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 $Re=O(10^5)$.

1 aHijazi, Saddam1 aStabile, Giovanni1 aMola, Andrea1 aRozza, Gianluigi uhttps://arxiv.org/abs/1907.0990902129nas a2200145 4500008004100000245011600041210006900157520162200226100002001848700002001868700001701888700002101905700002001926856003701946 2020 eng d00aEfficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method0 aEfficient computation of bifurcation diagrams with a deflated ap3 aThe majority of the most common physical phenomena can be described using partial differential equations (PDEs). However, they are very often characterized by strong nonlinearities. Such features lead to the coexistence of multiple solutions studied by the bifurcation theory. Unfortunately, in practical scenarios, one has to exploit numerical methods to compute the solutions of systems of PDEs, even if the classical techniques are usually able to compute only a single solution for any value of a parameter when more branches exist. In this work we implemented an elaborated deflated continuation method, that relies on the spectral element method (SEM) and on the reduced basis (RB) one, to efficiently compute bifurcation diagrams with more parameters and more bifurcation points. The deflated continuation method can be obtained combining the classical continuation method and the deflation one: the former is used to entirely track each known branch of the diagram, while the latter is exploited to discover the new ones. Finally, when more than one parameter is considered, the efficiency of the computation is ensured by the fact that the diagrams can be computed during the online phase while, during the offline one, one only has to compute one-dimensional diagrams. In this work, after a more detailed description of the method, we will show the results that can be obtained using it to compute a bifurcation diagram associated with a problem governed by the Navier-Stokes equations.

1 aPintore, Moreno1 aPichi, Federico1 aHess, Martin1 aRozza, Gianluigi1 aCanuto, Claudio uhttps://arxiv.org/abs/1912.0608901597nas a2200145 4500008004100000245008800041210006900129300001400198490000800212520112900220100002201349700002201371700002101393856003701414 2020 eng d00aEfficient Geometrical parametrization for finite-volume based reduced order methods0 aEfficient Geometrical parametrization for finitevolume based red a2655-26820 v1213 aIn 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

1 aStabile, Giovanni1 aZancanaro, Matteo1 aRozza, Gianluigi uhttps://arxiv.org/abs/1901.0637301462nas a2200145 4500008004100000245009400041210006900135520097900204100001901183700001701202700002201219700001701241700002101258856003701279 2020 eng d00aEnhancing CFD predictions in shape design problems by model and parameter space reduction0 aEnhancing CFD predictions in shape design problems by model and 3 aIn 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.

1 aTezzele, Marco1 aDemo, Nicola1 aStabile, Giovanni1 aMola, Andrea1 aRozza, Gianluigi uhttps://arxiv.org/abs/2001.0523701487nas a2200169 4500008004100000245008100041210006900122300001100191490000800202520096400210100002301174700002201197700001701219700002101236700002301257856003701280 2020 eng d00aA hybrid reduced order method for modelling turbulent heat transfer problems0 ahybrid reduced order method for modelling turbulent heat transfe a1046150 v2083 aA 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.

1 aGeorgaka, Sokratia1 aStabile, Giovanni1 aStar, Kelbij1 aRozza, Gianluigi1 aBluck, Michael, J. uhttps://arxiv.org/abs/1906.0872501465nas a2200193 4500008004100000245014700041210006900188260003800257520076900295100001901064700002201083700001701105700002101122700002601143700002401169700002001193700002101213856003701234 2020 eng d00aNon-Intrusive Polynomial Chaos Method Applied to Problems in Computational Fluid Dynamics with a Comparison to Proper Orthogonal Decomposition0 aNonIntrusive Polynomial Chaos Method Applied to Problems in Comp bSpringer International Publishing3 aIn 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.

1 aHijazi, Saddam1 aStabile, Giovanni1 aMola, Andrea1 aRozza, Gianluigi1 avan Brummelen, Harald1 aCorsini, Alessandro1 aPerotto, Simona1 aRozza, Gianluigi uhttps://arxiv.org/abs/1901.0228501640nas a2200121 4500008004100000245014500041210006900186520106800255100002201323700002401345700002101369856012801390 2020 eng d00aPOD-Galerkin Model Order Reduction for Parametrized Nonlinear Time Dependent Optimal Flow Control: an Application to Shallow Water Equations0 aPODGalerkin Model Order Reduction for Parametrized Nonlinear Tim3 aIn 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.

1 aStrazzullo, Maria1 aBallarin, Francesco1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/pod-galerkin-model-order-reduction-parametrized-nonlinear-time-dependent-optimal-flow02038nas a2200133 4500008004100000245011600041210006900157520156100226100001701787700002201804700002101826700002001847856003701867 2020 eng d00aA POD-Galerkin reduced order model of a turbulent convective buoyant flow of sodium over a backward-facing step0 aPODGalerkin reduced order model of a turbulent convective buoyan3 aA 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.

1 aStar, Kelbij1 aStabile, Giovanni1 aRozza, Gianluigi1 aDegroote, Joris uhttps://arxiv.org/abs/2003.0111401527nas a2200145 4500008004100000245011100041210006900152300001200221490000700233520104500240100001701285700002101302700002101323856003701344 2020 eng d00aReduced Basis Model Order Reduction for Navier-Stokes equations in domains with walls of varying curvature0 aReduced Basis Model Order Reduction for NavierStokes equations i a119-1260 v343 aWe consider the Navier-Stokes equations in a channel with a narrowing and walls of varying curvature. By applying the empirical interpolation method to generate an affine parameter dependency, the offline-online procedure can be used to compute reduced order solutions for parameter variations. The reduced order space is computed from the steady-state snapshot solutions by a standard POD procedure. The model is discretised with high-order spectral element ansatz functions, resulting in 4752 degrees of freedom. The proposed reduced order model produces accurate approximations of steady-state solutions for a wide range of geometries and kinematic viscosity values. The application that motivated the present study is the onset of asymmetries (i.e., symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the valve shape. Through our computational study, we found that the critical Reynolds number for the symmetry breaking increases as the wall curvature increases.

1 aHess, Martin1 aQuaini, Annalisa1 aRozza, Gianluigi uhttps://arxiv.org/abs/1901.0370801869nas a2200181 4500008004100000245012100041210006900162260003800231520122900269100002801498700002201526700001901548700002401567700002101591700001601612700002201628856003701650 2020 eng d00aA Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries0 aReduced Order Approach for the Embedded Shifted Boundary FEM and bSpringer International Publishing3 aA 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.

1 aKaratzas, Efthymios, N.1 aStabile, Giovanni1 aAtallah, Nabib1 aScovazzi, Guglielmo1 aRozza, Gianluigi1 aFehr, Jörg1 aHaasdonk, Bernard uhttps://arxiv.org/abs/1807.0775301433nas a2200145 4500008004100000245016600041210006900207260001300276520087600289100002201165700001801187700002401205700002101229856003701250 2020 eng d00aReduced order methods for parametrized non-linear and time dependent optimal flow control problems, towards applications in biomedical and environmental sciences0 aReduced order methods for parametrized nonlinear and time depend bSpringer3 aWe 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.

1 aStrazzullo, Maria1 aZainib, Zakia1 aBallarin, Francesco1 aRozza, Gianluigi uhttps://arxiv.org/abs/1912.0788601419nas a2200121 4500008004100000245010700041210006900148520098100217100002001198700002101218700002101239856003701260 2020 eng d00aA Reduced Order technique to study bifurcating phenomena: application to the Gross-Pitaevskii equation0 aReduced Order technique to study bifurcating phenomena applicati3 aWe propose a computationally efficient framework to treat nonlinear partial differential equations having bifurcating solutions as one or more physical control parameters are varied. Our focus is on steady bifurcations. Plotting a bifurcation diagram entails computing multiple solutions of a parametrized, nonlinear problem, which can be extremely expensive in terms of computational time. In order to reduce these demanding computational costs, our approach combines a continuation technique and Newton's method with a Reduced Order Modeling (ROM) technique, suitably supplemented with a hyper-reduction method. To demonstrate the effectiveness of our ROM approach, we trace the steady solution branches of a nonlinear Schrödinger equation, called Gross-Pitaevskii equation, as one or two physical parameters are varied. In the two parameter study, we show that our approach is 60 times faster in constructing a bifurcation diagram than a standard Full Order Method.

1 aPichi, Federico1 aQuaini, Annalisa1 aRozza, Gianluigi uhttps://arxiv.org/abs/1907.0708201427nas a2200121 4500008004100000245013900041210006900180520096200249100001701211700001901228700002101247856003701268 2020 eng d00aA supervised learning approach involving active subspaces for an efficient genetic algorithm in high-dimensional optimization problems0 asupervised learning approach involving active subspaces for an e3 aIn this work, we present an extension of the genetic algorithm (GA) which exploits the active subspaces (AS) property to evolve the individuals on a lower dimensional space. In many cases, GA requires in fact more function evaluations than others optimization method to converge to the optimum. Thus, complex and high-dimensional functions may result intractable with the standard algorithm. To address this issue, we propose to linearly map the input parameter space of the original function onto its AS before the evolution, performing the mutation and mate processes in a lower dimensional space. In this contribution, we describe the novel method called ASGA, presenting differences and similarities with the standard GA method. We test the proposed method over n-dimensional benchmark functions – Rosenbrock, Ackley, Bohachevsky, Rastrigin, Schaffer N. 7, and Zakharov – and finally we apply it to an aeronautical shape optimization problem.

1 aDemo, Nicola1 aTezzele, Marco1 aRozza, Gianluigi uhttps://arxiv.org/abs/2006.0728202383nas a2200205 4500008004100000022001400041245007400055210006900129300001100198490000800209520174300217653001301960653001801973653002201991653002702013653002002040100002302060700002302083856007102106 2020 eng d a0022-509600aSurface tension controls the onset of gyrification in brain organoids0 aSurface tension controls the onset of gyrification in brain orga a1037450 v1343 aUnderstanding the mechanics of brain embryogenesis can provide insights on pathologies related to brain development, such as lissencephaly, a genetic disease which causes a reduction of the number of cerebral sulci. Recent experiments on brain organoids have confirmed that gyrification, i.e. the formation of the folded structures of the brain, is triggered by the inhomogeneous growth of the peripheral region. However, the rheology of these cellular aggregates and the mechanics of lissencephaly are still matter of debate. In this work, we develop a mathematical model of brain organoids based on the theory of morpho-elasticity. We describe them as non-linear elastic bodies, composed of a disk surrounded by a growing layer called cortex. The external boundary is subjected to a tissue surface tension due the intercellular adhesion forces. We show that the resulting surface energy is relevant at the small length scales of brain organoids and affects the mechanics of cellular aggregates. We perform a linear stability analysis of the radially symmetric configuration and we study the post-buckling behaviour through finite element simulations. We find that the process of gyrification is triggered by the cortex growth and modulated by the competition between two length scales: the radius of the organoid and the capillary length generated by surface tension. We show that a solid model can reproduce the results of the in-vitro experiments. Furthermore, we prove that the lack of brain sulci in lissencephaly is caused by a reduction of the cell stiffness: the softening of the organoid strengthens the role of surface tension, delaying or even inhibiting the onset of a mechanical instability at the free boundary.

10aBuckling10aEmbryogenesis10aMorpho-elasticity10aPost-buckling analysis10aSurface tension1 aRiccobelli, Davide1 aBevilacqua, Giulia uhttp://www.sciencedirect.com/science/article/pii/S002250961930406500478nas a2200133 4500008004100000245006600041210006600107260001600173300001200189490000700201100002300208700001600231856009700247 2019 eng d00aActivation of a muscle as a mapping of stress–strain curves0 aActivation of a muscle as a mapping of stress–strain curves bElsevier BV a37–420 v281 aRiccobelli, Davide1 aAmbrosi, D. uhttps://www.math.sissa.it/publication/activation-muscle-mapping-stress%E2%80%93strain-curves02037nas a2200133 4500008004100000245013800041210006900179520154400248100001701792700001901809700001701828700002101845856003701866 2019 eng d00aA complete data-driven framework for the efficient solution of parametric shape design and optimisation in naval engineering problems0 acomplete datadriven framework for the efficient solution of para3 aIn the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples of the ROM application, in the naval field, can be found in [31, 24]. Mandatory ingredient for the ROM methods is the relation between the high-fidelity solutions and the parameters. Dealing with geometrical parameters, especially in the industrial context, this relation may be unknown and not trivial (simulations over hand morphed geometries) or very complex (high number of parameters or many nested morphing techniques). To overcome these scenarios, we propose in this contribution an efficient and complete data-driven framework involving ROM techniques for shape design and optimization, extending the pipeline presented in [7]. By applying the singular value decomposition (SVD) to the points coordinates defining the hull geometry –- assuming the topology is inaltered by the deformation –-, we are able to compute the optimal space which the deformed geometries belong to, hence using the modal coefficients as the new parameters we can reconstruct the parametric formulation of the domain. Finally the output of interest is approximated using the proper orthogonal decomposition with interpolation technique. To conclude, we apply this framework to a naval shape design problem where the bulbous bow is morphed to reduce the total resistance of the ship advancing in calm water.

1 aDemo, Nicola1 aTezzele, Marco1 aMola, Andrea1 aRozza, Gianluigi uhttps://arxiv.org/abs/1905.0598200896nas a2200109 4500008004100000245008200041210006900123260001000192520051200202100001800714856005400732 2019 en d00aA continuous dependence result for a dynamic debonding model in dimension one0 acontinuous dependence result for a dynamic debonding model in di bSISSA3 aIn this paper we address the problem of continuous dependence on initial and boundary data for a one-dimensional debonding model describing a thin ﬁlm peeled away from a substrate. The system underlying the process couples the weakly damped wave equation with a Griﬃth’s criterion which rules the evolution of the debonded region. We show that under general convergence assumptions on the data the corresponding solutions converge to the limit one with respect to diﬀerent natural topologies.

1 aRiva, Filippo uhttp://preprints.sissa.it/xmlui/handle/1963/3532901648nas a2200121 4500008004100000245009500041210006900136520122200205100002401427700001701451700002101468856003701489 2019 eng d00aDiscontinuous Galerkin Model Order Reduction of Geometrically Parametrized Stokes Equation0 aDiscontinuous Galerkin Model Order Reduction of Geometrically Pa3 aThe 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.

1 aShah, Nirav, Vasant1 aHess, Martin1 aRozza, Gianluigi uhttps://arxiv.org/abs/1912.0978702482nas a2200169 4500008004100000245009100041210006900132520193100201100001702132700001902149700002102168700002502189700001902214700002102233700002102254856003702275 2019 eng d00aEfficient Reduction in Shape Parameter Space Dimension for Ship Propeller Blade Design0 aEfficient Reduction in Shape Parameter Space Dimension for Ship 3 aIn this work, we present the results of a ship propeller design optimization campaign carried out in the framework of the research project PRELICA, funded by the Friuli Venezia Giulia regional government. The main idea of this work is to operate on a multidisciplinary level to identify propeller shapes that lead to reduced tip vortex-induced pressure and increased efficiency without altering the thrust. First, a specific tool for the bottom-up construction of parameterized propeller blade geometries has been developed. The algorithm proposed operates with a user defined number of arbitrary shaped or NACA airfoil sections, and employs arbitrary degree NURBS to represent the chord, pitch, skew and rake distribution as a function of the blade radial coordinate. The control points of such curves have been modified to generate, in a fully automated way, a family of blade geometries depending on as many as 20 shape parameters. Such geometries have then been used to carry out potential flow simulations with the Boundary Element Method based software PROCAL. Given the high number of parameters considered, such a preliminary stage allowed for a fast evaluation of the performance of several hundreds of shapes. In addition, the data obtained from the potential flow simulation allowed for the application of a parameter space reduction methodology based on active subspaces (AS) property, which suggested that the main propeller performance indices are, at a first but rather accurate approximation, only depending on a single parameter which is a linear combination of all the original geometric ones. AS analysis has also been used to carry out a constrained optimization exploiting response surface method in the reduced parameter space, and a sensitivity analysis based on such surrogate model. The few selected shapes were finally used to set up high fidelity RANS simulations and select an optimal shape.

1 aMola, Andrea1 aTezzele, Marco1 aGadalla, Mahmoud1 aValdenazzi, Federica1 aGrassi, Davide1 aPadovan, Roberta1 aRozza, Gianluigi uhttps://arxiv.org/abs/1905.0981501140nas a2200205 4500008004100000022001400041245005800055210005500113520049400168653002800662653002300690653002100713653002500734653002500759100001700784700002400801700001900825700001900844856007100863 2019 eng d a0304-414900aAn entropic interpolation proof of the HWI inequality0 aentropic interpolation proof of the HWI inequality3 aThe HWI inequality is an “interpolation”inequality between the Entropy H, the Fisher information I and the Wasserstein distance W. We present a pathwise proof of the HWI inequality which is obtained through a zero noise limit of the Schrödinger problem. Our approach consists in making rigorous the Otto–Villani heuristics in Otto and Villani (2000) taking advantage of the entropic interpolations, which are regular both in space and time, rather than the displacement ones.

10aEntropic interpolations10aFisher information10aRelative entropy10aSchrödinger problem10aWasserstein distance1 aGentil, Ivan1 aLéonard, Christian1 aRipani, Luigia1 aTamanini, Luca uhttp://www.sciencedirect.com/science/article/pii/S030441491830345400459nas a2200133 4500008004100000245009200041210006900133260001600202300001600218490000700234100001700241700001900258856004800277 2019 eng d00aError estimates in weighted Sobolev norms for finite element immersed interface methods0 aError estimates in weighted Sobolev norms for finite element imm bElsevier BV a3586–36040 v781 aHeltai, Luca1 aRotundo, Nella uhttps://doi.org/10.1016/j.camwa.2019.05.02900512nas a2200133 4500008004100000245007600041210006900117260002200186490000800208100002300216700001500239700002400254856010000278 2019 eng d00aOn the existence of elastic minimizers for initially stressed materials0 aexistence of elastic minimizers for initially stressed materials bThe Royal Society0 v3771 aRiccobelli, Davide1 aAgosti, A.1 aCiarletta, Pasquale uhttps://www.math.sissa.it/publication/existence-elastic-minimizers-initially-stressed-materials01763nas a2200145 4500008004100000245010400041210006900145300001000214490000800224520128300232100002301515700002101538700002101559856003701580 2019 eng d00aA Finite Volume approximation of the Navier-Stokes equations with nonlinear filtering stabilization0 aFinite Volume approximation of the NavierStokes equations with n a27-450 v1873 aWe consider a Leray model with a nonlinear differential low-pass filter for the simulation of incompressible fluid flow at moderately large Reynolds number (in the range of a few thousands) with under-refined meshes. For the implementation of the model, we adopt the three-step algorithm Evolve-Filter-Relax (EFR). The Leray model has been extensively applied within a Finite Element (FE) framework. Here, we propose to combine the EFR algorithm with a computationally efficient Finite Volume (FV) method. Our approach is validated against numerical data available in the literature for the 2D flow past a cylinder and against experimental measurements for the 3D fluid flow in an idealized medical device, as recommended by the U.S. Food and Drug Administration. We will show that for similar levels of mesh refinement FV and FE methods provide significantly different results. Through our numerical experiments, we are able to provide practical directions to tune the parameters involved in the model. Furthermore, we are able to investigate the impact of mesh features (element type, non-orthogonality, local refinement, and element aspect ratio) and the discretization method for the convective term on the agreement between numerical solutions and experimental data.

1 aGirfoglio, Michele1 aQuaini, Annalisa1 aRozza, Gianluigi uhttps://arxiv.org/abs/1901.0525102124nas a2200169 4500008004100000245008400041210006900125300001200194490000800206520160300214100001701817700002101834700002101855700002101876700002001897856003701917 2019 eng d00aA Localized Reduced-Order Modeling Approach for PDEs with Bifurcating Solutions0 aLocalized ReducedOrder Modeling Approach for PDEs with Bifurcati a379-4030 v3513 aReduced-order modeling (ROM) commonly refers to the construction, based on a few solutions (referred to as snapshots) of an expensive discretized partial differential equation (PDE), and the subsequent application of low-dimensional discretizations of partial differential equations (PDEs) that can be used to more efficiently treat problems in control and optimization, uncertainty quantification, and other settings that require multiple approximate PDE solutions. In this work, a ROM is developed and tested for the treatment of nonlinear PDEs whose solutions bifurcate as input parameter values change. In such cases, the parameter domain can be subdivided into subregions, each of which corresponds to a different branch of solutions. Popular ROM approaches such as proper orthogonal decomposition (POD), results in a global low-dimensional basis that does no respect not take advantage of the often large differences in the PDE solutions corresponding to different subregions. Instead, in the new method, the k-means algorithm is used to cluster snapshots so that within cluster snapshots are similar to each other and are dissimilar to those in other clusters. This is followed by the construction of local POD bases, one for each cluster. The method also can detect which cluster a new parameter point belongs to, after which the local basis corresponding to that cluster is used to determine a ROM approximation. Numerical experiments show the effectiveness of the method both for problems for which bifurcation cause continuous and discontinuous changes in the solution of the PDE.

