In this work we present a Reduced Order Model which is specifically designed to deal with turbulent flows in a finite volume setting. The method used to build the reduced order model is based on the idea of merging/combining projection-based techniques with data-driven reduction strategies. In particular, the work presents a mixed strategy that exploits a data-driven reduction method to approximate the eddy viscosity solution manifold and a classical POD-Galerkin projection approach for the velocity and the pressure fields, respectively. The newly proposed reduced order model has been validated on benchmark test cases in both steady and unsteady settings with Reynolds up to $Re=O(10^5)$.

%B Journal of Computational Physics %V 416 %P 109513 %G eng %U https://arxiv.org/abs/1907.09909 %R 10.1016/j.jcp.2020.109513 %0 Journal Article %J International Journal for Numerical Methods in Engineering %D 2020 %T Efficient Geometrical parametrization for finite-volume based reduced order methods %A Giovanni Stabile %A Matteo Zancanaro %A Gianluigi Rozza %XIn this work, we present an approach for the efficient treatment of parametrized geometries in the context of POD-Galerkin reduced order methods based on Finite Volume full order approximations. On the contrary to what is normally done in the framework of finite element reduced order methods, different geometries are not mapped to a common reference domain: the method relies on basis functions defined on an average deformed configuration and makes use of the Discrete Empirical Interpolation Method (D-EIM) to handle together non-affinity of the parametrization and non-linearities. In the first numerical example, different mesh motion strategies, based on a Laplacian smoothing technique and on a Radial Basis Function approach, are analyzed and compared on a heat transfer problem. Particular attention is devoted to the role of the non-orthogonal correction. In the second numerical example the methodology is tested on a geometrically parametrized incompressible Navier–Stokes problem. In this case, the reduced order model is constructed following the same segregated approach used at the full order level

%B International Journal for Numerical Methods in Engineering %V 121 %P 2655-2682 %G eng %U https://arxiv.org/abs/1901.06373 %R 10.1002/nme.6324 %0 Unpublished Work %D 2020 %T Enhancing CFD predictions in shape design problems by model and parameter space reduction %A Marco Tezzele %A Nicola Demo %A Giovanni Stabile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 %XIn 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.

%G eng %U https://arxiv.org/abs/2001.05237 %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 %XUsing 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 %J Computers & Fluids %D 2020 %T A hybrid reduced order method for modelling turbulent heat transfer problems %A Sokratia Georgaka %A Giovanni Stabile %A Kelbij Star %A Gianluigi Rozza %A Michael J. Bluck %XA parametric, hybrid reduced order model approach based on the Proper Orthogonal Decomposition with both Galerkin projection and interpolation based on Radial Basis Functions method is presented. This method is tested against a case of turbulent non-isothermal mixing in a T-junction pipe, a common ow arrangement found in nuclear reactor cooling systems. The reduced order model is derived from the 3D unsteady, incompressible Navier-Stokes equations weakly coupled with the energy equation. For high Reynolds numbers, the eddy viscosity and eddy diffusivity are incorporated into the reduced order model with a Proper Orthogonal Decomposition (nested and standard) with Interpolation (PODI), where the interpolation is performed using Radial Basis Functions. The reduced order solver, obtained using a k-ω SST URANS full order model, is tested against the full order solver in a 3D T-junction pipe with parametric velocity inlet boundary conditions.

%B Computers & Fluids %V 208 %P 104615 %G eng %U https://arxiv.org/abs/1906.08725 %R 10.1016/j.compfluid.2020.104615 %0 Journal Article %J Mat. Cult. Soc. Riv. Unione Mat. Ital. (I) %D 2020 %T Matematica ed elezioni, paradossi e problemi elettorali %A Saracco, A. %A Saracco, G. %B Mat. Cult. Soc. Riv. Unione Mat. Ital. (I) %V 5 %P 17–31 %G eng %0 Journal Article %J Mathematics in Engineering %D 2020 %T MicroMotility: State of the art, recent accomplishments and perspectives on the mathematical modeling of bio-motility at microscopic scales %A Daniele Agostinelli %A Roberto Cerbino %A Del Alamo, Juan C %A Antonio DeSimone %A Stephanie Höhn %A Cristian Micheletti %A Giovanni Noselli %A Eran Sharon %A Julia Yeomans %K active matter %K adhesive locomotion %K cell motility %K cell sheet folding %K knotted DNA %K topological defects %K unicellular swimmers %K unjamming transition %XMathematical modeling and quantitative study of biological motility (in particular, of motility at microscopic scales) is producing new biophysical insight and is offering opportunities for new discoveries at the level of both fundamental science and technology. These range from the explanation of how complex behavior at the level of a single organism emerges from body architecture, to the understanding of collective phenomena in groups of organisms and tissues, and of how these forms of swarm intelligence can be controlled and harnessed in engineering applications, to the elucidation of processes of fundamental biological relevance at the cellular and sub-cellular level. In this paper, some of the most exciting new developments in the fields of locomotion of unicellular organisms, of soft adhesive locomotion across scales, of the study of pore translocation properties of knotted DNA, of the development of synthetic active solid sheets, of the mechanics of the unjamming transition in dense cell collectives, of the mechanics of cell sheet folding in volvocalean algae, and of the self-propulsion of topological defects in active matter are discussed. For each of these topics, we provide a brief state of the art, an example of recent achievements, and some directions for future research.

%B Mathematics in Engineering %V 2 %P 230 %G eng %U http://dx.doi.org/10.3934/mine.2020011 %9 Perspective %R 10.3934/mine.2020011 %0 Journal Article %J ESAIM Control Optim. Calc. Var. %D 2020 %T Minimizers of the prescribed mean curvature functional in a Jordan domain with no necks %A Leonardi, G. P. %A Saracco, G. %B ESAIM Control Optim. Calc. Var. %V 26 %P 76 %G eng %R 10.1051/cocv/2020030 %0 Conference Paper %B QUIET Selected Contributions %D 2020 %T Non-Intrusive Polynomial Chaos Method Applied to Problems in Computational Fluid Dynamics with a Comparison to Proper Orthogonal Decomposition %A Saddam Hijazi %A Giovanni Stabile %A Andrea Mola %A Gianluigi Rozza %E van Brummelen, Harald %E Corsini, Alessandro %E Perotto, Simona %E Rozza, Gianluigi %XIn this work, Uncertainty Quantification (UQ) based on non-intrusive Polynomial Chaos Expansion (PCE) is applied to the CFD problem of the flow past an airfoil with parameterized angle of attack and inflow velocity. To limit the computational cost associated with each of the simulations required by the non-intrusive UQ algorithm used, we resort to a Reduced Order Model (ROM) based on Proper Orthogonal Decomposition (POD)-Galerkin approach. A first set of results is presented to characterize the accuracy of the POD-Galerkin ROM developed approach with respect to the Full Order Model (FOM) solver (OpenFOAM). A further analysis is then presented to assess how the UQ results are affected by substituting the FOM predictions with the surrogate ROM ones.

%B QUIET Selected Contributions %I Springer International Publishing %G eng %U https://arxiv.org/abs/1901.02285 %& Non-Intrusive Polynomial Chaos Method Applied to Problems in Computational Fluid Dynamics [...] %0 Journal Article %J NONLINEAR ANALYSIS %D 2020 %T Periodic solutions of nearly integrable Hamiltonian systems bifurcating from infinite-dimensional tori %A Alessandro Fonda %A Giuliano Klun %A Andrea Sfecci %XWe prove the existence of periodic solutions of some infinite-dimensional nearly integrable Hamiltonian systems, bifurcating from infinite-dimensional tori, by the use of a generalization of the Poincaré–Birkhoff Theorem.

%B NONLINEAR ANALYSIS %G eng %U https://doi.org/10.1016/j.na.2019.111720 %R 10.1016/j.na.2019.111720 %0 Unpublished Work %D 2020 %T POD-Galerkin Model Order Reduction for Parametrized Nonlinear Time Dependent Optimal Flow Control: an Application to Shallow Water Equations %A Maria Strazzullo %A Francesco Ballarin %A Gianluigi Rozza %XIn this work we propose reduced order methods as a reliable strategy to efficiently solve parametrized optimal control problems governed by shallow waters equations in a solution tracking setting. The physical parametrized model we deal with is nonlinear and time dependent: this leads to very time consuming simulations which can be unbearable e.g. in a marine environmental monitoring plan application. Our aim is to show how reduced order modelling could help in studying different configurations and phenomena in a fast way. After building the optimality system, we rely on a POD-Galerkin reduction in order to solve the optimal control problem in a low dimensional reduced space. The presented theoretical framework is actually suited to general nonlinear time dependent optimal control problems. The proposed methodology is finally tested with a numerical experiment: the reduced optimal control problem governed by shallow waters equations reproduces the desired velocity and height profiles faster than the standard model, still remaining accurate.

%G eng %0 Unpublished Work %D 2020 %T A POD-Galerkin reduced order model of a turbulent convective buoyant flow of sodium over a backward-facing step %A Kelbij Star %A Giovanni Stabile %A Gianluigi Rozza %A Joris Degroote %XA Finite-Volume based POD-Galerkin reduced order modeling strategy for steady-state Reynolds averaged Navier–Stokes (RANS) simulation is extended for low-Prandtl number flow. The reduced order model is based on a full order model for which the effects of buoyancy on the flow and heat transfer are characterized by varying the Richardson number. The Reynolds stresses are computed with a linear eddy viscosity model. A single gradient diffusion hypothesis, together with a local correlation for the evaluation of the turbulent Prandtl number, is used to model the turbulent heat fluxes. The contribution of the eddy viscosity and turbulent thermal diffusivity fields are considered in the reduced order model with an interpolation based data-driven method. The reduced order model is tested for buoyancy-aided turbulent liquid sodium flow over a vertical backward-facing step with a uniform heat flux applied on the wall downstream of the step. The wall heat flux is incorporated with a Neumann boundary condition in both the full order model and the reduced order model. The velocity and temperature profiles predicted with the reduced order model for the same and new Richardson numbers inside the range of parameter values are in good agreement with the RANS simulations. Also, the local Stanton number and skin friction distribution at the heated wall are qualitatively well captured. Finally, the reduced order simulations, performed on a single core, are about $10^5$ times faster than the RANS simulations that are performed on eight cores.

%G eng %U https://arxiv.org/abs/2003.01114 %0 Conference Paper %B IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22–25, 2018 %D 2020 %T A Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries %A Efthymios N. Karatzas %A Giovanni Stabile %A Nabib Atallah %A Guglielmo Scovazzi %A Gianluigi Rozza %E Fehr, Jörg %E Haasdonk, Bernard %XA model order reduction technique is combined with an embedded boundary finite element method with a POD-Galerkin strategy. The proposed methodology is applied to parametrized heat transfer problems and we rely on a sufficiently refined shape-regular background mesh to account for parametrized geometries. In particular, the employed embedded boundary element method is the Shifted Boundary Method (SBM) recently proposed. This approach is based on the idea of shifting the location of true boundary conditions to a surrogate boundary, with the goal of avoiding cut cells near the boundary of the computational domain. This combination of methodologies has multiple advantages. In the first place, since the Shifted Boundary Method always relies on the same background mesh, there is no need to update the discretized parametric domain. Secondly, we avoid the treatment of cut cell elements, which usually need particular attention. Thirdly, since the whole background mesh is considered in the reduced basis construction, the SBM allows for a smooth transition of the reduced modes across the immersed domain boundary. The performances of the method are verified in two dimensional heat transfer numerical examples.

%B IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22–25, 2018 %I Springer International Publishing %G eng %U https://arxiv.org/abs/1807.07753 %R 10.1007/978-3-030-21013-7_8 %0 Conference Paper %B ENUMATH2019 proceedings %D 2020 %T Reduced order methods for parametrized non-linear and time dependent optimal flow control problems, towards applications in biomedical and environmental sciences %A Maria Strazzullo %A Zakia Zainib %A Francesco Ballarin %A Gianluigi Rozza %XWe introduce reduced order methods as an efficient strategy to solve parametrized non-linear and time dependent optimal flow control problems governed by partial differential equations. Indeed, optimal control problems require a huge computational effort in order to be solved, most of all in a physical and/or geometrical parametrized setting. Reduced order methods are a reliably suitable approach, increasingly gaining popularity, to achieve rapid and accurate optimal solutions in several fields, such as in biomedical and environmental sciences. In this work, we exploit POD-Galerkin reduction over a parametrized optimality system, derived from Karush-Kuhn-Tucker conditions. The methodology presented is tested on two boundary control problems, governed respectively by (i) time dependent Stokes equations and (ii) steady non-linear Navier-Stokes equations.

%B ENUMATH2019 proceedings %I Springer %G eng %U https://arxiv.org/abs/1912.07886 %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 %J Adv. Nonlinear Stud. %D 2020 %T The $\varepsilon-\varepsilon^β$ property in the isoperimetric problem with double density, and the regularity of isoperimetric sets %A Pratelli, A. %A Saracco, G. %B Adv. Nonlinear Stud. %V 20 %P 539–555 %G eng %R 10.1515/ans-2020-2074 %0 Unpublished Work %D 2019 %T Discontinuous Galerkin Model Order Reduction of Geometrically Parametrized Stokes Equation %A Nirav Vasant Shah %A Martin Hess %A Gianluigi Rozza %XThe present work focuses on the geometric parametrization and the reduced order modeling of the Stokes equation. We discuss the concept of a parametrized geometry and its application within a reduced order modeling technique. The full order model is based on the discontinuous Galerkin method with an interior penalty formulation. We introduce the broken Sobolev spaces as well as the weak formulation required for an affine parameter dependency. The operators are transformed from a fixed domain to a parameter dependent domain using the affine parameter dependency. The proper orthogonal decomposition is used to obtain the basis of functions of the reduced order model. By using the Galerkin projection the linear system is projected onto the reduced space. During this process, the offline-online decomposition is used to separate parameter dependent operations from parameter independent operations. Finally this technique is applied to an obstacle test problem.The numerical outcomes presented include experimental error analysis, eigenvalue decay and measurement of online simulation time. Keywords: Discontinuous Galerkin method, Stokes flow, Geometric parametrization, Proper orthogonal decomposition.

%G eng %U https://arxiv.org/abs/1912.09787 %0 Journal Article %J Netw. Heterog. Media %D 2019 %T A discrete districting plan %A Saracco, A. %A Saracco, G. %B Netw. Heterog. Media %V 14 %P 771–788 %G eng %R 10.3934/nhm.2019031 %0 Report %D 2019 %T A dynamic model for viscoelastic materials with prescribed growing cracks %A Maicol Caponi %A Francesco Sapio %XIn this paper we prove the existence of solutions for a class of viscoelastic dynamic systems on time-dependent cracked domains, with possibly degenerate viscosity coefficients. Under stronger regularity assumptions we also show a uniqueness result. Finally, we exhibit an example where the energy-dissipation balance is not satisfied, showing there is an additional dissipation due to the crack growth.

%G eng %U http://preprints.sissa.it:8180/xmlui/handle/1963/35334 %0 Journal Article %J Communications in Computational Physics %D 2019 %T Parametric POD-Galerkin Model Order Reduction for Unsteady-State Heat Transfer Problems %A Sokratia Georgaka %A Giovanni Stabile %A Gianluigi Rozza %A Michael J. Bluck %XA parametric reduced order model based on proper orthogonal decom- position with Galerkin projection has been developed and applied for the modeling of heat transport in T-junction pipes which are widely found in nuclear power plants. Thermal mixing of different temperature coolants in T-junction pipes leads to tem- perature fluctuations and this could potentially cause thermal fatigue in the pipe walls. The novelty of this paper is the development of a parametric ROM considering the three dimensional, incompressible, unsteady Navier-Stokes equations coupled with the heat transport equation in a finite volume approximation. Two different paramet- ric cases are presented in this paper: parametrization of the inlet temperatures and parametrization of the kinematic viscosity. Different training spaces are considered and the results are compared against the full order model.

%B Communications in Computational Physics %V 27 %P 1–32 %G eng %U https://arxiv.org/abs/1808.05175 %R 10.4208/cicp.OA-2018-0207 %0 Journal Article %J Computers & Mathematics with Applications %D 2019 %T POD-Galerkin reduced order methods for combined Navier-Stokes transport equations based on a hybrid FV-FE solver %A S. Busto %A G. Stabile %A G. Rozza %A M.E. Vázquez-Cendón %XThe purpose of this work is to introduce a novel POD-Galerkin strategy for the hybrid finite volume/finite element solver introduced in Bermúdez et al. 2014 and Busto et al. 2018. The interest is into the incompressible Navier-Stokes equations coupled with an additional transport equation. The full order model employed in this article makes use of staggered meshes. This feature will be conveyed to the reduced order model leading to the definition of reduced basis spaces in both meshes. The reduced order model presented herein accounts for velocity, pressure, and a transport-related variable. The pressure term at both the full order and the reduced order level is reconstructed making use of a projection method. More precisely, a Poisson equation for pressure is considered within the reduced order model. Results are verified against three-dimensional manufactured test cases. Moreover a modified version of the classical cavity test benchmark including the transport of a species is analysed.

%B Computers & Mathematics with Applications %G eng %U https://arxiv.org/abs/1810.07999 %R 10.1016/j.camwa.2019.06.026 %0 Journal Article %J Complex Analysis and Operator Theory %D 2019 %T Point-Like Perturbed Fractional Laplacians Through Shrinking Potentials of Finite Range %A Alessandro Michelangeli %A Raffaele Scandone %XWe construct the rank-one, singular (point-like) perturbations of the d-dimensional fractional Laplacian in the physically meaningful norm-resolvent limit of fractional Schrödinger operators with regular potentials centred around the perturbation point and shrinking to a delta-like shape. We analyse both possible regimes, the resonance-driven and the resonance-independent limit, depending on the power of the fractional Laplacian and the spatial dimension. To this aim, we also qualify the notion of zero-energy resonance for Schrödinger operators formed by a fractional Laplacian and a regular potential.

%B Complex Analysis and Operator Theory %8 May %G eng %U https://doi.org/10.1007/s11785-019-00927-w %R 10.1007/s11785-019-00927-w %0 Journal Article %J Computer Methods in Applied Mechanics and Engineering %D 2019 %T A reduced basis approach for PDEs on parametrized geometries based on the shifted boundary finite element method and application to a Stokes flow %A Karatzas, Efthymios N %A Stabile, Giovanni %A Nouveau, Leo %A Scovazzi, Guglielmo %A Rozza, Gianluigi %XWe propose a model order reduction technique integrating the Shifted Boundary Method (SBM) with a POD-Galerkin strategy. This approach allows to treat more complex parametrized domains in an efficient and straightforward way. The impact of the proposed approach is threefold. First, problems involving parametrizations of complex geometrical shapes and/or large domain deformations can be efficiently solved at full-order by means of the SBM, an unfitted boundary method that avoids remeshing and the tedious handling of cut cells by introducing an approximate surrogate boundary. Second, the computational effort is further reduced by the development of a reduced order model (ROM) technique based on a POD-Galerkin approach. Third, the SBM provides a smooth mapping from the true to the surrogate domain, and for this reason, the stability and performance of the reduced order basis are enhanced. This feature is the net result of the combination of the proposed ROM approach and the SBM. Similarly, the combination of the SBM with a projection-based ROM gives the great advantage of an easy and fast to implement algorithm considering geometrical parametrization with large deformations. The transformation of each geometry to a reference geometry (morphing) is in fact not required. These combined advantages will allow the solution of PDE problems more efficiently. We illustrate the performance of this approach on a number of two-dimensional Stokes flow problems.

%B Computer Methods in Applied Mechanics and Engineering %V 347 %P 568–587 %G eng %U https://arxiv.org/abs/1807.07790 %R 10.1016/j.cma.2018.12.040 %0 Journal Article %J Annali di Matematica Pura ed Applicata (1923 -) %D 2019 %T On the relaxed area of the graph of discontinuous maps from the plane to the plane taking three values with no symmetry assumptions %A Giovanni Bellettini %A Alaa Elshorbagy %A Maurizio Paolini %A Riccardo Scala %XIn this paper, we estimate from above the area of the graph of a singular map u taking a disk to three vectors, the vertices of a triangle, and jumping along three $\mathcal{C}^2$-embedded curves that meet transversely at only one point of the disk. We show that the singular part of the relaxed area can be estimated from above by the solution of a Plateau-type problem involving three entangled nonparametric area-minimizing surfaces. The idea is to ``fill the hole'' in the graph of the singular map with a sequence of approximating smooth two-codimensional surfaces of graph-type, by imagining three minimal surfaces, placed vertically over the jump of u, coupled together via a triple point in the target triangle. Such a construction depends on the choice of a target triple point, and on a connection passing through it, which dictate the boundary condition for the three minimal surfaces. We show that the singular part of the relaxed area of u cannot be larger than what we obtain by minimizing over all possible target triple points and all corresponding connections.

%B Annali di Matematica Pura ed Applicata (1923 -) %8 Jul %G eng %U https://doi.org/10.1007/s10231-019-00887-0 %R 10.1007/s10231-019-00887-0 %0 Journal Article %J arXiv e-prints %D 2019 %T Strong Novikov conjecture for low degree cohomology and exotic group C*-algebras %A Paolo Antonini %A Buss, Alcides %A Engel, Alexander %A Siebenand , Timo %K Mathematics - K-Theory and Homology %K Mathematics - Operator Algebras %XWe strengthen a result of Hanke–Schick about the strong Novikov conjecture for low degree cohomology by showing that their non-vanishing result for the maximal group $C^*$-algebra even holds for the reduced group $C^*$-algebra. To achieve this we provide a Fell absorption principle for certain exotic crossed product functors.

