In this paper we prove that, within the framework of $\textsf{RCD}^\star(K,N)$ spaces with $N<\infty$, the entropic cost (i.e. the minimal value of the Schrödinger problem) admits:A threefold dynamical variational representation, in the spirit of the Benamou–Brenier formula for the Wasserstein distance; A Hamilton–Jacobi–Bellman dual representation, in line with Bobkov–Gentil–Ledoux and Otto–Villani results on the duality between Hamilton–Jacobi and continuity equation for optimal transport;A Kantorovich-type duality formula, where the Hopf–Lax semigroup is replaced by a suitable `entropic' counterpart.We thus provide a complete and unifying picture of the equivalent variational representations of the Schrödinger problem as well as a perfect parallelism with the analogous formulas for the Wasserstein distance. Riemannian manifolds with Ricci curvature bounded from below are a relevant class of $\textsf{RCD}^*(K,N)$ spaces and our results are new even in this setting.

UR - https://doi.org/10.1007/s00440-019-00909-1 ER - TY - CONF T1 - A complete data-driven framework for the efficient solution of parametric shape design and optimisation in naval engineering problems T2 - VIII International Conference on Computational Methods in Marine Engineering Y1 - 2019 A1 - Nicola Demo A1 - Marco Tezzele A1 - Andrea Mola A1 - Gianluigi Rozza AB -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.

JF - VIII International Conference on Computational Methods in Marine Engineering ER - TY - CONF T1 - Efficient Reduction in Shape Parameter Space Dimension for Ship Propeller Blade Design T2 - VIII International Conference on Computational Methods in Marine Engineering 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 - VIII International Conference on Computational Methods in Marine Engineering 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 - N=2 gauge theories on unoriented/open four-manifolds and their AGT counterparts JF - JHEP Y1 - 2019 A1 - Aditya Bawane A1 - Benvenuti, Sergio A1 - Giulio Bonelli A1 - Muteeb, Nouman A1 - Alessandro Tanzini VL - 07 UR - http://inspirehep.net/record/1631219/ ER - TY - CONF T1 - Shape optimization through proper orthogonal decomposition with interpolation and dynamic mode decomposition enhanced by active subspaces T2 - VIII International Conference on Computational Methods in Marine Engineering Y1 - 2019 A1 - Marco Tezzele A1 - Nicola Demo A1 - Gianluigi Rozza AB -We 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.

JF - VIII International Conference on Computational Methods in Marine Engineering ER - TY - RPRT T1 - On the Cauchy problem for the wave equation on time-dependent domains Y1 - 2018 A1 - Gianni Dal Maso A1 - Rodica Toader AB - We 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. PB - SISSA UR - http://preprints.sissa.it/handle/1963/35314 U1 - 35622 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - CHAP T1 - Combined parameter and model reduction of cardiovascular problems by means of active subspaces and POD-Galerkin methods T2 - Mathematical and Numerical Modeling of the Cardiovascular System and Applications Y1 - 2018 A1 - Marco Tezzele A1 - Francesco Ballarin A1 - Gianluigi Rozza JF - Mathematical and Numerical Modeling of the Cardiovascular System and Applications PB - Springer ER - TY - RPRT T1 - On the continuity of the trace operator in GSBV (Ω) and GSBD (Ω) Y1 - 2018 A1 - Emanuele Tasso AB - In 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. UR - http://preprints.sissa.it/handle/1963/35324 N1 - 27 pages U1 - 35634 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - The deal.II Library, Version 9.0 JF - JOURNAL OF NUMERICAL MATHEMATICS Y1 - 2018 A1 - Giovanni Alzetta A1 - Arndt, Daniel A1 - W. Bangerth A1 - Boddu, Vishal A1 - Brands, Benjamin A1 - Denis Davydov A1 - Gassmöller, Rene A1 - Timo Heister A1 - Luca Heltai A1 - Kormann, Katharina A1 - Martin Kronbichler A1 - Matthias Maier A1 - Pelteret, Jean-Paul A1 - B. Turcksin A1 - David Wells UR - https://doi.org/10.1515/jnma-2018-0054 ER - TY - JOUR T1 - Dimension reduction in heterogeneous parametric spaces with application to naval engineering shape design problems JF - Advanced Modeling and Simulation in Engineering Sciences Y1 - 2018 A1 - Marco Tezzele A1 - Filippo Salmoiraghi A1 - Andrea Mola A1 - Gianluigi Rozza AB -We present the results of the first application in the naval architecture field of a methodology based on active subspaces properties for parameters space reduction. The physical problem considered is the one of the simulation of the hydrodynamic flow past the hull of a ship advancing in calm water. Such problem is extremely relevant at the preliminary stages of the ship design, when several flow simulations are typically carried out by the engineers to assess the dependence of the hull total resistance on the geometrical parameters of the hull, and others related with flows and hull properties. Given the high number of geometric and physical parameters which might affect the total ship drag, the main idea of this work is to employ the active subspaces properties to identify possible lower dimensional structures in the parameter space. Thus, a fully automated procedure has been implemented to produce several small shape perturbations of an original hull CAD geometry, in order to exploit the resulting shapes to run high fidelity flow simulations with different structural and physical parameters as well, and then collect data for the active subspaces analysis. The free form deformation procedure used to morph the hull shapes, the high fidelity solver based on potential flow theory with fully nonlinear free surface treatment, and the active subspaces analysis tool employed in this work have all been developed and integrated within SISSA mathLab as open source tools. The contribution will also discuss several details of the implementation of such tools, as well as the results of their application to the selected target engineering problem.

VL - 5 ER - TY - 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 - Energy-dissipation balance of a smooth moving crack Y1 - 2018 A1 - Maicol Caponi A1 - Ilaria Lucardesi A1 - Emanuele Tasso 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 [S. Nicaise, A.M. Sandig - J. Math. Anal. Appl., 2007] valid for straight fractures. UR - http://preprints.sissa.it/handle/1963/35320 U1 - 35630 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 - JOUR T1 - Free-form deformation, mesh morphing and reduced-order methods: enablers for efficient aerodynamic shape optimisation JF - International Journal of Computational Fluid Dynamics Y1 - 2018 A1 - Filippo Salmoiraghi A1 - Scardigli, Angela A1 - Telib, Haysam A1 - Gianluigi Rozza AB -In 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.