1 aHess, Martin1 aAlla, Alessandro1 aQuaini, Annalisa1 aRozza, Gianluigi1 aGunzburger, Max uhttps://arxiv.org/abs/1807.0885100644nas a2200145 4500008004100000245006000041210005800101260003400159300001400193490000700207520015800214100001800372700001900390856008900409 2019 eng d00aA Note About the Strong Maximum Principle on RCD Spaces0 aNote About the Strong Maximum Principle on RCD Spaces bCanadian Mathematical Society a259–2660 v623 aWe give a direct proof of the strong maximum principle on finite dimensional RCD spaces based on the Laplacian comparison of the squared distance.

1 aGigli, Nicola1 aRigoni, Chiara uhttps://www.math.sissa.it/publication/note-about-strong-maximum-principle-rcd-spaces01425nas a2200169 4500008004100000022001400041245009200055210006900147300001100216490000700227520089500234100002301129700002201152700002101174700002301195856003701218 2019 eng d a1991-712000aParametric POD-Galerkin Model Order Reduction for Unsteady-State Heat Transfer Problems0 aParametric PODGalerkin Model Order Reduction for UnsteadyState H a1–320 v273 aA 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.

1 aGeorgaka, Sokratia1 aStabile, Giovanni1 aRozza, Gianluigi1 aBluck, Michael, J. uhttps://arxiv.org/abs/1808.0517501484nas a2200133 4500008004100000245011700041210006900158520101500227100001401242700001601256700001401272700002701286856003701313 2019 eng d00aPOD-Galerkin reduced order methods for combined Navier-Stokes transport equations based on a hybrid FV-FE solver0 aPODGalerkin reduced order methods for combined NavierStokes tran3 aThe 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.

1 aBusto, S.1 aStabile, G.1 aRozza, G.1 aVázquez-Cendón, M.E. uhttps://arxiv.org/abs/1810.0799902082nas a2200169 4500008004100000245015000041210006900191300001400260490000800274520148200282100002701764700002201791700001701813700002401830700002101854856003701875 2019 eng d00aA reduced basis approach for PDEs on parametrized geometries based on the shifted boundary finite element method and application to a Stokes flow0 areduced basis approach for PDEs on parametrized geometries based a568–5870 v3473 aWe 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.

1 aKaratzas, Efthymios, N1 aStabile, Giovanni1 aNouveau, Leo1 aScovazzi, Guglielmo1 aRozza, Gianluigi uhttps://arxiv.org/abs/1807.0779001370nas a2200133 4500008004100000245010900041210006900150300001400219490000700233520091800240100002001158700002101178856003701199 2019 eng d00aReduced basis approaches for parametrized bifurcation problems held by non-linear Von Kármán equations0 aReduced basis approaches for parametrized bifurcation problems h a112–1350 v813 aThis work focuses on the computationally efficient detection of the buckling phenomena and bifurcation analysis of the parametric Von Kármán plate equations based on reduced order methods and spectral analysis. The computational complexity - due to the fourth order derivative terms, the non-linearity and the parameter dependence - provides an interesting benchmark to test the importance of the reduction strategies, during the construction of the bifurcation diagram by varying the parameter(s). To this end, together the state equations, we carry out also an analysis of the linearized eigenvalue problem, that allows us to better understand the physical behaviour near the bifurcation points, where we lose the uniqueness of solution. We test this automatic methodology also in the two parameter case, understanding the evolution of the first buckling mode. journal = Journal of Scientific Computing

1 aPichi, Federico1 aRozza, Gianluigi uhttps://arxiv.org/abs/1804.0201402365nas a2200121 4500008004100000245014200041210006900183520189700252100001902149700001702168700002102185856003702206 2019 eng d00aShape optimization through proper orthogonal decomposition with interpolation and dynamic mode decomposition enhanced by active subspaces0 aShape optimization through proper orthogonal decomposition with 3 aWe propose a numerical pipeline for shape optimization in naval engineering involving two different non-intrusive reduced order method (ROM) techniques. Such methods are proper orthogonal decomposition with interpolation (PODI) and dynamic mode decomposition (DMD). The ROM proposed will be enhanced by active subspaces (AS) as a pre-processing tool that reduce the parameter space dimension and suggest better sampling of the input space. We will focus on geometrical parameters describing the perturbation of a reference bulbous bow through the free form deformation (FFD) technique. The ROM are based on a finite volume method (FV) to simulate the multi-phase incompressible flow around the deformed hulls. In previous works we studied the reduction of the parameter space in naval engineering through AS [38, 10] focusing on different parts of the hull. PODI and DMD have been employed for the study of fast and reliable shape optimization cycles on a bulbous bow in [9]. The novelty of this work is the simultaneous reduction of both the input parameter space and the output fields of interest. In particular AS will be trained computing the total drag resistance of a hull advancing in calm water and its gradients with respect to the input parameters. DMD will improve the performance of each simulation of the campaign using only few snapshots of the solution fields in order to predict the regime state of the system. Finally PODI will interpolate the coefficients of the POD decomposition of the output fields for a fast approximation of all the fields at new untried parameters given by the optimization algorithm. This will result in a non-intrusive data-driven numerical optimization pipeline completely independent with respect to the full order solver used and it can be easily incorporated into existing numerical pipelines, from the reference CAD to the optimal shape.

1 aTezzele, Marco1 aDemo, Nicola1 aRozza, Gianluigi uhttps://arxiv.org/abs/1905.0548301397nas a2200193 4500008004100000245006200041210006000103260003800163490000800201520080600209100002101015700002101036700002501057700001801082700001601100700002801116700002201144856003701166 2019 eng d00aA Spectral Element Reduced Basis Method in Parametric CFD0 aSpectral Element Reduced Basis Method in Parametric CFD bSpringer International Publishing0 v1263 aWe consider the Navier-Stokes equations in a channel with varying Reynolds numbers. The model is discretized with high-order spectral element ansatz functions, resulting in 14 259 degrees of freedom. The steady-state snapshot solu- tions define a reduced order space, which allows to accurately evaluate the steady- state solutions for varying Reynolds number with a reduced order model within a fixed-point iteration. In particular, we compare different aspects of implementing the reduced order model with respect to the use of a spectral element discretization. It is shown, how a multilevel static condensation in the pressure and velocity boundary degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios.

1 aHess, Martin, W.1 aRozza, Gianluigi1 aRadu, Florin, Adrian1 aKumar, Kundan1 aBerre, Inga1 aNordbotten, Jan, Martin1 aPop, Iuliu, Sorin uhttps://arxiv.org/abs/1712.0643200579nas a2200145 4500008004100000245010500041210006900146300001600215490000700231100001500238700001600253700001700269700001800286856012900304 2018 eng d00aAn authenticated theoretical modeling of electrified fluid jet in core–shell nanofibers production0 aauthenticated theoretical modeling of electrified fluid jet in c a1791–18110 v471 aRafiei, S.1 aNoroozi, B.1 aHeltai, Luca1 aHaghi, A., K. uhttps://www.math.sissa.it/publication/authenticated-theoretical-modeling-electrified-fluid-jet-core%E2%80%93shell-nanofibers00586nas a2200133 4500008004100000245010800041210006900149300001200218490000700230100002200237700002200259700002100281856015000302 2018 eng d00aCertified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models0 aCertified Reduced Basis Approximation for the Coupling of Viscou a197-2190 v741 aMartini, Immanuel1 aHaasdonk, Bernard1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85017156114&doi=10.1007%2fs10915-017-0430-y&partnerID=40&md5=023ef0bb95713f4442d1fa374c92a96400587nas a2200133 4500008004100000245012400041210006900165260001300234300001400247100001900261700002400280700002100304856012800325 2018 eng d00aCombined parameter and model reduction of cardiovascular problems by means of active subspaces and POD-Galerkin methods0 aCombined parameter and model reduction of cardiovascular problem bSpringer a185–2071 aTezzele, Marco1 aBallarin, Francesco1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/combined-parameter-and-model-reduction-cardiovascular-problems-means-active-subspaces00556nas a2200121 4500008004100000245010600041210006900147260002000216100002200236700002400258700002300282856012900305 2018 eng d00aA Comparison Between Active Strain and Active Stress in Transversely Isotropic Hyperelastic Materials0 aComparison Between Active Strain and Active Stress in Transverse bSpringer Nature1 aGiantesio, Giulia1 aMusesti, Alessandro1 aRiccobelli, Davide uhttps://www.math.sissa.it/publication/comparison-between-active-strain-and-active-stress-transversely-isotropic-hyperelastic01813nas a2200205 4500008004100000245005400041210005400095260001400149300000700163520117300170100002601343700001901369700002001388700002101408700002201429700002101451700002601472700002501498856008401523 2018 eng d00aComputational methods in cardiovascular mechanics0 aComputational methods in cardiovascular mechanics bCRC Press a543 aThe introduction of computational models in cardiovascular sciences has been progressively bringing new and unique tools for the investigation of the physiopathology. Together with the dramatic improvement of imaging and measuring devices on one side, and of computational architectures on the other one, mathematical and numerical models have provided a new, clearly noninvasive, approach for understanding not only basic mechanisms but also patient-specific conditions, and for supporting the design and the development of new therapeutic options. The terminology in silico is, nowadays, commonly accepted for indicating this new source of knowledge added to traditional in vitro and in vivo investigations. The advantages of in silico methodologies are basically the low cost in terms of infrastructures and facilities, the reduced invasiveness and, in general, the intrinsic predictive capabilities based on the use of mathematical models. The disadvantages are generally identified in the distance between the real cases and their virtual counterpart required by the conceptual modeling that can be detrimental for the reliability of numerical simulations.

1 aAuricchio, Ferdinando1 aConti, Michele1 aLefieux, Adrian1 aMorganti, Simone1 aReali, Alessandro1 aRozza, Gianluigi1 aVeneziani, Alessandro1 aLabrosse, Michel, F. uhttps://www.taylorfrancis.com/books/e/9781315280288/chapters/10.1201%2Fb21917-502307nas a2200169 4500008004100000245011900041210006900160260000800229300000700237490000600244520167500250100001901925700002501944700001701969700002101986856013002007 2018 eng d00aDimension reduction in heterogeneous parametric spaces with application to naval engineering shape design problems0 aDimension reduction in heterogeneous parametric spaces with appl cSep a250 v53 aWe present the results of the first application in the naval architecture field of a methodology based on active subspaces properties for parameters space reduction. The physical problem considered is the one of the simulation of the hydrodynamic flow past the hull of a ship advancing in calm water. Such problem is extremely relevant at the preliminary stages of the ship design, when several flow simulations are typically carried out by the engineers to assess the dependence of the hull total resistance on the geometrical parameters of the hull, and others related with flows and hull properties. Given the high number of geometric and physical parameters which might affect the total ship drag, the main idea of this work is to employ the active subspaces properties to identify possible lower dimensional structures in the parameter space. Thus, a fully automated procedure has been implemented to produce several small shape perturbations of an original hull CAD geometry, in order to exploit the resulting shapes to run high fidelity flow simulations with different structural and physical parameters as well, and then collect data for the active subspaces analysis. The free form deformation procedure used to morph the hull shapes, the high fidelity solver based on potential flow theory with fully nonlinear free surface treatment, and the active subspaces analysis tool employed in this work have all been developed and integrated within SISSA mathLab as open source tools. The contribution will also discuss several details of the implementation of such tools, as well as the results of their application to the selected target engineering problem.

1 aTezzele, Marco1 aSalmoiraghi, Filippo1 aMola, Andrea1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/dimension-reduction-heterogeneous-parametric-spaces-application-naval-engineering-shape02869nas a2200241 4500008004100000022002200041245016200063210006900225260007400294520193000368653002102298653002802319653003102347653003202378653002602410653003002436653002602466100001702492700001902509700001702528700002102545856006102566 2018 eng d a978-1-880653-87-600aAn efficient shape parametrisation by free-form deformation enhanced by active subspace for hull hydrodynamic ship design problems in open source environment0 aefficient shape parametrisation by freeform deformation enhanced aSapporo, JapanbInternational Society of Offshore and Polar Engineers3 aIn this contribution, we present the results of the application of a parameter space reduction methodology based on active subspaces to the hull hydrodynamic design problem. Several parametric deformations of an initial hull shape are considered to assess the influence of the shape parameters considered on the hull total drag. The hull resistance is typically computed by means of numerical simulations of the hydrodynamic flow past the ship. Given the high number of parameters involved - which might result in a high number of time consuming hydrodynamic simulations - assessing whether the parameters space can be reduced would lead to considerable computational cost reduction. Thus, the main idea of this work is to employ the active subspaces to identify possible lower dimensional structures in the parameter space, or to verify the parameter distribution in the position of the control points. To this end, a fully automated procedure has been implemented to produce several small shape perturbations of an original hull CAD geometry which are then used to carry out high-fidelity flow simulations and collect data for the active subspaces analysis. To achieve full automation of the open source pipeline described, both the free form deformation methodology employed for the hull perturbations and the solver based on unsteady potential flow theory, with fully nonlinear free surface treatment, are directly interfaced with CAD data structures and operate using IGES vendor-neutral file formats as input files. The computational cost of the fluid dynamic simulations is further reduced through the application of dynamic mode decomposition to reconstruct the steady state total drag value given only few initial snapshots of the simulation. The active subspaces analysis is here applied to the geometry of the DTMB-5415 naval combatant hull, which is which is a common benchmark in ship hydrodynamics simulations.10aActive subspaces10aBoundary element method10aDynamic mode decomposition10aFluid structure interaction10aFree form deformation10aFully nonlinear potential10aNumerical towing tank1 aDemo, Nicola1 aTezzele, Marco1 aMola, Andrea1 aRozza, Gianluigi uhttps://www.onepetro.org/conference-paper/ISOPE-I-18-48100590nas a2200133 4500008004100000245012000041210006900161100001900230700001700249700002200266700002400288700002100312856012300333 2018 eng d00aThe Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: from Laminar to Turbulent Flows0 aEffort of Increasing Reynolds Number in ProjectionBased Reduced 1 aHijazi, Saddam1 aAli, Shafqat1 aStabile, Giovanni1 aBallarin, Francesco1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/effort-increasing-reynolds-number-projection-based-reduced-order-methods-laminar00945nas a2200109 4500008004100000245010200041210006900143520053000212100002100742700001800763856005400781 2018 en d00aExistence and uniqueness of dynamic evolutions for a one dimensional debonding model with damping0 aExistence and uniqueness of dynamic evolutions for a one dimensi3 aIn this paper we analyse a one-dimensional debonding model for a thin film peeled from a substrate when friction is taken into account. It is described by the weakly damped wave equation whose domain, the debonded region, grows according to a Griffth's criterion. Firstly we prove that the equation admits a unique solution when the evolution of the debonding front is assigned. Finally we provide an existence and uniqueness result for the coupled problem given by the wave equation together with Griffth's criterion.

1 aNardini, Lorenzo1 aRiva, Filippo uhttp://preprints.sissa.it/xmlui/handle/1963/3531900373nas a2200133 4500008004100000245003700041210003600078300000800114490000600122100001700128700001900145700002100164856005400185 2018 eng d00aEZyRB: Easy Reduced Basis method0 aEZyRB Easy Reduced Basis method a6610 v31 aDemo, Nicola1 aTezzele, Marco1 aRozza, Gianluigi uhttps://joss.theoj.org/papers/10.21105/joss.0066100528nas a2200145 4500008004100000020002200041245007200063210006900135260004400204300001200248100002300260700002100283700003000304856004800334 2018 eng d a978-3-319-89800-100aFailure of the Chain Rule in the Non Steady Two-Dimensional Setting0 aFailure of the Chain Rule in the Non Steady TwoDimensional Setti aChambSpringer International Publishing a33–601 aBianchini, Stefano1 aBonicatto, Paolo1 aRassias, Themistocles, M. uhttps://doi.org/10.1007/978-3-319-89800-1_200462nas a2200109 4500008004100000245012400041210006900165260002300234100002200257700002100279856005200300 2018 eng d00aFinite volume POD-Galerkin stabilised reduced order methods for the parametrised incompressible Navier-Stokes equations0 aFinite volume PODGalerkin stabilised reduced order methods for t bElsevier {BV}cfeb1 aStabile, Giovanni1 aRozza, Gianluigi uhttps://doi.org/10.1016/j.compfluid.2018.01.03501597nas a2200169 4500008004100000245012200041210006900163260002100232300001200253490000700265520094600272100002501218700002201243700001801265700002101283856012301304 2018 eng d00aFree-form deformation, mesh morphing and reduced-order methods: enablers for efficient aerodynamic shape optimisation0 aFreeform deformation mesh morphing and reducedorder methods enab bTaylor & Francis a233-2470 v323 aIn this work, we provide an integrated pipeline for the model-order reduction of turbulent flows around parametrised geometries in aerodynamics. In particular, free-form deformation is applied for geometry parametrisation, whereas two different reduced-order models based on proper orthogonal decomposition (POD) are employed in order to speed-up the full-order simulations: the first method exploits POD with interpolation, while the second one is based on domain decomposition. For the sampling of the parameter space, we adopt a Greedy strategy coupled with Constrained Centroidal Voronoi Tessellations, in order to guarantee a good compromise between space exploration and exploitation. The proposed framework is tested on an industrially relevant application, i.e. the front-bumper morphing of the DrivAer car model, using the finite-volume method for the full-order resolution of the Reynolds-Averaged Navier–Stokes equations.

1 aSalmoiraghi, Filippo1 aScardigli, Angela1 aTelib, Haysam1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/free-form-deformation-mesh-morphing-and-reduced-order-methods-enablers-efficient00439nas a2200097 4500008004100000245008500041210006900126100001900195700002000214856010700234 2018 eng d00aLong time existence for fully nonlinear NLS with small Cauchy data on the circle0 aLong time existence for fully nonlinear NLS with small Cauchy da1 aRoberto, Feola1 aIandoli, Felice uhttps://www.math.sissa.it/publication/long-time-existence-fully-nonlinear-nls-small-cauchy-data-circle01777nas a2200157 4500008004100000245013300041210006900174260003000243520120300273100001901476700001701495700002101512700001701533700002101550856004801571 2018 eng d00aModel Order Reduction by means of Active Subspaces and Dynamic Mode Decomposition for Parametric Hull Shape Design Hydrodynamics0 aModel Order Reduction by means of Active Subspaces and Dynamic M aTrieste, ItalybIOS Press3 aWe present the results of the application of a parameter space reduction methodology based on active subspaces (AS) to the hull hydrodynamic design problem. Several parametric deformations of an initial hull shape are considered to assess the influence of the shape parameters on the hull wave resistance. Such problem is relevant at the preliminary stages of the ship design, when several flow simulations are carried out by the engineers to establish a certain sensibility with respect to the parameters, which might result in a high number of time consuming hydrodynamic simulations. The main idea of this work is to employ the AS to identify possible lower dimensional structures in the parameter space. The complete pipeline involves the use of free form deformation to parametrize and deform the hull shape, the full order solver based on unsteady potential flow theory with fully nonlinear free surface treatment directly interfaced with CAD, the use of dynamic mode decomposition to reconstruct the final steady state given only few snapshots of the simulation, and the reduction of the parameter space by AS, and shared subspace. Response surface method is used to minimize the total drag.1 aTezzele, Marco1 aDemo, Nicola1 aGadalla, Mahmoud1 aMola, Andrea1 aRozza, Gianluigi uhttp://ebooks.iospress.nl/publication/4927000512nas a2200145 4500008004100000245011100041210006900152300001600221490000700237100002200244700002400266700001600290700002100306856003900327 2018 eng d00aModel Reduction for Parametrized Optimal Control Problems in Environmental Marine Sciences and Engineering0 aModel Reduction for Parametrized Optimal Control Problems in Env aB1055-B10790 v401 aStrazzullo, Maria1 aBallarin, Francesco1 aMosetti, R.1 aRozza, Gianluigi uhttps://doi.org/10.1137/17M115059100454nas a2200133 4500008004100000245005600041210005500097260001600152300001000168490000800178100002300186700002400209856008700233 2018 eng d00aMorpho-elastic model of the tortuous tumour vessels0 aMorphoelastic model of the tortuous tumour vessels bElsevier BV a1–90 v1071 aRiccobelli, Davide1 aCiarletta, Pasquale uhttps://www.math.sissa.it/publication/morpho-elastic-model-tortuous-tumour-vessels00449nas a2200109 4500008004100000245006800041210006800109100001900177700002000196700001600216856010700232 2018 eng d00aNoncommutative Painlevé Equations and Systems of Calogero Type0 aNoncommutative Painlevé Equations and Systems of Calogero Type1 aBertola, Marco1 aCafasso, Mattia1 aRubtsov, V. uhttps://www.math.sissa.it/publication/noncommutative-painlev%C3%A9-equations-and-systems-calogero-type00402nas a2200133 4500008004100000245004500041210004400086300000800130490000600138100001700144700001900161700002100180856006700201 2018 eng d00aPyDMD: Python Dynamic Mode Decomposition0 aPyDMD Python Dynamic Mode Decomposition a5300 v31 aDemo, Nicola1 aTezzele, Marco1 aRozza, Gianluigi uhttps://joss.theoj.org/papers/734e4326edd5062c6e8ee98d03df9e1d00849nas a2200157 4500008004100000022001400041245009800055210006900153260000800222300000800230490000700238520036300245100001800608700001900626856004600645 2018 eng d a1432-083500aRecognizing the flat torus among RCD*(0,N) spaces via the study of the first cohomology group0 aRecognizing the flat torus among RCD0N spaces via the study of t cJun a1040 v573 aWe prove that if the dimension of the first cohomology group of a $\mathsf{RCD}^\star (0,N)$ space is $N$, then the space is a flat torus. This generalizes a classical result due to Bochner to the non-smooth setting and also provides a first example where the study of the cohomology groups in such synthetic framework leads to geometric consequences.

