The majority of the most common physical phenomena can be described using partial differential equations (PDEs). However, they are very often characterized by strong nonlinearities. Such features lead to the coexistence of multiple solutions studied by the bifurcation theory. Unfortunately, in practical scenarios, one has to exploit numerical methods to compute the solutions of systems of PDEs, even if the classical techniques are usually able to compute only a single solution for any value of a parameter when more branches exist. In this work, we implemented an elaborated deflated continuation method that relies on the spectral element method (SEM) and on the reduced basis (RB) one to efficiently compute bifurcation diagrams with more parameters and more bifurcation points. The deflated continuation method can be obtained combining the classical continuation method and the deflation one: the former is used to entirely track each known branch of the diagram, while the latter is exploited to discover the new ones. Finally, when more than one parameter is considered, the efficiency of the computation is ensured by the fact that the diagrams can be computed during the online phase while, during the offline one, one only has to compute one-dimensional diagrams. In this work, after a more detailed description of the method, we will show the results that can be obtained using it to compute a bifurcation diagram associated with a problem governed by the Navier-Stokes equations.

VL - 47 ER - TY - JOUR T1 - An efficient computational framework for naval shape design and optimization problems by means of data-driven reduced order modeling techniques JF - Bolletino dell Unione Matematica Italiana Y1 - 2021 A1 - Nicola Demo A1 - Giulio Ortali A1 - Gianluca Gustin A1 - Gianluigi Rozza A1 - Gianpiero Lavini AB -This contribution describes the implementation of a data-driven shape optimization pipeline in a naval architecture application. We adopt reduced order models in order to improve the efficiency of the overall optimization, keeping a modular and equation-free nature to target the industrial demand. We applied the above mentioned pipeline to a realistic cruise ship in order to reduce the total drag. We begin by defining the design space, generated by deforming an initial shape in a parametric way using free form deformation. The evaluation of the performance of each new hull is determined by simulating the flux via finite volume discretization of a two-phase (water and air) fluid. Since the fluid dynamics model can result very expensive—especially dealing with complex industrial geometries—we propose also a dynamic mode decomposition enhancement to reduce the computational cost of a single numerical simulation. The real-time computation is finally achieved by means of proper orthogonal decomposition with Gaussian process regression technique. Thanks to the quick approximation, a genetic optimization algorithm becomes feasible to converge towards the optimal shape.

VL - 14 ER - TY - JOUR T1 - Exactness of Linear Response in the Quantum Hall Effect JF - Annales Henri Poincaré Y1 - 2021 A1 - Sven Bachmann A1 - De Roeck, Wojciech A1 - Fraas, Martin A1 - Markus Lange PB - Springer Science and Business Media LLC VL - 22 UR - http://dx.doi.org/10.1007/s00023-020-00989-z ER - TY - JOUR T1 - Efficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method JF - Advances in Computational Mathematics Y1 - 2020 A1 - Moreno Pintore A1 - Federico Pichi A1 - Martin Hess A1 - Gianluigi Rozza A1 - Claudio Canuto AB -The majority of the most common physical phenomena can be described using partial differential equations (PDEs). However, they are very often characterized by strong nonlinearities. Such features lead to the coexistence of multiple solutions studied by the bifurcation theory. Unfortunately, in practical scenarios, one has to exploit numerical methods to compute the solutions of systems of PDEs, even if the classical techniques are usually able to compute only a single solution for any value of a parameter when more branches exist. In this work we implemented an elaborated deflated continuation method, that relies on the spectral element method (SEM) and on the reduced basis (RB) one, to efficiently compute bifurcation diagrams with more parameters and more bifurcation points. The deflated continuation method can be obtained combining the classical continuation method and the deflation one: the former is used to entirely track each known branch of the diagram, while the latter is exploited to discover the new ones. Finally, when more than one parameter is considered, the efficiency of the computation is ensured by the fact that the diagrams can be computed during the online phase while, during the offline one, one only has to compute one-dimensional diagrams. In this work, after a more detailed description of the method, we will show the results that can be obtained using it to compute a bifurcation diagram associated with a problem governed by the Navier-Stokes equations.

UR - https://arxiv.org/abs/1912.06089 ER - TY - JOUR T1 - Efficient Geometrical parametrization for finite-volume based reduced order methods JF - International Journal for Numerical Methods in Engineering Y1 - 2020 A1 - Giovanni Stabile A1 - Matteo Zancanaro A1 - Gianluigi Rozza AB -In this work, we present an approach for the efficient treatment of parametrized geometries in the context of POD-Galerkin reduced order methods based on Finite Volume full order approximations. On the contrary to what is normally done in the framework of finite element reduced order methods, different geometries are not mapped to a common reference domain: the method relies on basis functions defined on an average deformed configuration and makes use of the Discrete Empirical Interpolation Method (D-EIM) to handle together non-affinity of the parametrization and non-linearities. In the first numerical example, different mesh motion strategies, based on a Laplacian smoothing technique and on a Radial Basis Function approach, are analyzed and compared on a heat transfer problem. Particular attention is devoted to the role of the non-orthogonal correction. In the second numerical example the methodology is tested on a geometrically parametrized incompressible Navier–Stokes problem. In this case, the reduced order model is constructed following the same segregated approach used at the full order level

VL - 121 UR - https://arxiv.org/abs/1901.06373 ER - TY - CONF T1 - The Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: from Laminar to Turbulent Flows T2 - Lecture Notes in Computational Science and Engineering Y1 - 2020 A1 - Saddam Hijazi A1 - Shafqat Ali A1 - Giovanni Stabile A1 - F. Ballarin A1 - Gianluigi Rozza AB -We present in this double contribution two different reduced order strategies for incompressible parameterized Navier-Stokes equations characterized by varying Reynolds numbers. The first strategy deals with low Reynolds number (laminar flow) and is based on a stabilized finite element method during the offline stage followed by a Galerkin projection on reduced basis spaces generated by a greedy algorithm. The second methodology is based on a full order finite volume discretization. The latter methodology will be used for flows with moderate to high Reynolds number characterized by turbulent patterns. For the treatment of the mentioned turbulent flows at the reduced order level, a new POD-Galerkin approach is proposed. The new approach takes into consideration the contribution of the eddy viscosity also during the online stage and is based on the use of interpolation. The two methodologies are tested on classic benchmark test cases.

JF - Lecture Notes in Computational Science and Engineering PB - Springer International Publishing CY - Cham SN - 978-3-030-30705-9 ER - TY - JOUR T1 - Energy-dissipation balance of a smooth moving crack Y1 - 2020 A1 - Maicol Caponi A1 - Ilaria Lucardesi A1 - Emanuele Tasso KW - Energy-dissipation balance KW - Fracture dynamics KW - Wave equation in time-dependent domains AB -In 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 [10] valid for straight fractures.

