00400nas a2200085 4500008004100000245007900041210006900120100001900189856010600208 2022 eng d00aAn example of a weakly mixing BV vector field which is not strongly mixing0 aexample of a weakly mixing BV vector field which is not strongly1 aZizza, Martina uhttps://www.math.sissa.it/publication/example-weakly-mixing-bv-vector-field-which-not-strongly-mixing02134nas a2200157 4500008004100000245011600041210006900157490000700226520151300233100002001746700002001766700002101786700002101807700002001828856012801848 2021 eng d00aEfficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method0 aEfficient computation of bifurcation diagrams with a deflated ap0 v473 a

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

1 aPintore, Moreno1 aPichi, Federico1 aHess, Martin, W.1 aRozza, Gianluigi1 aCanuto, Claudio uhttps://www.math.sissa.it/publication/efficient-computation-bifurcation-diagrams-deflated-approach-reduced-basis-spectral-001870nas a2200169 4500008004100000245014800041210006900189300001200258490000700270520119600277100001701473700001901490700002101509700002101530700002201551856012701573 2021 eng d00aAn efficient computational framework for naval shape design and optimization problems by means of data-driven reduced order modeling techniques0 aefficient computational framework for naval shape design and opt a211-2300 v143 a

This contribution describes the implementation of a data-driven shape optimization pipeline in a naval architecture application. We adopt reduced order models in order to improve the efficiency of the overall optimization, keeping a modular and equation-free nature to target the industrial demand. We applied the above mentioned pipeline to a realistic cruise ship in order to reduce the total drag. We begin by defining the design space, generated by deforming an initial shape in a parametric way using free form deformation. The evaluation of the performance of each new hull is determined by simulating the flux via finite volume discretization of a two-phase (water and air) fluid. Since the fluid dynamics model can result very expensive—especially dealing with complex industrial geometries—we propose also a dynamic mode decomposition enhancement to reduce the computational cost of a single numerical simulation. The real-time computation is finally achieved by means of proper orthogonal decomposition with Gaussian process regression technique. Thanks to the quick approximation, a genetic optimization algorithm becomes feasible to converge towards the optimal shape.

1 aDemo, Nicola1 aOrtali, Giulio1 aGustin, Gianluca1 aRozza, Gianluigi1 aLavini, Gianpiero uhttps://www.math.sissa.it/publication/efficient-computational-framework-naval-shape-design-and-optimization-problems-means00408nas a2200109 4500008004100000245008400041210006900125260000900194100002600203700002700229856004200256 2021 eng d00aEquilibrium measure for a nonlocal dislocation energy with physical confinement0 aEquilibrium measure for a nonlocal dislocation energy with physi c20211 aMora, Maria, Giovanna1 aScagliotti, Alessandro uhttps://doi.org/10.1515/acv-2020-007600544nas a2200169 4500008004100000022001400041245006000055210006000115260004900175300001600224490000700240100001900247700002300266700001800289700001800307856004900325 2021 eng d a1424-066100aExactness of Linear Response in the Quantum Hall Effect0 aExactness of Linear Response in the Quantum Hall Effect bSpringer Science and Business Media LLCcJan a1113–11320 v221 aBachmann, Sven1 aDe Roeck, Wojciech1 aFraas, Martin1 aLange, Markus uhttp://dx.doi.org/10.1007/s00023-020-00989-z00935nas a2200133 4500008004100000020001400041245010200055210007100157260001500228520047100243100001900714700002100733856004700754 2021 eng d a1424-320200aAn existence result for the fractional Kelvin–Voigt’s model on time-dependent cracked domains0 aexistence result for the fractional Kelvin–Voigt s model on time c2021/06/043 a

We prove an existence result for the fractional Kelvin–Voigt’s model involving Caputo’s derivative on time-dependent cracked domains. We first show the existence of a solution to a regularized version of this problem. Then, we use a compactness argument to derive that the fractional Kelvin–Voigt’s model admits a solution which satisfies an energy-dissipation inequality. Finally, we prove that when the crack is not moving, the solution is unique.

1 aCaponi, Maicol1 aSapio, Francesco uhttps://doi.org/10.1007/s00028-021-00713-200523nas a2200109 4500008004100000245011200041210006900153100001700222700002200239700002100261856013100282 2021 eng d00aAN EXTENDED PHYSICS INFORMED NEURAL NETWORK FOR PRELIMINARY ANALYSIS OF PARAMETRIC OPTIMAL CONTROL PROBLEMS0 aEXTENDED PHYSICS INFORMED NEURAL NETWORK FOR PRELIMINARY ANALYSI1 aDemo, Nicola1 aStrazzullo, Maria1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/extended-physics-informed-neural-network-preliminary-analysis-parametric-optimal-control02133nas a2200145 4500008004100000245011600041210006900157520162200226100002001848700002001868700002101888700002101909700002001930856003701950 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 a

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

1 aPintore, Moreno1 aPichi, Federico1 aHess, Martin, W.1 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 a

In this work, we present an approach for the efficient treatment of parametrized geometries in the context of POD-Galerkin reduced order methods based on Finite Volume full order approximations. On the contrary to what is normally done in the framework of finite element reduced order methods, different geometries are not mapped to a common reference domain: the method relies on basis functions defined on an average deformed configuration and makes use of the Discrete Empirical Interpolation Method (D-EIM) to handle together non-affinity of the parametrization and non-linearities. In the first numerical example, different mesh motion strategies, based on a Laplacian smoothing technique and on a Radial Basis Function approach, are analyzed and compared on a heat transfer problem. Particular attention is devoted to the role of the non-orthogonal correction. In the second numerical example the methodology is tested on a geometrically parametrized incompressible Navier–Stokes problem. In this case, the reduced order model is constructed following the same segregated approach used at the full order level

1 aStabile, Giovanni1 aZancanaro, Matteo1 aRozza, Gianluigi uhttps://arxiv.org/abs/1901.0637301671nas a2200181 4500008004100000020002200041245012000063210006900183260004400252300001400296520095800310100001901268700001701287700002201304700001701326700002101343856012501364 2020 eng d a978-3-030-30705-900aThe Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: from Laminar to Turbulent Flows0 aEffort of Increasing Reynolds Number in ProjectionBased Reduced  aChambSpringer International Publishing a245–2643 a

We present in this double contribution two different reduced order strategies for incompressible parameterized Navier-Stokes equations characterized by varying Reynolds numbers. The first strategy deals with low Reynolds number (laminar flow) and is based on a stabilized finite element method during the offline stage followed by a Galerkin projection on reduced basis spaces generated by a greedy algorithm. The second methodology is based on a full order finite volume discretization. The latter methodology will be used for flows with moderate to high Reynolds number characterized by turbulent patterns. For the treatment of the mentioned turbulent flows at the reduced order level, a new POD-Galerkin approach is proposed. The new approach takes into consideration the contribution of the eddy viscosity also during the online stage and is based on the use of interpolation. The two methodologies are tested on classic benchmark test cases.

