also prove a corrector result which provides an explicit approximation of the solutions in the H^1-norm, and which is obtained by multiplying the corrector for the H-converging matrices by some special test function which depends both on the varying matrices and on the varying domains.1 aDal Maso, Gianni1 aMurat, Francois uhttp://hdl.handle.net/1963/161100778nas a2200109 4500008004300000245007400043210006900117520040200186100002400588700002000612856003600632 2004 en_Ud 00aBifurcation of free vibrations for completely resonant wave equations0 aBifurcation of free vibrations for completely resonant wave equa3 aWe prove existence of small amplitude, 2 pi/omega -periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for any frequency omega belonging to a Cantor-like set of positive measure and for a generic set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem.1 aBerti, Massimiliano1 aBolle, Philippe uhttp://hdl.handle.net/1963/224500908nas a2200145 4500008004300000245010400043210007000147260001300217520040600230100002000636700002900656700002000685700002100705856003600726 2004 en_Ud 00aBlow-up solutions for the Schrödinger equation in dimension three with a concentrated nonlinearity0 aBlowup solutions for the Schrödinger equation in dimension three bElsevier3 aWe present some results on the blow-up phenomenon for the Schroedinger equation in dimension three with a nonlinear term supported in a fixed point. We find sufficient conditions for the blow up exploiting the moment of inertia of the solution and the uncertainty principle. In the critical case, we discuss the additional symmetry of the equation and construct a family of explicit blow up solutions.1 aAdami, Riccardo1 aDell'Antonio, Gianfausto1 aFigari, Rodolfo1 aTeta, Alessandro uhttp://hdl.handle.net/1963/299800523nas a2200145 4500008004100000245006800041210006800109300001400177490000700191100001800198700001700216700002300233700001900256856010200275 2004 eng d00aCalculation of impulsively started incompressible viscous flows0 aCalculation of impulsively started incompressible viscous flows a877–9020 v461 aMarra, Andrea1 aMola, Andrea1 aQuartapelle, Luigi1 aRiviello, Luca uhttp://www.math.sissa.it/publication/calculation-impulsively-started-incompressible-viscous-flows00910nas a2200109 4500008004100000245008500041210006900126260001300195520053400208100002200742856003600764 2004 en d00aCoarse-grained models of materials with non-convex free-energy: two case studies0 aCoarsegrained models of materials with nonconvex freeenergy two bElsevier3 aBridging across length scales is one of the fundamental challenges in the computational modelling of material systems whose mechanical response is driven by rough energy landscapes. The typical feature of such systems is that of exhibiting fine scale microstructures. Two case studies, namely, nematic elastomers and ferromagnetic shape memory alloys, are presented to illustrate the use of modern techniques from (non-convex) calculus of variations in developing coarse-grained models of microstructure-driven material response.1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/488400697nas a2200097 4500008004300000245005500043210005500098520038800153100002200541856003600563 2004 en_Ud 00aCoherent control of open quantum dynamical systems0 aCoherent control of open quantum dynamical systems3 aA systematic analysis of the behavior of the quantum Markovian master equation driven by coherent control fields is proposed. Its irreversible character is formalized using control-theoretic notions and the sets of states that can be reached via cohere nt controls are described. The analysis suggests to which extent (and how) it is possible to counteract the effect of dissipation.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/222701240nas a2200121 4500008004300000245006600043210005900109260001000168520086800178100002101046700001501067856003601082 2004 en_Ud 00aOn the convergence rate of vanishing viscosity approximations0 aconvergence rate of vanishing viscosity approximations bWiley3 aGiven a strictly hyperbolic, genuinely nonlinear system of conservation laws, we prove the a priori bound $\\\\big\\\\|u(t,\\\\cdot)-u^\\\\ve(t,\\\\cdot)\\\\big\\\\|_{\\\\L^1}= \\\\O(1)(1+t)\\\\cdot \\\\sqrt\\\\ve|\\\\ln\\\\ve|$ on the distance between an exact BV solution $u$ and a viscous approximation $u^\\\\ve$, letting the viscosity coefficient $\\\\ve\\\\to 0$. In the proof, starting from $u$ we construct an approximation of the viscous solution $u^\\\\ve$ by taking a mollification $u*\\\\phi_{\\\\strut \\\\sqrt\\\\ve}$ and inserting viscous shock profiles at the locations of finitely many large shocks, for each fixed $\\\\ve$. Error estimates are then obtained by introducing new Lyapunov functionals which control shock interactions, interactions between waves of different families and by using sharp decay estimates for positive nonlinear waves.1 aBressan, Alberto1 aYang, Tong uhttp://hdl.handle.net/1963/291500854nas a2200133 4500008004100000020002200041245006500063210006000128260003400188520041800222653002300640100002100663856003600684 2004 en d a978-2-85629-229-700aThe elliptic representation of the sixth Painlevé equation.0 aelliptic representation of the sixth Painlevé equation bSociete Matematique de France3 aWe find a class of solutions of the sixth Painlev´e equation corresponding\r\nto almost all the monodromy data of the associated linear system; actually, all data\r\nbut one point in the space of data. We describe the critical behavior close to the\r\ncritical points by means of the elliptic representation, and we find the relation among\r\nthe parameters at the different critical points (connection problem).10aPainlevé equation1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/652901258nas a2200145 4500008004300000245008600043210006900129260001700198520078200215100002300997700001801020700002201038700001601060856003601076 2004 en_Ud 00aEnergetics and switching of quasi-uniform states in small ferromagnetic particles0 aEnergetics and switching of quasiuniform states in small ferroma bEDP Sciences3 aWe present a numerical algorithm to solve the micromagnetic equations based on tangential-plane minimization for the magnetization update and a homothethic-layer decomposition of outer space for the computation of the demagnetization field. As a first application, detailed results on the flower-vortex transition in the cube of Micromagnetic Standard Problem number 3 are obtained, which confirm, with a different method, those already present in the literature, and validate our method and code. We then turn to switching of small cubic or almost-cubic particles, in the single-domain limit. Our data show systematic deviations from the Stoner-Wohlfarth model due to the non-ellipsoidal shape of the particle, and in particular a non-monotone dependence on the particle size.1 aAlouges, François1 aConti, Sergio1 aDeSimone, Antonio1 aPokern, Ivo uhttp://hdl.handle.net/1963/299900881nas a2200121 4500008004100000245005300041210005200094260001800146520051800164100002100682700002000703856003600723 2004 en d00aExistence of H-bubbles in a perturbative setting0 aExistence of Hbubbles in a perturbative setting bSISSA Library3 aGiven a $C^{1}$ function $H: \\\\mathbb{R}^3 \\\\to \\\\mathbb{R}$, we look for $H$-bubbles, i.e., surfaces in $\\\\mathbb{R}^3$ parametrized by the sphere $\\\\mathbb{S}^2$ with mean curvature $H$ at every regular point. Here we study the case $H(u)=H_{0}(u)+\\\\epsilon H_{1}(u)$ where $H_{0}$ is some \\\"good\\\" curvature (for which there exist $H_{0}$-bubbles with minimal energy, uniformly bounded in $L^{\\\\infty}$), $\\\\epsilon$ is the smallness parameter, and $H_{1}$ is {\\\\em any} $C^{1}$ function.1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/160600305nas a2200109 4500008004300000245003200043210002800075100001800103700002000121700001800141856003600159 2004 en_Ud 00aThe Extended Toda Hierarchy0 aExtended Toda Hierarchy1 aCarlet, Guido1 aDubrovin, Boris1 aYoujin, Zhang uhttp://hdl.handle.net/1963/254201246nas a2200121 4500008004100000245005100041210005100092260001800143520089000161100001701051700002001068856003601088 2004 en d00aFredholm modules for quantum euclidean spheres0 aFredholm modules for quantum euclidean spheres bSISSA Library3 aThe quantum Euclidean spheres, $S_q^{N-1}$, are (noncommutative) homogeneous spaces of quantum orthogonal groups, $\\\\SO_q(N)$. The *-algebra $A(S^{N-1}_q)$ of polynomial functions on each of these is given by generators and relations which can be expressed in terms of a self-adjoint, unipotent matrix. We explicitly construct complete sets of generators for the K-theory (by nontrivial self-adjoint idempotents and unitaries) and the K-homology (by nontrivial Fredholm modules) of the spheres $S_q^{N-1}$. We also construct the corresponding Chern characters in cyclic homology and cohomology and compute the pairing of K-theory with K-homology. On odd spheres (i. e., for N even) we exhibit unbounded Fredholm modules by means of a natural unbounded operator D which, while failing to have compact resolvent, has bounded commutators with all elements in the algebra $A(S^{N-1}_q)$.1 aHawkins, Eli1 aLandi, Giovanni uhttp://hdl.handle.net/1963/163600797nas a2200121 4500008004300000245007900043210006900122520038600191100002200577700002100599700001900620856003600639 2004 en_Ud 00aA geometric approach to the separability of the Neumann-Rosochatius system0 ageometric approach to the separability of the NeumannRosochatius3 aWe study the separability of the Neumann-Rosochatius system on the n-dimensional sphere using the geometry of bi-Hamiltonian manifolds. Its well-known separation variables are recovered by means of a separability condition relating the Hamiltonian with a suitable (1,1) tensor field on the sphere. This also allows us to iteratively construct the integrals of motion of the system.1 aBartocci, Claudio1 aFalqui, Gregorio1 aPedroni, Marco uhttp://hdl.handle.net/1963/254101254nas a2200121 4500008004100000245008600041210006900127260001800196520084100214100002101055700002001076856003601096 2004 en d00aH-bubbles in a perturbative setting: the finite-dimensional reduction\\\'s method0 aHbubbles in a perturbative setting the finitedimensional reducti bSISSA Library3 aGiven a regular function $H\\\\colon\\\\mathbb{R}^{3}\\\\to\\\\mathbb{R}$, we look for $H$-bubbles, that is, regular surfaces in $\\\\mathbb{R}^{3}$ parametrized on the sphere $\\\\mathbb{S}+^{2}$ with mean curvature $H$ at every point. Here we study the case of $H(u)=H_{0}+\\\\varepsilon H_{1}(u)=:H_{\\\\varepsilon}(u)$, where $H_{0}$ is a nonzero constant, $\\\\varepsilon$ is the smallness parameter, and $H_{1}$ is any $C^{2}$-function. We prove that if $\\\\bar p\\\\in\\\\mathbb{R}^{3}$ is a ``good\\\'\\\' stationary point for the Melnikov-type function $\\\\Gamma(p)=-\\\\int_{|q-p|<|H_{0}|^{-1}}H_{1}(q)\\\\,dq$, then for $|\\\\varepsilon|$ small there exists an $H_{\\\\varepsilon}$-bubble $\\\\omega^{\\\\varepsilon}$ that converges to a sphere of radius $|H_{0}|^{-1}$ centered at $\\\\bar p$, as $\\\\varepsilon\\\\to 0$.1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/160701010nas a2200145 4500008004300000245005800043210005800101260001300159520057100172100002100743700001900764700002000783700002500803856003600828 2004 en_Ud 00aHigher order quasiconvexity reduces to quasiconvexity0 aHigher order quasiconvexity reduces to quasiconvexity bSpringer3 aIn this paper it is shown that higher order quasiconvex functions suitable in the variational treatment of problems involving second derivatives may be extended to the space of all matrices as classical quasiconvex functions. Precisely, it is proved that a smooth strictly 2-quasiconvex function with p-growth at infinity, p>1, is the restriction to symmetric matrices of a 1-quasiconvex function with the same growth. As a consequence, lower semicontinuity results for second-order variational problems are deduced as corollaries of well-known first order theorems.1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/291100956nas a2200133 4500008004100000245008400041210006900125260000900194520052900203100001700732700001700749700002000766856003600786 2004 en d00aOn the minimal degree of a common Lyapunov function for planar switched systems0 aminimal degree of a common Lyapunov function for planar switched bIEEE3 aIn this paper, we consider linear switched systems x(t) = Au(t)x(t), x ε Rn, u ε U, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching (UAS for short). We first prove that, given a UAS system, it is always possible to build a polynomial common Lyapunov function. Then our main result is that the degree of that the common polynomial Lyapunov function is not uniformly bounded over all the UAS systems. This result answers a question raised by Dayawansa and Martin.1 aMason, Paolo1 aBoscain, Ugo1 aChitour, Yacine uhttp://hdl.handle.net/1963/483400410nas a2200109 4500008004300000245008000043210006900123260002600192100002200218700002400240856003600264 2004 en_Ud 00aMultidimensional boundary layers for a singularly perturbed Neumann problem0 aMultidimensional boundary layers for a singularly perturbed Neum bDuke University Press1 aMalchiodi, Andrea1 aMontenegro, Marcelo uhttp://hdl.handle.net/1963/296000380nas a2200109 4500008004300000245006700043210006700110260001300177100002400190700002000214856003600234 2004 en_Ud 00aMultiplicity of periodic solutions of nonlinear wave equations0 aMultiplicity of periodic solutions of nonlinear wave equations bElsevier1 aBerti, Massimiliano1 aBolle, Philippe uhttp://hdl.handle.net/1963/297401171nas a2200133 4500008004300000245008600043210006900129260003700198520070300235100002400938700001700962700002200979856003601001 2004 en_Ud 00aPeriodic orbits close to elliptic tori and applications to the three-body problem0 aPeriodic orbits close to elliptic tori and applications to the t bScuola Normale Superiore di Pisa3 aWe prove, under suitable non-resonance and non-degeneracy ``twist\\\'\\\' conditions, a Birkhoff-Lewis type result showing the existence of infinitely many periodic solutions, with larger and larger minimal period, accumulating onto elliptic invariant tori (of Hamiltonian systems). We prove the applicability of this result to the spatial planetary three-body problem in the small eccentricity-inclination regime. Furthermore, we find other periodic orbits under some restrictions on the period and the masses of the ``planets\\\'\\\'. The proofs are based on averaging theory, KAM theory and variational methods. (Supported by M.U.R.S.T. Variational Methods and Nonlinear Differential Equations.)1 aBerti, Massimiliano1 aBiasco, Luca1 aValdinoci, Enrico uhttp://hdl.handle.net/1963/298500759nas a2200121 4500008004300000245007800043210006900121520034600190100002100536700002500557700001900582856003600601 2004 en_Ud 00aQuasi-static evolution in brittle fracture: the case of bounded solutions0 aQuasistatic evolution in brittle fracture the case of bounded so3 aThe main steps of the proof of the existence result for the quasi-static evolution of cracks in brittle materials, obtained in [7] in the vector case and for a general quasiconvex elastic energy, are presented here under the simplifying assumption that the minimizing sequences involved in the problem are uniformly bounded in $L^\\\\infty$.1 aDal Maso, Gianni1 aFrancfort, Gilles A.1 aToader, Rodica uhttp://hdl.handle.net/1963/222901711nas a2200109 4500008004300000245014800043210006900191260001700260520126600277100002201543856003601565 2004 en_Ud 00aReduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite Riemannian metric0 aReduction by group symmetry of second order variational problems bEDP Sciences3 aFor a Riemannian structure on a semidirect product of Lie groups, the variational problems can be reduced using the group symmetry. Choosing the Levi-Civita connection of a positive definite metric tensor, instead of any of the canonical connections for the Lie group, simplifies the reduction of the variations but complicates the expression for the Lie algebra valued covariant derivatives. The origin of the discrepancy is in the semidirect product structure, which implies that the Riemannian exponential map and the Lie group exponential map do not coincide. The consequence is that the reduced equations look more complicated than the original ones. The main scope of this paper is to treat the reduction of second order variational problems (corresponding to geometric splines) on such semidirect products of Lie groups. Due to the semidirect structure, a number of extra terms appears in the reduction, terms that are calculated explicitely. The result is used to compute the necessary conditions of an optimal control problem for a simple mechanical control system having invariant Lagrangian equal to the kinetic energy corresponding to the metric tensor. As an example, the case of a rigid body on the Special Euclidean group is considered in detail.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/352101168nas a2200097 4500008004300000245006600043210006600109520083700175100002201012856003601034 2004 en_Ud 00aRepresenting multiqubit unitary evolutions via Stokes tensors0 aRepresenting multiqubit unitary evolutions via Stokes tensors3 aFor the Stokes tensor parametrization of a multiqubit density operator, we provide an explicit formulation of the corresponding unitary dynamics at the infinitesimal level. The main advantage of this formalism (clearly reminiscent of the ideas of ``coherences\\\'\\\' and ``coupling Hamiltonians\\\'\\\' of spin systems) is that the pattern of correlation between qubits and the pattern of infinitesimal correlation are highlighted simultaneously and can be used constructively for qubit manipulation. For example, it allows to compute explicitly a Rodrigues\\\' formula for the one-parameter orbits of nonlocal Hamiltonians. The result is easily generalizable to orbits of Cartan subalgebras and allows to express the Cartan decomposition of unitary propagators as a linear action directly in terms of the infinitesimal generators.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/230701180nas a2200121 4500008004300000245007900043210006900122260001700191520077400208100001700982700002300999856003601022 2004 en_Ud 00aResonance of minimizers for n-level quantum systems with an arbitrary cost0 aResonance of minimizers for nlevel quantum systems with an arbit bEDP Sciences3 aWe consider an optimal control problem describing a laser-induced population transfer on a $n$-level quantum system.\\nFor a convex cost depending only on the moduli of controls (i.e. the lasers intensities), we prove that there always exists a minimizer in resonance. This permits to justify some strategies used in experimental physics. It is also quite important because it permits to reduce remarkably the complexity of the problem (and extend some of our previous results for $n=2$ and $n=3$): instead of looking for minimizers on the sphere $S^{2n-1}\\\\subset\\\\C^n$ one is reduced to look just for minimizers on the sphere $S^{n-1}\\\\subset \\\\R^n$. Moreover, for the reduced problem, we investigate on the question of existence of strict abnormal minimizer.1 aBoscain, Ugo1 aCharlot, Grégoire uhttp://hdl.handle.net/1963/291000388nas a2200097 4500008004300000245008700043210006900130260003500199100002000234856003600254 2004 en_Ud 00aThe role of the spectrum of the Laplace operator on \\\\S2 in the H-bubble problem0 arole of the spectrum of the Laplace operator on S2 in the Hbubbl bHebrew University Magnes Press1 aMusina, Roberta uhttp://hdl.handle.net/1963/289401012nas a2200121 4500008004300000245005300043210005300096260001300149520064100162100002200803700002900825856003600854 2004 en_Ud 00aRotating Singular Perturbations of the Laplacian0 aRotating Singular Perturbations of the Laplacian bSpringer3 aWe study a system of a quantum particle interacting with a singular time-dependent uniformly rotating potential in 2 and 3 dimensions: in particular we consider an interaction with support on a point (rotating point interaction) and on a set of codimension 1 (rotating blade). We prove the existence of the Hamiltonians of such systems as suitable self-adjoint operators and we give an explicit expression for their unitary semigroups. Moreover we analyze the asymptotic limit of large angular velocity and we prove strong convergence of the time-dependent propagator to some one-parameter unitary group as (\\\\omega \\\\to \\\\infty).1 aCorreggi, Michele1 aDell'Antonio, Gianfausto uhttp://hdl.handle.net/1963/294500849nas a2200121 