%B arXiv e-prints %P arXiv:1905.07730 %8 May %G eng %0 Report %D 2019 %T Zero modes and low-energy resolvent expansion for three dimensional Schrodinger operators with point interactions %A Raffaele Scandone %G eng %U https://arxiv.org/abs/1901.02449 %0 Journal Article %J ArXiv e-prints %D 2018 %T The Baum–Connes conjecture localised at the unit element of a discrete group %A Paolo Antonini %A Azzali, S. %A Skandalis, G. %K 19K35 %K 46L80 %K 46L85 %K 58J22 %K Mathematics - K-Theory and Homology %K Mathematics - Operator Algebras %B ArXiv e-prints %G eng %0 Report %D 2018 %T Characteristic boundary layers for mixed hyperbolic systems in one space dimension and applications to the Navier-Stokes and MHD equations %A Stefano Bianchini %A Laura Spinolo %X We provide a detailed analysis of the boundary layers for mixed hyperbolic-parabolic systems in one space dimension and small amplitude regimes. As an application of our results, we describe the solution of the so-called boundary Riemann problem recovered as the zero viscosity limit of the physical viscous approximation. In particular, we tackle the so called doubly characteristic case, which is considerably more demanding from the technical viewpoint and occurs when the boundary is characteristic for both the mixed hyperbolic-parabolic system and for the hyperbolic system obtained by neglecting the second order terms. Our analysis applies in particular to the compressible Navier-Stokes and MHD equations in Eulerian coordinates, with both positive and null conductivity. In these cases, the doubly characteristic case occurs when the velocity is close to 0. The analysis extends to non-conservative systems. %I SISSA %G en %U http://preprints.sissa.it/handle/1963/35325 %1 35635 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-10-16T11:48:42Z No. of bitstreams: 1 BiaSpiEuler116.pdf: 615669 bytes, checksum: 93b99e76a8c0a0f3e1753969d7170d1e (MD5) %0 Journal Article %J SOFTWAREX %D 2018 %T deal2lkit: A toolkit library for high performance programming in deal.II %A Alberto Sartori %A Nicola Giuliani %A Mauro Bardelloni %A Luca Heltai %B SOFTWAREX %V 7 %P 318–327 %G eng %R 10.1016/j.softx.2018.09.004 %0 Report %D 2018 %T Differential of metric valued Sobolev maps %A Nicola Gigli %A Enrico Pasqualetto %A Elefterios Soultanis %G eng %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 %XWe 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 Generic %D 2018 %T The Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: from Laminar to Turbulent Flows %A Saddam Hijazi %A Shafqat Ali %A Giovanni Stabile %A Francesco Ballarin %A Gianluigi Rozza %G eng %0 Journal Article %J Computers & Fluids %D 2018 %T Finite volume POD-Galerkin stabilised reduced order methods for the parametrised incompressible Navier-Stokes equations %A Giovanni Stabile %A Gianluigi Rozza %B Computers & Fluids %I Elsevier {BV} %8 feb %G eng %U https://doi.org/10.1016/j.compfluid.2018.01.035 %R 10.1016/j.compfluid.2018.01.035 %0 Journal Article %J Journal of Mathematical Physics %D 2018 %T Fractional powers and singular perturbations of quantum differential Hamiltonians %A Alessandro Michelangeli %A Andrea Ottolini %A Raffaele Scandone %XWe consider the fractional powers of singular (point-like) perturbations of the Laplacian and the singular perturbations of fractional powers of the Laplacian, and we compare two such constructions focusing on their perturbative structure for resolvents and on the local singularity structure of their domains. In application to the linear and non-linear Schrödinger equations for the corresponding operators, we outline a programme of relevant questions that deserve being investigated.

%B Journal of Mathematical Physics %V 59 %P 072106 %G eng %U https://doi.org/10.1063/1.5033856 %R 10.1063/1.5033856 %0 Journal Article %J Journal of Functional Analysis %D 2018 %T On fractional powers of singular perturbations of the Laplacian %A Vladimir Georgiev %A Alessandro Michelangeli %A Raffaele Scandone %K Point interactions %K Regular and singular component of a point-interaction operator %K Singular perturbations of the Laplacian %XWe qualify a relevant range of fractional powers of the so-called Hamiltonian of point interaction in three dimensions, namely the singular perturbation of the negative Laplacian with a contact interaction supported at the origin. In particular we provide an explicit control of the domain of such a fractional operator and of its decomposition into regular and singular parts. We also qualify the norms of the resulting singular fractional Sobolev spaces and their mutual control with the corresponding classical Sobolev norms.

%B Journal of Functional Analysis %V 275 %P 1551 - 1602 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022123618301046 %R https://doi.org/10.1016/j.jfa.2018.03.007 %0 Journal Article %J International Journal of Mathematics %D 2018 %T Framed symplectic sheaves on surfaces %A Jacopo Vittorio Scalise %XA framed symplectic sheaf on a smooth projective surface $X$ is a torsion-free sheaf $E$ together with a trivialization on a divisor $D \subset X$ and a morphism $\Lambda^2 E \rightarrow \mathcal{O}_X$ satisfying some additional conditions. We construct a moduli space for framed symplectic sheaves on a surface, and present a detailed study for $X =\mathbb{P}_\mathbb{C}^2$. In this case, the moduli space is irreducible and admits an ADHM-type description and a birational proper map onto the space of framed symplectic ideal instantons.

%B International Journal of Mathematics %V 29 %P 1850007 %G eng %U https://doi.org/10.1142/S0129167X18500076 %R 10.1142/S0129167X18500076 %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 %XIn 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 Journal Article %J Zeitschrift für angewandte Mathematik und Physik %D 2018 %T Global, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials %A Paolo Antonelli %A Alessandro Michelangeli %A Raffaele Scandone %XWe prove the existence of weak solutions in the space of energy for a class of nonlinear Schrödinger equations in the presence of a external, rough, time-dependent magnetic potential. Under our assumptions, it is not possible to study the problem by means of usual arguments like resolvent techniques or Fourier integral operators, for example. We use a parabolic regularisation, and we solve the approximating Cauchy problem. This is achieved by obtaining suitable smoothing estimates for the dissipative evolution. The total mass and energy bounds allow to extend the solution globally in time. We then infer sufficient compactness properties in order to produce a global-in-time finite energy weak solution to our original problem.

%B Zeitschrift für angewandte Mathematik und Physik %V 69 %P 46 %8 Mar %G eng %U https://doi.org/10.1007/s00033-018-0938-5 %R 10.1007/s00033-018-0938-5 %0 Journal Article %J Nonlinear Anal. %D 2018 %T On the isoperimetric problem with double density %A Pratelli, A. %A Saracco, G. %B Nonlinear Anal. %V 177 %P 733–752 %G eng %R 10.1016/j.na.2018.04.009 %0 Journal Article %J ASTRONOMY & ASTROPHYSICS %D 2018 %T Iterative map-making with two-level preconditioning for polarized cosmic microwave background data sets. A worked example for ground-based experiments %A Puglisi, Giuseppe %A Poletti, Davide %A Fabbian, Giulio %A Baccigalupi, Carlo %A Luca Heltai %A Stompor, Radek %B ASTRONOMY & ASTROPHYSICS %V 618 %P 1–14 %G eng %U https://arxiv.org/abs/1801.08937 %R 10.1051/0004-6361/201832710 %0 Journal Article %J Annales Henri Poincaré %D 2018 %T Lp-Boundedness of Wave Operators for the Three-Dimensional Multi-Centre Point Interaction %A Gianfausto Dell'Antonio %A Alessandro Michelangeli %A Raffaele Scandone %A Kenji Yajima %XWe prove that, for arbitrary centres and strengths, the wave operators for three-dimensional Schrödinger operators with multi-centre local point interactions are bounded in Lp(R3)for 1<p<3 and unbounded otherwise.

%B Annales Henri Poincaré %V 19 %P 283–322 %8 Jan %G eng %U https://doi.org/10.1007/s00023-017-0628-4 %R 10.1007/s00023-017-0628-4 %0 Journal Article %J SIAM Journal on Scientific Computing %D 2018 %T Model Reduction for Parametrized Optimal Control Problems in Environmental Marine Sciences and Engineering %A Maria Strazzullo %A Francesco Ballarin %A Mosetti, R. %A Gianluigi Rozza %B SIAM Journal on Scientific Computing %V 40 %P B1055-B1079 %G eng %U https://doi.org/10.1137/17M1150591 %R 10.1137/17M1150591 %0 Journal Article %D 2018 %T A novel reduced order model for vortex induced vibrations of long flexible cylinders %A Giovanni Stabile %A Hermann G. Matthies %A Claudio Borri %I Elsevier {BV} %V 156 %P 191–207 %8 may %G eng %U https://doi.org/10.1016/j.oceaneng.2018.02.064 %R 10.1016/j.oceaneng.2018.02.064 %0 Journal Article %J NoDEA Nonlinear Differ. Equ. Appl. %D 2018 %T The prescribed mean curvature equation in weakly regular domains %A Leonardi, G. P. %A Saracco, G. %B NoDEA Nonlinear Differ. Equ. Appl. %V 25 %P 9 %G eng %R 10.1007/s00030-018-0500-3 %0 Report %D 2018 %T On real resonances for the three-dimensional, multi-centre point interaction %A Alessandro Michelangeli %A Raffaele Scandone %G eng %0 Generic %D 2018 %T A Reduced Basis approach for PDEs on parametrized geometries based on the Shifted Boundary Finite Element Method and application to fluid dynamics %A Efthymios N. Karatzas %A Giovanni Stabile %A Leo Nouveau %A Guglielmo Scovazzi %A Gianluigi Rozza %G eng %0 Generic %D 2018 %T A Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries %A Efthymios N. Karatzas %A Giovanni Stabile %A N. Atallah %A Guglielmo Scovazzi %A Gianluigi Rozza %G eng %0 Journal Article %J Journal of Nonlinear Mathematical Physics %D 2018 %T Singular Hartree equation in fractional perturbed Sobolev spaces %A Alessandro Michelangeli %A Alessandro Olgiati %A Raffaele Scandone %XWe establish the local and global theory for the Cauchy problem of the singular Hartree equation in three dimensions, that is, the modification of the non-linear Schrödinger equation with Hartree non-linearity, where the linear part is now given by the Hamiltonian of point interaction. The latter is a singular, self-adjoint perturbation of the free Laplacian, modelling a contact interaction at a fixed point. The resulting non-linear equation is the typical effective equation for the dynamics of condensed Bose gases with fixed point-like impurities. We control the local solution theory in the perturbed Sobolev spaces of fractional order between the mass space and the operator domain. We then control the global solution theory both in the mass and in the energy space.

%B Journal of Nonlinear Mathematical Physics %I Taylor & Francis %V 25 %P 558-588 %G eng %U https://doi.org/10.1080/14029251.2018.1503423 %R 10.1080/14029251.2018.1503423 %0 Report %D 2018 %T Stochastic homogenisation of free-discontinuity problems %A Filippo Cagnetti %A Gianni Dal Maso %A Lucia Scardia %A Caterina Ida Zeppieri %X In this paper we study the stochastic homogenisation of free-discontinuity functionals. Assuming stationarity for the random volume and surface integrands, we prove the existence of a homogenised random free-discontinuity functional, which is deterministic in the ergodic case. Moreover, by establishing a connection between the deterministic convergence of the functionals at any fixed realisation and the pointwise Subadditive Ergodic Theorem by Akcoglou and Krengel, we characterise the limit volume and surface integrands in terms of asymptotic cell formulas. %G en %U http://preprints.sissa.it/handle/1963/35309 %1 35617 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-03-19T09:16:27Z No. of bitstreams: 1 Cag-DM-Sca-Zep-Stochastic.pdf: 427225 bytes, checksum: 758a4e21e1c47b4a34c774f5d4bff8c2 (MD5) %0 Journal Article %J Ann. Mat. Pura Appl. (4) %D 2018 %T Two examples of minimal Cheeger sets in the plane %A Leonardi, G. P. %A Saracco, G. %B Ann. Mat. Pura Appl. (4) %V 197 %P 1511–1531 %G eng %R 10.1007/s10231-018-0735-y %0 Journal Article %J Manuscripta Math. %D 2018 %T Weighted Cheeger sets are domains of isoperimetry %A Saracco, G. %B Manuscripta Math. %V 156 %P 371–381 %G eng %R 10.1007/s00229-017-0974-z %0 Journal Article %J Communication in Applied Industrial Mathematics %D 2017 %T Advances in Reduced order modelling for CFD: vortex shedding around a circular cylinder using a POD-Galerkin method %A Giovanni Stabile %A Saddam Hijazi %A Stefano Lorenzi %A Andrea Mola %A Gianluigi Rozza %K finite volume, CFD %K Reduced order methods %XVortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. In this work a Reduced Order Model (ROM) of the incompressible flow around a circular cylinder, built performing a Galerkin projection of the governing equations onto a lower dimensional space is presented. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pressure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) for this purpose the projection of the Governing equations (momentum equation and Poisson equation for pressure) is performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework are presented. The accuracy of the reduced order model is assessed against full order results.

%B Communication in Applied Industrial Mathematics %G eng %U https://arxiv.org/abs/1701.03424 %9 reviewed %0 Journal Article %J Calc. Var. Partial Differential Equations %D 2017 %T The Cheeger constant of a Jordan domain without necks %A Leonardi, G. P. %A Neumayer, R. %A Saracco, G. %B Calc. Var. Partial Differential Equations %V 56 %P 164 %G eng %R 10.1007/s00526-017-1263-0 %0 Journal Article %J Engineering with Computers %D 2017 %T Curvature-adapted remeshing of CAD surfaces %A Franco Dassi %A Andrea Mola %A Hang Si %B Engineering with Computers %I Springer Nature %V 34 %P 565–576 %8 dec %G eng %U https://doi.org/10.1007/s00366-017-0558-2 %R 10.1007/s00366-017-0558-2 %0 Book Section %B Advances in Quantum Mechanics: Contemporary Trends and Open Problems %D 2017 %T Dispersive Estimates for Schrödinger Operators with Point Interactions in ℝ3 %A Felice Iandoli %A Raffaele Scandone %E Alessandro Michelangeli %E Gianfausto Dell'Antonio %XThe study of dispersive properties of Schrödinger operators with point interactions is a fundamental tool for understanding the behavior of many body quantum systems interacting with very short range potential, whose dynamics can be approximated by non linear Schrödinger equations with singular interactions. In this work we proved that, in the case of one point interaction in $\mathbb{R}^3$, the perturbed Laplacian satisfies the same $L^p$−$L^q$ estimates of the free Laplacian in the smaller regime $q \in [2,3)$. These estimates are implied by a recent result concerning the Lpboundedness of the wave operators for the perturbed Laplacian. Our approach, however, is more direct and relatively simple, and could potentially be useful to prove optimal weighted estimates also in the regime $q \geq 3$.

%B Advances in Quantum Mechanics: Contemporary Trends and Open Problems %I Springer International Publishing %C Cham %P 187–199 %@ 978-3-319-58904-6 %G eng %U https://doi.org/10.1007/978-3-319-58904-6_11 %R 10.1007/978-3-319-58904-6_11 %0 Report %D 2017 %T Elliptic diffeomorphisms of symplectic 4-manifolds %A Vsevolod Shevchishin %A Gleb Smirnov %G eng %U https://arxiv.org/pdf/1708.01518.pdf %0 Report %D 2017 %T Gamma-Convergence of Free-discontinuity problems %A Filippo Cagnetti %A Gianni Dal Maso %A Lucia Scardia %A Caterina Ida Zeppieri %X We study the Gamma-convergence of sequences of free-discontinuity functionals depending on vector-valued functions u which can be discontinuous across hypersurfaces whose shape and location are not known a priori. The main novelty of our result is that we work under very general assumptions on the integrands which, in particular, are not required to be periodic in the space variable. Further, we consider the case of surface integrands which are not bounded from below by the amplitude of the jump of u. We obtain three main results: compactness with respect to Gamma-convergence, representation of the Gamma-limit in an integral form and identification of its integrands, and homogenisation formulas without periodicity assumptions. In particular, the classical case of periodic homogenisation follows as a by-product of our analysis. Moreover, our result covers also the case of stochastic homogenisation, as we will show in a forthcoming paper. %I SISSA %G en %U http://preprints.sissa.it/handle/1963/35276 %1 35583 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-03-20T13:20:54Z No. of bitstreams: 1 Cag-DM-Sca-Zep-sissa.pdf: 494285 bytes, checksum: 0da567323c828153382b08fc0f967af4 (MD5) %0 Journal Article %J Rev. Mat. Iberoam. %D 2017 %T On the generalized Cheeger problem and an application to 2d strips %A Pratelli, A. %A Saracco, G. %B Rev. Mat. Iberoam. %V 33 %P 219–237 %G eng %R 10.4171/RMI/934 %0 Journal Article %J ESAIM: COCV %D 2017 %T Limit of viscous dynamic processes in delamination as the viscosity and inertia vanish %A Riccardo Scala %XWe introduce a model of dynamic evolution of a delaminated visco-elastic body with viscous adhesive. We prove the existence of solutions of the corresponding system of PDEs and then study the behavior of such solutions when the data of the problem vary slowly. We prove that a rescaled version of the dynamic evolutions converge to a “local” quasistatic evolution, which is an evolution satisfying an energy inequality and a momentum balance at all times. In the one-dimensional case we give a more detailed description of the limit evolution and we show that it behaves in a very similar way to the limit of the solutions of the dynamic model in [T. Roubicek, SIAM J. Math. Anal. 45 (2013) 101–126], where no viscosity in the adhesive is taken into account.

%B ESAIM: COCV %V 23 %P 593-625 %G eng %U https://doi.org/10.1051/cocv/2016006 %R 10.1051/cocv/2016006 %0 Journal Article %J Biomechanics and Modeling in Mechanobiology %D 2017 %T Numerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts %A Francesco Ballarin %A Elena Faggiano %A Andrea Manzoni %A Alfio Quarteroni %A Gianluigi Rozza %A Sonia Ippolito %A Roberto Scrofani %B Biomechanics and Modeling in Mechanobiology %V 16 %P 1373-1399 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85015065851&doi=10.1007%2fs10237-017-0893-7&partnerID=40&md5=c388f20bd5de14187bad9ed7d9affbd0 %R 10.1007/s10237-017-0893-7 %0 Journal Article %J Communications in Applied and Industrial Mathematics %D 2017 %T POD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder %A Giovanni Stabile %A Saddam Hijazi %A Andrea Mola %A Stefano Lorenzi %A Gianluigi Rozza %B Communications in Applied and Industrial Mathematics %I Walter de Gruyter {GmbH} %V 8 %P 210–236 %8 dec %G eng %U https://doi.org/10.1515/caim-2017-0011 %R 10.1515/caim-2017-0011 %0 Journal Article %J J. Elast. %D 2017 %T Solid tumors are poroelastic solids with a chemo-mechanical feedback on growth %A D. Ambrosi %A Pezzuto, S. %A Davide Riccobelli %A Stylianopoulos, T. %A Pasquale Ciarletta %B J. Elast. %I Springer Netherlands %V 129 %P 107–124 %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 Francesco 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. %XSeveral 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 %D 2016 %T Confinement of dislocations inside a crystal with a prescribed external strain %A Ilaria Lucardesi %A Marco Morandotti %A Riccardo Scala %A Davide Zucco %X We study screw dislocations in an isotropic crystal undergoing antiplane shear. In the framework of linear elasticity, by fixing a suitable boundary condition for the strain (prescribed non-vanishing boundary integral), we manage to confine the dislocations inside the material. More precisely, in the presence of an external strain with circulation equal to n times the lattice spacing, it is energetically convenient to have n distinct dislocations lying inside the crystal. The novelty of introducing a Dirichlet boundary condition for the tangential strain is crucial to the confinement: it is well known that, if Neumann boundary conditions are imposed, the dislocations tend to migrate to the boundary. The results are achieved using PDE techniques and Ƭ-convergence theory, in the framework of the so-called core radius approach. %G en %U http://urania.sissa.it/xmlui/handle/1963/35247 %1 35558 %2 Mathematics %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2016-10-20T11:44:46Z No. of bitstreams: 1 LMSZ-preprint.pdf: 547676 bytes, checksum: 5c7add921deefef560aac54da6a584cc (MD5) %0 Journal Article %J Methods and Applications of Analysis %D 2016 %T Currents and dislocations at the continuum scale %A Riccardo Scala %A Nicolas Van Goethem %XA striking geometric property of elastic bodies with dislocations is that the deformation tensor cannot be written as the gradient of a one-to-one immersion, its curl being nonzero and equal to the density of the dislocations, a measure concentrated in the dislocation lines. In this work, we discuss the mathematical properties of such constrained deformations and study a variational problem in finite-strain elasticity, where Cartesian maps allow us to consider deformations in $L^p$ with $1\leq p<2$, as required for dislocation-induced strain singularities. Firstly, we address the problem of mathematical modeling of dislocations. It is a key purpose of the paper to build a framework where dislocations are described in terms of integral 1-currents and to extract from this theoretical setting a series of notions having a mechanical meaning in the theory of dislocations. In particular, the paper aims at classifying integral 1-currents, with modeling purposes. In the second part of the paper, two variational problems are solved for two classes of dislocations, at the mesoscopic and at the continuum scale. By continuum it is here meant that a countable family of dislocations is considered, allowing for branching and cluster formation, with possible complex geometric patterns. Therefore, modeling assumptions of the defect part of the energy must also be provided, and discussed.