1 aHijazi, Saddam1 aAli, Shafqat1 aStabile, Giovanni1 aBallarin, F.1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/effort-increasing-reynolds-number-projection-based-reduced-order-methods-laminar-000964nas a2200205 4500008004100000020001400041245005600055210005500111260001600166300001100182490000800193520032700201653003100528653002200559653004400581100001900625700002200644700002000666856007200686 2020 eng d a0022-247X00aEnergy-dissipation balance of a smooth moving crack0 aEnergydissipation balance of a smooth moving crack c2020/03/15/ a1236560 v4833 a

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

10aEnergy-dissipation balance10aFracture dynamics10aWave equation in time-dependent domains1 aCaponi, Maicol1 aLucardesi, Ilaria1 aTasso, Emanuele uhttps://www.sciencedirect.com/science/article/pii/S0022247X1930924201480nas a2200157 4500008004100000245009400041210006900135490000600204520097900210100001901189700001701208700002201225700001701247700002101264856003701285 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 0 v73 a

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

1 aTezzele, Marco1 aDemo, Nicola1 aStabile, Giovanni1 aMola, Andrea1 aRozza, Gianluigi uhttps://arxiv.org/abs/2001.0523701079nas a2200133 4500008004100000245010500041210006900146260001300215300001000228520061700238100002100855700001900876856005000895 2020 eng d00aExistence of Riemannian metrics with positive biorthogonal curvature on simply connected 5-manifolds0 aExistence of Riemannian metrics with positive biorthogonal curva bSpringer a1–93 a

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

1 aStupovski, Boris1 aTorres, Rafael uhttps://dx.doi.org/10.1007/s00013-020-01511-x01243nas a2200145 4500008004100000020001400041245010900055210007100164260001500235300000700250490000700257520076800264100001901032856004601051 2020 eng d a1420-900400aExistence of solutions to a phase–field model of dynamic fracture with a crack–dependent dissipation0 aExistence of solutions to a phase–field model of dynamic fractur c2020/02/11 a140 v273 a

We propose a phase–field model of dynamic fracture based on the Ambrosio–Tortorelli’s approximation, which takes into account dissipative effects due to the speed of the crack tips. By adapting the time discretization scheme contained in Larsen et al. (Math Models Methods Appl Sci 20:1021–1048, 2010), we show the existence of a dynamic crack evolution satisfying an energy–dissipation balance, according to Griffith’s criterion. Finally, we analyze the dynamic phase–field model of Bourdin et al. (Int J Fract 168:133–143, 2011) and Larsen (in: Hackl (ed) IUTAM symposium on variational concepts with applications to the mechanics of materials, IUTAM Bookseries, vol 21. Springer, Dordrecht, 2010, pp 131–140) with no dissipative terms.

1 aCaponi, Maicol uhttps://doi.org/10.1007/s00030-020-0617-z02563nas a2200169 4500008004100000245009100041210006900132520193100201100001702132700001902149700002102168700002502189700001902214700002102233700002102254856011802275 2019 eng d00aEfficient reduction in shape parameter space dimension for ship propeller blade design0 aEfficient reduction in shape parameter space dimension for ship 3 a

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

1 aMola, Andrea1 aTezzele, Marco1 aGadalla, Mahmoud1 aValdenazzi, Federica1 aGrassi, Davide1 aPadovan, Roberta1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85075395143&partnerID=40&md5=b6aa0fcedc2f88e78c295d0f437824d001140nas a2200205 4500008004100000022001400041245005800055210005500113520049400168653002800662653002300690653002100713653002500734653002500759100001700784700002400801700001900825700001900844856007100863 2019 eng d a0304-414900aAn entropic interpolation proof of the HWI inequality0 aentropic interpolation proof of the HWI inequality3 a

The HWI inequality is an “interpolation”inequality between the Entropy H, the Fisher information I and the Wasserstein distance W. We present a pathwise proof of the HWI inequality which is obtained through a zero noise limit of the Schrödinger problem. Our approach consists in making rigorous the Otto–Villani heuristics in Otto and Villani (2000) taking advantage of the entropic interpolations, which are regular both in space and time, rather than the displacement ones.

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-materials01371nas a2200145 4500008004100000245008000041210007100121260002400192300001100216490000700227520088900234100002901123700002401152856004901176 2018 eng d00aEffective non-linear spinor dynamics in a spin-1 Bose–Einstein condensate0 aEffective nonlinear spinor dynamics in a spin1 Bose–Einstein con bIOP Publishingcsep a4052010 v513 a

We derive from first principles the experimentally observed effective dynamics of a spinor Bose gas initially prepared as a Bose–Einstein condensate and then left free to expand ballistically. In spinor condensates, which represent one of the recent frontiers in the manipulation of ultra-cold atoms, particles interact with a two-body spatial interaction and a spin–spin interaction. The effective dynamics is well-known to be governed by a system of coupled semi-linear Schrödinger equations: we recover this system, in the sense of marginals in the limit of infinitely many particles, with a mean-field re-scaling of the many-body Hamiltonian. When the resulting control of the dynamical persistence of condensation is quantified with the parameters of modern observations, we obtain a bound that remains quite accurate for the whole typical duration of the experiment.

1 aMichelangeli, Alessandro1 aOlgiati, Alessandro uhttps://doi.org/10.1088%2F1751-8121%2Faadbc202869nas 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-18-48100945nas 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 a

In this paper we analyse a one-dimensional debonding model for a thin film peeled from a substrate when friction is taken into account. It is described by the weakly damped wave equation whose domain, the debonded region, grows according to a Griffth's criterion. Firstly we prove that the equation admits a unique solution when the evolution of the debonding front is assigned. Finally we provide an existence and uniqueness result for the coupled problem given by the wave equation together with Griffth's criterion.

1 aNardini, Lorenzo1 aRiva, Filippo uhttp://preprints.sissa.it/xmlui/handle/1963/3531900762nas a2200121 4500008004100000245009200041210006900133520032400202100002100526700002600547700001900573856004800592 2018 en d00aExistence for elastodynamic Griffith fracture with a weak maximal dissipation condition0 aExistence for elastodynamic Griffith fracture with a weak maxima3 aWe consider a model of elastodynamics with fracture evolution, based on energy-dissipation balance and a maximal dissipation condition. We prove an existence result in the case of planar elasticity with a free crack path, where the maximal dissipation condition is satisfied among suitably regular competitor cracks.1 aDal Maso, Gianni1 aLarsen, Cristopher J.1 aToader, Rodica uhttp://preprints.sissa.it/handle/1963/3530800373nas 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.0066101090nas a2200121 4500008004100000245009000041210006900131520064600200100002300846700002400869700002400893856005100917 2017 en d00aOn the effect of interactions beyond nearest neighbours on non-convex lattice systems0 aeffect of interactions beyond nearest neighbours on nonconvex la3 aWe analyse the rigidity of non-convex discrete energies where at least nearest and next-to-nearest neighbour interactions are taken into account. Our purpose is to show that interactions beyond nearest neighbours have the role of penalising changes of orientation and, to some extent, they may replace the positive-determinant constraint that is usually required when only nearest neighbours are accounted for. In a discrete to continuum setting, we prove a compactness result for a family of surface-scaled energies and we give bounds on its possible Gamma-limit in terms of interfacial energies that penalise changes of orientation.1 aAlicandro, Roberto1 aLazzaroni, Giuliano1 aPalombaro, Mariapia uhttp://urania.sissa.it/xmlui/handle/1963/3526801139nas a2200157 4500008004100000020002200041245007400063210006900137260004400206300001400250520058600264100002400850700002900874700002900903856004900932 2017 eng d a978-3-319-58904-600aEffective Non-linear Dynamics of Binary Condensates and Open Problems0 aEffective Nonlinear Dynamics of Binary Condensates and Open Prob aChambSpringer International Publishing a239–2563 a

We report on a recent result concerning the effective dynamics for a mixture of Bose-Einstein condensates, a class of systems much studied in physics and receiving a large amount of attention in the recent literature in mathematical physics; for such models, the effective dynamics is described by a coupled system of non-linear Schödinger equations. After reviewing and commenting our proof in the mean-field regime from a previous paper, we collect the main details needed to obtain the rigorous derivation of the effective dynamics in the Gross-Pitaevskii scaling limit.