4500008004300000245005800043210005800101260001900159520046100178100002900639700002300668856003600691 2004 en_Ud 00aSemiclassical analysis of constrained quantum systems0 aSemiclassical analysis of constrained quantum systems bIOP Publishing3 aWe study the dynamics of a quantum particle in R^(n+m) constrained by a strong potential force to stay within a distance of order hbar (in suitable units) from a smooth n-dimensional submanifold M. We prove that in the semiclassical limit the evolution of the wave function is approximated in norm, up to terms of order hbar^(1/2), by the evolution of a semiclassical wave packet centred on the trajectory of the corresponding classical constrained system.1 aDell'Antonio, Gianfausto1 aTenuta, Lucattilio uhttp://hdl.handle.net/1963/299701056nas a2200121 4500008004300000245005500043210005400098260001300152520069800165100002100863700001400884856003600898 2004 en_Ud 00aSemi-cooperative strategies for differential games0 aSemicooperative strategies for differential games bSpringer3 aThe paper is concerned with a non-cooperative differential game for two players. We first consider Nash equilibrium solutions in feedback form. In this case, we show that the Cauchy problem for the value functions is generically ill-posed. Looking at vanishing viscosity approximations, one can construct special solutions in the form of chattering controls, but these also appear to be unstable. In the second part of the paper we propose an alternative \\\"semi-cooperative\\\" pair of strategies for the two players, seeking a Pareto optimum instead of a Nash equilibrium. In this case, we prove that the corresponding Hamiltonian system for the value functions is always weakly hyperbolic.1 aBressan, Alberto1 aShen, Wen uhttp://hdl.handle.net/1963/289300741nas a2200121 4500008004300000245005600043210005400099260000900153520038500162100002100547700001500568856003600583 2004 en_Ud 00aA sharp decay estimate for positive nonlinear waves0 asharp decay estimate for positive nonlinear waves bSIAM3 aWe consider a strictly hyperbolic, genuinely nonlinear system of conservation laws in one space dimension. A sharp decay estimate is proved for the positive waves in an entropy weak solution. The result is stated in terms of a partial ordering among positive measures, using symmetric rearrangements and a comparison with a solution of Burgers\\\' equation with impulsive sources.1 aBressan, Alberto1 aYang, Tong uhttp://hdl.handle.net/1963/291601974nas a2200109 4500008004300000245009900043210006900142520157600211100002301787700001801810856003601828 2004 en_Ud 00aSingular Z_N curves, Riemann-Hilbert problem and modular solutions of the Schlesinger equation0 aSingular ZN curves RiemannHilbert problem and modular solutions 3 aWe are solving the classical Riemann-Hilbert problem of rank N>1 on the extended complex plane punctured in 2m+2 points, for NxN quasi-permutation monodromy matrices. Following Korotkin we solve the Riemann-Hilbert problem in terms of the Szego kernel of certain Riemann surfaces branched over the given 2m+2 points. These Riemann surfaces are constructed from a permutation representation of the symmetric group S_N to which the quasi-permutation monodromy representation has been reduced. The permutation representation of our problem generates the cyclic subgroup Z_N. For this reason the corresponding Riemann surfaces of genus N(m-1) have Z_N symmetry. This fact enables us to write the matrix entries of the solution of the NxN Riemann-Hilbert problem as a product of an algebraic function and theta-function quotients. The algebraic function turns out to be related to the Szego kernel with zero characteristics. From the solution of the Riemann- Hilbert problem we automatically obtain a particular solution of the Schlesinger system. The tau-function of the Schlesinger system is computed explicitly. The rank 3 problem with four singular points (0,t,1,\\\\infty) is studied in detail. The corresponding solution of the Riemann-Hilbert problem and the Schlesinger system is given in terms of Jacobi\\\'s theta-function with modulus T=T(t), Im(T)>0. The function T=T(t) is invertible if it belongs to the Siegel upper half space modulo the subgroup \\\\Gamma_0(3) of the modular group. The inverse function t=t(T) generates a solution of a general Halphen system.1 aEnolski, Victor Z.1 aGrava, Tamara uhttp://hdl.handle.net/1963/254000490nas a2200121 4500008004100000245011600041210006900157260004300226100002400269700002200293700001700315856003600332 2004 en d00aSingularity perturbed elliptic equations with symmetry: existence of solutions concetrating on spheres, Part II0 aSingularity perturbed elliptic equations with symmetry existence bIndiana University Mathematics Journal1 aAmbrosetti, Antonio1 aMalchiodi, Andrea1 aNi, Wei-Ming uhttp://hdl.handle.net/1963/166300818nas a2200121 4500008004300000245007100043210006900114260000900183520043300192100002100625700001400646856003600660 2004 en_Ud 00aSmall BV solutions of hyperbolic noncooperative differential games0 aSmall BV solutions of hyperbolic noncooperative differential gam bSIAM3 aThe paper is concerned with an n-persons differential game in one space dimension. We state conditions for which the system of Hamilton-Jacobi equations for the value functions is strictly hyperbolic. In the positive case, we show that the weak solution of a corresponding system of conservation laws determines an n-tuple of feedback strategies. These yield a Nash equilibrium solution to the non-cooperative differential game.1 aBressan, Alberto1 aShen, Wen uhttp://hdl.handle.net/1963/291700759nas a2200121 4500008004100000245005300041210005300094260001800147520038500165100002800550700002300578856003600601 2004 en d00aSolitary waves for Maxwell Schrodinger equations0 aSolitary waves for Maxwell Schrodinger equations bSISSA Library3 aIn this paper we study solitary waves for the coupled system of Schrodinger-Maxwell equations in the three-dimensional space. We prove the existence of a sequence of radial solitary waves for these equations with a fixed L^2 norm. We study the asymptotic behavior and the smoothness of these solutions. We show also that the eigenvalues are negative and the first one is isolated.1 aCoclite, Giuseppe Maria1 aGeorgiev, Vladimir uhttp://hdl.handle.net/1963/158200365nas a2200097 4500008004100000245008600041210006900127260001300196100002200209856003600231 2004 en d00aSolutions concentrating at curves for some singularly perturbed elliptic problems0 aSolutions concentrating at curves for some singularly perturbed bElsevier1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/486900322nas a2200097 4500008004100000245004600041210004600087260003100133100002400164856003600188 2004 en d00aSoluzioni periodiche di PDEs Hamiltoniane0 aSoluzioni periodiche di PDEs Hamiltoniane bUnione Matematica Italiana1 aBerti, Massimiliano uhttp://hdl.handle.net/1963/458200736nas a2200109 4500008004300000245006600043210006600109260003500175520035900210100002100569856003600590 2004 en_Ud 00aSome remarks on multidimensional systems of conservation laws0 aSome remarks on multidimensional systems of conservation laws bAccademia Nazionale dei Lincei3 aThis note is concerned with the Cauchy problem for hyperbolic systems of conservation\\nlaws in several space dimensions. We first discuss an example of ill-posedness, for a special system\\nhaving a radial symmetry property. Some conjectures are formulated, on the compactness of the set of\\nflow maps generated by vector fields with bounded variation.1 aBressan, Alberto uhttp://hdl.handle.net/1963/364200882nas a2200121 4500008004300000245004500043210004500088260001700133520053500150100001800685700002100703856003600724 2004 en_Ud 00aStability rates for patchy vector fields0 aStability rates for patchy vector fields bEDP Sciences3 aThis paper is concerned with the stability of the set of trajectories of a patchy vector field, in the presence of impulsive perturbations. Patchy vector fields are discontinuous, piecewise smooth vector fields that were introduced in Ancona and Bressan (1999) to study feedback stabilization problems. For patchy vector fields in the plane, with polygonal patches in generic position, we show that the distance between a perturbed trajectory and an unperturbed one is of the same order of magnitude as the impulsive forcing term.1 aAncona, Fabio1 aBressan, Alberto uhttp://hdl.handle.net/1963/295900859nas a2200121 4500008004300000245007000043210006900113260001300182520046800195100001600663700002200679856003600701 2004 en_Ud 00aSuperlocalization formulas and supersymmetric Yang-Mills theories0 aSuperlocalization formulas and supersymmetric YangMills theories bElsevier3 aBy using supermanifold techniques we prove a generalization of the localization formula in equivariant cohomology which is suitable for studying supersymmetric Yang-Mills theories in terms of ADHM data. With these techniques one can compute the reduced partition functions of topological super Yang-Mills theory with 4, 8 or 16 supercharges. More generally, the superlocalization formula can be applied to any topological field theory in any number of dimensions.1 aBruzzo, Ugo1 aFucito, Francesco uhttp://hdl.handle.net/1963/288601375nas a2200109 4500008004300000245010700043210006900150260003000219520095800249100002201207856003601229 2004 en_Ud 00aTensor of coherences parametrization of multiqubit density operators for entanglement characterization0 aTensor of coherences parametrization of multiqubit density opera bAmerican Physical Society3 aFor multiqubit densities, the tensor of coherences (or Stokes tensor) is a real parameterization obtained by the juxtaposition of the affine Bloch vectors of each qubit. While it maintains the tensorial structure of the underlying space, it highlights the pattern of correlations, both classical and quantum, between the subsystems and, due to the affine parameterization, it contains in its components all reduced densities of all orders. The main purpose of our use of this formalism is to deal with entanglement. For example, the detection of bipartite entanglement is straightforward, as it is the synthesis of densities having positive partial transposes between desired qubits. In addition, finding explicit mixtures for families of separable states becomes a feasible issue for few qubit symmetric densities (we compute it for Werner states) and, more important, it provides some insight on the possible origin of entanglement for such densities.