PB - Taylor & Francis VL - 32 ER - TY - CONF T1 - Model Order Reduction by means of Active Subspaces and Dynamic Mode Decomposition for Parametric Hull Shape Design Hydrodynamics T2 - Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship & Maritime Research Y1 - 2018 A1 - Marco Tezzele A1 - Nicola Demo A1 - Mahmoud Gadalla A1 - Andrea Mola A1 - Gianluigi Rozza AB - We 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. JF - Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship & Maritime Research PB - IOS Press CY - Trieste, Italy UR - http://ebooks.iospress.nl/publication/49270 ER - TY - JOUR T1 - PyDMD: Python Dynamic Mode Decomposition 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/734e4326edd5062c6e8ee98d03df9e1d ER - TY - JOUR T1 - Second order differentiation formula on RCD(K, N) spaces JF - Rendiconti Lincei-Matematica e Applicazioni Y1 - 2018 A1 - Nicola Gigli A1 - Luca Tamanini VL - 29 ER - TY - RPRT T1 - Second order differentiation formula on RCD*(K,N) spaces Y1 - 2018 A1 - Nicola Gigli A1 - Luca Tamanini ER - TY - CONF T1 - Shape Optimization by means of Proper Orthogonal Decomposition and Dynamic Mode Decomposition T2 - Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship & Maritime Research Y1 - 2018 A1 - Nicola Demo A1 - Marco Tezzele A1 - Gianluca Gustin A1 - Gianpiero Lavini A1 - Gianluigi Rozza AB - Shape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling, applied to a naval hull design problem. The advantage introduced by this method is that the solution for a specific parameter can be expressed as the combination of few numerical solutions computed at properly chosen parametric points. The reduced model is built using the proper orthogonal decomposition with interpolation (PODI) method. We use the free form deformation (FFD) for an automated perturbation of the shape, and the finite volume method to simulate the multiphase incompressible flow around the deformed hulls. Further computational reduction is done by the dynamic mode decomposition (DMD) technique: from few high dimensional snapshots, the system evolution is reconstructed and the final state of the simulation is faithfully approximated. Finally the global optimization algorithm iterates over the reduced space: the approximated drag and lift coefficients are projected to the hull surface, hence the resistance is evaluated for the new hulls until the convergence to the optimal shape is achieved. We will present the results obtained applying the described procedure to a typical Fincantieri cruise ship. JF - Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship & Maritime Research PB - IOS Press CY - Trieste, Italy UR - http://ebooks.iospress.nl/publication/49229 ER - TY - RPRT T1 - Weak formulation of elastodynamics in domains with growing cracks Y1 - 2018 A1 - Emanuele Tasso AB - In this paper we formulate and study the system of elastodynamics on domains with arbitrary growing cracks. This includes homogeneous Neumann conditions on the crack sets and mixed general Dirichlet-Neumann conditions on the boundary. The only assumptions on the crack sets are to be (n − 1)-rectifiable with finite surface measure, and increasing in the sense of set inclusions. In particular they might be dense, hence the weak formulation must fall outside the usual context of Sobolev spaces and Korn's inequality. We prove existence of a solution both for the damped and undamped systems, while in the damped case we are also able to prove uniqueness and an energy balance. PB - SISSA UR - http://preprints.sissa.it/handle/1963/35328 U1 - 35639 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - The deal.II Library, Version 8.5 JF - JOURNAL OF NUMERICAL MATHEMATICS Y1 - 2017 A1 - Arndt, Daniel A1 - W. Bangerth A1 - Denis Davydov A1 - Timo Heister A1 - Luca Heltai A1 - Martin Kronbichler A1 - Matthias Maier A1 - Pelteret, Jean-Paul A1 - B. Turcksin A1 - David Wells VL - 25 UR - https://www.dealii.org/deal85-preprint.pdf ER - TY - JOUR T1 - Gauge theories on compact toric surfaces, conformal field theories and equivariant Donaldson invariants JF - Journal of Geometry and Physics Y1 - 2017 A1 - Mikhail Bershtein A1 - Giulio Bonelli A1 - Massimiliano Ronzani A1 - Alessandro Tanzini KW - AGT KW - Donaldson invariants KW - Equivariant localization KW - Exact partition function KW - Supersymmetry KW - Virasoro conformal blocks AB -We show that equivariant Donaldson polynomials of compact toric surfaces can be calculated as residues of suitable combinations of Virasoro conformal blocks, by building on AGT correspondence between $\mathcal{N}=2$ supersymmetric gauge theories and two-dimensional conformal field theory. Talk presented by A.T. at the conference Interactions between Geometry and Physics — in honor of Ugo Bruzzo’s 60th birthday 17–22 August 2015, Guarujá, São Paulo, Brazil, mostly based on Bawane et al. (0000) and Bershtein et al. (0000).

VL - 118 UR - http://www.sciencedirect.com/science/article/pii/S0393044017300165 N1 - Interactions between Geometry and Physics. A Special Issue in Honor of Ugo Bruzzo’s 60th Birthday ER - TY - JOUR T1 - Integrability of dominated decompositions on three-dimensional manifolds JF - Ergodic Theory and Dynamical Systems Y1 - 2017 A1 - Stefano Luzzatto A1 - Sina Türeli A1 - Khadim Mbacke War AB -

We investigate the integrability of two-dimensional invariant distributions (tangent sub-bundles) which arise naturally in the context of dynamical systems on 3-manifolds. In particular, we prove unique integrability of dynamically dominated and volume-dominated Lipschitz continuous invariant decompositions as well as distributions with some other regularity conditions.

We study the lower semicontinuity of some free discontinuity functionals with linear growth defined on the space of functions with bounded deformation. The volume term is convex and depends only on the Euclidean norm of the symmetrized gradient. We introduce a suitable class of surface terms, which make the functional lower semicontinuous with respect to $L^1$ convergence.

PB - De Gruyter VL - 10 ER - TY - JOUR T1 - A lower semicontinuity result for a free discontinuity functional with a boundary term JF - Journal de Mathématiques Pures et Appliquées Y1 - 2017 A1 - Stefano Almi A1 - Gianni Dal Maso A1 - Rodica Toader AB -We 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.

VL - 108 UR - http://hdl.handle.net/20.500.11767/15979 IS - 6 U1 - 34731 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Maximal amplitudes of finite-gap solutions for the focusing Nonlinear Schrödinger Equation JF - Comm. Math. Phys. Y1 - 2017 A1 - Marco Bertola A1 - Alexander Tovbis VL - 354 UR - http://dx.doi.org/10.1007/s00220-017-2895-9 ER - TY - JOUR T1 - Real topological string amplitudes JF - Journal of High Energy Physics Y1 - 2017 A1 - Narain, K. S. A1 - Nicolò Piazzalunga A1 - Alessandro Tanzini AB -We discuss the physical superstring correlation functions in type I theory (or equivalently type II with orientifold) that compute real topological string amplitudes. We consider the correlator corresponding to holomorphic derivative of the real topological amplitude $\mathcal{G_\chi}$, at fixed worldsheet Euler characteristic $\chi$. This corresponds in the low-energy effective action to $\mathcal{N}=2$ Weyl multiplet, appropriately reduced to the orientifold invariant part, and raised to the power $g'= −\chi+ 1$. We show that the physical string correlator gives precisely the holomorphic derivative of topological amplitude. Finally, we apply this method to the standard closed oriented case as well, and prove a similar statement for the topological amplitude $\mathcal{F}_g$.

VL - 2017 UR - https://doi.org/10.1007/JHEP03(2017)080 ER - TY - RPRT T1 - Second order differentiation formula on compact RCD*(K,N) spaces Y1 - 2017 A1 - Nicola Gigli A1 - Luca Tamanini ER - TY - JOUR T1 - Universality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schrödinger Equation JF - Phys. Rev. Lett. Y1 - 2017 A1 - Tikan, Alexey A1 - Billet, Cyril A1 - Gennady El A1 - Alexander Tovbis A1 - Marco Bertola A1 - Sylvestre, Thibaut A1 - Gustave, Francois A1 - Randoux, Stephane A1 - Genty, Goëry A1 - Suret, Pierre A1 - Dudley, John M. PB - American Physical Society VL - 119 UR - https://link.aps.org/doi/10.1103/PhysRevLett.119.033901 ER - TY - CONF T1 - Advances in geometrical parametrization and reduced order models and methods for computational fluid dynamics problems in applied sciences and engineering: overview and perspectives T2 - Proceedings of the ECCOMAS Congress 2016, VII European Conference on Computational Methods in Applied Sciences and Engineering, Y1 - 2016 A1 - Filippo Salmoiraghi A1 - Francesco Ballarin A1 - Giovanni Corsi A1 - Andrea Mola A1 - Marco Tezzele A1 - Gianluigi Rozza ED - Papadrakakis, M. ED - Papadopoulos, V. ED - Stefanou, G. ED - Plevris, V. AB -Several 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.

JF - Proceedings of the ECCOMAS Congress 2016, VII European Conference on Computational Methods in Applied Sciences and Engineering, PB - ECCOMAS CY - Crete, Greece U1 - 35466 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - On the area of the graph of a piecewise smooth map from the plane to the plane with a curve discontinuity JF - ESAIM: COCV Y1 - 2016 A1 - Giovanni Bellettini A1 - Lucia Tealdi A1 - Maurizio Paolini KW - Area functional AB -In 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.