%B Methods and Applications of Analysis %I International Press of Boston %V 23 %P 1–34 %G eng %R 10.4310/MAA.2016.v23.n1.a1 %0 Report %D 2016 %T A fast virtual surgery platform for many scenarios haemodynamics of patient-specific coronary artery bypass grafts %A Francesco Ballarin %A Elena Faggiano %A Andrea Manzoni %A Gianluigi Rozza %A Alfio Quarteroni %A Sonia Ippolito %A Roberto Scrofani %A Carlo Antona %X A fast computational framework is devised to the study of several configurations of patient-specific coronary artery bypass grafts. This is especially useful to perform a sensitivity analysis of the haemodynamics for different flow conditions occurring in native coronary arteries and bypass grafts, the investigation of the progression of the coronary artery disease and the choice of the most appropriate surgical procedure. A complete pipeline, from the acquisition of patientspecific medical images to fast parametrized computational simulations, is proposed. Complex surgical configurations employed in the clinical practice, such as Y-grafts and sequential grafts, are studied. A virtual surgery platform based on model reduction of unsteady Navier Stokes equations for blood dynamics is proposed to carry out sensitivity analyses in a very rapid and reliable way. A specialized geometrical parametrization is employed to compare the effect of stenosis and anastomosis variation on the outcome of the surgery in several relevant cases. %I Submitted %G en %U http://urania.sissa.it/xmlui/handle/1963/35240 %1 35545 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2016-10-14T23:07:40Z No. of bitstreams: 1 BMMB_SISSA_report.pdf: 16374062 bytes, checksum: 7ee82fd9d989ed91bf9cc721ae2114a0 (MD5) %0 Thesis %D 2016 %T Frames symplectic sheaves on surfaces and their ADHM data %A Jacopo Vittorio Scalise %K moduli spaces %X This dissertation is centered on the moduli space of what we call framed symplectic sheaves on a surface, compactifying the corresponding moduli space of framed principal SP−bundles. It contains the construction of the moduli space, which is carried out for every smooth projective surface X with a big and nef framing divisor, and a study of its deformation theory. We also develop an in-depth analysis of the examples X = P2 and X = Blp (P2 ), showing that the corresponding moduli spaces enjoy an ADHM-type description. In the former case, we prove irreducibility of the space and exhibit a relation with the space of framed ideal instantons on S4 in type C. %I SISSA %G en %1 35517 %2 Mathematics %4 1 %# MAT/03 %$ Submitted by jscalise@sissa.it (jscalise@sissa.it) on 2016-09-16T08:14:20Z No. of bitstreams: 1 Framed symplectic sheaves on surfaces and their ADHM data.pdf: 939059 bytes, checksum: f36f5bbc16875fdbb60776eed86a41c0 (MD5) %0 Report %D 2016 %T Isogeometric analysis-based reduced order modelling for incompressible linear viscous flows in parametrized shapes %A Filippo Salmoiraghi %A Francesco Ballarin %A Luca Heltai %A Gianluigi Rozza %X In this work we provide a combination of isogeometric analysis with reduced order modelling techniques, based on proper orthogonal decomposition, to guarantee computational reduction for the numerical model, and with free-form deformation, for versatile geometrical parametrization. We apply it to computational fluid dynamics problems considering a Stokes flow model. The proposed reduced order model combines efficient shape deformation and accurate and stable velocity and pressure approximation for incompressible viscous flows, computed with a reduced order method. Efficient offine-online computational decomposition is guaranteed in view of repetitive calculations for parametric design and optimization problems. Numerical test cases show the efficiency and accuracy of the proposed reduced order model. %I Springer, AMOS Advanced Modelling and Simulation in Engineering Sciences %G en %U http://urania.sissa.it/xmlui/handle/1963/35199 %1 35493 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2016-06-20T23:55:25Z No. of bitstreams: 1 MAIN_IGA_FFD_ROM.pdf: 1631282 bytes, checksum: b050e472f11943b95d8307915a50b6da (MD5) %0 Journal Article %J Annals of Nuclear Energy, 87, 2 (2016): pp. 198-208 %D 2016 %T A multi-physics reduced order model for the analysis of Lead Fast Reactor single channel %A Alberto Sartori %A Antonio Cammi %A Lelio Luzzi %A Gianluigi Rozza %X In this work, a Reduced Basis method, with basis functions sampled by a Proper Orthogonal Decomposition technique, has been employed to develop a reduced order model of a multi-physics parametrized Lead-cooled Fast Reactor single-channel. Being the first time that a reduced order model is developed in this context, the work focused on a methodological approach and the coupling between the neutronics and the heat transfer, where the thermal feedbacks on neutronics are explicitly taken into account, in time-invariant settings. In order to address the potential of such approach, two different kinds of varying parameters have been considered, namely one related to a geometric quantity (i.e., the inner radius of the fuel pellet) and one related to a physical quantity (i.e., the inlet lead velocity). The capabilities of the presented reduced order model (ROM) have been tested and compared with a high-fidelity finite element model (upon which the ROM has been constructed) on different aspects. In particular, the comparison focused on the system reactivity prediction (with and without thermal feedbacks on neutronics), the neutron flux and temperature field reconstruction, and on the computational time. The outcomes provided by the reduced order model are in good agreement with the high-fidelity finite element ones, and a computational speed-up of at least three orders of magnitude is achieved as well. %B Annals of Nuclear Energy, 87, 2 (2016): pp. 198-208 %I Elsevier %V 87 %P 208 %G en %U http://urania.sissa.it/xmlui/handle/1963/35191 %1 35471 %2 Mathematics %4 1 %# MAT/08 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2016-06-16T11:08:05Z (GMT) No. of bitstreams: 0 %& 198 %R doi:10.1016/j.anucene.2015.09.002 %0 Book Section %B Noncommutative Analysis, Operator Theory and Applications %D 2016 %T Pimsner Algebras and Circle Bundles %A Francesca Arici %A Francesco D'Andrea %A Giovanni Landi %E Alpay, Daniel %E Cipriani, Fabio %E Colombo, Fabrizio %E Guido, Daniele %E Sabadini, Irene %E Sauvageot, Jean-Luc %XWe report on the connections between noncommutative principal circle bundles, Pimsner algebras and strongly graded algebras. We illustrate several results with examples of quantum weighted projective and lens spaces and θ-deformations.

%B Noncommutative Analysis, Operator Theory and Applications %I Springer International Publishing %C Cham %P 1–25 %@ 978-3-319-29116-1 %G eng %U https://doi.org/10.1007/978-3-319-29116-1_1 %R 10.1007/978-3-319-29116-1_1 %0 Journal Article %J NERS-14-1062; ASME J of Nuclear Rad Sci, 2, 2 (2016) 021019 %D 2016 %T A Reduced Basis Approach for Modeling the Movement of Nuclear Reactor Control Rods %A Alberto Sartori %A Antonio Cammi %A Lelio Luzzi %A Gianluigi Rozza %X This work presents a reduced order model (ROM) aimed at simulating nuclear reactor control rods movement and featuring fast-running prediction of reactivity and neutron flux distribution as well. In particular, the reduced basis (RB) method (built upon a high-fidelity finite element (FE) approximation) has been employed. The neutronics has been modeled according to a parametrized stationary version of the multigroup neutron diffusion equation, which can be formulated as a generalized eigenvalue problem. Within the RB framework, the centroidal Voronoi tessellation is employed as a sampling technique due to the possibility of a hierarchical parameter space exploration, without relying on a “classical” a posteriori error estimation, and saving an important amount of computational time in the offline phase. Here, the proposed ROM is capable of correctly predicting, with respect to the high-fidelity FE approximation, both the reactivity and neutron flux shape. In this way, a computational speedup of at least three orders of magnitude is achieved. If a higher precision is required, the number of employed basis functions (BFs) must be increased. %B NERS-14-1062; ASME J of Nuclear Rad Sci, 2, 2 (2016) 021019 %I ASME %V 2 %P 8 %8 02/2016 %G en %U http://urania.sissa.it/xmlui/handle/1963/35192 %N 2 %1 35473 %2 Mathematics %4 1 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2016-05-30T00:18:10Z No. of bitstreams: 1 sartori_post-icone.pdf: 1377810 bytes, checksum: 5c09a1296518bbbd4b61b709ced8dbca (MD5) %R 10.1115/1.4031945 %0 Journal Article %J Communications in Computational Physics %D 2016 %T Reduced basis approaches in time-dependent noncoercive settings for modelling the movement of nuclear reactor control rods %A Alberto Sartori %A Antonio Cammi %A Lelio Luzzi %A Gianluigi Rozza %XIn this work, two approaches, based on the certified Reduced Basis method, have been developed for simulating the movement of nuclear reactor control rods, in time-dependent non-coercive settings featuring a 3D geometrical framework. In particular, in a first approach, a piece-wise affine transformation based on subdomains division has been implemented for modelling the movement of one control rod. In the second approach, a “staircase” strategy has been adopted for simulating the movement of all the three rods featured by the nuclear reactor chosen as case study. The neutron kinetics has been modelled according to the so-called multi-group neutron diffusion, which, in the present case, is a set of ten coupled parametrized parabolic equations (two energy groups for the neutron flux, and eight for the precursors). Both the reduced order models, developed according to the two approaches, provided a very good accuracy compared with high-fidelity results, assumed as “truth” solutions. At the same time, the computational speed-up in the Online phase, with respect to the fine “truth” finite element discretization, achievable by both the proposed approaches is at least of three orders of magnitude, allowing a real-time simulation of the rod movement and control.

%B Communications in Computational Physics %I SISSA %8 2016 %G en %U http://urania.sissa.it/xmlui/handle/1963/34963 %N in press %1 35188 %2 Mathematics %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2015-11-05T15:06:51Z No. of bitstreams: 1 manuscript.pdf: 2056729 bytes, checksum: 2a2fad22dc931e8c4094642e21c479cd (MD5) %0 Journal Article %J Communications in Partial Differential Equations %D 2016 %T Spectral analysis and the Aharonov-Bohm effect on certain almost-Riemannian manifolds %A Ugo Boscain %A Dario Prandi %A M. Seri %XWe study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. This operator contains first order diverging terms caused by the divergence of the volume. We get explicit descriptions of the spectrum and the eigenfunctions. In particular in both cases we get a Weyl's law with leading term Elog E. We then study the drastic effect of Aharonov-Bohm magnetic potentials on the spectral properties. Other generalized Riemannian structures including conic and anti-conic type manifolds are also studied. In this case, the Aharonov-Bohm magnetic potential may affect the self-adjointness of the Laplace-Beltrami operator.

%B Communications in Partial Differential Equations %I Taylor & Francis %V 41 %P 32-50 %G eng %U https://doi.org/10.1080/03605302.2015.1095766 %R 10.1080/03605302.2015.1095766 %0 Journal Article %J Computers and Mathematics with Applications 69 (2015) 1167–1188 %D 2015 %T Benchmarking the Immersed Finite Element Method for Fluid-Structure Interaction Problems %A Roy Saswati %A Luca Heltai %A Francesco Costanzo %X We present an implementation of a fully variational formulation of an immersed methods for fluid-structure interaction problems based on the finite element method. While typical implementation of immersed methods are characterized by the use of approximate Dirac delta distributions, fully variational formulations of the method do not require the use of said distributions. In our implementation the immersed solid is general in the sense that it is not required to have the same mass density and the same viscous response as the surrounding fluid. We assume that the immersed solid can be either viscoelastic of differential type or hyperelastic. Here we focus on the validation of the method via various benchmarks for fluid-structure interaction numerical schemes. This is the first time that the interaction of purely elastic compressible solids and an incompressible fluid is approached via an immersed method allowing a direct comparison with established benchmarks. %B Computers and Mathematics with Applications 69 (2015) 1167–1188 %G en %1 34633 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Luca Heltai (heltai@sissa.it) on 2015-04-20T15:26:58Z No. of bitstreams: 1 rhc_feibm_validation-v3.pdf: 7039131 bytes, checksum: 705f28e17037504f00766fc4e84a10a4 (MD5) %R 10.1016/j.camwa.2015.03.012 %0 Book %B Springer Briefs in Mathematics %D 2015 %T Certified Reduced Basis Methods for Parametrized Partial Differential Equations %A Jan S Hesthaven %A Gianluigi Rozza %A Benjamin Stamm %K a posteriori error bounds %K empirical interpolation %K parametrized partial differential equations %K reduced basis methods, greedy algorithms %XThis book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.

%B Springer Briefs in Mathematics %7 1 %I Springer %C Switzerland %P 135 %@ 978-3-319-22469-5 %G eng %6 1 %0 Journal Article %J Mathematical Methods in the Applied Sciences %D 2015 %T A compatible-incompatible decomposition of symmetric tensors in Lp with application to elasticity %A Maggiani, Giovanni Battista %A Riccardo Scala %A Nicolas Van Goethem %K 35J58 %K 35Q74 %K compatibility conditions %K elasticity %K Korn inequality %K strain decomposition %K subclass74B05 %XIn this paper, we prove the Saint-Venant compatibility conditions in $L^p$ for $p\in(1,∞)$, in a simply connected domain of any space dimension. As a consequence, alternative, simple, and direct proofs of some classical Korn inequalities in Lp are provided. We also use the Helmholtz decomposition in $L^p$ to show that every symmetric tensor in a smooth domain can be decomposed in a compatible part, which is the symmetric part of a displacement gradient, and in an incompatible part, which is the incompatibility of a certain divergence-free tensor. Moreover, under a suitable Dirichlet boundary condition, this Beltrami-type decomposition is proved to be unique. This decomposition result has several applications, one of which being in dislocation models, where the incompatibility part is related to the dislocation density and where $1 < p < 2$. This justifies the need to generalize and prove these rather classical results in the Hilbertian case ($p = 2$), to the full range $p\in(1,∞)$. Copyright © 2015 John Wiley & Sons, Ltd.

%B Mathematical Methods in the Applied Sciences %V 38 %P 5217-5230 %G eng %U https://onlinelibrary.wiley.com/doi/abs/10.1002/mma.3450 %R 10.1002/mma.3450 %0 Journal Article %D 2015 %T Deal2lkit: a Toolkit Library for High Performance Programming in deal.II %A Alberto Sartori %A Nicola Giuliani %A Mauro Bardelloni %A Luca Heltai %X We present version 1.0.0 of the deal2lkit (deal.II ToolKit) library. deal2lkit is a collection of modules and classes for the general purpose finite element library deal.II. Its principal aim is to provide a high level interface, controlled via parameter files, for those steps that are common in all finite element programs: mesh generation, selection of the finite element type, application of boundary conditions and many others. Each module can be used as a building block independently on the others, and can be integrated in existing finite element codes based on deal.II, drastically reducing the size of programs, rendering their use automatically parametrised, and reducing the overall time-to-market of finite element programming. Moreover, deal2lkit features interfaces with the SUNDIALS (SUite of Nonlinear and DIfferential/ALgebraic equation Solvers) and ASSIMP (Open Asset Import Library) libraries. Some examples are provided which show the aim and scopes of deal2lkit. The deal2lkit library is released under the GNU Lesser General Public License (LGPL) and can be retrieved from the deal2lkit repository https://github.com/mathLab/deal2lkit. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/35006 %1 35235 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by asartori@sissa.it (asartori@sissa.it) on 2015-11-13T13:12:29Z No. of bitstreams: 1 paper_deal2lkit.pdf: 1085486 bytes, checksum: 1dc7e9b9790fe38d2ced7b5328633cd8 (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 Report %D 2015 %T Extended affine Weyl groups of BCD type, Frobenius manifolds and their Landau-Ginzburg superpotentials %A Boris Dubrovin %A Ian A.B. Strachan %A Youjin Zhang %A Dafeng Zuo %X For the root systems of type Bl, Cl and Dl, we generalize the result of [7] by showing the existence of Frobenius manifold structures on the orbit spaces of the extended affine Weyl groups that correspond to any vertex of the Dynkin diagram instead of a particular choice made in [7]. It also depends on certain additional data. We also construct LG superpotentials for these Frobenius manifold structures. %I SISSA %G en %U http://preprints.sissa.it/handle/1963/35316 %1 35625 %2 Mathematics %4 1 %# MAT/07 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-05-23T10:53:54Z No. of bitstreams: 1 1510.08690.pdf: 433692 bytes, checksum: 0cd6111d36bb3b57262400e1f1cebe3a (MD5) %0 Report %D 2015 %T Fast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization %A Francesco Ballarin %A Elena Faggiano %A Sonia Ippolito %A Andrea Manzoni %A Alfio Quarteroni %A Gianluigi Rozza %A Roberto Scrofani %X In this work a reduced-order computational framework for the study of haemodynamics in three-dimensional patient-specific configurations of coronary artery bypass grafts dealing with a wide range of scenarios is proposed. We combine several efficient algorithms to face at the same time both the geometrical complexity involved in the description of the vascular network and the huge computational cost entailed by time dependent patient-specific flow simulations. Medical imaging procedures allow to reconstruct patient-specific configurations from clinical data. A centerlines-based parametrization is proposed to efficiently handle geometrical variations. POD–Galerkin reduced-order models are employed to cut down large computational costs. This computational framework allows to characterize blood flows for different physical and geometrical variations relevant in the clinical practice, such as stenosis factors and anastomosis variations, in a rapid and reliable way. Several numerical results are discussed, highlighting the computational performance of the proposed framework, as well as its capability to perform sensitivity analysis studies, so far out of reach. %G en %U http://urania.sissa.it/xmlui/handle/1963/34623 %1 34824 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2015-10-07T00:30:27Z No. of bitstreams: 1 REPORT.pdf: 10426315 bytes, checksum: 6e5ddf4eb4cacdc7e803c2db1a540fc9 (MD5) %0 Journal Article %J Advances in Computational Mathematics %D 2015 %T Model order reduction of parameterized systems (MoRePaS): Preface to the special issue of advances in computational mathematics %A Peter Benner %A Mario Ohlberger %A Anthony Patera %A Gianluigi Rozza %A Sorensen, D.C. %A Karsten Urban %B Advances in Computational Mathematics %V 41 %P 955–960 %G eng %R 10.1007/s10444-015-9443-y %0 Report %D 2015 %T Poisson cohomology of scalar multidimensional Dubrovin-Novikov brackets %A Guido Carlet %A Matteo Casati %A Sergey Shadrin %X We compute the Poisson cohomology of a scalar Poisson bracket of Dubrovin-Novikov type with D independent variables. We find that the second and third cohomology groups are generically non-vanishing in D>1. Hence, in contrast with the D=1 case, the deformation theory in the multivariable case is non-trivial. %G en %1 35389 %2 Mathematics %4 1 %# MAT/03 %0 Journal Article %J Comput Methods Appl Mech Eng. 2015;284:1147–1180 %D 2015 %T Reduced Basis Isogeometric Methods (RB-IGA) for the real-time simulation of potential flows about parametrized NACA airfoils %A Andrea Manzoni %A Filippo Salmoiraghi %A Luca Heltai %X We present a Reduced Basis (RB) method based on Isogeometric Analysis (IGA) for the rapid and reliable evaluation of PDE systems characterized by complex geometrical features. At the current state of the art, this is the first case of coupling between RB and IGA methods. The construction of the RB method relies on an Isogeometric Boundary Element Method (IGA-BEM) as the high-fidelity technique, allowing a direct interface with Computer Aided Design (CAD) tools. A suitable Empirical Interpolation Method (EIM) ensures an efficient offline/online decomposition between the construction and the evaluation of the RB method. We consider the real-time simulation of potential flows past airfoils, parametrized with respect to the angle of attack and the NACA number identifying their shape, and we provide a validation of our methodology with respect to experimental data and reference numerical codes, showing in both cases a very good agreement.We present a Reduced Basis (RB) method based on Isogeometric Analysis (IGA) for the rapid and reliable evaluation of PDE systems characterized by complex geometrical features. At the current state of the art, this is the first case of coupling between RB and IGA methods. The construction of the RB method relies on an Isogeometric Boundary Element Method (IGA-BEM) as the high-fidelity technique, allowing a direct interface with Computer Aided Design (CAD) tools. A suitable Empirical Interpolation Method (EIM) ensures an efficient offline/online decomposition between the construction and the evaluation of the RB method. We consider the real-time simulation of potential flows past airfoils, parametrized with respect to the angle of attack and the NACA number identifying their shape, and we provide a validation of our methodology with respect to experimental data and reference numerical codes, showing in both cases a very good agreement. %B Comput Methods Appl Mech Eng. 2015;284:1147–1180 %G en %1 34587 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Luca Heltai (heltai@sissa.it) on 2015-03-03T16:15:31Z No. of bitstreams: 1 RB_IGA_BEM.pdf: 725470 bytes, checksum: e2fe6fabfdbe6118e9ef07fb185113af (MD5) %R 10.1016/j.cma.2014.11.037 %0 Report %D 2015 %T Rigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires %A Giuliano Lazzaroni %A Mariapia Palombaro %A Anja Schlomerkemper %X In the context of nanowire heterostructures we perform a discrete to continuum limit of the corresponding free energy by means of Γ-convergence techniques. Nearest neighbours are identified by employing the notions of Voronoi diagrams and Delaunay triangulations. The scaling of the nanowire is done in such a way that we perform not only a continuum limit but a dimension reduction simultaneously. The main part of the proof is a discrete geometric rigidity result that we announced in an earlier work and show here in detail for a variety of three-dimensional lattices. We perform the passage from discrete to continuum twice: once for a system that compensates a lattice mismatch between two parts of the heterogeneous nanowire without defects and once for a system that creates dislocations. It turns out that we can verify the experimentally observed fact that the nanowires show dislocations when the radius of the specimen is large %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/7494 %1 7623 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-01-30T07:54:33Z No. of bitstreams: 1 LaPaSc-3dim.pdf: 249836 bytes, checksum: 8b8edddc952b9a4a084c1c0c85514051 (MD5) %0 Journal Article %D 2014 %T Buckling dynamics of a solvent-stimulated stretched elastomeric sheet %A Alessandro Lucantonio %A Matthieu Roché %A Paola Nardinocchi %A Howard A. Stone %X When stretched uniaxially, a thin elastic sheet may exhibit buckling. The occurrence of buckling depends on the geometrical properties of the sheet and the magnitude of the applied strain. Here we show that an elastomeric sheet initially stable under uniaxial stretching can destabilize when exposed to a solvent that swells the elastomer. We demonstrate experimentally and computationally that the features of the buckling pattern depend on the magnitude of stretching, and this observation offers a new way for controlling the shape of a swollen homogeneous thin sheet. %I Royal Society of Chemistry %G en %U http://urania.sissa.it/xmlui/handle/1963/34967 %1 35197 %2 Physics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-11-10T09:50:41Z No. of bitstreams: 1 preprint2014.pdf: 2111018 bytes, checksum: 568652d2ca6c44cdad3e520342c8042d (MD5) %R 10.1039/c3sm52941j %0 Journal Article %J Comm. Math. Phys. %D 2014 %T Cauchy-Laguerre two-matrix model and the Meijer-G random point field %A Marco Bertola %A Gekhtman, M. %A Szmigielski, J. %B Comm. Math. Phys. %V 326 %P 111–144 %G eng %U http://dx.doi.org/10.1007/s00220-013-1833-8 %R 10.1007/s00220-013-1833-8 %0 Journal Article %J Annals of Nuclear Energy %D 2014 %T Comparison of a Modal Method and a Proper Orthogonal Decomposition approach for multi-group time-dependent reactor spatial kinetics %A Alberto Sartori %A Davide Baroli %A Antonio Cammi %A Davide Chiesa %A Lelio Luzzi %A Roberto R. Ponciroli %A Ezio Previtali %A Marco E. Ricotti %A Gianluigi Rozza %A Monica Sisti %XIn this paper, two modelling approaches based on a Modal Method (MM) and on the Proper Orthogonal Decomposition (POD) technique, for developing a control-oriented model of nuclear reactor spatial kinetics, are presented and compared. Both these methods allow developing neutronics description by means of a set of ordinary differential equations. The comparison of the outcomes provided by the two approaches focuses on the capability of evaluating the reactivity and the neutron flux shape in different reactor configurations, with reference to a TRIGA Mark II reactor. The results given by the POD-based approach are higher-fidelity with respect to the reference solution than those computed according to the MM-based approach, in particular when the perturbation concerns a reduced region of the core. If the perturbation is homogeneous throughout the core, the two approaches allow obtaining comparable accuracy results on the quantities of interest. As far as the computational burden is concerned, the POD approach ensures a better efficiency rather than direct Modal Method, thanks to the ability of performing a longer computation in the preprocessing that leads to a faster evaluation during the on-line phase.