1 aOlgiati, Alessandro1 aMichelangeli, Alessandro1 aDell'Antonio, Gianfausto uhttps://doi.org/10.1007/978-3-319-58904-6_1400333nas a2200097 4500008004100000245005500041210005400096100002600150700001800176856004100194 2017 eng d00aElliptic diffeomorphisms of symplectic 4-manifolds0 aElliptic diffeomorphisms of symplectic 4manifolds1 aShevchishin, Vsevolod1 aSmirnov, Gleb uhttps://arxiv.org/pdf/1708.01518.pdf00962nas a2200133 4500008004100000245012600041210006900167260002600236300001400262490000700276520044200283100001800725856008500743 2017 eng d00aEnergy release rate and quasi-static evolution via vanishing viscosity in a fracture model depending on the crack opening0 aEnergy release rate and quasistatic evolution via vanishing visc bEDP Sciencesc05/2017 a791–8260 v233 a

In the setting of planar linearized elasticity, we study a fracture model depending on the crack opening. Assuming that the crack path is known a priori and sufficiently smooth, we prove that the energy release rate is well defined. Then, we consider the problem of quasi-static evolution for our model. Thanks to a vanishing viscosity approach, we show the existence of such an evolution satisfying a weak Griffith’s criterion.

1 aAlmi, Stefano uhttps://www.esaim-cocv.org/component/article?access=doi&doi=10.1051/cocv/201601400471nas a2200097 4500008004100000245009600041210006900137100001800206700002400224856012500248 2016 eng d00aEquivalence of two different notions of tangent bundle on rectifiable metric measure spaces0 aEquivalence of two different notions of tangent bundle on rectif1 aGigli, Nicola1 aPasqualetto, Enrico uhttps://www.math.sissa.it/publication/equivalence-two-different-notions-tangent-bundle-rectifiable-metric-measure-spaces00590nas 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-circulation00458nas a2200121 4500008004100000245009600041210006900137260001300206100002200219700002300241700002100264856005100285 2016 en d00aEulerian, Lagrangian and Broad continuous solutions to a balance law with non-convex flux I0 aEulerian Lagrangian and Broad continuous solutions to a balance  bElsevier1 aAlberti, Giovanni1 aBianchini, Stefano1 aCaravenna, Laura uhttp://urania.sissa.it/xmlui/handle/1963/3520700434nas a2200109 4500008004100000245009700041210006900138100002200207700002300229700002100252856005100273 2016 en d00aEulerian, Lagrangian and Broad continuous solutions to a balance law with non convex flux II0 aEulerian Lagrangian and Broad continuous solutions to a balance 1 aAlberti, Giovanni1 aBianchini, Stefano1 aCaravenna, Laura uhttp://urania.sissa.it/xmlui/handle/1963/3519701475nas 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 a

We provide a contour integral formula for the exact partition function of $\mathcal{N}=2$ supersymmetric $U(N)$ gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the contour integral for $U(2)\; \mathcal{N}=2^\star$ theory on $\mathbb{P}^2$ for all instanton numbers. In the zero mass case, corresponding to the $\mathcal{N}=4$ supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of mock-modular forms. In the decoupling limit of infinite mass we find that the generating function of local and surface observables computes equivariant Donaldson invariants, thus proving in this case a longstanding conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new.

1 aBershtein, Mikhail1 aBonelli, Giulio1 aRonzani, Massimiliano1 aTanzini, Alessandro uhttps://doi.org/10.1007/JHEP07(2016)02301307nas a2200193 4500008004100000022001400041245009500055210006900150300001600219490000800235520066200243653002900905653002400934653002600958653001600984100002001000700002201020856007101042 2016 eng d a0022-123600aExistence and non-existence results for the SU(3) singular Toda system on compact surfaces0 aExistence and nonexistence results for the SU3 singular Toda sys a3750 - 38070 v2703 a

We consider the SU(3) singular Toda system on a compact surface (Σ,g)−Δu1=2ρ1(h1eu1∫Σh1eu1dVg−1)−ρ2(h2eu2∫Σh2eu2dVg−1)−4π∑m=1Mα1m(δpm−1)−Δu2=2ρ2(h2eu2∫Σh2eu2dVg−1)−ρ1(h1eu1∫Σh1eu1dVg−1)−4π∑m=1Mα2m(δpm−1), where hi are smooth positive functions on Σ, ρi∈R+, pm∈Σ and αim>−1. We give both existence and non-existence results under some conditions on the parameters ρi and αim. Existence results are obtained using variational methods, which involve a geometric inequality of new type; non-existence results are obtained using blow-up analysis and localized Pohožaev-type identities."

10aLiouville-type equations10aMin–max solutions10aNon-existence results10aToda system1 aBattaglia, Luca1 aMalchiodi, Andrea uhttp://www.sciencedirect.com/science/article/pii/S002212361500494201120nas a2200229 4500008004100000022001400041245008700055210006900142300001600211490000800227520034000235653002200575653003200597653002100629653002500650653003400675653004400709100002100753700002400774700002100798856007100819 2016 eng d a0022-039600aExistence and uniqueness of dynamic evolutions for a peeling test in dimension one0 aExistence and uniqueness of dynamic evolutions for a peeling tes a4897 - 49230 v2613 a

In this paper we present a one-dimensional model of a dynamic peeling test for a thin film, where the wave equation is coupled with a Griffith criterion for the propagation of the debonding front. Our main results provide existence and uniqueness for the solution to this coupled problem under different assumptions on the data.

10aDynamic debonding10aDynamic energy release rate10aDynamic fracture10aGriffith's criterion10aMaximum dissipation principle10aWave equation in time-dependent domains1 aDal Maso, Gianni1 aLazzaroni, Giuliano1 aNardini, Lorenzo uhttp://www.sciencedirect.com/science/article/pii/S002203961630177201187nas a2200193 4500008004100000022001400041245006700055210006700122300001200189490000800201520057400209653002100783653002900804653002400833653002900857653001600886100002000902856007100922 2015 eng d a0022-247X00aExistence and multiplicity result for the singular Toda system0 aExistence and multiplicity result for the singular Toda system a49 - 850 v4243 a

We consider the Toda system on a compact surface (Σ,g)−Δu1=2ρ1(h1eu1∫Σh1eu1dVg−1)−ρ2(h2eu2∫Σh2eu2dVg−1)−4π∑j=1Jα1j(δpj−1),−Δu2=2ρ2(h2eu2∫Σh2eu2dVg−1)−ρ1(h1eu1∫Σh1eu1dVg−1)−4π∑j=1Jα2j(δpj−1), where hi are smooth positive functions, ρi are positive real parameters, pj are given points on Σ and αij are numbers greater than −1. We give existence and multiplicity results, using variational and Morse-theoretical methods. It is the first existence result when some of the αij's are allowed to be negative."