VL - 22 UR - https://www.esaim-cocv.org/articles/cocv/abs/2016/01/cocv140065/cocv140065.html IS - 1 U1 - 7257 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - On asymptotic regimes of orthogonal polynomials with complex varying quartic exponential weight JF - SIGMA Symmetry Integrability Geom. Methods Appl. Y1 - 2016 A1 - Marco Bertola A1 - Alexander Tovbis VL - 12 UR - http://dx.doi.org/10.3842/SIGMA.2016.118 ER - TY - JOUR T1 - The deal.II Library, Version 8.3 JF - ARCHIVE OF NUMERICAL SOFTWARE Y1 - 2016 A1 - W. Bangerth A1 - Timo Heister A1 - Luca Heltai A1 - G. Kanschat A1 - Martin Kronbichler A1 - Matthias Maier A1 - B. Turcksin VL - 4 UR - http://nbn-resolving.de/urn:nbn:de:bsz:16-ans-231226 ER - TY - JOUR T1 - The deal.II library, Version 8.4 JF - JOURNAL OF NUMERICAL MATHEMATICS Y1 - 2016 A1 - W. Bangerth A1 - Denis Davydov A1 - Timo Heister A1 - Luca Heltai A1 - G. Kanschat A1 - Martin Kronbichler A1 - Matthias Maier A1 - B. Turcksin A1 - David Wells VL - 24 UR - https://www.math.clemson.edu/ heister/preprints/deal84-preprint.pdf ER - TY - JOUR T1 - 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 - Fracture models for elasto-plastic materials as limits of gradient damage models coupled with plasticity: the antiplane case JF - Calculus of Variations and Partial Differential Equations Y1 - 2016 A1 - Gianni Dal Maso A1 - Gianluca Orlando A1 - Rodica Toader AB -We study the asymptotic behavior of a variational model for damaged elasto-plastic materials in the case of antiplane shear. The energy functionals we consider depend on a small parameter $\varepsilon$, which forces damage concentration on regions of codimension one. We determine the $\Gamma$-limit as $\varepsilon$ tends to zero and show that it contains an energy term involving the crack opening.

VL - 55 UR - https://doi.org/10.1007/s00526-016-0981-z ER - TY - JOUR T1 - A Frobenius theorem for corank-1 continuous distributions in dimensions two and three JF - International Journal of Mathematics Y1 - 2016 A1 - Stefano Luzzatto A1 - Sina Türeli A1 - Khadim Mbacke War AB -We formulate a notion of (uniform) asymptotic involutivity and show that it implies (unique) integrability of corank-1 continuous distributions in dimensions three or less. This generalizes and extends a classical Frobenius theorem, which says that an involutive C1 distribution is uniquely integrable.

VL - 27 UR - https://doi.org/10.1142/S0129167X16500610 ER - TY - JOUR T1 - Integrability of C1 invariant splittings JF - Dynamical Systems Y1 - 2016 A1 - Stefano Luzzatto A1 - Sina Türeli A1 - Khadim Mbacke War AB -We derive some new conditions for integrability of dynamically defined C1 invariant splittings, formulated in terms of the singular values of the iterates of the derivative of the diffeomorphism which defines the splitting.

PB - Taylor & Francis VL - 31 UR - https://doi.org/10.1080/14689367.2015.1057480 ER - TY - JOUR T1 - Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation JF - Proc. A. Y1 - 2016 A1 - Marco Bertola A1 - Gennady El A1 - Alexander Tovbis VL - 472 UR - http://dx.doi.org/10.1098/rspa.2016.0340 ER - TY - JOUR T1 - On Sobolev instability of the interior problem of tomography JF - Journal of Mathematical Analysis and Applications Y1 - 2016 A1 - Marco Bertola A1 - Alexander Katsevich A1 - Alexander Tovbis ER - TY - JOUR T1 - Symmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index JF - Journal of High Energy Physics Y1 - 2016 A1 - Benvenuti, Sergio A1 - Giulio Bonelli A1 - Massimiliano Ronzani A1 - Alessandro Tanzini AB -We explore $\mathcal{N}=(1,0)$ superconformal six-dimensional theories arising from M5 branes probing a transverse $A_k$ singularity. Upon circle compactification to 5 dimensions, we describe this system with a dual pq-web of five-branes and propose the spectrum of basic five-dimensional instanton 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 that S-duality of the pq-web implies new relations among vertex correlators of $q\mathcal{W}$ algebrae.

VL - 2016 UR - https://doi.org/10.1007/JHEP09(2016)053 ER - TY - JOUR T1 - Anisotropic mean curvature on facets and relations with capillarity Y1 - 2015 A1 - Stefano Amato A1 - Lucia Tealdi A1 - Giovanni Bellettini AB -We 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.

PB - de Gruyter UR - http://urania.sissa.it/xmlui/handle/1963/34481 U1 - 34663 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Asymptotics of orthogonal polynomials with complex varying quartic weight: global structure, critical point behavior and the first Painlevé equation JF - Constr. Approx. Y1 - 2015 A1 - Marco Bertola A1 - Alexander Tovbis VL - 41 UR - http://dx.doi.org/10.1007/s00365-015-9288-0 ER - TY - RPRT T1 - A class of Hamiltonians for a three-particle fermionic system at unitarity Y1 - 2015 A1 - Michele Correggi A1 - Gianfausto Dell'Antonio A1 - Domenico Finco A1 - Alessandro Michelangeli A1 - Alessandro Teta AB - We 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. UR - http://urania.sissa.it/xmlui/handle/1963/34469 N1 - This SISSA preprint is composed of 29 pages and is recorded in PDF format U1 - 34644 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - The deal.II Library, Version 8.2 JF - Archive of Numerical Software, vol. 3, n. 100, (2015), pages : 1-8 Y1 - 2015 A1 - W. Bangerth A1 - Timo Heister A1 - Luca Heltai A1 - G. Kanschat A1 - Martin Kronbichler A1 - Matthias Maier A1 - B. Turcksin A1 - T. D. Young AB - This paper provides an overview of the new features of the finite element library deal.II version 8.2 UR - http://urania.sissa.it/xmlui/handle/1963/34464 U1 - 34637 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - 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 - 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 - THES T1 - Integrability of Continuous Tangent Sub-bundles Y1 - 2015 A1 - Sina Türeli KW - Dynamical Systems, Global Analysis, Frobenius Theorem, Integrability AB - In 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. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/34630 U1 - 34833 U2 - Mathematics U5 - MAT/05 ER - TY - JOUR T1 - Meromorphic differentials with imaginary periods on degenerating hyperelliptic curves JF - Anal. Math. Phys. Y1 - 2015 A1 - Marco Bertola A1 - Alexander Tovbis VL - 5 UR - http://dx.doi.org/10.1007/s13324-014-0088-7 ER - TY - JOUR T1 - N=2 supersymmetric gauge theories on S^2xS^2 and Liouville Gravity JF - Journal of High Energy Physics Y1 - 2015 A1 - Aditya Bawane A1 - Giulio Bonelli A1 - Massimiliano Ronzani A1 - Alessandro Tanzini AB -We consider $\mathcal{N}=2$ 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 $S^2 \times S^2$ 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.

VL - 2015 UR - https://doi.org/10.1007/JHEP07(2015)054 ER - TY - JOUR T1 - The phototransduction machinery in the rod outer segment has a strong efficacy gradient Y1 - 2015 A1 - Monica Mazzolini A1 - Giuseppe Facchetti A1 - L. Andolfi A1 - R. Proietti Zaccaria A1 - S. Tuccio A1 - J. Treud A1 - Claudio Altafini A1 - Enzo M. Di Fabrizio A1 - Marco Lazzarino A1 - G. Rapp A1 - Vincent Torre PB - National Academy of Sciences UR - http://urania.sissa.it/xmlui/handle/1963/35157 N1 - Open Access article U1 - 35382 U2 - Neuroscience ER - TY - THES T1 - The relaxed area of maps from the plane to the plane with a line discontinuity, and the role of semicartesian surfaces. Y1 - 2015 A1 - Lucia Tealdi KW - Area functional AB - In 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. PB - SISSA U1 - 34732 U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - Results on the minimization of the Dirichlet functional among semicartesian parametrizations Y1 - 2015 A1 - Lucia Tealdi A1 - Giovanni Bellettini A1 - Maurizio Paolini AB -We 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.

