%0 Generic %D 2024 %T Optimisation–Based Coupling of Finite Element Model and Reduced Order Model for Computational Fluid Dynamics %A Ivan Prusak %A Davide Torlo %A Monica Nonino %A Gianluigi Rozza %G eng %0 Generic %D 2023 %T An optimisation-based domain-decomposition reduced order model for parameter-dependent non-stationary fluid dynamics problems %A Ivan Prusak %A Davide Torlo %A Monica Nonino %A Gianluigi Rozza %G eng %0 Journal Article %D 2023 %T An optimisation–based domain–decomposition reduced order model for the incompressible Navier-Stokes equations %A Ivan Prusak %A Monica Nonino %A Davide Torlo %A Francesco Ballarin %A Gianluigi Rozza %K Computational fluid dynamics %K Domain decomposition %K Optimal control %K Proper orthogonal decomposition %K Reduced order modelling %X

The aim of this work is to present a model reduction technique in the framework of optimal control problems for partial differential equations. We combine two approaches used for reducing the computational cost of the mathematical numerical models: domain–decomposition (DD) methods and reduced–order modelling (ROM). In particular, we consider an optimisation–based domain–decomposition algorithm for the parameter–dependent stationary incompressible Navier–Stokes equations. Firstly, the problem is described on the subdomains coupled at the interface and solved through an optimal control problem, which leads to the complete separation of the subdomain problems in the DD method. On top of that, a reduced model for the obtained optimal–control problem is built; the procedure is based on the Proper Orthogonal Decomposition technique and a further Galerkin projection. The presented methodology is tested on two fluid dynamics benchmarks: the stationary backward–facing step and lid-driven cavity flow. The numerical tests show a significant reduction of the computational costs in terms of both the problem dimensions and the number of optimisation iterations in the domain–decomposition algorithm.

%V 151 %P 172 - 189 %8 2023/12/01/ %@ 0898-1221 %G eng %U https://www.sciencedirect.com/science/article/pii/S0898122123004248 %! Computers & Mathematics with Applications %0 Journal Article %J International Journal for Numerical Methods in Engineering %D 2022 %T Kernel-based active subspaces with application to computational fluid dynamics parametric problems using discontinuous Galerkin method %A Francesco Romor %A Marco Tezzele %A Andrea Lario %A Gianluigi Rozza %B International Journal for Numerical Methods in Engineering %V 123 %P 6000-6027 %G eng %R 10.1002/nme.7099 %0 Journal Article %J Networks and Heterogeneous Media %D 2022 %T An SIR–like kinetic model tracking individuals' viral load %A Rossella Della Marca %A Nadia Loy %A Andrea Tosin %B Networks and Heterogeneous Media %P - %G eng %0 Journal Article %J Journal of Numerical Mathematics %D 2022 %T The \textttdeal.II Library, Version 9.4 %A Daniel Arndt %A Wolfgang Bangerth Marco Feder %A Marc Fehling %A Rene Gassmöller %A Timo Heister %A Luca Heltai %A Martin Kronbichler %A Matthias Maier %A Peter Munch %A Jean-Paul Pelteret %A Simon Sticko %A Bruno Turcksin %A David Wells %B Journal of Numerical Mathematics %G eng %0 Journal Article %J Journal of Non-Equilibrium Thermodynamics %D 2022 %T Variational Approach to Fluid–Structure Interaction via GENERIC %A Dirk Peschka %A Andrea Zafferi %A Luca Heltai %A Marita Thomas %B Journal of Non-Equilibrium Thermodynamics %G eng %0 Journal Article %J Software Impacts %D 2021 %T ATHENA: Advanced Techniques for High dimensional parameter spaces to Enhance Numerical Analysis %A Francesco Romor %A Marco Tezzele %A Gianluigi Rozza %B Software Impacts %V 10 %P 100133 %G eng %R 10.1016/j.simpa.2021.100133 %0 Journal Article %J Computers & Fluids %D 2021 %T On the comparison of LES data-driven reduced order approaches for hydroacoustic analysis %A Mahmoud Gadalla %A Marta Cianferra %A Marco Tezzele %A Giovanni Stabile %A Andrea Mola %A Gianluigi Rozza %K Dynamic mode decomposition %K Ffowcs Williams and Hawkings %K Hydroacoustics %K Large eddy simulation %K Model reduction %K Proper orthogonal decomposition %X

In this work, Dynamic Mode Decomposition (DMD) and Proper Orthogonal Decomposition (POD) methodologies are applied to hydroacoustic dataset computed using Large Eddy Simulation (LES) coupled with Ffowcs Williams and Hawkings (FWH) analogy. First, a low-dimensional description of the flow fields is presented with modal decomposition analysis. Sensitivity towards the DMD and POD bases truncation rank is discussed, and extensive dataset is provided to demonstrate the ability of both algorithms to reconstruct the flow fields with all the spatial and temporal frequencies necessary to support accurate noise evaluation. Results show that while DMD is capable to capture finer coherent structures in the wake region for the same amount of employed modes, reconstructed flow fields using POD exhibit smaller magnitudes of global spatiotemporal errors compared with DMD counterparts. Second, a separate set of DMD and POD modes generated using half the snapshots is employed into two data-driven reduced models respectively, based on DMD mid cast and POD with Interpolation (PODI). In that regard, results confirm that the predictive character of both reduced approaches on the flow fields is sufficiently accurate, with a relative superiority of PODI results over DMD ones. This infers that, discrepancies induced due to interpolation errors in PODI is relatively low compared with errors induced by integration and linear regression operations in DMD, for the present setup. Finally, a post processing analysis on the evaluation of FWH acoustic signals utilizing reduced fluid dynamic fields as input demonstrates that both DMD and PODI data-driven reduced models are efficient and sufficiently accurate in predicting acoustic noises.

%B Computers & Fluids %V 216 %P 104819 %G eng %U https://www.sciencedirect.com/science/article/pii/S0045793020303893 %R https://doi.org/10.1016/j.compfluid.2020.104819 %0 Thesis %D 2021 %T Data-driven parameter and model order reduction for industrial optimisation problems with applications in naval engineering %A Marco Tezzele %I SISSA - International School for Advanced Studies %G eng %9 phd %0 Unpublished Work %D 2021 %T A data-driven partitioned approach for the resolution of time-dependent optimal control problems with dynamic mode decomposition %A Eleonora Donadini %A Maria Strazzullo %A Marco Tezzele %A Gianluigi Rozza %G eng %0 Journal Article %J Journal of Numerical Mathematics %D 2021 %T The deal.II Library, Version 9.3 %A Daniel Arndt %A Wolfgang Bangerth %A Bruno Blais %A Marc Fehling %A Rene Gassmöller %A Timo Heister %A Luca Heltai %A Uwe Köcher %A Martin Kronbichler %A Matthias Maier %A Peter Munch %A Jean-Paul Pelteret %A Sebastian Proell %A Konrad Simon %A Bruno Turcksin %A David Wells %A Jiaqi Zhang %B Journal of Numerical Mathematics %G eng %U https://doi.org/10.1515/jnma-2021-0081 %0 Journal Article %J Complex Analysis and Operator Theory %D 2021 %T Doulbeault and J-invariant Cohomologies on Almost Complex Manifolds %A Lorenzo Sillari %A Adriano Tomassini %K Almost Complex Manifolds %K Cohomology of Lie Algebra %K Compact four-manifold %K Dolbeault Cohomology %K Frölicher Spectral Sequence %K Solvmanifold %X In this paper we relate the cohomology of $J$-invariant forms to the Dolbeault cohomology of an almost complex manifold. We find necessary and sufficient condition for the inclusion of the former into the latter to be true up to isomorphism. We also extend some results obtained by J. Cirici and S. O. Wilson about the computation of the left-invariant cohomology of nilmanifolds to the setting of solvmanifolds. Several examples are given. %B Complex Analysis and Operator Theory %V 15 %8 09/2021 %G eng %U https://link.springer.com/article/10.1007/s11785-021-01156-w %9 Article %R https://doi.org/10.1007/s11785-021-01156-w %0 Journal Article %J Journal of Marine Science and Engineering %D 2021 %T Hull Shape Design Optimization with Parameter Space and Model Reductions, and Self-Learning Mesh Morphing %A Nicola Demo %A Marco Tezzele %A Andrea Mola %A Gianluigi Rozza %X

In the field of parametric partial differential equations, shape optimization represents a challenging problem due to the required computational resources. In this contribution, a data-driven framework involving multiple reduction techniques is proposed to reduce such computational burden. Proper orthogonal decomposition (POD) and active subspace genetic algorithm (ASGA) are applied for a dimensional reduction of the original (high fidelity) model and for an efficient genetic optimization based on active subspace property. The parameterization of the shape is applied directly to the computational mesh, propagating the generic deformation map applied to the surface (of the object to optimize) to the mesh nodes using a radial basis function (RBF) interpolation. Thus, topology and quality of the original mesh are preserved, enabling application of POD-based reduced order modeling techniques, and avoiding the necessity of additional meshing steps. Model order reduction is performed coupling POD and Gaussian process regression (GPR) in a data-driven fashion. The framework is validated on a benchmark ship.

%B Journal of Marine Science and Engineering %V 9 %P 185 %G eng %U https://www.mdpi.com/2077-1312/9/2/185 %R 10.3390/jmse9020185 %0 Unpublished Work %D 2021 %T A local approach to parameter space reduction for regression and classification tasks %A Francesco Romor %A Marco Tezzele %A Gianluigi Rozza %B arXiv preprint arXiv:2107.10867 %G eng %0 Conference Paper %B Proceedings in Applied Mathematics & Mechanics %D 2021 %T Multi-fidelity data fusion for the approximation of scalar functions with low intrinsic dimensionality through active subspaces %A Francesco Romor %A Marco Tezzele %A Gianluigi Rozza %B Proceedings in Applied Mathematics & Mechanics %I Wiley Online Library %V 20 %G eng %R 10.1002/pamm.202000349 %0 Journal Article %J arXiv preprint arXiv:2110.14396 %D 2021 %T Multi-fidelity data fusion through parameter space reduction with applications to automotive engineering %A Francesco Romor %A Marco Tezzele %A Markus Mrosek %A Carsten Othmer %A Gianluigi Rozza %B arXiv preprint arXiv:2110.14396 %G eng %0 Journal Article %J Software Impacts %D 2021 %T PyGeM: Python Geometrical Morphing %A Marco Tezzele %A Nicola Demo %A Andrea Mola %A Gianluigi Rozza %K Free form deformation %K Geometrical morphing %K Inverse distance weighting %K Python %K Radial basis functions interpolation %X PyGeM is an open source Python package which allows to easily parametrize and deform 3D object described by CAD files or 3D meshes. It implements several morphing techniques such as free form deformation, radial basis function interpolation, and inverse distance weighting. Due to its versatility in dealing with different file formats it is particularly suited for researchers and practitioners both in academia and in industry interested in computational engineering simulations and optimization studies. %B Software Impacts %V 7 %P 100047 %G eng %R 10.1016/j.simpa.2020.100047 %0 Journal Article %J SIAM Journal on Scientific Computing %D 2021 %T A supervised learning approach involving active subspaces for an efficient genetic algorithm in high-dimensional optimization problems %A Nicola Demo %A Marco Tezzele %A Gianluigi Rozza %X

In this work, we present an extension of the genetic algorithm (GA) which exploits the active subspaces (AS) property to evolve the individuals on a lower dimensional space. In many cases, GA requires in fact more function evaluations than others optimization method to converge to the optimum. Thus, complex and high-dimensional functions may result intractable with the standard algorithm. To address this issue, we propose to linearly map the input parameter space of the original function onto its AS before the evolution, performing the mutation and mate processes in a lower dimensional space. In this contribution, we describe the novel method called ASGA, presenting differences and similarities with the standard GA method. We test the proposed method over n-dimensional benchmark functions – Rosenbrock, Ackley, Bohachevsky, Rastrigin, Schaffer N. 7, and Zakharov – and finally we apply it to an aeronautical shape optimization problem.

%B SIAM Journal on Scientific Computing %V 43 %G eng %U https://arxiv.org/abs/2006.07282 %N 3 %& B831 %R https://doi.org/10.1137/20M1345219 %0 Conference Paper %B Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018 %D 2020 %T Advances in reduced order methods for parametric industrial problems in computational fluid dynamics %A Gianluigi Rozza %A M.H. Malik %A Nicola Demo %A Marco Tezzele %A Michele Girfoglio %A Giovanni Stabile %A Andrea Mola %X

Reduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of model order reduction techniques in various engineering and scientific applications including but not limited to mechanical, naval and aeronautical engineering. The focus here is kept limited to computational fluid mechanics and related applications. The advances in the reduced order modeling with proper orthogonal decomposition and reduced basis method are presented as well as a brief discussion of dynamic mode decomposition and also some present advances in the parameter space reduction. Here, an overview of the challenges faced and possible solutions are presented with examples from various problems.

%B Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075395686&partnerID=40&md5=fb0b1a3cfdfd35a104db9921bc9be675 %0 Book Section %B Model Order Reduction, Volume 2 Snapshot-Based Methods and Algorithms %D 2020 %T Basic ideas and tools for projection-based model reduction of parametric partial differential equations %A Gianluigi Rozza %A Martin W. Hess %A Giovanni Stabile %A Marco Tezzele %A F. Ballarin %B Model Order Reduction, Volume 2 Snapshot-Based Methods and Algorithms %I De Gruyter %C Berlin, Boston %P 1 - 47 %@ 9783110671490 %G eng %U https://www.degruyter.com/view/book/9783110671490/10.1515/9783110671490-001.xml %R https://doi.org/10.1515/9783110671490-001 %0 Journal Article %J Advances in Calculus of Variations %D 2020 %T On the blow-up of GSBV functions under suitable geometric properties of the jump set %A Emanuele Tasso %B Advances in Calculus of Variations %8 2020 %G eng %U https://doi.org/10.1515/acv-2019-0068 %0 Journal Article %J ESAIM: COCV %D 2020 %T On the continuity of the trace operator in GSBV (Ω) and GSBD (Ω) %A Emanuele Tasso %B ESAIM: COCV %V 26 %8 2020/// %G eng %U https://doi.org/10.1051/cocv/2019014 %0 Journal Article %J Computers and Mathematics with Applications %D 2020 %T The deal.II finite element library: Design, features, and insights %A Daniel Arndt %A Wolfgang Bangerth %A Denis Davydov %A Timo Heister %A Luca Heltai %A Martin Kronbichler %A Matthias Maier %A Jean-Paul Pelteret %A Bruno Turcksin %A David Wells %B Computers and Mathematics with Applications %G eng %U https://doi.org/10.1016/j.camwa.2020.02.022 %0 Journal Article %J Journal of Numerical Mathematics %D 2020 %T The deal.II library, Version 9.2 %A Daniel Arndt %A Wolfgang Bangerth %A Bruno Blais %A Thomas C. Clevenger %A Marc Fehling %A Alexander V. Grayver %A Timo Heister %A Luca Heltai %A Martin Kronbichler %A Matthias Maier %A Peter Munch %A Jean-Paul Pelteret %A Reza Rastak %A Ignacio Tomas %A Bruno Turcksin %A Zhuoran Wang %A David Wells %B Journal of Numerical Mathematics %V 28 %P 131–146 %G eng %0 Journal Article %D 2020 %T Energy-dissipation balance of a smooth moving crack %A Maicol Caponi %A Ilaria Lucardesi %A Emanuele Tasso %K Energy-dissipation balance %K Fracture dynamics %K Wave equation in time-dependent domains %X

In this paper we provide necessary and sufficient conditions in order to guarantee the energy-dissipation balance of a Mode III crack, growing on a prescribed smooth path. Moreover, we characterize the singularity of the displacement near the crack tip, generalizing the result in [10] valid for straight fractures.