VL - 483 SN - 0022-247X UR - https://www.sciencedirect.com/science/article/pii/S0022247X19309242 IS - 2 JO - Journal of Mathematical Analysis and Applications ER - TY - JOUR T1 - Enhancing CFD predictions in shape design problems by model and parameter space reduction JF - Advanced Modeling and Simulation in Engineering Sciences Y1 - 2020 A1 - Marco Tezzele A1 - Nicola Demo A1 - Giovanni Stabile A1 - Andrea Mola A1 - Gianluigi Rozza AB -In this work we present an advanced computational pipeline for the approximation and prediction of the lift coefficient of a parametrized airfoil profile. The non-intrusive reduced order method is based on dynamic mode decomposition (DMD) and it is coupled with dynamic active subspaces (DyAS) to enhance the future state prediction of the target function and reduce the parameter space dimensionality. The pipeline is based on high-fidelity simulations carried out by the application of finite volume method for turbulent flows, and automatic mesh morphing through radial basis functions interpolation technique. The proposed pipeline is able to save 1/3 of the overall computational resources thanks to the application of DMD. Moreover exploiting DyAS and performing the regression on a lower dimensional space results in the reduction of the relative error in the approximation of the time-varying lift coefficient by a factor 2 with respect to using only the DMD.

VL - 7 UR - https://arxiv.org/abs/2001.05237 IS - 40 ER - TY - JOUR T1 - Existence of Riemannian metrics with positive biorthogonal curvature on simply connected 5-manifolds JF - Archiv der Mathematik Y1 - 2020 A1 - Boris Stupovski A1 - Rafael Torres AB -Using the recent work of Bettiol, we show that a first-order conformal deformation of Wilking’s metric of almost-positive sectional curvature on $S2\times S3$ yields a family of metrics with strictly positive average of sectional curvatures of any pair of 2-planes that are separated by a minimal distance in the 2-Grassmanian. A result of Smale allows us to conclude that every closed simply connected 5-manifold with torsion-free homology and trivial second Stiefel–Whitney class admits a Riemannian metric with a strictly positive average of sectional curvatures of any pair of orthogonal 2-planes.

PB - Springer UR - https://dx.doi.org/10.1007/s00013-020-01511-x ER - TY - JOUR T1 - Existence of solutions to a phase–field model of dynamic fracture with a crack–dependent dissipation Y1 - 2020 A1 - Maicol Caponi AB -We propose a phase–field model of dynamic fracture based on the Ambrosio–Tortorelli’s approximation, which takes into account dissipative effects due to the speed of the crack tips. By adapting the time discretization scheme contained in Larsen et al. (Math Models Methods Appl Sci 20:1021–1048, 2010), we show the existence of a dynamic crack evolution satisfying an energy–dissipation balance, according to Griffith’s criterion. Finally, we analyze the dynamic phase–field model of Bourdin et al. (Int J Fract 168:133–143, 2011) and Larsen (in: Hackl (ed) IUTAM symposium on variational concepts with applications to the mechanics of materials, IUTAM Bookseries, vol 21. Springer, Dordrecht, 2010, pp 131–140) with no dissipative terms.

VL - 27 SN - 1420-9004 UR - https://doi.org/10.1007/s00030-020-0617-z IS - 2 JO - Nonlinear Differential Equations and Applications NoDEA ER - TY - CONF T1 - Efficient reduction in shape parameter space dimension for ship propeller blade design T2 - 8th International Conference on Computational Methods in Marine Engineering, MARINE 2019 Y1 - 2019 A1 - Andrea Mola A1 - Marco Tezzele A1 - Mahmoud Gadalla A1 - Valdenazzi, Federica A1 - Grassi, Davide A1 - Padovan, Roberta A1 - Gianluigi Rozza AB -In 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.

JF - 8th International Conference on Computational Methods in Marine Engineering, MARINE 2019 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075395143&partnerID=40&md5=b6aa0fcedc2f88e78c295d0f437824d0 ER - TY - JOUR T1 - An entropic interpolation proof of the HWI inequality JF - Stochastic Processes and their Applications Y1 - 2019 A1 - Ivan Gentil A1 - Christian Léonard A1 - Luigia Ripani A1 - Luca Tamanini KW - Entropic interpolations KW - Fisher information KW - Relative entropy KW - Schrödinger problem KW - Wasserstein distance AB -The HWI inequality is an “interpolation”inequality between the Entropy H, the Fisher information I and the Wasserstein distance W. We present a pathwise proof of the HWI inequality which is obtained through a zero noise limit of the Schrödinger problem. Our approach consists in making rigorous the Otto–Villani heuristics in Otto and Villani (2000) taking advantage of the entropic interpolations, which are regular both in space and time, rather than the displacement ones.

UR - http://www.sciencedirect.com/science/article/pii/S0304414918303454 ER - TY - JOUR T1 - Error estimates in weighted Sobolev norms for finite element immersed interface methods JF - Computers & Mathematics with Applications Y1 - 2019 A1 - Luca Heltai A1 - Nella Rotundo PB - Elsevier BV VL - 78 UR - https://doi.org/10.1016/j.camwa.2019.05.029 ER - TY - JOUR T1 - On the existence of elastic minimizers for initially stressed materials JF - Phil. Trans. R. Soc. A Y1 - 2019 A1 - Davide Riccobelli A1 - A. Agosti A1 - Pasquale Ciarletta PB - The Royal Society VL - 377 ER - TY - JOUR T1 - Effective non-linear spinor dynamics in a spin-1 Bose–Einstein condensate JF - Journal of Physics A: Mathematical and Theoretical Y1 - 2018 A1 - Alessandro Michelangeli A1 - Alessandro Olgiati AB -We 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 many-body 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.

PB - IOP Publishing VL - 51 UR - https://doi.org/10.1088%2F1751-8121%2Faadbc2 ER - TY - Generic T1 - An efficient shape parametrisation by free-form deformation enhanced by active subspace for hull hydrodynamic ship design problems in open source environment T2 - The 28th International Ocean and Polar Engineering Conference Y1 - 2018 A1 - Nicola Demo A1 - Marco Tezzele A1 - Andrea Mola A1 - Gianluigi Rozza KW - Active subspaces KW - Boundary element method KW - Dynamic mode decomposition KW - Fluid structure interaction KW - Free form deformation KW - Fully nonlinear potential KW - Numerical towing tank AB - In 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. JF - The 28th International Ocean and Polar Engineering Conference PB - International Society of Offshore and Polar Engineers CY - Sapporo, Japan UR - https://www.onepetro.org/conference-paper/ISOPE-I-18-481 ER - TY - RPRT T1 - Existence and uniqueness of dynamic evolutions for a one dimensional debonding model with damping Y1 - 2018 A1 - Lorenzo Nardini A1 - Filippo Riva AB -In 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.