UR - http://urania.sissa.it/xmlui/handle/1963/34488 N1 - The article is compsed of 18 pages and is recorded in PDF format U1 - 34671 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - Semicartesian surfaces and the relaxed area of maps from the plane to the plane with a line discontinuity Y1 - 2015 A1 - Lucia Tealdi A1 - Giovanni Bellettini A1 - Maurizio Paolini AB -We 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.

UR - http://urania.sissa.it/xmlui/handle/1963/34483 N1 - The preprint is compsed of 37 pages and is recorded in PDF format U1 - 34670 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Discrete one-dimensional crawlers on viscous substrates: achievable net displacements and their energy cost Y1 - 2014 A1 - Giovanni Noselli A1 - Amabile Tatone A1 - Antonio DeSimone KW - Cell migration AB - We study model one-dimensional crawlers, namely, model mechanical systems that can achieve self-propulsion by controlled shape changes of their body (extension or contraction of portions of the body), thanks to frictional interactions with a rigid substrate. We evaluate the achievable net displacement and the related energetic cost for self-propulsion by discrete crawlers (i.e., whose body is made of a discrete number of contractile or extensile segments) moving on substrates with either a Newtonian (linear) or a Bingham-type (stick-slip) rheology. Our analysis is aimed at constructing the basic building blocks towards an integrative, multi-scale description of crawling cell motility. PB - Elsevier UR - http://urania.sissa.it/xmlui/handle/1963/34449 U1 - 34591 U2 - Mathematics ER - TY - JOUR T1 - Laplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length Y1 - 2014 A1 - Gianni Dal Maso A1 - Gianluca Orlando A1 - Rodica Toader KW - cracked domains, energy release rate, higher order derivatives, asymptotic expansion of solutions AB -We 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.

PB - SISSA UR - http://hdl.handle.net/1963/7271 U1 - 7316 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Pfaffian representations of cubic surfaces Y1 - 2014 A1 - Fabio Tanturri AB -Let 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.

PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34688 U1 - 34900 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Quasi-static crack growth in hydraulic fracture JF - Nonlinear Analysis Y1 - 2014 A1 - Stefano Almi A1 - Gianni Dal Maso A1 - Rodica Toader AB -We 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.

PB - Elsevier VL - 109 UR - http://hdl.handle.net/20.500.11767/17350 IS - Nov U1 - 34741 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - Rate-independent damage in thermo-viscoelastic materials with inertia Y1 - 2014 A1 - Giuliano Lazzaroni A1 - Riccarda Rossi A1 - Marita Thomas A1 - Rodica Toader AB - We 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. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7444 U1 - 7542 ER - TY - JOUR T1 - Singular Value Decomposition of a Finite Hilbert Transform Defined on Several Intervals and the Interior Problem of Tomography: The Riemann-Hilbert Problem Approach JF - Comm. Pure Appl. Math. Y1 - 2014 A1 - Marco Bertola A1 - Alexander Katsevich A1 - Alexander Tovbis ER - TY - JOUR T1 - Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics Y1 - 2014 A1 - Giulio Bonelli A1 - Antonio Sciarappa A1 - Alessandro Tanzini A1 - Petr Vasko AB - We 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. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34546 U1 - 34771 U2 - Physics U4 - 2 ER - TY - RPRT T1 - Some remarks on a model for rate-independent damage in thermo-visco-elastodynamics Y1 - 2014 A1 - Giuliano Lazzaroni A1 - Riccarda Rossi A1 - Marita Thomas A1 - Rodica Toader AB - This 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. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7463 U1 - 7566 ER - TY - JOUR T1 - The stringy instanton partition function Y1 - 2014 A1 - Giulio Bonelli A1 - Antonio Sciarappa A1 - Alessandro Tanzini A1 - Petr Vasko AB - We 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. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34589 U1 - 34796 U2 - Physics U4 - 2 ER - TY - JOUR T1 - A variational model for the quasi-static growth of fractional dimensional brittle fractures Y1 - 2014 A1 - Simone Racca A1 - Rodica Toader KW - Variational models AB -We 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.

PB - European Mathematical Society UR - http://hdl.handle.net/1963/6983 U1 - 6973 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - Vortex Partition Functions, Wall Crossing and Equivariant Gromov–Witten Invariants Y1 - 2014 A1 - Giulio Bonelli A1 - Antonio Sciarappa A1 - Alessandro Tanzini A1 - Petr Vasko AB - In 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. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34652 U1 - 34859 U2 - Physics ER - TY - RPRT T1 - Where best to place a Dirichlet condition in an anisotropic membrane? Y1 - 2014 A1 - Paolo Tilli A1 - Davide Zucco AB - We 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. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/7481 U1 - 7592 ER - TY - JOUR T1 - Asymptotics of the first Laplace eigenvalue with Dirichlet regions of prescribed length Y1 - 2013 A1 - Paolo Tilli A1 - Davide Zucco AB - We 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. PB - Society for Industrial and Applied Mathematics UR - http://urania.sissa.it/xmlui/handle/1963/35141 U1 - 35379 U2 - Physics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Common dynamical features of sensory adaptation in photoreceptors and olfactory sensory neurons. JF - Nature. Scientific Reports 3, Article number: 1251, Published : 13 February 2013 Y1 - 2013 A1 - Giovanna De Palo A1 - Giuseppe Facchetti A1 - Monica Mazzolini A1 - Anna Menini A1 - Vincent Torre A1 - Claudio Altafini AB -Sensory 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.

PB - SISSA U1 - 6453 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Crawlers in viscous environments: linear vs nonlinear rheology JF - International Journal of Non-Linear Mechanics 56, 142-147 (2013) Y1 - 2013 A1 - Antonio DeSimone A1 - Federica Guarnieri A1 - Giovanni Noselli A1 - Amabile Tatone AB - We 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. PB - Elsevier U1 - 34590 U2 - Mathematics ER - TY - RPRT T1 - The deal.II Library, Version 8.1 Y1 - 2013 A1 - W. Bangerth A1 - Timo Heister A1 - Luca Heltai A1 - G. Kanschat A1 - Martin Kronbichler A1 - Matthias Maier A1 - B. Turcksin A1 - T. D. Young AB - This paper provides an overview of the new features of the finite element library deal.II version 8.0. PB - SISSA UR - http://hdl.handle.net/1963/7236 N1 - 5 pages U1 - 7272 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - 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 - Inversion formulae for the $\romancosh$-weighted Hilbert transform JF - Proc. Amer. Math. Soc. Y1 - 2013 A1 - Marco Bertola A1 - Katsevich, A. A1 - Alexander Tovbis VL - 141 UR - http://dx.doi.org/10.1090/S0002-9939-2013-11642-4 ER - TY - RPRT T1 - N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae Y1 - 2013 A1 - Giulio Bonelli A1 - Kazunobu Maruyoshi A1 - Alessandro Tanzini A1 - Futoshi Yagi AB - We 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. PB - SISSA UR - http://hdl.handle.net/1963/6577 N1 - 33 pages, 1 figure; v2: discussions on U(1) gauge theory and\r\n Frenkel-Kac construction have been added in section 5.1, and typos corrected;\r\n v3: published version; v4: typos corrected U1 - 6522 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - Nonabelian Lie algebroid extensions Y1 - 2013 A1 - Ugo Bruzzo A1 - Igor Mencattini A1 - Pietro Tortella A1 - Vladimir Rubtsov KW - Lie algebroids, nonabelian extensions, spectral sequences AB -We 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 $d_2$

U1 - 7293 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Some remarks on the viscous approximation of crack growth JF - Discrete Contin. Dyn. Syst. Ser. S Y1 - 2013 A1 - Giuliano Lazzaroni A1 - Rodica Toader KW - Variational models AB -We 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.