%V 483 %P 123656 %8 2020/03/15/ %@ 0022-247X %G eng %U https://www.sciencedirect.com/science/article/pii/S0022247X19309242 %N 2 %! Journal of Mathematical Analysis and Applications %0 Journal Article %J Advanced Modeling and Simulation in Engineering Sciences %D 2020 %T Enhancing CFD predictions in shape design problems by model and parameter space reduction %A Marco Tezzele %A Nicola Demo %A Giovanni Stabile %A Andrea Mola %A Gianluigi Rozza %X

In this work we present an advanced computational pipeline for the approximation and prediction of the lift coefficient of a parametrized airfoil profile. The non-intrusive reduced order method is based on dynamic mode decomposition (DMD) and it is coupled with dynamic active subspaces (DyAS) to enhance the future state prediction of the target function and reduce the parameter space dimensionality. The pipeline is based on high-fidelity simulations carried out by the application of finite volume method for turbulent flows, and automatic mesh morphing through radial basis functions interpolation technique. The proposed pipeline is able to save 1/3 of the overall computational resources thanks to the application of DMD. Moreover exploiting DyAS and performing the regression on a lower dimensional space results in the reduction of the relative error in the approximation of the time-varying lift coefficient by a factor 2 with respect to using only the DMD.

%B Advanced Modeling and Simulation in Engineering Sciences %V 7 %G eng %U https://arxiv.org/abs/2001.05237 %N 40 %R https://doi.org/10.1186/s40323-020-00177-y %0 Journal Article %J Archiv der Mathematik %D 2020 %T Existence of Riemannian metrics with positive biorthogonal curvature on simply connected 5-manifolds %A Boris Stupovski %A Rafael Torres %X

Using the recent work of Bettiol, we show that a first-order conformal deformation of Wilking’s metric of almost-positive sectional curvature on $S2\times S3$ yields a family of metrics with strictly positive average of sectional curvatures of any pair of 2-planes that are separated by a minimal distance in the 2-Grassmanian. A result of Smale allows us to conclude that every closed simply connected 5-manifold with torsion-free homology and trivial second Stiefel–Whitney class admits a Riemannian metric with a strictly positive average of sectional curvatures of any pair of orthogonal 2-planes.

%B Archiv der Mathematik %I Springer %P 1–9 %G eng %U https://dx.doi.org/10.1007/s00013-020-01511-x %R 10.1007/s00013-020-01511-x %0 Journal Article %D 2020 %T Gauge theories on compact toric manifolds %A Giulio Bonelli %A Francesco Fucito %A Morales, Jose Francisco %A Massimiliano Ronzani %A Sysoeva, Ekaterina %A Alessandro Tanzini %8 7 %G eng %R 10.1007/s11005-021-01419-9 %0 Book %D 2020 %T Kernel-based Active Subspaces with application to CFD parametric problems using Discontinuous Galerkin method %A Francesco Romor %A Marco Tezzele %A Lario, Andrea %A Gianluigi Rozza %G eng %0 Journal Article %J Lecture Notes in Computational Science and Engineering %D 2020 %T Reduced order isogeometric analysis approach for pdes in parametrized domains %A Fabrizio Garotta %A Nicola Demo %A Marco Tezzele %A Massimo Carraturo %A Alessandro Reali %A Gianluigi Rozza %X

In this contribution, we coupled the isogeometric analysis to a reduced order modelling technique in order to provide a computationally efficient solution in parametric domains. In details, we adopt the free-form deformation method to obtain the parametric formulation of the domain and proper orthogonal decomposition with interpolation for the computational reduction of the model. This technique provides a real-time solution for any parameter by combining several solutions, in this case computed using isogeometric analysis on different geometrical configurations of the domain, properly mapped into a reference configuration. We underline that this reduced order model requires only the full-order solutions, making this approach non-intrusive. We present in this work the results of the application of this methodology to a heat conduction problem inside a deformable collector pipe.

%B Lecture Notes in Computational Science and Engineering %V 137 %P 153-170 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85089615035&doi=10.1007%2f978-3-030-48721-8_7&partnerID=40&md5=7b15836ae65fa28dcfe8733788d7730c %R 10.1007/978-3-030-48721-8_7 %0 Journal Article %J International Journal for Numerical Methods in Biomedical EngineeringInternational Journal for Numerical Methods in Biomedical EngineeringInt J Numer Meth Biomed Engng %D 2020 %T Reduced order methods for parametric optimal flow control in coronary bypass grafts, toward patient-specific data assimilation %A Zakia Zainib %A F. Ballarin %A Stephen E. Fremes %A Piero Triverio %A Laura Jiménez-Juan %A Gianluigi Rozza %K coronary artery bypass grafts %K data assimilation %K flow control %K Galerkin methods %K hemodynamics modeling %K Optimization %K patient-specific simulations %K Proper orthogonal decomposition %K reduced order methods %X

Abstract Coronary artery bypass grafts (CABG) surgery is an invasive procedure performed to circumvent partial or complete blood flow blockage in coronary artery disease. In this work, we apply a numerical optimal flow control model to patient-specific geometries of CABG, reconstructed from clinical images of real-life surgical cases, in parameterized settings. The aim of these applications is to match known physiological data with numerical hemodynamics corresponding to different scenarios, arisen by tuning some parameters. Such applications are an initial step toward matching patient-specific physiological data in patient-specific vascular geometries as best as possible. Two critical challenges that reportedly arise in such problems are: (a) lack of robust quantification of meaningful boundary conditions required to match known data as best as possible and (b) high computational cost. In this work, we utilize unknown control variables in the optimal flow control problems to take care of the first challenge. Moreover, to address the second challenge, we propose a time-efficient and reliable computational environment for such parameterized problems by projecting them onto a low-dimensional solution manifold through proper orthogonal decomposition-Galerkin.

%B International Journal for Numerical Methods in Biomedical EngineeringInternational Journal for Numerical Methods in Biomedical EngineeringInt J Numer Meth Biomed Engng %V n/a %P e3367 %8 2020/05/27 %@ 2040-7939 %G eng %U https://onlinelibrary.wiley.com/doi/10.1002/cnm.3367?af=R %N n/a %! International Journal for Numerical Methods in Biomedical Engineering %R https://doi.org/10.1002/cnm.3367 %0 Journal Article %J Transactions of the american mathematical society %D 2020 %T Topology change and selection rules for high-dimensional spin(1,n)0-Lorentzian cobordisms %A Gleb Smirnov %A Rafael Torres %B Transactions of the american mathematical society %V 373 %P 1731-1747 %G eng %U http://hdl.handle.net/20.500.11767/108858 %N 3 %9 Journal article %& 1731 %R 10.1090/tran/7939 %0 Journal Article %D 2020 %T Weak formulation of elastodynamics in domains with growing cracks %A Emanuele Tasso %X

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 for both the damped and undamped systems, while in the damped case we are also able to prove uniqueness and an energy balance.

%V 199 %P 1571 - 1595 %8 2020/08/01 %@ 1618-1891 %G eng %U https://doi.org/10.1007/s10231-019-00932-y %N 4 %! Annali di Matematica Pura ed Applicata (1923 -) %0 Journal Article %J Probability Theory and Related Fields %D 2019 %T Benamou–Brenier and duality formulas for the entropic cost on RCD*(K,N) spaces %A Nicola Gigli %A Luca Tamanini %X

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.

%B Probability Theory and Related Fields %8 Apr %G eng %U https://doi.org/10.1007/s00440-019-00909-1 %R 10.1007/s00440-019-00909-1 %0 Journal Article %J The Journal of Open Source Software %D 2019 %T BladeX: Python Blade Morphing %A Mahmoud Gadalla %A Marco Tezzele %A Andrea Mola %A Gianluigi Rozza %B The Journal of Open Source Software %V 4 %P 1203 %G eng %R 10.21105/joss.01203 %0 Conference Paper %B 8th International Conference on Computational Methods in Marine Engineering, MARINE 2019 %D 2019 %T A complete data-driven framework for the efficient solution of parametric shape design and optimisation in naval engineering problems %A Nicola Demo %A Marco Tezzele %A Andrea Mola %A Gianluigi Rozza %X

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.

%B 8th International Conference on Computational Methods in Marine Engineering, MARINE 2019 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075342565&partnerID=40&md5=d76b8a1290053e7a84fb8801c0e6bb3d %0 Conference Paper %B VIII International Conference on Computational Methods in Marine Engineering %D 2019 %T A complete data-driven framework for the efficient solution of parametric shape design and optimisation in naval engineering problems %A Nicola Demo %A Marco Tezzele %A Andrea Mola %A Gianluigi Rozza %X

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.

%B VIII International Conference on Computational Methods in Marine Engineering %G eng %U https://arxiv.org/abs/1905.05982 %0 Journal Article %J Journal of Numerical Mathematics %D 2019 %T The deal.II Library, Version 9.1 %A Daniel Arndt %A Wolfgang Bangerth %A Thomas C. Clevenger %A Denis Davydov %A Marc Fehling %A Garcia-Sanchez, Daniel %A Harper, Graham %A Timo Heister %A Luca Heltai %A Martin Kronbichler %A Maguire Kynch, Ross %A Matthias Maier %A Jean-Paul Pelteret %A Bruno Turcksin %A David Wells %B Journal of Numerical Mathematics %G eng %0 Journal Article %J Journal of Numerical Mathematics %D 2019 %T The deal.II Library, Version 9.1 %A Daniel Arndt %A Wolfgang Bangerth %A Thomas C. Clevenger %A Denis Davydov %A Marc Fehling %A Garcia-Sanchez, Daniel %A Harper, Graham %A Timo Heister %A Luca Heltai %A Martin Kronbichler %A Maguire Kynch, Ross %A Matthias Maier %A Jean-Paul Pelteret %A Bruno Turcksin %A David Wells %X This paper provides an overview of the new features of the finite element library deal.II, version 9.1. %B Journal of Numerical Mathematics %G eng %R 10.1515/jnma-2019-0064 %0 Conference Paper %B 8th International Conference on Computational Methods in Marine Engineering, MARINE 2019 %D 2019 %T Efficient reduction in shape parameter space dimension for ship propeller blade design %A Andrea Mola %A Marco Tezzele %A Mahmoud Gadalla %A Valdenazzi, Federica %A Grassi, Davide %A Padovan, Roberta %A Gianluigi Rozza %X

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.

%B 8th International Conference on Computational Methods in Marine Engineering, MARINE 2019 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075395143&partnerID=40&md5=b6aa0fcedc2f88e78c295d0f437824d0 %0 Journal Article %J Stochastic Processes and their Applications %D 2019 %T An entropic interpolation proof of the HWI inequality %A Ivan Gentil %A Christian Léonard %A Luigia Ripani %A Luca Tamanini %K Entropic interpolations %K Fisher information %K Relative entropy %K Schrödinger problem %K Wasserstein distance %X

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.

%B Stochastic Processes and their Applications %G eng %U http://www.sciencedirect.com/science/article/pii/S0304414918303454 %R https://doi.org/10.1016/j.spa.2019.04.002 %0 Journal Article %J JHEP %D 2019 %T N=2 gauge theories on unoriented/open four-manifolds and their AGT counterparts %A Aditya Bawane %A Benvenuti, Sergio %A Giulio Bonelli %A Muteeb, Nouman %A Alessandro Tanzini %B JHEP %V 07 %P 040 %G eng %U http://inspirehep.net/record/1631219/ %R 10.1007/JHEP07(2019)040 %0 Journal Article %J Comptes Rendus - Mecanique %D 2019 %T A non-intrusive approach for the reconstruction of POD modal coefficients through active subspaces %A Nicola Demo %A Marco Tezzele %A Gianluigi Rozza %X

Reduced order modeling (ROM) provides an efficient framework to compute solutions of parametric problems. Basically, it exploits a set of precomputed high-fidelity solutions—computed for properly chosen parameters, using a full-order model—in order to find the low dimensional space that contains the solution manifold. Using this space, an approximation of the numerical solution for new parameters can be computed in real-time response scenario, thanks to the reduced dimensionality of the problem. In a ROM framework, the most expensive part from the computational viewpoint is the calculation of the numerical solutions using the full-order model. Of course, the number of collected solutions is strictly related to the accuracy of the reduced order model. In this work, we aim at increasing the precision of the model also for few input solutions by coupling the proper orthogonal decomposition with interpolation (PODI)—a data-driven reduced order method—with the active subspace (AS) property, an emerging tool for reduction in parameter space. The enhanced ROM results in a reduced number of input solutions to reach the desired accuracy. In this contribution, we present the numerical results obtained by applying this method to a structural problem and in a fluid dynamics one.

%B Comptes Rendus - Mecanique %V 347 %P 873-881 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075379471&doi=10.1016%2fj.crme.2019.11.012&partnerID=40&md5=dcb27af39dc14dc8c3a4a5f681f7d84b %R https://doi.org/10.1016/j.crme.2019.11.012 %0 Conference Paper %B 8th International Conference on Computational Methods in Marine Engineering, MARINE 2019 %D 2019 %T Shape optimization through proper orthogonal decomposition with interpolation and dynamic mode decomposition enhanced by active subspaces %A Marco Tezzele %A Nicola Demo %A Gianluigi Rozza %X

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.

%B 8th International Conference on Computational Methods in Marine Engineering, MARINE 2019 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075390244&partnerID=40&md5=3e1f2e9a2539d34594caff13766c94b8 %0 Journal Article %J PoliTO Springer Series %D 2019 %T Weighted Reduced Order Methods for Parametrized Partial Differential Equations with Random Inputs %A L. Venturi %A D. Torlo %A F. Ballarin %A Gianluigi Rozza %X

In this manuscript we discuss weighted reduced order methods for stochastic partial differential equations. Random inputs (such as forcing terms, equation coefficients, boundary conditions) are considered as parameters of the equations. We take advantage of the resulting parametrized formulation to propose an efficient reduced order model; we also profit by the underlying stochastic assumption in the definition of suitable weights to drive to reduction process. Two viable strategies are discussed, namely the weighted reduced basis method and the weighted proper orthogonal decomposition method. A numerical example on a parametrized elasticity problem is shown.