UR - http://preprints.sissa.it/xmlui/handle/1963/35319 U1 - 35629 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Existence for elastodynamic Griffith fracture with a weak maximal dissipation condition Y1 - 2018 A1 - Gianni Dal Maso A1 - Cristopher J. Larsen A1 - Rodica Toader AB - We 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. UR - http://preprints.sissa.it/handle/1963/35308 U1 - 35616 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - EZyRB: Easy Reduced Basis method JF - The Journal of Open Source Software Y1 - 2018 A1 - Nicola Demo A1 - Marco Tezzele A1 - Gianluigi Rozza VL - 3 UR - https://joss.theoj.org/papers/10.21105/joss.00661 ER - TY - RPRT T1 - On the effect of interactions beyond nearest neighbours on non-convex lattice systems Y1 - 2017 A1 - Roberto Alicandro A1 - Giuliano Lazzaroni A1 - Mariapia Palombaro AB - We 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. UR - http://urania.sissa.it/xmlui/handle/1963/35268 U1 - 35574 U2 - Mathematics U4 - 1 ER - TY - CHAP T1 - Effective Non-linear Dynamics of Binary Condensates and Open Problems T2 - Advances in Quantum Mechanics: Contemporary Trends and Open Problems Y1 - 2017 A1 - Alessandro Olgiati ED - Alessandro Michelangeli ED - Gianfausto Dell'Antonio AB -We report on a recent result concerning the effective dynamics for a mixture of Bose-Einstein condensates, a class of systems much studied in physics and receiving a large amount of attention in the recent literature in mathematical physics; for such models, the effective dynamics is described by a coupled system of non-linear Schödinger equations. After reviewing and commenting our proof in the mean-field regime from a previous paper, we collect the main details needed to obtain the rigorous derivation of the effective dynamics in the Gross-Pitaevskii scaling limit.

JF - Advances in Quantum Mechanics: Contemporary Trends and Open Problems PB - Springer International Publishing CY - Cham SN - 978-3-319-58904-6 UR - https://doi.org/10.1007/978-3-319-58904-6_14 ER - TY - RPRT T1 - Elliptic diffeomorphisms of symplectic 4-manifolds Y1 - 2017 A1 - Vsevolod Shevchishin A1 - Gleb Smirnov UR - https://arxiv.org/pdf/1708.01518.pdf ER - TY - JOUR T1 - Energy release rate and quasi-static evolution via vanishing viscosity in a fracture model depending on the crack opening JF - ESAIM: Control, Optimisation and Calculus of Variations Y1 - 2017 A1 - Stefano Almi AB -In 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.

PB - EDP Sciences VL - 23 UR - https://www.esaim-cocv.org/component/article?access=doi&doi=10.1051/cocv/2016014 ER - TY - RPRT T1 - Equivalence of two different notions of tangent bundle on rectifiable metric measure spaces Y1 - 2016 A1 - Nicola Gigli A1 - Enrico Pasqualetto ER - TY - JOUR T1 - Error Estimates of B-spline based finite-element method for the wind-driven ocean circulation JF - JOURNAL OF SCIENTIFIC COMPUTING Y1 - 2016 A1 - Rotundo, N. A1 - Kim, T. -Y. A1 - Jiang, W. A1 - Luca Heltai A1 - Fried, E. VL - 69 ER - TY - RPRT T1 - Eulerian, Lagrangian and Broad continuous solutions to a balance law with non convex flux II Y1 - 2016 A1 - Giovanni Alberti A1 - Stefano Bianchini A1 - Laura Caravenna UR - http://urania.sissa.it/xmlui/handle/1963/35197 U1 - 35494 U2 - Mathematics ER - TY - JOUR T1 - Eulerian, Lagrangian and Broad continuous solutions to a balance law with non-convex flux I JF - Journal of Differential Equations, vol. 261, issue 8 (2016): 4298-4337 Y1 - 2016 A1 - Giovanni Alberti A1 - Stefano Bianchini A1 - Laura Caravenna PB - Elsevier UR - http://urania.sissa.it/xmlui/handle/1963/35207 U1 - 35507 U2 - Mathematics ER - TY - JOUR T1 - Exact results for N=2 supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants JF - Journal of High Energy Physics Y1 - 2016 A1 - Mikhail Bershtein A1 - Giulio Bonelli A1 - Massimiliano Ronzani A1 - Alessandro Tanzini AB -We provide a contour integral formula for the exact partition function of $\mathcal{N}=2$ 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 $U(2)\; \mathcal{N}=2^\star$ theory on $\mathbb{P}^2$ for all instanton numbers. In the zero mass case, corresponding to the $\mathcal{N}=4$ 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 longstanding conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new.

VL - 2016 UR - https://doi.org/10.1007/JHEP07(2016)023 ER - TY - JOUR T1 - Existence and non-existence results for the SU(3) singular Toda system on compact surfaces JF - Journal of Functional Analysis Y1 - 2016 A1 - Luca Battaglia A1 - Andrea Malchiodi KW - Liouville-type equations KW - Min–max solutions KW - Non-existence results KW - Toda system AB -We consider the SU(3) singular Toda system on a compact surface (Σ,g)−Δu1=2ρ1(h1eu1∫Σh1eu1dVg−1)−ρ2(h2eu2∫Σh2eu2dVg−1)−4π∑m=1Mα1m(δpm−1)−Δu2=2ρ2(h2eu2∫Σh2eu2dVg−1)−ρ1(h1eu1∫Σh1eu1dVg−1)−4π∑m=1Mα2m(δpm−1), where hi are smooth positive functions on Σ, ρi∈R+, pm∈Σ and αim>−1. We give both existence and non-existence results under some conditions on the parameters ρi and αim. Existence results are obtained using variational methods, which involve a geometric inequality of new type; non-existence results are obtained using blow-up analysis and localized Pohožaev-type identities."

VL - 270 UR - http://www.sciencedirect.com/science/article/pii/S0022123615004942 ER - TY - JOUR T1 - Existence and uniqueness of dynamic evolutions for a peeling test in dimension one JF - Journal of Differential Equations Y1 - 2016 A1 - Gianni Dal Maso A1 - Giuliano Lazzaroni A1 - Lorenzo Nardini KW - Dynamic debonding KW - Dynamic energy release rate KW - Dynamic fracture KW - Griffith's criterion KW - Maximum dissipation principle KW - Wave equation in time-dependent domains AB -In 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.