10aExistence result10aLiouville-type equations10aMultiplicity result10aPDEs on compact surfaces10aToda system1 aBattaglia, Luca uhttp://www.sciencedirect.com/science/article/pii/S0022247X1401019101267nas a2200121 4500008004100000245009800041210006900139520082000208100002101028700002601049700001901075856005101094 2015 en d00aExistence for constrained dynamic Griffith fracture with a weak maximal dissipation condition0 aExistence for constrained dynamic Griffith fracture with a weak 3 aThere are very few existence results for fracture evolution, outside of globally minimizing quasi-static evolutions. Dynamic evolutions are particularly problematic, due to the difficulty of showing energy balance, as well as of showing that solutions obey a maximal dissipation condition, or some similar condition that prevents stationary cracks from always being solutions. Here we introduce a new weak maximal dissipation condition and show that it is compatible with cracks constrained to grow smoothly on a smooth curve. In particular, we show existence of dynamic fracture evolutions satisfying this maximal dissipation condition, subject to the above smoothness constraints, and exhibit explicit examples to show that this maximal dissipation principle can indeed rule out stationary cracks as solutions.1 aDal Maso, Gianni1 aLarsen, Cristopher J.1 aToader, Rodica uhttp://urania.sissa.it/xmlui/handle/1963/3504501084nas a2200121 4500008004100000245013700041210006900178260002300247520059900270100002300869700001900892856005100911 2015 en d00aExistence of positive solutions in the superlinear case via coincidence degree: the Neumann and the periodic boundary value problems0 aExistence of positive solutions in the superlinear case via coin bKhayyam Publishing3 a

We prove the existence of positive periodic solutions for the second order nonlinear equation u'' + a(x) g(u) = 0, where g(u) has superlinear growth at zero and at infinity. The weight function a(x) is allowed to change its sign. Necessary and sufficient conditions for the existence of nontrivial solutions are obtained. The proof is based on Mawhin's coincidence degree and applies also to Neumann boundary conditions. Applications are given to the search of positive solutions for a nonlinear PDE in annular domains and for a periodic problem associated to a non-Hamiltonian equation.

1 aFeltrin, Guglielmo1 aZanolin, Fabio uhttp://projecteuclid.org/euclid.ade/143506451801364nas a2200181 4500008004100000022001400041245009900055210006900154300000800223490000900231520072700240653002700967653002300994653004101017653002501058100002301083856007601106 2015 eng d a0133-018900aExistence of positive solutions of a superlinear boundary value problem with indefinite weight0 aExistence of positive solutions of a superlinear boundary value  a4360 v20153 a

We deal with the existence of positive solutions for a two-point boundary value problem associated with the nonlinear second order equation $u''+a(x)g(u)=0$. The weight $a(x)$ is allowed to change sign. We assume that the function $g\colon\mathopen[0,+∞\mathclose[\to\mathbb{R}$ is continuous, $g(0)=0$ and satisfies suitable growth conditions, including the superlinear case $g(s)=s^p$, with $p>1$. In particular we suppose that $g(s)/s$ is large near infinity, but we do not require that $g(s)$ is non-negative in a neighborhood of zero. Using a topological approach based on the Leray-Schauder degree we obtain a result of existence of at least a positive solution that improves previous existence theorems.