%B PoliTO Springer Series %P 27-40 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85084009379&doi=10.1007%2f978-3-030-04870-9_2&partnerID=40&md5=446bcc1f331167bbba67bc00fb170150 %R 10.1007/978-3-030-04870-9_2 %0 Report %D 2018 %T On the Cauchy problem for the wave equation on time-dependent domains %A Gianni Dal Maso %A Rodica Toader %X 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. %I SISSA %G en %U http://preprints.sissa.it/handle/1963/35314 %1 35622 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-04-23T06:03:52Z No. of bitstreams: 1 DM-Toa-18-sissa.pdf: 404543 bytes, checksum: 73bb5b0c57b574d05b3d6f33417016e0 (MD5) %0 Book Section %B Mathematical and Numerical Modeling of the Cardiovascular System and Applications %D 2018 %T Combined parameter and model reduction of cardiovascular problems by means of active subspaces and POD-Galerkin methods %A Marco Tezzele %A F. Ballarin %A Gianluigi Rozza %B Mathematical and Numerical Modeling of the Cardiovascular System and Applications %I Springer %P 185–207 %G eng %0 Journal Article %J JOURNAL OF NUMERICAL MATHEMATICS %D 2018 %T The deal.II Library, Version 9.0 %A Giovanni Alzetta %A Daniel Arndt %A Wolfgang Bangerth %A Boddu, Vishal %A Brands, Benjamin %A Denis Davydov %A Rene Gassmöller %A Timo Heister %A Luca Heltai %A Kormann, Katharina %A Martin Kronbichler %A Matthias Maier %A Jean-Paul Pelteret %A Bruno Turcksin %A David Wells %B JOURNAL OF NUMERICAL MATHEMATICS %G eng %U https://doi.org/10.1515/jnma-2018-0054 %R 10.1515/jnma-2018-0054 %0 Journal Article %J Advanced Modeling and Simulation in Engineering Sciences %D 2018 %T Dimension reduction in heterogeneous parametric spaces with application to naval engineering shape design problems %A Marco Tezzele %A Filippo Salmoiraghi %A Andrea Mola %A Gianluigi Rozza %X

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.

%B Advanced Modeling and Simulation in Engineering Sciences %V 5 %P 25 %8 Sep %G eng %R 10.1186/s40323-018-0118-3 %0 Conference Proceedings %B The 28th International Ocean and Polar Engineering Conference %D 2018 %T An efficient shape parametrisation by free-form deformation enhanced by active subspace for hull hydrodynamic ship design problems in open source environment %A Nicola Demo %A Marco Tezzele %A Andrea Mola %A Gianluigi Rozza %K Active subspaces %K Boundary element method %K Dynamic mode decomposition %K Fluid structure interaction %K Free form deformation %K Fully nonlinear potential %K Numerical towing tank %X 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. %B The 28th International Ocean and Polar Engineering Conference %I International Society of Offshore and Polar Engineers %C Sapporo, Japan %G eng %U https://www.onepetro.org/conference-paper/ISOPE-I-18-481 %0 Report %D 2018 %T Existence for elastodynamic Griffith fracture with a weak maximal dissipation condition %A Gianni Dal Maso %A Cristopher J. Larsen %A Rodica Toader %X 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. %G en %U http://preprints.sissa.it/handle/1963/35308 %1 35616 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-03-19T09:02:45Z No. of bitstreams: 1 DM-Lar-Toa-sissa.pdf: 429343 bytes, checksum: 82817f96da6dcabff29c2c322590fb66 (MD5) %0 Journal Article %J The Journal of Open Source Software %D 2018 %T EZyRB: Easy Reduced Basis method %A Nicola Demo %A Marco Tezzele %A Gianluigi Rozza %B The Journal of Open Source Software %V 3 %P 661 %G eng %U https://joss.theoj.org/papers/10.21105/joss.00661 %R 10.21105/joss.00661 %0 Journal Article %J International Journal of Computational Fluid Dynamics %D 2018 %T Free-form deformation, mesh morphing and reduced-order methods: enablers for efficient aerodynamic shape optimisation %A Filippo Salmoiraghi %A Scardigli, Angela %A Telib, Haysam %A Gianluigi Rozza %X

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.

%B International Journal of Computational Fluid Dynamics %I Taylor & Francis %V 32 %P 233-247 %G eng %R 10.1080/10618562.2018.1514115 %0 Conference Paper %B Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship & Maritime Research %D 2018 %T Model Order Reduction by means of Active Subspaces and Dynamic Mode Decomposition for Parametric Hull Shape Design Hydrodynamics %A Marco Tezzele %A Nicola Demo %A Mahmoud Gadalla %A Andrea Mola %A Gianluigi Rozza %X 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. %B Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship & Maritime Research %I IOS Press %C Trieste, Italy %G eng %U http://ebooks.iospress.nl/publication/49270 %R 10.3233/978-1-61499-870-9-569 %0 Journal Article %J The Journal of Open Source Software %D 2018 %T PyDMD: Python Dynamic Mode Decomposition %A Nicola Demo %A Marco Tezzele %A Gianluigi Rozza %B The Journal of Open Source Software %V 3 %P 530 %G eng %U https://joss.theoj.org/papers/734e4326edd5062c6e8ee98d03df9e1d %R 10.21105/joss.00530 %0 Journal Article %J Rendiconti Lincei-Matematica e Applicazioni %D 2018 %T Second order differentiation formula on RCD(K, N) spaces %A Nicola Gigli %A Luca Tamanini %B Rendiconti Lincei-Matematica e Applicazioni %V 29 %P 377–386 %G eng %0 Report %D 2018 %T Second order differentiation formula on RCD*(K,N) spaces %A Nicola Gigli %A Luca Tamanini %G eng %0 Conference Paper %B Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship & Maritime Research %D 2018 %T Shape Optimization by means of Proper Orthogonal Decomposition and Dynamic Mode Decomposition %A Nicola Demo %A Marco Tezzele %A Gianluca Gustin %A Gianpiero Lavini %A Gianluigi Rozza %X 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. %B Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship & Maritime Research %I IOS Press %C Trieste, Italy %G eng %U http://ebooks.iospress.nl/publication/49229 %& 212 %R 10.3233/978-1-61499-870-9-212 %0 Conference Paper %B Technology and Science for the Ships of the Future - Proceedings of NAV 2018: 19th International Conference on Ship and Maritime Research %D 2018 %T SRTP 2.0 - The evolution of the safe return to port concept %A D. Cangelosi %A A. Bonvicini %A M. Nardo %A Andrea Mola %A A. Marchese %A Marco Tezzele %A Gianluigi Rozza %X

In 2010 IMO (International Maritime Organisation) introduced new rules in SOLAS with the aim of intrinsically increase the safety of passenger ships. This requirement is achieved by providing safe areas for passengers and essential services for allowing ship to Safely Return to Port (SRtP). The entry into force of these rules has changed the way to design passenger ships. In this respect big effort in the research has been done by industry to address design issues related to the impact on failure analysis of the complex interactions among systems. Today the research activity is working to bring operational matters in the design stage. This change of research focus was necessary because human factor and the way to operate the ship itself after a casualty on board may have a big impact in the design of the ship/systems. Also the management of the passengers after a casualty is becoming a major topic for safety. This paper presents the state of the art of Italian knowledge in the field of system engineering applied to passenger ship address to safety improvement and design reliability. An overview of present tools and methodologies will be offered together with future focuses in the research activity.

%B Technology and Science for the Ships of the Future - Proceedings of NAV 2018: 19th International Conference on Ship and Maritime Research %G eng %R 10.3233/978-1-61499-870-9-665 %0 Journal Article %J SIAM-ASA Journal on Uncertainty Quantification %D 2018 %T Stabilized weighted reduced basis methods for parametrized advection dominated problems with random inputs %A D. Torlo %A F. Ballarin %A Gianluigi Rozza %X

In this work, we propose viable and eficient strategies for stabilized parametrized advection dominated problems, with random inputs. In particular, we investigate the combination of the wRB (weighted reduced basis) method for stochastic parametrized problems with the stabilized RB (reduced basis) method, which is the integration of classical stabilization methods (streamline/upwind Petrov-Galerkin (SUPG) in our case) in the ofine-online structure of the RB method. Moreover, we introduce a reduction method that selectively enables online stabilization; this leads to a sensible reduction of computational costs, while keeping a very good accuracy with respect to high-fdelity solutions. We present numerical test cases to assess the performance of the proposed methods in steady and unsteady problems related to heat transfer phenomena.

%B SIAM-ASA Journal on Uncertainty Quantification %V 6 %P 1475-1502 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85058246502&doi=10.1137%2f17M1163517&partnerID=40&md5=6c54e2f0eb727cb85060e988486b8ac8 %R 10.1137/17M1163517 %0 Journal Article %J JOURNAL OF NUMERICAL MATHEMATICS %D 2017 %T The deal.II Library, Version 8.5 %A Daniel Arndt %A Wolfgang Bangerth %A Denis Davydov %A Timo Heister %A Luca Heltai %A Martin Kronbichler %A Matthias Maier %A Jean-Paul Pelteret %A Bruno Turcksin %A David Wells %B JOURNAL OF NUMERICAL MATHEMATICS %V 25 %P 137–145 %G eng %U https://www.dealii.org/deal85-preprint.pdf %R 10.1515/jnma-2017-0058 %0 Journal Article %J Journal of Geometry and Physics %D 2017 %T Gauge theories on compact toric surfaces, conformal field theories and equivariant Donaldson invariants %A Mikhail Bershtein %A Giulio Bonelli %A Massimiliano Ronzani %A Alessandro Tanzini %K AGT %K Donaldson invariants %K Equivariant localization %K Exact partition function %K Supersymmetry %K Virasoro conformal blocks %X

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).

%B Journal of Geometry and Physics %V 118 %P 40 - 50 %G eng %U http://www.sciencedirect.com/science/article/pii/S0393044017300165 %R https://doi.org/10.1016/j.geomphys.2017.01.012 %0 Journal Article %J Ergodic Theory and Dynamical Systems %D 2017 %T Integrability of dominated decompositions on three-dimensional manifolds %A Stefano Luzzatto %A Sina Türeli %A Khadim Mbacke War %X


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.

%B Ergodic Theory and Dynamical Systems %I Cambridge University Press %V 37 %P 606–620 %G eng %R 10.1017/etds.2015.64 %0 Journal Article %J Advances in Calculus of Variations %D 2017 %T Lower semicontinuity of a class of integral functionals on the space of functions of bounded deformation %A Gianni Dal Maso %A Gianluca Orlando %A Rodica Toader %X

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.

%B Advances in Calculus of Variations %I De Gruyter %V 10 %P 183–207 %G eng %R 10.1515/acv-2015-0036 %0 Journal Article %J Journal de Mathématiques Pures et Appliquées %D 2017 %T A lower semicontinuity result for a free discontinuity functional with a boundary term %A Stefano Almi %A Gianni Dal Maso %A Rodica Toader %X

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.

%B Journal de Mathématiques Pures et Appliquées %V 108 %P 952-990 %G en %U http://hdl.handle.net/20.500.11767/15979 %N 6 %1 34731 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by salmi@sissa.it (salmi@sissa.it) on 2015-12-15T14:37:19Z No. of bitstreams: 1 Alm-DM-Toa-15-sissa.pdf: 351559 bytes, checksum: b6adddc4944478676c7d4b34028a347c (MD5) %& 952 %R 10.1016/j.matpur.2017.05.018 %0 Journal Article %J Comm. Math. Phys. %D 2017 %T Maximal amplitudes of finite-gap solutions for the focusing Nonlinear Schrödinger Equation %A Marco Bertola %A Alexander Tovbis %B Comm. Math. Phys. %V 354 %P 525–547 %G eng %U http://dx.doi.org/10.1007/s00220-017-2895-9 %R 10.1007/s00220-017-2895-9 %0 Journal Article %J Journal of High Energy Physics %D 2017 %T Real topological string amplitudes %A Narain, K. S. %A Nicolò Piazzalunga %A Alessandro Tanzini %X

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 $\mathcal{F}_g$.

%B Journal of High Energy Physics %V 2017 %P 80 %8 Mar %G eng %U https://doi.org/10.1007/JHEP03(2017)080 %R 10.1007/JHEP03(2017)080 %0 Report %D 2017 %T Second order differentiation formula on compact RCD*(K,N) spaces %A Nicola Gigli %A Luca Tamanini %G eng %0 Journal Article %J Phys. Rev. Lett. %D 2017 %T Universality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schrödinger Equation %A Tikan, Alexey %A Billet, Cyril %A Gennady El %A Alexander Tovbis %A Marco Bertola %A Sylvestre, Thibaut %A Gustave, Francois %A Randoux, Stephane %A Genty, Goëry %A Suret, Pierre %A Dudley, John M. %B Phys. Rev. Lett. %I American Physical Society %V 119 %P 033901 %8 Jul %G eng %U https://link.aps.org/doi/10.1103/PhysRevLett.119.033901 %R 10.1103/PhysRevLett.119.033901 %0 Conference Paper %B Proceedings of the ECCOMAS Congress 2016, VII European Conference on Computational Methods in Applied Sciences and Engineering, %D 2016 %T Advances in geometrical parametrization and reduced order models and methods for computational fluid dynamics problems in applied sciences and engineering: overview and perspectives %A Filippo Salmoiraghi %A F. Ballarin %A Giovanni Corsi %A Andrea Mola %A Marco Tezzele %A Gianluigi Rozza %E Papadrakakis, M. %E Papadopoulos, V. %E Stefanou, G. %E Plevris, V. %X

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.

%B Proceedings of the ECCOMAS Congress 2016, VII European Conference on Computational Methods in Applied Sciences and Engineering, %I ECCOMAS %C Crete, Greece %8 06/2016 %G en %1 35466 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2016-05-13T00:28:01Z No. of bitstreams: 1 eccomas2016_AROMA.pdf: 1846196 bytes, checksum: 9636e713df80de178d87fd2feff76f91 (MD5) %0 Journal Article %J ESAIM: COCV %D 2016 %T On the area of the graph of a piecewise smooth map from the plane to the plane with a curve discontinuity %A Giovanni Bellettini %A Lucia Tealdi %A Maurizio Paolini %K Area functional %X

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.