VL - 261 UR - http://www.sciencedirect.com/science/article/pii/S0022039616301772 ER - TY - JOUR T1 - Existence and multiplicity result for the singular Toda system JF - Journal of Mathematical Analysis and Applications Y1 - 2015 A1 - Luca Battaglia KW - Existence result KW - Liouville-type equations KW - Multiplicity result KW - PDEs on compact surfaces KW - Toda system AB -We consider the Toda system on a compact surface (Σ,g)−Δu1=2ρ1(h1eu1∫Σh1eu1dVg−1)−ρ2(h2eu2∫Σh2eu2dVg−1)−4π∑j=1Jα1j(δpj−1),−Δu2=2ρ2(h2eu2∫Σh2eu2dVg−1)−ρ1(h1eu1∫Σh1eu1dVg−1)−4π∑j=1Jα2j(δpj−1), where hi are smooth positive functions, ρi are positive real parameters, pj are given points on Σ and αij are numbers greater than −1. We give existence and multiplicity results, using variational and Morse-theoretical methods. It is the first existence result when some of the αij's are allowed to be negative."

VL - 424 UR - http://www.sciencedirect.com/science/article/pii/S0022247X14010191 ER - TY - RPRT T1 - Existence for constrained dynamic Griffith fracture with a weak maximal dissipation condition Y1 - 2015 A1 - Gianni Dal Maso A1 - Cristopher J. Larsen A1 - Rodica Toader AB - There 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. UR - http://urania.sissa.it/xmlui/handle/1963/35045 U1 - 35277 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Existence of positive solutions in the superlinear case via coincidence degree: the Neumann and the periodic boundary value problems JF - Adv. Differential Equations 20 (2015), 937–982. Y1 - 2015 A1 - Guglielmo Feltrin A1 - Fabio Zanolin AB -We 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.

PB - Khayyam Publishing UR - http://projecteuclid.org/euclid.ade/1435064518 N1 - AMS Subject Classification: 34B18, 34B15, 34C25, 47H11. U1 - 35388 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Existence of positive solutions of a superlinear boundary value problem with indefinite weight JF - Conference Publications Y1 - 2015 A1 - Guglielmo Feltrin KW - boundary value problem KW - indefinite weight KW - Positive solution; existence result. KW - superlinear equation AB -We deal with the existence of positive solutions for a two-point boundary value problem associated with the nonlinear second order equation $u''+a(x)g(u)=0$. The weight $a(x)$ is allowed to change sign. We assume that the function $g\colon\mathopen[0,+∞\mathclose[\to\mathbb{R}$ is continuous, $g(0)=0$ and satisfies suitable growth conditions, including the superlinear case $g(s)=s^p$, with $p>1$. In particular we suppose that $g(s)/s$ is large near infinity, but we do not require that $g(s)$ is non-negative in a neighborhood of zero. Using a topological approach based on the Leray-Schauder degree we obtain a result of existence of at least a positive solution that improves previous existence theorems.

VL - 2015 UR - http://aimsciences.org//article/id/b3c1c765-e8f5-416e-8130-05cc48478026 ER - TY - CONF T1 - Experience on vectorizing lattice Boltzmann kernels for multi-and many-core architectures T2 - International Conference on Parallel Processing and Applied Mathematics Y1 - 2015 A1 - Calore, Enrico A1 - Nicola Demo A1 - Schifano, Sebastiano Fabio A1 - Tripiccione, Raffaele JF - International Conference on Parallel Processing and Applied Mathematics PB - Springer ER - TY - RPRT T1 - Explicit formulas for relaxed disarrangement densities arising from structured deformations Y1 - 2015 A1 - Ana Cristina Barroso A1 - Jose Matias A1 - Marco Morandotti A1 - David R. Owen AB - Structured 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. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/34492 U1 - 34687 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Extended affine Weyl groups of BCD type, Frobenius manifolds and their Landau-Ginzburg superpotentials Y1 - 2015 A1 - Boris Dubrovin A1 - Ian A.B. Strachan A1 - Youjin Zhang A1 - Dafeng Zuo AB - For 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. PB - SISSA UR - http://preprints.sissa.it/handle/1963/35316 U1 - 35625 U2 - Mathematics U4 - 1 U5 - MAT/07 ER - TY - JOUR T1 - Editorial Y1 - 2014 A1 - Ciro Ciliberto A1 - Gianni Dal Maso A1 - Pasquale Vetro PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34712 U1 - 34926 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - An effective model for nematic liquid crystal composites with ferromagnetic inclusions Y1 - 2014 A1 - Maria Carme Calderer A1 - Antonio DeSimone A1 - Dmitry Golovaty A1 - Alexander Panchenko AB - Molecules 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. PB - Society for Industrial and Applied Mathematics Publications UR - http://urania.sissa.it/xmlui/handle/1963/34940 U1 - 35194 U2 - Physics U4 - 1 ER - TY - RPRT T1 - An efficient computational framework for reduced basis approximation and a posteriori error estimation of parametrized Navier-Stokes flows Y1 - 2014 A1 - Andrea Manzoni KW - Reduced Basis Method, parametrized Navier-Stokes equations, steady incompressible fluids, a posteriori error estimation, approximation stability AB - We 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. U1 - 7291 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems JF - International Journal of Computational Fluid Dynamics Y1 - 2014 A1 - Forti, D. A1 - Gianluigi Rozza AB - We 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. VL - 28 ER - TY - JOUR T1 - Existence and uniqueness of the gradient flow of the Entropy in the space of probability measures Y1 - 2014 A1 - Stefano Bianchini A1 - Alexander Dabrowski AB - After 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. PB - EUT Edizioni Universita di Trieste UR - http://urania.sissa.it/xmlui/handle/1963/34693 N1 - This paper resumes the main part of the Bachelor thesis of the second author, discussed in 2013 at the University of Trieste. U1 - 34907 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds JF - Mathematische Annalen Y1 - 2014 A1 - Kuwert, Ernst A1 - Andrea Mondino A1 - Johannes Schygulla AB -We study curvature functionals for immersed 2-spheres in a compact, three-dimensional Riemannian manifold $M$. Under the assumption that the sectional curvature $K^M$ is strictly positive, we prove the existence of a smooth immersion $f:{\mathbb{S}}^2 \rightarrow M$ minimizing the $L^2$ integral of the second fundamental form. Assuming instead that $K^M \leq 2 $ and that there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})>6$, we obtain a smooth minimizer $f:{\mathbb{S}}^2 \rightarrow M$ for the functional $\int \frac{1}{4}|H|^2+1$, where $H$ is the mean curvature.