1 aGigli, Nicola1 aRigoni, Chiara uhttps://doi.org/10.1007/s00526-018-1377-z00631nas a2200133 4500008004100000245015100041210006900192100002800261700002200289700001700311700002400328700002100352856012400373 2018 eng d00aA Reduced Basis approach for PDEs on parametrized geometries based on the Shifted Boundary Finite Element Method and application to fluid dynamics0 aReduced Basis approach for PDEs on parametrized geometries based1 aKaratzas, Efthymios, N.1 aStabile, Giovanni1 aNouveau, Leo1 aScovazzi, Guglielmo1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduced-basis-approach-pdes-parametrized-geometries-based-shifted-boundary-finite00501nas a2200121 4500008004100000245013400041210006900175490000700244100002100251700002000272700002100292856006600313 2018 eng d00aReduced Basis Approximation and A Posteriori Error Estimation: Applications to Elasticity Problems in Several Parametric Settings0 aReduced Basis Approximation and A Posteriori Error Estimation Ap0 v151 aHuynh, D., B. P.1 aPichi, Federico1 aRozza, Gianluigi uhttps://link.springer.com/chapter/10.1007/978-3-319-94676-4_800596nas a2200133 4500008004100000245012100041210006900162100002800231700002200259700001600281700002400297700002100321856012000342 2018 eng d00aA Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries0 aReduced Order Approach for the Embedded Shifted Boundary FEM and1 aKaratzas, Efthymios, N.1 aStabile, Giovanni1 aAtallah, N.1 aScovazzi, Guglielmo1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduced-order-approach-embedded-shifted-boundary-fem-and-heat-exchange-system01912nas a2200157 4500008004100000245009800041210006900139260003000208520136800238100001701606700001901623700002101642700002201663700002101685856004801706 2018 eng d00aShape Optimization by means of Proper Orthogonal Decomposition and Dynamic Mode Decomposition0 aShape Optimization by means of Proper Orthogonal Decomposition a aTrieste, ItalybIOS Press3 aShape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling, applied to a naval hull design problem. The advantage introduced by this method is that the solution for a specific parameter can be expressed as the combination of few numerical solutions computed at properly chosen parametric points. The reduced model is built using the proper orthogonal decomposition with interpolation (PODI) method. We use the free form deformation (FFD) for an automated perturbation of the shape, and the finite volume method to simulate the multiphase incompressible flow around the deformed hulls. Further computational reduction is done by the dynamic mode decomposition (DMD) technique: from few high dimensional snapshots, the system evolution is reconstructed and the final state of the simulation is faithfully approximated. Finally the global optimization algorithm iterates over the reduced space: the approximated drag and lift coefficients are projected to the hull surface, hence the resistance is evaluated for the new hulls until the convergence to the optimal shape is achieved. We will present the results obtained applying the described procedure to a typical Fincantieri cruise ship.1 aDemo, Nicola1 aTezzele, Marco1 aGustin, Gianluca1 aLavini, Gianpiero1 aRozza, Gianluigi uhttp://ebooks.iospress.nl/publication/4922900543nas a2200133 4500008004100000245007700041210006900118260004700187300001600234490000700250100002300257700002400280856010500304 2018 eng d00aShape transitions in a soft incompressible sphere with residual stresses0 aShape transitions in a soft incompressible sphere with residual bSAGE Publications Sage UK: London, England a1507–15240 v231 aRiccobelli, Davide1 aCiarletta, Pasquale uhttps://www.math.sissa.it/publication/shape-transitions-soft-incompressible-sphere-residual-stresses01821nas a2200181 4500008004100000024003700041245012000078210006900198520118600267653002301453653002601476100002201502700001901524700002101543700001701564700002101581856003701602 2017 eng d ahttps://arxiv.org/abs/1701.0342400aAdvances in Reduced order modelling for CFD: vortex shedding around a circular cylinder using a POD-Galerkin method0 aAdvances in Reduced order modelling for CFD vortex shedding arou3 aVortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. In this work a Reduced Order Model (ROM) of the incompressible flow around a circular cylinder, built performing a Galerkin projection of the governing equations onto a lower dimensional space is presented. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pressure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) for this purpose the projection of the Governing equations (momentum equation and Poisson equation for pressure) is performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework are presented. The accuracy of the reduced order model is assessed against full order results.

10afinite volume, CFD10aReduced order methods1 aStabile, Giovanni1 aHijazi, Saddam1 aLorenzi, Stefano1 aMola, Andrea1 aRozza, Gianluigi uhttps://arxiv.org/abs/1701.0342401212nas a2200109 4500008004100000245010500041210006900146520071800215100002100933700002100954856012700975 2017 eng d00aOn the Application of Reduced Basis Methods to Bifurcation Problems in Incompressible Fluid Dynamics0 aApplication of Reduced Basis Methods to Bifurcation Problems in 3 aIn this paper we apply a reduced basis framework for the computation of flow bifurcation (and stability) problems in fluid dynamics. The proposed method aims at reducing the complexity and the computational time required for the construction of bifurcation and stability diagrams. The method is quite general since it can in principle be specialized to a wide class of nonlinear problems, but in this work we focus on an application in incompressible fluid dynamics at low Reynolds numbers. The validation of the reduced order model with the full order computation for a benchmark cavity flow problem is promising.

1 aPitton, Giuseppe1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/application-reduced-basis-methods-bifurcation-problems-incompressible-fluid-dynamics02454nas a2200169 4500008004100000020002200041024003400063245010200097210006900199250004300268260002500311490000900336520177800345100001802123700002102141856012202162 2017 eng d a978-3-319-65869-8 aDOI 10.1007/978-3-319-65870-400aCertified Reduced Basis Method for Affinely Parametric Isogeometric Analysis NURBS Approximation0 aCerti fied Reduced Basis Method for Affinely Parametric Isogeome aBittencourt, Dumont, Hesthaven. (Eds). aHeildebergbSpringer0 v 1193 aIn this work we apply reduced basis methods for parametric PDEs to an isogeometric formulation based on

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

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

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

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

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

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

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

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

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

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

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

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

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

1 aDevaud, Denis1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/certi-fied-reduced-basis-method-affinely-parametric-isogeometric-analysis-nurbs00579nas a2200157 4500008004100000245006200041210005700103300001400160490000700174100001800181700001700199700001700216700002400233700002100257856014300278 2017 eng d00aOn a certified smagorinsky reduced basis turbulence model0 acertified smagorinsky reduced basis turbulence model a3047-30670 v551 aRebollo, T.C.1 aÁvila, E.D.1 aMarmol, M.G.1 aBallarin, Francesco1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85039928218&doi=10.1137%2f17M1118233&partnerID=40&md5=221d9cd2bcc74121fcef93efd9d3d76c01188nas a2200181 4500008004100000022001400041245007200055210007100127300001600198490000800214520059300222653002900815653001900844653003300863653002100896100001800917856007100935 2017 eng d a0022-039600aClifford Tori and the singularly perturbed Cahn–Hilliard equation0 aClifford Tori and the singularly perturbed Cahn–Hilliard equatio a5306 - 53620 v2623 aIn this paper we construct entire solutions uε to the Cahn–Hilliard equation −ε2Δ(−ε2Δu+W′(u))+W″(u)(−ε2Δu+W′(u))=ε4λε(1−uε), under the volume constraint ∫R3(1−uε)2dx=82π2cε, with cε→1 as ε→0, whose nodal set approaches the Clifford Torus, that is the Torus with radii of ratio 1/2 embedded in R3, as ε→0. It is crucial that the Clifford Torus is a Willmore hypersurface and it is non-degenerate, up to conformal transformations. The proof is based on the Lyapunov–Schmidt reduction and on careful geometric expansions of the Laplacian.

10aCahn–Hilliard equation10aClifford Torus10aLyapunov–Schmidt reduction10aWillmore surface1 aRizzi, Matteo uhttp://www.sciencedirect.com/science/article/pii/S002203961730053002413nas a2200205 4500008004100000245015800041210006900199260001200268300000800280490000800288520159500296653004301891653002501934653002301959653003401982100002102016700002102037700002102058856012802079 2017 eng d00aComputational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: Applications to Coanda effect in cardiology0 aComputational reduction strategies for the detection of steady b c09/2017 a5570 v3443 aWe focus on reducing the computational costs associated with the hydrodynamic stability of solutions of the incompressible Navier–Stokes equations for a Newtonian and viscous fluid in contraction–expansion channels. In particular, we are interested in studying steady bifurcations, occurring when non-unique stable solutions appear as physical and/or geometric control parameters are varied. The formulation of the stability problem requires solving an eigenvalue problem for a partial differential operator. An alternative to this approach is the direct simulation of the flow to characterize the asymptotic behavior of the solution. Both approaches can be extremely expensive in terms of computational time. We propose to apply Reduced Order Modeling (ROM) techniques to reduce the demanding computational costs associated with the detection of a type of steady bifurcations in fluid dynamics. The application that motivated the present study is the onset of asymmetries (i.e., symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the regurgitant mitral valve orifice shape.

We show that equivariant Donaldson polynomials of compact toric surfaces can be calculated as residues of suitable combinations of Virasoro conformal blocks, by building on AGT correspondence between $\mathcal{N}=2$ supersymmetric gauge theories and two-dimensional conformal field theory. Talk presented by A.T. at the conference Interactions between Geometry and Physics — in honor of Ugo Bruzzo’s 60th birthday 17–22 August 2015, Guarujá, São Paulo, Brazil, mostly based on Bawane et al. (0000) and Bershtein et al. (0000).

10aAGT10aDonaldson invariants10aEquivariant localization10aExact partition function10aSupersymmetry10aVirasoro conformal blocks1 aBershtein, Mikhail1 aBonelli, Giulio1 aRonzani, Massimiliano1 aTanzini, Alessandro uhttp://www.sciencedirect.com/science/article/pii/S039304401730016501991nas a2200157 4500008004100000245002800041210002800069260002200097300000900119520158000128100002401708700002001732700002101752700001901773856004101792 2017 eng d00aModel Reduction Methods0 aModel Reduction Methods bJohn Wiley & Sons a1-363 aThis chapter presents an overview of model order reduction – a new paradigm in the field of simulation-based engineering sciences, and one that can tackle the challenges and leverage the opportunities of modern ICT technologies. Despite the impressive progress attained by simulation capabilities and techniques, a number of challenging problems remain intractable. These problems are of different nature, but are common to many branches of science and engineering. Among them are those related to high-dimensional problems, problems involving very different time scales, models defined in degenerate domains with at least one of the characteristic dimensions much smaller than the others, model requiring real-time simulation, and parametric models. All these problems represent a challenge for standard mesh-based discretization techniques; yet the ability to solve these problems efficiently would open unexplored routes for real-time simulation, inverse analysis, uncertainty quantification and propagation, real-time optimization, and simulation-based control – critical needs in many branches of science and engineering. Model order reduction offers new simulation alternatives by circumventing, or at least alleviating, otherwise intractable computational challenges. In the present chapter, we revisit three of these model reduction techniques: proper orthogonal decomposition, proper generalized decomposition, and reduced basis methodologies.} preprint = {http://preprints.sissa.it/xmlui/bitstream/handle/1963/35194/ECM_MOR.pdf?sequence=1&isAllowed=y

1 aChinesta, Francisco1 aHuerta, Antonio1 aRozza, Gianluigi1 aWillcox, Karen uhttps://www.math.sissa.it/node/1294900506nas a2200145 4500008004100000245009700041210006900138300001400207490000800221100001700229700001500246700002200261700002200283856005500305 2017 eng d00aA natural framework for isogeometric fluid-structure interaction based on BEM-shell coupling0 anatural framework for isogeometric fluidstructure interaction ba a522–5460 v3161 aHeltai, Luca1 aKiendl, J.1 aDeSimone, Antonio1 aReali, Alessandro uhttp://cdsads.u-strasbg.fr/abs/2017CMAME.316..522H00711nas a2200181 4500008004100000245009900041210006900140300001400209490000700223100002400230700002000254700002000274700002200294700002100316700002000337700002200357856015000379 2017 eng d00aNumerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts0 aNumerical modeling of hemodynamics scenarios of patientspecific a1373-13990 v161 aBallarin, Francesco1 aFaggiano, Elena1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi1 aIppolito, Sonia1 aScrofani, Roberto uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85015065851&doi=10.1007%2fs10237-017-0893-7&partnerID=40&md5=c388f20bd5de14187bad9ed7d9affbd000603nas a2200169 4500008004100000245012600041210006900167260003400236300001400270490000600284100002200290700001900312700001700331700002100348700002100369856004300390 2017 eng d00aPOD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder0 aPODGalerkin reduced order methods for CFD using Finite Volume Di bWalter de Gruyter {GmbH}cdec a210–2360 v81 aStabile, Giovanni1 aHijazi, Saddam1 aMola, Andrea1 aLorenzi, Stefano1 aRozza, Gianluigi uhttps://doi.org/10.1515/caim-2017-001100452nas a2200121 4500008004100000245005700041210005700098260002200155490000800177100002300185700002400208856009800232 2017 eng d00aRayleigh–Taylor instability in soft elastic layers0 aRayleigh–Taylor instability in soft elastic layers bThe Royal Society0 v3751 aRiccobelli, Davide1 aCiarletta, Pasquale uhttps://www.math.sissa.it/publication/rayleigh%E2%80%93taylor-instability-soft-elastic-layers02504nas a2200157 4500008004100000245005700041210005700098260001200155300000800167490000600175520201600181100001502197700002202212700002102234856009102255 2017 eng d00aReduced Basis Methods for Uncertainty Quantification0 aReduced Basis Methods for Uncertainty Quantification c08/2017 a8690 v53 aIn this work we review a reduced basis method for the solution of uncertainty quantification problems. Based on the basic setting of an elliptic partial differential equation with random input, we introduce the key ingredients of the reduced basis method, including proper orthogonal decomposition and greedy algorithms for the construction of the reduced basis functions, a priori and a posteriori error estimates for the reduced basis approximations, as well as its computational advantages and weaknesses in comparison with a stochastic collocation method [I. Babuška, F. Nobile, and R. Tempone, *SIAM Rev.*, 52 (2010), pp. 317--355]. We demonstrate its computational efficiency and accuracy for a benchmark problem with parameters ranging from a few to a few hundred dimensions. Generalizations to more complex models and applications to uncertainty quantification problems in risk prediction, evaluation of statistical moments, Bayesian inversion, and optimal control under uncertainty are also presented to illustrate how to use the reduced basis method in practice. Further challenges, advancements, and research opportunities are outlined.

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

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

1 aBallarin, Francesco1 aRozza, Gianluigi1 aMaday, Yvon1 aBenner, Peter1 aOhlberger, Mario1 aPatera, Anthony1 aRozza, Gianluigi1 aUrban, Karsten uhttps://www.math.sissa.it/node/1294800623nas a2200169 4500008004100000245008300041210006900124260002500193300001400218490000800232100001600240700001600256700002300272700002300295700002400318856011100342 2017 eng d00aSolid tumors are poroelastic solids with a chemo-mechanical feedback on growth0 aSolid tumors are poroelastic solids with a chemomechanical feedb bSpringer Netherlands a107–1240 v1291 aAmbrosi, D.1 aPezzuto, S.1 aRiccobelli, Davide1 aStylianopoulos, T.1 aCiarletta, Pasquale uhttps://www.math.sissa.it/publication/solid-tumors-are-poroelastic-solids-chemo-mechanical-feedback-growth00795nas a2200241 4500008004100000245011200041210006900153260003500222300001100257490000800268100001800276700001800294700001600312700002200328700001900350700002300369700002200392700002200414700001800436700001800454700002100472856006000493 2017 eng d00aUniversality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schrödinger Equation0 aUniversality of the Peregrine Soliton in the Focusing Dynamics o bAmerican Physical SocietycJul a0339010 v1191 aTikan, Alexey1 aBillet, Cyril1 aEl, Gennady1 aTovbis, Alexander1 aBertola, Marco1 aSylvestre, Thibaut1 aGustave, Francois1 aRandoux, Stephane1 aGenty, Goëry1 aSuret, Pierre1 aDudley, John, M. uhttps://link.aps.org/doi/10.1103/PhysRevLett.119.03390102112nas a2200217 4500008004100000245018600041210006900227260003600296520123100332100002501563700002401588700002001612700001701632700001901649700002101668700002101689700002101710700001701731700001601748856013001764 2016 en d00aAdvances in geometrical parametrization and reduced order models and methods for computational fluid dynamics problems in applied sciences and engineering: overview and perspectives0 aAdvances in geometrical parametrization and reduced order models aCrete, GreecebECCOMASc06/20163 aSeveral problems in applied sciences and engineering require reduction techniques in order to allow computational tools to be employed in the daily practice, especially in iterative procedures such as optimization or sensitivity analysis. Reduced order methods need to face increasingly complex problems in computational mechanics, especially into a multiphysics setting. Several issues should be faced: stability of the approximation, efficient treatment of nonlinearities, uniqueness or possible bifurcations of the state solutions, proper coupling between fields, as well as offline-online computing, computational savings and certification of errors as measure of accuracy. Moreover, efficient geometrical parametrization techniques should be devised to efficiently face shape optimization problems, as well as shape reconstruction and shape assimilation problems. A related aspect deals with the management of parametrized interfaces in multiphysics problems, such as fluid-structure interaction problems, and also a domain decomposition based approach for complex parametrized networks. We present some illustrative industrial and biomedical problems as examples of recent advances on methodological developments.

1 aSalmoiraghi, Filippo1 aBallarin, Francesco1 aCorsi, Giovanni1 aMola, Andrea1 aTezzele, Marco1 aRozza, Gianluigi1 aPapadrakakis, M.1 aPapadopoulos, V.1 aStefanou, G.1 aPlevris, V. uhttps://www.math.sissa.it/publication/advances-geometrical-parametrization-and-reduced-order-models-and-methods-computational00357nas a2200085 4500008004100000245006000041210005900101100001800160856009300178 2016 eng d00aCritical points of a perturbed Otha-Kawasaki functional0 aCritical points of a perturbed OthaKawasaki functional1 aRizzi, Matteo uhttps://www.math.sissa.it/publication/critical-points-perturbed-otha-kawasaki-functional00590nas a2200157 4500008004100000245009800041210006900139300001400208490000700222100001600229700001700245700001400262700001700276700001400293856012500307 2016 eng d00aError Estimates of B-spline based finite-element method for the wind-driven ocean circulation0 aError Estimates of Bspline based finiteelement method for the wi a430–4590 v691 aRotundo, N.1 aKim, T., -Y.1 aJiang, W.1 aHeltai, Luca1 aFried, E. uhttps://www.math.sissa.it/publication/error-estimates-b-spline-based-finite-element-method-wind-driven-ocean-circulation01475nas a2200181 4500008004100000022001400041245012000055210006900175260000800244300000700252490000900259520088800268100002301156700002001179700002601199700002401225856004401249 2016 eng d a1029-847900aExact results for N=2 supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants0 aExact results for N2 supersymmetric gauge theories on compact to cJul a230 v20163 aWe provide a contour integral formula for the exact partition function of $\mathcal{N}=2$ supersymmetric $U(N)$ gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the contour integral for $U(2)\; \mathcal{N}=2^\star$ theory on $\mathbb{P}^2$ for all instanton numbers. In the zero mass case, corresponding to the $\mathcal{N}=4$ supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of mock-modular forms. In the decoupling limit of infinite mass we find that the generating function of local and surface observables computes equivariant Donaldson invariants, thus proving in this case a longstanding conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new.