10aboundary value problem10aindefi nite weight10aPositive solution; existence result.10asuperlinear equation1 aFeltrin, Guglielmo uhttp://aimsciences.org//article/id/b3c1c765-e8f5-416e-8130-05cc4847802600594nas a2200145 4500008004100000245009400041210006900135260001300204300001200217100001900229700001700248700003200265700002600297856012500323 2015 eng d00aExperience on vectorizing lattice Boltzmann kernels for multi-and many-core architectures0 aExperience on vectorizing lattice Boltzmann kernels for multiand bSpringer a53–621 aCalore, Enrico1 aDemo, Nicola1 aSchifano, Sebastiano, Fabio1 aTripiccione, Raffaele uhttps://www.math.sissa.it/publication/experience-vectorizing-lattice-boltzmann-kernels-multi-and-many-core-architectures02252nas a2200145 4500008004100000245009600041210006900137260001000206520175300216100002701969700001701996700002202013700002002035856005102055 2015 en d00aExplicit formulas for relaxed disarrangement densities arising from structured deformations0 aExplicit formulas for relaxed disarrangement densities arising f bSISSA3 aStructured deformations provide a multiscale geometry that captures the contributions at the macrolevel of both smooth geometrical changes and non-smooth geometrical changes (disarrangements) at submacroscopic levels. For each (first-order) structured deformation (g,G) of a continuous body, the tensor field G is known to be a measure of deformations without disarrangements, and M:=∇g−G is known to be a measure of deformations due to disarrangements. The tensor fields G and M together deliver not only standard notions of plastic deformation, but M and its curl deliver the Burgers vector field associated with closed curves in the body and the dislocation density field used in describing geometrical changes in bodies with defects. Recently, Owen and Paroni [13] evaluated explicitly some relaxed energy densities arising in Choksi and Fonseca’s energetics of structured deformations [4] and thereby showed: (1) (trM)+ , the positive part of trM, is a volume density of disarrangements due to submacroscopic separations, (2) (trM)−, the negative part of trM, is a volume density of disarrangements due to submacroscopic switches and interpenetrations, and (3) trM, the absolute value of trM, is a volume density of all three of these non-tangential disarrangements: separations, switches, and interpenetrations. The main contribution of the present research is to show that a different approach to the energetics of structured deformations, that due to Ba\'{i}a, Matias, and Santos [1], confirms the roles of (trM)+, (trM)−, and trM established by Owen and Paroni. In doing so, we give an alternative, shorter proof of Owen and Paroni’s results, and we establish additional explicit formulas for other measures of disarrangements.1 aBarroso, Ana, Cristina1 aMatias, Jose1 aMorandotti, Marco1 aOwen, David, R. uhttp://urania.sissa.it/xmlui/handle/1963/3449200912nas a2200145 4500008004100000245010700041210006900148260001000217520041300227100002000640700002400660700001800684700001600702856004800718 2015 en d00aExtended affine Weyl groups of BCD type, Frobenius manifolds and their Landau-Ginzburg superpotentials0 aExtended affine Weyl groups of BCD type Frobenius manifolds and  bSISSA3 aFor the root systems of type Bl, Cl and Dl, we generalize the result of [7] by showing the existence of Frobenius manifold structures on the orbit spaces of the extended affine Weyl groups that correspond to any vertex of the Dynkin diagram instead of a particular choice made in [7]. It also depends on certain additional data. We also construct LG superpotentials for these Frobenius manifold structures.1 aDubrovin, Boris1 aStrachan, Ian, A.B.1 aZhang, Youjin1 aZuo, Dafeng uhttp://preprints.sissa.it/handle/1963/3531600316nas a2200121 4500008004100000245001400041210001400055260001300069100002000082700002100102700002000123856005100143 2014 en d00aEditorial0 aEditorial bSpringer1 aCiliberto, Ciro1 aDal Maso, Gianni1 aVetro, Pasquale uhttp://urania.sissa.it/xmlui/handle/1963/3471201955nas a2200145 4500008004100000245009100041210006900132260006400201520139800265100002701663700002201690700002101712700002501733856005101758 2014 en d00aAn effective model for nematic liquid crystal composites with ferromagnetic inclusions0 aeffective model for nematic liquid crystal composites with ferro bSociety for Industrial and Applied Mathematics Publications3 aMolecules of a nematic liquid crystal respond to an applied magnetic field by reorienting themselves in the direction of the field. Since the dielectric anisotropy of a nematic is small, it takes relatively large fields to elicit a significant liquid crystal response. The interaction may be enhanced in colloidal suspensions of ferromagnetic particles in a liquid crystalline matrix- ferronematics-as proposed by Brochard and de Gennes in 1970. The ability of these particles to align with the field and simultaneously cause reorientation of the nematic molecules greatly increases the magnetic response of the mixture. Essentially the particles provide an easy axis of magnetization that interacts with the liquid crystal via surface anchoring. We derive an expression for the effective energy of ferronematic in the dilute limit, that is, when the number of particles tends to infinity while their total volume fraction tends to zero. The total energy of the mixture is assumed to be the sum of the bulk elastic liquid crystal contribution, the anchoring energy of the liquid crystal on the surfaces of the particles, and the magnetic energy of interaction between the particles and the applied magnetic field. The homogenized limiting ferronematic energy is obtained rigorously using a variational approach. It generalizes formal expressions previously reported in the physical literature.1 aCalderer, Maria, Carme1 aDeSimone, Antonio1 aGolovaty, Dmitry1 aPanchenko, Alexander uhttp://urania.sissa.it/xmlui/handle/1963/3494001997nas a2200109 4500008004100000245014300041210006900184520134000253653014901593100002001742856012501762 2014 en d00aAn efficient computational framework for reduced basis approximation and a posteriori error estimation of parametrized Navier-Stokes flows0 aefficient computational framework for reduced basis approximatio3 aWe present the current Reduced Basis framework for the efficient numerical approximation of parametrized steady Navier-Stokes equations. We have extended the existing setting developed in the last decade (see e.g. [Deparis, Veroy & Patera, Quarteroni & Rozza] to more general affine and nonaffine parametrizations (such as volume-based techniques), to a simultaneous velocity-pressure error estimates and to a fully decoupled Offline/Online procedure in order to speedup the solution of the reduced-order problem. This is particularly suitable for real-time and many-query contexts, which are both part of our final goal. Furthermore, we present an efficient numerical implementation for treating nonlinear advection terms in a convenient way. A residual-based a posteriori error estimation with respect to a truth, full-order Finite Element approximation is provided for joint pressure/velocity errors, according to the Brezzi-Rappaz-Raviart stability theory. To do this, we take advantage of an extension of the Successive Constraint Method for the estimation of stability factors and of a suitable fixed-point algorithm for the approximation of Sobolev embedding constants. Finally, we present some numerical test cases, in order to show both the approximation properties and the computational efficiency of the derived framework.10aReduced Basis Method, parametrized Navier-Stokes equations, steady incompressible fluids, a posteriori error estimation, approximation stability1 aManzoni, Andrea uhttps://www.math.sissa.it/publication/efficient-computational-framework-reduced-basis-approximation-and-posteriori-error01443nas 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-modelling00833nas a2200121 4500008004100000245010200041210006900143260003900212520036100251100002300612700002500635856005100660 2014 en d00aExistence and uniqueness of the gradient flow of the Entropy in the space of probability measures0 aExistence and uniqueness of the gradient flow of the Entropy in  bEUT Edizioni Universita di Trieste3 aAfter a brief introduction on gradient flows in metric spaces and on geodesically convex functionals, we give an account of the proof (following the outline of [3, 7]) of the existence and uniqueness of the gradient flow of the Entropy in the space of Borel probability measures over a compact geodesic metric space with Ricci curvature bounded from below.1 aBianchini, Stefano1 aDabrowski, Alexander uhttp://urania.sissa.it/xmlui/handle/1963/3469301126nas a2200169 4500008004100000022001400041245009000055210006900145260000800214300001400222490000800236520060400244100001800848700002000866700002400886856004600910 2014 eng d a1432-180700aExistence of immersed spheres minimizing curvature functionals in compact 3-manifolds0 aExistence of immersed spheres minimizing curvature functionals i cJun a379–4250 v3593 a

We study curvature functionals for immersed 2-spheres in a compact, three-dimensional Riemannian manifold $M$. Under the assumption that the sectional curvature $K^M$ is strictly positive, we prove the existence of a smooth immersion $f:{\mathbb{S}}^2 \rightarrow M$ minimizing the $L^2$ integral of the second fundamental form. Assuming instead that $K^M \leq 2 $ and that there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})>6$, we obtain a smooth minimizer $f:{\mathbb{S}}^2 \rightarrow M$ for the functional $\int \frac{1}{4}|H|^2+1$, where $H$ is the mean curvature.

1 aKuwert, Ernst1 aMondino, Andrea1 aSchygulla, Johannes uhttps://doi.org/10.1007/s00208-013-1005-303135nas a2200205 4500008004100000022001400041245009400055210006900149300001400218490000700232520242200239653004902661653002302710653002902733653002802762653002402790100002002814700002402834856007102858 2014 eng d a0294-144900aExistence of immersed spheres minimizing curvature functionals in non-compact 3-manifolds0 aExistence of immersed spheres minimizing curvature functionals i a707 - 7240 v313 a

We study curvature functionals for immersed 2-spheres in non-compact, three-dimensional Riemannian manifold $(M,h)$ without boundary. First, under the assumption that $(M,h)$ is the euclidean 3-space endowed with a semi-perturbed metric with perturbation small in $C^1$ norm and of compact support, we prove that if there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})>0$ then there exists a smooth embedding $ f:\mathbb{S}^2 \hookrightarrow M$ minimizing the Willmore functional $\frac{1}{4}\int |H|^2$, where $H$ is the mean curvature. Second, assuming that $(M,h)$ is of bounded geometry (i.e. bounded sectional curvature and strictly positive injectivity radius) and asymptotically euclidean or hyperbolic we prove that if there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})>6$ then there exists a smooth immersion $f:\mathbb{S}^2\hookrightarrow M$ minimizing the functional $\int (\frac{1}{2}|A|^2+1)$, where $A$ is the second fundamental form. Finally, adding the bound $K^M \leq 2$ to the last assumptions, we obtain a smooth minimizer $f:\mathbb{S}^2 \hookrightarrow M$ for the functional $\int \frac{1}{4}(|H|^2+1)$. The assumptions of the last two theorems are satisfied in a large class of 3-manifolds arising as spacelike timeslices solutions of the Einstein vacuum equation in case of null or negative cosmological constant.