%B Annals of Nuclear Energy %I Elsevier %V 71 %P 229 %8 09/2014 %G en %U http://urania.sissa.it/xmlui/handle/1963/35039 %1 35270 %2 Physics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-11-18T12:07:02Z (GMT) No. of bitstreams: 0 %& 217 %R 10.1016/j.anucene.2014.03.043 %0 Journal Article %D 2014 %T On conjugate times of LQ optimal control problems %A Andrei A. Agrachev %A Luca Rizzi %A Pavel Silveira %K Optimal control, Lagrange Grassmannian, Conjugate point %X Motivated by the study of linear quadratic optimal control problems, we consider a dynamical system with a constant, quadratic Hamiltonian, and we characterize the number of conjugate times in terms of the spectrum of the Hamiltonian vector field $\vec{H}$. We prove the following dichotomy: the number of conjugate times is identically zero or grows to infinity. The latter case occurs if and only if $\vec{H}$ has at least one Jordan block of odd dimension corresponding to a purely imaginary eigenvalue. As a byproduct, we obtain bounds from below on the number of conjugate times contained in an interval in terms of the spectrum of $\vec{H}$. %I Springer %G en %U http://hdl.handle.net/1963/7227 %1 7261 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-12-03T08:50:15Z No. of bitstreams: 1 1311.2009v1.pdf: 401341 bytes, checksum: 5c32a0e534e70539f1823acdad41ddca (MD5) %R 10.1007/s10883-014-9251-6 %0 Journal Article %J Procedia Engineering %D 2014 %T Curvature-adapted remeshing of CAD surfaces %A Franco Dassi %A Andrea Mola %A Hang Si %XA common representation of surfaces with complicated topology and geometry is through composite parametric surfaces as is the case for most CAD modelers. A challenging problem is how to generate a mesh of such a surface that well approximates the geometry of the surface, preserves its topology and important geometric features, and contains nicely shaped elements. In this work, we present an optimization-based surface remeshing method that is able to satisfy many of these requirements simultaneously. This method is inspired by the recent work of Lévy and Bonneel (Proc. 21th International Meshing Roundtable, October 2012), which embeds a smooth surface into a high-dimensional space and remesh it uniformly in that embedding space. Our method works directly in the 3d spaces and uses an embedding space in R6 to evaluate mesh size and mesh quality. It generates a curvatureadapted anisotropic surface mesh that well represents the geometry of the surface with a low number of elements. We illustrate our approach through various examples.

%B Procedia Engineering %I Elsevier %V 82 %P 253–265 %G en %U https://doi.org/10.1016/j.proeng.2014.10.388 %1 35220 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-11-11T16:19:16Z No. of bitstreams: 1 art2014.pdf: 3913220 bytes, checksum: ba78b55b28c0eed195d2abc48bd7ca4b (MD5) %R 10.1016/j.proeng.2014.10.388 %0 Journal Article %D 2014 %T Dirac operators on noncommutative principal circle bundles %A Andrzej Sitarz %A Alessandro Zucca %A Ludwik Dabrowski %X We study spectral triples over noncommutative principal U(1)-bundles of arbitrary dimension and a compatibility condition between the connection and the Dirac operator on the total space and on the base space of the bundle. Examples of low-dimensional noncommutative tori are analyzed in more detail and all connections found that are compatible with an admissible Dirac operator. Conversely, a family of new Dirac operators on the noncommutative tori, which arise from the base-space Dirac operator and a suitable connection is exhibited. These examples are extended to the theta-deformed principal U(1)-bundle S 3 θ → S2. %I World Scientific Publishing %G en %U http://urania.sissa.it/xmlui/handle/1963/35125 %1 35363 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-12-02T15:58:16Z No. of bitstreams: 1 preprint2014.pdf: 282573 bytes, checksum: 862ea930b67b00c451a0c6f093be973d (MD5) %R 10.1142/S0219887814500121 %0 Report %D 2014 %T Dislocations at the continuum scale: functional setting and variational properties %A Riccardo Scala %A Nicolas Van Goethem %G eng %U http://cvgmt.sns.it/paper/2294/ %0 Journal Article %J Annales de l'Institut Henri Poincare (C) Non Linear Analysis %D 2014 %T Existence of immersed spheres minimizing curvature functionals in non-compact 3-manifolds %A Andrea Mondino %A Johannes Schygulla %K Direct methods in the calculus of variations %K General Relativity %K Geometric measure theory %K second fundamental form %K Willmore functional %XWe study curvature functionals for immersed 2-spheres in non-compact, three-dimensional Riemannian manifold $(M,h)$ without boundary. First, under the assumption that $(M,h)$ is the euclidean 3-space endowed with a semi-perturbed metric with perturbation small in $C^1$ norm and of compact support, we prove that if there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})>0$ then there exists a smooth embedding $ f:\mathbb{S}^2 \hookrightarrow M$ minimizing the Willmore functional $\frac{1}{4}\int |H|^2$, where $H$ is the mean curvature. Second, assuming that $(M,h)$ is of bounded geometry (i.e. bounded sectional curvature and strictly positive injectivity radius) and asymptotically euclidean or hyperbolic we prove that if there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})>6$ then there exists a smooth immersion $f:\mathbb{S}^2\hookrightarrow M$ minimizing the functional $\int (\frac{1}{2}|A|^2+1)$, where $A$ is the second fundamental form. Finally, adding the bound $K^M \leq 2$ to the last assumptions, we obtain a smooth minimizer $f:\mathbb{S}^2 \hookrightarrow M$ for the functional $\int \frac{1}{4}(|H|^2+1)$. The assumptions of the last two theorems are satisfied in a large class of 3-manifolds arising as spacelike timeslices solutions of the Einstein vacuum equation in case of null or negative cosmological constant.

%B Annales de l'Institut Henri Poincare (C) Non Linear Analysis %V 31 %P 707 - 724 %G eng %U http://www.sciencedirect.com/science/article/pii/S0294144913000851 %R https://doi.org/10.1016/j.anihpc.2013.07.002 %0 Journal Article %J Mathematische Annalen %D 2014 %T Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds %A Kuwert, Ernst %A Andrea Mondino %A Johannes Schygulla %XWe study curvature functionals for immersed 2-spheres in a compact, three-dimensional Riemannian manifold $M$. Under the assumption that the sectional curvature $K^M$ is strictly positive, we prove the existence of a smooth immersion $f:{\mathbb{S}}^2 \rightarrow M$ minimizing the $L^2$ integral of the second fundamental form. Assuming instead that $K^M \leq 2 $ and that there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})>6$, we obtain a smooth minimizer $f:{\mathbb{S}}^2 \rightarrow M$ for the functional $\int \frac{1}{4}|H|^2+1$, where $H$ is the mean curvature.

%B Mathematische Annalen %V 359 %P 379–425 %8 Jun %G eng %U https://doi.org/10.1007/s00208-013-1005-3 %R 10.1007/s00208-013-1005-3 %0 Report %D 2014 %T Homogenization of functional with linear growth in the context of A-quasiconvexity %A Jose Matias %A Marco Morandotti %A Pedro M. Santos %X This work deals with the homogenization of functionals with linear growth in the context of A-quasiconvexity. A representation theorem is proved, where the new integrand function is obtained by solving a cell problem where the coupling between homogenization and the A-free condition plays a crucial role. This result extends some previous work to the linear case, thus allowing for concentration effects. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/7436 %1 7528 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-10-07T06:20:26Z No. of bitstreams: 1 Mat-Mor-San-14.pdf: 352795 bytes, checksum: de708e4c922915ea1f523eb23165cb83 (MD5) %0 Book Section %D 2014 %T Lecture notes on gradient flows and optimal transport %A Sara Daneri %A Giuseppe Savarè %X We present a short overview on the strongest variational formulation for gradient flows of geodesically λ-convex functionals in metric spaces, with applications to diffusion equations in Wasserstein spaces of probability measures. These notes are based on a series of lectures given by the second author for the Summer School "Optimal transportation: Theory and applications" in Grenoble during the week of June 22-26, 2009. %I Cambridge University Press %G en %U http://urania.sissa.it/xmlui/handle/1963/35093 %1 35348 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-12-02T11:28:52Z No. of bitstreams: 1 preprint2014.pdf: 448708 bytes, checksum: b8b01c6463b81dc26c42c74009c43406 (MD5) %R 10.1017/CBO9781107297296 %0 Journal Article %D 2014 %T N = 2 Quiver Gauge Theories on A-type ALE Spaces %A Ugo Bruzzo %A Francesco Sala %A Richard J. Szabo %X We survey and compare recent approaches to the computation of the partition functions and correlators of chiral BPS observables in N = 2 gauge theories on ALE spaces based on quiver varieties and the minimal resolution Xk of the Ak-1 toric singularity C2/Zk, in light of their recently conjectured duality with two-dimensional coset conformal field theories. We review and elucidate the rigorous constructions of gauge theories for a particular family of ALE spaces, using their relation to the cohomology of moduli spaces of framed torsion-free sheaves on a suitable orbifold compactification of Xk. We extend these computations to generic N = 2 superconformal quiver gauge theories, obtaining in these instances new constraints on fractional instanton charges, a rigorous proof of the Nekrasov master formula, and new quantizations of Hitchin systems based on the underlying Seiberg–Witten geometry. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34719 %1 34918 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-10-22T12:43:35Z No. of bitstreams: 1 preprint2014.pdf: 715288 bytes, checksum: aa2d57d1d2ee3b6602bdcef73696035c (MD5) %R 10.1007/s11005-014-0734-x %0 Journal Article %J Journal of Dynamics and Differential Equations %D 2014 %T Quasistatic Evolution in Perfect Plasticity as Limit of Dynamic Processes %A Gianni Dal Maso %A Riccardo Scala %XWe introduce a model of dynamic visco-elasto-plastic evolution in the linearly elastic regime and prove an existence and uniqueness result. Then we study the limit of (a rescaled version of) the solutions when the data vary slowly. We prove that they converge, up to a subsequence, to a quasistatic evolution in perfect plasticity.

%B Journal of Dynamics and Differential Equations %V 26 %P 915–954 %8 Dec %G eng %U https://doi.org/10.1007/s10884-014-9409-7 %R 10.1007/s10884-014-9409-7 %0 Thesis %D 2014 %T Rational curves and instantons on the Fano threefold Y_5 %A Giangiacomo Sanna %K Moduli space of vector bundles %X This thesis is an investigation of the moduli spaces of instanton bundles on the Fano threefold Y_5 (a linear section of Gr(2,5)). It contains new proofs of classical facts about lines, conics and cubics on Y_5, and about linear sections of Y_5. The main original results are a Grauert-Mülich theorem for the splitting type of instantons on conics, a bound to the splitting type of instantons on lines and an SL_2-equivariant description of the moduli space in charge 2 and 3. Using these results we prove the existence of a unique SL_2-equivariant instanton of minimal charge and we show that for all instantons of charge 2 the divisor of jumping lines is smooth. In charge 3, we provide examples of instantons with reducible divisor of jumping lines. Finally, we construct a natural compactification for the moduli space of instantons of charge 3, together with a small resolution of singularities for it. %I arXiv preprint %G en %U http://urania.sissa.it/xmlui/handle/1963/7482 %1 7594 %2 Mathematics %4 1 %# MAT/02 %$ Submitted by gggsanna@sissa.it (gggsanna@sissa.it) on 2014-12-01T10:51:46Z No. of bitstreams: 1 (Official) G. Sanna - Rational curves and instantons on the Fano threefold Y5 copia.pdf: 2005901 bytes, checksum: bd001232412f102490968ba3b21e1c20 (MD5) %0 Conference Proceedings %B 22nd International Conference on Nuclear Engineering ICONE22 %D 2014 %T A reduced order model for multi-group time-dependent parametrized reactor spatial kinetics %A Alberto Sartori %A Davide Baroli %A Antonio Cammi %A Lelio Luzzi %A Gianluigi Rozza %XIn this work, a Reduced Order Model (ROM) for multigroup time-dependent parametrized reactor spatial kinetics is presented. The Reduced Basis method (built upon a high-fidelity "truth" finite element approximation) has been applied to model the neutronics behavior of a parametrized system composed by a control rod surrounded by fissile material. The neutron kinetics has been described by means of a parametrized multi-group diffusion equation where the height of the control rod (i.e., how much the rod is inserted) plays the role of the varying parameter. In order to model a continuous movement of the rod, a piecewise affine transformation based on subdomain division has been implemented. The proposed ROM is capable to efficiently reproduce the neutron flux distribution allowing to take into account the spatial effects induced by the movement of the control rod with a computational speed-up of 30000 times, with respect to the "truth" model.

%B 22nd International Conference on Nuclear Engineering ICONE22 %7 American Society Mechanical Engineering %I American Society of Mechanical Engineers (ASME) %C Prague, Czech Republic %P V005T17A048-V005T17A048 %8 07/2014 %@ 978-079184595-0 %G en %U http://urania.sissa.it/xmlui/handle/1963/35123 %1 35360 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-12-03T10:06:02Z (GMT) No. of bitstreams: 0 %R 10.1115/ICONE22-30707 %0 Journal Article %D 2014 %T Shape Optimization by Free-Form Deformation: Existence Results and Numerical Solution for Stokes Flows %A Francesco Ballarin %A Andrea Manzoni %A Gianluigi Rozza %A Sandro Salsa %X Shape optimization problems governed by PDEs result from many applications in computational fluid dynamics. These problems usually entail very large computational costs and require also a suitable approach for representing and deforming efficiently the shape of the underlying geometry, as well as for computing the shape gradient of the cost functional to be minimized. Several approaches based on the displacement of a set of control points have been developed in the last decades, such as the so-called free-form deformations. In this paper we present a new theoretical result which allows to recast free-form deformations into the general class of perturbation of identity maps, and to guarantee the compactness of the set of admissible shapes. Moreover, we address both a general optimization framework based on the continuous shape gradient and a numerical procedure for solving efficiently three-dimensional optimal design problems. This framework is applied to the optimal design of immersed bodies in Stokes flows, for which we consider the numerical solution of a benchmark case study from literature. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34698 %1 34914 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-10-22T11:24:27Z (GMT) No. of bitstreams: 0 %R 10.1007/s10915-013-9807-8 %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 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 Swelling dynamics of a thin elastomeric sheet under uniaxial pre-stretch %A Alessandro Lucantonio %A Paola Nardinocchi %A Howard A. Stone %X It has been demonstrated experimentally that pre-stretch affects the swelling of an elastomeric membrane when it is exposed to a solvent. We study theoretically the one-dimensional swelling of a pre-stretched thin elastomeric sheet, bonded to an impermeable rigid substrate, to quantify the influence of pre-stretch. We show that the solvent uptake increases when pre-stretch increases, both at equilibrium and during the swelling transient, where it exhibits two different scaling regimes. The coupling between the solvent uptake and pre-stretch may be practically exploited to design soft actuators where the swelling-induced deformations can be controlled by varying the pre-stretch. %I American Institute of Physics %G en %U http://urania.sissa.it/xmlui/handle/1963/35113 %1 35370 %2 Physics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-12-02T16:28:53Z No. of bitstreams: 1 art2014.pdf: 777840 bytes, checksum: 2362b6250fd872264208d0d3b846a551 (MD5) %R 10.1063/1.4866576 %0 Thesis %D 2014 %T A variational approach to statics and dynamics of elasto-plastic systems %A Riccardo Scala %K delamination %X We prove some existence results for dynamic evolutions in elasto-plasticity and delamination. We study the limit as the data vary very slowly and prove convergence results to quasistatic evolutions. We model dislocations by mean of currents, we introduce the space of deformations in the presence of dislocations and study the graphs of these maps. We prove existence results for minimum problems. We study the properties of minimizers. %I SISSA %G en_US %U http://urania.sissa.it/xmlui/handle/1963/7471 %1 7583 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Riccardo Scala (rscala@sissa.it) on 2014-10-29T12:04:30Z No. of bitstreams: 1 tesi.pdf: 1322338 bytes, checksum: 5fcf0395d13a0dc16eac4edaef440913 (MD5) %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 Journal Article %J Journal of Mathematical Physics. Volume 54, Issue 1, 22 January 2013, Article number 013518 %D 2013 %T Curved noncommutative torus and Gauss--Bonnet %A Ludwik Dabrowski %A Andrzej Sitarz %K Geometry %X We study perturbations of the flat geometry of the noncommutative two-dimensional torus T^2_\theta (with irrational \theta). They are described by spectral triples (A_\theta, \H, D), with the Dirac operator D, which is a differential operator with coefficients in the commutant of the (smooth) algebra A_\theta of T_\theta. We show, up to the second order in perturbation, that the zeta-function at 0 vanishes and so the Gauss-Bonnet theorem holds. We also calculate first two terms of the perturbative expansion of the corresponding local scalar curvature. %B Journal of Mathematical Physics. Volume 54, Issue 1, 22 January 2013, Article number 013518 %I American Institute of Physics %G en %U http://hdl.handle.net/1963/7376 %1 7424 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-06-17T13:10:21Z No. of bitstreams: 1 1204.0420v1.pdf: 126064 bytes, checksum: ffa850e50f99585d61676b1d2398af2f (MD5) %R 10.1063/1.4776202 %0 Journal Article %D 2013 %T Framed sheaves on projective stacks %A Ugo Bruzzo %A Francesco Sala %X Given a normal projective irreducible stack $\mathscr X$ over an algebraically closed field of characteristic zero we consider {\em framed sheaves} on $\mathscr X$, i.e., pairs $(\mathcal E,\phi_{\mathcal E})$, where $\mathcal E$ is a coherent sheaf on $\mathscr X$ and $\phi_{\mathcal E}$ is a morphism from $\mathcal E$ to a fixed coherent sheaf $\mathcal F$. After introducing a suitable notion of (semi)stability, we construct a projective scheme, which is a moduli space for semistable framed sheaves with fixed Hilbert polynomial, and an open subset of it, which is a fine moduli space for stable framed sheaves. If $\mathscr X$ is a projective irreducible orbifold of dimension two and $\mathcal F$ a locally free sheaf on a smooth divisor $\mathscr D\subset \mathscr X$ satisfying certain conditions, we consider {\em $(\mathscr{D}, \mathcal{F})$-framed sheaves}, i.e., framed sheaves $(\mathcal E,\phi_{\mathcal E})$ with $\mathcal E$ a torsion-free sheaf which is locally free in a neighborhood of $\mathscr D$, and ${\phi_{\mathcal{E}}}_{\vert \mathscr{D}}$ an isomorphism. These pairs are $\mu$-stable for a suitable choice of a parameter entering the (semi)stability condition, and of the polarization of $\mathscr X$. This implies the existence of a fine moduli space parameterizing isomorphism classes of $(\mathscr{D}, \mathcal{F})$-framed sheaves on $\mathscr{X}$ with fixed Hilbert polynomial, which is a quasi-projective scheme. In an appendix we develop the example of stacky Hirzebruch surfaces. This is the first paper of a project aimed to provide an algebro-geometric approach to the study of gauge theories on a wide class of 4-dimensional Riemannian manifolds by means of framed sheaves on ``stacky" compactifications of them. In particular, in a subsequent paper \cite{art:bruzzopedrinisalaszabo2013} these results are used to study gauge theories on ALE spaces of type $A_k$. %G en %U http://urania.sissa.it/xmlui/handle/1963/7438 %1 7532 %$ Submitted by Ugo Bruzzo (bruzzo@sissa.it) on 2014-10-08T20:01:07Z No. of bitstreams: 1 FramedStacks-v3.pdf: 649302 bytes, checksum: 5a25742224d8e74e823bc6f3406a1a8e (MD5) %0 Journal Article %J Journal of Geometric Analysis %D 2013 %T Lipschitz Classification of Almost-Riemannian Distances on Compact Oriented Surfaces %A Ugo Boscain %A Grégoire Charlot %A Roberta Ghezzi %A Mario Sigalotti %XTwo-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We consider the Carnot–Carathéodory distance canonically associated with an almost-Riemannian structure and study the problem of Lipschitz equivalence between two such distances on the same compact oriented surface. We analyze the generic case, allowing in particular for the presence of tangency points, i.e., points where two generators of the distribution and their Lie bracket are linearly dependent. The main result of the paper provides a characterization of the Lipschitz equivalence class of an almost-Riemannian distance in terms of a labeled graph associated with it.