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/284500335nas a2200109 4500008004100000245004100041210004000082260001000122653003500132100002200167856003600189 2004 en d00aTime-dependent singular interactions0 aTimedependent singular interactions bSISSA10aRotating singular interactions1 aCorreggi, Michele uhttp://hdl.handle.net/1963/531001068nas a2200109 4500008004300000245005500043210005500098520073100153100002000884700001800904856003600922 2004 en_Ud 00aVirasoro Symmetries of the Extended Toda Hierarchy0 aVirasoro Symmetries of the Extended Toda Hierarchy3 aWe prove that the extended Toda hierarchy of \\\\cite{CDZ} admits nonabelian Lie algebra of infinitesimal symmetries isomorphic to the half of the Virasoro algebra. The generators $L_m$, $m\\\\geq -1$ of the Lie algebra act by linear differential operators onto the tau function of the hierarchy. We also prove that the tau function of a generic solution to the extended Toda hierarchy is annihilated by a combination of the Virasoro operators and the flows of the hierarchy. As an application we show that the validity of the Virasoro constraints for the $CP^1$ Gromov-Witten invariants and their descendents implies that their generating function is the logarithm of a particular tau function of the extended Toda hierarchy.1 aDubrovin, Boris1 aYoujin, Zhang uhttp://hdl.handle.net/1963/254400369nas a2200109 4500008004100000245006400041210006300105260001800168100001800186700001900204856003600223 2004 en d00aWell-posedness for general 2x2 systems of conservation laws0 aWellposedness for general 2x2 systems of conservation laws bSISSA Library1 aAncona, Fabio1 aMarson, Andrea uhttp://hdl.handle.net/1963/124100496nas a2200109 4500008004100000245017800041210006900219260001800288100002100306700002300327856003600350 2003 en d00aAutonomous integral functionals with discontinous nonconvex integrands: Lipschitz regularity of mimimizers, DuBois-Reymond necessary conditions and Hamilton-Jacobi equations0 aAutonomous integral functionals with discontinous nonconvex inte bSISSA Library1 aDal Maso, Gianni1 aFrankowska, Helene uhttp://hdl.handle.net/1963/162500482nas a2200121 4500008004100000022001400041245008000055210006900135300001200204490000800216100001900224856011700243 2003 eng d a0021-904500aBilinear semiclassical moment functionals and their integral representation0 aBilinear semiclassical moment functionals and their integral rep a71–990 v1211 aBertola, Marco uhttp://www.math.sissa.it/publication/bilinear-semiclassical-moment-functionals-and-their-integral-representation00697nas a2200133 4500008004300000245009100043210006900134260001300203520024900216100002200465700001900487700002100506856003600527 2003 en_Ud 00aThe calibration method for the Mumford-Shah functional and free-discontinuity problems0 acalibration method for the MumfordShah functional and freediscon bSpringer3 aWe present a minimality criterion for the Mumford-Shah functional, and more generally for non convex variational integrals on SBV which couple a surface and a bulk term. This method provides short and easy proofs for several minimality results.1 aAlberti, Giovanni1 aBouchitte, Guy1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/305100362nas a2200109 4500008004100000245005400041210005400095260001000149653002900159100002800188856003600216 2003 en d00aControl Problems for Systems of Conservation Laws0 aControl Problems for Systems of Conservation Laws bSISSA10aAsymptotic Stabilization1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/532500974nas a2200109 4500008004300000245008900043210006900132260003400201520057100235100002200806856003600828 2003 en_Ud 00aControllability properties for finite dimensional quantum Markovian master equations0 aControllability properties for finite dimensional quantum Markov bAmerican Institute of Physics3 aVarious notions from geometric control theory are used to characterize the behavior of the Markovian master equation for N-level quantum mechanical systems driven by unitary control and to describe the structure of the sets of reachable states. It is shown that the system can be accessible but neither small-time controllable nor controllable in finite time. In particular, if the generators of quantum dynamical semigroups are unital, then the reachable sets admit easy characterizations as they monotonically grow in time. The two level case is treated in detail.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/290900595nas a2200145 4500008004100000022001400041245012600055210006900181300001400250490000800264100001900272700001500291700001500306856012800321 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. uhttp://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/1963/302000498nas a2200145 4500008004100000022001400041245006800055210006300123300001200186490000800198100001900206700001900225700001800244856009000262 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 aÈ\u\inard, B.1 aKharnad, Dzh. uhttp://www.math.sissa.it/publication/duality-spectral-curves-arises-two-matrix-models01206nas a2200133 4500008004300000245007600043210006900119260001300188520077600201100002100977700001900998700001901017856003601036 2003 en_Ud 00aEffective dynamics for Bloch electrons: Peierls substitution and beyond0 aEffective dynamics for Bloch electrons Peierls substitution and bSpringer3 aWe consider an electron moving in a periodic potential and subject to an additional slowly varying external electrostatic potential, $\\\\phi(\\\\epsi x)$, and vector potential $A(\\\\epsi x)$, with $x \\\\in \\\\R^d$ and $\\\\epsi \\\\ll 1$. We prove that associated to an isolated family of Bloch bands there exists an almost invariant subspace of $L^2(\\\\R^d)$ and an effective Hamiltonian governing the evolution inside this subspace to all orders in $\\\\epsi$. To leading order the effective Hamiltonian is given through the Peierls substitution. We explicitly compute the first order correction. From a semiclassical analysis of this effective quantum Hamiltonian we establish the first order correction to the standard semiclassical model of solid state physics.1 aPanati, Gianluca1 aSpohn, Herbert1 aTeufel, Stefan uhttp://hdl.handle.net/1963/304000803nas a2200109 4500008004100000245008400041210006900125260001800194520042700212100001800639856003600657 2003 en d00aA finite element approximation of the Griffith\\\'s model in fracture mechanics0 afinite element approximation of the Griffiths model in fracture bSISSA Library3 aThe Griffith model for the mechanics of fractures in brittle materials is consider in the weak formulation of SBD spaces. We suggest an approximation, in the sense of Gamma-convergence, by a sequence of discrete functionals defined on finite elements spaces over structured and adaptive triangulations. The quasi-static evolution for boundary value problems is also taken into account and some numerical results are shown.1 aNegri, Matteo uhttp://hdl.handle.net/1963/154800421nas a2200121 4500008004100000022001400041245005900055210005600114300001400170490000800184100001900192856008800211 2003 eng d a0550-321300aFree energy of the two-matrix model/dToda tau-function0 aFree energy of the twomatrix modeldToda taufunction a435–4610 v6691 aBertola, Marco uhttp://www.math.sissa.it/publication/free-energy-two-matrix-modeldtoda-tau-function01156nas a2200121 4500008004300000245006500043210006400108260001900172520076900191100002100960700001700981856003600998 2003 en_Ud 00aGaudin models and bending flows: a geometrical point of view0 aGaudin models and bending flows a geometrical point of view bIOP Publishing3 aIn this paper we discuss the bihamiltonian formulation of the (rational XXX) Gaudin models of spin-spin interaction, generalized to the case of sl(r)-valued spins. In particular, we focus on the homogeneous models. We find a pencil of Poisson brackets that recursively define a complete set of integrals of the motion, alternative to the set of integrals associated with the \\\'standard\\\' Lax representation of the Gaudin model. These integrals, in the case of su(2), coincide wih the Hamiltonians of the \\\'bending flows\\\' in the moduli space of polygons in Euclidean space introduced by Kapovich and Millson. We finally address the problem of separability of these flows and explicitly find separation coordinates and separation relations for the r=2 case.1 aFalqui, Gregorio1 aMusso, Fabio uhttp://hdl.handle.net/1963/288401411nas a2200109 4500008004300000245012000043210006900163260001000232520100100242100002201243856003601265 2003 en_Ud 00aGeometric motion control for a kinematically redundant robotic chain: application to a holonomic mobile manipulator0 aGeometric motion control for a kinematically redundant robotic c bWiley3 aFor kinematically redundant robotic manipulators, the extra degrees of freedom available allows freedom in the generation of the trajectories of the end-effector. In this paper, for this scope, we use techniques for motion control of rigid bodies on Riemannian manifolds (and Lie groups in particular) to design workspace control algorithms for the end-effector of the robotic chain and then to pull them back to joint space, all respecting the different geometric structures of the two underlying model spaces. The trajectory planner makes use of geometric splines. Examples of the different kinds of curves that are obtained via the De Casteljau algorithm in correspondence of different metric structures in SE(3) are reported. The feedback module, instead, consists of a Lyapunov based PD controller defined from a suitable notion of error distance on the Lie group. The motivating application of our work is a holonomic mobile manipulator for which simulation results are described in detail.