10aDirect methods in the calculus of variations10aGeneral Relativity10aGeometric measure theory10asecond fundamental form10aWillmore functional1 aMondino, Andrea1 aSchygulla, Johannes uhttp://www.sciencedirect.com/science/article/pii/S029414491300085101095nas a2200145 4500008004100000022001400041245011100055210006900166260000800235300001400243490000700257520061900264100002000883856004600903 2014 eng d a1432-083500aExistence of integral m-varifolds minimizing $\int |A|^p $ and $\int |H|^p$ , p>m, in Riemannian manifolds0 aExistence of integral mvarifolds minimizing int Ap and int Hp pm cJan a431–4700 v493 a

We prove existence of integral rectifiable $m$-dimensional varifolds minimizing functionals of the type $\int |H|^p$ and $\int |A|^p$ in a given Riemannian $n$-dimensional manifold $(N,g)$, $2 \leq m<n$ and $p>m$ under suitable assumptions on $N$ (in the end of the paper we give many examples of such ambient manifolds). To this aim we introduce the following new tools: some monotonicity formulas for varifolds in ${\mathbb{R }^S}$ involving $\int  |H|^p$to  avoid degeneracy of the minimizer, and a sort of isoperimetric inequality to bound the mass in terms of the mentioned functionals.

1 aMondino, Andrea uhttps://doi.org/10.1007/s00526-012-0588-y01988nas a2200133 4500008004100000245010500041210006900146260003000215520151100245100002101756700002201777700001901799856003601818 2013 en d00aEarly phase of plasticity-related gene regulation and SRF dependent transcription in the hippocampus0 aEarly phase of plasticityrelated gene regulation and SRF depende bPublic Library of Science3 aHippocampal organotypic cultures are a highly reliable in vitro model for studying neuroplasticity: in this paper, we analyze the early phase of the transcriptional response induced by a 20 µM gabazine treatment (GabT), a GABA-Ar antagonist, by using Affymetrix oligonucleotide microarray, RT-PCR based time-course and chromatin-immuno-precipitation. The transcriptome profiling revealed that the pool of genes up-regulated by GabT, besides being strongly related to the regulation of growth and synaptic transmission, is also endowed with neuro-protective and pro-survival properties. By using RT-PCR, we quantified a time-course of the transient expression for 33 of the highest up-regulated genes, with an average sampling rate of 10 minutes and covering the time interval [10:90] minutes. The cluster analysis of the time-course disclosed the existence of three different dynamical patterns, one of which proved, in a statistical analysis based on results from previous works, to be significantly related with SRF-dependent regulation (p-value<0.05). The chromatin immunoprecipitation (chip) assay confirmed the rich presence of working CArG boxes in the genes belonging to the latter dynamical pattern and therefore validated the statistical analysis. Furthermore, an in silico analysis of the promoters revealed the presence of additional conserved CArG boxes upstream of the genes Nr4a1 and Rgs2. The chip assay confirmed a significant SRF signal in the Nr4a1 CArG box but not in the Rgs2 CArG box.1 aIacono, Giovanni1 aAltafini, Claudio1 aTorre, Vincent uhttp://hdl.handle.net/1963/728701025nas a2200109 4500008004100000245008100041210006900122260001700191520065100208100002000859856003600879 2013 en d00aEpitaxially strained elastic films: the case of anisotropic surface energies0 aEpitaxially strained elastic films the case of anisotropic surfa bEDP Sciences3 a

In the context of a variational model for the epitaxial growth of strained elastic films, we study the effects of the presence of anisotropic surface energies in the determination of equilibrium configurations. We show that the threshold effect that describes the stability of flat morphologies in the isotropic case remains valid for weak anisotropies, but is no longer present in the case of highly anisotropic surface energies, where we show that the flat configuration is always a local minimizer of the total energy. The main tool used to obtain these results is a minimality criterion based on the positivity of the second variation.

1 aBonacini, Marco uhttp://hdl.handle.net/1963/426801024nas a2200121 4500008004100000245008800041210006900129260001000198520062200208100001900830700001700849856003600866 2013 en d00aEquilibrium measures for a class of potentials with discrete rotational symmetries0 aEquilibrium measures for a class of potentials with discrete rot bSISSA3 aIn this note the logarithmic energy problem with external potential $|z|^{2n}+tz^d+\bar{t}\bar{z}^d$ is considered in the complex plane, where $n$ and $d$ are positive integers satisfying $d\leq 2n$. Exploiting the discrete rotational invariance of the potential, a simple symmetry reduction procedure is used to calculate the equilibrium measure for all admissible values of $n,d$ and $t$. It is shown that, for fixed $n$ and $d$, there is a critical value $|t|=t_{cr}$ such that the support of the equilibrium measure is simply connected for $|t|t_{cr}$.1 aBalogh, Ferenc1 aMerzi, Dario uhttp://hdl.handle.net/1963/723001347nas a2200289 4500008004100000022001300041245008600054210006900140300001200209490000700221520039800228653002600626653002200652653002800674653002500702653001700727653002500744653002200769653002100791653002800812653001900840653001900859100002400878700001700902700002100919856011700940 2013 eng d a1120633000aExistence and stability of quasi-periodic solutions for derivative wave equations0 aExistence and stability of quasiperiodic solutions for derivativ a199-2140 v243 aIn this note we present the new KAM result in [3] which proves the existence of Cantor families of small amplitude, analytic, quasi-periodic solutions of derivative wave equations, with zero Lyapunov exponents and whose linearized equation is reducible to constant coefficients. In turn, this result is derived by an abstract KAM theorem for infinite dimensional reversible dynamical systems*.10aConstant coefficients10aDynamical systems10aExistence and stability10aInfinite dimensional10aKAM for PDEs10aLinearized equations10aLyapunov exponent10aLyapunov methods10aQuasi-periodic solution10aSmall divisors10aWave equations1 aBerti, Massimiliano1 aBiasco, Luca1 aProcesi, Michela uhttps://www.math.sissa.it/publication/existence-and-stability-quasi-periodic-solutions-derivative-wave-equations00989nas a2200133 4500008004100000245010200041210006900143260002600212520042000238100002100658700002500679700002200704856012900726 2013 en d00aExistence and symmetry results for a Schrodinger type problem involving the fractional Laplacian0 aExistence and symmetry results for a Schrodinger type problem in bUniversity of Catania3 a

This paper deals with the following class of nonlocal Schr\"odinger equations $$ \displaystyle (-\Delta)^s u + u = |u|^{p-1}u \ \ \text{in} \ \mathbb{R}^N, \quad \text{for} \ s\in (0,1). $$ We prove existence and symmetry results for the solutions $u$ in the fractional Sobolev space $H^s(\mathbb{R}^N)$. Our results are in clear accordance with those for the classical local counterpart, that is when $s=1$.