VL - 359 UR - https://doi.org/10.1007/s00208-013-1005-3 ER - TY - JOUR T1 - Existence of immersed spheres minimizing curvature functionals in non-compact 3-manifolds JF - Annales de l'Institut Henri Poincare (C) Non Linear Analysis Y1 - 2014 A1 - Andrea Mondino A1 - Johannes Schygulla KW - Direct methods in the calculus of variations KW - General Relativity KW - Geometric measure theory KW - second fundamental form KW - Willmore functional AB -We study curvature functionals for immersed 2-spheres in non-compact, three-dimensional Riemannian manifold $(M,h)$ without boundary. First, under the assumption that $(M,h)$ is the euclidean 3-space endowed with a semi-perturbed metric with perturbation small in $C^1$ norm and of compact support, we prove that if there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})>0$ then there exists a smooth embedding $ f:\mathbb{S}^2 \hookrightarrow M$ minimizing the Willmore functional $\frac{1}{4}\int |H|^2$, where $H$ is the mean curvature. Second, assuming that $(M,h)$ is of bounded geometry (i.e. bounded sectional curvature and strictly positive injectivity radius) and asymptotically euclidean or hyperbolic we prove that if there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})>6$ then there exists a smooth immersion $f:\mathbb{S}^2\hookrightarrow M$ minimizing the functional $\int (\frac{1}{2}|A|^2+1)$, where $A$ is the second fundamental form. Finally, adding the bound $K^M \leq 2$ to the last assumptions, we obtain a smooth minimizer $f:\mathbb{S}^2 \hookrightarrow M$ for the functional $\int \frac{1}{4}(|H|^2+1)$. The assumptions of the last two theorems are satisfied in a large class of 3-manifolds arising as spacelike timeslices solutions of the Einstein vacuum equation in case of null or negative cosmological constant.

VL - 31 UR - http://www.sciencedirect.com/science/article/pii/S0294144913000851 ER - TY - JOUR T1 - Existence of integral m-varifolds minimizing $\int |A|^p $ and $\int |H|^p$ , p>m, in Riemannian manifolds JF - Calculus of Variations and Partial Differential Equations Y1 - 2014 A1 - Andrea Mondino AB -We prove existence of integral rectifiable $m$-dimensional varifolds minimizing functionals of the type $\int |H|^p$ and $\int |A|^p$ in a given Riemannian $n$-dimensional manifold $(N,g)$, $2 \leq m<n$ and $p>m$ under suitable assumptions on $N$ (in the end of the paper we give many examples of such ambient manifolds). To this aim we introduce the following new tools: some monotonicity formulas for varifolds in ${\mathbb{R }^S}$ involving $\int |H|^p$to avoid degeneracy of the minimizer, and a sort of isoperimetric inequality to bound the mass in terms of the mentioned functionals.

VL - 49 UR - https://doi.org/10.1007/s00526-012-0588-y ER - TY - JOUR T1 - Early phase of plasticity-related gene regulation and SRF dependent transcription in the hippocampus JF - PloS one. Volume 8, Issue 7, July 2013 : e68078 Y1 - 2013 A1 - Giovanni Iacono A1 - Claudio Altafini A1 - Vincent Torre AB - Hippocampal 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. PB - Public Library of Science UR - http://hdl.handle.net/1963/7287 N1 - The article is composed of 15 pages U1 - 7332 U2 - Neuroscience U4 - -1 ER - TY - JOUR T1 - Epitaxially strained elastic films: the case of anisotropic surface energies JF - ESAIM Control. Optim. Calc. Var. 19 (2013) 167-189 Y1 - 2013 A1 - Marco Bonacini AB -In 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.

PB - EDP Sciences UR - http://hdl.handle.net/1963/4268 U1 - 3999 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - RPRT T1 - Equilibrium measures for a class of potentials with discrete rotational symmetries Y1 - 2013 A1 - Ferenc Balogh A1 - Dario Merzi AB - In 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|This paper deals with the following class of nonlocal Schr\"odinger equations $$ \displaystyle (-\Delta)^s u + u = |u|^{p-1}u \ \ \text{in} \ \mathbb{R}^N, \quad \text{for} \ s\in (0,1). $$ We prove existence and symmetry results for the solutions $u$ in the fractional Sobolev space $H^s(\mathbb{R}^N)$. Our results are in clear accordance with those for the classical local counterpart, that is when $s=1$.

PB - University of Catania U1 - 7318 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - An existence result for the mean-field equation on compact surfaces in a doubly supercritical regime JF - Proceedings of the Royal Society of Edinburgh: Section A Mathematics Y1 - 2013 A1 - Aleks Jevnikar PB - Royal Society of Edinburgh Scotland Foundation VL - 143 ER - TY - JOUR T1 - Expanded degenerations and pairs JF - Communications in Algebra. Volume 41, Issue 6, May 2013, Pages 2346-2386 Y1 - 2013 A1 - Dan Abramovich A1 - Charles Cadman A1 - Barbara Fantechi A1 - Jonathan Wise KW - Expanded pairs AB - Since Jun Li's original definition, several other definitions of expanded pairs and expanded degenerations have appeared in the literature. We explain how these definitions are related and introduce several new variants and perspectives. Among these are the twisted expansions used by Abramovich and Fantechi as a basis for orbifold techniques in degeneation formulas. PB - Taylor and Francis UR - http://hdl.handle.net/1963/7383 N1 - This article is composed of 41 pages and is recorded in PDF format U1 - 7431 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Exploring the low-energy landscape of large-scale signed social networks JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. Volume 86, Issue 3, 26 September 2012, Article number036116 Y1 - 2012 A1 - Giuseppe Facchetti A1 - Giovanni Iacono A1 - Claudio Altafini AB - Analogously 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. PB - SISSA UR - http://hdl.handle.net/1963/6504 U1 - 6451 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Embedding theorems and existence results for nonlinear Schrödinger–Poisson systems with unbounded and vanishing potentials JF - Journal of Differential Equations Y1 - 2011 A1 - Bonheure, Denis A1 - Mercuri, Carlo AB -Motivated 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.

PB - Elsevier VL - 251 UR - https://doi.org/10.1016/j.jde.2011.04.010 ER - TY - JOUR T1 - Energy release rate and stress intensity factor in antiplane elasticity JF - Journal de Mathematiques Pures et Appliquees 95 (2011) 565-584 Y1 - 2011 A1 - Giuliano Lazzaroni A1 - Rodica Toader AB - In 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. PB - Elsevier UR - http://hdl.handle.net/1963/3780 U1 - 546 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Ennio De Giorgi and Γ-convergence JF - Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1017-1021 Y1 - 2011 A1 - Gianni Dal Maso AB - Γ-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. PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/5308 U1 - 5138 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - An Estimate on the Flow Generated by Monotone Operators JF - Communications in Partial Differential Equations 36 (2011) 777-796 Y1 - 2011 A1 - Stefano Bianchini A1 - Matteo Gloyer PB - Taylor & Francis UR - http://hdl.handle.net/1963/3646 U1 - 658 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - An Existence and Uniqueness Result for the Motion of Self-Propelled Microswimmers JF - SIAM J. Math. Anal. Y1 - 2011 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Marco Morandotti AB -We 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.