PB - SISSA VL - 6 UR - http://hdl.handle.net/1963/4206 U1 - 3945 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Stabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control JF - IEEE Transactions on Automatic Control. Volume 58, Issue 1, 2013, Article number6228517, Pages 74-85 Y1 - 2013 A1 - Claudio Altafini A1 - Francesco Ticozzi A1 - K. Nishio AB - In 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 control UR - http://hdl.handle.net/1963/6503 U1 - 6448 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Symplectic instanton bundles on P3 and 't Hooft instantons Y1 - 2013 A1 - Ugo Bruzzo A1 - Dimitri Markushevich A1 - Alexander Tikhomirov AB - We 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. PB - arXiv:1312.5554 [math.AG] UR - http://urania.sissa.it/xmlui/handle/1963/34486 N1 - This preprint has been published with the title "Moduli of symplectic instanton vector bundles of higher rank on projective space P-3 " in CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, Volume: 10, issue 4, Augst 2012, pages 1232-1245. U1 - 34675 U2 - Mathematics U4 - 1 U5 - MAT/03 ER - TY - JOUR T1 - Universality for the focusing nonlinear Schrödinger equation at the gradient catastrophe point: rational breathers and poles of the \it Tritronquée solution to Painlevé I JF - Comm. Pure Appl. Math. Y1 - 2013 A1 - Marco Bertola A1 - Alexander Tovbis VL - 66 UR - http://dx.doi.org/10.1002/cpa.21445 ER - TY - JOUR T1 - Crawling motility through the analysis of model locomotors: two case studies JF - The European Physical Journal E, Volume 35, Issue 9, September 2012, Article number85 Y1 - 2012 A1 - Antonio DeSimone A1 - Amabile Tatone AB - We 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. PB - Springer UR - http://hdl.handle.net/1963/7017 U1 - 7014 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Gauge Theories on ALE Space and Super Liouville Correlation Functions JF - Lett. Math. Phys. 101 (2012) 103-124 Y1 - 2012 A1 - Giulio Bonelli A1 - Kazunobu Maruyoshi A1 - Alessandro Tanzini AB - We 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. PB - SISSA UR - http://hdl.handle.net/1963/4305 N1 - 21 pages U1 - 4068 U2 - Physics U3 - Elementary Particle Theory U4 - -1 ER - TY - JOUR T1 - Modeling and control of quantum systems: An introduction JF - IEEE Transactions on Automatic Control. Volume 57, Issue 8, 2012, Article number6189035, Pages 1898-1917 Y1 - 2012 A1 - Claudio Altafini A1 - Francesco Ticozzi AB - The 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 studies PB - Institute of Electrical and Electronics Engineers UR - http://hdl.handle.net/1963/6505 U1 - 6449 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Moduli of symplectic instanton vector bundles of higher rank on projective space $\\mathbbP^3$ JF - Central European Journal of Mathematics 10, nr. 4 (2012) 1232 Y1 - 2012 A1 - Ugo Bruzzo A1 - Dimitri Markushevich A1 - Alexander Tikhomirov AB - Symplectic 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 $4n(r+1)-r(2r+1)$. PB - SISSA UR - http://hdl.handle.net/1963/4656 N1 - 14 pages U1 - 4406 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - SBV regularity for Hamilton-Jacobi equations with Hamiltonian depending on (t,x) JF - Siam Journal on Mathematical Analysis Y1 - 2012 A1 - Stefano Bianchini A1 - Daniela Tonon PB - SISSA VL - 44 UR - http://hdl.handle.net/20.500.11767/14066 IS - 3 U1 - 3890 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - SBV-like regularity for Hamilton-Jacobi equations with a convex Hamiltonian JF - Journal of Mathematical Analysis and Applications Y1 - 2012 A1 - Stefano Bianchini A1 - Daniela Tonon PB - SISSA VL - 391 UR - http://hdl.handle.net/20.500.11767/13909 IS - 1 U1 - 4352 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Some applications of the SBV Regularity Theorem for entropy solutions of 1D scalar conservation laws to ConvectionTheory and sticky particles JF - Riv. Mat. Univ. Parma Y1 - 2012 A1 - Daniela Tonon AB -We 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.

VL - 3 UR - https://hal.archives-ouvertes.fr/hal-00918409 ER - TY - JOUR T1 - Stability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions JF - Rev. Math. Phys. 24 (2012), 1250017 Y1 - 2012 A1 - Michele Correggi A1 - Gianfausto Dell'Antonio A1 - Domenico Finco A1 - Alessandro Michelangeli A1 - Alessandro Teta AB - We 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. PB - World Scientific UR - http://hdl.handle.net/1963/6069 U1 - 5955 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Vertices, vortices & interacting surface operators JF - JHEP 06(2012)178 Y1 - 2012 A1 - Giulio Bonelli A1 - Alessandro Tanzini A1 - Zhao Jian AB - We 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. PB - SISSA UR - http://hdl.handle.net/1963/4134 N1 - 22 pages, 4 figures U1 - 3874 U2 - Physics U3 - Elementary Particle Theory U4 - -1 ER - TY - JOUR T1 - Wild quiver gauge theories JF - JHEP 02(2012)031 Y1 - 2012 A1 - Giulio Bonelli A1 - Kazunobu Maruyoshi A1 - Alessandro Tanzini AB -We 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.

PB - SISSA UR - http://hdl.handle.net/1963/5184 N1 - 34 pages U1 - 4999 U2 - Physics U3 - Elementary Particle Theory U4 - -1 ER - TY - JOUR T1 - Adaptation as a genome-wide autoregulatory principle in the stress response of yeast. JF - IET systems biology. 2011 Jul; 5(4):269-79 Y1 - 2011 A1 - F Eduati A1 - B Di Camillo A1 - G Toffolo A1 - Claudio Altafini A1 - Giovanna De Palo A1 - Mattia Zampieri AB - The 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. PB - The Institution of Engineering and Technology UR - http://hdl.handle.net/1963/5106 U1 - 4922 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Covered by lines and Conic connected varieties JF - Le Matematiche 66 (2011) 137-151 Y1 - 2011 A1 - Simone Marchesi A1 - Alex Massarenti A1 - Saeed Tafazolian AB - We 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. PB - Universita\\\' di Catania, Dipartimento di Matematica e Informatica UR - http://hdl.handle.net/1963/5788 U1 - 5641 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - A Decomposition Theorem for BV functions JF - Communications on Pure and Applied Analysis Y1 - 2011 A1 - Stefano Bianchini A1 - Daniela Tonon PB - American Institute of Mathematical Sciences VL - 10 UR - http://hdl.handle.net/20.500.11767/14599 IS - 6 U1 - 693 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - 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 - Generalized matrix models and AGT correspondence at all genera JF - JHEP, Volume 2011, Issue 7, 2011, Article number055 Y1 - 2011 A1 - Giulio Bonelli A1 - Kazunobu Maruyoshi A1 - Alessandro Tanzini A1 - Futoshi Yagib AB - We 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. PB - SISSA UR - http://hdl.handle.net/1963/6568 N1 - This version is published in : Journal of High Energy Physics, Volume 2011, Issue 7, 2011, Article number055 U1 - 6530 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Instantons on ALE spaces and Super Liouville Conformal Field Theories Y1 - 2011 A1 - Giulio Bonelli A1 - Kazunobu Maruyoshi A1 - Alessandro Tanzini AB - We 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). PB - SISSA UR - http://hdl.handle.net/1963/4262 N1 - 10 pages U1 - 3987 U2 - Physics U3 - Elementary Particle Theory U4 - -1 ER - TY - JOUR T1 - The Liouville side of the vortex JF - JHEP 09(2011)096 Y1 - 2011 A1 - Giulio Bonelli A1 - Alessandro Tanzini A1 - Jian Zhao AB - We 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. PB - SISSA UR - http://hdl.handle.net/1963/4304 N1 - 25pages,11figures U1 - 4019 U2 - Physics U3 - Elementary Particle Theory U4 - -1 ER - TY - JOUR T1 - Metastable equilibria of capillary drops on solid surfaces: a phase field approach JF - Continuum Mechanics and Thermodynamics Y1 - 2011 A1 - Livio Fedeli A1 - Turco, Alessandro A1 - Antonio DeSimone AB -We 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.