1 aBershtein, Mikhail1 aBonelli, Giulio1 aRonzani, Massimiliano1 aTanzini, Alessandro uhttps://doi.org/10.1007/JHEP07(2016)02301717nas a2200193 4500008004100000245011900041210006900160260001400229520106200243100002401305700002001329700002001349700002101369700002201390700002001412700002201432700001801454856005101472 2016 en d00aA fast virtual surgery platform for many scenarios haemodynamics of patient-specific coronary artery bypass grafts0 afast virtual surgery platform for many scenarios haemodynamics o bSubmitted3 aA fast computational framework is devised to the study of several configurations of patient-specific coronary artery bypass grafts. This is especially useful to perform a sensitivity analysis of the haemodynamics for different flow conditions occurring in native coronary arteries and bypass grafts, the investigation of the progression of the coronary artery disease and the choice of the most appropriate surgical procedure. A complete pipeline, from the acquisition of patientspecific medical images to fast parametrized computational simulations, is proposed. Complex surgical configurations employed in the clinical practice, such as Y-grafts and sequential grafts, are studied. A virtual surgery platform based on model reduction of unsteady Navier Stokes equations for blood dynamics is proposed to carry out sensitivity analyses in a very rapid and reliable way. A specialized geometrical parametrization is employed to compare the effect of stenosis and anastomosis variation on the outcome of the surgery in several relevant cases.1 aBallarin, Francesco1 aFaggiano, Elena1 aManzoni, Andrea1 aRozza, Gianluigi1 aQuarteroni, Alfio1 aIppolito, Sonia1 aScrofani, Roberto1 aAntona, Carlo uhttp://urania.sissa.it/xmlui/handle/1963/3524002791nas a2200121 4500008004100000245004400041210004400085260001000129520243500139653001802574100002602592856005102618 2016 en d00aInstanton counting on compact manifolds0 aInstanton counting on compact manifolds bSISSA3 aIn this thesis we analyze supersymmetric gauge theories on compact manifolds and their relation with representation theory of infinite Lie algebras associated to conformal field theories, and with the computation of geometric invariants and superconformal indices. The thesis contains the work done by the candidate during the doctorate programme at SISSA under the supervision of A. Tanzini and G. Bonelli. • in Chapter 2, we consider N = 2 supersymmetric gauge theories on four manifolds admitting an isometry. Generalized Killing spinor equations are derived from the consistency of supersymmetry algebrae and solved in the case of four manifolds admitting a U(1) isometry. This is used to explicitly compute the supersymmetric path integral on S2 × S2 via equivariant localization. The building blocks of the resulting partition function are shown to contain the three point functions and the conformal blocks of Liouville Gravity. • in Chapter 3, we provide a contour integral formula for the exact partition function of N = 2 supersymmetric U(N) gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the contour integral for U(2) N = 2∗ theory on P2 for all instanton numbers. In the zero mass case, corresponding to the N = 4 supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of mock-modular forms. In the decoupling limit of infinite mass we find that the generating function of local and surface observables computes equivariant Donaldson invariants, thus proving in this case a long-standing conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new. • in Chapter 4, we explore N = (1, 0) superconformal six-dimensional theories arising from M5 branes probing a transverse Ak singularity. Upon circle compactification to five dimensions, we describe this system with a dual pq-web of five-branes and propose the spectrum of basic five-dimensional in- stanton operators driving global symmetry enhancement. For a single M5 brane, we find that the exact partition function of the 5d quiver gauge theory matches the 6d (1, 0) index, which we compute by letter counting. We finally show which relations among vertex correlators of qW algebrae are implied by the S-duality of the pq-web.10aSupersymmetry1 aRonzani, Massimiliano uhttp://urania.sissa.it/xmlui/handle/1963/3521901409nas a2200145 4500008004100000245011900041210006900160260007700229520081900306100002501125700002401150700001701174700002101191856005101212 2016 en d00aIsogeometric analysis-based reduced order modelling for incompressible linear viscous flows in parametrized shapes0 aIsogeometric analysisbased reduced order modelling for incompres bSpringer, AMOS Advanced Modelling and Simulation in Engineering Sciences3 aIn this work we provide a combination of isogeometric analysis with reduced order modelling techniques, based on proper orthogonal decomposition, to guarantee computational reduction for the numerical model, and with free-form deformation, for versatile geometrical parametrization. We apply it to computational fluid dynamics problems considering a Stokes flow model. The proposed reduced order model combines efficient shape deformation and accurate and stable velocity and pressure approximation for incompressible viscous flows, computed with a reduced order method. Efficient offine-online computational decomposition is guaranteed in view of repetitive calculations for parametric design and optimization problems. Numerical test cases show the efficiency and accuracy of the proposed reduced order model.1 aSalmoiraghi, Filippo1 aBallarin, Francesco1 aHeltai, Luca1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3519900391nas a2200133 4500008004100000245003600041210003500077260001000112100002400122700002000146700002100166700001900187856005100206 2016 en d00aModel Order Reduction: a survey0 aModel Order Reduction a survey bWiley1 aChinesta, Francisco1 aHuerta, Antonio1 aRozza, Gianluigi1 aWillcox, Karen uhttp://urania.sissa.it/xmlui/handle/1963/3519401951nas a2200169 4500008004100000245009300041210006900134260001300203300000800216490000700224520142100231100002101652700001901673700001701692700002101709856005101730 2016 en d00aA multi-physics reduced order model for the analysis of Lead Fast Reactor single channel0 amultiphysics reduced order model for the analysis of Lead Fast R bElsevier a2080 v873 aIn this work, a Reduced Basis method, with basis functions sampled by a Proper Orthogonal Decomposition technique, has been employed to develop a reduced order model of a multi-physics parametrized Lead-cooled Fast Reactor single-channel. Being the first time that a reduced order model is developed in this context, the work focused on a methodological approach and the coupling between the neutronics and the heat transfer, where the thermal feedbacks on neutronics are explicitly taken into account, in time-invariant settings. In order to address the potential of such approach, two different kinds of varying parameters have been considered, namely one related to a geometric quantity (i.e., the inner radius of the fuel pellet) and one related to a physical quantity (i.e., the inlet lead velocity). The capabilities of the presented reduced order model (ROM) have been tested and compared with a high-fidelity finite element model (upon which the ROM has been constructed) on different aspects. In particular, the comparison focused on the system reactivity prediction (with and without thermal feedbacks on neutronics), the neutron flux and temperature field reconstruction, and on the computational time. The outcomes provided by the reduced order model are in good agreement with the high-fidelity finite element ones, and a computational speed-up of at least three orders of magnitude is achieved as well.1 aSartori, Alberto1 aCammi, Antonio1 aLuzzi, Lelio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3519102275nas a2200145 4500008004100000245009200041210006900133260006800202520165800270100002101928700001901949700001701968700002101985856012302006 2016 en d00aPOD-Galerkin Method for Finite Volume Approximation of Navier-Stokes and RANS Equations0 aPODGalerkin Method for Finite Volume Approximation of NavierStok bComputer Methods in Applied Mechanics and Engineering, Elsevier3 aNumerical simulation of fluid flows requires important computational efforts but it is essential in engineering applications. Reduced Order Model (ROM) can be employed whenever fast simulations are required, or in general, whenever a trade-off between computational cost and solution accuracy is a preeminent issue as in process optimization and control. In this work, the efforts have been put to develop a ROM for Computational Fluid Dynamics (CFD) application based on Finite Volume approximation, starting from the results available in turbulent Reynold-Averaged Navier Stokes simulations in order to enlarge the application field of Proper Orthogonal Decomposition – Reduced Order Model (POD – ROM) technique to more industrial fields. The approach is tested in the classic benchmark of the numerical simulation of the 2D lid-driven cavity. In particular, two simulations at Re = 103 and Re = 105 have been considered in order to assess both a laminar and turbulent case. Some quantities have been compared with the Full Order Model in order to assess the performance of the proposed ROM procedure i.e., the kinetic energy of the system and the reconstructed quantities of interest (velocity, pressure and turbulent viscosity). In addition, for the laminar case, the comparison between the ROM steady-state solution and the data available in literature has been presented. The results have turned out to be very satisfactory both for the accuracy and the computational times. As a major outcome, the approach turns out not to be affected by the energy blow up issue characterizing the results obtained by classic turbulent POD-Galerkin methods.1 aLorenzi, Stefano1 aCammi, Antonio1 aLuzzi, Lelio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/pod-galerkin-method-finite-volume-approximation-navier-stokes-and-rans-equations01502nas a2200121 4500008004100000245010500041210007100146260001000217520097200227100002401199700002101223856013601244 2016 en d00aPOD–Galerkin monolithic reduced order models for parametrized fluid-structure interaction problems0 aPOD–Galerkin monolithic reduced order models for parametrized fl bWiley3 aIn this paper we propose a monolithic approach for reduced order modelling of parametrized fluid-structure interaction problems based on a proper orthogonal decomposition (POD)–Galerkin method. Parameters of the problem are related to constitutive properties of the fluid or structural problem, or to geometrical parameters related to the domain configuration at the initial time. We provide a detailed description of the parametrized formulation of the multiphysics problem in its components, together with some insights on how to obtain an offline-online efficient computational procedure through the approximation of parametrized nonlinear tensors. Then, we present the monolithic POD–Galerkin method for the online computation of the global structural displacement, fluid velocity and pressure of the coupled problem. Finally, we show some numerical results to highlight the capabilities of the proposed reduced order method and its computational performances1 aBallarin, Francesco1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/pod%E2%80%93galerkin-monolithic-reduced-order-models-parametrized-fluid-structure-interaction00972nas a2200121 4500008004100000245009000041210006900131260001000200520038100210653011700591100001800708856012400726 2016 en d00aQualitative properties and construction of solutions to some semilinear elliptic PDEs0 aQualitative properties and construction of solutions to some sem bSISSA3 aThis thesis is devoted to the study of elliptic equations. On the one hand, we study some qualitative properties, such as symmetry of solutions, on the other hand we explicitly construct some solutions vanishing near some fixed manifold. The main techniques are the moving planes method, in order to investigate the qualitative properties and the Lyapunov-Schmidt reduction.10amoving planes method, maximum principle, Lyapunov-Schmidt reduction, Willmore surfaces, Otha-Kawasaki functional1 aRizzi, Matteo uhttps://www.math.sissa.it/publication/qualitative-properties-and-construction-solutions-some-semilinear-elliptic-pdes-001691nas a2200169 4500008004100000245008700041210006900128260001800197300000600215490000600221520116500227100002101392700001901413700001701432700002101449856005101470 2016 en d00aA Reduced Basis Approach for Modeling the Movement of Nuclear Reactor Control Rods0 aReduced Basis Approach for Modeling the Movement of Nuclear Reac bASMEc02/2016 a80 v23 aThis work presents a reduced order model (ROM) aimed at simulating nuclear reactor control rods movement and featuring fast-running prediction of reactivity and neutron flux distribution as well. In particular, the reduced basis (RB) method (built upon a high-fidelity finite element (FE) approximation) has been employed. The neutronics has been modeled according to a parametrized stationary version of the multigroup neutron diffusion equation, which can be formulated as a generalized eigenvalue problem. Within the RB framework, the centroidal Voronoi tessellation is employed as a sampling technique due to the possibility of a hierarchical parameter space exploration, without relying on a “classical” a posteriori error estimation, and saving an important amount of computational time in the offline phase. Here, the proposed ROM is capable of correctly predicting, with respect to the high-fidelity FE approximation, both the reactivity and neutron flux shape. In this way, a computational speedup of at least three orders of magnitude is achieved. If a higher precision is required, the number of employed basis functions (BFs) must be increased.1 aSartori, Alberto1 aCammi, Antonio1 aLuzzi, Lelio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3519201826nas a2200145 4500008004100000245012700041210006900168260001600237520129800253100002101551700001901572700001701591700002101608856005101629 2016 en d00aReduced basis approaches in time-dependent noncoercive settings for modelling the movement of nuclear reactor control rods0 aReduced basis approaches in timedependent noncoercive settings f bSISSAc20163 aIn this work, two approaches, based on the certified Reduced Basis method, have been developed for simulating the movement of nuclear reactor control rods, in time-dependent non-coercive settings featuring a 3D geometrical framework. In particular, in a first approach, a piece-wise affine transformation based on subdomains division has been implemented for modelling the movement of one control rod. In the second approach, a “staircase” strategy has been adopted for simulating the movement of all the three rods featured by the nuclear reactor chosen as case study. The neutron kinetics has been modelled according to the so-called multi-group neutron diffusion, which, in the present case, is a set of ten coupled parametrized parabolic equations (two energy groups for the neutron flux, and eight for the precursors). Both the reduced order models, developed according to the two approaches, provided a very good accuracy compared with high-fidelity results, assumed as “truth” solutions. At the same time, the computational speed-up in the Online phase, with respect to the fine “truth” finite element discretization, achievable by both the proposed approaches is at least of three orders of magnitude, allowing a real-time simulation of the rod movement and control.

1 aSartori, Alberto1 aCammi, Antonio1 aLuzzi, Lelio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3496301905nas a2200157 4500008004100000245012000041210006900161260002200230300000800252490000700260520128900267100002101556700002201577700002101599856012701620 2016 en d00aReduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries0 aReduced basis method and domain decomposition for elliptic probl bElsevierc01/2016 a4300 v713 aThe aim of this work is to solve parametrized partial differential equations in computational domains represented by networks of repetitive geometries by combining reduced basis and domain decomposition techniques. The main idea behind this approach is to compute once, locally and for few reference shapes, some representative finite element solutions for different values of the parameters and with a set of different suitable boundary conditions on the boundaries: these functions will represent the basis of a reduced space where the global solution is sought for. The continuity of the latter is assured by a classical domain decomposition approach. Test results on Poisson problem show the flexibility of the proposed method in which accuracy and computational time may be tuned by varying the number of reduced basis functions employed, or the set of boundary conditions used for defining locally the basis functions. The proposed approach simplifies the pre-computation of the reduced basis space by splitting the global problem into smaller local subproblems. Thanks to this feature, it allows dealing with arbitrarily complex network and features more flexibility than a classical global reduced basis approximation where the topology of the geometry is fixed.1 aIapichino, Laura1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduced-basis-method-and-domain-decomposition-elliptic-problems-networks-and-complex01192nas a2200181 4500008004100000022001400041245008800055210006900143260000800212300000700220490000900227520063800236100002200874700002000896700002600916700002400942856004400966 2016 eng d a1029-847900aSymmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index0 aSymmetry enhancements via 5d instantons qWalgebrae and 10 superc cSep a530 v20163 aWe explore $\mathcal{N}=(1,0)$ superconformal six-dimensional theories arising from M5 branes probing a transverse $A_k$ singularity. Upon circle compactification to 5 dimensions, we describe this system with a dual pq-web of five-branes and propose the spectrum of basic five-dimensional instanton operators driving global symmetry enhancement. For a single M5 brane, we find that the exact partition function of the 5d quiver gauge theory matches the 6d (1, 0) index, which we compute by letter counting. We finally show that S-duality of the pq-web implies new relations among vertex correlators of $q\mathcal{W}$ algebrae.

1 aBenvenuti, Sergio1 aBonelli, Giulio1 aRonzani, Massimiliano1 aTanzini, Alessandro uhttps://doi.org/10.1007/JHEP09(2016)05300553nas a2200145 4500008004100000245008000041210006900121260002200190300001600212490000700228100002000235700002200255700001800277856011200295 2016 eng d00aSymmetry properties of some solutions to some semilinear elliptic equations0 aSymmetry properties of some solutions to some semilinear ellipti bClasse di Scienze a1209–12340 v161 aFarina, Alberto1 aMalchiodi, Andrea1 aRizzi, Matteo uhttps://www.math.sissa.it/publication/symmetry-properties-some-solutions-some-semilinear-elliptic-equations00968nas a2200145 4500008004100000022001400041245003700055210003700092300000900129490000700138520055900145100002200704700002000726856007600746 2016 eng d a1078-094700aYoung towers for product systems0 aYoung towers for product systems a14650 v363 aWe show that the direct product of maps with Young towers admits a Young tower whose return times decay at a rate which is bounded above by the slowest of the rates of decay of the return times of the component maps. An application of this result, together with other results in the literature, yields various statistical properties for the direct product of various classes of systems, including Lorenz-like maps, multimodal maps, piecewise $C^2$ interval maps with critical points and singularities, Hénon maps and partially hyperbolic systems.

1 aLuzzatto, Stefano1 aRuziboev, Marks uhttp://aimsciences.org//article/id/18d4526e-470d-467e-967a-a0345ad4c64201368nam a2200229 4500008004100000020002200041022001400063245008400077210006900161250000600230260002600236300000800262520053600270653003000806653002800836653004800864653004500912100002200957700002100979700002001000856011801020 2015 eng d a978-3-319-22469-5 a2191-820100aCertified Reduced Basis Methods for Parametrized Partial Differential Equations0 aCertified Reduced Basis Methods for Parametrized Partial Differe a1 aSwitzerlandbSpringer a1353 aThis book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.

10aa posteriori error bounds10aempirical interpolation10aparametrized partial differential equations10areduced basis methods, greedy algorithms1 aHesthaven, Jan, S1 aRozza, Gianluigi1 aStamm, Benjamin uhttps://www.math.sissa.it/publication/certified-reduced-basis-methods-parametrized-partial-differential-equations00709nas a2200133 4500008004100000245007500041210007000116260002100186300001200207490000700219520027900226100002000505856005000525 2015 eng d00aDecay of correlations for invertible maps with non-Hölder observables0 aDecay of correlations for invertible maps with nonHölder observa bTaylor & Francis a341-3520 v303 aAn invertible dynamical system with some hyperbolic structure is considered. Upper estimates for the correlations of continuous observables are given in terms of modulus of continuity. The result is applied to certain Hénon maps and Solenoid maps with intermittency.

1 aRuziboev, Marks uhttps://doi.org/10.1080/14689367.2015.104681601820nas a2200169 4500008004100000245015600041210006900197520118400266100002401450700002001474700002001494700002001514700002201534700002101556700002201577856005101599 2015 en d00aFast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization0 aFast simulations of patientspecific haemodynamics of coronary ar3 aIn this work a reduced-order computational framework for the study of haemodynamics in three-dimensional patient-specific configurations of coronary artery bypass grafts dealing with a wide range of scenarios is proposed. We combine several efficient algorithms to face at the same time both the geometrical complexity involved in the description of the vascular network and the huge computational cost entailed by time dependent patient-specific flow simulations. Medical imaging procedures allow to reconstruct patient-specific configurations from clinical data. A centerlines-based parametrization is proposed to efficiently handle geometrical variations. POD–Galerkin reduced-order models are employed to cut down large computational costs. This computational framework allows to characterize blood flows for different physical and geometrical variations relevant in the clinical practice, such as stenosis factors and anastomosis variations, in a rapid and reliable way. Several numerical results are discussed, highlighting the computational performance of the proposed framework, as well as its capability to perform sensitivity analysis studies, so far out of reach.1 aBallarin, Francesco1 aFaggiano, Elena1 aIppolito, Sonia1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi1 aScrofani, Roberto uhttp://urania.sissa.it/xmlui/handle/1963/3462301381nas a2200205 4500008004100000022001400041245007100055210006900126300001400195490000800209520074400217653001900961653002200980653002401002100002001026700002001046700002201066700001601088856007101104 2015 eng d a0001-870800aA general existence result for the Toda system on compact surfaces0 ageneral existence result for the Toda system on compact surfaces a937 - 9790 v2853 aIn this paper we consider the following Toda system of equations on a compact surface:−Δu1=2ρ1(h1eu1∫Σh1eu1dVg−1)−ρ2(h2eu2∫Σh2eu2dVg−1)−Δu1=−4π∑j=1mα1,j(δpj−1),−Δu2=2ρ2(h2eu2∫Σh2eu2dVg−1)−ρ1(h1eu1∫Σh1eu1dVg−1)−Δu2=−4π∑j=1mα2,j(δpj−1), which is motivated by the study of models in non-abelian Chern–Simons theory. Here h1,h2 are smooth positive functions, ρ1,ρ2 two positive parameters, pi points of the surface and α1,i,α2,j non-negative numbers. We prove a general existence result using variational methods. The same analysis applies to the following mean field equation−Δu=ρ1(heu∫ΣheudVg−1)−ρ2(he−u∫Σhe−udVg−1), which arises in fluid dynamics."