%B Journal of Geometric Analysis %V 23 %P 438–455 %8 Jan %G eng %U https://doi.org/10.1007/s12220-011-9262-4 %R 10.1007/s12220-011-9262-4 %0 Journal Article %J Communications in Mathematical Physics. Volume 318, Issue 1, 2013, Pages 111-130 %D 2013 %T Noncommutative circle bundles and new Dirac operators %A Ludwik Dabrowski %A Andrzej Sitarz %K Quantum principal bundles %X We study spectral triples over noncommutative principal U(1) bundles. Basing on the classical situation and the abstract algebraic approach, we propose an operatorial definition for a connection and compatibility between the connection and the Dirac operator on the total space and on the base space of the bundle. We analyze in details the example of the noncommutative three-torus viewed as a U(1) bundle over the noncommutative two-torus and find all connections compatible with an admissible Dirac operator. Conversely, we find a family of new Dirac operators on the noncommutative tori, which arise from the base-space Dirac operator and a suitable connection. %B Communications in Mathematical Physics. Volume 318, Issue 1, 2013, Pages 111-130 %I Springer %G en %U http://hdl.handle.net/1963/7384 %1 7432 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-06-18T10:06:43Z No. of bitstreams: 1 1012.3055v2.pdf: 181206 bytes, checksum: be182e0f568384847efe0f656a70634b (MD5) %R 10.1007/s00220-012-1550-8 %0 Journal Article %J Advanced Nonlinear Studies %D 2013 %T Periodic bouncing solutions for nonlinear impact oscillators %A Alessandro Fonda %A Andrea Sfecci %B Advanced Nonlinear Studies %I Advanced Nonlinear Studies, Inc. %V 13 %P 179–189 %G eng %R 10.1515/ans-2013-0110 %0 Journal Article %J J. Math. Phys. %D 2013 %T Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two-matrix model %A Marco Bertola %A Gekhtman, M. %A Szmigielski, J. %B J. Math. Phys. %V 54 %P 043517, 25 %G eng %0 Journal Article %J Theoretical and Mathematical Physics. Volume 172, Issue 1, July 2012, Pages 911-931 %D 2012 %T Classical double, R-operators, and negative flows of integrable hierarchies %A Boris Dubrovin %A Taras V. Skrypnyk %X Using the classical double G of a Lie algebra g equipped with the classical R-operator, we define two sets of functions commuting with respect to the initial Lie–Poisson bracket on g and its extensions. We consider examples of Lie algebras g with the “Adler–Kostant–Symes” R-operators and the two corresponding sets of mutually commuting functions in detail. Using the constructed commutative Hamiltonian flows on different extensions of g, we obtain zero-curvature equations with g-valued U–V pairs. The so-called negative flows of soliton hierarchies are among such equations. We illustrate the proposed approach with examples of two-dimensional Abelian and non-Abelian Toda field equations. %B Theoretical and Mathematical Physics. Volume 172, Issue 1, July 2012, Pages 911-931 %I SISSA %G en %U http://hdl.handle.net/1963/6468 %1 6413 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-02-11T14:56:54Z (GMT) No. of bitstreams: 0 %R 10.1007/s11232-012-0086-6 %0 Journal Article %D 2012 %T Convergence of equilibria of thin elastic plates under physical growth conditions for the energy density %A Maria Giovanna Mora %A Lucia Scardia %XThe asymptotic behaviour of the equilibrium configurations of a thin elastic plate is studied, as the thickness $h$ of the plate goes to zero. More precisely, it is shown that critical points of the nonlinear elastic functional $\mathcal E^h$, whose energies (per unit thickness) are bounded by $Ch^4$, converge to critical points of the $\Gamma$-limit of $h^{-4}\mathcal E^h$. This is proved under the physical assumption that the energy density $W(F)$ blows up as $\det F\to0$.

%I Elsevier %G en %U http://hdl.handle.net/1963/3466 %1 7112 %2 Mathematics %4 -1 %$ Submitted by Francesca Arici (farici@sissa.it) on 2013-09-18T08:46:46Z No. of bitstreams: 1 0901.4041v1.pdf: 233717 bytes, checksum: 3fc33c8ee52cddb0adf0a197c87d0ce8 (MD5) %R 10.1016/j.jde.2011.09.009 %0 Journal Article %J Bioinformatics (Oxford, England). 2012 Jan; 28(1):76-83 %D 2012 %T Decompositions of large-scale biological systems based on dynamical properties %A Nicola Soranzo %A Fahimeh Ramezani %A Giovanni Iacono %A Claudio Altafini %X MOTIVATION: Given a large-scale biological network represented as an influence graph, in this article we investigate possible decompositions of the network aimed at highlighting specific dynamical properties.\\r\\nRESULTS: The first decomposition we study consists in finding a maximal directed acyclic subgraph of the network, which dynamically corresponds to searching for a maximal open-loop subsystem of the given system. Another dynamical property investigated is strong monotonicity. We propose two methods to deal with this property, both aimed at decomposing the system into strongly monotone subsystems, but with different structural characteristics: one method tends to produce a single large strongly monotone component, while the other typically generates a set of smaller disjoint strongly monotone subsystems.\\r\\nAVAILABILITY: Original heuristics for the methods investigated are described in the article. %B Bioinformatics (Oxford, England). 2012 Jan; 28(1):76-83 %I Oxford University Press %G en %U http://hdl.handle.net/1963/5226 %1 5049 %2 Physics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-01-16T15:13:23Z\\nNo. of bitstreams: 1\\nSoIaRaAl10.pdf: 185656 bytes, checksum: df5605453eb314d79ada4355b16ad3cd (MD5) %R 10.1093/bioinformatics/btr620 %0 Journal Article %J Nucleic Acids Research, Volume 40, Issue 15, August 2012, Pages 7132-7149 %D 2012 %T Detection of transcriptional triggers in the dynamics of microbial growth: application to the respiratory-versatile bacterium Shewanella oneidensis %A Q Beg %A Mattia Zampieri %A N Klitgord %A S Collins %A M Serres %A Daniel Segrè %A Claudio Altafini %X The capacity of microorganisms to respond to variable external conditions requires a coordination of environment-sensing mechanisms and decisionmaking regulatory circuits. Here, we seek to understand the interplay between these two processes by combining high-throughput measurement of time-dependent mRNA profiles with a novel computational approach that searches for key genetic triggers of transcriptional changes. Our approach helped us understand the regulatory strategies of a respiratorily versatile bacterium with promising bioenergy and bioremediation applications, Shewanella oneidensis, in minimal and rich media. By comparing expression profiles across these two conditions, we unveiled components of the transcriptional program that depend mainly on the growth phase. Conversely, by integrating our time-dependent data with a previously available large compendium of static perturbation responses, we identified transcriptional changes that cannot be explained solely by internal network dynamics, but are rather triggered by specific genes acting as key mediators of an environment-dependent response. These transcriptional triggers include known and novel regulators that respond to carbon, nitrogen and oxygen limitation. Our analysis suggests a sequence of physiological responses, including a coupling between nitrogen depletion and glycogen storage, partially recapitulated through dynamic flux balance analysis, and experimentally confirmed by metabolite measurements. Our approach is broadly applicable to other systems %B Nucleic Acids Research, Volume 40, Issue 15, August 2012, Pages 7132-7149 %I SISSA %G en %U http://hdl.handle.net/1963/6506 %1 6452 %2 Mathematics %4 1 %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-02-27T15:39:07Z (GMT) No. of bitstreams: 0 %R 10.1093/nar/gks467 %0 Journal Article %J Journal of Differential Equations %D 2012 %T A general method for the existence of periodic solutions of differential systems in the plane %A Alessandro Fonda %A Andrea Sfecci %K Nonlinear dynamics %K Periodic solutions %XWe propose a general method to prove the existence of periodic solutions for planar systems of ordinary differential equations, which can be used in many different circumstances. Applications are given to some nonresonant cases, even for systems with superlinear growth in some direction, or with a singularity. Systems “at resonance” are also considered, provided a Landesman–Lazer type of condition is assumed.

%B Journal of Differential Equations %V 252 %P 1369 - 1391 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022039611003196 %R https://doi.org/10.1016/j.jde.2011.08.005 %0 Journal Article %J Nonlinear Analysis: Theory, Methods & Applications %D 2012 %T A nonresonance condition for radial solutions of a nonlinear Neumann elliptic problem %A Andrea Sfecci %K Neumann problem %K Nonresonance %K Radial solutions %K Time-map %XWe prove an existence result for radial solutions of a Neumann elliptic problem whose nonlinearity asymptotically lies between the first two eigenvalues. To this aim, we introduce an alternative nonresonance condition with respect to the second eigenvalue which, in the scalar case, generalizes the classical one, in the spirit of Fonda et al. (1991) [2]. Our approach also applies for nonlinearities which do not necessarily satisfy a subcritical growth assumption.

%B Nonlinear Analysis: Theory, Methods & Applications %V 75 %P 6191 - 6202 %G eng %U http://www.sciencedirect.com/science/article/pii/S0362546X12002659 %R https://doi.org/10.1016/j.na.2012.06.023 %0 Journal Article %J Differential Integral Equations %D 2012 %T Periodic solutions of a system of coupled oscillators with one-sided superlinear retraction forces %A Alessandro Fonda %A Andrea Sfecci %B Differential Integral Equations %I Khayyam Publishing, Inc. %V 25 %P 993–1010 %8 11 %G eng %U https://projecteuclid.org:443/euclid.die/1356012248 %0 Journal Article %J Calculus of variations and partial differential equations 44 (2012) 495-541 %D 2012 %T Quasistatic evolution for Cam-Clay plasticity: properties of the viscosity solution %A Gianni Dal Maso %A Antonio DeSimone %A Francesco Solombrino %XCam-Clay plasticity is a well established model for the description of the mechanics of fine grained soils. As solutions can develop discontinuities in time, a weak notion of solution, in terms of a rescaled time s , has been proposed in [8] to give a meaning to this discontinuous evolution. In this paper we first prove that this rescaled evolution satisfies the flow-rule for the rate of plastic strain, in a suitable measure-theoretical sense. In the second part of the paper we consider the behavior of the evolution in terms of the original time variable t . We prove that the unrescaled solution satisfies an energy-dissipation balance and an evolution law for the internal variable, which can be expressed in terms of integrals depending only on the original time. Both these integral identities contain terms concentrated on the jump times, whose size can only be determined by looking at the rescaled formulation.

%B Calculus of variations and partial differential equations 44 (2012) 495-541 %I Springer %G en_US %U http://hdl.handle.net/1963/3900 %1 809 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-07-26T09:17:50Z\\r\\nNo. of bitstreams: 1\\r\\nSolombrino_46M.pdf: 382911 bytes, checksum: dd118cc7f80d4cb1902713eb18747ac6 (MD5) %R 10.1007/s00526-011-0443-6 %0 Journal Article %J PNAS 108 (2011) 13978 %D 2011 %T Cytoskeletal actin networks in motile cells are critically self-organized systems synchronized by mechanical interactions %A Luca Cardamone %A Alessandro Laio %A Rajesh Shahapure %A Antonio DeSimone %B PNAS 108 (2011) 13978 %I National Academy of Sciences %G en %U http://hdl.handle.net/1963/4358 %1 4066 %2 Physics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-28T06:31:24Z\\nNo. of bitstreams: 0 %R 10.1073/pnas.1100549108 %0 Journal Article %J Journal of Differential Equations 250 (2011) 1788-1827 %D 2011 %T Invariant manifolds for a singular ordinary differential equation %A Stefano Bianchini %A Laura Spinolo %B Journal of Differential Equations 250 (2011) 1788-1827 %I Elsevier %G en_US %U http://hdl.handle.net/1963/2554 %1 1565 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-01-15T10:35:53Z\\r\\nNo. of bitstreams: 1\\r\\nSissa0408M.pdf: 296248 bytes, checksum: 7563bf5d03a78a0e2c2c606a9b609827 (MD5) %R 10.1016/j.jde.2010.11.010 %0 Journal Article %J J. Phys. A 44 (2011) 315302 %D 2011 %T On the number of eigenvalues of a model operator related to a system of three particles on lattices %A Gianfausto Dell'Antonio %A Zahriddin I. Muminov %A Y.M. Shermatova %B J. Phys. A 44 (2011) 315302 %I IOP Publishing %G en %U http://hdl.handle.net/1963/5496 %1 5340 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-02-16T07:58:53Z\\nNo. of bitstreams: 0 %] We consider a quantum mechanical system on a lattice \\\\mathbb {Z}^3 in which three particles, two of them being identical, interact through a zero-range potential. We admit a very general form for the \\\'kinetic\\\' part H0γ of the Hamiltonian, which contains a parameter γ to distinguish the two identical particles from the third one (in the continuum case this parameter would be the inverse of the mass). We prove that there is a value γ* of the parameter such that only for γ < γ* the Efimov effect (infinite number of bound states if the two-body interactions have a resonance) is absent for the sector of the Hilbert space which contains functions which are antisymmetric with respect to the two identical particles, while it is present for all values of γ on the symmetric sector. We comment briefly on the relation of this result with previous investigations on the Thomas effect. We also establish the following asymptotics for the number N(z) of eigenvalues z below Emin, the lower limit of the essential spectrum of H0. In the symmetric subspace \\\\lim _{z \\\\rightarrow E_{\\\\rm min}^- } { N^s(z) \\\\over | \\\\log | E_{\\\\rm min} -z| | } = \\\\mathcal {U}_0^s (\\\\gamma ), \\\\quad \\\\forall\\\\ \\\\gamma, whereas in the antisymmetric subspace \\\\lim _{z \\\\rightarrow E_{\\\\rm min}^- } { N^{as}(z) \\\\over | \\\\log | E_{\\\\rm min} -z| | } = \\\\mathcal {U}_0^{as} (\\\\gamma ), \\\\quad \\\\forall\\\\ \\\\gamma \\\\gt \\\\gamma ^*, where \\\\mathcal {U}_0^{ as } (\\\\gamma ), \\\\mathcal {U}_0^s (\\\\gamma ) are written explicitly as a function of the integral kernel of operators acting on L^2((0,r) \\\\times (L^2 (\\\\mathbb {S}^2) \\\\otimes L^2 (\\\\mathbb {S}^2)) (\\\\mathbb {S}^2 is the unit sphere in \\\\mathbb {R}^3). %R 10.1088/1751-8113/44/31/315302 %0 Journal Article %J Calculus of Variations and Partial Differential Equations 40 (2011) 125-181 %D 2011 %T Quasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling %A Gianni Dal Maso %A Antonio DeSimone %A Francesco Solombrino %K Cam-Clay plasticity %XCam-Clay nonassociative plasticity exhibits both hardening and softening behaviour, depending on the loading. For many initial data the classical formulation of the quasistatic evolution problem has no smooth solution. We propose here a notion of generalized solution, based on a viscoplastic approximation. To study the limit of the viscoplastic evolutions we rescale time, in such a way that the plastic strain is uniformly Lipschitz with respect to the rescaled time. The limit of these rescaled solutions, as the viscosity parameter tends to zero, is characterized through an energy-dissipation balance, that can be written in a natural way using the rescaled time. As shown in [4] and [6], the proposed solution may be discontinuous with respect to the original time. Our formulation allows to compute the amount of viscous dissipation occurring instantaneously at each discontinuity time.

%B Calculus of Variations and Partial Differential Equations 40 (2011) 125-181 %I Springer %G en_US %U http://hdl.handle.net/1963/3670 %1 635 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-07-20T08:26:03Z\\r\\nNo. of bitstreams: 1\\r\\nDM-DeS-Sol-36_2009_preprint.pdf: 421582 bytes, checksum: 011806364200378d6deec80b88978550 (MD5) %R 10.1007/s00526-010-0336-0 %0 Journal Article %J Bioinformatics (Oxford, England). 2011 Dec; 27(24):3407-14 %D 2011 %T A system-level approach for deciphering the transcriptional response to prion infection %A Mattia Zampieri %A Giuseppe Legname %A Daniel Segrè %A Claudio Altafini %X MOTIVATION: Deciphering the response of a complex biological system to an insulting event, at the gene expression level, requires adopting theoretical models that are more sophisticated than a one-to-one comparison (i.e. t-test). Here, we investigate the ability of a novel reverse engineering approach (System Response Inference) to unveil non-obvious transcriptional signatures of the system response induced by prion infection.\\r\\nRESULTS: To this end, we analyze previously published gene expression data, from which we extrapolate a putative full-scale model of transcriptional gene-gene dependencies in the mouse central nervous system. Then, we use this nominal model to interpret the gene expression changes caused by prion replication, aiming at selecting the genes primarily influenced by this perturbation. Our method sheds light on the mode of action of prions by identifying key transcripts that are the most likely to be responsible for the overall transcriptional rearrangement from a nominal regulatory network. As a first result of our inference, we have been able to predict known targets of prions (i.e. PrP(C)) and to unveil the potential role of previously unsuspected genes.\\r\\nCONTACT: altafini@sissa.it\\r\\nSUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online. %B Bioinformatics (Oxford, England). 2011 Dec; 27(24):3407-14 %I Oxford University Press %G en %U http://hdl.handle.net/1963/5745 %1 5600 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-04-23T08:12:17Z\\nNo. of bitstreams: 1\\nZaLeSeAl11.pdf: 1229345 bytes, checksum: eb5500741d42ed30ef38112ebd4eae91 (MD5) %R 10.1093/bioinformatics/btr580 %0 Journal Article %J Nonlinear Analysis: Theory, Methods & Applications %D 2011 %T Uniqueness and nondegeneracy of the ground state for a quasilinear Schrödinger equation with a small parameter %A Alessandro Selvitella %K Bifurcation theory %K Nonlinear Schrödinger equations %K Stationary solutions %XWe study least energy solutions of a quasilinear Schrödinger equation with a small parameter. We prove that the ground state is nondegenerate and unique up to translations and phase shifts using bifurcation theory.