PB - Society for Industrial and Applied Mathematics VL - 43 UR - http://hdl.handle.net/1963/3894 U1 - 815 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence for wave equations on domains with arbitrary growing cracks JF - Rend. Lincei Mat. Appl. 22 (2011) 387-408 Y1 - 2011 A1 - Gianni Dal Maso A1 - Cristopher J. Larsen KW - Wave equation AB - In 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. PB - European Mathematical Society UR - http://hdl.handle.net/1963/4284 U1 - 4015 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Effective Schroedinger dynamics on $ ε$-thin Dirichlet waveguides via Quantum Graphs I: star-shaped graphs JF - J. Phys. A 43 (2010) 474014 Y1 - 2010 A1 - Gianfausto Dell'Antonio A1 - Emanuele Costa AB - We 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. PB - IOP Publishing UR - http://hdl.handle.net/1963/4106 U1 - 298 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Estimates on path functionals over Wasserstein Spaces JF - SIAM J. Math. Anal. 42 (2010) 1179-1217 Y1 - 2010 A1 - Stefano Bianchini A1 - Alessio Brancolini AB - In 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. UR - http://hdl.handle.net/1963/3583 U1 - 717 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the Euler-Lagrange equation for a variational problem : the general case II JF - Math. Z. 265 (2010) 889-923 Y1 - 2010 A1 - Stefano Bianchini A1 - Matteo Gloyer UR - http://hdl.handle.net/1963/2551 U1 - 1568 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Exact reconstruction of damaged color images using a total variation model JF - Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 1291-1331 Y1 - 2010 A1 - Irene Fonseca A1 - Giovanni Leoni A1 - Francesco Maggi A1 - Massimiliano Morini AB - In 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. PB - Elsevier UR - http://hdl.handle.net/1963/4039 U1 - 363 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence of planar curves minimizing length and curvature JF - Proc. Steklov Inst. Math. 270 (2010) 43-56 Y1 - 2010 A1 - Ugo Boscain A1 - Grégoire Charlot A1 - Francesco Rossi AB - In 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. PB - Springer UR - http://hdl.handle.net/1963/4107 U1 - 297 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Equivariant cohomology and localization for Lie algebroids JF - Funct. Anal. Appl. 43 (2009) 18-29 Y1 - 2009 A1 - Ugo Bruzzo A1 - Lucio Cirio A1 - Paolo Rossi A1 - Vladimir Rubtsov AB - Let 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. SN - 978-981-270-377-4 UR - http://hdl.handle.net/1963/1724 U1 - 2427 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - ERNEST: a toolbox for chemical reaction network theory JF - Bioinformatics 25 (2009) 2853-2854 Y1 - 2009 A1 - Nicola Soranzo A1 - Claudio Altafini AB - Summary: 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. PB - Oxford University Press UR - http://hdl.handle.net/1963/3826 U1 - 501 U2 - Physics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Exact results for topological strings on resolved Yp,q singularities JF - Comm. Math. Phys. 289 (2009) 205-252 Y1 - 2009 A1 - Andrea Brini A1 - Alessandro Tanzini UR - http://hdl.handle.net/1963/2631 U1 - 1492 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Existence of extremals for the Maz\\\'ya and for the Caffarelli-Kohn-Nirenberg inequalities JF - Nonlinear Anal. 70 (2009) 3002-3007 Y1 - 2009 A1 - Roberta Musina AB - This paper deals with some Sobolev-type inequalities with weights that were proved by Maz\\\'ya in 1980 and by Caffarelli-Kohn-Nirenberg in 1984. UR - http://hdl.handle.net/1963/2739 U1 - 1961 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - An existence result for the Monge problem in R^n with norm cost Y1 - 2009 A1 - Laura Caravenna UR - http://hdl.handle.net/1963/3647 U1 - 657 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the extremality, uniqueness and optimality of transference plans JF - Bull. Inst. Math. Acad. Sin. (N.S.) 4 (2009) 353-458 Y1 - 2009 A1 - Stefano Bianchini A1 - Laura Caravenna AB - We 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. UR - http://hdl.handle.net/1963/3692 U1 - 613 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Entire solutions of autonomous equations on Rn with nontrivial asymptotics JF - Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 19 (2008) 65-72 Y1 - 2008 A1 - Andrea Malchiodi AB - We 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. UR - http://hdl.handle.net/1963/2640 U1 - 1483 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - An entropy based Glimm-type functional JF - J. Hyperbolic Differ. Equ. 5 (2008) 643-662 Y1 - 2008 A1 - Laura Caravenna PB - World Scientific UR - http://hdl.handle.net/1963/4051 U1 - 351 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Equivalent definitions of asymptotic 100% B.E.C. JF - Nuovo Cimento B 123 (2008) 181-192 Y1 - 2008 A1 - Alessandro Michelangeli AB - In 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. UR - http://hdl.handle.net/1963/2546 U1 - 1573 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Eulerian calculus for the displacement convexity in the Wasserstein distance JF - SIAM J. Math. Anal. 40 (2008) 1104-1122 Y1 - 2008 A1 - Sara Daneri A1 - Giuseppe Savarè AB - In 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. PB - SIAM UR - http://hdl.handle.net/1963/3413 U1 - 922 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence of conformal metrics with constant $Q$-curvature JF - Ann. of Math. 168 (2008) 813-858 Y1 - 2008 A1 - Zindine Djadli A1 - Andrea Malchiodi AB - Given 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. UR - http://hdl.handle.net/1963/2308 U1 - 1708 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Effective inverse spectral problem for rational Lax matrices and applications JF - Int. Math. Res. Not. IMRN Y1 - 2007 A1 - Marco Bertola A1 - Gekhtman, M. ER - TY - JOUR T1 - Equilibrium configurations of epitaxially strained crystalline films: existence and regularity results JF - Arch. Ration. Mech. Anal. 186 (2007) 477-537 Y1 - 2007 A1 - Irene Fonseca A1 - Nicola Fusco A1 - Giovanni Leoni A1 - Massimiliano Morini AB - Strained epitaxial films grown on a relatively thick substrate are considered in the context of plane linear elasticity. The total free energy of the system is assumed to be the sum of the energy of