VL - 23 UR - https://doi.org/10.1007/s00161-011-0189-6 ER - TY - JOUR T1 - A MODEL FOR CRACK PROPAGATION BASED ON VISCOUS APPROXIMATION JF - {MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES} Y1 - 2011 A1 - Giuliano Lazzaroni A1 - Rodica Toader KW - Brittle fracture KW - Crack propagation KW - energy derivative KW - energy release rate KW - free-discontinuity problems KW - Griffith's criterion KW - local minimizers KW - stress intensity factor} KW - vanishing viscosity KW - {Variational models AB -{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.}

PB - {WORLD SCIENTIFIC PUBL CO PTE LTD} CY - {5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE} VL - {21} ER - TY - JOUR T1 - Poincaré polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces JF - Communications in Mathematical Physics 304 (2011) 395-409 Y1 - 2011 A1 - Ugo Bruzzo A1 - Rubik Poghossian A1 - Alessandro Tanzini AB -We 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.

PB - Springer VL - 304 UR - http://hdl.handle.net/1963/3738 IS - 2 U1 - 579 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Quantum Hitchin Systems via beta-deformed Matrix Models Y1 - 2011 A1 - Giulio Bonelli A1 - Kazunobu Maruyoshi A1 - Alessandro Tanzini AB -We 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.

PB - SISSA UR - http://hdl.handle.net/1963/4181 N1 - 29 pages; v2. refs. added and typos corrected U1 - 3904 U2 - Physics U3 - Elementary Particle Theory U4 - -1 ER - TY - JOUR T1 - Quasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a Young measures approach JF - ESAIM: COCV 17 (2011) 1-27 Y1 - 2011 A1 - Filippo Cagnetti A1 - Rodica Toader AB - A 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. PB - Cambridge University Press / EDP Sciences UR - http://hdl.handle.net/1963/2355 U1 - 1662 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Chern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality JF - J. Geom. Phys. 60 (2010) 417-429 Y1 - 2010 A1 - Andrea Brini A1 - Luca Griguolo A1 - Domenico Seminara A1 - Alessandro Tanzini AB - We 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. UR - http://hdl.handle.net/1963/2938 U1 - 1762 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Hitchin systems, N=2 gauge theories and W-gravity JF - Phys. Lett. B 691 (2010) 111-115 Y1 - 2010 A1 - Giulio Bonelli A1 - Alessandro Tanzini AB - We 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. UR - http://hdl.handle.net/1963/3831 U1 - 496 U2 - Physics U3 - Elementary Particle Theory ER - TY - RPRT T1 - Moore-Read Fractional Quantum Hall wavefunctions and SU(2) quiver gauge theories Y1 - 2010 A1 - Raoul Santachiara A1 - Alessandro Tanzini AB - We 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. UR - http://hdl.handle.net/1963/3852 U1 - 857 U2 - Mathematics U3 - Mathematical Physics ER - TY - CONF T1 - A Phase Field Approach to Wetting and Contact Angle Hysteresis Phenomena T2 - IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials Y1 - 2010 A1 - Antonio DeSimone A1 - Livio Fedeli A1 - Turco, Alessandro ED - Hackl, Klaus AB -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.

JF - IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials PB - Springer Netherlands CY - Dordrecht SN - 978-90-481-9195-6 ER - TY - JOUR T1 - Quasistatic crack growth in elasto-plastic materials: the two-dimensional case JF - Arch. Ration. Mech. Anal. 196 (2010) 867-906 Y1 - 2010 A1 - Gianni Dal Maso A1 - Rodica Toader AB - We study a variational model for the quasistatic evolution of elasto-plastic materials with cracks in the case of planar small strain associative elasto-plasticity. UR - http://hdl.handle.net/1963/2964 U1 - 1736 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Taming open/closed string duality with a Losev trick JF - JHEP 06(2010)063 Y1 - 2010 A1 - Giulio Bonelli A1 - Andrea Prudenziati A1 - Alessandro Tanzini AB - A 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. UR - http://hdl.handle.net/1963/3855 U1 - 854 U2 - Physics U3 - Mathematical Physics ER - TY - JOUR T1 - A time-dependent perturbative analysis for a quantum particle in a cloud chamber JF - Annales Henri Poincare 11 (2010) 539-564 Y1 - 2010 A1 - Gianfausto Dell'Antonio A1 - Rodolfo Figari A1 - Alessandro Teta AB - We 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. PB - Springer UR - http://hdl.handle.net/1963/3969 U1 - 432 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Uhlenbeck-Donaldson compactification for framed sheaves on projective surfaces Y1 - 2010 A1 - Ugo Bruzzo A1 - Dimitri Markushevich A1 - Alexander Tikhomirov AB - We 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. UR - http://hdl.handle.net/1963/4049 U1 - 353 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Universality in the profile of the semiclassical limit solutions to the focusing nonlinear Schrödinger equation at the first breaking curve JF - Int. Math. Res. Not. IMRN Y1 - 2010 A1 - Marco Bertola A1 - Alexander Tovbis UR - http://0-dx.doi.org.mercury.concordia.ca/10.1093/imrn/rnp196 ER - TY - JOUR T1 - Characterization of the time course of changes of the evoked electrical activity in a model of a chemically-induced neuronal plasticity JF - BMC Research Notes (2009) 2:13 Y1 - 2009 A1 - Frederic D. Broccard A1 - Silvia Pegoraro A1 - Maria Elisabetta Ruaro A1 - Claudio Altafini A1 - Vincent Torre AB - BACKGROUND: 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. PB - BioMed Central UR - http://hdl.handle.net/1963/3706 U1 - 599 U2 - Neuroscience U3 - Neurobiology ER - TY - JOUR T1 - Decoupling A and B model in open string theory: topological adventures in the world of tadpoles JF - JHEP 06 (2009) 046 Y1 - 2009 A1 - Giulio Bonelli A1 - Andrea Prudenziati A1 - Alessandro Tanzini A1 - Yang Jie AB - In this paper we analyze the problem of tadpole cancellation in open topological strings. We prove that the inclusion of unorientable worldsheet diagrams guarantees a consistent decoupling of A and B model for open superstring amplitudes at all genera. This is proven by direct microscopic computation in Super Conformal Field Theory. For the B-model we explicitly calculate one loop amplitudes in terms of analytic Ray-Singer torsions of appropriate vector bundles and obtain that the decoupling corresponds to the cancellation of D-brane and orientifold charges. Local tadpole cancellation on the worldsheet then guarantees the decoupling at all loops. The holomorphic anomaly equations for open topological strings at one loop are also obtained and compared with the results of the Quillen formula. UR - http://hdl.handle.net/1963/3632 U1 - 672 U2 - Physics U3 - Mathematical Physics ER - TY - JOUR T1 - 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 - Initial value problem of the Whitham equations for the Camassa-Holm equation JF - Physica D 238 (2009) 55-66 Y1 - 2009 A1 - Tamara Grava A1 - Virgil U. Pierce A1 - Fei-Ran Tian AB - We 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. PB - Elsevier UR - http://hdl.handle.net/1963/3429 U1 - 906 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Topological branes, p-algebras and generalized Nahm equations JF - Phys. Lett. B 672 (2009) 390-395 Y1 - 2009 A1 - Giulio Bonelli A1 - Alessandro Tanzini A1 - Maxim Zabzine AB - Inspired 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 theory UR - http://hdl.handle.net/1963/2702 U1 - 1398 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Decomposition results for functions with bounded variation JF - Boll. Unione Mat. Ital. (9) 1 (2008) 497-505 Y1 - 2008 A1 - Gianni Dal Maso A1 - Rodica Toader PB - Unione Matematica Italiana UR - http://hdl.handle.net/1963/3535 U1 - 729 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Fulde-Ferrell-Larkin-Ovchinnikov pairing in one-dimensional optical lattices JF - Phys. Rev. B 77 (2008) 245105 Y1 - 2008 A1 - Matteo Rizzi A1 - Marco Polini A1 - Miguel A. Cazalilla A1 - M.R. Bakhtiari A1 - Mario P. Tosi A1 - Rosario Fazio AB -Spin-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.