%B Nonlinear Analysis: Theory, Methods & Applications %V 74 %P 1731 - 1737 %G eng %U http://www.sciencedirect.com/science/article/pii/S0362546X10007613 %R https://doi.org/10.1016/j.na.2010.10.045 %0 Journal Article %J J. Approx. Theory %D 2010 %T Cauchy biorthogonal polynomials %A Marco Bertola %A Gekhtman, M. %A Szmigielski, J. %B J. Approx. Theory %V 162 %P 832–867 %G eng %U http://0-dx.doi.org.mercury.concordia.ca/10.1016/j.jat.2009.09.008 %R 10.1016/j.jat.2009.09.008 %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 The European journal of neuroscience. 2010 Oct; 32(8):1364-79 %D 2010 %T Gene expression analysis of the emergence of epileptiform activity after focal injection of kainic acid into mouse hippocampus. %A Dario Motti %A Caroline Le Duigou %A Nicole Chemaly %A Lucia Wittner %A Dejan Lazarevic %A Helena Krmac %A Troels Torben Marstrand %A Eivind Valen %A Remo Sanges %A Elia Stupka %A Albin Sandelin %A Enrico Cherubini %A Stefano Gustincich %A Richard Miles %XWe report gene profiling data on genomic processes underlying the progression towards recurrent seizures after injection of kainic acid (KA) into the mouse hippocampus. Focal injection enabled us to separate the effects of proepileptic stimuli initiated by KA injection. Both the injected and contralateral hippocampus participated in the status epilepticus. However, neuronal death induced by KA treatment was restricted to the injected hippocampus, although there was some contralateral axonal degeneration. We profiled gene expression changes in dorsal and ventral regions of both the injected and contralateral hippocampus. Changes were detected in the expression of 1526 transcripts in samples from three time-points: (i) during the KA-induced status epilepticus, (ii) at 2 weeks, before recurrent seizures emerged, and (iii) at 6 months after seizures emerged. Grouping genes with similar spatio-temporal changes revealed an early transcriptional response, strong immune, cell death and growth responses at 2 weeks and an activation of immune and extracellular matrix genes persisting at 6 months. Immunostaining for proteins coded by genes identified from array studies provided evidence for gliogenesis and suggested that the proteoglycan biglycan is synthesized by astrocytes and contributes to a glial scar. Gene changes at 6 months after KA injection were largely restricted to tissue from the injection site. This suggests that either recurrent seizures might depend on maintained processes including immune responses and changes in extracellular matrix proteins near the injection site or alternatively might result from processes, such as growth, distant from the injection site and terminated while seizures are maintained.

%B The European journal of neuroscience. 2010 Oct; 32(8):1364-79 %I Wiley %G en %U http://hdl.handle.net/1963/4480 %1 4244 %2 Neuroscience %3 Neurobiology %4 -1 %$ Approved for entry into archive by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-05T07:58:51Z (GMT) No. of bitstreams: 0 %R 10.1111/j.1460-9568.2010.07403.x %0 Journal Article %J Phys. Rev. A 81 (2010) 062335 %D 2010 %T Homogeneous binary trees as ground states of quantum critical Hamiltonians %A Pietro Silvi %A Vittorio Giovannetti %A Simone Montangero %A Matteo Rizzi %A J. Ignacio Cirac %A Rosario Fazio %XMany-body states whose wave-function admits a representation in terms of a uniform binary-tree tensor decomposition are shown to obey to power-law two-body correlations functions. Any such state can be associated with the ground state of a translational invariant Hamiltonian which, depending on the dimension of the systems sites, involve at most couplings between third-neighboring sites. A detailed analysis of their spectra shows that they admit an exponentially large ground space.

%B Phys. Rev. A 81 (2010) 062335 %I American Physical Society %G en_US %U http://hdl.handle.net/1963/3909 %1 800 %2 Physics %3 Condensed Matter Theory %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-07-27T07:32:21Z\\nNo. of bitstreams: 1\\n0912.0466v1.pdf: 336415 bytes, checksum: 7220d67cfb58f794aa50037140db23e6 (MD5) %R 10.1103/PhysRevA.81.062335 %0 Journal Article %J New J. Phys. 12 (2010) 075018 %D 2010 %T Homogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems %A Matteo Rizzi %A Simone Montangero %A Pietro Silvi %A Vittorio Giovannetti %A Rosario Fazio %XIn this paper, we review the properties of homogeneous multiscale entanglement renormalization ansatz (MERA) to describe quantum critical systems.We discuss in more detail our results for one-dimensional (1D) systems (the Ising and Heisenberg models) and present new data for the 2D Ising model. Together with the results for the critical exponents, we provide a detailed description of the numerical algorithm and a discussion of new optimization\\nstrategies. The relation between the critical properties of the system and the tensor structure of the MERA is expressed using the formalism of quantum channels, which we review and extend.

%B New J. Phys. 12 (2010) 075018 %I IOP Publishing %G en_US %U http://hdl.handle.net/1963/4067 %1 335 %2 Physics %3 Condensed Matter Theory %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-09-16T09:50:44Z\\nNo. of bitstreams: 1\\n10081611392421027.pdf: 1233170 bytes, checksum: 39da921aa8c098e7c8d6451b0ce08c15 (MD5) %R 10.1088/1367-2630/12/7/075018 %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 Journal Article %J Netw. Heterog. Media 5 (2010) 97-132 %D 2010 %T Quasistatic evolution for Cam-Clay plasticity: the spatially homogeneous case %A Gianni Dal Maso %A Francesco Solombrino %K Cam-Clay plasticity %XWe study the spatially uniform case of the problem of quasistatic evolution in small strain nonassociative elastoplasticity (Cam-Clay model). Through the introdution of a viscous approximation, the problem reduces to determine the limit behavior of the solutions of a singularly perturbed system of ODE\\\'s in a finite dimensional Banach space. Depending on the sign of two explicit scalar indicators, we see that the limit dynamics presents, under quite generic assumptions, the alternation of three possible regimes: the elastic regime, when the limit equation is just the equation of linearized elasticity, the slow dynamics, when the strain evolves smoothly on the yield surface and plastic flow is produced, and the fast dynamics, which may happen only in the softening regime, where\\nviscous solutions exhibit a jump across a heteroclinic orbit of an auxiliary system.

%B Netw. Heterog. Media 5 (2010) 97-132 %G en_US %U http://hdl.handle.net/1963/3671 %1 634 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-07-20T08:35:17Z\\nNo. of bitstreams: 1\\nDM-Sol2-39_2009_preprint.pdf: 345995 bytes, checksum: 073ce622e3320be1f56a1cc9f8904fae (MD5) %R 10.3934/nhm.2010.5.97 %0 Journal Article %J Discrete & Continuous Dynamical Systems - A %D 2010 %T Quasistatic evolution for plasticity with softening: The spatially homogeneous case %A Francesco Solombrino %K plasticity with softening %K rate independent processes %XThe spatially uniform case of the problem of quasistatic evolution in small strain associative elastoplasticity with softening is studied. Through the introdution of a viscous approximation, the problem reduces to determine the limit behaviour of the solutions of a singularly perturbed system of ODE's in a finite dimensional Banach space. We see that the limit dynamics presents, for a generic choice of the initial data, the alternation of three possible regimes (elastic regime, slow dynamics, fast dynamics), which is determined by the sign of two scalar indicators, whose explicit expression is given.

%B Discrete & Continuous Dynamical Systems - A %V 27 %P 1189 %G eng %U http://aimsciences.org//article/id/4c2301d8-f553-493e-b672-b4f76a3ede2f %R 10.3934/dcds.2010.27.1189 %0 Journal Article %J Adv. Differential Equations %D 2010 %T Semiclassical evolution of two rotating solitons for the Nonlinear Schrödinger Equation with electric potential %A Alessandro Selvitella %B Adv. Differential Equations %I Khayyam Publishing, Inc. %V 15 %P 315–348 %8 03 %G eng %U https://projecteuclid.org:443/euclid.ade/1355854752 %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire %D 2010 %T Two-dimensional almost-Riemannian structures with tangency points %A Andrei A. Agrachev %A Ugo Boscain %A Grégoire Charlot %A Roberta Ghezzi %A Mario Sigalotti %XTwo-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We study the relation between the topological invariants of an almost-Riemannian structure on a compact oriented surface and the rank-two vector bundle over the surface which defines the structure. We analyse the generic case including the presence of tangency points, i.e. points where two generators of the distribution and their Lie bracket are linearly dependent. The main result of the paper provides a classification of oriented almost-Riemannian structures on compact oriented surfaces in terms of the Euler number of the vector bundle corresponding to the structure. Moreover, we present a Gauss-Bonnet formula for almost-Riemannian structures with tangency points.

%B Ann. Inst. H. Poincare Anal. Non Lineaire %I Elsevier %V 27 %P 793-807 %G en_US %U http://hdl.handle.net/1963/3870 %1 839 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-05-31T14:15:39Z\\nNo. of bitstreams: 1\\n0908.2564v1.pdf: 302590 bytes, checksum: 15369151ee10bb886dc6678350dee7f5 (MD5) %R 10.1016/j.anihpc.2009.11.011 %0 Journal Article %J Arch. Ration. Mech. Anal. 191 (2009) 1-96 %D 2009 %T The boundary Riemann solver coming from the real vanishing viscosity approximation %A Stefano Bianchini %A Laura Spinolo %X We study the limit of the hyperbolic-parabolic approximation $$ \\\\begin{array}{lll} v_t + \\\\tilde{A} ( v, \\\\, \\\\varepsilon v_x ) v_x = \\\\varepsilon \\\\tilde{B}(v ) v_{xx} \\\\qquad v \\\\in R^N\\\\\\\\ \\\\tilde \\\\beta (v (t, \\\\, 0)) = \\\\bar g \\\\\\\\ v (0, \\\\, x) = \\\\bar v_0. \\\\\\\\ \\\\end{array} \\\\right. $$\\nThe function $\\\\tilde \\\\beta$ is defined in such a way to guarantee that the initial boundary value problem is well posed even if $\\\\tilde \\\\beta$ is not invertible.\\nThe data $\\\\bar g$ and $\\\\bar v_0$ are constant. When $\\\\tilde B$ is invertible, the previous problem takes the simpler form $$ \\\\left\\\\{ \\\\begin{array}{lll} v_t + \\\\tilde{A} \\\\big( v, \\\\, \\\\varepsilon v_x \\\\big) v_x = \\\\varepsilon \\\\tilde{B}(v ) v_{xx} \\\\qquad v \\\\in \\\\mathbb{R}^N\\\\\\\\ v (t, \\\\, 0) \\\\equiv \\\\bar v_b \\\\\\\\ v (0, \\\\, x) \\\\equiv \\\\bar{v}_0. \\\\\\\\ \\\\end{array} \\\\right. $$\\nAgain, the data $\\\\bar v_b$ and $\\\\bar v_0$ are constant. The conservative case is included in the previous formulations. It is assumed convergence of the v, smallness of the total variation and other technical hypotheses and it is provided a complete characterization of the limit. The most interesting points are the following two. First, the boundary characteristic case is considered, i.e. one eigenvalue of $\\\\tilde A$ can be 0.\\n Second, as pointed out before we take into account the possibility that $\\\\tilde B$ is not invertible. To deal with this case, we take as hypotheses conditions that were introduced by Kawashima and Shizuta relying on physically meaningful examples. We also introduce a new condition of block linear degeneracy. We prove that, if it is not satisfied, then pathological behaviours may occur. %B Arch. Ration. Mech. Anal. 191 (2009) 1-96 %G en_US %U http://hdl.handle.net/1963/1831 %1 2385 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-06-08T11:20:08Z\\nNo. of bitstreams: 1\\nmath.AP-0605575.pdf: 716141 bytes, checksum: 7686c7f41f7b1f82a595f668049640f2 (MD5) %R 10.1007/s00205-008-0177-6 %0 Journal Article %J Comm. Math. Phys. %D 2009 %T The Cauchy two–matrix model %A Marco Bertola %A M Gekhtman %A J Szmigielski %B Comm. Math. Phys. %V 287 %P 983–1014 %G eng %0 Journal Article %J Rend. Istit. Mat. Univ. Trieste 41 (2009) 35-41 %D 2009 %T A connection between viscous profiles and singular ODEs %A Stefano Bianchini %A Laura Spinolo %B Rend. Istit. Mat. Univ. Trieste 41 (2009) 35-41 %G en_US %U http://hdl.handle.net/1963/2555 %1 1564 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-01-15T10:38:45Z\\nNo. of bitstreams: 1\\nSissa0508M.pdf: 107079 bytes, checksum: 5af029f1d9bcd4f14be2d8774cfa251e (MD5) %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire 26 (2009) 329-349 %D 2009 %T Controllability of the discrete-spectrum Schrodinger equation driven by an external field %A Thomas Chambrion %A Paolo Mason %A Mario Sigalotti %A Ugo Boscain %X We prove approximate controllability of the bilinear Schrodinger equation in the case in which the uncontrolled Hamiltonian has discrete nonresonant\\nspectrum. The results that are obtained apply both to bounded or unbounded domains and to the case in which the control potential is bounded or unbounded. The method relies on finite-dimensional techniques applied to the\\nGalerkin approximations and permits, in addition, to get some controllability properties for the density matrix. Two examples are presented: the harmonic oscillator and the 3D well of potential controlled by suitable potentials. %B Ann. Inst. H. Poincare Anal. Non Lineaire 26 (2009) 329-349 %G en_US %U http://hdl.handle.net/1963/2547 %1 1572 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-01-10T13:32:19Z\\nNo. of bitstreams: 1\\n2008-ttinger.pdf: 270196 bytes, checksum: e706dbae08d996576cefe55f53d7284e (MD5) %R 10.1016/j.anihpc.2008.05.001 %0 Journal Article %J J. Phys. A %D 2009 %T Cubic string boundary value problems and Cauchy biorthogonal polynomials %A Marco Bertola %A Gekhtman, M. %A Szmigielski, J. %B J. Phys. A %V 42 %P 454006, 13 %G eng %U http://0-dx.doi.org.mercury.concordia.ca/10.1088/1751-8113/42/45/454006 %R 10.1088/1751-8113/42/45/454006 %0 Journal Article %J Bioinformatics 25 (2009) 2853-2854 %D 2009 %T ERNEST: a toolbox for chemical reaction network theory %A Nicola Soranzo %A Claudio Altafini %X Summary: ERNEST Reaction Network Equilibria Study Toolbox is a MATLAB package which, by checking various different criteria on the structure of a chemical reaction network, can exclude the multistationarity of the corresponding reaction system. The results obtained are independent of the rate constants of the reactions, and can be used for model discrimination.\\nAvailability and Implementation: The software, implemented in MATLAB, is available under the GNU GPL free software license from http://people.sissa.it/~altafini/papers/SoAl09/. It requires the MATLAB Optimization Toolbox. %B Bioinformatics 25 (2009) 2853-2854 %I Oxford University Press %G en_US %U http://hdl.handle.net/1963/3826 %1 501 %2 Physics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-01-22T11:56:56Z\\nNo. of bitstreams: 1\\nSoAl09.pdf: 30345 bytes, checksum: a3c73c1a74eb623da69be9a9eba3ca72 (MD5) %R 10.1093/bioinformatics/btp513 %0 Journal Article %J BMC Systems Biology (2009) 3:18 %D 2009 %T mRNA stability and the unfolding of gene expression in the long-period yeast metabolic cycle %A Nicola Soranzo %A Mattia Zampieri %A Lorenzo Farina %A Claudio Altafini %X Background: In yeast, genome-wide periodic patterns associated with energy-metabolic oscillations have been shown recently for both short (approx. 40 min) and long (approx. 300 min) periods.\\nResults: The dynamical regulation due to mRNA stability is found to be an important aspect of the genome-wide coordination of the long-period yeast metabolic cycle. It is shown that for periodic genes, arranged in classes according either to expression profile or to function, the pulses of mRNA abundance have phase and width which are directly proportional to the corresponding turnover rates.\\nConclusion: The cascade of events occurring during the yeast metabolic cycle (and their correlation with mRNA turnover) reflects to a large extent the gene expression program observable in other dynamical contexts such as the response to stresses/stimuli. %B BMC Systems Biology (2009) 3:18 %I BioMed Central %G en_US %U http://hdl.handle.net/1963/3630 %1 674 %2 Physics %3 Statistical and Biological Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-05-07T10:19:22Z\\nNo. of bitstreams: 1\\n1752-0509-3-18.pdf: 1143957 bytes, checksum: 3f6f6d33e3da5ee922c0a2c47af61560 (MD5) %R 10.1186/1752-0509-3-18 %0 Journal Article %J J. Convex Anal. %D 2009 %T Quasistatic evolution problems for nonhomogeneous elastic plastic materials %A Francesco Solombrino %XThe paper studies the quasistatic evolution for elastoplastic materials when the yield surface depends on the position in the reference configuration. The main results are obtained when the yield surface is continuous with respect to the space variable. The case of piecewise constant dependence is also considered. The evolution is studied in the framework of the variational formulation for rate independent problems developed by Mielke. The results are proved by adapting the arguments introduced for a constant yield surface, using some properties of convex valued semicontinuous multifunctions. A strong formulation of the problem is also obtained, which includes a pointwise version of the plastic flow rule. Some examples are considered, which show that strain concentration may occur as a consequence of a nonconstant yield surface.

%B J. Convex Anal. %V 16 %P 89–119 %G eng %0 Journal Article %J Journal of Differential Equations %D 2008 %T Asymptotic evolution for the semiclassical nonlinear Schrödinger equation in presence of electric and magnetic fields %A Alessandro Selvitella %XIn this paper we study the semiclassical limit for the solutions of a subcritical focusing NLS with electric and magnetic potentials. We consider in particular the Cauchy problem for initial data close to solitons and show that, when the Planck constant goes to zero, the motion shadows that of a classical particle. Several works were devoted to the case of standing waves: differently from these we show that, in the dynamic version, the Lorentz force appears crucially.