%B ESAIM: COCV %V 22 %P 29-63 %G en %U https://www.esaim-cocv.org/articles/cocv/abs/2016/01/cocv140065/cocv140065.html %N 1 %1 7257 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Lucia Tealdi (ltealdi@sissa.it) on 2013-11-29T13:51:49Z No. of bitstreams: 1 bellettini_paolini_tealdi_SISSAprprint.pdf: 705021 bytes, checksum: 98a550aeb5925de05f6b419569ccd283 (MD5) %R 10.1051/cocv/2014065 %0 Journal Article %J SIGMA Symmetry Integrability Geom. Methods Appl. %D 2016 %T On asymptotic regimes of orthogonal polynomials with complex varying quartic exponential weight %A Marco Bertola %A Alexander Tovbis %B SIGMA Symmetry Integrability Geom. Methods Appl. %V 12 %P Paper No. 118, 50 pages %G eng %U http://dx.doi.org/10.3842/SIGMA.2016.118 %R 10.3842/SIGMA.2016.118 %0 Journal Article %J ARCHIVE OF NUMERICAL SOFTWARE %D 2016 %T The deal.II Library, Version 8.3 %A Wolfgang Bangerth %A Timo Heister %A Luca Heltai %A G. Kanschat %A Martin Kronbichler %A Matthias Maier %A Bruno Turcksin %B ARCHIVE OF NUMERICAL SOFTWARE %V 4 %P 1–11 %G eng %U http://nbn-resolving.de/urn:nbn:de:bsz:16-ans-231226 %R 10.11588/ans.2016.100.23122 %0 Journal Article %J JOURNAL OF NUMERICAL MATHEMATICS %D 2016 %T The deal.II library, Version 8.4 %A Wolfgang Bangerth %A Denis Davydov %A Timo Heister %A Luca Heltai %A G. Kanschat %A Martin Kronbichler %A Matthias Maier %A Bruno Turcksin %A David Wells %B JOURNAL OF NUMERICAL MATHEMATICS %V 24 %P 135–141 %G eng %U https://www.math.clemson.edu/ heister/preprints/deal84-preprint.pdf %R 10.1515/jnma-2016-1045 %0 Journal Article %J Journal of High Energy Physics %D 2016 %T Exact results for N=2 supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants %A Mikhail Bershtein %A Giulio Bonelli %A Massimiliano Ronzani %A Alessandro Tanzini %X

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.

%B Journal of High Energy Physics %V 2016 %P 23 %8 Jul %G eng %U https://doi.org/10.1007/JHEP07(2016)023 %R 10.1007/JHEP07(2016)023 %0 Journal Article %J Calculus of Variations and Partial Differential Equations %D 2016 %T Fracture models for elasto-plastic materials as limits of gradient damage models coupled with plasticity: the antiplane case %A Gianni Dal Maso %A Gianluca Orlando %A Rodica Toader %X

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.

%B Calculus of Variations and Partial Differential Equations %V 55 %P 45 %8 Apr %G eng %U https://doi.org/10.1007/s00526-016-0981-z %R 10.1007/s00526-016-0981-z %0 Journal Article %J International Journal of Mathematics %D 2016 %T A Frobenius theorem for corank-1 continuous distributions in dimensions two and three %A Stefano Luzzatto %A Sina Türeli %A Khadim Mbacke War %X

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.

%B International Journal of Mathematics %V 27 %P 1650061 %G eng %U https://doi.org/10.1142/S0129167X16500610 %R 10.1142/S0129167X16500610 %0 Journal Article %J Dynamical Systems %D 2016 %T Integrability of C1 invariant splittings %A Stefano Luzzatto %A Sina Türeli %A Khadim Mbacke War %X

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.

%B Dynamical Systems %I Taylor & Francis %V 31 %P 79-88 %G eng %U https://doi.org/10.1080/14689367.2015.1057480 %R 10.1080/14689367.2015.1057480 %0 Journal Article %J Proc. A. %D 2016 %T Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation %A Marco Bertola %A Gennady El %A Alexander Tovbis %B Proc. A. %V 472 %P 20160340, 12 %G eng %U http://dx.doi.org/10.1098/rspa.2016.0340 %R 10.1098/rspa.2016.0340 %0 Journal Article %J Journal of Mathematical Analysis and Applications %D 2016 %T On Sobolev instability of the interior problem of tomography %A Marco Bertola %A Alexander Katsevich %A Alexander Tovbis %B Journal of Mathematical Analysis and Applications %G eng %0 Journal Article %J Journal of High Energy Physics %D 2016 %T Symmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index %A Benvenuti, Sergio %A Giulio Bonelli %A Massimiliano Ronzani %A Alessandro Tanzini %X

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.

%B Journal of High Energy Physics %V 2016 %P 53 %8 Sep %G eng %U https://doi.org/10.1007/JHEP09(2016)053 %R 10.1007/JHEP09(2016)053 %0 Journal Article %D 2015 %T Anisotropic mean curvature on facets and relations with capillarity %A Stefano Amato %A Lucia Tealdi %A Giovanni Bellettini %X

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.

%I de Gruyter %G en_US %U http://urania.sissa.it/xmlui/handle/1963/34481 %1 34663 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Stefano Amato (samato@sissa.it) on 2015-08-06T08:33:21Z No. of bitstreams: 1 amato_bellettini_tealdi.pdf: 561517 bytes, checksum: ee2370b8b8ae04078e1e8eae84d37bdd (MD5) %R 10.1515/geofl-2015-0005 %0 Journal Article %J Constr. Approx. %D 2015 %T Asymptotics of orthogonal polynomials with complex varying quartic weight: global structure, critical point behavior and the first Painlevé equation %A Marco Bertola %A Alexander Tovbis %B Constr. Approx. %V 41 %P 529–587 %G eng %U http://dx.doi.org/10.1007/s00365-015-9288-0 %R 10.1007/s00365-015-9288-0 %0 Report %D 2015 %T A class of Hamiltonians for a three-particle fermionic system at unitarity %A Michele Correggi %A Gianfausto Dell'Antonio %A Domenico Finco %A Alessandro Michelangeli %A Alessandro Teta %X 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. %G en %U http://urania.sissa.it/xmlui/handle/1963/34469 %1 34644 %2 Mathematics %4 1 %$ Submitted by Alessandro Michelangeli (alemiche@sissa.it) on 2015-05-21T06:33:20Z No. of bitstreams: 1 SISSA_preprint_22-2015-MATE.pdf: 438261 bytes, checksum: ca05e5e2c5d78d87225a11073cb09d47 (MD5) %0 Journal Article %J Archive of Numerical Software, vol. 3, n. 100, (2015), pages : 1-8 %D 2015 %T The deal.II Library, Version 8.2 %A Wolfgang Bangerth %A Timo Heister %A Luca Heltai %A G. Kanschat %A Martin Kronbichler %A Matthias Maier %A Bruno Turcksin %A T. D. Young %X This paper provides an overview of the new features of the finite element library deal.II version 8.2 %B Archive of Numerical Software, vol. 3, n. 100, (2015), pages : 1-8 %G en %U http://urania.sissa.it/xmlui/handle/1963/34464 %1 34637 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Luca Heltai (heltai@sissa.it) on 2015-04-20T15:40:46Z No. of bitstreams: 1 18031-44567-1-PB (1).pdf: 137014 bytes, checksum: 9a5fddeccfa389c32ca89a466e653074 (MD5) %R 10.11588/ans.2015.100.18031 %0 Report %D 2015 %T Existence for constrained dynamic Griffith fracture with a weak maximal dissipation condition %A Gianni Dal Maso %A Cristopher J. Larsen %A Rodica Toader %X 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. %G en %U http://urania.sissa.it/xmlui/handle/1963/35045 %1 35277 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2015-11-18T15:46:32Z No. of bitstreams: 1 DM-Lar-Toa-SISSA.pdf: 313034 bytes, checksum: 76419fd2c8c435ae7deeca773b424667 (MD5) %0 Conference Paper %B International Conference on Parallel Processing and Applied Mathematics %D 2015 %T Experience on vectorizing lattice Boltzmann kernels for multi-and many-core architectures %A Calore, Enrico %A Nicola Demo %A Schifano, Sebastiano Fabio %A Tripiccione, Raffaele %B International Conference on Parallel Processing and Applied Mathematics %I Springer %P 53–62 %G eng %0 Thesis %D 2015 %T Integrability of Continuous Tangent Sub-bundles %A Sina Türeli %K Dynamical Systems, Global Analysis, Frobenius Theorem, Integrability %X 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. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/34630 %1 34833 %2 Mathematics %# MAT/05 %$ Submitted by stureli@sissa.it (stureli@sissa.it) on 2015-10-13T01:32:04Z No. of bitstreams: 1 thesis-sina-tureli-2015.pdf: 526450 bytes, checksum: 9ff71f05dd4ee459ef37ff150ebb272e (MD5) %0 Journal Article %J Anal. Math. Phys. %D 2015 %T Meromorphic differentials with imaginary periods on degenerating hyperelliptic curves %A Marco Bertola %A Alexander Tovbis %B Anal. Math. Phys. %V 5 %P 1–22 %G eng %U http://dx.doi.org/10.1007/s13324-014-0088-7 %R 10.1007/s13324-014-0088-7 %0 Journal Article %J Journal of High Energy Physics %D 2015 %T N=2 supersymmetric gauge theories on S^2xS^2 and Liouville Gravity %A Aditya Bawane %A Giulio Bonelli %A Massimiliano Ronzani %A Alessandro Tanzini %X

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.

%B Journal of High Energy Physics %V 2015 %P 54 %8 Jul %G eng %U https://doi.org/10.1007/JHEP07(2015)054 %R 10.1007/JHEP07(2015)054 %0 Journal Article %D 2015 %T The phototransduction machinery in the rod outer segment has a strong efficacy gradient %A Monica Mazzolini %A Giuseppe Facchetti %A L. Andolfi %A R. Proietti Zaccaria %A S. Tuccio %A J. Treud %A Claudio Altafini %A Enzo M. Di Fabrizio %A Marco Lazzarino %A G. Rapp %A Vincent Torre %I National Academy of Sciences %G en %U http://urania.sissa.it/xmlui/handle/1963/35157 %1 35382 %2 Neuroscience %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2016-01-21T09:29:28Z (GMT) No. of bitstreams: 0 %R 10.1073/pnas.1423162112 %0 Thesis %D 2015 %T The relaxed area of maps from the plane to the plane with a line discontinuity, and the role of semicartesian surfaces. %A Lucia Tealdi %K Area functional %X 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. %I SISSA %G en %1 34732 %4 1 %# MAT/05 %$ Submitted by Lucia Tealdi (ltealdi@sissa.it) on 2015-09-21T12:23:44Z No. of bitstreams: 1 Tealdi_PhD_thesis.pdf: 917244 bytes, checksum: a6bfc90b8457a030be4c7314ee1f426f (MD5) %0 Report %D 2015 %T Results on the minimization of the Dirichlet functional among semicartesian parametrizations %A Lucia Tealdi %A Giovanni Bellettini %A Maurizio Paolini %X

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.

%G en %U http://urania.sissa.it/xmlui/handle/1963/34488 %1 34671 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Lucia Tealdi (ltealdi@sissa.it) on 2015-08-07T16:12:37Z No. of bitstreams: 1 bellettini_paolini_tealdi_semicart.pdf: 338138 bytes, checksum: c689a5b64d30dc600fe0429b72996c7d (MD5) %0 Report %D 2015 %T Semicartesian surfaces and the relaxed area of maps from the plane to the plane with a line discontinuity %A Lucia Tealdi %A Giovanni Bellettini %A Maurizio Paolini %X

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.

%G en %U http://urania.sissa.it/xmlui/handle/1963/34483 %1 34670 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Lucia Tealdi (ltealdi@sissa.it) on 2015-08-07T16:06:48Z No. of bitstreams: 1 bellettini_paolini_tealdi_semicartesian.pdf: 623410 bytes, checksum: 871f66c4686a39ad7d1bc996f0e2b0aa (MD5) %0 Journal Article %D 2014 %T Discrete one-dimensional crawlers on viscous substrates: achievable net displacements and their energy cost %A Giovanni Noselli %A Amabile Tatone %A Antonio DeSimone %K Cell migration %X We study model one-dimensional crawlers, namely, model mechanical systems that can achieve self-propulsion by controlled shape changes of their body (extension or contraction of portions of the body), thanks to frictional interactions with a rigid substrate. We evaluate the achievable net displacement and the related energetic cost for self-propulsion by discrete crawlers (i.e., whose body is made of a discrete number of contractile or extensile segments) moving on substrates with either a Newtonian (linear) or a Bingham-type (stick-slip) rheology. Our analysis is aimed at constructing the basic building blocks towards an integrative, multi-scale description of crawling cell motility. %I Elsevier %G en %U http://urania.sissa.it/xmlui/handle/1963/34449 %1 34591 %2 Mathematics %$ Submitted by gnoselli@sissa.it (gnoselli@sissa.it) on 2015-03-07T17:44:40Z No. of bitstreams: 1 N-link_crawlers.pdf: 1005838 bytes, checksum: 685d5b41e7de190ec65c60090d397f93 (MD5) %R 10.1016/j.mechrescom.2013.10.023 %0 Journal Article %D 2014 %T Laplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length %A Gianni Dal Maso %A Gianluca Orlando %A Rodica Toader %K cracked domains, energy release rate, higher order derivatives, asymptotic expansion of solutions %X

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.

%I SISSA %G en %U http://hdl.handle.net/1963/7271 %1 7316 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2014-03-11T15:17:50Z No. of bitstreams: 1 DM-Orl-Toa-sissa.pdf: 251851 bytes, checksum: 59273a217a11dcfc5a9ed89d2c34c6cd (MD5) %R 10.1007/s00030-014-0291-0 %0 Journal Article %D 2014 %T Pfaffian representations of cubic surfaces %A Fabio Tanturri %X

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.

%I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34688 %1 34900 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-10-21T16:49:49Z No. of bitstreams: 1 preprint2014.pdf: 289546 bytes, checksum: 0a8213f23936fd48edde60b3d788f158 (MD5) %R 10.1007/s10711-012-9818-x %0 Journal Article %J Nonlinear Analysis %D 2014 %T Quasi-static crack growth in hydraulic fracture %A Stefano Almi %A Gianni Dal Maso %A Rodica Toader %X

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.