10aGeometric PDEs10aMin–max schemes10aVariational methods1 aBattaglia, Luca1 aJevnikar, Aleks1 aMalchiodi, Andrea1 aRuiz, David uhttp://www.sciencedirect.com/science/article/pii/S000187081500307201836nas a2200121 4500008004100000245006000041210005800101260001000159520139100169653003901560100002001599856009501619 2015 en d00aGibbs-Markov-Young Structures and Decay of Correlations0 aGibbsMarkovYoung Structures and Decay of Correlations bSISSA3 aIn this work we study mixing properties of discrete dynamical systems and related to them geometric structure. In the first chapter we show that the direct product of maps with Young towers admits a Young tower whose return times decay at a rate which is bounded above by the slowest of the rates of decay of the return times of the component maps. An application of this result, together with other results in the literature, yields various statistical properties for the direct product of various classes of systems, including Lorenz-like maps, multimodal maps, piecewise $C^2$ interval maps with critical points and singularities, H\'enon maps and partially hyperbolic systems. The second chapter is dedicated to the problem of decay of correlations for continuous observables. First we show that if the underlying system admits Young tower then the rate of decay of correlations for continuous observables can be estimated in terms of modulus of continuity and the decay rate of tail of Young tower. In the rest of the second chapter we study the relations between the rates of decay of correlations for smooth observables and continuous observables. We show that if the rates of decay of correlations is known for $C^r,$ observables ($r\ge 1$) then it is possible to obtain decay of correlations for continuous observables in terms of modulus of continuity.10aDecay of Correlations, GMY-towers1 aRuziboev, Marks uhttps://www.math.sissa.it/publication/gibbs-markov-young-structures-and-decay-correlations00678nas a2200169 4500008004100000245013400041210006900175300001400244490000700258100001800265700002100283700002000304700002100324700001900345700001900364856012500383 2015 eng d00aModel order reduction of parameterized systems ({MoRePaS}): Preface to the special issue of advances in computational mathematics0 aModel order reduction of parameterized systems MoRePaS Preface t a955–9600 v411 aBenner, Peter1 aOhlberger, Mario1 aPatera, Anthony1 aRozza, Gianluigi1 aSorensen, D.C.1 aUrban, Karsten uhttps://www.math.sissa.it/publication/model-order-reduction-parameterized-systems-morepas-preface-special-issue-advances01516nas a2200133 4500008004100000245012100041210006900162260001300231520102900244100002101273700001501294700002201309856005101331 2015 en d00aMultilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations0 aMultilevel and weighted reduced basis method for stochastic opti bSpringer3 aIn this paper we develop and analyze a multilevel weighted reduced basis method for solving stochastic optimal control problems constrained by Stokes equations. We prove the analytic regularity of the optimal solution in the probability space under certain assumptions on the random input data. The finite element method and the stochastic collocation method are employed for the numerical approximation of the problem in the deterministic space and the probability space, respectively, resulting in many large-scale optimality systems to solve. In order to reduce the unaffordable computational effort, we propose a reduced basis method using a multilevel greedy algorithm in combination with isotropic and anisotropic sparse-grid techniques. A weighted a posteriori error bound highlights the contribution stemming from each method. Numerical tests on stochastic dimensions ranging from 10 to 100 demonstrate that our method is very efficient, especially for solving high-dimensional and large-scale optimization problems.1 aRozza, Gianluigi1 aChen, Peng1 aQuarteroni, Alfio uhttp://urania.sissa.it/xmlui/handle/1963/3449101077nas a2200181 4500008004100000022001400041245007100055210006800126260000800194300000700202490000900209520054400218100001900762700002000781700002600801700002400827856004400851 2015 eng d a1029-847900aN=2 supersymmetric gauge theories on S^2xS^2 and Liouville Gravity0 aN2 supersymmetric gauge theories on S2xS2 and Liouville Gravity cJul a540 v20153 aWe consider $\mathcal{N}=2$ supersymmetric gauge theories on four manifolds admitting an isometry. Generalized Killing spinor equations are derived from the consistency of supersymmetry algebrae and solved in the case of four manifolds admitting a $U(1)$ isometry. This is used to explicitly compute the supersymmetric path integral on $S^2 \times S^2$ via equivariant localization. The building blocks of the resulting partition function are shown to contain the three point functions and the conformal blocks of Liouville Gravity.

1 aBawane, Aditya1 aBonelli, Giulio1 aRonzani, Massimiliano1 aTanzini, Alessandro uhttps://doi.org/10.1007/JHEP07(2015)05400719nas a2200217 4500008004100000245009200041210006900133260003300202100002200235700002400257700001600281700002300297700001500320700001400335700002200349700002600371700002100397700001300418700001900431856005100450 2015 en d00aThe phototransduction machinery in the rod outer segment has a strong efficacy gradient0 aphototransduction machinery in the rod outer segment has a stron bNational Academy of Sciences1 aMazzolini, Monica1 aFacchetti, Giuseppe1 aAndolfi, L.1 aZaccaria, Proietti1 aTuccio, S.1 aTreud, J.1 aAltafini, Claudio1 aDi Fabrizio, Enzo, M.1 aLazzarino, Marco1 aRapp, G.1 aTorre, Vincent uhttp://urania.sissa.it/xmlui/handle/1963/3515702042nas a2200217 4500008004100000022001400041245010200055210006900157490003500226520122900261653002501490653002101515653002501536653002701561653002501588653001601613100002201629700002101651700002201672856013001694 2015 eng d a1019-716800aReduced basis approximation and a-posteriori error estimation for the coupled Stokes-Darcy system0 aReduced basis approximation and aposteriori error estimation for0 vspecial issue for MoRePaS 20123 aThe coupling of a free flow with a flow through porous media has many potential applications in several fields related with computational science and engineering, such as blood flows, environmental problems or food technologies. We present a reduced basis method for such coupled problems. The reduced basis method is a model order reduction method applied in the context of parametrized systems. Our approach is based on a heterogeneous domain decomposition formulation, namely the Stokes-Darcy problem. Thanks to an offline/online-decomposition, computational times can be drastically reduced. At the same time the induced error can be bounded by fast evaluable a-posteriori error bounds. In the offline-phase the proposed algorithms make use of the decomposed problem structure. Rigorous a-posteriori error bounds are developed, indicating the accuracy of certain lifting operators used in the offline-phase as well as the accuracy of the reduced coupled system. Also, a strategy separately bounding pressure and velocity errors is extended. Numerical experiments dealing with groundwater flow scenarios demonstrate the efficiency of the approach as well as the limitations regarding a-posteriori error estimation.

10aDomain decomposition10aError estimation10aNon-coercive problem10aPorous medium equation10aReduced basis method10aStokes flow1 aMartini, Immanuel1 aRozza, Gianluigi1 aHaasdonk, Bernard uhttps://www.math.sissa.it/publication/reduced-basis-approximation-and-posteriori-error-estimation-coupled-stokes-darcy-system01086nas a2200133 4500008004100000245009800041210006900139300001400208490000800222520055000230100001900780700002100799856013200820 2015 eng d00aReduced basis approximation of parametrized advection-diffusion PDEs with high Péclet number0 aReduced basis approximation of parametrized advectiondiffusion P a419–4260 v1033 aIn this work we show some results about the reduced basis approximation of advection dominated parametrized problems, i.e. advection-diffusion problems with high Péclet number. These problems are of great importance in several engineering applications and it is well known that their numerical approximation can be affected by instability phenomena. In this work we compare two possible stabilization strategies in the framework of the reduced basis method, by showing numerical results obtained for a steady advection-diffusion problem.

1 aPacciarini, P.1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduced-basis-approximation-parametrized-advection-diffusion-pdes-high-p%C3%A9clet-number01235nas a2200145 4500008004100000245010300041210006900144300001400213490000700227520066400234100002000898700002000918700002100938856013000959 2015 eng d00aReduced basis approximation of parametrized optimal flow control problems for the Stokes equations0 aReduced basis approximation of parametrized optimal flow control a319–3360 v693 aThis paper extends the reduced basis method for the solution of parametrized optimal control problems presented in Negri et al. (2013) to the case of noncoercive (elliptic) equations, such as the Stokes equations. We discuss both the theoretical properties-with particular emphasis on the stability of the resulting double nested saddle-point problems and on aggregated error estimates-and the computational aspects of the method. Then, we apply it to solve a benchmark vorticity minimization problem for a parametrized bluff body immersed in a two or a three-dimensional flow through boundary control, demonstrating the effectivity of the methodology.

1 aNegri, Federico1 aManzoni, Andrea1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduced-basis-approximation-parametrized-optimal-flow-control-problems-stokes-equations00689nas a2200145 4500008004100000245009900041210006900140260001000209520018600219100002400405700002000429700002200449700002100471856005100492 2015 en d00aSupremizer stabilization of POD-Galerkin approximation of parametrized Navier-Stokes equations0 aSupremizer stabilization of PODGalerkin approximation of paramet bWiley3 aIn this work, we present a stable proper orthogonal decomposition–Galerkin approximation for parametrized steady incompressible Navier–Stokes equations with low Reynolds number.1 aBallarin, Francesco1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3470101081nas a2200145 4500008004100000245007400041210006900115260003100184520057600215100002700791700002100818700002300839700002200862856005100884 2014 en d00aBuckling dynamics of a solvent-stimulated stretched elastomeric sheet0 aBuckling dynamics of a solventstimulated stretched elastomeric s bRoyal Society of Chemistry3 aWhen stretched uniaxially, a thin elastic sheet may exhibit buckling. The occurrence of buckling depends on the geometrical properties of the sheet and the magnitude of the applied strain. Here we show that an elastomeric sheet initially stable under uniaxial stretching can destabilize when exposed to a solvent that swells the elastomer. We demonstrate experimentally and computationally that the features of the buckling pattern depend on the magnitude of stretching, and this observation offers a new way for controlling the shape of a swollen homogeneous thin sheet.1 aLucantonio, Alessandro1 aRoché, Matthieu1 aNardinocchi, Paola1 aStone, Howard, A. uhttp://urania.sissa.it/xmlui/handle/1963/3496702162nas a2200133 4500008004100000245009400041210006900135260001300204520170200217100001501919700002201934700002101956856005101977 2014 en d00aComparison between reduced basis and stochastic collocation methods for elliptic problems0 aComparison between reduced basis and stochastic collocation meth bSpringer3 aThe stochastic collocation method (Babuška et al. in SIAM J Numer Anal 45(3):1005-1034, 2007; Nobile et al. in SIAM J Numer Anal 46(5):2411-2442, 2008a; SIAM J Numer Anal 46(5):2309-2345, 2008b; Xiu and Hesthaven in SIAM J Sci Comput 27(3):1118-1139, 2005) has recently been applied to stochastic problems that can be transformed into parametric systems. Meanwhile, the reduced basis method (Maday et al. in Comptes Rendus Mathematique 335(3):289-294, 2002; Patera and Rozza in Reduced basis approximation and a posteriori error estimation for parametrized partial differential equations Version 1.0. Copyright MIT, http://augustine.mit.edu, 2007; Rozza et al. in Arch Comput Methods Eng 15(3):229-275, 2008), primarily developed for solving parametric systems, has been recently used to deal with stochastic problems (Boyaval et al. in Comput Methods Appl Mech Eng 198(41-44):3187-3206, 2009; Arch Comput Methods Eng 17:435-454, 2010). In this work, we aim at comparing the performance of the two methods when applied to the solution of linear stochastic elliptic problems. Two important comparison criteria are considered: (1), convergence results of the approximation error; (2), computational costs for both offline construction and online evaluation. Numerical experiments are performed for problems from low dimensions O (1) to moderate dimensions O (10) and to high dimensions O (100). The main result stemming from our comparison is that the reduced basis method converges better in theory and faster in practice than the stochastic collocation method for smooth problems, and is more suitable for large scale and high dimensional stochastic problems when considering computational costs.1 aChen, Peng1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3472702011nas a2200241 4500008004100000245013600041210006900177260002200246300000800268490000700276520123100283100002101514700001901535700001901554700001901573700001701592700002701609700002001636700002301656700002101679700001801700856005101718 2014 en d00aComparison of a Modal Method and a Proper Orthogonal Decomposition approach for multi-group time-dependent reactor spatial kinetics0 aComparison of a Modal Method and a Proper Orthogonal Decompositi bElsevierc09/2014 a2290 v713 aIn this paper, two modelling approaches based on a Modal Method (MM) and on the Proper Orthogonal Decomposition (POD) technique, for developing a control-oriented model of nuclear reactor spatial kinetics, are presented and compared. Both these methods allow developing neutronics description by means of a set of ordinary differential equations. The comparison of the outcomes provided by the two approaches focuses on the capability of evaluating the reactivity and the neutron flux shape in different reactor configurations, with reference to a TRIGA Mark II reactor. The results given by the POD-based approach are higher-fidelity with respect to the reference solution than those computed according to the MM-based approach, in particular when the perturbation concerns a reduced region of the core. If the perturbation is homogeneous throughout the core, the two approaches allow obtaining comparable accuracy results on the quantities of interest. As far as the computational burden is concerned, the POD approach ensures a better efficiency rather than direct Modal Method, thanks to the ability of performing a longer computation in the preprocessing that leads to a faster evaluation during the on-line phase.

1 aSartori, Alberto1 aBaroli, Davide1 aCammi, Antonio1 aChiesa, Davide1 aLuzzi, Lelio1 aPonciroli, Roberto, R.1 aPrevitali, Ezio1 aRicotti, Marco, E.1 aRozza, Gianluigi1 aSisti, Monica uhttp://urania.sissa.it/xmlui/handle/1963/3503901122nas a2200145 4500008004100000245005400041210005100095260001300146520066000159653006000819100002500879700001600904700002000920856003600940 2014 en d00aOn conjugate times of LQ optimal control problems0 aconjugate times of LQ optimal control problems bSpringer3 aMotivated by the study of linear quadratic optimal control problems, we consider a dynamical system with a constant, quadratic Hamiltonian, and we characterize the number of conjugate times in terms of the spectrum of the Hamiltonian vector field $\vec{H}$. We prove the following dichotomy: the number of conjugate times is identically zero or grows to infinity. The latter case occurs if and only if $\vec{H}$ has at least one Jordan block of odd dimension corresponding to a purely imaginary eigenvalue. As a byproduct, we obtain bounds from below on the number of conjugate times contained in an interval in terms of the spectrum of $\vec{H}$.10aOptimal control, Lagrange Grassmannian, Conjugate point1 aAgrachev, Andrei, A.1 aRizzi, Luca1 aSilveira, Pavel uhttp://hdl.handle.net/1963/722701220nas a2200121 4500008004100000245009100041210006900132260001000201520080700211653002801018100001601046856003601062 2014 en d00aThe curvature of optimal control problems with applications to sub-Riemannian geometry0 acurvature of optimal control problems with applications to subRi bSISSA3 aOptimal control theory is an extension of the calculus of variations, and deals with the optimal behaviour of a system under a very general class of constraints. This field has been pioneered by the group of mathematicians led by Lev Pontryagin in the second half of the 50s and nowadays has countless applications to the real worlds (robotics, trains, aerospace, models for human behaviour, human vision, image reconstruction, quantum control, motion of self-propulsed micro-organism). In this thesis we introduce a novel definition of curvature for an optimal control problem. In particular it works for any sub-Riemannian and sub-Finsler structure. Related problems, such as comparison theorems for sub-Riemannian manifolds, LQ optimal control problem and Popp's volume and are also investigated.10aSub-Riemannian geometry1 aRizzi, Luca uhttp://hdl.handle.net/1963/732101443nas a2200133 4500008004100000245015900041210006900200300001400269490000700283520085800290100001401148700002101162856012601183 2014 eng d00aEfficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems0 aEfficient geometrical parametrisation techniques of interfaces f a158–1690 v283 aWe present some recent advances and improvements in shape parametrisation techniques of interfaces for reduced-order modelling with special attention to fluid–structure interaction problems and the management of structural deformations, namely, to represent them into a low-dimensional space (by control points). This allows to reduce the computational effort, and to significantly simplify the (geometrical) deformation procedure, leading to more efficient and fast reduced-order modelling applications in this kind of problems. We propose an efficient methodology to select the geometrical control points for the radial basis functions based on a modal greedy algorithm to improve the computational efficiency in view of more complex fluid–structure applications in several fields. The examples provided deal with aeronautics and wind engineering.1 aForti, D.1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/efficient-geometrical-parametrisation-techniques-interfaces-reduced-order-modelling01604nas a2200133 4500008004100000245010100041210006900142260001900211490000800230520099000238653009201228100002101320856012901341 2014 eng d00aFundamentals of Reduced Basis Method for problems governed by parametrized PDEs and applications0 aFundamentals of Reduced Basis Method for problems governed by pa aWienbSpringer0 v5543 aIn this chapter we consider Reduced Basis (RB) approximations of parametrized Partial Differential Equations (PDEs). The the idea behind RB is to decouple the generation and projection stages (Offline/Online computational procedures) of the approximation process in order to solve parametrized PDEs in a fast, inexpensive and reliable way. The RB method, especially applied to 3D problems, allows great computational savings with respect to the classical Galerkin Finite Element (FE) Method. The standard FE method is typically ill suited to (i) iterative contexts like optimization, sensitivity analysis and many-queries in general, and (ii) real time evaluation. We consider for simplicity coercive PDEs. We discuss all the steps to set up a RB approximation, either from an analytical and a numerical point of view. Then we present an application of the RB method to a steady thermal conductivity problem in heat transfer with emphasis on geometrical and physical parameters.

10areduced basis method, linear elasticity, heat transfer, error bounds, parametrized PDEs1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/fundamentals-reduced-basis-method-problems-governed-parametrized-pdes-and-applications01082nas a2200145 4500008004100000245007200041210006900113300001400182490000800196520057300204100001600777700002100793700002100814856010100835 2014 eng d00aAn improvement on geometrical parameterizations by transfinite maps0 aimprovement on geometrical parameterizations by transfinite maps a263–2680 v3523 aWe present a method to generate a non-affine transfinite map from a given reference domain to a family of deformed domains. The map is a generalization of the Gordon-Hall transfinite interpolation approach. It is defined globally over the reference domain. Once we have computed some functions over the reference domain, the map can be generated by knowing the parametric expressions of the boundaries of the deformed domain. Being able to define a suitable map from a reference domain to a desired deformation is useful for the management of parameterized geometries.1 aJäggli, C.1 aIapichino, Laura1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/improvement-geometrical-parameterizations-transfinite-maps01687nas a2200145 4500008004100000245005600041210005400097260001000151300001100161490000700172520119700179653007701376100001801453856007001471 2014 en d00aA model for crack growth with branching and kinking0 amodel for crack growth with branching and kinking bSISSA a63-1100 v893 aWe study an evolution model for fractured elastic materials in the 2-dimensional case, for which the crack path is not assumed to be known a priori. We introduce some general assumptions on the structure of the fracture sets suitable to remove the restrictions on the regularity of the crack sets and to allow for kinking and branching to develop. In addition we define the front of the fracture and its velocity. By means of a time-discretization approach, we prove the existence of a continuous-time evolution that satisfies an energy inequality and a stability criterion. The energy balance also takes into account the energy dissipated at the front of the fracture. The stability criterion is stated in the framework of Griffith's theory, in terms of the energy release rate, when the crack grows at least at one point of its front.

10aquasistatic crack evolution, branching, kinking, Griffith\\\'s criterion1 aRacca, Simone uhttps://content.iospress.com/articles/asymptotic-analysis/asy123301650nas a2200145 4500008004100000245007300041210006900114260001300183520112000196100001801316700002001334700002201354700002101376856010701397 2014 en d00aModel Order Reduction in Fluid Dynamics: Challenges and Perspectives0 aModel Order Reduction in Fluid Dynamics Challenges and Perspecti bSpringer3 aThis chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities - which are mainly related either to nonlinear convection terms and/or some geometric variability - that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration. We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of inf-sup stability, certification through error estimation, computational issues and-in the unsteady case - long-time stability of the reduced model. Moreover, we provide an extensive list of literature references.1 aLassila, Toni1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/model-order-reduction-fluid-dynamics-challenges-and-perspectives01353nas a2200145 4500008004100000245007400041210006900115260001000184520088100194100002401075700002001099700001901119700001901138856005001157 2014 en d00aRate-independent damage in thermo-viscoelastic materials with inertia0 aRateindependent damage in thermoviscoelastic materials with iner bSISSA3 aWe present a model for rate-independent, unidirectional, partial damage in visco-elastic materials with inertia and thermal effects. The damage process is modeled by means of an internal variable, governed by a rate-independent flow rule. The heat equation and the momentum balance for the displacements are coupled in a highly nonlinear way. Our assumptions on the corresponding energy functional also comprise the case of the Ambrosio-Tortorelli phase-field model (without passage to the brittle limit). We discuss a suitable weak formulation and prove an existence theorem obtained with the aid of a (partially) decoupled time-discrete scheme and variational convergence methods. We also carry out the asymptotic analysis for vanishing viscosity and inertia and obtain a fully rate-independent limit model for displacements and damage, which is Independent of temperature.1 aLazzaroni, Giuliano1 aRossi, Riccarda1 aThomas, Marita1 aToader, Rodica uhttp://urania.sissa.it/xmlui/handle/1963/744400566nas a2200133 4500008004100000245010000041210006900141300001000210100002100220700002200241700002100263700002100284856012700305 2014 eng d00aReduced basis method for the Stokes equations in decomposable domains using greedy optimization0 aReduced basis method for the Stokes equations in decomposable do a1–71 aIapichino, Laura1 aQuarteroni, Alfio1 aRozza, Gianluigi1 aVolkwein, Stefan uhttps://www.math.sissa.it/publication/reduced-basis-method-stokes-equations-decomposable-domains-using-greedy-optimization01878nam a2200181 4500008004100000022002200041245006700063210006700130250000600197260002100203300000800224490000600232520123600238653007801474100002201552700002101574856010101595 2014 eng d a978-3-319-02089-100aReduced Order Methods for Modeling and Computational Reduction0 aReduced Order Methods for Modeling and Computational Reduction a1 aMilanobSpringer a3340 v93 aThis monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics.