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/301900868nas a2200145 4500008004300000245005900043210005800102260002300160520042200183100001800605700002100623700001900644700002300663856003600686 2003 en_Ud 00aHybrid optimal control: case study of a car with gears0 aHybrid optimal control case study of a car with gears bTaylor and Francis3 aThe purpose of this paper is to show the use of some analytical tools for hybrid optimal control. We illustrate both the hybrid maximum principle and the hybrid necessary principle at work on a simple example of a car with gears. The model is sufficiently rich to generate non-trivial optimization problems and the obtained results match with intuition. Finally, computer simulations confirm the theoretical analysis.1 aD'Apice, Ciro1 aGaravello, Mauro1 aManzo, Rosanna1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/302200871nas a2200109 4500008004300000245008000043210006900123260002600192520048600218100002100704856003600725 2003 en_Ud 00aAn ill posed Cauchy problem for a hyperbolic system in two space dimensions0 aill posed Cauchy problem for a hyperbolic system in two space di bUniversità di Padova3 aThe theory of weak solutions for nonlinear conservation laws is now well developed in the case of scalar equations [3] and for one-dimensional hyperbolic systems [1, 2]. For systems in several space dimensions, however, even the global existence of solutions to the Cauchy problem remains a challenging open question. In this note we construct a conterexample showing that, even for a simple class of hyperbolic systems, in two space dimensions the Cauchy problem can be ill posed.1 aBressan, Alberto uhttp://hdl.handle.net/1963/291300338nas a2200097 4500008004100000245006000041210005700101260001800158100002800176856003600204 2003 en d00aAn interior estimate for a nonlinear parabolic equation0 ainterior estimate for a nonlinear parabolic equation bSISSA Library1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/162200867nas a2200109 4500008004300000245005900043210005700102260002600159520051500185100002100700856003600721 2003 en_Ud 00aA lemma and a conjecture on the cost of rearrangements0 alemma and a conjecture on the cost of rearrangements bUniversità di Padova3 aConsider a stack of books, containing both white and black books. Suppose that we want to sort them out, putting the white books on the right, and the black books on the left (fig.~1). This will be done by a finite sequence of elementary transpositions. In other words, if we have a stack of all black books of length $a$ followed by a stack of all white books of length $b$, we are allowed to reverse their order at the cost of $a+b$. We are interested in a lower bound on the total cost of the rearrangement.1 aBressan, Alberto uhttp://hdl.handle.net/1963/291400867nas a2200121 4500008004100000245005700041210005000098260001800148520049700166100002500663700002100688856003600709 2003 en d00aOn the local structure of optimal trajectories in R30 alocal structure of optimal trajectories in R3 bSISSA Library3 aWe analyze the structure of a control function u(t) corresponding to an optimal trajectory for the system $\\\\dot q =f(q)+u\\\\, g(q)$ in a three-dimensional manifold, near a point where some nondegeneracy conditions are satisfied. The kind of optimality which is studied includes time-optimality. The control turns out to be the concatenation of some bang and some singular arcs. Studying the index of the second variation of the switching times, the number of such arcs is bounded by four.1 aAgrachev, Andrei, A.1 aSigalotti, Mario uhttp://hdl.handle.net/1963/161200443nas a2200133 4500008004100000022001400041245005600055210005500111300001600166490000700182100001900189700001500208856008600223 2003 eng d a0305-447000aMixed correlation functions of the two-matrix model0 aMixed correlation functions of the twomatrix model a7733–77500 v361 aBertola, Marco1 aEynard, B. uhttp://www.math.sissa.it/publication/mixed-correlation-functions-two-matrix-model01197nas a2200121 4500008004300000245012700043210006900170260001300239520074500252100002200997700002001019856003601039 2003 en_Ud 00aMotion on submanifolds of noninvariant holonomic constraints for a kinematic control system evolving on a matrix Lie group0 aMotion on submanifolds of noninvariant holonomic constraints for bElsevier3 aFor a control system on a matrix Lie group with one or more configuration constraints that are not left/right invariant, finding the combinations of (kinematic) control inputs satisfying the motion constraints is not a trivial problem. Two methods, one coordinate-dependent and the other coordinate-free are suggested. The first is based on the Wei-Norman formula; the second on the calculation of the annihilator of the coadjoint action of the constraint one-form at each point of the group manifold. The results are applied to a control system on SE(3) with a holonomic inertial constraint involving the noncommutative part in a nontrivial way. The difference in terms of compactness of the result between the two methods is considerable.1 aAltafini, Claudio1 aFrezza, Ruggero uhttp://hdl.handle.net/1963/301800423nas a2200133 4500008004100000245005600041210005500097260001800152100001600170700002100186700002200207700002400229856003600253 2003 en d00aMulti-instanton calculus and equivariant cohomology0 aMultiinstanton calculus and equivariant cohomology bSISSA Library1 aBruzzo, Ugo1 aMorales, Jose F.1 aFucito, Francesco1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/164500815nas a2200133 4500008004300000245009200043210006900135260002100204520035600225100002200581700002200603700002000625856003600645 2003 en_Ud 00aNon-linear sigma-models in noncommutative geometry: fields with values in finite spaces0 aNonlinear sigmamodels in noncommutative geometry fields with val bWorld Scientific3 aWe study sigma-models on noncommutative spaces, notably on noncommutative tori. We construct instanton solutions carrying a nontrivial topological charge q and satisfying a Belavin-Polyakov bound. The moduli space of these instantons is conjectured to consists of an ordinary torus endowed with a complex structure times a projective space $CP^{q-1}$.1 aDabrowski, Ludwik1 aKrajewski, Thomas1 aLandi, Giovanni uhttp://hdl.handle.net/1963/321500845nas a2200109 4500008004100000245007300041210006900114260001800183520047500201100002300676856003600699 2003 en d00aA note on singular limits to hyperbolic systems of conservation laws0 anote on singular limits to hyperbolic systems of conservation la bSISSA Library3 aIn this note we consider two different singular limits to hyperbolic system of conservation laws, namely the standard backward schemes for non linear semigroups and the semidiscrete scheme. \\nUnder the assumption that the rarefaction curve of the corresponding hyperbolic system are straight lines, we prove the stability of the solution and the convergence to the perturbed system to the unique solution of the limit system for initial data with small total variation.1 aBianchini, Stefano uhttp://hdl.handle.net/1963/154200630nas a2200121 4500008004300000245007700043210006900120260002900189520021200218100002300430700001900453856003600472 2003 en_Ud 00aA note on the integral representation of functionals in the space SBD(O)0 anote on the integral representation of functionals in the space bRendiconti di Matematica3 aIn this paper we study the integral representation in the space SBD(O) of special functions with bounded deformation of some L^1-norm lower semicontinuous functionals invariant with respect to rigid motions.1 aEbobisse, Francois1 aToader, Rodica uhttp://hdl.handle.net/1963/306400793nas a2200109 4500008004300000245010200043210006900145260001300214520039800227100002200625856003600647 2003 en_Ud 00aParameter differentiation and quantum state decomposition for time varying Schrödinger equations0 aParameter differentiation and quantum state decomposition for ti bElsevier3 aFor the unitary operator, solution of the Schroedinger equation corresponding to a time-varying Hamiltonian, the relation between the Magnus and the product of exponentials expansions can be expressed in terms of a system of first order differential equations in the parameters of the two expansions. A method is proposed to compute such differential equations explicitly and in a closed form.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/301700523nas a2200145 4500008004100000022001400041245007400055210006900129300001600198490000700214100001900221700001500240700001500255856010700270 2003 eng d a0305-447000aPartition functions for matrix models and isomonodromic tau functions0 aPartition functions for matrix models and isomonodromic tau func a3067–30830 v361 aBertola, Marco1 aEynard, B.1 aHarnad, J. uhttp://www.math.sissa.it/publication/partition-functions-matrix-models-and-isomonodromic-tau-functions00397nas a2200109 4500008004100000245007900041210006900120260001800189100002400207700002000231856003600251 2003 en d00aPeriodic solutions of nonlinear wave equations with general nonlinearities0 aPeriodic solutions of nonlinear wave equations with general nonl bSISSA Library1 aBerti, Massimiliano1 aBolle, Philippe uhttp://hdl.handle.net/1963/164800961nas a2200109 4500008004300000245006400043210006200107260001000169520061500179100002100794856003600815 2003 en_Ud 00aPoisson Pencils, Integrability, and Separation of Variables0 aPoisson Pencils Integrability and Separation of Variables bSISSA3 aIn this paper we will review a recently introduced method for solving the Hamilton-Jacobi equations by the method of Separation of Variables. This method is based on the notion of pencil of Poisson brackets and on the bihamiltonian approach to integrable systems. We will discuss how separability conditions can be intrinsically characterized within such a geometrical set-up, the definition of the separation coordinates being encompassed in the \\\\bih structure itself. We finally discuss these constructions studying in details a particular example, based on a generalization of the classical Toda Lattice.1 aFalqui, Gregorio uhttp://hdl.handle.net/1963/302600551nas a2200121 4500008004100000245007300041210006900114260004800183520011800231100002400349700002000373856003600393 2003 en d00aPositive solutions to a class of quasilinear elliptic equations on R0 aPositive solutions to a class of quasilinear elliptic equations bAmerican Institute of Mathematical Sciences3 aWe discuss the existence of positive solutions of perturbation to a class of quasilinear elliptic equations on R.1 aAmbrosetti, Antonio1 aZhi-Qiang, Wang uhttp://hdl.handle.net/1963/162800736nas a2200133 4500008004300000245008800043210006900131260001300200520028300213100002000496700002200516700002800538856003600566 