%B Journal of Differential Equations %V 245 %P 2566 - 2584 %G eng %U http://www.sciencedirect.com/science/article/pii/S002203960800243X %R https://doi.org/10.1016/j.jde.2008.05.012 %0 Journal Article %J Bioinformatics 24 (2008) 1510-1515 %D 2008 %T Discerning static and causal interactions in genome-wide reverse engineering problems %A Mattia Zampieri %A Nicola Soranzo %A Claudio Altafini %X Background. In the past years devicing methods for discovering gene regulatory mechanisms at a genome-wide level has become a fundamental topic in the field of system biology. The aim is to infer gene-gene interactions in a more sophisticated and reliable way through the continuously improvement of reverse engineering algorithms exploiting microarray technologies. Motivation. This work is inspired by the several studies suggesting that co-expression is mostly related to \\\"static\\\" stable binding relationships, like belonging to the same protein complex, rather than other types of interactions more of a \\\"causal\\\" and transient nature (metabolic pathway or transcription factor-binding site interaction). Discerning static relationships from causal ones on the basis of their characteristic regulatory structures and in particular identifing \\\"dense modules\\\" with protein complex, and \\\"sparse modules\\\" with causal interactions such as those between transcription factor and corresponding binding site, the performances of different network inference algorithms in artificial and real networks (derived from E.coli and S.cerevisiae) can be tested and compared. Results. Our study shows that methods that try to prune indirect interactions from the inferred gene networks may fail to retrieve genes co-participating in a protein complex. On the other hand they are more robust in the identification of transcription factor-binding sites dependences when multiple transcription factors regulate the expression of the same gene. In the end we confirm the stronger co-expression regarding genes belonging to a protein complex than transcription factor-binding site, according, also, to the effect of multiple transcription factors and a low expression variance. %B Bioinformatics 24 (2008) 1510-1515 %G en_US %U http://hdl.handle.net/1963/2757 %1 1943 %2 Physics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-08-29T08:29:34Z\\nNo. of bitstreams: 1\\nZaSoAl08.pdf: 5513978 bytes, checksum: a0f45096ba7e82edddd03194f8623b1f (MD5) %R 10.1093/bioinformatics/btn220 %0 Journal Article %J SIAM J. Math. Anal. 40 (2008) 1104-1122 %D 2008 %T Eulerian calculus for the displacement convexity in the Wasserstein distance %A Sara Daneri %A Giuseppe Savarè %X In this paper we give a new proof of the (strong) displacement convexity of a class of integral functionals defined on a compact Riemannian manifold satisfying a lower Ricci curvature bound. Our approach does not rely on existence and regularity results for optimal transport maps on Riemannian manifolds, but it is based on the Eulerian point of view recently introduced by Otto and Westdickenberg [SIAM J. Math. Anal., 37 (2005), pp. 1227-1255] and on the metric characterization of the gradient flows generated by the functionals in the Wasserstein space. %B SIAM J. Math. Anal. 40 (2008) 1104-1122 %I SIAM %G en_US %U http://hdl.handle.net/1963/3413 %1 922 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-09T12:32:55Z\\nNo. of bitstreams: 1\\n0801.2455v1.pdf: 504916 bytes, checksum: 7ccfac515ef559e376c7e7d213bd4091 (MD5) %R 10.1137/08071346X %0 Journal Article %J Adv. Math. 219 (2008) 780-837 %D 2008 %T Frobenius Manifolds and Central Invariants for the Drinfeld - Sokolov Bihamiltonian Structures %A Boris Dubrovin %A Liu Si-Qi %A Zhang Youjin %X The Drinfeld - Sokolov construction associates a hierarchy of bihamiltonian integrable systems with every untwisted affine Lie algebra. We compute the complete set of invariants of the related bihamiltonian structures with respect to the group of Miura type transformations. %B Adv. Math. 219 (2008) 780-837 %G en_US %U http://hdl.handle.net/1963/2523 %1 1595 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-11T12:52:04Z\\nNo. of bitstreams: 1\\n0710.3115v1.pdf: 569666 bytes, checksum: e3e72944ffd5f097ccaf975d2df90986 (MD5) %R 10.1016/j.aim.2008.06.009 %0 Journal Article %J Discrete Contin. Dyn. Syst. 20 (2008) 801-822 %D 2008 %T A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds %A Andrei A. Agrachev %A Ugo Boscain %A Mario Sigalotti %X We consider a generalization of Riemannian geometry that naturally arises in the framework of control theory. Let $X$ and $Y$ be two smooth vector fields on a two-dimensional manifold $M$. If $X$ and $Y$ are everywhere linearly independent, then they define a classical Riemannian metric on $M$ (the metric for which they are orthonormal) and they give to $M$ the structure of metric space. If $X$ and $Y$ become linearly dependent somewhere on $M$, then the corresponding Riemannian metric has singularities, but under generic conditions the metric structure is still well defined. Metric structures that can be defined locally in this way are called almost-Riemannian structures. They are special cases of rank-varying sub-Riemannian structures, which are naturally defined in terms of submodules of the space of smooth vector fields on $M$. Almost-Riemannian structures show interesting phenomena, in particular for what concerns the relation between curvature, presence of conjugate points, and topology of the manifold. The main result of the paper is a generalization to almost-Riemannian structures of the Gauss-Bonnet formula. %B Discrete Contin. Dyn. Syst. 20 (2008) 801-822 %G en_US %U http://hdl.handle.net/1963/1869 %1 2353 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-10-11T07:14:06Z\\nNo. of bitstreams: 1\\nmath.oc0609566.pdf: 920147 bytes, checksum: c6f020bc9676ee3966b64f4135e4ce52 (MD5) %R 10.3934/dcds.2008.20.801 %0 Report %D 2008 %T Invariant Manifolds for Viscous Profiles of a Class of Mixed Hyperbolic-Parabolic Systems %A Stefano Bianchini %A Laura Spinolo %G en_US %U http://hdl.handle.net/1963/3400 %1 932 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-12-15T12:03:08Z\\nNo. of bitstreams: 1\\nBianchini_Spinolo.pdf: 146920 bytes, checksum: 27283c16ae26e782e9f0d17c1fbb29d4 (MD5) %0 Journal Article %J SIAM J. Control Optim. 47 (2008) 111-143 %D 2008 %T Limit Time Optimal Syntheses for a control-affine system on S² %A Paolo Mason %A Rebecca Salmoni %A Ugo Boscain %A Yacine Chitour %X For $\\\\alpha \\\\in ]0,\\\\pi/2[$, let $(\\\\Sigma)_\\\\alpha$ be the control system $\\\\dot{x}=(F+uG)x$, where $x$ belongs to the two-dimensional unit sphere $S^2$, $u\\\\in [-1,1]$, and $F,G$ are $3\\\\times3$ skew-symmetric matrices generating rotations with perpendicular axes and of respective norms $\\\\cos(\\\\alpha)$ and $\\\\sin(\\\\alpha)$. In this paper, we study the time optimal synthesis (TOS) from the north pole $(0,0,1)^T$ associated to $(\\\\Sigma)_\\\\alpha$, as the parameter $\\\\alpha$ tends to zero; this problem is motivated by specific issues in the control of quantum systems. We first prove that the TOS is characterized by a \\\"two-snakes\\\" configuration on the whole $S^2$, except for a neighborhood $U_\\\\alpha$ of the south pole $(0,0,-1)^T$ of diameter at most ${\\\\cal O}(\\\\alpha)$. We next show that, inside $U_\\\\alpha$, the TOS depends on the relationship between $r(\\\\alpha):=\\\\pi/2\\\\alpha-[\\\\pi/2\\\\alpha]$ and $\\\\alpha$. More precisely, we characterize three main relationships by considering sequences $(\\\\alpha_k)_{k\\\\geq 0}$ satisfying (a) $r(\\\\alpha_k)=\\\\bar{r}$, (b) $r(\\\\alpha_k)=C\\\\alpha_k$, and (c) $r(\\\\alpha_k)=0$, where $\\\\bar{r}\\\\in (0,1)$ and $C>0$. In each case, we describe the TOS and provide, after a suitable rescaling, the limiting behavior, as $\\\\alpha$ tends to zero, of the corresponding TOS inside $U_\\\\alpha$. %B SIAM J. Control Optim. 47 (2008) 111-143 %G en_US %U http://hdl.handle.net/1963/1862 %1 2360 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-09-28T11:24:18Z\\nNo. of bitstreams: 1\\n48-M.pdf: 5823285 bytes, checksum: 7f66cf9d280da78b56a423c415d9078c (MD5) %R 10.1137/060675988 %0 Journal Article %J PLoS ONE 3 (2008) e2981 %D 2008 %T Origin of Co-Expression Patterns in E.coli and S.cerevisiae Emerging from Reverse Engineering Algorithms %A Mattia Zampieri %A Nicola Soranzo %A Daniele Bianchini %A Claudio Altafini %X Background: The concept of reverse engineering a gene network, i.e., of inferring a genome-wide graph of putative genegene interactions from compendia of high throughput microarray data has been extensively used in the last few years to deduce/integrate/validate various types of \\\"physical\\\" networks of interactions among genes or gene products. Results: This paper gives a comprehensive overview of which of these networks emerge significantly when reverse engineering large collections of gene expression data for two model organisms, E.coli and S.cerevisiae, without any prior information. For the first organism the pattern of co-expression is shown to reflect in fine detail both the operonal structure of the DNA and the regulatory effects exerted by the gene products when co-participating in a protein complex. For the second organism we find that direct transcriptional control (e.g., transcription factor-binding site interactions) has little statistical significance in comparison to the other regulatory mechanisms (such as co-sharing a protein complex, colocalization on a metabolic pathway or compartment), which are however resolved at a lower level of detail than in E.coli. Conclusion: The gene co-expression patterns deduced from compendia of profiling experiments tend to unveil functional categories that are mainly associated to stable bindings rather than transient interactions. The inference power of this systematic analysis is substantially reduced when passing from E.coli to S.cerevisiae. This extensive analysis provides a way to describe the different complexity between the two organisms and discusses the critical limitations affecting this type of methodologies. %B PLoS ONE 3 (2008) e2981 %G en_US %U http://hdl.handle.net/1963/2722 %1 1379 %2 Physics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-08-25T15:50:20Z\\nNo. of bitstreams: 1\\nPLOSe2981.pdf: 853455 bytes, checksum: 91361e24e96e09bbaa6f3083a73e3db4 (MD5) %R 10.1371/journal.pone.0002981 %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 Journal Article %J Bioinformatics 23 (2007) 1640-1647 %D 2007 %T Comparing association network algorithms for reverse engineering of large scale gene regulatory networks: synthetic vs real data %A Nicola Soranzo %A Ginestra Bianconi %A Claudio Altafini %X Motivation: Inferring a gene regulatory network exclusively from microarray expression profiles is a difficult but important task. The aim of this work is to compare the predictive power of some of the most popular algorithms in different conditions (like data taken at equilibrium or time courses) and on both synthetic and real microarray data. We are in particular interested in comparing similarity measures both of linear type (like correlations and partial correlations) and of nonlinear type (mutual information and conditional mutual information), and in investigating the underdetermined case (less samples than genes). Results: In our simulations we see that all network inference algorithms obtain better performances from data produced with \\\"structural\\\" perturbations, like gene knockouts at steady state, than with any dynamical perturbation. The predictive power of all algorithms is confirmed on a reverse engineering problem from E. coli gene profiling data: the edges of the \\\"physical\\\" network of transcription factor-binding sites are significantly overrepresented among the highest weighting edges of the graph that we infer directly from the data without any structure supervision. Comparing synthetic and in vivo data on the same network graph allows us to give an indication of how much more complex a real transcriptional regulation program is with respect to an artificial model. Availability: Software and supplementary material are freely available at the URL http://people.sissa.it/~altafini/papers/SoBiAl07/ %B Bioinformatics 23 (2007) 1640-1647 %G en_US %U http://hdl.handle.net/1963/2028 %1 2168 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-03T12:44:53Z\\nNo. of bitstreams: 1\\nSoBiAl07.pdf: 261510 bytes, checksum: dde8f62bdbd57a761204f8533569885a (MD5) %R 10.1093/bioinformatics/btm163 %0 Journal Article %J Indiana Univ. Math. J. 56 (2007) 2413-2438 %D 2007 %T Convergence of equilibria of planar thin elastic beams %A Maria Giovanna Mora %A Stefan Müller %A Maximilian G. Schultz %X We consider a thin elastic strip of thickness h and we show that stationary points of the nonlinear elastic energy (per unit height) whose energy is of order h^2 converge to stationary points of the Euler-Bernoulli functional. The proof uses the rigidity estimate for low-energy deformations by Friesecke, James, and Mueller (Comm. Pure Appl. Math. 2002), and a compensated compactness argument in a singular geometry. In addition, possible concentration effects are ruled out by a careful truncation argument. %B Indiana Univ. Math. J. 56 (2007) 2413-2438 %G en_US %U http://hdl.handle.net/1963/1830 %1 2386 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-06-08T11:03:04Z\\nNo. of bitstreams: 1\\nmath.fa-0604554.pdf: 263517 bytes, checksum: 1ad7fad8323aa78951b53178a78c3030 (MD5) %R 10.1512/iumj.2007.56.3023 %0 Journal Article %J Ann. Inst. Henri Poincare-Prob. Stat. 43 (2007) 399-415 %D 2007 %T On finite-dimensional projections of distributions for solutions of randomly forced PDE\\\'s %A Andrei A. Agrachev %A Sergei Kuksin %A Andrey Sarychev %A Armen Shirikyan %X The paper is devoted to studying the image of probability measures on a Hilbert space under finite-dimensional analytic maps. We establish sufficient conditions under which the image of a measure has a density with respect to the Lebesgue measure and continuously depends on the map. The results obtained are applied to the 2D Navier-Stokes equations perturbed by various random forces of low dimension. %B Ann. Inst. Henri Poincare-Prob. Stat. 43 (2007) 399-415 %G en_US %U http://hdl.handle.net/1963/2012 %1 2184 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-08-31T09:21:55Z\\nNo. of bitstreams: 1\\nmathAP0603295v1.pdf: 316127 bytes, checksum: 6686ad78dcb2dbc5efb64a959b30750c (MD5) %R 10.1016/j.anihpb.2006.06.001 %0 Report %D 2007 %T High-order angles in almost-Riemannian geometry %A Ugo Boscain %A Mario Sigalotti %X Let X and Y be two smooth vector fields on a two-dimensional manifold M. If X and Y are everywhere linearly independent, then they define a Riemannian metric on M (the metric for which they are orthonormal) and they give to M the structure of metric space. If X and Y become linearly dependent somewhere on M, then the corresponding Riemannian metric has singularities, but under generic conditions the metric structure is still well defined. Metric structures that can be defined locally in this way are called almost-Riemannian structures. The main result of the paper is a generalization to almost-Riemannian structures of the Gauss-Bonnet formula for domains with piecewise-C2 boundary. The main feature of such formula is the presence of terms that play the role of high-order angles at the intersection points with the set of singularities. %G en_US %U http://hdl.handle.net/1963/1995 %1 2201 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-08-24T12:00:46Z\\nNo. of bitstreams: 1\\nhigh-order.pdf: 168685 bytes, checksum: 11d6f55bf9b07b4da01dae3f3deb969a (MD5) %0 Journal Article %J Arch. Rational Mech. Anal. 183 (2007) 411-456 %D 2007 %T Surfactants in Foam Stability: A Phase-Field Model %A Irene Fonseca %A Massimiliano Morini %A Valeriy Slastikov %X The role of surfactants in stabilizing the formation of bubbles in foams is studied using a phase-field model. The analysis is centered on a van der Walls-Cahn-Hilliard-type energy with an added term accounting for the interplay between the presence of a surfactant density and the creation of interfaces. In particular, it is concluded that the surfactant segregates to the interfaces, and that the prescriptionof the distribution of surfactant will dictate the locus of interfaces, what is in agreement with experimentation. %B Arch. Rational Mech. Anal. 183 (2007) 411-456 %G en_US %U http://hdl.handle.net/1963/2035 %1 2161 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-03T15:51:40Z\\nNo. of bitstreams: 1\\n05-CNA-012.pdf: 414998 bytes, checksum: 3c44841388edba53080d531beadad798 (MD5) %R 10.1007/s00205-006-0012-x %0 Journal Article %J Molecular pharmacology. 2006 Jul; 70(1):373-82 %D 2006 %T Experimental and modeling studies of desensitization of P2X3 receptors. %A Elena Sokolova %A Andrei Skorinkin %A Igor Moiseev %A Andrei A. Agrachev %A Andrea Nistri %A Rashid Giniatullin %X The function of ATP-activated P2X3 receptors involved in pain sensation is modulated by desensitization, a phenomenon poorly understood. The present study used patch-clamp recording from cultured rat or mouse sensory neurons and kinetic modeling to clarify the properties of P2X3 receptor desensitization. Two types of desensitization were observed, a fast process (t1/2 = 50 ms; 10 microM ATP) following the inward current evoked by micromolar agonist concentrations, and a slow process (t1/2 = 35 s; 10 nM ATP) that inhibited receptors without activating them. We termed the latter high-affinity desensitization (HAD). Recovery from fast desensitization or HAD was slow and agonist-dependent. When comparing several agonists, there was analogous ranking order for agonist potency, rate of desensitization and HAD effectiveness, with 2-methylthioadenosine triphosphate the strongest and beta,gamma-methylene-ATP the weakest. HAD was less developed with recombinant (ATP IC50 = 390 nM) than native P2X3 receptors (IC50 = 2.3 nM). HAD could also be induced by nanomolar ATP when receptors seemed to be nondesensitized, indicating that resting receptors could express high-affinity binding sites. Desensitization properties were well accounted for by a cyclic model in which receptors could be desensitized from either open or closed states. Recovery was assumed to be a multistate process with distinct kinetics dependent on the agonist-dependent dissociation rate from desensitized receptors. Thus, the combination of agonist-specific mechanisms such as desensitization onset, HAD, and resensitization could shape responsiveness of sensory neurons to P2X3 receptor agonists. By using subthreshold concentrations of an HAD-potent agonist, it might be possible to generate sustained inhibition of P2X3 receptors for controlling chronic pain. %B Molecular pharmacology. 2006 Jul; 70(1):373-82 %I the American Society for Pharmacology and Experimental Therapeutics %G en %U http://hdl.handle.net/1963/4974 %1 4799 %2 Neuroscience %3 Neurobiology %4 -1 %$ Submitted by Alireza Alemi-neissi (alemi@sissa.it) on 2011-10-30T18:23:32Z\\nNo. of bitstreams: 0 %R 10.1124/mol.106.023564 %0 Journal Article %J Comm. Pure Appl. Math. 59 (2006) 559-615 %D 2006 %T On Hamiltonian perturbations of hyperbolic systems of conservation laws I: quasitriviality of bihamiltonian perturbations %A Boris Dubrovin %A Liu Si-Qi %A Zhang Youjin %X We study the general structure of formal perturbative solutions to the Hamiltonian perturbations of spatially one-dimensional systems of hyperbolic PDEs. Under certain genericity assumptions it is proved that any bihamiltonian perturbation can be eliminated in all orders of the perturbative expansion by a change of coordinates on the infinite jet space depending rationally on the derivatives. The main tools is in constructing of the so-called quasi-Miura transformation of jet coordinates eliminating an arbitrary deformation of a semisimple bihamiltonian structure of hydrodynamic type (the quasitriviality theorem). We also describe, following \\\\cite{LZ1}, the invariants of such bihamiltonian structures with respect to the group of Miura-type transformations depending polynomially on the derivatives. %B Comm. Pure Appl. Math. 59 (2006) 559-615 %G en_US %U http://hdl.handle.net/1963/2535 %1 1583 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-18T13:01:41Z\\nNo. of bitstreams: 1\\n0410027v2.pdf: 508002 bytes, checksum: 4e8fc8db5fc7512dd54eb832cc52192d (MD5) %R 10.1002/cpa.20111 %0 Journal Article %J J. Differential Geom. 73 (2006) 1-44 %D 2006 %T Q-curvature flow on S^4 %A Andrea Malchiodi %A Michael Struwe %B J. Differential Geom. 73 (2006) 1-44 %G en_US %U http://hdl.handle.net/1963/2193 %1 2051 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-10T11:52:21Z\\nNo. of bitstreams: 1\\nQ-curv-Nov-05.pdf: 298052 bytes, checksum: 2916315e6ffcef99b7748745e768d831 (MD5) %0 Report %D 2006 %T Stability of planar nonlinear switched systems %A Ugo Boscain %A Grégoire Charlot %A Mario Sigalotti %X We consider the time-dependent nonlinear system ˙ q(t) = u(t)X(q(t)) + (1 − u(t))Y (q(t)), where q ∈ R2, X and Y are two smooth vector fields, globally asymptotically stable at the origin and u : [0,∞) → {0, 1} is an arbitrary measurable function. Analysing the topology of the set where X and Y are parallel, we give some sufficient and some necessary conditions for global asymptotic stability, uniform with respect to u(.). Such conditions can be verified without any integration or construction of a Lyapunov function, and they are robust under small perturbations of the vector fields. %B Discrete Contin. Dyn. Syst. 15 (2006) 415-432 %G en_US %U http://hdl.handle.net/1963/1710 %1 2441 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-01-18T08:35:31Z\\nNo. of bitstreams: 1\\nmath.OC0502361.pdf: 322404 bytes, checksum: e56f0d709d97e2e300e3cb9d4a629a1b (MD5) %0 Journal Article %J Commun. Math. Phys. 259 (2005) 729-759 %D 2005 %T The Dirac operator on SU_q(2) %A Ludwik Dabrowski %A Giovanni Landi %A Andrzej Sitarz %A Walter van Suijlekom %A Joseph C. Varilly %X We construct a 3^+ summable spectral triple (A(SU_q(2)),H,D) over the quantum group SU_q(2) which is equivariant with respect to a left and a right action of U_q(su(2)). The geometry is isospectral to the classical case since the spectrum of the operator D is the same as that of the usual Dirac operator on the 3-dimensional round sphere. The presence of an equivariant real structure J demands a modification in the axiomatic framework of spectral geometry, whereby the commutant and first-order properties need be satisfied only modulo infinitesimals of arbitrary high order. %B Commun. Math. Phys. 259 (2005) 729-759 %I Springer %G en %U