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

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

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

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

1 aSartori, Alberto1 aBaroli, Davide1 aCammi, Antonio1 aLuzzi, Lelio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3512301626nas a2200145 4500008004100000245010700041210006900148260001300217520111600230100002401346700002001370700002101390700001801411856005101429 2014 en d00aShape Optimization by Free-Form Deformation: Existence Results and Numerical Solution for Stokes Flows0 aShape Optimization by FreeForm Deformation Existence Results and bSpringer3 aShape optimization problems governed by PDEs result from many applications in computational fluid dynamics. These problems usually entail very large computational costs and require also a suitable approach for representing and deforming efficiently the shape of the underlying geometry, as well as for computing the shape gradient of the cost functional to be minimized. Several approaches based on the displacement of a set of control points have been developed in the last decades, such as the so-called free-form deformations. In this paper we present a new theoretical result which allows to recast free-form deformations into the general class of perturbation of identity maps, and to guarantee the compactness of the set of admissible shapes. Moreover, we address both a general optimization framework based on the continuous shape gradient and a numerical procedure for solving efficiently three-dimensional optimal design problems. This framework is applied to the optimal design of immersed bodies in Stokes flows, for which we consider the numerical solution of a benchmark case study from literature.1 aBallarin, Francesco1 aManzoni, Andrea1 aRozza, Gianluigi1 aSalsa, Sandro uhttp://urania.sissa.it/xmlui/handle/1963/3469800987nas a2200145 4500008004100000245008700041210006900128260001000197520050200207100002400709700002000733700001900753700001900772856005000791 2014 en d00aSome remarks on a model for rate-independent damage in thermo-visco-elastodynamics0 aSome remarks on a model for rateindependent damage in thermovisc bSISSA3 aThis note deals with the analysis of a model for partial damage, where the rateindependent, unidirectional flow rule for the damage variable is coupled with the rate-dependent heat equation, and with the momentum balance featuring inertia and viscosity according to Kelvin-Voigt rheology. The results presented here combine the approach from Roubicek [1] with the methods from Lazzaroni/Rossi/Thomas/Toader [2] and extend the analysis to the setting of inhomogeneous time-dependent Dirichlet data.1 aLazzaroni, Giuliano1 aRossi, Riccarda1 aThomas, Marita1 aToader, Rodica uhttp://urania.sissa.it/xmlui/handle/1963/746301201nas a2200133 4500008004100000245007800041210006900119300001100188490000800199520070800207100001900915700002100934856011200955 2014 eng d00aStabilized reduced basis method for parametrized advection-diffusion PDEs0 aStabilized reduced basis method for parametrized advectiondiffus a1–180 v2743 aIn this work, we propose viable and efficient strategies for the stabilization of the reduced basis approximation of an advection dominated problem. In particular, we investigate the combination of a classic stabilization method (SUPG) with the Offline-Online structure of the RB method. We explain why the stabilization is needed in both stages and we identify, analytically and numerically, which are the drawbacks of a stabilization performed only during the construction of the reduced basis (i.e. only in the Offline stage). We carry out numerical tests to assess the performances of the ``double'' stabilization both in steady and unsteady problems, also related to heat transfer phenomena.

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

1 aPacciarini, P.1 aRozza, Gianluigi uhttps://infoscience.epfl.ch/record/203327/files/ECCOMAS_PP_GR.pdf00848nas a2200133 4500008004100000245009600041210006900137260003400206520037800240653002300618100001800641700001900659856003600678 2014 en d00aA variational model for the quasi-static growth of fractional dimensional brittle fractures0 avariational model for the quasistatic growth of fractional dimen bEuropean Mathematical Society3 aWe propose a variational model for the irreversible quasi-static evolution of brittle fractures having fractional Hausdorff dimension in the setting of two-dimensional antiplane and plane elasticity. The evolution along such irregular crack paths can be obtained as $\Gamma$-limit of evolutions along one-dimensional cracks when the fracture toughness tends to zero.

10aVariational models1 aRacca, Simone1 aToader, Rodica uhttp://hdl.handle.net/1963/698301557nas a2200133 4500008004100000245009400041210006900135260001700204520109300221100001501314700002201329700002101351856005101372 2014 en d00aA weighted empirical interpolation method: A priori convergence analysis and applications0 aweighted empirical interpolation method A priori convergence ana bEDP Sciences3 aWe extend the classical empirical interpolation method [M. Barrault, Y. Maday, N.C. Nguyen and A.T. Patera, An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations. Compt. Rend. Math. Anal. Num. 339 (2004) 667-672] to a weighted empirical interpolation method in order to approximate nonlinear parametric functions with weighted parameters, e.g. random variables obeying various probability distributions. A priori convergence analysis is provided for the proposed method and the error bound by Kolmogorov N-width is improved from the recent work [Y. Maday, N.C. Nguyen, A.T. Patera and G.S.H. Pau, A general, multipurpose interpolation procedure: the magic points. Commun. Pure Appl. Anal. 8 (2009) 383-404]. We apply our method to geometric Brownian motion, exponential Karhunen-Loève expansion and reduced basis approximation of non-affine stochastic elliptic equations. We demonstrate its improved accuracy and efficiency over the empirical interpolation method, as well as sparse grid stochastic collocation method.1 aChen, Peng1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3502101890nas a2200145 4500008004100000245011800041210006900159260001300228520137300241653003501614100001801649700002001667700002101687856003601708 2013 en d00aA combination between the reduced basis method and the ANOVA expansion: On the computation of sensitivity indices0 acombination between the reduced basis method and the ANOVA expan bElsevier3 aWe consider a method to efficiently evaluate in a real-time context an output based on the numerical solution of a partial differential equation depending on a large number of parameters. We state a result allowing to improve the computational performance of a three-step RB-ANOVA-RB method. This is a combination of the reduced basis (RB) method and the analysis of variations (ANOVA) expansion, aiming at compressing the parameter space without affecting the accuracy of the output. The idea of this method is to compute a first (coarse) RB approximation of the output of interest involving all the parameter components, but with a large tolerance on the a posteriori error estimate; then, we evaluate the ANOVA expansion of the output and freeze the least important parameter components; finally, considering a restricted model involving just the retained parameter components, we compute a second (fine) RB approximation with a smaller tolerance on the a posteriori error estimate. The fine RB approximation entails lower computational costs than the coarse one, because of the reduction of parameter dimensionality. Our result provides a criterion to avoid the computation of those terms in the ANOVA expansion that are related to the interaction between parameters in the bilinear form, thus making the RB-ANOVA-RB procedure computationally more feasible.

10aPartial differential equations1 aDevaud, Denis1 aManzoni, Andrea1 aRozza, Gianluigi uhttp://hdl.handle.net/1963/738901043nas a2200145 4500008004100000245004200041210003700083260001000120520060700130653006200737100002500799700002100824700001600845856003600861 2013 en d00aThe curvature: a variational approach0 acurvature a variational approach bSISSA3 aThe curvature discussed in this paper is a rather far going generalization of the Riemannian sectional curvature. We define it for a wide class of optimal control problems: a unified framework including geometric structures such as Riemannian, sub-Riemannian, Finsler and sub-Finsler structures; a special attention is paid to the sub-Riemannian (or Carnot-Caratheodory) metric spaces. Our construction of the curvature is direct and naive, and it is similar to the original approach of Riemann. Surprisingly, it works in a very general setting and, in particular, for all sub-Riemannian spaces.10aCrurvature, subriemannian metric, optimal control problem1 aAgrachev, Andrei, A.1 aBarilari, Davide1 aRizzi, Luca uhttp://hdl.handle.net/1963/722601318nas a2200121 4500008004100000245007900041210006900120520083000189100002001019700002201039700002101061856011401082 2013 eng d00aFree Form Deformation Techniques Applied to 3D Shape Optimization Problems0 aFree Form Deformation Techniques Applied to 3D Shape Optimizatio3 aThe purpose of this work is to analyse and study an efficient parametrization technique for a 3D shape optimization problem. After a brief review of the techniques and approaches already available in literature, we recall the Free Form Deformation parametrization, a technique which proved to be efficient and at the same time versatile, allowing to manage complex shapes even with few parameters. We tested and studied the FFD technique by establishing a path, from the geometry definition, to the method implementation, and finally to the simulation and to the optimization of the shape. In particular, we have studied a bulb and a rudder of a race sailing boat as model applications, where we have tested a complete procedure from Computer-Aided-Design to build the geometrical model to discretization and mesh generation.1 aKoshakji, Anwar1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/free-form-deformation-techniques-applied-3d-shape-optimization-problems00733nas a2200133 4500008004100000245005300041210005300094520025800147653004800405100002200453700001600475700002400491856008400515 2013 en d00aMonads for framed sheaves on Hirzebruch surfaces0 aMonads for framed sheaves on Hirzebruch surfaces3 aWe define monads for framed torsion-free sheaves on Hirzebruch surfaces and use them to construct moduli spaces for these objects. These moduli spaces are smooth algebraic varieties, and we show that they are fine by constructing a universal monad.10aMonads, framed sheaves, Hirzebruch surfaces1 aBartocci, Claudio1 aBruzzo, Ugo1 aRava, Claudio, L.S. uhttps://www.math.sissa.it/publication/monads-framed-sheaves-hirzebruch-surfaces00840nas a2200145 4500008004100000245004000041210004000081520035300121653006200474100001600536700002100552700002100573700002200594856007800616 2013 en d00aNonabelian Lie algebroid extensions0 aNonabelian Lie algebroid extensions3 aWe classify nonabelian extensions of Lie algebroids in the holomorphic or algebraic category, and introduce and study a spectral sequence that one can attach to any such extension and generalizes the Hochschild-Serre spectral sequence associated to an ideal in a Lie algebra. We compute the differentials of the spectral sequence up to $d_2$

10aLie algebroids, nonabelian extensions, spectral sequences1 aBruzzo, Ugo1 aMencattini, Igor1 aTortella, Pietro1 aRubtsov, Vladimir uhttps://www.math.sissa.it/publication/nonabelian-lie-algebroid-extensions02183nas a2200145 4500008004100000245015300041210006900194260001300263520163200276653003401908100002101942700001801963700002001981856003602001 2013 en d00aReduced basis approximation and a posteriori error estimation for Stokes flows in parametrized geometries: roles of the inf-sup stability constants0 aReduced basis approximation and a posteriori error estimation fo bSpringer3 aIn this paper we review and we extend the reduced basis approximation and a posteriori error estimation for steady Stokes flows in a ffinely parametrized geometries, focusing on the role played by the Brezzi\\\'s and Babu ska\\\'s stability constants. The crucial ingredients of the methodology are a Galerkin projection onto a low-dimensional space of basis functions properly selected, an a ne parametric dependence enabling to perform competitive Off ine-Online splitting in the computational\\r\\nprocedure and a rigorous a posteriori error estimation on eld variables.\\r\\nThe combination of these three factors yields substantial computational savings which are at the basis of an e fficient model order reduction, ideally suited for real-time simulation and many-query contexts (e.g. optimization, control or parameter identi cation). In particular, in this work we focus on i) the stability of the reduced basis approximation based on the Brezzi\\\'s saddle point theory and the introduction of a supremizer operator on the pressure terms, ii) a rigorous a posteriori error estimation procedure for velocity and pressure elds based on the Babu ska\\\'s inf-sup constant (including residuals calculations), iii) the computation of a lower bound of the stability constant, and iv) di erent options for the reduced basis spaces construction. We present some illustrative results for both\\r\\ninterior and external steady Stokes flows in parametrized geometries representing two parametrized classical Poiseuille and Couette \\r\\nflows, a channel contraction and a simple flow control problem around a curved obstacle.10aparametrized Stokes equations1 aRozza, Gianluigi1 aHuynh, Phuong1 aManzoni, Andrea uhttp://hdl.handle.net/1963/633900531nas a2200121 4500008004100000245011700041210006900158300001100227490000700238100001800245700002100263856012500284 2013 eng d00aReduced Basis Approximation for the Structural-Acoustic Design based on Energy Finite Element Analysis (RB-EFEA)0 aReduced Basis Approximation for the StructuralAcoustic Design ba a98-1150 v481 aDevaud, Denis1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduced-basis-approximation-structural-acoustic-design-based-energy-finite-element01701nas a2200157 4500008004100000245007600041210006900117300001800186490000700204520113900211100002001350700002101370700002001391700002201411856011001433 2013 eng d00aReduced basis method for parametrized elliptic optimal control problems0 aReduced basis method for parametrized elliptic optimal control p aA2316–A23400 v353 aWe propose a suitable model reduction paradigm-the certified reduced basis method (RB)-for the rapid and reliable solution of parametrized optimal control problems governed by partial differential equations. In particular, we develop the methodology for parametrized quadratic optimization problems with elliptic equations as a constraint and infinite-dimensional control variable. First, we recast the optimal control problem in the framework of saddle-point problems in order to take advantage of the already developed RB theory for Stokes-type problems. Then, the usual ingredients of the RB methodology are called into play: a Galerkin projection onto a low-dimensional space of basis functions properly selected by an adaptive procedure; an affine parametric dependence enabling one to perform competitive offline-online splitting in the computational procedure; and an efficient and rigorous a posteriori error estimate on the state, control, and adjoint variables as well as on the cost functional. Finally, we address some numerical tests that confirm our theoretical results and show the efficiency of the proposed technique.1 aNegri, Federico1 aRozza, Gianluigi1 aManzoni, Andrea1 aQuarteroni, Alfio uhttps://www.math.sissa.it/publication/reduced-basis-method-parametrized-elliptic-optimal-control-problems00548nas a2200133 4500008004100000245009200041210006900133260001000202100001800212700002000230700002200250700002100272856012100293 2013 en d00aA Reduced Computational and Geometrical Framework for Inverse Problems in Haemodynamics0 aReduced Computational and Geometrical Framework for Inverse Prob bSISSA1 aLassila, Toni1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduced-computational-and-geometrical-framework-inverse-problems-haemodynamics00568nas a2200133 4500008004100000245010500041210006900146260001000215100001800225700002000243700002200263700002100285856012800306 2013 en d00aA reduced-order strategy for solving inverse Bayesian identification problems in physiological flows0 areducedorder strategy for solving inverse Bayesian identificatio bSISSA1 aLassila, Toni1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduced-order-strategy-solving-inverse-bayesian-identification-problems-physiological00490nas a2200121 4500008004100000245007900041210006900120260001000189100001800199700002000217700002100237856011000258 2013 en d00aReduction Strategies for Shape Dependent Inverse Problems in Haemodynamics0 aReduction Strategies for Shape Dependent Inverse Problems in Hae bSISSA1 aLassila, Toni1 aManzoni, Andrea1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduction-strategies-shape-dependent-inverse-problems-haemodynamics00403nas a2200109 4500008004100000245005300041210005300094260001000147653003300157100001800190856008500208 2013 en d00aSome models of crack growth in brittle materials0 aSome models of crack growth in brittle materials bSISSA10aQuasi-static crack evolution1 aRacca, Simone uhttps://www.math.sissa.it/publication/some-models-crack-growth-brittle-materials01509nas a2200145 4500008004100000245009700041210006900138300001600207490000700223520095300230100001501183700002201198700002101220856012201241 2013 eng d00aStochastic optimal robin boundary control problems of advection-dominated elliptic equations0 aStochastic optimal robin boundary control problems of advectiond a2700–27220 v513 aIn this work we deal with a stochastic optimal Robin boundary control problem constrained by an advection-diffusion-reaction elliptic equation with advection-dominated term. We assume that the uncertainty comes from the advection field and consider a stochastic Robin boundary condition as control function. A stochastic saddle point system is formulated and proved to be equivalent to the first order optimality system for the optimal control problem, based on which we provide the existence and uniqueness of the optimal solution as well as some results on stochastic regularity with respect to the random variables. Stabilized finite element approximations in physical space and collocation approximations in stochastic space are applied to discretize the optimality system. A global error estimate in the product of physical space and stochastic space for the numerical approximation is derived. Illustrative numerical experiments are provided.1 aChen, Peng1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/stochastic-optimal-robin-boundary-control-problems-advection-dominated-elliptic00725nas a2200121 4500008004100000245006600041210006400107260001000171520034800181100002200529700001600551856003600567 2013 en d00aA variational Analysis of the Toda System on Compact Surfaces0 avariational Analysis of the Toda System on Compact Surfaces bWiley3 aIn this paper we consider the Toda system of equations on a compact surface. We will give existence results by using variational methods in a non coercive case. A key tool in our analysis is a new Moser-Trudinger type inequality under suitable conditions on the center of mass and the scale of concentration of the two components u_1, u_2.1 aMalchiodi, Andrea1 aRuiz, David uhttp://hdl.handle.net/1963/655801375nas a2200145 4500008004100000245010300041210006900144300001600213490000700229520080500236100001501041700002201056700002101078856013001099 2013 eng d00aA weighted reduced basis method for elliptic partial differential equations with random input data0 aweighted reduced basis method for elliptic partial differential a3163–31850 v513 aIn this work we propose and analyze a weighted reduced basis method to solve elliptic partial differential equations (PDEs) with random input data. The PDEs are first transformed into a weighted parametric elliptic problem depending on a finite number of parameters. Distinctive importance of the solution at different values of the parameters is taken into account by assigning different weights to the samples in the greedy sampling procedure. A priori convergence analysis is carried out by constructive approximation of the exact solution with respect to the weighted parameters. Numerical examples are provided for the assessment of the advantages of the proposed method over the reduced basis method and the stochastic collocation method in both univariate and multivariate stochastic problems.1 aChen, Peng1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/weighted-reduced-basis-method-elliptic-partial-differential-equations-random-input-data01501nas a2200157 4500008004100000245010600041210006900147260003100216520095600247653002301203100001801226700002001244700002201264700002101286856003601307 2012 en d00aBoundary control and shape optimization for the robust design of bypass anastomoses under uncertainty0 aBoundary control and shape optimization for the robust design of bCambridge University Press3 aWe review the optimal design of an arterial bypass graft following either a (i) boundary optimal control approach, or a (ii) shape optimization formulation. The main focus is quantifying and treating the uncertainty in the residual flow when the hosting artery is not completely occluded,\\r\\nfor which the worst-case in terms of recirculation e ffects is inferred to correspond to a strong ori fice flow through near-complete occlusion. A worst-case optimal control approach is applied to the steady\\r\\nNavier-Stokes equations in 2D to identify an anastomosis angle and a cu ed shape that are robust with respect to a possible range of residual \\r\\nflows. We also consider a reduced order modelling framework\\r\\nbased on reduced basis methods in order to make the robust design problem computationally feasible. The results obtained in 2D are compared with simulations in a 3D geometry but without model\\r\\nreduction or the robust framework.10ashape optimization1 aLassila, Toni1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://hdl.handle.net/1963/633701113nas a2200145 4500008004100000245009600041210006900137260001300206300001200219490000700231520057100238100002000809700002400829856011400853 2012 en d00aOn a class of vector fields with discontinuity of divide-by-zero type and its applications0 aclass of vector fields with discontinuity of dividebyzero type a bSpringer a135-1580 v183 aWe study phase portraits and singular points of vector fields of a special type, that is, vector fields whose components are fractions with a common denominator vanishing on a smooth regular hypersurface in the phase space. We assume also some additional conditions, which are fulfilled, for instance, if the vector field is divergence-free. This problem is motivated by a large number of applications. In this paper, we consider three of them in the framework of differential geometry: singularities of geodesic flows in various singular metrics on surfaces.