the free surface of the film and the strain energy. Because of the lattice mismatch between film and substrate, flat configurations are in general energetically unfavorable and a corrugated or islanded morphology is the preferred growth mode of the strained film. After specifying the functional setup in which the existence problem can be properly framed, a study of the qualitative properties of the solutions is undertaken. New regularity results for volume-constrained local minimizers of the total free energy are established, leading, as a byproduct, to a rigorous proof of the zero-contact-angle condition between islands and wetting layers. UR - http://hdl.handle.net/1963/2350 U1 - 1666 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the Euler-Lagrange equation for a variational problem JF - Discrete Contin. Dynam. Systems A 17 (2007) 449-480 Y1 - 2007 A1 - Stefano Bianchini UR - http://hdl.handle.net/1963/1792 U1 - 2752 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - An estimation of the controllability time for single-input systems on compact Lie Groups JF - ESAIM Control Optim. Calc. Var. 12 (2006) 409-441 Y1 - 2006 A1 - Andrei A. Agrachev A1 - Thomas Chambrion AB - Geometric 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. UR - http://hdl.handle.net/1963/2135 U1 - 2108 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Experimental and modeling studies of desensitization of P2X3 receptors. JF - Molecular pharmacology. 2006 Jul; 70(1):373-82 Y1 - 2006 A1 - Elena Sokolova A1 - Andrei Skorinkin A1 - Igor Moiseev A1 - Andrei A. Agrachev A1 - Andrea Nistri A1 - Rashid Giniatullin AB - The 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. PB - the American Society for Pharmacology and Experimental Therapeutics UR - http://hdl.handle.net/1963/4974 U1 - 4799 U2 - Neuroscience U3 - Neurobiology U4 - -1 ER - TY - RPRT T1 - Extended affine Weyl groups and Frobenius manifolds -- II Y1 - 2006 A1 - Boris Dubrovin A1 - Zhang Youjin A1 - Zuo Dafeng AB - For 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}. UR - http://hdl.handle.net/1963/1787 U1 - 2757 U2 - Mathematics U3 - Mathematical Physics ER - TY - CHAP T1 - Enhanced residual-free bubble method for convection-diffusion problems T2 - Internat. J. Numer. Methods Fluids Y1 - 2005 A1 - Andrea Cangiani A1 - Süli, E. JF - Internat. J. Numer. Methods Fluids VL - 47 UR - https://doi.org/10.1002/fld.859 N1 - 8th ICFD Conference on Numerical Methods for Fluid Dynamics. Part 2 ER - TY - JOUR T1 - Enhanced RFB method JF - Numer. Math. Y1 - 2005 A1 - Andrea Cangiani A1 - Süli, Endre VL - 101 UR - https://doi.org/10.1007/s00211-005-0620-7 ER - TY - JOUR T1 - Explicit Wei–Norman formulae for matrix Lie groups via Putzer\\\'s method JF - Systems and Control Letters, 54 (11):1121-1130, 2005 Y1 - 2005 A1 - Claudio Altafini AB - The 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. PB - Elsevier UR - http://hdl.handle.net/1963/4538 U1 - 4299 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - Generic T1 - The elliptic representation of the sixth Painlevé equation. T2 - Théories asymptotiques et équations de Painlevé : [colloque], Angers, juin 2004 / édité par Éric Delabaere, Michèle Loday-Richaud. - Paris : Société mathématique de France, 2006. - Collection SMF. Séminaires et congrès. - page : 83-101 Y1 - 2004 A1 - Davide Guzzetti KW - Painlevé equation AB - We 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). JF - Théories asymptotiques et équations de Painlevé : [colloque], Angers, juin 2004 / édité par Éric Delabaere, Michèle Loday-Richaud. - Paris : Société mathématique de France, 2006. - Collection SMF. Séminaires et congrès. - page : 83-101 PB - Societe Matematique de France SN - 978-2-85629-229-7 UR - http://hdl.handle.net/1963/6529 U1 - 6482 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Energetics and switching of quasi-uniform states in small ferromagnetic particles JF - M2AN Math. Model. Numer. Anal. 38 (2004) 235-248 Y1 - 2004 A1 - François Alouges A1 - Sergio Conti A1 - Antonio DeSimone A1 - Ivo Pokern AB - We 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. PB - EDP Sciences UR - http://hdl.handle.net/1963/2999 U1 - 1334 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence of H-bubbles in a perturbative setting JF - Rev. Mat. Iberoamericana 20 (2004) 611-626 Y1 - 2004 A1 - Paolo Caldiroli A1 - Roberta Musina AB - Given 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. PB - SISSA Library UR - http://hdl.handle.net/1963/1606 U1 - 2512 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The Extended Toda Hierarchy JF - Moscow Math. J. 4 (2004)\\n313-332. Y1 - 2004 A1 - Guido Carlet A1 - Boris Dubrovin A1 - Zhang Youjin UR - http://hdl.handle.net/1963/2542 U1 - 1577 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Effective dynamics for Bloch electrons: Peierls substitution and beyond Y1 - 2003 A1 - Gianluca Panati A1 - Herbert Spohn A1 - Stefan Teufel AB - We 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. PB - Springer UR - http://hdl.handle.net/1963/3040 U1 - 1293 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - The Elliptic Representation of the General Painlevé 6 Equation JF - Communications on Pure and Applied Mathematics, Volume 55, Issue 10, October 2002, Pages 1280-1363 Y1 - 2002 A1 - Davide Guzzetti AB - We 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. PB - SISSA UR - http://hdl.handle.net/1963/6523 N1 - 60 pages; Latex; 3 figures. The statements of theorems have been\r\n simplified U1 - 6475 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - Generic T1 - The Elliptic Representation of the Painleve 6 Equation T2 - Deformation of differential equations and asymptotic analysis / Yoshishige Haraoka. - Kyōto : Kyoto University, Research Institute for Mathematical Sciences, 2002. - RIMS kokyuroku, volume 1296 . - page: 112-123 Y1 - 2002 A1 - Davide Guzzetti KW - Painleve equations AB - We review our results on the elliptic representation of the sixth Painleve’ equation JF - Deformation of differential equations and asymptotic analysis / Yoshishige Haraoka. - Kyōto : Kyoto University, Research Institute for Mathematical Sciences, 2002. - RIMS kokyuroku, volume 1296 . - page: 112-123 PB - Kyoto University, Research Institute for Mathematical Sciences UR - http://hdl.handle.net/1963/6530 U1 - 6481 