2003 en_Ud 00aPrescribing scalar and boundary mean curvature on the three dimensional half sphere0 aPrescribing scalar and boundary mean curvature on the three dime bSpringer3 aWe consider the problem of prescribing the scalar curvature and the boundary mean curvature of the standard half three sphere, by deforming conformally its standard metric. Using blow up analysis techniques and minimax arguments, we prove some existence and compactness results.1 aDjadli, Zindine1 aMalchiodi, Andrea1 aAhmedou, Mohameden Ould uhttp://hdl.handle.net/1963/308600751nas a2200121 4500008004100000245004200041210004200083260001900125520040900144100002200553700001800575856003600593 2003 en d00aQuantum spin coverings and statistics0 aQuantum spin coverings and statistics bIOP Publishing3 aSL_q(2) at odd roots of unity q^l =1 is studied as a quantum cover of the complex rotation group SO(3,C), in terms of the associated Hopf algebras of (quantum) polynomial functions. We work out the irreducible corepresentations, the decomposition of their tensor products and a coquasitriangular structure, with the associated braiding (or statistics). As an example, the case l=3 is discussed in detail.1 aDabrowski, Ludwik1 aReina, Cesare uhttp://hdl.handle.net/1963/166700431nas a2200109 4500008004100000022001400041245006300055210006200118300002900180100001900209856009300228 2003 eng d a1126-670800aSecond and third order observables of the two-matrix model0 aSecond and third order observables of the twomatrix model a062, 30 pp. (electronic)1 aBertola, Marco uhttp://www.math.sissa.it/publication/second-and-third-order-observables-two-matrix-model00998nas a2200121 4500008004100000245005500041210005400096260001800150520063200168100002100800700001900821856003600840 2003 en d00aSeparation of variables for Bi-Hamiltonian systems0 aSeparation of variables for BiHamiltonian systems bSISSA Library3 aWe address the problem of the separation of variables for the Hamilton-Jacobi equation within the theoretical scheme of bi-Hamiltonian geometry. We use the properties of a special class of bi-Hamiltonian manifolds, called omega-N manifolds, to give intrisic tests of separability (and Staeckel separability) for Hamiltonian systems. The separation variables are naturally associated with the geometrical structures of the omega-N manifold itself. We apply these results to bi-Hamiltonian systems of the Gel\\\'fand-Zakharevich type and we give explicit procedures to find the separated coordinates and the separation relations.1 aFalqui, Gregorio1 aPedroni, Marco uhttp://hdl.handle.net/1963/159800579nas a2200109 4500008004300000245008900043210006900132260000900201520019800210100002500408856003600433 2003 en_Ud 00aSequences of Singularly Perturbed Functionals Generating Free-Discontinuity Problems0 aSequences of Singularly Perturbed Functionals Generating FreeDis bSIAM3 aWe prove that a wide class of singularly perturbed functionals generates as $\\\\Gamma$-limit a functional related to a free-discontinuity problem. Several applications of the result are shown.1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/307100397nas a2200097 4500008004100000245012200041210006900163260001000232100002100242856003600263 2003 en d00aSingle-Input Control Affine Systems: Local Regularity of Optimal Trajectories and a Geometric Controllability Problem0 aSingleInput Control Affine Systems Local Regularity of Optimal T bSISSA1 aSigalotti, Mario uhttp://hdl.handle.net/1963/534200459nas a2200121 4500008004100000245011500041210006900156260001300225100002400238700002200262700001700284856003600301 2003 en d00aSingularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres, Part I0 aSingularly perturbed elliptic equations with symmetry existence bSpringer1 aAmbrosetti, Antonio1 aMalchiodi, Andrea1 aNi, Wei-Ming uhttp://hdl.handle.net/1963/163300426nas a2200121 4500008004100000245007300041210006900114260001800183100002100201700001800222700002800240856003600268 2003 en d00aSome results on the boundary control of systems of conservation laws0 aSome results on the boundary control of systems of conservation bSISSA Library1 aBressan, Alberto1 aAncona, Fabio1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/161501403nas a2200133 4500008004300000245004000043210003900083260002400122520102800146100002101174700001901195700001901214856003601233 2003 en_Ud 00aSpace-adiabatic perturbation theory0 aSpaceadiabatic perturbation theory bInternational Press3 aWe study approximate solutions to the Schr\\\\\\\"odinger equation $i\\\\epsi\\\\partial\\\\psi_t(x)/\\\\partial t = H(x,-i\\\\epsi\\\\nabla_x) \\\\psi_t(x)$ with the Hamiltonian given as the Weyl quantization of the symbol $H(q,p)$ taking values in the space of bounded operators on the Hilbert space $\\\\Hi_{\\\\rm f}$ of fast ``internal\\\'\\\' degrees of freedom. By assumption $H(q,p)$ has an isolated energy band. Using a method of Nenciu and Sordoni \\\\cite{NS} we prove that interband transitions are suppressed to any order in $\\\\epsi$. As a consequence, associated to that energy band there exists a subspace of $L^2(\\\\mathbb{R}^d,\\\\Hi _{\\\\rm f})$ almost invariant under the unitary time evolution. We develop a systematic perturbation scheme for the computation of effective Hamiltonians which govern approximately the intraband time evolution. As examples for the general perturbation scheme we discuss the Dirac and Born-Oppenheimer type Hamiltonians and we reconsider also the time-adiabatic theory.1 aPanati, Gianluca1 aSpohn, Herbert1 aTeufel, Stefan uhttp://hdl.handle.net/1963/304100672nas a2200133 4500008004100000245008000041210006900121260001800190520022400208100002100432700002300453700002600476856003600502 2003 en d00aA stability result for nonlinear Neumann problems under boundary variations0 astability result for nonlinear Neumann problems under boundary v bSISSA Library3 aIn this paper we study, in dimension two, the stability of the solutions of some nonlinear elliptic equations with Neumann boundary conditions, under perturbations of the domains in the Hausdorff complementary topology.1 aDal Maso, Gianni1 aEbobisse, Francois1 aPonsiglione, Marcello uhttp://hdl.handle.net/1963/161800399nas a2200109 4500008004100000245007900041210006900120260001800189100002300207700002300230856003600253 2002 en d00aAdmissible Riemann solvers for genuinely nonlinear P-systems of mixed type0 aAdmissible Riemann solvers for genuinely nonlinear Psystems of m bSISSA Library1 aMercier, Jean-Marc1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/149100799nas a2200109 4500008004100000245005300041210005200094260003600146520039600182100002400578856008700602 2002 en d00aArnold diffusion: a functional analysis approach0 aArnold diffusion a functional analysis approach bNatsīonal. Akad. Nauk Ukraïni3 aWe present, in the context of nearly integrable Hamiltonian systems, a functional analysis approach to study the “splitting of the whiskers” and the “shadowing problem” developed in collaboration with P. Bolle in the recent papers [1] and [2] . This method is applied to the problem of Arnold diffusion for nearly integrable partially isochronous systems improving known results.1 aBerti, Massimiliano uhttp://www.math.sissa.it/publication/arnold-diffusion-functional-analysis-approach00716nas a2200121 4500008004300000245006000043210005300103260000900156520034400165100002100509700002800530856003600558 2002 en_Ud 00aOn the Boundary Control of Systems of Conservation Laws0 aBoundary Control of Systems of Conservation Laws bSIAM3 aThe paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand, we give an example showing that exact controllability in finite time cannot be achieved, in general.1 aBressan, Alberto1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/307000668nas a2200109 4500008004300000245008100043210006900124260002200193520028200215100002500497856003600522 2002 en_Ud 00aThe Calibration Method for Free-Discontinuity Problems on Vector-Valued Maps0 aCalibration Method for FreeDiscontinuity Problems on VectorValue bHeldermann Verlag3 aThe calibration method is a classical minimality criterion, which has been recently adapted to functionals with free discontinuities by Alberti, Bouchitté, Dal Maso. In this paper we present a further generalization of this theory to functionals defined on vector-valued maps.1 aMora, Maria Giovanna uhttp://hdl.handle.net/1963/304900816nas a2200121 4500008004300000245005800043210005600101260004800157520040900205100002300614700002100637856003600658 2002 en_Ud 00aA center manifold technique for tracing viscous waves0 acenter manifold technique for tracing viscous waves bAmerican Institute of Mathematical Sciences3 aIn this paper we introduce a new technique for tracing viscous travelling profiles. To illustrate the method, we consider a special 2 x 2 hyperbolic system of conservation laws with viscosity, and show that any solution can be locally decomposed as the sum of 2 viscous travelling profiles. This yields the global existence, stability and uniform BV bounds for every solution with suitably small BV data.1 aBianchini, Stefano1 aBressan, Alberto uhttp://hdl.handle.net/1963/307500397nas a2200109 4500008004100000245008300041210006900124260001300193100002400206700002100230856003600251 2002 en d00aChaotic dynamics for perturbations of infinite-dimensional Hamiltonian systems0 aChaotic dynamics for perturbations of infinitedimensional Hamilt bElsevier1 aBerti, Massimiliano1 aCarminati, Carlo uhttp://hdl.handle.net/1963/127900460nas a2200133 4500008004100000022001400041245006600055210005700121300001600178490000700194100002100201700001900222856008500241 2002 eng d a0022-248800aCoherent state realizations of $\rm su(n+1)$ on the $n$-torus0 aCoherent state realizations of rm sun1 on the ntorus a3425–34440 v431 ade Guise, Hubert1 aBertola, Marco uhttp://www.math.sissa.it/publication/coherent-state-realizations-rm-sun1-n-torus00371nas a2200097 4500008004100000245008700041210006900128260001800197100002200215856003600237 2002 en d00aControllability of quantum mechanical systems by root space decomposition of su(N)0 aControllability of quantum mechanical systems by root space deco bSISSA Library1 aAltafini, Claudio uhttp://hdl.handle.net/1963/161300727nas a2200121 4500008004300000245006600043210006400109260003400173520032000207100002000527700002200547856003600569 