1 aGhezzi, Roberta1 aRemizov, Alexey, O. uhttps://www.math.sissa.it/publication/class-vector-fields-discontinuity-divide-zero-type-and-its-applications01414nas a2200145 4500008004100000245008300041210006900124260002800193520092600221100002001147700002201167700002101189700002201210856003601232 2012 en d00aDecompositions of large-scale biological systems based on dynamical properties0 aDecompositions of largescale biological systems based on dynamic bOxford University Press3 aMOTIVATION: Given a large-scale biological network represented as an influence graph, in this article we investigate possible decompositions of the network aimed at highlighting specific dynamical properties.\\r\\nRESULTS: The first decomposition we study consists in finding a maximal directed acyclic subgraph of the network, which dynamically corresponds to searching for a maximal open-loop subsystem of the given system. Another dynamical property investigated is strong monotonicity. We propose two methods to deal with this property, both aimed at decomposing the system into strongly monotone subsystems, but with different structural characteristics: one method tends to produce a single large strongly monotone component, while the other typically generates a set of smaller disjoint strongly monotone subsystems.\\r\\nAVAILABILITY: Original heuristics for the methods investigated are described in the article.1 aSoranzo, Nicola1 aRamezani, Fahimeh1 aIacono, Giovanni1 aAltafini, Claudio uhttp://hdl.handle.net/1963/522602150nas a2200157 4500008004100000245008500041210006900126260003000195520152900225653003001754100003001784700002301814700001901837700002001856856011601876 2012 en d00aDeformed Lorentz symmetry and relative locality in a curved/expanding spacetime0 aDeformed Lorentz symmetry and relative locality in a curvedexpan bAmerican Physical Society3 aThe interest of part of the quantum-gravity community in the possibility of\r\nPlanck-scale-deformed Lorentz symmetry is also fueled by the opportunities for testing the relevant scenarios with analyses, from a signal-propagation perspective, of observations of bursts of particles from cosmological distances. In this respect the fact that so far the implications of deformed Lorentz symmetry have been investigated only for flat (Minkowskian) spacetimes represents a very significant limitation, since for propagation over cosmological distances the curvature/expansion of spacetime is evidently tangible. We here provide a significant step toward filling this gap by exhibiting an explicit example of Planck-scale-deformed relativistic symmetries of a spacetime with constant rate of expansion (deSitterian). Technically we obtain the first ever example of a relativistic theory of worldlines of particles with 3 nontrivial relativistic invariants: a large speed scale (\"speed-of-light scale\"), a large distance scale (inverse of the \"expansion-rate scale\"), and a large momentum scale (\"Planck scale\"). We address some of the challenges that had obstructed success for previous attempts by exploiting the recent understanding of the connection between deformed Lorentz symmetry and relativity of spacetime locality. We also offer a preliminary analysis of the differences between the scenario we here propose and the most studied scenario for broken (rather than deformed) Lorentz symmetry in expanding spacetimes.10aDoubly special relativity1 aAmelino-Camelia, Giovanni1 aMarciano, Antonino1 aMatassa, Marco1 aRosati, Giacomo uhttps://www.math.sissa.it/publication/deformed-lorentz-symmetry-and-relative-locality-curvedexpanding-spacetime01179nas a2200133 4500008004100000245006000041210005500101260001000156520076500166653004100931100001600972700002100988856003601009 2012 en d00aA formula for Popp\'s volume in sub-Riemannian geometry0 aformula for Popps volume in subRiemannian geometry bSISSA3 aFor an equiregular sub-Riemannian manifold M, Popp\'s volume is a smooth\r\nvolume which is canonically associated with the sub-Riemannian structure, and\r\nit is a natural generalization of the Riemannian one. In this paper we prove a\r\ngeneral formula for Popp\'s volume, written in terms of a frame adapted to the\r\nsub-Riemannian distribution. As a first application of this result, we prove an\r\nexplicit formula for the canonical sub-Laplacian, namely the one associated\r\nwith Popp\'s volume. Finally, we discuss sub-Riemannian isometries, and we prove\r\nthat they preserve Popp\'s volume. We also show that, under some hypotheses on\r\nthe action of the isometry group of M, Popp\'s volume is essentially the unique\r\nvolume with such a property.10asubriemannian, volume, Popp, control1 aRizzi, Luca1 aBarilari, Davide uhttp://hdl.handle.net/1963/650100909nas a2200109 4500008004100000245007800041210006900119260001300188520054100201100002100742856003600763 2012 en d00aFrobenius manifold for the dispersionless Kadomtsev-Petviashvili equation0 aFrobenius manifold for the dispersionless KadomtsevPetviashvili bSpringer3 aWe consider a Frobenius structure associated with the dispersionless\\r\\nKadomtsev-Petviashvili equation. This is done, essentially, by applying a\\r\\ncontinuous analogue of the finite dimensional theory in the space of Schwartz\\r\\nfunctions on the line. The potential of the Frobenius manifold is found to be a\\r\\nlogarithmic potential with quadratic external field. Following the construction\\r\\nof the principal hierarchy, we construct a set of infinitely many commuting\\r\\nflows, which extends the classical dKP hierarchy.1 aRaimondo, Andrea uhttp://hdl.handle.net/1963/604001763nas a2200169 4500008004100000245010700041210006900148260001000217520118200227653002601409653002901435653003501464100001701499700001701516700002401533856003601557 2012 en d00aA Fully Coupled Immersed Finite Element Method for Fluid Structure Interaction via the Deal.II Library0 aFully Coupled Immersed Finite Element Method for Fluid Structure bSISSA3 aWe present the implementation of a solution scheme for fluid-structure\\r\\ninteraction problems via the finite element software library deal.II. The\\r\\nsolution scheme is an immersed finite element method in which two independent discretizations are used for the fluid and immersed deformable body. In this type of formulation the support of the equations of motion of the fluid is extended to cover the union of the solid and fluid domains. The equations of motion over the extended solution domain govern the flow of a fluid under the action of a body force field. This body force field informs the fluid of the presence of the immersed solid. The velocity field of the immersed solid is the restriction over the immersed domain of the velocity field in the extended equations of motion. The focus of this paper is to show how the determination of the motion of the immersed domain is carried out in practice. We show that our implementation is general, that is, it is not dependent on a specific choice of the finite element spaces over the immersed solid and the extended fluid domains. We present some preliminary results concerning the accuracy of the proposed method.10aFinite Element Method10aImmersed Boundary Method10aImmersed Finite Element Method1 aHeltai, Luca1 aRoy, Saswati1 aCostanzo, Francesco uhttp://hdl.handle.net/1963/625501643nas a2200157 4500008004100000245012600041210006900167260001300236520109700249653002201346100001801368700002001386700002201406700002101428856003601449 2012 en d00aGeneralized reduced basis methods and n-width estimates for the approximation of the solution manifold of parametric PDEs0 aGeneralized reduced basis methods and nwidth estimates for the a bSpringer3 aThe set of solutions of a parameter-dependent linear partial di fferential equation with smooth coe fficients typically forms a compact manifold in a Hilbert space. In this paper we review the generalized reduced basis method as a fast computational tool for the uniform approximation of the solution manifold. We focus on operators showing an affi ne parametric dependence, expressed as a linear combination of parameter-independent operators through some smooth, parameter-dependent scalar functions. In the case that the parameter-dependent operator has a dominant term in its affi ne expansion, one can prove the existence of exponentially convergent uniform approximation spaces for the entire solution manifold. These spaces can be constructed without any assumptions on the parametric regularity of the manifold \\r\\nonly spatial regularity of the solutions is required. The exponential convergence rate is then inherited by the generalized reduced basis method. We provide a numerical example related to parametrized elliptic\\r\\nequations con rming the predicted convergence rates.10asolution manifold1 aLassila, Toni1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://hdl.handle.net/1963/634000646nas a2200133 4500008004100000245005800041210005500099260001300154520025200167653001900419100001600438700002200454856003600476 2012 en d00aOn localization in holomorphic equivariant cohomology0 alocalization in holomorphic equivariant cohomology bSpringer3 aWe prove a localization formula for a "holomorphic equivariant cohomology" attached to the Atiyah algebroid of an equivariant holomorphic vector bundle. This generalizes Feng-Ma, Carrell-Liebermann, Baum-Bott and K. Liu's localization formulas.10aLie algebroids1 aBruzzo, Ugo1 aRubtsov, Vladimir uhttp://hdl.handle.net/1963/658401651nas a2200133 4500008004100000245008400041210006900125520120500194653002101399100002101420700002001441700002001461856003601481 2012 en d00aReduction strategies for PDE-constrained oprimization problems in Haemodynamics0 aReduction strategies for PDEconstrained oprimization problems in3 aSolving optimal control problems for many different scenarios obtained by varying a set of parameters in the state system is a computationally extensive task. In this paper we present a new reduced framework for the formulation, the analysis and the numerical solution of parametrized PDE-constrained optimization problems. This framework is based on a suitable saddle-point formulation of the optimal control problem and exploits the reduced basis method for the rapid and reliable solution of parametrized PDEs, leading to a relevant computational reduction with respect to traditional discretization techniques such as the finite element method. This allows a very efficient evaluation of state solutions and cost functionals, leading to an effective solution of repeated optimal control problems, even on domains of variable shape, for which a further (geometrical) reduction is pursued, relying on flexible shape parametrization techniques. This setting is applied to the solution of two problems arising from haemodynamics, dealing with both data reconstruction and data assimilation over domains of variable shape,\\r\\nwhich can be recast in a common PDE-constrained optimization formulation.10ainverse problems1 aRozza, Gianluigi1 aManzoni, Andrea1 aNegri, Federico uhttp://hdl.handle.net/1963/633801580nas a2200145 4500008004100000245008700041210006900128260001000197520093400207653011301141100001501254700002201269700002101291856012201312 2012 en d00aSimulation-based uncertainty quantification of human arterial network hemodynamics0 aSimulationbased uncertainty quantification of human arterial net bWiley3 aThis work aims at identifying and quantifying uncertainties from various sources in human cardiovascular\r\nsystem based on stochastic simulation of a one dimensional arterial network. A general analysis of\r\ndifferent uncertainties and probability characterization with log-normal distribution of these uncertainties\r\nis introduced. Deriving from a deterministic one dimensional fluid structure interaction model, we establish\r\nthe stochastic model as a coupled hyperbolic system incorporated with parametric uncertainties to describe\r\nthe blood flow and pressure wave propagation in the arterial network. By applying a stochastic collocation\r\nmethod with sparse grid technique, we study systemically the statistics and sensitivity of the solution with\r\nrespect to many different uncertainties in a relatively complete arterial network with potential physiological\r\nand pathological implications for the first time.10auncertainty quantification, mathematical modelling of the cardiovascular system, fluid-structure interaction1 aChen, Peng1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/simulation-based-uncertainty-quantification-human-arterial-network-hemodynamics01110nas a2200109 4500008004100000245003900041210003600080260001000116520082000126100001800946856003600964 2012 en d00aA Viscosity-driven crack evolution0 aViscositydriven crack evolution bSISSA3 aWe present a model of crack growth in brittle materials which couples dissipative effects on the crack tip and viscous effects. We consider the 2 -dimensional antiplane case with pre-assigned crack path, and firstly prove an existence result for a rate-dependent evolution problem by means of time-discretization. The next goal is to describe the rate-independent evolution as limit of the rate-dependent ones when the dissipative and viscous effects vanish. The rate-independent evolution satisfies a Griffith’s criterion for the crack growth, but, in general, it does not fulfil a global minimality condition; its fracture set may exhibit jump discontinuities with respect to time. Under suitable regularity assumptions, the quasi-static crack growth is described by solving a finite-dimensional problem.

1 aRacca, Simone uhttp://hdl.handle.net/1963/513000505nas a2200133 4500008004100000245010600041210007000147260004400217300001400261490000700275100001600282700001700298856005600315 2011 eng d00aCluster solutions for the Schrödinger-Poisson-Slater problem around a local minimum of the potential0 aCluster solutions for the SchrödingerPoissonSlater problem aroun bReal Sociedad Matemática Españolac01 a253–2710 v271 aRuiz, David1 aVaira, Giusi uhttps://projecteuclid.org:443/euclid.rmi/129682883400729nas a2200121 4500008004300000245009900043210006900142260001300211520030900224100002200533700001600555856003600571 2011 en_Ud 00aNew improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces0 aNew improved MoserTrudinger inequalities and singular Liouville bSpringer3 aWe consider a singular Liouville equation on a compact surface, arising from the study of Chern-Simons vortices in a self dual regime. Using new improved versions of the Moser-Trudinger inequalities (whose main feature is to be scaling invariant) and a variational scheme, we prove new existence results.1 aMalchiodi, Andrea1 aRuiz, David uhttp://hdl.handle.net/1963/409900804nas a2200133 4500008004100000245005600041210005400097260001300151520040700164100002300571700002300594700001700617856003600634 2011 en d00aSBV regularity for Hamilton-Jacobi equations in R^n0 aSBV regularity for HamiltonJacobi equations in Rn bSpringer3 aIn this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$ \partial_t u + H(D_{x} u)=0 \qquad \textrm{in}\quad \Omega\subset \mathbb{R}\times \mathbb{R}^{n} . $$ In particular, under the assumption that the Hamiltonian $H\in C^2(\mathbb{R}^n)$ is uniformly convex, we prove that $D_{x}u$ and $\partial_t u$ belong to the class $SBV_{loc}(\Omega)$.

1 aBianchini, Stefano1 aDe Lellis, Camillo1 aRobyr, Roger uhttp://hdl.handle.net/1963/491100560nas a2200109 4500008004300000245005000043210004900093520023400142100001600376700002200392856003600414 2010 en_Ud 00aCohomology of Skew-holomorphic lie algebroids0 aCohomology of Skewholomorphic lie algebroids3 aWe introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.1 aBruzzo, Ugo1 aRubtsov, Vladimir uhttp://hdl.handle.net/1963/385301347nas a2200133 4500008004300000245006300043210006300106260001300169520093400182100001701116700002301133700002101156856003601177 2010 en_Ud 00aExistence of planar curves minimizing length and curvature0 aExistence of planar curves minimizing length and curvature bSpringer3 aIn this paper we consider the problem of reconstructing a curve that is partially hidden or corrupted by minimizing the functional $\\\\int \\\\sqrt{1+K_\\\\gamma^2} ds$, depending both on length and curvature $K$. We fix starting and ending points as well as initial and final directions.\\nFor this functional we discuss the problem of existence of minimizers on various functional spaces. We find non-existence of minimizers in cases in which initial and final directions are considered with orientation. In this case, minimizing sequences of trajectories can converge to curves with angles.\\nWe instead prove existence of minimizers for the \\\"time-reparameterized\\\" functional $$\\\\int \\\\| \\\\dot\\\\gamma(t) \\\\|\\\\sqrt{1+K_\\\\ga^2} dt$$ for all boundary conditions if initial and final directions are considered regardless to orientation. In this case, minimizers can present cusps (at most two) but not angles.1 aBoscain, Ugo1 aCharlot, Grégoire1 aRossi, Francesco uhttp://hdl.handle.net/1963/410701051nas a2200169 4500008004300000245007900043210006900122260003000191520049800221100001800719700002600737700002300763700001800786700002200804700001900826856003600845 2010 en_Ud 00aHomogeneous binary trees as ground states of quantum critical Hamiltonians0 aHomogeneous binary trees as ground states of quantum critical Ha bAmerican Physical Society3 aMany-body states whose wave-function admits a representation in terms of a uniform binary-tree tensor decomposition are shown to obey to power-law two-body correlations functions. Any such state can be associated with the ground state of a translational invariant Hamiltonian which, depending on the dimension of the systems sites, involve at most couplings between third-neighboring sites. A detailed analysis of their spectra shows that they admit an exponentially large ground space.

1 aSilvi, Pietro1 aGiovannetti, Vittorio1 aMontangero, Simone1 aRizzi, Matteo1 aCirac, J. Ignacio1 aFazio, Rosario uhttp://hdl.handle.net/1963/390901188nas a2200157 4500008004300000245010800043210006900151260001900220520065100239100001800890700002300908700001800931700002600949700001900975856003600994 2010 en_Ud 00aHomogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems0 aHomogeneous multiscale entanglement renormalization ansatz tenso bIOP Publishing3 aIn this paper, we review the properties of homogeneous multiscale entanglement renormalization ansatz (MERA) to describe quantum critical systems.We discuss in more detail our results for one-dimensional (1D) systems (the Ising and Heisenberg models) and present new data for the 2D Ising model. Together with the results for the critical exponents, we provide a detailed description of the numerical algorithm and a discussion of new optimization\\nstrategies. The relation between the critical properties of the system and the tensor structure of the MERA is expressed using the formalism of quantum channels, which we review and extend.

1 aRizzi, Matteo1 aMontangero, Simone1 aSilvi, Pietro1 aGiovannetti, Vittorio1 aFazio, Rosario uhttp://hdl.handle.net/1963/406701299nas a2200109 4500008004300000245006000043210005600103520095600159100001701115700002101132856003601153 2010 en_Ud 00aProjective Reeds-Shepp car on $S^2$ with quadratic cost0 aProjective ReedsShepp car on S2 with quadratic cost3 aFix two points $x,\\\\bar{x}\\\\in S^2$ and two directions (without orientation) $\\\\eta,\\\\bar\\\\eta$ of the velocities in these points. In this paper we are interested to the problem of minimizing the cost $$ J[\\\\gamma]=\\\\int_0^T g_{\\\\gamma(t)}(\\\\dot\\\\gamma(t),\\\\dot\\\\gamma(t))+\\nK^2_{\\\\gamma(t)}g_{\\\\gamma(t)}(\\\\dot\\\\gamma(t),\\\\dot\\\\gamma(t)) ~dt$$ along all smooth curves starting from $x$ with direction $\\\\eta$ and ending in $\\\\bar{x}$ with direction $\\\\bar\\\\eta$. Here $g$ is the standard Riemannian metric on $S^2$ and $K_\\\\gamma$ is the corresponding geodesic curvature.\\nThe interest of this problem comes from mechanics and geometry of vision. It can be formulated as a sub-Riemannian problem on the lens space L(4,1).\\nWe compute the global solution for this problem: an interesting feature is that some optimal geodesics present cusps. The cut locus is a stratification with non trivial topology.1 aBoscain, Ugo1 aRossi, Francesco uhttp://hdl.handle.net/1963/266800741nas a2200133 4500008004300000245009200043210006900135260001900204520028800223100001800511700002100529700002100550856003600571 2010 en_Ud 00aThe reductions of the dispersionless 2D Toda hierarchy and their Hamiltonian structures0 areductions of the dispersionless 2D Toda hierarchy and their Ham bIOP Publishing3 aWe study finite-dimensional reductions of the dispersionless 2D Toda hierarchy showing that the consistency conditions for such reductions are given by a system of radial Loewner equations. We then construct their Hamiltonian structures, following an approach proposed by Ferapontov.1 aCarlet, Guido1 aLorenzoni, Paolo1 aRaimondo, Andrea uhttp://hdl.handle.net/1963/384602219nas a2200157 4500008004300000245014000043210006900183260001900252520163800271100002601909700002101935700002801956700002201984700001902006856003602025 2009 en_Ud 00aCharacterization of the time course of changes of the evoked electrical activity in a model of a chemically-induced neuronal plasticity0 aCharacterization of the time course of changes of the evoked ele bBioMed Central3 aBACKGROUND: Neuronal plasticity is initiated by transient elevations of neuronal networks activity leading to changes of synaptic properties and providing the basis for memory and learning 1. An increase of electrical activity can be caused by electrical stimulation 2 or by pharmacological manipulations: elevation of extracellular K+ 3, blockage of inhibitory pathways 4 or by an increase of second messengers intracellular concentrations 5. Neuronal plasticity is mediated by several biochemical pathways leading to the modulation of synaptic strength, density of ionic channels and morphological changes of neuronal arborisation 6. On a time scale of a few minutes, neuronal plasticity is mediated by local protein trafficking 7 while, in order to sustain modifications beyond 2-3 h, changes of gene expression are required 8. FINDINGS: In the present manuscript we analysed the time course of changes of the evoked electrical activity during neuronal plasticity and we correlated it with a transcriptional analysis of the underlying changes of gene expression. Our investigation shows that treatment for 30 min. with the GABAA receptor antagonist gabazine (GabT) causes a potentiation of the evoked electrical activity occurring 2-4 hours after GabT and the concomitant up-regulation of 342 genes. Inhibition of the ERK1/2 pathway reduced but did not abolish the potentiation of the evoked response caused by GabT. In fact not all the genes analysed were blocked by ERK1/2 inhibitors. CONCLUSION: These results are in agreement with the notion that neuronal plasticity is mediated by several distinct pathways working in unison.1 aBroccard, Frederic D.1 aPegoraro, Silvia1 aRuaro, Maria Elisabetta1 aAltafini, Claudio1 aTorre, Vincent uhttp://hdl.handle.net/1963/370600760nas a2200145 4500008004300000020002200043245006300065210006300128520031500191100001600506700001700522700001700539700002200556856003600578 2009 en_Ud a978-981-270-377-400aEquivariant cohomology and localization for Lie algebroids0 aEquivariant cohomology and localization for Lie algebroids3 aLet M be a manifold carrying the action of a Lie group G, and A a Lie algebroid on M equipped with a compatible infinitesimal G-action. Out of these data we construct an equivariant Lie algebroid cohomology and prove for compact G a related localization formula. As an application we prove a Bott-type formula.1 aBruzzo, Ugo1 aCirio, Lucio1 aRossi, Paolo1 aRubtsov, Vladimir uhttp://hdl.handle.net/1963/172400873nas a2200133 4500008004300000245004600043210004600089260001300135520049300148100002000641700001800661700002400679856003600703 2009 en_Ud 00aGauged Laplacians on quantum Hopf bundles0 aGauged Laplacians on quantum Hopf bundles bSpringer3 aWe study gauged Laplacian operators on line bundles on a quantum 2-dimensional sphere. Symmetry under the (co)-action of a quantum group allows for their complete diagonalization. These operators describe `excitations moving on the quantum sphere\\\' in the field of a magnetic monopole. The energies are not invariant under the exchange monopole/antimonopole, that is under inverting the direction of the magnetic field. There are potential applications to models of quantum Hall effect.1 aLandi, Giovanni1 aReina, Cesare1 aZampini, Alessandro uhttp://hdl.handle.net/1963/354000361nas a2200097 4500008004300000245007700043210006900120100001600189700002200205856003600227 2009 en_Ud 00aHolomorphic equivariant cohomology of Atiyah algebroids and localization0 aHolomorphic equivariant cohomology of Atiyah algebroids and loca1 aBruzzo, Ugo1 aRubtsov, Vladimir uhttp://hdl.handle.net/1963/377401520nas a2200133 4500008004300000245008600043210006900129520106500198100002501263700001701288700002401305700002101329856003601350 2009 en_Ud 00aThe intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups0 aintrinsic hypoelliptic Laplacian and its heat kernel on unimodul3 aWe present an invariant definition of the hypoelliptic Laplacian on sub-Riemannian structures with constant growth vector, using the Popp\\\'s volume form introduced by Montgomery. This definition generalizes the one of the Laplace-Beltrami operator in Riemannian geometry. In the case of left-invariant problems on unimodular Lie groups we prove that it coincides with the usual sum of squares.\\nWe then extend a method (first used by Hulanicki on the Heisenberg group) to compute explicitly the kernel of the hypoelliptic heat equation on any unimodular Lie group of type I. The main tool is the noncommutative Fourier transform. We then study some relevant cases: SU(2), SO(3), SL(2) (with the metrics inherited by the Killing form), and the group SE(2) of rototranslations of the plane.\\nOur study is motivated by some recent results about the cut and conjugate loci on these sub-Riemannian manifolds. The perspective is to understand how singularities of the sub-Riemannian distance reflect on the kernel of the corresponding hypoelliptic heat equation.1 aAgrachev, Andrei, A.1 aBoscain, Ugo1 aGauthier, Jean-Paul1 aRossi, Francesco uhttp://hdl.handle.net/1963/266901559nas a2200157 4500008004300000245008100043210006900124520105300193100001801246700001801264700002501282700002001307700001901327700001901346856003601365 2008 en_Ud 00aFulde-Ferrell-Larkin-Ovchinnikov pairing in one-dimensional optical lattices0 aFuldeFerrellLarkinOvchinnikov pairing in onedimensional optical 3 aSpin-polarized attractive Fermi gases in one-dimensional (1D) optical lattices are expected to be remarkably good candidates for the observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We model these systems with an attractive Hubbard model with population imbalance. By means of the density-matrix renormalization-group method we compute the pairing correlations as well as the static spin and charge structure factors in the whole range from weak to strong coupling. We demonstrate that pairing correlations exhibit quasi-long range order and oscillations at the wave number expected from FFLO theory. However, we also show by numerically computing the mixed spin-charge static structure factor that charge and spin degrees of freedom appear to be coupled already for small imbalance. We discuss the consequences of this coupling for the observation of the FFLO phase, as well as for the stabilization of the quasi-long range order into long-range order by coupling many identical 1D systems, as in quasi-1D optical lattices.