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Existence of minimal H-bubbles JF - Commun. Contemp. Math. 4 (2002) 177-209 Y1 - 2002 A1 - Paolo Caldiroli A1 - Roberta Musina PB - SISSA Library UR - http://hdl.handle.net/1963/1525 U1 - 2638 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence and nonexistence results for a class of nonlinear, singular Sturm-Liouville equations JF - Adv. Differential Equations 6 (2001), no. 3, 303-326 Y1 - 2001 A1 - Paolo Caldiroli A1 - Roberta Musina PB - SISSA Library UR - http://hdl.handle.net/1963/1319 U1 - 3136 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Extremal synthesis for generic planar systems JF - J. Dynam. Control Systems, 2001, 7, 209 Y1 - 2001 A1 - Ugo Boscain A1 - Benedetto Piccoli PB - SISSA Library UR - http://hdl.handle.net/1963/1503 U1 - 2660 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - An elementary approach to the polynomial $\\\\tau$-functions of the KP Hierarchy JF - Theor. Math. Phys. 122 (2000) 17-28 Y1 - 2000 A1 - Gregorio Falqui A1 - Franco Magri A1 - Marco Pedroni A1 - Jorge P. Zubelli AB - We give an elementary construction of the solutions of the KP hierarchy associated with polynomial τ-functions starting with a geometric approach to soliton equations based on the concept of a bi-Hamiltonian system. As a consequence, we establish a Wronskian formula for the polynomial τ-functions of the KP hierarchy. This formula, known in the literature, is obtained very directly. PB - Springer UR - http://hdl.handle.net/1963/3223 U1 - 1078 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Elliptic variational problems in $ R\\\\sp N$ with critical growth JF - J. Differential Equations 168 (2000), no. 1, 10--32 Y1 - 2000 A1 - Antonio Ambrosetti A1 - Jesus Garcia Azorero A1 - Ireneo Peral PB - SISSA Library UR - http://hdl.handle.net/1963/1258 U1 - 3197 ER - TY - JOUR T1 - Existence and multiplicity results for some nonlinear elliptic equations: a survey. JF - Rend. Mat. Appl., 2000, 20, 167 Y1 - 2000 A1 - Antonio Ambrosetti A1 - Jesus Garcia Azorero A1 - Ireneo Peral PB - SISSA Library UR - http://hdl.handle.net/1963/1462 U1 - 3078 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Existence and multiplicity results for some problems in Riemannian geometry Y1 - 2000 A1 - Andrea Malchiodi KW - Yamabe problem PB - SISSA UR - http://hdl.handle.net/1963/5948 U1 - 5808 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Enhanced gauge symmetries on elliptic K3 JF - Phys.Lett. B452 (1999) 244-250 Y1 - 1999 A1 - Loriano Bonora A1 - Cesare Reina A1 - Alessandro Zampa AB - We show that the geometry of K3 surfaces with singularities of type A-D-E contains enough information to reconstruct a copy of the Lie algebra associated to the given Dynkin diagram. We apply this construction to explain the enhancement of symmetry in F and IIA theories compactified on singular K3\\\'s. PB - Elsevier UR - http://hdl.handle.net/1963/3366 U1 - 964 U2 - Physics U3 - Elementary Particle Theory ER - TY - JOUR T1 - Evans-Vasilesco theorem in Dirichlet spaces JF - Rendiconti di Matematica e delle sue Applicazioni. vol. 19, Issue 7, (1999), pages : 1-15 Y1 - 1999 A1 - Gianni Dal Maso A1 - Virginia De Cicco PB - SISSA UR - http://hdl.handle.net/1963/6436 U1 - 6376 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Extremal faces of the range of a vector measure and a theorem of Lyapunov JF - J. Math. Anal. Appl. 231 (1999) 301-318 Y1 - 1999 A1 - Stefano Bianchini PB - Elsevier UR - http://hdl.handle.net/1963/3370 U1 - 960 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Error bounds for a deterministic version of the Glimm scheme JF - Arch. Rational Mech. Anal. 142 (1998), no. 2, 155-176 Y1 - 1998 A1 - Andrea Marson A1 - Alberto Bressan AB - Consider the hyperbolic system of conservation laws $u_t F(u)_x=0. Let $u$ be the unique viscosity solution with initial condition $u(0,x)=\\\\bar u(x)$ and let $u^\\\\varepsilon$ be an approximate solution constructed by the Glimm scheme, corresponding to the mesh sizes $\\\\Delta x,\\\\Delta t=O(\\\\Delta x). With a suitable choise of the sampling sequence, we prove the estimate $$ \\\\left\\\\Vert u^\\\\varepsilon(t,\\\\cdot)-u(t,\\\\cdot) \\\\right\\\\Vert_1=o(1)\\\\cdot\\\\sqrt{\\\\Delta x}\\\\vert\\\\ln\\\\Delta x\\\\vert. $$ PB - Springer UR - http://hdl.handle.net/1963/1045 U1 - 2811 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Extended affine Weyl groups and Frobenius manifolds JF - Compositio Mathematica. Volume 111, Issue 2, 1998, Pages 167-219 Y1 - 1998 A1 - Boris Dubrovin A1 - Youjin Zhang PB - Kluwer UR - http://hdl.handle.net/1963/6486 U1 - 6424 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - THES T1 - On Existence and Continuous Dependence for Systems of Conservation Laws Y1 - 1997 A1 - Paolo Baiti KW - Conservation laws PB - SISSA UR - http://hdl.handle.net/1963/5588 U1 - 5418 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - An existence result in a problem of the vectorial case of the calculus of variations Y1 - 1995 A1 - Arrigo Cellina A1 - Sandro Zagatti AB - SIAM J. Control Optim. 33 (1995) 960-970 PB - SIAM UR - http://hdl.handle.net/1963/3513 U1 - 751 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence and continuous dependence for discontinuous O.D.E.s JF - Boll. Un. Mat. Ital. B (7) 4 (1990), no. 2, 295--311 Y1 - 1990 A1 - Alberto Bressan A1 - Giovanni Colombo PB - SISSA Library UR - http://hdl.handle.net/1963/716 U1 - 3210 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence of solutions for a class of non-convex differential inclusions JF - Rend.Sem.Mat.Univ. Padova, 83 (1990), 71-76 Y1 - 1990 A1 - Fabio Ancona A1 - Giovanni Colombo PB - SISSA Library UR - http://hdl.handle.net/1963/792 U1 - 2999 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Einstein algebras and the algebraic Kaluza-Klein monopole. JF - Phys. Lett. B 210 (1988), no. 1-2, 68--72. Y1 - 1988 A1 - Giovanni Landi A1 - Giuseppe Marmo PB - SISSA Library UR - http://hdl.handle.net/1963/603 U1 - 3301 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Extensions of Lie superalgebras and supersymmetric Abelian gauge fields. JF - Phys. Lett. B 193 (1987), no. 1, 61-66. Y1 - 1987 A1 - Giovanni Landi A1 - Giuseppe Marmo PB - SISSA Library UR - http://hdl.handle.net/1963/507 U1 - 3397 U2 - Mathematics U3 - Mathematical Physics ER -