UR - http://hdl.handle.net/1963/2694 U1 - 1406 U2 - Physics U3 - Condensed Matter Theory ER - TY - RPRT T1 - Instanton counting on Hirzebruch surfaces Y1 - 2008 A1 - Ugo Bruzzo A1 - Rubik Poghossian A1 - Alessandro Tanzini AB - We 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. UR - http://hdl.handle.net/1963/2852 U1 - 1848 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Topological Gauge Theories on Local Spaces and Black Hole Entropy Countings JF - Adv. Theor. Math. Phys. 12 (2008) 1429-1446 Y1 - 2008 A1 - Giulio Bonelli A1 - Alessandro Tanzini AB - We 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. UR - http://hdl.handle.net/1963/1992 U1 - 2204 U2 - Physics U3 - Elementary Particle Theory ER - TY - RPRT T1 - Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory Y1 - 2007 A1 - Luca Griguolo A1 - Domenico Seminara A1 - Richard J. Szabo A1 - Alessandro Tanzini AB - We 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. JF - Nucl. Phys. B 772 (2007) 1-24 UR - http://hdl.handle.net/1963/1888 U1 - 2347 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - The complete one-loop spin chain for N=2 Super-Yang-Mills Y1 - 2007 A1 - Paolo Di Vecchia A1 - Alessandro Tanzini AB - We 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. UR - http://hdl.handle.net/1963/2309 N1 - Contributed to NATO Advanced Study Institute and EC Summer School on String Theory: From Gauge Interactions to Cosmology, Cargese, France, 7-19 Jun 2004. U1 - 1707 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Computing Amplitudes in topological M-theory Y1 - 2007 A1 - Giulio Bonelli A1 - Alessandro Tanzini A1 - Maxim Zabzine AB - We 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. JF - JHEP 03 (2007) 023 UR - http://hdl.handle.net/1963/1901 U1 - 2335 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Critical voltages and blocking stresses in nematic gels JF - Eur. Phys. J. E 24 (2007) 303-310 Y1 - 2007 A1 - Antonio DeSimone A1 - Antonio Di Carlo A1 - Luciano Teresi AB - We use a recently proposed model to study the dynamics of director remodeling in nematic gels under combined electro-mechanical loading. Focusing on a model specimen, we describe the critical volt-ages that must be exceeded to achieve mesogen reorientation, and the blocking stresses that prevent alignment of the nematic mesogens with the electric field. The corresponding phase diagram shows that the dynamic thresholds defined above are different from those predicted on the sole basis of energetics. Multistep loading programs are used to explore the energy landscape of our model specimen, showing the existence of multiple local minima under the same voltage and applied stress. This leads us to conclude that hysteresis should be expected in the electro-mechanical response of nematic gels. UR - http://hdl.handle.net/1963/2553 U1 - 1566 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The holomorphic anomaly for open string moduli JF - JHEP 10 (2007) 060 Y1 - 2007 A1 - Giulio Bonelli A1 - Alessandro Tanzini AB - We 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. UR - http://hdl.handle.net/1963/2113 U1 - 2576 U2 - Physics U3 - Elementary Particle Theory ER - TY - JOUR T1 - Luther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas JF - Phys. Rev. Lett. 98 (2007) 030404 Y1 - 2007 A1 - Gao Xianlong A1 - Matteo Rizzi A1 - Marco Polini A1 - Rosario Fazio A1 - Mario P. Tosi A1 - Vivaldo L. Jr. Campo A1 - Klaus Capelle AB -The 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.