%B Nonlinear Analysis %I Elsevier %V 109 %P 301-318 %G en %U http://hdl.handle.net/20.500.11767/17350 %N Nov %9 Journal article %1 34741 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by salmi@sissa.it (salmi@sissa.it) on 2015-09-24T08:10:23Z No. of bitstreams: 1 A-DM-T-070714.pdf: 283645 bytes, checksum: 68056ef27e9dcfa246029148c0016c0f (MD5) %& 301 %R 10.1016/j.na.2014.07.009 %0 Report %D 2014 %T Rate-independent damage in thermo-viscoelastic materials with inertia %A Giuliano Lazzaroni %A Riccarda Rossi %A Marita Thomas %A Rodica Toader %X 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. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/7444 %1 7542 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-10-15T09:00:07Z No. of bitstreams: 1 LRTT-SISSA-preprint-14_10_15.pdf: 498065 bytes, checksum: 0de0c4a77dafb5df12747fd9947cec5c (MD5) %0 Journal Article %J Comm. Pure Appl. Math. %D 2014 %T Singular Value Decomposition of a Finite Hilbert Transform Defined on Several Intervals and the Interior Problem of Tomography: The Riemann-Hilbert Problem Approach %A Marco Bertola %A Alexander Katsevich %A Alexander Tovbis %B Comm. Pure Appl. Math. %G eng %0 Journal Article %D 2014 %T Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics %A Giulio Bonelli %A Antonio Sciarappa %A Alessandro Tanzini %A Petr Vasko %X 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. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34546 %1 34771 %2 Physics %4 2 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-09-28T10:16:32Z No. of bitstreams: 1 art2014.pdf: 600092 bytes, checksum: 8a020f470fff4ce83b5d820436def73f (MD5) %R 10.1007/JHEP07(2014)141 %0 Report %D 2014 %T Some remarks on a model for rate-independent damage in thermo-visco-elastodynamics %A Giuliano Lazzaroni %A Riccarda Rossi %A Marita Thomas %A Rodica Toader %X 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. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/7463 %1 7566 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-10-23T09:01:52Z No. of bitstreams: 1 MURPHYS_LRTT14_SISSA-preprint(1).pdf: 246259 bytes, checksum: a67369f4eab98d39fb2165d882d97592 (MD5) %0 Journal Article %D 2014 %T The stringy instanton partition function %A Giulio Bonelli %A Antonio Sciarappa %A Alessandro Tanzini %A Petr Vasko %X 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. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34589 %1 34796 %2 Physics %4 2 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-09-28T14:48:41Z No. of bitstreams: 1 art2014.pdf: 719350 bytes, checksum: 2c296ad8eb7995f07c16f6d4e36c6813 (MD5) %R 10.1007/JHEP01(2014)038 %0 Journal Article %D 2014 %T A variational model for the quasi-static growth of fractional dimensional brittle fractures %A Simone Racca %A Rodica Toader %K Variational models %X

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.

%I European Mathematical Society %G en %U http://hdl.handle.net/1963/6983 %1 6973 %2 Mathematics %4 -1 %$ Submitted by Simone Racca (sracca@sissa.it) on 2013-07-18T08:39:00Z No. of bitstreams: 1 Racca_Toader.pdf: 416939 bytes, checksum: cf459548a10944037e56b7504fe60f51 (MD5) %R 10.4171/IFB/328 %0 Journal Article %D 2014 %T Vortex Partition Functions, Wall Crossing and Equivariant Gromov–Witten Invariants %A Giulio Bonelli %A Antonio Sciarappa %A Alessandro Tanzini %A Petr Vasko %X 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. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34652 %1 34859 %2 Physics %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-10-20T12:25:03Z No. of bitstreams: 1 preprint2014.pdf: 652465 bytes, checksum: 355132ee06625045b6adf8b1f4862533 (MD5) %R 10.1007/s00220-014-2193-8 %0 Report %D 2014 %T Where best to place a Dirichlet condition in an anisotropic membrane? %A Paolo Tilli %A Davide Zucco %X 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. %I SISSA %G en_US %U http://urania.sissa.it/xmlui/handle/1963/7481 %1 7592 %$ Submitted by dzucco@sissa.it (dzucco@sissa.it) on 2014-11-07T16:09:28Z No. of bitstreams: 1 Tilli_Zucco_varifold.pdf: 379650 bytes, checksum: 341cfa2d9d25e41789652de4c99c22fe (MD5) %0 Journal Article %D 2013 %T Asymptotics of the first Laplace eigenvalue with Dirichlet regions of prescribed length %A Paolo Tilli %A Davide Zucco %X 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. %I Society for Industrial and Applied Mathematics %G en %U http://urania.sissa.it/xmlui/handle/1963/35141 %1 35379 %2 Physics %4 1 %# MAT/05 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-12-09T16:12:39Z (GMT) No. of bitstreams: 0 %R 10.1137/130916825 %0 Journal Article %J Nature. Scientific Reports 3, Article number: 1251, Published : 13 February 2013 %D 2013 %T Common dynamical features of sensory adaptation in photoreceptors and olfactory sensory neurons. %A Giovanna De Palo %A Giuseppe Facchetti %A Monica Mazzolini %A Anna Menini %A Vincent Torre %A Claudio Altafini %X

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.

%B Nature. Scientific Reports 3, Article number: 1251, Published : 13 February 2013 %I SISSA %G en %1 6453 %2 Mathematics %4 1 %$ Submitted by Claudio Altafini (altafini@sissa.it) on 2013-02-27T14:00:21Z\nNo. of bitstreams: 0 %R 10.1038/srep01251 %0 Journal Article %J International Journal of Non-Linear Mechanics 56, 142-147 (2013) %D 2013 %T Crawlers in viscous environments: linear vs nonlinear rheology %A Antonio DeSimone %A Federica Guarnieri %A Giovanni Noselli %A Amabile Tatone %X 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. %B International Journal of Non-Linear Mechanics 56, 142-147 (2013) %I Elsevier %G en %1 34590 %2 Mathematics %$ Submitted by gnoselli@sissa.it (gnoselli@sissa.it) on 2015-03-07T17:29:52Z No. of bitstreams: 1 viscous_crawlers.pdf: 887755 bytes, checksum: 6022e4160d2eced97b51326bf51e0827 (MD5) %R 10.1016/j.ijnonlinmec.2013.02.007 %0 Report %D 2013 %T The deal.II Library, Version 8.1 %A Wolfgang Bangerth %A Timo Heister %A Luca Heltai %A G. Kanschat %A Martin Kronbichler %A Matthias Maier %A Bruno Turcksin %A T. D. Young %X This paper provides an overview of the new features of the finite element library deal.II version 8.0. %I SISSA %G en %U http://hdl.handle.net/1963/7236 %1 7272 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Luca Heltai (heltai@sissa.it) on 2013-12-10T10:43:08Z No. of bitstreams: 1 1312.2266v1.pdf: 245445 bytes, checksum: e00fcd6d7d9ac6e2076208958b07eef3 (MD5) %0 Journal Article %J PloS one. Volume 8, Issue 7, July 2013 : e68078 %D 2013 %T Early phase of plasticity-related gene regulation and SRF dependent transcription in the hippocampus %A Giovanni Iacono %A Claudio Altafini %A Vincent Torre %X 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. %B PloS one. Volume 8, Issue 7, July 2013 : e68078 %I Public Library of Science %G en %U http://hdl.handle.net/1963/7287 %1 7332 %2 Neuroscience %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-03-14T11:26:18Z No. of bitstreams: 1 journal.pone.0068078.pdf: 1188661 bytes, checksum: 29e83864b33fd1a072fe4ab4da6fcc17 (MD5) %R 10.1371/journal.pone.0068078 %0 Journal Article %J Proc. Amer. Math. Soc. %D 2013 %T Inversion formulae for the $\romancosh$-weighted Hilbert transform %A Marco Bertola %A Katsevich, A. %A Alexander Tovbis %B Proc. Amer. Math. Soc. %V 141 %P 2703–2718 %G eng %U http://dx.doi.org/10.1090/S0002-9939-2013-11642-4 %R 10.1090/S0002-9939-2013-11642-4 %0 Report %D 2013 %T N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae %A Giulio Bonelli %A Kazunobu Maruyoshi %A Alessandro Tanzini %A Futoshi Yagi %X 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. %I SISSA %G en %U http://hdl.handle.net/1963/6577 %1 6522 %2 Mathematics %4 -1 %$ Submitted by Alessandro Tanzini (tanzini@sissa.it) on 2013-04-04T10:00:01Z\nNo. of bitstreams: 1\n1208.0790v4.pdf: 372527 bytes, checksum: 5fae7067b646df2fca0b20daa82b5cff (MD5) %0 Journal Article %D 2013 %T Nonabelian Lie algebroid extensions %A Ugo Bruzzo %A Igor Mencattini %A Pietro Tortella %A Vladimir Rubtsov %K Lie algebroids, nonabelian extensions, spectral sequences %X

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 $d_2$

%G en %1 7293 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Ugo Bruzzo (bruzzo@sissa.it) on 2014-02-14T14:16:47Z No. of bitstreams: 1 nonabelian-9.pdf: 401046 bytes, checksum: 3ebfee7dd06925fea31100611bc7e2ca (MD5) %0 Journal Article %J Discrete Contin. Dyn. Syst. Ser. S %D 2013 %T Some remarks on the viscous approximation of crack growth %A Giuliano Lazzaroni %A Rodica Toader %K Variational models %X

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.

%B Discrete Contin. Dyn. Syst. Ser. S %I SISSA %V 6 %G en %U http://hdl.handle.net/1963/4206 %1 3945 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-23T10:54:36Z No. of bitstreams: 1 Lazzaroni_Toader_24_M.pdf: 225564 bytes, checksum: 4c5000d79e83902639a8efb34ba9c0c8 (MD5) %& 131-146 %0 Journal Article %J IEEE Transactions on Automatic Control. Volume 58, Issue 1, 2013, Article number6228517, Pages 74-85 %D 2013 %T Stabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control %A Claudio Altafini %A Francesco Ticozzi %A K. Nishio %X 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 %B IEEE Transactions on Automatic Control. Volume 58, Issue 1, 2013, Article number6228517, Pages 74-85 %G en %U http://hdl.handle.net/1963/6503 %1 6448 %2 Mathematics %4 1 %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-02-27T15:06:12Z (GMT) No. of bitstreams: 0 %R 10.1109/TAC.2012.2206713 %0 Report %D 2013 %T Symplectic instanton bundles on P3 and 't Hooft instantons %A Ugo Bruzzo %A Dimitri Markushevich %A Alexander Tikhomirov %X 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. %I arXiv:1312.5554 [math.AG] %G en %U http://urania.sissa.it/xmlui/handle/1963/34486 %1 34675 %2 Mathematics %4 1 %# MAT/03 %$ Submitted by Ugo Bruzzo (bruzzo@sissa.it) on 2015-08-07T20:57:05Z No. of bitstreams: 1 Symplectic_instantons_II-rev-dec2014.pdf: 340035 bytes, checksum: 8d0a2dfeea126810645c06e8b6352903 (MD5) %0 Journal Article %J Comm. Pure Appl. Math. %D 2013 %T Universality for the focusing nonlinear Schrödinger equation at the gradient catastrophe point: rational breathers and poles of the \it Tritronquée solution to Painlevé I %A Marco Bertola %A Alexander Tovbis %B Comm. Pure Appl. Math. %V 66 %P 678–752 %G eng %U http://dx.doi.org/10.1002/cpa.21445 %R 10.1002/cpa.21445 %0 Journal Article %J The European Physical Journal E, Volume 35, Issue 9, September 2012, Article number85 %D 2012 %T Crawling motility through the analysis of model locomotors: two case studies %A Antonio DeSimone %A Amabile Tatone %X 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. %B The European Physical Journal E, Volume 35, Issue 9, September 2012, Article number85 %I Springer %G en %U http://hdl.handle.net/1963/7017 %1 7014 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-08-12T11:01:46Z No. of bitstreams: 0 %R 10.1140/epje/i2012-12085-x %0 Journal Article %J Lett. Math. Phys. 101 (2012) 103-124 %D 2012 %T Gauge Theories on ALE Space and Super Liouville Correlation Functions %A Giulio Bonelli %A Kazunobu Maruyoshi %A Alessandro Tanzini %X 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. %B Lett. Math. Phys. 101 (2012) 103-124 %I SISSA %G en %U http://hdl.handle.net/1963/4305 %1 4068 %2 Physics %3 Elementary Particle Theory %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-28T07:00:50Z\\r\\nNo. of bitstreams: 1\\r\\n1107.4609v1.pdf: 256160 bytes, checksum: f34c8fc8ed919adff7b4d65312b81db1 (MD5) %R 10.1007/s11005-012-0553-x %0 Journal Article %J IEEE Transactions on Automatic Control. Volume 57, Issue 8, 2012, Article number6189035, Pages 1898-1917 %D 2012 %T Modeling and control of quantum systems: An introduction %A Claudio Altafini %A Francesco Ticozzi %X 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 %B IEEE Transactions on Automatic Control. Volume 57, Issue 8, 2012, Article number6189035, Pages 1898-1917 %I Institute of Electrical and Electronics Engineers %G en %U http://hdl.handle.net/1963/6505 %1 6449 %2 Mathematics %4 1 %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-02-27T15:32:35Z (GMT) No. of bitstreams: 0 %R 10.1109/TAC.2012.2195830 %0 Journal Article %J Central European Journal of Mathematics 10, nr. 4 (2012) 1232 %D 2012 %T Moduli of symplectic instanton vector bundles of higher rank on projective space $\\mathbbP^3$ %A Ugo Bruzzo %A Dimitri Markushevich %A Alexander Tikhomirov %X 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 $4n(r+1)-r(2r+1)$. %B Central European Journal of Mathematics 10, nr. 4 (2012) 1232 %I SISSA %G en %U http://hdl.handle.net/1963/4656 %1 4406 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-10-10T09:47:24Z\r\nNo. of bitstreams: 1\r\n1109.2292v1.pdf: 243006 bytes, checksum: 39feac60657ccc939b3d688db3738e0e (MD5) %R 10.2478/s11533-012-0062-2 %0 Journal Article %J Siam Journal on Mathematical Analysis %D 2012 %T SBV regularity for Hamilton-Jacobi equations with Hamiltonian depending on (t,x) %A Stefano Bianchini %A Daniela Tonon %B Siam Journal on Mathematical Analysis %I SISSA %V 44 %P 2179-2203 %G en %U http://hdl.handle.net/20.500.11767/14066 %N 3 %1 3890 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-20T13:28:47Z\r\nNo. of bitstreams: 1\r\nBianchini_Tonon_13M.pdf: 249849 bytes, checksum: 461aecb2ce41d2bff011ba0062ed1cfb (MD5) %R 10.1137/110827272 %0 Journal Article %J Journal of Mathematical Analysis and Applications %D 2012 %T SBV-like regularity for Hamilton-Jacobi equations with a convex Hamiltonian %A Stefano Bianchini %A Daniela Tonon %B Journal of Mathematical Analysis and Applications %I SISSA %V 391 %P 190-208 %G en %U http://hdl.handle.net/20.500.11767/13909 %N 1 %1 4352 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-10-07T11:24:37Z\\r\\nNo. of bitstreams: 1\\r\\n45M_Tonon_Bianchini.pdf: 179519 bytes, checksum: c157fc19ae52c2fb8bcd2ca28815d26e (MD5) %R 10.1016/j.jmaa.2012.02.017 %0 Journal Article %J Riv. Mat. Univ. Parma %D 2012 %T Some applications of the SBV Regularity Theorem for entropy solutions of 1D scalar conservation laws to ConvectionTheory and sticky particles %A Daniela Tonon %X

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.