http://hdl.handle.net/1963/4425 %1 4175 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-04T08:01:47Z No. of bitstreams: 1 math_0411609v2.pdf: 293099 bytes, checksum: cfa2846ded2ecf161e83f4269b65e9b2 (MD5) %R 10.1007/s00220-005-1383-9 %0 Journal Article %J K-Theory 35 (2005) 375-394 %D 2005 %T The local index formula for SUq(2) %A Walter van Suijlekom %A Ludwik Dabrowski %A Giovanni Landi %A Andrzej Sitarz %A Joseph C. Varilly %X We discuss the local index formula of Connes-Moscovici for the isospectral noncommutative geometry that we have recently constructed on quantum SU(2). We work out the cosphere bundle and the dimension spectrum as well as the local cyclic cocycles yielding the index formula. %B K-Theory 35 (2005) 375-394 %G en_US %U http://hdl.handle.net/1963/1713 %1 2438 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-01-18T10:14:50Z\\nNo. of bitstreams: 1\\nmath.QA0501287.pdf: 189281 bytes, checksum: 75a780cbe958f6093e340102ad9bf176 (MD5) %R 10.1007/s10977-005-3116-4 %0 Journal Article %J Journal of Mathematical Sciences 126 (2005) 1561-1573 %D 2005 %T Regularity properties of optimal trajectories of single-input control systems in dimension three %A Mario Sigalotti %X Let q=f(q)+ug(q) be a smooth control system on a three-dimensional manifold. Given a point q 0 of the manifold at which the iterated Lie brackets of f and g satisfy some prescribed independence condition, we analyze the structure of a control function u(t) corresponding to a time-optimal trajectory lying in a neighborhood of q 0. The control turns out to be the concatenation of some bang-bang and some singular arcs. More general optimality criteria than time-optimality are considered. The paper is a step toward to the analysis of generic single-input systems affine in the control in dimension 3. The main techniques used are second-order optimality conditions and, in particular, the index of the second variation of the switching times for bang-bang trajectories. %B Journal of Mathematical Sciences 126 (2005) 1561-1573 %I Springer %G en %U http://hdl.handle.net/1963/4794 %1 4564 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-17T08:06:19Z\\nNo. of bitstreams: 1\\nsuz.pdf: 199707 bytes, checksum: 1d18998eb7281177da4a442135d9b77d (MD5) %R 10.1007/s10958-005-0044-z %0 Journal Article %J C. R. Math. 340 (2005) 819-822 %D 2005 %T The spectral geometry of the equatorial Podles sphere %A Ludwik Dabrowski %A Giovanni Landi %A Mario Paschke %A Andrzej Sitarz %X We propose a slight modification of the properties of a spectral geometry a la Connes, which allows for some of the algebraic relations to be satisfied only modulo compact operators. On the equatorial Podles sphere we construct suq2-equivariant Dirac operator and real structure which satisfy these modified properties. %B C. R. Math. 340 (2005) 819-822 %G en_US %U http://hdl.handle.net/1963/2275 %1 1972 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-22T09:37:10Z\\nNo. of bitstreams: 1\\n0408034v2.pdf: 95565 bytes, checksum: 1c0e7836d4006a796eb943f128938773 (MD5) %R 10.1016/j.crma.2005.04.003 %0 Journal Article %J Internat. J. Game Theory 32 (2004) 561-593 %D 2004 %T Semi-cooperative strategies for differential games %A Alberto Bressan %A Wen Shen %X The paper is concerned with a non-cooperative differential game for two players. We first consider Nash equilibrium solutions in feedback form. In this case, we show that the Cauchy problem for the value functions is generically ill-posed. Looking at vanishing viscosity approximations, one can construct special solutions in the form of chattering controls, but these also appear to be unstable. In the second part of the paper we propose an alternative \\\"semi-cooperative\\\" pair of strategies for the two players, seeking a Pareto optimum instead of a Nash equilibrium. In this case, we prove that the corresponding Hamiltonian system for the value functions is always weakly hyperbolic. %B Internat. J. Game Theory 32 (2004) 561-593 %I Springer %G en_US %U http://hdl.handle.net/1963/2893 %1 1807 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T08:11:56Z\\nNo. of bitstreams: 1\\n069.pdf: 389569 bytes, checksum: 3cea0d9a5adfd0be673a7d69218e238a (MD5) %R 10.1007/s001820400180 %0 Journal Article %J SIAM J. Control Optim. 43 (2004) 194-215 %D 2004 %T Small BV solutions of hyperbolic noncooperative differential games %A Alberto Bressan %A Wen Shen %X The paper is concerned with an n-persons differential game in one space dimension. We state conditions for which the system of Hamilton-Jacobi equations for the value functions is strictly hyperbolic. In the positive case, we show that the weak solution of a corresponding system of conservation laws determines an n-tuple of feedback strategies. These yield a Nash equilibrium solution to the non-cooperative differential game. %B SIAM J. Control Optim. 43 (2004) 194-215 %I SIAM %G en_US %U http://hdl.handle.net/1963/2917 %1 1783 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T13:46:04Z\\nNo. of bitstreams: 1\\n021.pdf: 296267 bytes, checksum: 16f3c148f2a00551188fee22ac90f666 (MD5) %R 10.1137/S0363012903425581 %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 SIAM J. Control Optim. 42 (2003) 513-531 %D 2003 %T On the local structure of optimal trajectories in R3 %A Andrei A. Agrachev %A Mario Sigalotti %X We analyze the structure of a control function u(t) corresponding to an optimal trajectory for the system $\\\\dot q =f(q)+u\\\\, g(q)$ in a three-dimensional manifold, near a point where some nondegeneracy conditions are satisfied. The kind of optimality which is studied includes time-optimality. The control turns out to be the concatenation of some bang and some singular arcs. Studying the index of the second variation of the switching times, the number of such arcs is bounded by four. %B SIAM J. Control Optim. 42 (2003) 513-531 %I SISSA Library %G en %U http://hdl.handle.net/1963/1612 %1 2506 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:18Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002 %R 10.1137/S0363012902409246 %0 Thesis %D 2003 %T Single-Input Control Affine Systems: Local Regularity of Optimal Trajectories and a Geometric Controllability Problem %A Mario Sigalotti %I SISSA %G en %U http://hdl.handle.net/1963/5342 %1 5170 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Gerardina Cargnelutti (gerry@sissa.it) on 2012-02-02T12:08:29Z\\nNo. of bitstreams: 1\\nPhD_Sigalotti_Mario.pdf: 8050196 bytes, checksum: e113b00d1c0f5b37484c26f023914baa (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 Proc. Steklov Inst. Math. 236 (2002) 395-414 %D 2002 %T The passage from nonconvex discrete systems to variational problems in Sobolev spaces: the one-dimensional case %A Andrea Braides %A Maria Stella Gelli %A Mario Sigalotti %B Proc. Steklov Inst. Math. 236 (2002) 395-414 %I MAIK Nauka/Interperiodica %G en_US %U http://hdl.handle.net/1963/3130 %1 1203 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-16T15:53:06Z\\nNo. of bitstreams: 1\\npassage.pdf: 242138 bytes, checksum: 1874bdb2ad8c185c3fe84d7deb988b5b (MD5) %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 Noncommutative geometry and quantum groups (Warsaw 2001),49,Banach Center Publ., 61, Polish Acad.Sci., Warsaw,2003 %D 2001 %T Dirac operator on the standard Podles quantum sphere %A Ludwik Dabrowski %A Andrzej Sitarz %B Noncommutative geometry and quantum groups (Warsaw 2001),49,Banach Center Publ., 61, Polish Acad.Sci., Warsaw,2003 %I SISSA Library %G en %U http://hdl.handle.net/1963/1668 %1 2450 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T13:06:10Z (GMT). No. of bitstreams: 1\\nmath.QA0209048.pdf: 89749 bytes, checksum: e1bc2f04a36a957d4fb3131860296c18 (MD5)\\n Previous issue date: 2002 %0 Journal Article %J Adv. Math. Sci. Appl. 11 (2001) 721-751 %D 2001 %T A monotonicity approach to nonlinear Dirichlet problems in perforated domains %A Gianni Dal Maso %A Igor V. Skrypnik %X We study the asymptotic behaviour of solutions to Dirichlet problems in perforated domains for nonlinear elliptic equations associated with monotone operators. The main difference with respect to the previous papers on this subject is that no uniformity is assumed in the monotonicity condition. Under a very general hypothesis on the holes of the domains, we construct a limit equation, which is satisfied by the weak limits of the solutions. The additional term in the limit problem depends only on the local behaviour of the holes, which can be expressed in terms of suitable nonlinear capacities associated with the monotone operator. %B Adv. Math. Sci. Appl. 11 (2001) 721-751 %I SISSA Library %G en %U http://hdl.handle.net/1963/1555 %1 2563 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:04Z (GMT). No. of bitstreams: 1\\nmath.AP0010232.pdf: 246554 bytes, checksum: 691b6fb5c795a48324b128ced5a3cc44 (MD5)\\n Previous issue date: 2000 %0 Journal Article %J Arch. Ration. Mech. An., 2001, 159, 253 %D 2001 %T Multiplicity results for some nonlinear Schrodinger equations with potentials %A Antonio Ambrosetti %A Andrea Malchiodi %A Simone Secchi %B Arch. Ration. Mech. An., 2001, 159, 253 %I SISSA Library %G en %U http://hdl.handle.net/1963/1564 %1 2554 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:12Z (GMT). No. of bitstreams: 1\\nmath.AP0011195.pdf: 190473 bytes, checksum: a234c5a09c7dc021355fabc212c8ccb4 (MD5)\\n Previous issue date: 2000 %R 10.1007/s002050100152 %0 Journal Article %J Proc. Roy. Soc. Edinburgh Sect. A 131 (2001) 909-925 %D 2001 %T On the spreading of characteristics for non-convex conservation laws %A Helge Kristian Jenssen %A Carlo Sinestrari %X We study the spreading of characteristics for a class of one-dimensional scalar conservation laws for which the flux function has one point of inflection. It is well known that in the convex case the characteristic speed satisfies a one-sided Lipschitz estimate. Using Dafermos\\\' theory of generalized characteristics, we show that the characteristic speed in the non-convex case satisfies an Hölder estimate. In addition, we give a one-sided Lipschitz estimate with an error term given by the decrease of the total variation of the solution. %B Proc. Roy. Soc. Edinburgh Sect. A 131 (2001) 909-925 %I Cambridge University Press %G en_US %U http://hdl.handle.net/1963/3265 %1 1436 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-11-10T13:53:07Z\\nNo. of bitstreams: 1\\nJS2.pdf: 302742 bytes, checksum: 563821a822c34aef0ca1b4c55065827c (MD5) %R 10.1017/S0308210500001189 %0 Journal Article %J Discrete Contin. Dynam. Systems 6 (2000) 21-38 %D 2000 %T BV estimates for multicomponent chromatography with relaxation %A Alberto Bressan %A Wen Shen %X We consider the Cauchy problem for a system of $2n$ balance laws which arises from the modelling of multi-component chromatography: $$\\\\left\\\\{ \\\\eqalign{u_t+u_x&=-{1\\\\over\\\\ve}\\\\big( F(u)-v\\\\big),\\\\cr v_t&={1\\\\over\\\\ve}\\\\big( F(u)-v\\\\big),\\\\cr}\\\\right. \\\\eqno(1)$$ This model describes a liquid flowing with unit speed over a solid bed. Several chemical substances are partly dissolved in the liquid, partly deposited on the solid bed. Their concentrations are represented respectively by the vectors $u=(u_1,\\\\ldots,u_n)$ and $v=(v_1,\\\\ldots,v_n)$. We show that, if the initial data have small total variation, then the solution of (1) remains with small variation for all times $t\\\\geq 0$. Moreover, using the $\\\\L^1$ distance, this solution depends Lipschitz continuously on the initial data, with a Lipschitz constant uniform w.r.t.~$\\\\ve$. Finally we prove that as $\\\\ve\\\\to 0$, the solutions of (1) converge to a limit described by the system $$\\\\big(u+F(u)\\\\big)_t+u_x=0,\\\\qquad\\\\qquad v=F(u).\\\\eqno(2)$$ The proof of the uniform BV estimates relies on the application of probabilistic techniques. It is shown that the components of the gradients $v_x,u_x$ can be interpreted as densities of random particles travelling with speed 0 or 1. The amount of coupling between different components is estimated in terms of the expected number of crossing of these random particles. This provides a first example where BV estimates are proved for general solutions to a class of $2n\\\\times 2n$ systems with relaxation. %B Discrete Contin. Dynam. Systems 6 (2000) 21-38 %I SISSA Library %G en %U http://hdl.handle.net/1963/1336 %1 3119 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:56:27Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %0 Journal Article %J Nuclear Phys. B %D 2000 %T Decomposing quantum fields on branes %A Marco Bertola %A Bros, Jacques %A Gorini, Vittorio %A Moschella, Ugo %A Schaeffer, Richard %B Nuclear Phys. B %V 581 %P 575–603 %G eng %0 Journal Article %J Nuclear Phys. B %D 2000 %T A general construction of conformal field theories from scalar anti-de Sitter quantum field theories %A Marco Bertola %A Bros, Jacques %A Moschella, Ugo %A Schaeffer, Richard %B Nuclear Phys. B %V 587 %P 619–644 %G eng %0 Journal Article %D 2000 %T High-order Averaging and Stability of Time-Varying Systems %A Andrey Sarychev %I SISSA Library %G en %U http://hdl.handle.net/1963/1465 %1 3075 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:02:47Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %0 Journal Article %J SIAM J. Control Optim. 39 (2000) 359-410 %D 2000 %T Regular Synthesis and Sufficiency Conditions for Optimality %A Benedetto Piccoli %A Hector J. Sussmann %X We propose a definition of \\\"regular synthesis\\\" that is more general than those suggested by other authors such as Boltyanskii and Brunovsky, and an even more general notion of \\\"regular presynthesis.\\\" We give a complete proof of the corresponding sufficiency theorem, a slightly weaker version of which had been stated in an earlier article, with only a rough outline of the proof. We illustrate the strength of our result by showing that the optimal synthesis for the famous Fuller problem satisfies our hypotheses. We also compare our concept of synthesis with the simpler notion of a \\\"family of solutions of the closed-loop equation arising from an optimal feedback law,\\\" and show by means of examples why the latter is inadequate, and why the difficulty cannot be resolved byusing other concepts of solution--such as Filippov solutions, or the limits of sample-and-hold solutions recently proposed as feedback solutions by Clarke, Ledyaev, Subbotin and Sontag -for equations with a non-Lipschitz and possibly discontinuous right-hand side. %B SIAM J. Control Optim. 39 (2000) 359-410 %I SIAM %G en_US %U http://hdl.handle.net/1963/3213 %1 1088 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-30T10:03:13Z\\nNo. of bitstreams: 1\\npiccolisussmann.pdf: 302609 bytes, checksum: 5cd7041b7e00172b4670a5e17f815e63 (MD5) %R 10.1137/S0363012999322031 %0 Journal Article %J Journal d\\\'Analyse Mathematique, Volume 79, 1999, Pages: 63-112 %D 1999 %T Asymptotic behaviour of nonlinear elliptic higher order equations in perforated domains %A Gianni Dal Maso %A Igor V. Skrypnik %B Journal d\\\'Analyse Mathematique, Volume 79, 1999, Pages: 63-112 %@ 1618-1891 %G en %U http://hdl.handle.net/1963/6433 %1 6374 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-31T18:25:49Z\\nNo. of bitstreams: 0 %R 10.1007/BF01759365 %0 Journal Article %J Comm. in Partial Differential Equations 24 (1999) 2237-2261 %D 1999 %T Blowup asymptotics for scalar conservation laws with a source %A Helge Kristian Jenssen %A Carlo Sinestrari %B Comm. in Partial Differential Equations 24 (1999) 2237-2261 %I Taylor and Francis %G en_US %U http://hdl.handle.net/1963/3482 %1 782 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-04T09:24:17Z\\nNo. of bitstreams: 1\\nJenssen_Sinestrari.pdf: 273573 bytes, checksum: 309317a9fa20bd7a5c05c98b059384b8 (MD5) %R 10.1080/03605309908821500 %0 Journal Article %J Comm. Math. Phys. 206 (1999) 265-272 %D 1999 %T Categorial mirror symmetry for K3 surfaces %A Claudio Bartocci %A Ugo Bruzzo %A Guido Sanguinetti %X We study the structure of a modified Fukaya category ${\\\\frak F}(X)$ associated with a K3 surface $X$, and prove that whenever $X$ is an elliptic K3 surface with a section, the derived category of $\\\\fF(X)$ is equivalent to a subcategory of the derived category ${\\\\bold D}(\\\\hat X)$ of coherent sheaves on the mirror K3 surface $\\\\hat X$. %B Comm. Math. Phys. 206 (1999) 265-272 %I Springer %G en_US %U http://hdl.handle.net/1963/2887 %1 1813 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-10T10:27:18Z\\nNo. of bitstreams: 1\\n9811004v2.pdf: 164135 bytes, checksum: 85c711ba84f77d68351d95af3caad50c (MD5) %R 10.1007/s002200050705 %0 Journal Article %J Phys. Lett. B %D 1999 %T Correspondence between Minkowski and de Sitter quantum field theory %A Marco Bertola %A Gorini, Vittorio %A Moschella, Ugo %A Schaeffer, Richard %B Phys. Lett. B %V 462 %P 249–253 %G eng %0 Journal Article %J Ann. Mat. Pura Appl. (4) 174 (1998), 13--72 %D 1998 %T Asymptotic behavior of nonlinear Dirichlet problems in perforated domains %A Gianni Dal Maso %A Igor V. Skrypnik %B Ann. Mat. Pura Appl. (4) 174 (1998), 13--72 %I SISSA Library %G en %U http://hdl.handle.net/1963/1064 %1 2738 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:42:20Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Journal Article %J Gravit. Cosmol. %D 1998 %T Generation of primordial fluctuations in curved spaces %A Schaeffer, Richard %A Moschella, Ugo %A Marco Bertola %A Gorini, Vittorio %B Gravit. Cosmol. %V 4 %P 121–127 %G eng %0 Journal Article %J Lett. Math. Phys. 45 (1998) 295-301 %D 1998 %T Mirror Symmetry on K3 Surfaces as a Hyper-Kähler Rotation %A Ugo Bruzzo %A Guido Sanguinetti %X We show that under the hypotheses of Strominger, Yau and Zaslow\\\'s paper, a mirror partner of a K3 surface $X$ with a fibration in special Lagrangian tori can be obtained by rotating the complex structure of $X$ within its hyperk\\\\\\\"ahler family of complex structures. The same hypotheses force the B-field to vanish. %B Lett. Math. Phys. 45 (1998) 295-301 %I Springer %G en_US %U http://hdl.handle.net/1963/2888 %1 1812 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-10T10:35:22Z\\nNo. of bitstreams: 1\\n9802044v2.pdf: 129367 bytes, checksum: 369a1a7e15b37b7dc68701a87a156cd9 (MD5) %R 10.1023/A:1007446916202 %0 Journal Article %J Nonlinear Analysis 34 (1998) 637-652 %D 1998 %T Uniqueness for discontinuous ODE and conservation laws %A Alberto Bressan %A Wen Shen %X Consider a scalar O.D.E. of the form $\\\\dot x=f(t,x),$ where $f$ is possibly discontinuous w.r.t. both variables $t,x$. Under suitable assumptions, we prove that the corresponding Cauchy problem admits a unique solution, which depends H\\\\\\\"older continuously on the initial data.\\nOur result applies in particular to the case where $f$ can be written in the form $f(t,x)\\\\doteq g\\\\big( u(t,x)\\\\big)$, for some function $g$ and some solution $u$ of a scalar conservation law, say $u_t+F(u)_x=0$. In turn, this yields the uniqueness and continuous dependence of solutions to a class of $2\\\\times 2$ strictly hyperbolic systems, with initial data in $\\\\L^\\\\infty$. %B Nonlinear Analysis 34 (1998) 637-652 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3699 %1 606 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-07-28T09:39:33Z\\nNo. of bitstreams: 1\\nbressan.pdf: 182373 bytes, checksum: 0eb82866d65dea9685ab7ff75c16c0d2 (MD5) %R 10.1016/S0362-546X(97)00590-7 %0 Journal Article %J Potential Anal. 7 (1997), no. 4, 765-803 %D 1997 %T Capacity theory for monotone operators %A Gianni Dal Maso %A Igor V. Skrypnik %X If $Au=-div(a(x,Du))$ is a monotone operator defined on the Sobolev space $W^{1,p}(R^n)$, $1< p <+\\\\infty$, with $a(x,0)=0$ for a.e. $x\\\\in R^n$, the capacity $C_A(E,F)$ relative to $A$ can be defined for every pair $(E,F)$ of bounded sets in $R^n$ with $E\\\\subset F$. We prove that $C_A(E,F)$ is increasing and countably subadditive with respect to $E$ and decreasing with respect to $F$. Moreover we investigate the continuity properties of $C_A(E,F)$ with respect to $E$ and $F$. %B Potential Anal. 7 (1997), no. 4, 765-803 %I Springer %G en %U http://hdl.handle.net/1963/911 %1 2880 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:40:26Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %R 10.1023/A:1017987405983 %0 Journal Article %J Studies in Applied Mathematics. Year : 1997 ; Volume: 99 ; Issue: 2 ; Pages: 137-203 %D 1997 %T Three-Phase Solutions of the Kadomtsev - Petviashvili Equation %A Boris Dubrovin %A Ron Flickinger %A Harvey Segur %X The Kadomtsev]Petviashvili KP. equation is known to admit explicit periodic\\r\\nand quasiperiodic solutions with N independent phases, for any integer\\r\\nN, based on a Riemann theta-function of N variables. For Ns1 and 2,\\r\\nthese solutions have been used successfully in physical applications. This\\r\\narticle addresses mathematical problems that arise in the computation of\\r\\ntheta-functions of three variables and with the corresponding solutions of\\r\\nthe KP equation. We identify a set of parameters and their corresponding\\r\\nranges, such that e¨ery real-valued, smooth KP solution associated with a\\r\\nRiemann theta-function of three variables corresponds to exactly one choice\\r\\nof these parameters in the proper range. Our results are embodied in a\\r\\nprogram that computes these solutions efficiently and that is available to the\\r\\nreader. We also discuss some properties of three-phase solutions. %B Studies in Applied Mathematics. Year : 1997 ; Volume: 99 ; Issue: 2 ; Pages: 137-203 %I SISSA %G en %U http://hdl.handle.net/1963/6484 %1 6426 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T15:19:00Z\\nNo. of bitstreams: 1\\ndubrovin_flickinger_segur.pdf: 1081636 bytes, checksum: a10c5af7339b1422cb469d18823c5c92 (MD5) %R 10.1111/1467-9590.00059 %0 Journal Article %J Duke Mathematical Journal. Volume: 76, Issue: 2, Pages: 645-668 %D 1994 %T Integrable functional equations and algebraic geometry %A Boris Dubrovin %A A.S. Fokas %A P.M. Santini %B Duke Mathematical Journal. Volume: 76, Issue: 2, Pages: 645-668 %I SISSA %G en %U http://hdl.handle.net/1963/6482 %1 6428 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T15:25:35Z\\nNo. of bitstreams: 1\\ndubrovin_fokas_santini_1994.pdf: 19581899 bytes, checksum: 25c6a7352fa60a95d891bf8ae238f20c (MD5) %R 10.1215/S0012-7094-94-07623-0 %0 Journal Article %J Acta Math. 168 (1992), no.1-2, p. 89-151 %D 1992 %T A variational method in image segmentation: existence and approximation result %A Gianni Dal Maso %A Jean-Michel Morel %A Sergio Solimini %B Acta Math. 168 (1992), no.1-2, p. 89-151 %I SISSA Library %G en %U http://hdl.handle.net/1963/808 %1 2983 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:38:13Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1989