2002 en_Ud 00aCurvature theory of boundary phases: the two-dimensional case0 aCurvature theory of boundary phases the twodimensional case bEuropean Mathematical Society3 aWe describe the behaviour of minimum problems involving non-convex surface integrals in 2D, singularly perturbed by a curvature term. We show that their limit is described by functionals which take into account energies concentrated on vertices of polygons. Non-locality and non-compactness effects are highlighted.1 aBraides, Andrea1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/353700491nas a2200145 4500008004100000022001400041245006200055210006000117300001300177490000800190100001900198700001500217700001500232856009800247 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. uhttp://www.math.sissa.it/publication/duality-biorthogonal-polynomials-and-multi-matrix-models00651nas a2200109 4500008004100000245006800041210006400109260001000173520030100183100002100484856003600505 2002 en d00aThe Elliptic Representation of the General Painlevé 6 Equation0 aElliptic Representation of the General Painlevé 6 Equation bSISSA3 aWe study the analytic properties and the critical behavior of the elliptic\r\nrepresentation of solutions of the Painlev\\\'e 6 equation. We solve the\r\nconnection problem for elliptic representation in the generic case and in a\r\nnon-generic case equivalent to WDVV equations of associativity.1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/652300515nas a2200121 4500008004100000245005900041210005500100260006700155520009100222653002300313100002100336856003600357 2002 en d00aThe Elliptic Representation of the Painleve 6 Equation0 aElliptic Representation of the Painleve 6 Equation bKyoto University, Research Institute for Mathematical Sciences3 aWe review our results on the elliptic representation of the sixth Painleve’ equation10aPainleve equations1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/653000315nas a2200109 4500008004100000245003500041210003400076260001800110100002100128700002000149856003600169 2002 en d00aExistence of minimal H-bubbles0 aExistence of minimal Hbubbles bSISSA Library1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/152500795nas a2200121 4500008004300000245006000043210006000103260004800163520038200211100002400593700002000617856003600637 2002 en_Ud 00aFast Arnold diffusion in systems with three time scales0 aFast Arnold diffusion in systems with three time scales bAmerican Institute of Mathematical Sciences3 aWe consider the problem of Arnold Diffusion for nearly integrable partially isochronous Hamiltonian systems with three time scales. By means of a careful shadowing analysis, based on a variational technique, we prove that, along special directions, Arnold diffusion takes place with fast (polynomial) speed, even though the \\\"splitting determinant\\\" is exponentially small.1 aBerti, Massimiliano1 aBolle, Philippe uhttp://hdl.handle.net/1963/305800809nas a2200121 4500008004300000245007700043210006900120260000900189520041400198100001800612700002100630856003600651 2002 en_Ud 00aFlow Stability of Patchy Vector Fields and Robust Feedback Stabilization0 aFlow Stability of Patchy Vector Fields and Robust Feedback Stabi bSIAM3 aThe paper is concerned with patchy vector fields, a class of discontinuous, piecewise smooth vector fields that were introduced in AB to study feedback stabilization problems. We prove the stability of the corresponding solution set w.r.t. a wide class of impulsive perturbations. These results yield the robusteness of patchy feedback controls in the presence of measurement errors and external disturbances.1 aAncona, Fabio1 aBressan, Alberto uhttp://hdl.handle.net/1963/307300768nas a2200109 4500008004300000245007400043210006900117260000900186520040500195100002200600856003600622 2002 en_Ud 00aFollowing a path of varying curvature as an output regulation problem0 aFollowing a path of varying curvature as an output regulation pr bIEEE3 aGiven a path of nonconstant curvature, local asymptotic stability can be proven for the general n trailer whenever the curvature can be considered as the output of an exogenous dynamical system. The controllers that provide convergence to zero of the tracking error chosen for the path-following problem are composed of a prefeedback that input-output linearizes the system, plus a linear controller.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/314300697nas a2200121 4500008004300000245005500043210005300098260001300151520033100164100002400495700002000519856003600539 2002 en_Ud 00aA functional analysis approach to Arnold diffusion0 afunctional analysis approach to Arnold diffusion bElsevier3 aWe discuss in the context of nearly integrable Hamiltonian systems a functional analysis approach to the \\\"splitting of separatrices\\\" and to the \\\"shadowing problem\\\". As an application we apply our method to the problem of Arnold Diffusion for nearly integrable partially isochronous systems improving known results.1 aBerti, Massimiliano1 aBolle, Philippe uhttp://hdl.handle.net/1963/315100403nas a2200097 4500008004100000245011900041210006900160260001800229100002200247856003600269 2002 en d00aOn the generation of sequential unitary gates from continuous time Schrodinger equations driven by external fields0 ageneration of sequential unitary gates from continuous time Schr bSISSA Library1 aAltafini, Claudio uhttp://hdl.handle.net/1963/161401353nas a2200121 4500008004300000245003200043210003200075260001300107520103200120100002501152700001801177856003601195 2002 en_Ud 00aGeometry of Jacobi Curves I0 aGeometry of Jacobi Curves I bSpringer3 aJacobi curves are deep generalizations of the spaces of \\\"Jacobi fields\\\" along Riemannian geodesics. Actually, Jacobi curves are curves in the Lagrange Grassmannians. In our paper we develop differential geometry of these curves which provides basic feedback or gauge invariants for a wide class of smooth control systems and geometric structures. Two principal invariants are the generalized Ricci curvature, which is an invariant of the parametrized curve in the Lagrange Grassmannian endowing the curve with a natural projective structure, and a fundamental form, which is a fourth-order differential on the curve. The so-called rank 1 curves are studied in more detail. Jacobi curves of this class are associated with systems with scalar controls and with rank 2 vector distributions.\\nIn the forthcoming second part of the paper we will present the comparison theorems (i.e., the estimates for the conjugate points in terms of our invariants( for rank 1 curves an introduce an important class of \\\"flat curves\\\".1 aAgrachev, Andrei, A.1 aZelenko, Igor uhttp://hdl.handle.net/1963/311000314nas a2200109 4500008004100000245003300041210003300074260001800107100002500125700001800150856003600168 2002 en d00aGeometry of Jacobi curves II0 aGeometry of Jacobi curves II bSISSA Library1 aAgrachev, Andrei, A.1 aZelenko, Igor uhttp://hdl.handle.net/1963/158901286nas a2200109 4500008004300000245007200043210006900115260003700184520089400221100002501115856003601140 2002 en_Ud 00aGlobal calibrations for the non-homogeneous Mumford-Shah functional0 aGlobal calibrations for the nonhomogeneous MumfordShah functiona bScuola Normale Superiore di Pisa3 aUsing a calibration method we prove that, if $\\\\Gamma\\\\subset \\\\Omega$ is a closed regular hypersurface and if the function $g$ is discontinuous along $\\\\Gamma$ and regular outside, then the function $u_{\\\\beta}$ which solves $$ \\\\begin{cases} \\\\Delta u_{\\\\beta}=\\\\beta(u_{\\\\beta}-g)& \\\\text{in $\\\\Omega\\\\setminus\\\\Gamma$} \\\\partial_{\\\\nu} u_{\\\\beta}=0 & \\\\text{on $\\\\partial\\\\Omega\\\\cup\\\\Gamma$} \\\\end{cases} $$ is in turn discontinuous along $\\\\Gamma$ and it is the unique absolute minimizer of the non-homogeneous Mumford-Shah functional $$ \\\\int_{\\\\Omega\\\\setminus S_u}|\\\\nabla u|^2 dx +{\\\\cal H}^{n-1}(S_u)+\\\\beta\\\\int_{\\\\Omega\\\\setminus S_u}(u-g)^2 dx, $$ over $SBV(\\\\Omega)$, for $\\\\beta$ large enough. Applications of the result to the study of the gradient flow by the method of minimizing movements are shown.1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/308900932nas a2200121 4500008004300000245004500043210004400088260001300132520058700145100002200732700002000754856003600774 2002 en_Ud 00aInstanton algebras and quantum 4-spheres0 aInstanton algebras and quantum 4spheres bElsevier3 aWe study some generalized instanton algebras which are required to describe `instantonic complex rank 2 bundles\\\'. The spaces on which the bundles are defined are not prescribed from the beginning but rather are obtained from some natural requirements on the instantons. They turn out to be quantum 4-spheres $S^4_q$, with $q\\\\in\\\\IC$, and the instantons are described by self-adjoint idempotents e. We shall also clarify some issues related to the vanishing of the first Chern-Connes class $ch_1(e)$ and on the use of the second Chern-Connes class $ch_2(e)$ as a volume form.1 aDabrowski, Ludwik1 aLandi, Giovanni uhttp://hdl.handle.net/1963/313400439nas a2200121 4500008004100000245005500041210005400096260003700150300001300187490000700200100001900207856009100226 2002 eng d00aJacobi groups, Jacobi forms and their applications0 aJacobi groups Jacobi forms and their applications aProvidence, RIbAmer. Math. Soc. a99–1110 v311 aBertola, Marco uhttp://www.math.sissa.it/publication/jacobi-groups-jacobi-forms-and-their-applications00435nas a2200121 4500008004100000245008600041210006900127260001800196100001700214700002200231700002400253856003600277 2002 en d00aOn the K+P problem for a three-level quantum system: optimality implies resonance0 aKP problem for a threelevel quantum system optimality implies re bSISSA Library1 aBoscain, Ugo1 aChambrion, Thomas1 aGauthier, Jean-Paul uhttp://hdl.handle.net/1963/160100398nas a2200121 4500008004300000245006200043210006100105260001300166100002100179700001800200700002200218856003600240 2002 en_Ud 00aLinearized elasticity as gamma-limit of finite elasticity0 aLinearized elasticity as gammalimit of finite elasticity bSpringer1 aDal Maso, Gianni1 aNegri, Matteo1 aPercivale, Danilo uhttp://hdl.handle.net/1963/305200836nas a2200109 4500008004300000245009200043210006900135260002100204520044000225100002500665856003600690 