%B Riv. Mat. Univ. Parma %V 3 %P 163–175 %G eng %U https://hal.archives-ouvertes.fr/hal-00918409 %0 Journal Article %J Rev. Math. Phys. 24 (2012), 1250017 %D 2012 %T Stability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions %A Michele Correggi %A Gianfausto Dell'Antonio %A Domenico Finco %A Alessandro Michelangeli %A Alessandro Teta %X 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. %B Rev. Math. Phys. 24 (2012), 1250017 %I World Scientific %G en %U http://hdl.handle.net/1963/6069 %1 5955 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-08-02T07:19:59Z\\nNo. of bitstreams: 1\\n1201.5740v1.pdf: 303047 bytes, checksum: eb2df0afd547514c235422e82f494584 (MD5) %R 10.1142/S0129055X12500171 %0 Journal Article %J JHEP 06(2012)178 %D 2012 %T Vertices, vortices & interacting surface operators %A Giulio Bonelli %A Alessandro Tanzini %A Zhao Jian %X 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. %B JHEP 06(2012)178 %I SISSA %G en %U http://hdl.handle.net/1963/4134 %1 3874 %2 Physics %3 Elementary Particle Theory %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-15T08:59:30Z\\r\\nNo. of bitstreams: 1\\r\\n1102.0184v1.pdf: 250685 bytes, checksum: b0209b95cc58d31e3cd28c41cd8b0f25 (MD5) %R 10.1007/JHEP06(2012)178 %0 Journal Article %J JHEP 02(2012)031 %D 2012 %T Wild quiver gauge theories %A Giulio Bonelli %A Kazunobu Maruyoshi %A Alessandro Tanzini %X

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.

%B JHEP 02(2012)031 %I SISSA %G en %U http://hdl.handle.net/1963/5184 %1 4999 %2 Physics %3 Elementary Particle Theory %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-12-12T14:57:36Z\\r\\nNo. of bitstreams: 1\\r\\n1112.1691v1.pdf: 374306 bytes, checksum: d108d1f4f381124a4ff917b4c621f359 (MD5) %R 10.1007/JHEP02(2012)031 %0 Journal Article %J IET systems biology. 2011 Jul; 5(4):269-79 %D 2011 %T Adaptation as a genome-wide autoregulatory principle in the stress response of yeast. %A F Eduati %A B Di Camillo %A G Toffolo %A Claudio Altafini %A Giovanna De Palo %A Mattia Zampieri %X 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. %B IET systems biology. 2011 Jul; 5(4):269-79 %I The Institution of Engineering and Technology %G en %U http://hdl.handle.net/1963/5106 %1 4922 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-11-25T13:05:49Z\\r\\nNo. of bitstreams: 1\\r\\nDePaEdal10.pdf: 2390366 bytes, checksum: f6550b1052efeb53942e47cae9632899 (MD5) %R 10.1049/iet-syb.2009.0050 %0 Journal Article %J Le Matematiche 66 (2011) 137-151 %D 2011 %T Covered by lines and Conic connected varieties %A Simone Marchesi %A Alex Massarenti %A Saeed Tafazolian %X 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. %B Le Matematiche 66 (2011) 137-151 %I Universita\\\' di Catania, Dipartimento di Matematica e Informatica %G en %U http://hdl.handle.net/1963/5788 %1 5641 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-05-03T14:43:36Z\\nNo. of bitstreams: 2\\n1105.5918v2.pdf: 279 bytes, checksum: a3b0f104eb894295409bae95af5b2e16 (MD5)\\n844-3335-1-PB.pdf: 186181 bytes, checksum: b32fc90e8bb7277d82a3c3705174e89a (MD5) %R 10.4418/2011.66.2.12 %0 Journal Article %J Communications on Pure and Applied Analysis %D 2011 %T A Decomposition Theorem for BV functions %A Stefano Bianchini %A Daniela Tonon %B Communications on Pure and Applied Analysis %I American Institute of Mathematical Sciences %V 10 %P 1549-1566 %G en_US %U http://hdl.handle.net/20.500.11767/14599 %N 6 %1 693 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-04-07T15:11:02Z\\r\\nNo. of bitstreams: 1\\r\\narticoloBV-preprint.pdf: 278021 bytes, checksum: db1d8f4c30a60313b69e105977010165 (MD5) %R 10.3934/cpaa.2011.10.1549 %0 Journal Article %J Journal de Mathematiques Pures et Appliquees 95 (2011) 565-584 %D 2011 %T Energy release rate and stress intensity factor in antiplane elasticity %A Giuliano Lazzaroni %A Rodica Toader %X 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. %B Journal de Mathematiques Pures et Appliquees 95 (2011) 565-584 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3780 %1 546 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-11-17T11:50:32Z\\r\\nNo. of bitstreams: 2\\r\\nLazzaroni_67M_2009.pdf: 259616 bytes, checksum: 3c3adef52607bc6238c11a84904a9fb9 (MD5)\\r\\nLazzaroni_67M_2009: 259616 bytes, checksum: 3c3adef52607bc6238c11a84904a9fb9 (MD5) %R 10.1016/j.matpur.2011.01.001 %0 Journal Article %J JHEP, Volume 2011, Issue 7, 2011, Article number055 %D 2011 %T Generalized matrix models and AGT correspondence at all genera %A Giulio Bonelli %A Kazunobu Maruyoshi %A Alessandro Tanzini %A Futoshi Yagib %X 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. %B JHEP, Volume 2011, Issue 7, 2011, Article number055 %I SISSA %G en %U http://hdl.handle.net/1963/6568 %1 6530 %2 Mathematics %4 1 %$ Submitted by Alessandro Tanzini (tanzini@sissa.it) on 2013-04-04T10:07:44Z\nNo. of bitstreams: 1\n1011.5417v2.pdf: 288213 bytes, checksum: 4ffb3884bb05de0280c0f8a0dc7847ab (MD5) %R 10.1007/JHEP07(2011)055 %0 Report %D 2011 %T Instantons on ALE spaces and Super Liouville Conformal Field Theories %A Giulio Bonelli %A Kazunobu Maruyoshi %A Alessandro Tanzini %X 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). %I SISSA %G en %U http://hdl.handle.net/1963/4262 %1 3987 %2 Physics %3 Elementary Particle Theory %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-26T14:31:56Z\\nNo. of bitstreams: 1\\n1106.2505v1.pdf: 137191 bytes, checksum: 721cf25d724b7aca87a3429a0119e201 (MD5) %0 Journal Article %J JHEP 09(2011)096 %D 2011 %T The Liouville side of the vortex %A Giulio Bonelli %A Alessandro Tanzini %A Jian Zhao %X 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. %B JHEP 09(2011)096 %I SISSA %G en %U http://hdl.handle.net/1963/4304 %1 4019 %2 Physics %3 Elementary Particle Theory %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-27T09:53:04Z\\r\\nNo. of bitstreams: 1\\r\\n1107.2787v1.pdf: 990433 bytes, checksum: 1dc28192f585097bc1e32987afd97aa7 (MD5) %R 10.1007/JHEP09(2011)096 %0 Journal Article %J Continuum Mechanics and Thermodynamics %D 2011 %T Metastable equilibria of capillary drops on solid surfaces: a phase field approach %A Livio Fedeli %A Turco, Alessandro %A Antonio DeSimone %X

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.

%B Continuum Mechanics and Thermodynamics %V 23 %P 453–471 %8 Sep %G eng %U https://doi.org/10.1007/s00161-011-0189-6 %R 10.1007/s00161-011-0189-6 %0 Journal Article %J {MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES} %D 2011 %T A MODEL FOR CRACK PROPAGATION BASED ON VISCOUS APPROXIMATION %A Giuliano Lazzaroni %A Rodica Toader %K Brittle fracture %K Crack propagation %K energy derivative %K energy release rate %K free-discontinuity problems %K Griffith's criterion %K local minimizers %K stress intensity factor} %K vanishing viscosity %K {Variational models %X

{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.}

%B {MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES} %I {WORLD SCIENTIFIC PUBL CO PTE LTD} %C {5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE} %V {21} %P {2019-2047} %8 {OCT} %G eng %9 {Article} %R {10.1142/S0218202511005647} %0 Journal Article %J Communications in Mathematical Physics 304 (2011) 395-409 %D 2011 %T Poincaré polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces %A Ugo Bruzzo %A Rubik Poghossian %A Alessandro Tanzini %X

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.

%B Communications in Mathematical Physics 304 (2011) 395-409 %I Springer %V 304 %P 395-409 %8 06/2011 %G en_US %U http://hdl.handle.net/1963/3738 %N 2 %1 579 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-09-09T09:26:43Z\\r\\nNo. of bitstreams: 1\\r\\nBPT-8.pdf: 250954 bytes, checksum: 984c30f0144339468a97f54d6b22ce05 (MD5) %R 10.1007/s00220-011-1231-z %0 Report %D 2011 %T Quantum Hitchin Systems via beta-deformed Matrix Models %A Giulio Bonelli %A Kazunobu Maruyoshi %A Alessandro Tanzini %X

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.

%I SISSA %G en %U http://hdl.handle.net/1963/4181 %1 3904 %2 Physics %3 Elementary Particle Theory %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-22T10:22:35Z\\nNo. of bitstreams: 1\\n1104.4016v2.pdf: 317021 bytes, checksum: 92bcb534e0e6fdeb2e5c51517f28d510 (MD5) %0 Journal Article %J ESAIM: COCV 17 (2011) 1-27 %D 2011 %T Quasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a Young measures approach %A Filippo Cagnetti %A Rodica Toader %X 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. %B ESAIM: COCV 17 (2011) 1-27 %I Cambridge University Press / EDP Sciences %G en_US %U http://hdl.handle.net/1963/2355 %1 1662 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-11-07T13:38:16Z\\r\\nNo. of bitstreams: 1\\r\\nQuasCrack.pdf: 298737 bytes, checksum: 127034af65efce0ab97317eccb47e76c (MD5) %R 10.1051/cocv/2009037 %0 Journal Article %J J. Geom. Phys. 60 (2010) 417-429 %D 2010 %T Chern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality %A Andrea Brini %A Luca Griguolo %A Domenico Seminara %A Alessandro Tanzini %X 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. %B J. Geom. Phys. 60 (2010) 417-429 %G en_US %U http://hdl.handle.net/1963/2938 %1 1762 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-12T16:01:18Z\\nNo. of bitstreams: 1\\n0809.1610v1.pdf: 287875 bytes, checksum: feadff501b37135585a6f62946b628de (MD5) %R 10.1016/j.geomphys.2009.11.006 %0 Journal Article %J Phys. Lett. B 691 (2010) 111-115 %D 2010 %T Hitchin systems, N=2 gauge theories and W-gravity %A Giulio Bonelli %A Alessandro Tanzini %X 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. %B Phys. Lett. B 691 (2010) 111-115 %G en_US %U http://hdl.handle.net/1963/3831 %1 496 %2 Physics %3 Elementary Particle Theory %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-01-26T15:40:23Z\\nNo. of bitstreams: 1\\n0909.4031.pdf: 120604 bytes, checksum: 7f2242b71035ba7cad650ea81a13d801 (MD5) %R 10.1016/j.physletb.2010.06.027 %0 Report %D 2010 %T Moore-Read Fractional Quantum Hall wavefunctions and SU(2) quiver gauge theories %A Raoul Santachiara %A Alessandro Tanzini %X 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. %G en_US %U http://hdl.handle.net/1963/3852 %1 857 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-03-02T08:00:48Z\\nNo. of bitstreams: 1\\n14_2010_FM.pdf: 390526 bytes, checksum: 871ac8b351d4f1610b0120a9e7a5201a (MD5) %0 Conference Paper %B IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials %D 2010 %T A Phase Field Approach to Wetting and Contact Angle Hysteresis Phenomena %A Antonio DeSimone %A Livio Fedeli %A Turco, Alessandro %E Hackl, Klaus %X

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.