1 aDipierro, Serena1 aPalatucci, Giampiero1 aValdinoci, Enrico uhttps://www.math.sissa.it/publication/existence-and-symmetry-results-schrodinger-type-problem-involving-fractional-laplacian00556nas a2200121 4500008004100000245010500041210006900146260005100215300001600266490000800282100002000290856012400310 2013 eng d00aAn existence result for the mean-field equation on compact surfaces in a doubly supercritical regime0 aexistence result for the meanfield equation on compact surfaces  bRoyal Society of Edinburgh Scotland Foundation a1021–10450 v1431 aJevnikar, Aleks uhttps://www.math.sissa.it/publication/existence-result-mean-field-equation-compact-surfaces-doubly-supercritical-regime00809nas a2200157 4500008004100000245003700041210003700078260002300115520037700138653001900515100002000534700002000554700002200574700001900596856003600615 2013 en d00aExpanded degenerations and pairs0 aExpanded degenerations and pairs bTaylor and Francis3 aSince Jun Li's original definition, several other definitions of expanded pairs and expanded degenerations have appeared in the literature. We explain how these definitions are related and introduce several new variants and perspectives. Among these are the twisted expansions used by Abramovich and Fantechi as a basis for orbifold techniques in degeneation formulas.10aExpanded pairs1 aAbramovich, Dan1 aCadman, Charles1 aFantechi, Barbara1 aWise, Jonathan uhttp://hdl.handle.net/1963/738301741nas a2200133 4500008004100000245007700041210006900118260001000187520130700197100002401504700002101528700002201549856003601571 2012 en d00aExploring the low-energy landscape of large-scale signed social networks0 aExploring the lowenergy landscape of largescale signed social ne bSISSA3 aAnalogously to a spin glass, a large-scale signed social network is characterized by the presence of disorder, expressed in this context (and in the social network literature) by the concept of structural balance. If, as we have recently shown, the signed social networks currently available have a limited amount of true disorder (or frustration), it is also interesting to investigate how this frustration is organized, by exploring the landscape of near-optimal structural balance. What we obtain in this paper is that while one of the networks analyzed shows a unique valley of minima, and a funneled landscape that gradually and smoothly worsens as we move away from the optimum, another network shows instead several distinct valleys of optimal or near-optimal structural balance, separated by energy barriers determined by internally balanced subcommunities of users, a phenomenon similar to the replica-symmetry breaking of spin glasses. Multiple, essentially isoenergetic, arrangements of these communities are possible. Passing from one valley to another requires one to destroy the internal arrangement of these balanced subcommunities and then to reform it again. It is essentially this process of breaking the internal balance of the subcommunities which gives rise to the energy barriers.1 aFacchetti, Giuseppe1 aIacono, Giovanni1 aAltafini, Claudio uhttp://hdl.handle.net/1963/650401116nas a2200145 4500008004100000245013000041210007000171260001300241300001600254490000800270520060700278100002000885700001900905856004600924 2011 eng d00aEmbedding theorems and existence results for nonlinear Schrödinger–Poisson systems with unbounded and vanishing potentials0 aEmbedding theorems and existence results for nonlinear Schröding bElsevier a1056–10850 v2513 a

Motivated by existence results for positive solutions of non-autonomous nonlinear Schrödinger–Poisson systems with potentials possibly unbounded or vanishing at infinity, we prove embedding theorems for weighted Sobolev spaces. We both consider a general framework and spaces of radially symmetric functions when assuming radial symmetry of the potentials.

1 aBonheure, Denis1 aMercuri, Carlo uhttps://doi.org/10.1016/j.jde.2011.04.01000728nas a2200121 4500008004300000245007600043210006900119260001300188520032600201100002400527700001900551856003600570 2011 en_Ud 00aEnergy release rate and stress intensity factor in antiplane elasticity0 aEnergy release rate and stress intensity factor in antiplane ela bElsevier3 aIn the setting of antiplane linearized elasticity, we show the existence of the stress intensity factor and its relation with the energy release rate when the crack path is a C1,1 curve. Finally, we show that the energy release rate is continuous with respect to the Hausdorff convergence in a class of admissible cracks.1 aLazzaroni, Giuliano1 aToader, Rodica uhttp://hdl.handle.net/1963/378000628nas a2200109 4500008004100000245003900041210003800080260004800118520029500166100002100461856003600482 2011 en d00aEnnio De Giorgi and Γ-convergence0 aEnnio De Giorgi and Γconvergence bAmerican Institute of Mathematical Sciences3 aΓ-convergence was introduced by Ennio De Giorgi in a series of papers published between 1975 and 1983. In the same years he developed many applications of this tool to a great variety of asymptotic problems in the calculus of variations and in the theory of partial differential equations.1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/530800369nas a2200109 4500008004300000245006000043210005700103260002100160100002300181700001900204856003600223 2011 en_Ud 00aAn Estimate on the Flow Generated by Monotone Operators0 aEstimate on the Flow Generated by Monotone Operators bTaylor & Francis1 aBianchini, Stefano1 aGloyer, Matteo uhttp://hdl.handle.net/1963/364601548nas a2200157 4500008004300000245008600043210006900129260005100198300001400249490000800263520101800271100002101289700002201310700002201332856003601354 2011 en_Ud 00aAn Existence and Uniqueness Result for the Motion of Self-Propelled Microswimmers0 aExistence and Uniqueness Result for the Motion of SelfPropelled  bSociety for Industrial and Applied Mathematics a1345-13680 v 433 a

We present an analytical framework to study the motion of micro-swimmers in a viscous fluid. Our main result is that, under very mild regularity assumptions, the change of shape determines uniquely the motion of the swimmer. We assume that the Reynolds number is very small, so that the velocity field of the surrounding, infinite fluid is governed by the Stokes system and all inertial effects can be neglected. Moreover, we enforce the self propulsion constraint (no external forces and torques). Therefore, Newton\\\'s equations of motion reduce to the vanishing of the viscous drag force and torque acting on the body. By exploiting an integral representation of viscous force and torque, the equations of motion can be reduced to a system of six ordinary differential equations. Variational techniques are used to prove the boundedness and measurability of its coefficients, so that classical results on ordinary differential equations can be invoked to prove existence and uniqueness of the solution.