2002 en_Ud 00aLocal calibrations for minimizers of the Mumford-Shah functional with a triple junction0 aLocal calibrations for minimizers of the MumfordShah functional bWorld Scientific3 aWe prove that, if u is a function satisfying all Euler conditions for the Mumford-Shah functional and the discontinuity set of u is given by three line segments meeting at the origin with equal angles, then there exists a neighbourhood U of the origin such that u is a minimizer of the Mumford-Shah functional on U with respect to its own boundary conditions on the boundary of U. The proof is obtained by using the calibration method.1 aMora, Maria Giovanna uhttp://hdl.handle.net/1963/305000788nas a2200121 4500008004100000245008600041210006900127260001300196520037700209100002300586700002100609856003600630 2002 en d00aOn a Lyapunov functional relating shortening curves and viscous conservation laws0 aLyapunov functional relating shortening curves and viscous conse bElsevier3 aWe study a nonlinear functional which controls the area swept by a curve moving in the plane in the direction of curvature. In turn, this yields a priori estimates on solutions to a class of parabolic equations and of scalar viscous conservation laws. A further application provides an estimate on the \\\"change of shape\\\" of a BV solution to a scalar conservation law.1 aBianchini, Stefano1 aBressan, Alberto uhttp://hdl.handle.net/1963/133701609nas a2200121 4500008004100000245009900041210006900140260001800209520118400227100002101411700001901432856003601451 2002 en d00aA model for the quasi-static growth of a brittle fracture: existence and approximation results0 amodel for the quasistatic growth of a brittle fracture existence bSISSA Library3 aWe study a variant of the variational model for the quasi-static growth of brittle fractures proposed by Francfort and Marigo.9 The main feature of our model is that, in the discrete-time formulation, in each step we do not consider absolute minimizers of the energy, but, in a sense, we look for local minimizers which are sufficiently close to the approximate solution obtained in the previous step. This is done by introducing in the variational problem an additional term which penalizes the L2-distance between the approximate solutions at two consecutive times. We study the continuous-time version of this model, obtained by passing to the limit as the time step tends to zero, and show that it satisfies (for almost every time) some minimality conditions which are slightly different from those considered in Refs. 9 and 8, but are still enough to prove (under suitable regularity assumptions on the crack path) that the classical Griffith\\\'s criterion holds at the crack tips. We also prove that, if no initial crack is present and if the data of the problem are sufficiently smooth, no crack will develop in this model, provided the penalization term is large enough.1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/1963/157101599nas a2200121 4500008004100000245008900041210006900130260001800199520118400217100002101401700001901422856003601441 2002 en d00aA model for the quasi-static growth of brittle fractures based on local minimization0 amodel for the quasistatic growth of brittle fractures based on l bSISSA Library3 aWe study a variant of the variational model for the quasi-static growth of brittle fractures proposed by Francfort and Marigo.9 The main feature of our model is that, in the discrete-time formulation, in each step we do not consider absolute minimizers of the energy, but, in a sense, we look for local minimizers which are sufficiently close to the approximate solution obtained in the previous step. This is done by introducing in the variational problem an additional term which penalizes the L2-distance between the approximate solutions at two consecutive times. We study the continuous-time version of this model, obtained by passing to the limit as the time step tends to zero, and show that it satisfies (for almost every time) some minimality conditions which are slightly different from those considered in Refs. 9 and 8, but are still enough to prove (under suitable regularity assumptions on the crack path) that the classical Griffith\\\'s criterion holds at the crack tips. We also prove that, if no initial crack is present and if the data of the problem are sufficiently smooth, no crack will develop in this model, provided the penalization term is large enough.1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/1963/162101237nas a2200121 4500008004300000245009800043210006900141260001300210520081600223100002101039700001901060856003601079 2002 en_Ud 00aA Model for the Quasi-Static Growth of Brittle Fractures: Existence and Approximation Results0 aModel for the QuasiStatic Growth of Brittle Fractures Existence bSpringer3 aWe give a precise mathematical formulation of a variational model for the irreversible quasi-static evolution of brittle fractures proposed by G.A. Francfort and J.-J. Marigo, and based on Griffith\\\'s theory of crack growth. In the two-dimensional case we prove an existence result for the quasi-static evolution and show that the total energy is an absolutely continuous function of time, although we can not exclude that the bulk energy and the surface energy may present some jump discontinuities. This existence result is proved by a time discretization process, where at each step a global energy minimization is performed, with the constraint that the new crack contains all cracks formed at the previous time steps. This procedure provides an effective way to approximate the continuous time evolution.1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/1963/305600546nas a2200109 4500008004300000245008800043210006900131260001000200520016200210100002800372856003600400 2002 en_Ud 00aA multiplicity result for the Schrodinger-Maxwell equations with negative potential0 amultiplicity result for the SchrodingerMaxwell equations with ne bIMPAN3 aWe prove the existence of a sequence of radial solutions with negative energy of the Schrödinger-Maxwell equations under the action of a negative potential.1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/305300451nas a2200109 4500008004100000245005400041210005400095260003300149520009900182100002400281856003600305 2002 en d00aMultiplicity results for the Yamabe problem on Sn0 aMultiplicity results for the Yamabe problem on Sn bNational Academy of Sciences3 aWe discuss some results related to the existence of multiple solutions for the Yamabe problem.1 aAmbrosetti, Antonio uhttp://hdl.handle.net/1963/588500423nas a2200121 4500008004100000245007600041210006900117260001800186100001700204700002400221700002000245856003600265 2002 en d00aAn optimal fast-diffusion variational method for non isochronous system0 aoptimal fastdiffusion variational method for non isochronous sys bSISSA Library1 aBiasco, Luca1 aBerti, Massimiliano1 aBolle, Philippe uhttp://hdl.handle.net/1963/157900446nas a2200121 4500008004100000245009900041210006900140260001800209100002400227700001700251700002000268856003600288 2002 en d00aOptimal stability and instability results for a class of nearly integrable Hamiltonian systems0 aOptimal stability and instability results for a class of nearly bSISSA Library1 aBerti, Massimiliano1 aBiasco, Luca1 aBolle, Philippe uhttp://hdl.handle.net/1963/159600481nas a2200121 4500008004300000245011600043210006900159260003000228100002000258700002400278700002100302856003600323 2002 en_Ud 00aThe passage from nonconvex discrete systems to variational problems in Sobolev spaces: the one-dimensional case0 apassage from nonconvex discrete systems to variational problems bMAIK Nauka/Interperiodica1 aBraides, Andrea1 aGelli, Maria Stella1 aSigalotti, Mario uhttp://hdl.handle.net/1963/313000365nas a2200109 4500008004100000245006500041210005500106260001800161100002100179700001900200856003600219 2002 en d00aOn a Poisson reduction for Gel\\\'fand-Zakharevich manifolds0 aPoisson reduction for GelfandZakharevich manifolds bSISSA Library1 aFalqui, Gregorio1 aPedroni, Marco uhttp://hdl.handle.net/1963/160200474nas a2200121 4500008004100000245011800041210006900159260001800228100002000246700002200266700002800288856003600316 2002 en d00aPrescribing a fourth oder conformal invariant on the standard sphere - Part II: blow up analysis and applications0 aPrescribing a fourth oder conformal invariant on the standard sp bSISSA Library1 aDjadli, Zindine1 aMalchiodi, Andrea1 aAhmedou, Mohameden Ould uhttp://hdl.handle.net/1963/154000461nas a2200121 4500008004100000245010500041210006900146260001800215100002000233700002800253700002200281856003600303 2002 en d00aPrescribing a fourth oder conformal invariant on the standard sphere - Part I: a perturbation result0 aPrescribing a fourth oder conformal invariant on the standard sp bSISSA Library1 aDjadli, Zindine1 aAhmedou, Mohameden Ould1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/153900411nas a2200109 4500008004100000245009300041210006900134260001800203100002200221700002200243856003600265 2002 en d00aQuantum mechanics and stochastic mechanics for compatible observables at different times0 aQuantum mechanics and stochastic mechanics for compatible observ bSISSA Library1 aCorreggi, Michele1 aMorchio, Giovanni uhttp://hdl.handle.net/1963/157701129nas a2200133 4500008004100000245005300041210004600094260001800140520073800158100002000896700002000916700002300936856003600959 2002 en d00aOn the reachability of quantized control systems0 areachability of quantized control systems bSISSA Library3 aIn this paper, we study control systems whose input sets are quantized, i.e., finite or regularly distributed on a mesh. We specifically focus on problems relating to the structure of the reachable set of such systems, which may turn out to be either dense or discrete. We report results on the reachable set of linear quantized systems, and on a particular but interesting class of nonlinear systems, i.e., nonholonomic chained-form systems. For such systems, we provide a complete characterization of the reachable set, and, in case the set is discrete, a computable method to completely and succinctly describe its structure. Implications and open problems in the analysis and synthesis of quantized control systems are addressed.1 aBicchi, Antonio1 aMarigo, Alessia1