%B IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials %I Springer Netherlands %C Dordrecht %P 51–63 %@ 978-90-481-9195-6 %G eng %0 Journal Article %J Arch. Ration. Mech. Anal. 196 (2010) 867-906 %D 2010 %T Quasistatic crack growth in elasto-plastic materials: the two-dimensional case %A Gianni Dal Maso %A Rodica Toader %X 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. %B Arch. Ration. Mech. Anal. 196 (2010) 867-906 %G en_US %U http://hdl.handle.net/1963/2964 %1 1736 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-23T17:17:34Z\\nNo. of bitstreams: 1\\nDM-Toa-07-preprint.pdf: 320979 bytes, checksum: e4f2a1856f9bd91d63fc45557cbd6a16 (MD5) %R 10.1007/s00205-009-0258-1 %0 Journal Article %J JHEP 06(2010)063 %D 2010 %T Taming open/closed string duality with a Losev trick %A Giulio Bonelli %A Andrea Prudenziati %A Alessandro Tanzini %X 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. %B JHEP 06(2010)063 %G en_US %U http://hdl.handle.net/1963/3855 %1 854 %2 Physics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-04-27T10:19:29Z\\nNo. of bitstreams: 1\\nBonelli_1003.2519v2.pdf: 244116 bytes, checksum: e9e48e420eda839f478ab8a4da3e7136 (MD5) %R 10.1007/JHEP06(2010)063 %0 Journal Article %J Annales Henri Poincare 11 (2010) 539-564 %D 2010 %T A time-dependent perturbative analysis for a quantum particle in a cloud chamber %A Gianfausto Dell'Antonio %A Rodolfo Figari %A Alessandro Teta %X 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. %B Annales Henri Poincare 11 (2010) 539-564 %I Springer %G en_US %U http://hdl.handle.net/1963/3969 %1 432 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-08-05T08:05:00Z\\nNo. of bitstreams: 1\\n0907.5503v1.pdf: 273181 bytes, checksum: 781ee2f8d4ce957ebbfbf866bcc40d2b (MD5) %R 10.1007/s00023-010-0037-4 %0 Report %D 2010 %T Uhlenbeck-Donaldson compactification for framed sheaves on projective surfaces %A Ugo Bruzzo %A Dimitri Markushevich %A Alexander Tikhomirov %X 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. %G en_US %U http://hdl.handle.net/1963/4049 %1 353 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-09-08T08:00:00Z\\nNo. of bitstreams: 1\\nBruzzo59FM.pdf: 496341 bytes, checksum: 3e67e590463152505d393721e3a2c10a (MD5) %0 Journal Article %J Int. Math. Res. Not. IMRN %D 2010 %T Universality in the profile of the semiclassical limit solutions to the focusing nonlinear Schrödinger equation at the first breaking curve %A Marco Bertola %A Alexander Tovbis %B Int. Math. Res. Not. IMRN %P 2119–2167 %G eng %U http://0-dx.doi.org.mercury.concordia.ca/10.1093/imrn/rnp196 %R 10.1093/imrn/rnp196 %0 Journal Article %J BMC Research Notes (2009) 2:13 %D 2009 %T Characterization of the time course of changes of the evoked electrical activity in a model of a chemically-induced neuronal plasticity %A Frederic D. Broccard %A Silvia Pegoraro %A Maria Elisabetta Ruaro %A Claudio Altafini %A Vincent Torre %X 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. %B BMC Research Notes (2009) 2:13 %I BioMed Central %G en_US %U http://hdl.handle.net/1963/3706 %1 599 %2 Neuroscience %3 Neurobiology %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-08-12T11:40:38Z\\nNo. of bitstreams: 1\\n1756-0500-2-13.pdf: 518127 bytes, checksum: 0cd264c3567a0d1776a5141b6dc5ef4e (MD5) %R 10.1186/1756-0500-2-13 %0 Journal Article %J JHEP 06 (2009) 046 %D 2009 %T Decoupling A and B model in open string theory: topological adventures in the world of tadpoles %A Giulio Bonelli %A Andrea Prudenziati %A Alessandro Tanzini %A Yang Jie %X In this paper we analyze the problem of tadpole cancellation in open topological strings. We prove that the inclusion of unorientable worldsheet diagrams guarantees a consistent decoupling of A and B model for open superstring amplitudes at all genera. This is proven by direct microscopic computation in Super Conformal Field Theory. For the B-model we explicitly calculate one loop amplitudes in terms of analytic Ray-Singer torsions of appropriate vector bundles and obtain that the decoupling corresponds to the cancellation of D-brane and orientifold charges. Local tadpole cancellation on the worldsheet then guarantees the decoupling at all loops. The holomorphic anomaly equations for open topological strings at one loop are also obtained and compared with the results of the Quillen formula. %B JHEP 06 (2009) 046 %G en_US %U http://hdl.handle.net/1963/3632 %1 672 %2 Physics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-05-14T12:10:45Z\\nNo. of bitstreams: 1\\n0905.1286v1.pdf: 335944 bytes, checksum: fe5d3723cd904f1c7123c5bc83356013 (MD5) %R 10.1088/1126-6708/2009/06/046 %0 Journal Article %J Comm. Math. Phys. 289 (2009) 205-252 %D 2009 %T Exact results for topological strings on resolved Yp,q singularities %A Andrea Brini %A Alessandro Tanzini %B Comm. Math. Phys. 289 (2009) 205-252 %G en_US %U http://hdl.handle.net/1963/2631 %1 1492 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-04-16T11:13:40Z\\nNo. of bitstreams: 1\\npicard-b.pdf: 387933 bytes, checksum: 2261a0d091c9829eb1d1b55b77b1a42e (MD5) %R 10.1007/s00220-009-0814-4 %0 Journal Article %J Physica D 238 (2009) 55-66 %D 2009 %T Initial value problem of the Whitham equations for the Camassa-Holm equation %A Tamara Grava %A Virgil U. Pierce %A Fei-Ran Tian %X 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. %B Physica D 238 (2009) 55-66 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3429 %1 906 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-13T13:01:16Z\\nNo. of bitstreams: 1\\n0805.2558v1.pdf: 498872 bytes, checksum: 4d721f99d6ae9840be2332f3cc6a4118 (MD5) %R 10.1016/j.physd.2008.08.016 %0 Journal Article %J Phys. Lett. B 672 (2009) 390-395 %D 2009 %T Topological branes, p-algebras and generalized Nahm equations %A Giulio Bonelli %A Alessandro Tanzini %A Maxim Zabzine %X 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 %B Phys. Lett. B 672 (2009) 390-395 %G en_US %U http://hdl.handle.net/1963/2702 %1 1398 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-08-08T15:57:12Z\\nNo. of bitstreams: 1\\n0807.5113v1.pdf: 246583 bytes, checksum: 0013b3623fd81d20db0fb541bd4b9dd4 (MD5) %R 10.1016/j.physletb.2009.01.051 %0 Journal Article %J Boll. Unione Mat. Ital. (9) 1 (2008) 497-505 %D 2008 %T Decomposition results for functions with bounded variation %A Gianni Dal Maso %A Rodica Toader %B Boll. Unione Mat. Ital. (9) 1 (2008) 497-505 %I Unione Matematica Italiana %G en_US %U http://hdl.handle.net/1963/3535 %1 729 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-23T10:23:36Z\\nNo. of bitstreams: 1\\nDM-Toa.pdf: 186814 bytes, checksum: bbc754f60013f0d8fd61b90a278ac837 (MD5) %0 Journal Article %J Phys. Rev. B 77 (2008) 245105 %D 2008 %T Fulde-Ferrell-Larkin-Ovchinnikov pairing in one-dimensional optical lattices %A Matteo Rizzi %A Marco Polini %A Miguel A. Cazalilla %A M.R. Bakhtiari %A Mario P. Tosi %A Rosario Fazio %X

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.

%B Phys. Rev. B 77 (2008) 245105 %G en_US %U http://hdl.handle.net/1963/2694 %1 1406 %2 Physics %3 Condensed Matter Theory %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-07-14T09:46:14Z\\nNo. of bitstreams: 1\\n0712.3364v1.pdf: 305409 bytes, checksum: 13081c375909264afc4c0282b9de9f68 (MD5) %R 10.1103/PhysRevB.77.245105 %0 Report %D 2008 %T Instanton counting on Hirzebruch surfaces %A Ugo Bruzzo %A Rubik Poghossian %A Alessandro Tanzini %X 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. %G en_US %U http://hdl.handle.net/1963/2852 %1 1848 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-05T18:06:43Z\\nNo. of bitstreams: 1\\n0809.0155v1.pdf: 212427 bytes, checksum: f5060bd4e1da6a5215a488041ef018ff (MD5) %0 Journal Article %J Adv. Theor. Math. Phys. 12 (2008) 1429-1446 %D 2008 %T Topological Gauge Theories on Local Spaces and Black Hole Entropy Countings %A Giulio Bonelli %A Alessandro Tanzini %X 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. %B Adv. Theor. Math. Phys. 12 (2008) 1429-1446 %G en_US %U http://hdl.handle.net/1963/1992 %1 2204 %2 Physics %3 Elementary Particle Theory %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-08-09T12:45:15Z\\nNo. of bitstreams: 1\\nhep-th0706.2633v1.pdf: 170115 bytes, checksum: 16cdd3d36705e91d5d429948e55b15a5 (MD5) %0 Report %D 2007 %T Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory %A Luca Griguolo %A Domenico Seminara %A Richard J. Szabo %A Alessandro Tanzini %X 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. %B Nucl. Phys. B 772 (2007) 1-24 %G en_US %U http://hdl.handle.net/1963/1888 %1 2347 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-11-09T10:57:35Z\\nNo. of bitstreams: 1\\nhep-th0610155.pdf: 340757 bytes, checksum: fb3e5bfec5e2a4c15d97a9ca6f2e8a0a (MD5) %R 10.1016/j.nuclphysb.2007.02.030 %0 Report %D 2007 %T The complete one-loop spin chain for N=2 Super-Yang-Mills %A Paolo Di Vecchia %A Alessandro Tanzini %X 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. %G en_US %U http://hdl.handle.net/1963/2309 %1 1707 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-29T14:28:13Z\\nNo. of bitstreams: 1\\n0412283v1.pdf: 110673 bytes, checksum: 9f881078e3eb69765e2c6e294569fd70 (MD5) %0 Report %D 2007 %T Computing Amplitudes in topological M-theory %A Giulio Bonelli %A Alessandro Tanzini %A Maxim Zabzine %X 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. %B JHEP 03 (2007) 023 %G en_US %U http://hdl.handle.net/1963/1901 %1 2335 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-12-07T16:26:28Z\\nNo. of bitstreams: 1\\nhep-th0611327.pdf: 307312 bytes, checksum: 9a3a9891aca40624a44c7a531765695b (MD5) %R 10.1088/1126-6708/2007/03/023 %0 Journal Article %J Eur. Phys. J. E 24 (2007) 303-310 %D 2007 %T Critical voltages and blocking stresses in nematic gels %A Antonio DeSimone %A Antonio Di Carlo %A Luciano Teresi %X 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. %B Eur. Phys. J. E 24 (2007) 303-310 %G en_US %U http://hdl.handle.net/1963/2553 %1 1566 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-01-15T10:18:57Z\\nNo. of bitstreams: 1\\nBlockStress-Preprint.pdf: 477394 bytes, checksum: 8cab00d44de821fc24a7ef2b832ea48c (MD5) %R 10.1140/epje/i2007-10240-2 %0 Journal Article %J JHEP 10 (2007) 060 %D 2007 %T The holomorphic anomaly for open string moduli %A Giulio Bonelli %A Alessandro Tanzini %X 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. %B JHEP 10 (2007) 060 %G en_US %U http://hdl.handle.net/1963/2113 %1 2576 %2 Physics %3 Elementary Particle Theory %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-17T09:24:42Z\\nNo. of bitstreams: 1\\n0708.2627v2.pdf: 199897 bytes, checksum: 38929fe4fa52ddd01dd4af02292f3058 (MD5) %R 10.1088/1126-6708/2007/10/060 %0 Journal Article %J Phys. Rev. Lett. 98 (2007) 030404 %D 2007 %T Luther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas %A Gao Xianlong %A Matteo Rizzi %A Marco Polini %A Rosario Fazio %A Mario P. Tosi %A Vivaldo L. Jr. Campo %A Klaus Capelle %X

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.