UR - http://hdl.handle.net/1963/2056 U1 - 2140 U2 - Physics U3 - Condensed Matter Theory ER - TY - JOUR T1 - On a notion of unilateral slope for the Mumford-Shah functional JF - NoDEA 13 (2007) 713-734 Y1 - 2007 A1 - Gianni Dal Maso A1 - Rodica Toader AB - In 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. UR - http://hdl.handle.net/1963/2059 U1 - 2137 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Almost Global Stochastic Feedback Stabilization of Conditional Quantum Dynamics Y1 - 2006 A1 - Claudio Altafini A1 - Francesco Ticozzi AB - We 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. UR - http://hdl.handle.net/1963/1727 U1 - 2424 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - An artificial viscosity approach to quasistatic crack growth Y1 - 2006 A1 - Rodica Toader A1 - Chiara Zanini AB - We 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. UR - http://hdl.handle.net/1963/1850 U1 - 2367 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Large Parameter Behavior of Equilibrium Measures Y1 - 2006 A1 - Tamara Grava A1 - Fei-Ran Tian AB - We 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). JF - Commun. Math. Sci. 4 (2006) 551-573 UR - http://hdl.handle.net/1963/1789 U1 - 2755 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - N=1 superpotentials from multi-instanton calculus Y1 - 2006 A1 - Francesco Fucito A1 - Jose F. Morales A1 - Rubik Poghossian A1 - Alessandro Tanzini AB - In 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. JF - JHEP01(2006)031 UR - http://hdl.handle.net/1963/1773 U1 - 2771 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - On topological M-theory Y1 - 2006 A1 - Giulio Bonelli A1 - Alessandro Tanzini A1 - Maxim Zabzine AB - We 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. JF - Adv. Theor. Math. Phys. 10 (2006) 239-260 UR - http://hdl.handle.net/1963/1765 U1 - 2779 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Topological symmetry of forms, N=1 supersymmetry and S-duality on special manifolds JF - J. Geom. Phys. 56 (2006) 2379-2401 Y1 - 2006 A1 - Laurent Baulieu A1 - Alessandro Tanzini AB - We 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. UR - http://hdl.handle.net/1963/2168 U1 - 2076 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Quasistatic Crack Growth in Nonlinear Elasticity JF - Arch. Ration. Mech. Anal. 176 (2005) 165-225 Y1 - 2005 A1 - Gianni Dal Maso A1 - Gilles A. Francfort A1 - Rodica Toader AB - In 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. UR - http://hdl.handle.net/1963/2293 U1 - 1723 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Stress-dilatancy based modelling of granular materials and extensions to soils with crushable grains JF - Int. J. Numer. Anal. Met. 29 (2005) 73-101 Y1 - 2005 A1 - Antonio DeSimone A1 - Claudio Tamagnini AB - Stress-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. UR - http://hdl.handle.net/1963/2165 U1 - 2079 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Topological vector symmetry, topological gauge fixing of BRSTQFT and construction of maximal supersymmetry Y1 - 2005 A1 - Laurent Baulieu A1 - Guillaume Bossard A1 - Alessandro Tanzini AB - The 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. JF - JHEP 0508 (2005) 037 UR - http://hdl.handle.net/1963/1741 U1 - 2411 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Blow-up solutions for the Schrödinger equation in dimension three with a concentrated nonlinearity JF - Ann. Inst. H. Poincare Anal. Non Lineaire 21 (2004) 121-137 Y1 - 2004 A1 - Riccardo Adami A1 - Gianfausto Dell'Antonio A1 - Rodolfo Figari A1 - Alessandro Teta AB - We 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. PB - Elsevier UR - http://hdl.handle.net/1963/2998 U1 - 1335 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Quasi-static evolution in brittle fracture: the case of bounded solutions JF - Quad. Mat. Dip. Mat. Seconda Univ. Napoli 14 (2004) 245-266 Y1 - 2004 A1 - Gianni Dal Maso A1 - Gilles A. Francfort A1 - Rodica Toader AB - The 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 $L^\\\\infty$. UR - http://hdl.handle.net/1963/2229 U1 - 2015 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Semiclassical analysis of constrained quantum systems JF - J. Phys. A 37 (2004) 5605-5624 Y1 - 2004 A1 - Gianfausto Dell'Antonio A1 - Lucattilio Tenuta AB - We 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. PB - IOP Publishing UR - http://hdl.handle.net/1963/2997 U1 - 1336 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 - Multi-instanton calculus and equivariant cohomology JF - J.High Energy Phys. 2003,no.5,054,24 pp. Y1 - 2003 A1 - Ugo Bruzzo A1 - Jose F. Morales A1 - Francesco Fucito A1 - Alessandro Tanzini PB - SISSA Library UR - http://hdl.handle.net/1963/1645 U1 - 2473 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - A note on the integral representation of functionals in the space SBD(O) JF - Rend. Mat. Appl. 23 (2003) 189-201 Y1 - 2003 A1 - Francois Ebobisse A1 - Rodica Toader AB - In 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. PB - Rendiconti di Matematica UR - http://hdl.handle.net/1963/3064 U1 - 1269 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Space-adiabatic perturbation theory JF - Adv. Theor. Math. Phys. 7 (2003) 145-204 Y1 - 2003 A1 - Gianluca Panati A1 - Herbert Spohn A1 - Stefan Teufel AB - We 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. PB - International Press UR - http://hdl.handle.net/1963/3041 U1 - 1292 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - A model for the quasi-static growth of a brittle fracture: existence and approximation results JF - Math. Models Methods Appl. Sci., 12 (2002), no. 12, 1773 Y1 - 2002 A1 - Gianni Dal Maso A1 - Rodica Toader AB - We 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. PB - SISSA Library UR - http://hdl.handle.net/1963/1571 U1 - 2547 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A model for the quasi-static growth of brittle fractures based on local minimization JF - Math.Models Methods Appl. Sci., 12 (2002) , p.1773-1800. Y1 - 2002 A1 - Gianni Dal Maso A1 - Rodica Toader AB - We 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. PB - SISSA Library UR - http://hdl.handle.net/1963/1621 U1 - 2497 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A Model for the Quasi-Static Growth of Brittle Fractures: Existence and Approximation Results JF - Arch. Ration. Mech. Anal. 162 (2002) 101-135 Y1 - 2002 A1 - Gianni Dal Maso A1 - Rodica Toader AB - We 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. PB - Springer UR - http://hdl.handle.net/1963/3056 U1 - 1277 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Space-adiabatic perturbation theory in quantum dynamics JF - Physical review letters. 2002 Jun; 88(25 Pt 1):250405 Y1 - 2002 A1 - Gianluca Panati A1 - Herbert Spohn A1 - Stefan Teufel AB - A systematic perturbation scheme is developed for approximate solutions to the time-dependent Schrödinger equation with a space-adiabatic Hamiltonian. For a particular isolated energy band, the basic approach is to separate kinematics from dynamics. The kinematics is defined through a subspace of the full Hilbert space for which transitions to other band subspaces are suppressed to all orders, and the dynamics operates in that subspace in terms of an effective intraband Hamiltonian. As novel applications, we discuss the Born-Oppenheimer theory to second order and derive for the first time the nonperturbative definition of the g factor of the electron within nonrelativistic quantum electrodynamics. PB - American Physical Society UR - http://hdl.handle.net/1963/5985 U1 - 5841 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Gamma-limit of periodic obstacles JF - Acta Appl. Math., 2001, 65, 207-215 Y1 - 2001 A1 - Gianni Dal Maso A1 - Paola Trebeschi AB - We compute the Gamma-limit of a sequence obstacle functionals in the case of periodic obstacles. PB - SISSA Library UR - http://hdl.handle.net/1963/1495 U1 - 2668 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the Multi-Instanton Measure for Super Yang-Mills Theories JF - Nuclear Phys. B 611 (2001), no. 1-3, 205--226. Y1 - 2001 A1 - Ugo Bruzzo A1 - Francesco Fucito A1 - Alessandro Tanzini A1 - Gabriele Travaglini PB - SISSA Library UR - http://hdl.handle.net/1963/1531 U1 - 2632 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - 3D superconformal theories from Sasakian seven-manifolds: new nontrivial evidences for AdS_4/CFT_3 JF - Nucl.Phys. B577 (2000) 547-608 Y1 - 2000 A1 - Davide Fabbri A1 - Pietro Fré A1 - Leonardo Gualtieri A1 - Cesare Reina A1 - Alessandro Tomasiello A1 - Alberto Zaffaroni A1 - Alessandro Zampa PB - SISSA Library UR - http://hdl.handle.net/1963/1327 U1 - 3128 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Reduction of bi-Hamiltonian systems and separation of variables: an example from the Boussinesq hierarchy JF - Theor. Math. Phys. 122 (2000) 176-192 Y1 - 2000 A1 - Gregorio Falqui A1 - Franco Magri A1 - G. Tondo AB - We discuss the Boussinesq system with $t_5$ stationary, within a general framework for the analysis of stationary flows of n-Gel\\\'fand-Dickey hierarchies. We show how a careful use of its bihamiltonian structure can be used to provide a set of separation coordinates for the corresponding Hamilton--Jacobi equations. PB - Springer UR - http://hdl.handle.net/1963/3219 U1 - 1082 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Diffusion of a particle in presence of N moving point sources JF - Annales Poincare Phys.Theor.69:413-424,1998 Y1 - 1998 A1 - Gianfausto Dell'Antonio A1 - Rodolfo Figari A1 - Alessandro Teta PB - SISSA Library UR - http://hdl.handle.net/1963/134 U1 - 75 U2 - LISNU U3 - Interdisciplinary Laboratory for Advanced Studies ER - TY - JOUR T1 - Limits of variational problems for Dirichlet forms in varying domains JF - Journal des Mathematiques Pures et Appliquees. Volume 77, Issue 1, January 1998, Pages 89-116 Y1 - 1998 A1 - Gianni Dal Maso A1 - Virginia De Cicco A1 - Lino Notarantonio A1 - Nicoletta A. Tchou PB - SISSA UR - http://hdl.handle.net/1963/6440 U1 - 6377 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - THES T1 - Some Problems in the Asymptotic Analysis of Partial Differential Equations in Perforated Domains Y1 - 1997 A1 - Rodica Toader KW - Dirichlet problems PB - SISSA UR - http://hdl.handle.net/1963/5698 U1 - 5541 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Statistics in space dimension two JF - Lett. Math. Phys. 40 (1997), no. 3, 235-256 Y1 - 1997 A1 - Gianfausto Dell'Antonio A1 - Rodolfo Figari A1 - Alessandro Teta AB - We construct as a selfadjoint operator the Schroedinger hamiltonian for a system of $N$ identical particles on a plane, obeying the statistics defined by a representation $\\\\pi_1$ of the braid group. We use quadratic forms and potential theory, and give details only for the free case; standard arguments provide the extension of our approach to the case of potentials which are small in the sense of forms with respect to the laplacian. We also comment on the relation between the analysis given here and other approaches to the problem, and also on the connection with the description of a quantum particle on a plane under the influence of a shielded magnetic field (Aharanov-Bohm effect). PB - SISSA Library UR - http://hdl.handle.net/1963/130 U1 - 12 U2 - LISNU U3 - Interdisciplinary Laboratory for Advanced Studies ER - TY - JOUR T1 - A capacity method for the study of Dirichlet problems for elliptic systems in varying domains JF - Rend. Sem. Mat. Univ. Padova 96 (1996), 257--277 Y1 - 1996 A1 - Gianni Dal Maso A1 - Rodica Toader PB - SISSA Library UR - http://hdl.handle.net/1963/989 U1 - 2867 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Limits of Dirichlet problems in perforated domains: a new formulation JF - Rend. Istit. Mat. Univ. Trieste 26 (1994) 339-360 Y1 - 1994 A1 - Gianni Dal Maso A1 - Rodica Toader PB - Università degli Studi di Trieste, Dipartimento di Scienze Matematiche UR - http://hdl.handle.net/1963/3649 U1 - 656 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quadratic forms for singular perturbations of the Laplacian JF - Publ. Res. Inst. Math. Sci. 26 (1990), no. 5, 803--817 Y1 - 1990 A1 - Alessandro Teta PB - SISSA Library UR - http://hdl.handle.net/1963/757 U1 - 3034 U2 - Mathematics U3 - Mathematical Physics ER - TY - THES T1 - Singular perturbation of the Laplacian and connections with models of random media Y1 - 1989 A1 - Alessandro Teta PB - SISSA UR - http://hdl.handle.net/1963/6348 U1 - 6281 U2 - Mathematics U4 - -1 ER -