1 aRizzi, Matteo1 aPolini, Marco1 aCazalilla, Miguel A.1 aBakhtiari, M.R.1 aTosi, Mario P.1 aFazio, Rosario uhttp://hdl.handle.net/1963/269400870nas a2200109 4500008004300000245007800043210006900121520049600190100001700686700002100703856003600724 2008 en_Ud 00aInvariant Carnot-Caratheodory metrics on S3, SO(3), SL(2) and Lens Spaces0 aInvariant CarnotCaratheodory metrics on S3 SO3 SL2 and Lens Spac3 aIn this paper we study the invariant Carnot-Caratheodory metrics on SU(2) \\\' S3,\\nSO(3) and SL(2) induced by their Cartan decomposition. Beside computing explicitly geodesics and conjugate loci, we compute the cut loci (globally) and we give the expression of the Carnot-Caratheodory distance as the inverse of an elementary function. We then prove that the metric\\ngiven on SU(2) projects on the so called Lens Spaces L(p; q). Also for Lens Spaces, we compute\\nthe cut loci (globally).1 aBoscain, Ugo1 aRossi, Francesco uhttp://hdl.handle.net/1963/214400342nas a2200097 4500008004300000245006300043210006200106100002400168700001600192856003600208 2008 en_Ud 00aMultiple bound states for the Schroedinger-Poisson problem0 aMultiple bound states for the SchroedingerPoisson problem1 aAmbrosetti, Antonio1 aRuiz, David uhttp://hdl.handle.net/1963/267900746nas a2200145 4500008004300000245004200043210004200085260002800127520032600155100002000481700001900501700001800520700002600538856003600564 2008 en_Ud 00aNoncommutative families of instantons0 aNoncommutative families of instantons bOxford University Press3 aWe construct $\\\\theta$-deformations of the classical groups SL(2,H) and Sp(2). Coacting on the basic instanton on a noncommutative four-sphere $S^4_\\\\theta$, we construct a noncommutative family of instantons of charge 1. The family is parametrized by the quantum quotient of $SL_\\\\theta(2,H)$ by $Sp_\\\\theta(2)$.1 aLandi, Giovanni1 aPagani, Chiara1 aReina, Cesare1 avan Suijlekom, Walter uhttp://hdl.handle.net/1963/341700611nas a2200121 4500008004300000245008600043210006900129520019400198100002400392700002100416700001600437856003600453 2008 en_Ud 00aSolitons of linearly coupled systems of semilinear non-autonomous equations on Rn0 aSolitons of linearly coupled systems of semilinear nonautonomous3 aUsing concentration compactness type arguments, we prove some results about the existence of positive ground and bound state of linearly coupled systems of nonlinear Schrödinger equations.1 aAmbrosetti, Antonio1 aCerami, Giovanna1 aRuiz, David uhttp://hdl.handle.net/1963/217501450nas a2200169 4500008004300000245007300043210006900116520092200185100001801107700001801125700001801143700001901161700001901180700002601199700001901225856003601244 2007 en_Ud 00aLuther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas0 aLutherEmery Phase and AtomicDensity Waves in a Trapped Fermion G3 aThe Luther-Emery liquid is a state of matter that is predicted to occur in one-dimensional systems of interacting fermions and is characterized by a gapless charge spectrum and a gapped spin spectrum. In this Letter we discuss a realization of the Luther-Emery phase in a trapped cold-atom gas. We study by means of the density-matrix renormalization-group technique a two-component atomic Fermi gas with attractive interactions subject to parabolic trapping inside an optical lattice. We demonstrate how this system exhibits compound phases characterized by the coexistence of spin pairing and atomic-density waves. A smooth crossover occurs with increasing magnitude of the atom-atom attraction to a state in which tightly bound spin-singlet dimers occupy the center of the trap. The existence of atomic-density waves could be detected in the elastic contribution to the light-scattering diffraction pattern.

1 aXianlong, Gao1 aRizzi, Matteo1 aPolini, Marco1 aFazio, Rosario1 aTosi, Mario P.1 aCampo, Vivaldo L. Jr.1 aCapelle, Klaus uhttp://hdl.handle.net/1963/205600408nas a2200109 4500008004300000245008800043210006900131100002400200700002200224700001600246856003600262 2007 en_Ud 00aMulti-bump solitons to linearly coupled systems of nonlinear Schrödinger equations0 aMultibump solitons to linearly coupled systems of nonlinear Schr1 aAmbrosetti, Antonio1 aColorado, Eduardo1 aRuiz, David uhttp://hdl.handle.net/1963/183501073nas a2200121 4500008004300000245008500043210006900128260002100197520064400218100002800862700002500890856003600915 2007 en_Ud 00aViscosity solutions of Hamilton-Jacobi equations with discontinuous coefficients0 aViscosity solutions of HamiltonJacobi equations with discontinuo bWorld Scientific3 aWe consider Hamilton--Jacobi equations, where the Hamiltonian depends discontinuously on both the spatial and temporal location. Our main results are the existence and well--posedness of a viscosity solution to the Cauchy problem. We define a viscosity solution by treating the discontinuities in the coefficients analogously to \\\"internal boundaries\\\". By defining an appropriate penalization function, we prove that viscosity solutions are unique. The existence of viscosity solutions is established by showing that a sequence of front tracking approximations is compact in $L^\\\\infty$, and that the limits are viscosity solutions.1 aCoclite, Giuseppe Maria1 aRisebro, Nils Henrik uhttp://hdl.handle.net/1963/290701031nas a2200121 4500008004300000245007500043210006900118520062400187100001800811700002500829700001900854856003600873 2006 en_Ud 00a4e-condensation in a fully frustrated Josephson junction diamond chain0 a4econdensation in a fully frustrated Josephson junction diamond 3 aFully frustrated one-dimensional diamond Josephson chains have been shown [B. Dou\\\\c{c}ot and J. Vidal, Phys. Rev. Lett. {\\\\bf 88}, 227005 (2002)] to posses a remarkable property: The superfluid phase occurs through the condensation of pairs of Cooper pairs. By means of Monte Carlo simulations we analyze quantitatively the Insulator to $4e$-Superfluid transition. We determine the location of the critical point and discuss the behaviour of the phase-phase correlators. For comparison we also present the case of a diamond chain at zero and 1/3 frustration where the standard $2e$-condensation is observed.

1 aRizzi, Matteo1 aCataudella, Vittorio1 aFazio, Rosario uhttp://hdl.handle.net/1963/240000412nas a2200109 4500008004300000245009200043210006900135100002400204700002200228700001600250856003600266 2006 en_Ud 00aBound states of Nonlinear Schroedinger Equations with Potentials Vanishing at Infinity0 aBound states of Nonlinear Schroedinger Equations with Potentials1 aAmbrosetti, Antonio1 aMalchiodi, Andrea1 aRuiz, David uhttp://hdl.handle.net/1963/175601156nas a2200121 4500008004300000245007100043210006800114520075900182100002000941700001900961700001800980856003600998 2006 en_Ud 00aA Hopf bundle over a quantum four-sphere from the symplectic group0 aHopf bundle over a quantum foursphere from the symplectic group3 aWe construct a quantum version of the SU(2) Hopf bundle $S^7 \\\\to S^4$. The quantum sphere $S^7_q$ arises from the symplectic group $Sp_q(2)$ and a quantum 4-sphere $S^4_q$ is obtained via a suitable self-adjoint idempotent $p$ whose entries generate the algebra $A(S^4_q)$ of polynomial functions over it. This projection determines a deformation of an (anti-)instanton bundle over the classical sphere $S^4$. We compute the fundamental $K$-homology class of $S^4_q$ and pair it with the class of $p$ in the $K$-theory getting the value -1 for the topological charge. There is a right coaction of $SU_q(2)$ on $S^7_q$ such that the algebra $A(S^7_q)$ is a non trivial quantum principal bundle over $A(S^4_q)$ with structure quantum group $A(SU_q(2))$.1 aLandi, Giovanni1 aPagani, Chiara1 aReina, Cesare uhttp://hdl.handle.net/1963/217900736nas a2200109 4500008004300000245007600043210006900119520036700188100001600555700001900571856003600590 2006 en_Ud 00aNormal bundles to Laufer rational curves in local Calabi-Yau threefolds0 aNormal bundles to Laufer rational curves in local CalabiYau thre3 aWe prove a conjecture by F. Ferrari. Let X be the total space of a nonlinear deformation of a rank 2 holomorphic vector bundle on a smooth rational curve, such that X has trivial canonical bundle and has sections. Then the normal bundle to such sections is computed in terms of the rank of the Hessian of a suitably defined superpotential at its critical points.1 aBruzzo, Ugo1 aRicco, Antonio uhttp://hdl.handle.net/1963/178500669nas a2200109 4500008004300000245010800043210007000151520026200221100002400483700001600507856003600523 2006 en_Ud 00aRadial solutions concentrating on spheres of nonlinear Schrödinger equations with vanishing potentials0 aRadial solutions concentrating on spheres of nonlinear Schröding3 aWe prove the existence of radial solutions of 1.2) concentrating at a sphere for potentials which might be zero and might decay to zero at\\r\\ninfinity. The proofs use a perturbation technique in a variational setting, through a Lyapunov-Schmidt reduction.1 aAmbrosetti, Antonio1 aRuiz, David uhttp://hdl.handle.net/1963/175500982nas a2200121 4500008004100000245006900041210006900110260001800179520057400197100002800771700002500799856003600824 2005 en d00aConservation laws with time dependent discontinuous coefficients0 aConservation laws with time dependent discontinuous coefficients bSISSA Library3 aWe consider scalar conservation laws where the flux function depends discontinuously on both the spatial and temporal location. Our main results are the existence and well-posedness of an entropy solution to the Cauchy problem. The existence is established by showing that a sequence of front tracking approximations is compact in L1, and that the limits are entropy solutions. Then, using the definition of an entropy solution taken form [11], we show that the solution operator is L1 contractive. These results generalize the corresponding results from [16] and [11].1 aCoclite, Giuseppe Maria1 aRisebro, Nils Henrik uhttp://hdl.handle.net/1963/166600524nas a2200145 4500008004100000245006800041210006800109300001400177490000700191100001800198700001700216700002300233700001900256856010300275 2004 eng d00aCalculation of impulsively started incompressible viscous flows0 aCalculation of impulsively started incompressible viscous flows a877–9020 v461 aMarra, Andrea1 aMola, Andrea1 aQuartapelle, Luigi1 aRiviello, Luca uhttps://www.math.sissa.it/publication/calculation-impulsively-started-incompressible-viscous-flows00751nas a2200121 4500008004100000245004200041210004200083260001900125520040900144100002200553700001800575856003600593 2003 en d00aQuantum spin coverings and statistics0 aQuantum spin coverings and statistics bIOP Publishing3 aSL_q(2) at odd roots of unity q^l =1 is studied as a quantum cover of the complex rotation group SO(3,C), in terms of the associated Hopf algebras of (quantum) polynomial functions. We work out the irreducible corepresentations, the decomposition of their tensor products and a coquasitriangular structure, with the associated braiding (or statistics). As an example, the case l=3 is discussed in detail.1 aDabrowski, Ludwik1 aReina, Cesare uhttp://hdl.handle.net/1963/166700873nas a2200133 4500008004100000245003800041210003600079260001800115520050900133100002100642700001800663700002200681856003600703 2001 en d00aA note on the super Krichever map0 anote on the super Krichever map bSISSA Library3 aWe consider the geometrical aspects of the Krichever map in the context of Jacobian Super KP hierarchy. We use the representation of the hierarchy based\\non the Fa`a di Bruno recursion relations, considered as the cocycle condition for the natural double complex associated with the deformations of super Krichever data. Our approach is based on the construction of the universal super divisor (of degree g), and a local universal family of geometric data which give the map into the Super Grassmannian.1 aFalqui, Gregorio1 aReina, Cesare1 aZampa, Alessandro uhttp://hdl.handle.net/1963/149400587nas a2200169 4500008004100000245010300041210006900144260001800213100001900231700001700250700002400267700001800291700002700309700002300336700002200359856003600381 2000 en d00a3D superconformal theories from Sasakian seven-manifolds: new nontrivial evidences for AdS_4/CFT_30 a3D superconformal theories from Sasakian sevenmanifolds new nont bSISSA Library1 aFabbri, Davide1 aFré, Pietro1 aGualtieri, Leonardo1 aReina, Cesare1 aTomasiello, Alessandro1 aZaffaroni, Alberto1 aZampa, Alessandro uhttp://hdl.handle.net/1963/132700397nas a2200121 4500008004100000245006300041210005500104260001800159100002200177700001800199700002200217856003600239 2000 en d00aA(SLq(2)) at roots of unity is a free module over A(SL(2))0 aASLq2 at roots of unity is a free module over ASL2 bSISSA Library1 aDabrowski, Ludwik1 aReina, Cesare1 aZampa, Alessandro uhttp://hdl.handle.net/1963/150000454nas a2200121 4500008004100000245010700041210006900148260001800217100002100235700001800256700002200274856003600296 2000 en d00aSuper KP equations and Darboux transformations: another perspective on the Jacobian super KP hierarchy0 aSuper KP equations and Darboux transformations another perspecti bSISSA Library1 aFalqui, Gregorio1 aReina, Cesare1 aZampa, Alessandro uhttp://hdl.handle.net/1963/136700685nas a2200133 4500008004300000245004500043210004500088260001300133520030900146100002000455700001800475700002200493856003600515 1999 en_Ud 00aEnhanced gauge symmetries on elliptic K30 aEnhanced gauge symmetries on elliptic K3 bElsevier3 aWe show that the geometry of K3 surfaces with singularities of type A-D-E contains enough information to reconstruct a copy of the Lie algebra associated to the given Dynkin diagram. We apply this construction to explain the enhancement of symmetry in F and IIA theories compactified on singular K3\\\'s.1 aBonora, Loriano1 aReina, Cesare1 aZampa, Alessandro uhttp://hdl.handle.net/1963/336601059nas a2200133 4500008004300000245007500043210007000118260001300188520062700201100002100828700001800849700002200867856003600889 1997 en_Ud 00aKrichever maps, Faà di Bruno polynomials, and cohomology in KP theory0 aKrichever maps Faà di Bruno polynomials and cohomology in KP the bSpringer3 aWe study the geometrical meaning of the Faa\\\' di Bruno polynomials in the context of KP theory. They provide a basis in a subspace W of the universal Grassmannian associated to the KP hierarchy. When W comes from geometrical data via the Krichever map, the Faa\\\' di Bruno recursion relation turns out to be the cocycle condition for (the Welters hypercohomology group describing) the deformations of the dynamical line bundle on the spectral curve together with the meromorphic sections which give rise to the Krichever map. Starting from this, one sees that the whole KP hierarchy has a similar cohomological meaning.1 aFalqui, Gregorio1 aReina, Cesare1 aZampa, Alessandro uhttp://hdl.handle.net/1963/353900343nas a2200109 4500008004100000245004900041210004900090260001800139100001800157700002200175856003600197 1995 en d00aQuantum homogeneous spaces at roots of unity0 aQuantum homogeneous spaces at roots of unity bSISSA Library1 aReina, Cesare1 aZampa, Alessandro uhttp://hdl.handle.net/1963/102200706nas a2200121 4500008004300000245007200043210006200115260001300177520032100190100001900511700001800530856003600548 1993 en_Ud 00aA Borel-Weil-Bott approach to representations of {\rm sl}\sb q(2,C)0 aBorelWeilBott approach to representations of rm sl sb q2C bSpringer3 aWe use a quite concrete and simple realization of $\slq$ involving finite difference operators. We interpret them as derivations (in the non-commutative sense) on a suitable graded algebra, which gives rise to the double of the projective line as the non commutative version of the standard homogeneous space.

1 aFranco, Davide1 aReina, Cesare uhttp://hdl.handle.net/1963/353801654nas a2200121 4500008004300000245006200043210006000105260001300165520127600178100002401454700001801478856003601496 1992 en_Ud 00aTopological "observables" in semiclassical field theories0 aTopological observables in semiclassical field theories bElsevier3 aWe give a geometrical set up for the semiclassical approximation to euclidean field theories having families of minima (instantons) parametrized by suitable moduli spaces ${\mathcal{M}}$. The standard examples are of course Yang-Mills theory and non-linear $\sigma$-models. The relevant space here is a family of measure spaces $\tilde{\mathcal{N}} \rightarrow \mathcal{M}$, with standard fibre a distribution space, given by a suitable extension of the normal bundle to $\mathcal{M}$ in the space of smooth fields. Over $\tilde{\mathcal{N}}$ there is a probability measure $d\mu$ given by the twisted product of the (normalized) volume element on $\mathcal{M}$ and the family of gaussian measures with covariance given by the tree propagator $C_\phi$ in the background of an instanton $\phi \in \mathcal{M}$. The space of "observables", i.e. measurable functions on ($\tilde{\mathcal{N}},\, d\mu$), is studied and it is shown to contain a topological sector, corresponding to the intersection theory on $\mathcal{M}$. The expectation value of these topological "observables" does not depend on the covariance; it is therefore exact at all orders in perturbation theory and can moreover be computed in the topological regime by setting the covariance to zero.

1 aNolasco, Margherita1 aReina, Cesare uhttp://hdl.handle.net/1963/354100391nas a2200109 4500008004100000245007600041210006900117260001800186100002100204700002100225856003500246 1991 en d00aOn systems of ordinary differential equations with measures as controls0 asystems of ordinary differential equations with measures as cont bSISSA Library1 aDal Maso, Gianni1 aRampazzo, Franco uhttp://hdl.handle.net/1963/84000855nas a2200121 4500008004100000245005400041210005300095260003400148520047700182100001800659700002100677856003500698 1990 en d00aN=2 super Riemann surfaces and algebraic geometry0 aN2 super Riemann surfaces and algebraic geometry bAmerican Institute of Physics3 aThe geometric framework for N=2 superconformal field theories are described by studying susy2 curves-a nickname for N=2 super Riemann surfaces. It is proved that \\\"single\\\'\\\' susy2 curves are actually split supermanifolds, and their local model is a Serre self-dual locally free sheaf of rank two over a smooth algebraic curve. Superconformal structures on these sheaves are then examined by setting up deformation theory as a first step in studying moduli problems.1 aReina, Cesare1 aFalqui, Gregorio uhttp://hdl.handle.net/1963/80700355nas a2200109 4500008004100000245005700041210005500098260001800153100001800171700002100189856003500210 1990 en d00aA note on the global structure of supermoduli spaces0 anote on the global structure of supermoduli spaces bSISSA Library1 aReina, Cesare1 aFalqui, Gregorio uhttp://hdl.handle.net/1963/80600375nas a2200109 4500008004100000245006700041210006200108260001800170100002100188700002100209856003500230 1988 en d00aOn differential systems with vector-valued impulsive controls.0 adifferential systems with vectorvalued impulsive controls bSISSA Library1 aBressan, Alberto1 aRampazzo, Franco uhttp://hdl.handle.net/1963/53500306nas a2200109 4500008004100000245003200041210003100073260001800104100002100122700001800143856003500161 1988 en d00aSusy-curves and supermoduli0 aSusycurves and supermoduli bSISSA Library1 aFalqui, Gregorio1 aReina, Cesare uhttp://hdl.handle.net/1963/761