%B Phys. Rev. Lett. 98 (2007) 030404 %G en_US %U http://hdl.handle.net/1963/2056 %1 2140 %2 Physics %3 Condensed Matter Theory %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-06T11:46:28Z\\nNo. of bitstreams: 1\\ncond-mat0609346v1.pdf: 218755 bytes, checksum: 06a409d540e05ece03bbac85198ee19c (MD5) %R 10.1103/PhysRevLett.98.030404 %0 Journal Article %J NoDEA 13 (2007) 713-734 %D 2007 %T On a notion of unilateral slope for the Mumford-Shah functional %A Gianni Dal Maso %A Rodica Toader %X 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. %B NoDEA 13 (2007) 713-734 %G en_US %U http://hdl.handle.net/1963/2059 %1 2137 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-06T14:02:51Z\\nNo. of bitstreams: 1\\n0410525v1.pdf: 214576 bytes, checksum: 3722f413401cdb51f778a8c15eeebe71 (MD5) %R 10.1007/s00030-006-4054-4 %0 Report %D 2006 %T Almost Global Stochastic Feedback Stabilization of Conditional Quantum Dynamics %A Claudio Altafini %A Francesco Ticozzi %X 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. %G en_US %U http://hdl.handle.net/1963/1727 %1 2424 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-01-30T12:56:41Z\\nNo. of bitstreams: 1\\nquant-ph0510222.pdf: 574764 bytes, checksum: d53ebd4e4afe123a6476bed544c4b9df (MD5) %0 Report %D 2006 %T An artificial viscosity approach to quasistatic crack growth %A Rodica Toader %A Chiara Zanini %X 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. %G en_US %U http://hdl.handle.net/1963/1850 %1 2367 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-07-26T10:13:38Z\\nNo. of bitstreams: 1\\nmath.AP-0607596.pdf: 297980 bytes, checksum: 7a13d5d5fe36a4577923b3ccd0b0acaf (MD5) %0 Report %D 2006 %T Large Parameter Behavior of Equilibrium Measures %A Tamara Grava %A Fei-Ran Tian %X 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). %B Commun. Math. Sci. 4 (2006) 551-573 %G en_US %U http://hdl.handle.net/1963/1789 %1 2755 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-30T13:50:45Z\\nNo. of bitstreams: 1\\n92FM-2005.pdf: 291341 bytes, checksum: 132e37e5c4fc64315d52903eed85753f (MD5) %0 Report %D 2006 %T N=1 superpotentials from multi-instanton calculus %A Francesco Fucito %A Jose F. Morales %A Rubik Poghossian %A Alessandro Tanzini %X 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. %B JHEP01(2006)031 %G en_US %U http://hdl.handle.net/1963/1773 %1 2771 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-29T07:58:23Z\\nNo. of bitstreams: 1\\n73FM-2005.pdf: 325303 bytes, checksum: 89f205e907378d543e7a51042f437c8a (MD5) %R 10.1088/1126-6708/2006/01/031 %0 Report %D 2006 %T On topological M-theory %A Giulio Bonelli %A Alessandro Tanzini %A Maxim Zabzine %X 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. %B Adv. Theor. Math. Phys. 10 (2006) 239-260 %G en_US %U http://hdl.handle.net/1963/1765 %1 2779 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-23T14:41:22Z\\nNo. of bitstreams: 1\\n64FM.pdf: 240192 bytes, checksum: 3c2a8717b7a8a0d235cc7a6ef9e76369 (MD5) %0 Journal Article %J J. Geom. Phys. 56 (2006) 2379-2401 %D 2006 %T Topological symmetry of forms, N=1 supersymmetry and S-duality on special manifolds %A Laurent Baulieu %A Alessandro Tanzini %X 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. %B J. Geom. Phys. 56 (2006) 2379-2401 %G en_US %U http://hdl.handle.net/1963/2168 %1 2076 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-03T07:58:25Z\\nNo. of bitstreams: 1\\n0412014v2.pdf: 317935 bytes, checksum: a9478cff2fa4dc504efece63810fb6ed (MD5) %R 10.1016/j.geomphys.2005.12.006 %0 Journal Article %J Arch. Ration. Mech. Anal. 176 (2005) 165-225 %D 2005 %T Quasistatic Crack Growth in Nonlinear Elasticity %A Gianni Dal Maso %A Gilles A. Francfort %A Rodica Toader %X 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. %B Arch. Ration. Mech. Anal. 176 (2005) 165-225 %G en_US %U http://hdl.handle.net/1963/2293 %1 1723 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-24T09:12:09Z\\nNo. of bitstreams: 1\\n0401196v1.pdf: 664295 bytes, checksum: cb1000c44e6ae356984e24b55ee97117 (MD5) %R 10.1007/s00205-004-0351-4 %0 Journal Article %J Int. J. Numer. Anal. Met. 29 (2005) 73-101 %D 2005 %T Stress-dilatancy based modelling of granular materials and extensions to soils with crushable grains %A Antonio DeSimone %A Claudio Tamagnini %X 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. %B Int. J. Numer. Anal. Met. 29 (2005) 73-101 %G en_US %U http://hdl.handle.net/1963/2165 %1 2079 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-02T12:02:04Z\\nNo. of bitstreams: 1\\nDeSimoneTamagnini_2005.pdf: 1179767 bytes, checksum: 23b892b2314ea8e2199cc2b2449386b0 (MD5) %R 10.1002/nag.405 %0 Report %D 2005 %T Topological vector symmetry, topological gauge fixing of BRSTQFT and construction of maximal supersymmetry %A Laurent Baulieu %A Guillaume Bossard %A Alessandro Tanzini %X 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. %B JHEP 0508 (2005) 037 %G en_US %U http://hdl.handle.net/1963/1741 %1 2411 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-02-23T10:07:01Z\\nNo. of bitstreams: 1\\nhep-th0504224.pdf: 434040 bytes, checksum: 925f48080ebdefb366d603cd196cba76 (MD5) %R 10.1088/1126-6708/2005/08/037 %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire 21 (2004) 121-137 %D 2004 %T Blow-up solutions for the Schrödinger equation in dimension three with a concentrated nonlinearity %A Riccardo Adami %A Gianfausto Dell'Antonio %A Rodolfo Figari %A Alessandro Teta %X 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. %B Ann. Inst. H. Poincare Anal. Non Lineaire 21 (2004) 121-137 %I Elsevier %G en_US %U http://hdl.handle.net/1963/2998 %1 1335 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-01T10:06:49Z\\nNo. of bitstreams: 1\\nadami.pdf: 209114 bytes, checksum: ea6a7059ff0728c6d55cdc3a16071631 (MD5) %R 10.1016/j.anihpc.2003.01.002 %0 Journal Article %J Quad. Mat. Dip. Mat. Seconda Univ. Napoli 14 (2004) 245-266 %D 2004 %T Quasi-static evolution in brittle fracture: the case of bounded solutions %A Gianni Dal Maso %A Gilles A. Francfort %A Rodica Toader %X 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 $L^\\\\infty$. %B Quad. Mat. Dip. Mat. Seconda Univ. Napoli 14 (2004) 245-266 %G en_US %U http://hdl.handle.net/1963/2229 %1 2015 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-15T15:04:28Z\\r\\nNo. of bitstreams: 1\\r\\n0401198v1.pdf: 166634 bytes, checksum: c21fba2b1fbbaec4fe14c56595b0664e (MD5) %0 Journal Article %J J. Phys. A 37 (2004) 5605-5624 %D 2004 %T Semiclassical analysis of constrained quantum systems %A Gianfausto Dell'Antonio %A Lucattilio Tenuta %X 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. %B J. Phys. A 37 (2004) 5605-5624 %I IOP Publishing %G en_US %U http://hdl.handle.net/1963/2997 %1 1336 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-01T08:52:42Z\\nNo. of bitstreams: 1\\n0312034v2.pdf: 270295 bytes, checksum: ade82e7ba05cc6dbf50709fd277e1323 (MD5) %R 10.1088/0305-4470/37/21/007 %0 Journal Article %D 2003 %T Effective dynamics for Bloch electrons: Peierls substitution and beyond %A Gianluca Panati %A Herbert Spohn %A Stefan Teufel %X 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. %I Springer %G en_US %U http://hdl.handle.net/1963/3040 %1 1293 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-08T12:11:51Z\\nNo. of bitstreams: 1\\n0212041v2.pdf: 395908 bytes, checksum: 7b198d3311402d34945989b8f6edd8b8 (MD5) %0 Journal Article %J J.High Energy Phys. 2003,no.5,054,24 pp. %D 2003 %T Multi-instanton calculus and equivariant cohomology %A Ugo Bruzzo %A Jose F. Morales %A Francesco Fucito %A Alessandro Tanzini %B J.High Energy Phys. 2003,no.5,054,24 pp. %I SISSA Library %G en %U http://hdl.handle.net/1963/1645 %1 2473 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T13:05:48Z (GMT). No. of bitstreams: 1\\nhep-th0211108.pdf: 318316 bytes, checksum: 6253a1679129f66f68bcd94e85931a56 (MD5)\\n Previous issue date: 2002 %R 10.1088/1126-6708/2003/05/054 %0 Journal Article %J Rend. Mat. Appl. 23 (2003) 189-201 %D 2003 %T A note on the integral representation of functionals in the space SBD(O) %A Francois Ebobisse %A Rodica Toader %X 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. %B Rend. Mat. Appl. 23 (2003) 189-201 %I Rendiconti di Matematica %G en_US %U http://hdl.handle.net/1963/3064 %1 1269 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-10T08:08:06Z\\nNo. of bitstreams: 1\\n0104264v1.pdf: 157593 bytes, checksum: 8afd09d4c0f34e5fa55e357804395f3d (MD5) %0 Journal Article %J Adv. Theor. Math. Phys. 7 (2003) 145-204 %D 2003 %T Space-adiabatic perturbation theory %A Gianluca Panati %A Herbert Spohn %A Stefan Teufel %X 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. %B Adv. Theor. Math. Phys. 7 (2003) 145-204 %I International Press %G en_US %U http://hdl.handle.net/1963/3041 %1 1292 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-08T12:17:36Z\\nNo. of bitstreams: 1\\n0201055v3.pdf: 449361 bytes, checksum: a37ea04fc4a4f59a75d03e4b2ec3df16 (MD5) %0 Journal Article %J Math. Models Methods Appl. Sci., 12 (2002), no. 12, 1773 %D 2002 %T A model for the quasi-static growth of a brittle fracture: existence and approximation results %A Gianni Dal Maso %A Rodica Toader %X 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. %B Math. Models Methods Appl. Sci., 12 (2002), no. 12, 1773 %I SISSA Library %G en %U http://hdl.handle.net/1963/1571 %1 2547 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:18Z (GMT). No. of bitstreams: 1\\nmath.AP0101089.pdf: 313965 bytes, checksum: 0373da7254cb4d172659dd2402174562 (MD5)\\n Previous issue date: 2000 %R 10.1142/S0218202502002331 %0 Journal Article %J Math.Models Methods Appl. Sci., 12 (2002) , p.1773-1800. %D 2002 %T A model for the quasi-static growth of brittle fractures based on local minimization %A Gianni Dal Maso %A Rodica Toader %X 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. %B Math.Models Methods Appl. Sci., 12 (2002) , p.1773-1800. %I SISSA Library %G en %U http://hdl.handle.net/1963/1621 %1 2497 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:26Z (GMT). No. of bitstreams: 1\\r\\nmath.AP0207002.pdf: 268810 bytes, checksum: 00401d0491ec9d938b05dcdb884832b7 (MD5)\\r\\n Previous issue date: 2002 %R 10.1142/S0218202502002331 %0 Journal Article %J Arch. Ration. Mech. Anal. 162 (2002) 101-135 %D 2002 %T A Model for the Quasi-Static Growth of Brittle Fractures: Existence and Approximation Results %A Gianni Dal Maso %A Rodica Toader %X 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. %B Arch. Ration. Mech. Anal. 162 (2002) 101-135 %I Springer %G en_US %U http://hdl.handle.net/1963/3056 %1 1277 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-09T16:01:33Z\\nNo. of bitstreams: 1\\n0103221v1.pdf: 340988 bytes, checksum: 433e8545f072a326fc7a6d80a9e7a401 (MD5) %R 10.1007/s002050100187 %0 Journal Article %J Physical review letters. 2002 Jun; 88(25 Pt 1):250405 %D 2002 %T Space-adiabatic perturbation theory in quantum dynamics %A Gianluca Panati %A Herbert Spohn %A Stefan Teufel %X 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. %B Physical review letters. 2002 Jun; 88(25 Pt 1):250405 %I American Physical Society %G en %U http://hdl.handle.net/1963/5985 %1 5841 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Marta Maurutto (maurutto@sissa.it) on 2012-07-15T14:04:06Z\\nNo. of bitstreams: 0 %R 10.1103/PhysRevLett.88.250405 %0 Journal Article %J Acta Appl. Math., 2001, 65, 207-215 %D 2001 %T Gamma-limit of periodic obstacles %A Gianni Dal Maso %A Paola Trebeschi %X We compute the Gamma-limit of a sequence obstacle functionals in the case of periodic obstacles. %B Acta Appl. Math., 2001, 65, 207-215 %I SISSA Library %G en %U http://hdl.handle.net/1963/1495 %1 2668 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:12Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1023/A:1010668530972 %0 Journal Article %J Nuclear Phys. B 611 (2001), no. 1-3, 205--226. %D 2001 %T On the Multi-Instanton Measure for Super Yang-Mills Theories %A Ugo Bruzzo %A Francesco Fucito %A Alessandro Tanzini %A Gabriele Travaglini %B Nuclear Phys. B 611 (2001), no. 1-3, 205--226. %I SISSA Library %G en %U http://hdl.handle.net/1963/1531 %1 2632 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T13:03:42Z (GMT). No. of bitstreams: 1\\nhep-th0008225.pdf: 293471 bytes, checksum: 20088b444ac5b59f0f868d44e40731cc (MD5)\\n Previous issue date: 2000 %R 10.1016/S0550-3213(01)00349-2 %0 Journal Article %J Nucl.Phys. B577 (2000) 547-608 %D 2000 %T 3D superconformal theories from Sasakian seven-manifolds: new nontrivial evidences for AdS_4/CFT_3 %A Davide Fabbri %A Pietro Fré %A Leonardo Gualtieri %A Cesare Reina %A Alessandro Tomasiello %A Alberto Zaffaroni %A Alessandro Zampa %B Nucl.Phys. B577 (2000) 547-608 %I SISSA Library %G en %U http://hdl.handle.net/1963/1327 %1 3128 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:56:21Z (GMT). No. of bitstreams: 1\\nhep-th9907219.pdf: 628836 bytes, checksum: c75d99f0a2296bdcc428232f3907ed15 (MD5)\\n Previous issue date: 1999 %R 10.1016/S0550-3213(00)00098-5 %0 Journal Article %J Theor. Math. Phys. 122 (2000) 176-192 %D 2000 %T Reduction of bi-Hamiltonian systems and separation of variables: an example from the Boussinesq hierarchy %A Gregorio Falqui %A Franco Magri %A G. Tondo %X 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. %B Theor. Math. Phys. 122 (2000) 176-192 %I Springer %G en_US %U http://hdl.handle.net/1963/3219 %1 1082 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-30T17:15:49Z\\nNo. of bitstreams: 1\\n9906009v1.pdf: 207707 bytes, checksum: 488733797e10a7277aa5f36438c6b2d8 (MD5) %R 10.1007/BF02551195 %0 Journal Article %J Annales Poincare Phys.Theor.69:413-424,1998 %D 1998 %T Diffusion of a particle in presence of N moving point sources %A Gianfausto Dell'Antonio %A Rodolfo Figari %A Alessandro Teta %B Annales Poincare Phys.Theor.69:413-424,1998 %I SISSA Library %G en %U http://hdl.handle.net/1963/134 %1 75 %2 LISNU %3 Interdisciplinary Laboratory for Advanced Studies %$ Made available in DSpace on 2004-09-01T12:22:22Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1996 %0 Journal Article %J Journal des Mathematiques Pures et Appliquees. Volume 77, Issue 1, January 1998, Pages 89-116 %D 1998 %T Limits of variational problems for Dirichlet forms in varying domains %A Gianni Dal Maso %A Virginia De Cicco %A Lino Notarantonio %A Nicoletta A. Tchou %B Journal des Mathematiques Pures et Appliquees. Volume 77, Issue 1, January 1998, Pages 89-116 %I SISSA %G en %U http://hdl.handle.net/1963/6440 %1 6377 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-31T18:44:35Z\\nNo. of bitstreams: 2\\nDM-DeC-96.pdf: 145467 bytes, checksum: 0cf974ac5cc090ff7f9faae3d433043f (MD5)\\nDM-DeC-96-cover.pdf: 35849 bytes, checksum: cde85af897042e1ee2c1b1a8c724b8eb (MD5) %R 10.1016/S0362-546X(98)00067-4 %0 Thesis %D 1997 %T Some Problems in the Asymptotic Analysis of Partial Differential Equations in Perforated Domains %A Rodica Toader %K Dirichlet problems %I SISSA %G en %U http://hdl.handle.net/1963/5698 %1 5541 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Gerardina Cargnelutti (gerry@sissa.it) on 2012-04-12T11:43:37Z\\nNo. of bitstreams: 1\\nPhD_Toader_Rodica.pdf: 6894510 bytes, checksum: 8a7aced562b9372ebb9d7421262ea7f6 (MD5) %0 Journal Article %J Lett. Math. Phys. 40 (1997), no. 3, 235-256 %D 1997 %T Statistics in space dimension two %A Gianfausto Dell'Antonio %A Rodolfo Figari %A Alessandro Teta %X 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). %B Lett. Math. Phys. 40 (1997), no. 3, 235-256 %I SISSA Library %G en %U http://hdl.handle.net/1963/130 %1 12 %2 LISNU %3 Interdisciplinary Laboratory for Advanced Studies %$ Made available in DSpace on 2004-09-01T12:22:20Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1996 %R 10.1023/A:1007361832622 %0 Journal Article %J Rend. Sem. Mat. Univ. Padova 96 (1996), 257--277 %D 1996 %T A capacity method for the study of Dirichlet problems for elliptic systems in varying domains %A Gianni Dal Maso %A Rodica Toader %B Rend. Sem. Mat. Univ. Padova 96 (1996), 257--277 %I SISSA Library %G en %U http://hdl.handle.net/1963/989 %1 2867 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:41:21Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Journal Article %J Rend. Istit. Mat. Univ. Trieste 26 (1994) 339-360 %D 1994 %T Limits of Dirichlet problems in perforated domains: a new formulation %A Gianni Dal Maso %A Rodica Toader %B Rend. Istit. Mat. Univ. Trieste 26 (1994) 339-360 %I Università degli Studi di Trieste, Dipartimento di Scienze Matematiche %G en_US %U http://hdl.handle.net/1963/3649 %1 656 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-06-16T11:02:31Z\\nNo. of bitstreams: 1\\ndalmaso18.pdf: 255148 bytes, checksum: e857ab6de9d63e187905170895a65ccf (MD5) %0 Journal Article %J Publ. Res. Inst. Math. Sci. 26 (1990), no. 5, 803--817 %D 1990 %T Quadratic forms for singular perturbations of the Laplacian %A Alessandro Teta %B Publ. Res. Inst. Math. Sci. 26 (1990), no. 5, 803--817 %I SISSA Library %G en %U http://hdl.handle.net/1963/757 %1 3034 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:37:11Z (GMT). No. of bitstreams: 1\\n165_88.pdf: 420094 bytes, checksum: 84ec202153b3f40e2584898048015e2a (MD5)\\n Previous issue date: 1988 %0 Thesis %D 1989 %T Singular perturbation of the Laplacian and connections with models of random media %A Alessandro Teta %I SISSA %G en %U http://hdl.handle.net/1963/6348 %1 6281 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-12-20T10:24:13Z\\nNo. of bitstreams: 1\\nPhD_Teta_Alessandro.pdf: 7132993 bytes, checksum: 95123d37874902a4392f102bb70cd46f (MD5)