1 aDal Maso, Gianni1 aDeSimone, Antonio1 aMorandotti, Marco uhttp://hdl.handle.net/1963/389401004nas a2200133 4500008004100000245007400041210006900115260003400184520055100218653001800769100002100787700002600808856003600834 2011 en d00aExistence for wave equations on domains with arbitrary growing cracks0 aExistence for wave equations on domains with arbitrary growing c bEuropean Mathematical Society3 aIn this paper we formulate and study scalar wave equations on domains with arbitrary growing cracks. This includes a zero Neumann condition on the crack sets, and the only assumptions on these sets are that they have bounded surface measure and are growing in the sense of set inclusion. In particular, they may be dense, so the weak formulations must fall outside of the usual weak formulations using Sobolev spaces. We study both damped and undamped equations, showing existence and, for the damped equation, uniqueness and energy conservation.10aWave equation1 aDal Maso, Gianni1 aLarsen, Cristopher J. uhttp://hdl.handle.net/1963/428400702nas a2200121 4500008004300000245011200043210007000155260001900225520025100244100002900495700002000524856003600544 2010 en_Ud 00aEffective Schroedinger dynamics on $ ε$-thin Dirichlet waveguides via Quantum Graphs I: star-shaped graphs0 aEffective Schroedinger dynamics on εthin Dirichlet waveguides vi bIOP Publishing3 aWe describe the boundary conditions at the vertex that one must choose to obtain a dynamical system that best describes the low-energy part of the evolution of a quantum system confined to a very small neighbourhood of a star-shaped metric graph.1 aDell'Antonio, Gianfausto1 aCosta, Emanuele uhttp://hdl.handle.net/1963/410601221nas a2200109 4500008004300000245005800043210005800101520086900159100002301028700002401051856003601075 2010 en_Ud 00aEstimates on path functionals over Wasserstein Spaces0 aEstimates on path functionals over Wasserstein Spaces3 aIn this paper we consider the class a functionals (introduced in [Brancolini, Buttazzo, and Santambrogio, J. Eur. Math. Soc. (JEMS), 8 (2006), pp. 415-434] $\\\\mathcal{G}_{r,p}$ defined on Lipschitz curves $\\\\gamma$ valued in the $p$-Wasserstein space. The problem considered is the following: given a measure $\\\\mu$, give conditions in order to assure the existence of a curve $\\\\gamma$ such that $\\\\gamma(0)=\\\\mu$, $\\\\gamma(1)=\\\\delta_{x_0}$, and $\\\\mathcal{G}_{r,p}(\\\\gamma)<+\\\\infty$. To this end, new estimates on $\\\\mathcal{G}_{r,p}(\\\\mu)$ are given, and a notion of dimension of a measure (called path dimension) is introduced: the path dimension specifies the values of the parameters $(r,p)$ for which the answer to the previous reachability problem is positive. Finally, we compare the path dimension with other known dimensions.1 aBianchini, Stefano1 aBrancolini, Alessio uhttp://hdl.handle.net/1963/358300371nas a2200097 4500008004300000245008300043210006900126100002300195700001900218856003600237 2010 en_Ud 00aOn the Euler-Lagrange equation for a variational problem : the general case II0 aEulerLagrange equation for a variational problem the general cas1 aBianchini, Stefano1 aGloyer, Matteo uhttp://hdl.handle.net/1963/255100773nas a2200145 4500008004300000245007900043210006900122260001300191520030200204100001900506700002000525700002100545700002500566856003600591 2010 en_Ud 00aExact reconstruction of damaged color images using a total variation model0 aExact reconstruction of damaged color images using a total varia bElsevier3 aIn this paper the reconstruction of damaged piecewice constant color images is studied using a RGB total variation based model for colorization/inpainting. In particular, it is shown that when color is known in a uniformly distributed region, then reconstruction is possible with maximal fidelity.1 aFonseca, Irene1 aLeoni, Giovanni1 aMaggi, Francesco1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/403901347nas 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/1963/410700760nas 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/1963/172400980nas a2200121 4500008004300000245005900043210005800102260002800160520059200188100002000780700002200800856003600822 2009 en_Ud 00aERNEST: a toolbox for chemical reaction network theory0 aERNEST a toolbox for chemical reaction network theory bOxford University Press3 aSummary: ERNEST Reaction Network Equilibria Study Toolbox is a MATLAB package which, by checking various different criteria on the structure of a chemical reaction network, can exclude the multistationarity of the corresponding reaction system. The results obtained are independent of the rate constants of the reactions, and can be used for model discrimination.\\nAvailability and Implementation: The software, implemented in MATLAB, is available under the GNU GPL free software license from http://people.sissa.it/~altafini/papers/SoAl09/. It requires the MATLAB Optimization Toolbox.1 aSoranzo, Nicola1 aAltafini, Claudio uhttp://hdl.handle.net/1963/382600361nas a2200097 4500008004300000245007300043210006900116100001800185700002400203856003600227 2009 en_Ud 00aExact results for topological strings on resolved Yp,q singularities0 aExact results for topological strings on resolved Ypq singularit1 aBrini, Andrea1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/263100512nas a2200097 4500008004300000245009600043210006900139520015000208100002000358856003600378 2009 en_Ud 00aExistence of extremals for the Maz\\\'ya and for the Caffarelli-Kohn-Nirenberg inequalities0 aExistence of extremals for the Mazya and for the CaffarelliKohnN3 aThis paper deals with some Sobolev-type inequalities with weights that were proved by Maz\\\'ya in 1980 and by Caffarelli-Kohn-Nirenberg in 1984.1 aMusina, Roberta uhttp://hdl.handle.net/1963/273900318nas a2200085 4500008004300000245006800043210006400111100002100175856003600196 2009 en_Ud 00aAn existence result for the Monge problem in R^n with norm cost0 aexistence result for the Monge problem in Rn with norm cost1 aCaravenna, Laura uhttp://hdl.handle.net/1963/364700624nas a2200109 4500008004300000245007200043210006400115520025500179100002300434700002100457856003600478 2009 en_Ud 00aOn the extremality, uniqueness and optimality of transference plans0 aextremality uniqueness and optimality of transference plans3 aWe consider the following standard problems appearing in optimal mass transportation theory: when a transference plan is extremal; when a transference plan is the unique transference plan concentrated on a set A,; when a transference plan is optimal.1 aBianchini, Stefano1 aCaravenna, Laura uhttp://hdl.handle.net/1963/369200657nas a2200097 4500008004300000245007900043210006900122520031000191100002200501856003600523 2008 en_Ud 00aEntire solutions of autonomous equations on Rn with nontrivial asymptotics0 aEntire solutions of autonomous equations on Rn with nontrivial a3 aWe prove existence of a new type of solutions for the semilinear equation $- \\\\D u + u = u^p$ on $\\\\R^n$, with $1 < p < \\\\frac{n+2}{n-2}$. These solutions are positive, bounded, decay exponentially to zero away from three half-lines with a common origin, and at infinity are asymptotically periodic.1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/264000301nas a2200097 4500008004300000245004300043210003900086260002100125100002100146856003600167 2008 en_Ud 00aAn entropy based Glimm-type functional0 aentropy based Glimmtype functional bWorld Scientific1 aCaravenna, Laura uhttp://hdl.handle.net/1963/405100767nas a2200097 4500008004300000245005300043210004900096520045900145100002900604856003600633 2008 en_Ud 00aEquivalent definitions of asymptotic 100% B.E.C.0 aEquivalent definitions of asymptotic 100 BEC3 aIn the mathematical analysis Bose-Einstein condensates, in particular in the study of the quantum dynamics, some kind of factorisation property has been recently proposed as a convenient technical assumption of condensation. After having surveyed both the standard definition of complete Bose-Einstein condensation in the limit of infinitely many particles and some forms of asymptotic factorisation, we prove that these characterisations are equivalent.1 aMichelangeli, Alessandro uhttp://hdl.handle.net/1963/254600962nas a2200121 4500008004300000245008100043210006900124260000900193520056300202100001700765700002200782856003600804 2008 en_Ud 00aEulerian calculus for the displacement convexity in the Wasserstein distance0 aEulerian calculus for the displacement convexity in the Wasserst bSIAM3 aIn this paper we give a new proof of the (strong) displacement convexity of a class of integral functionals defined on a compact Riemannian manifold satisfying a lower Ricci curvature bound. Our approach does not rely on existence and regularity results for optimal transport maps on Riemannian manifolds, but it is based on the Eulerian point of view recently introduced by Otto and Westdickenberg [SIAM J. Math. Anal., 37 (2005), pp. 1227-1255] and on the metric characterization of the gradient flows generated by the functionals in the Wasserstein space.1 aDaneri, Sara1 aSavarè, Giuseppe uhttp://hdl.handle.net/1963/341300797nas a2200109 4500008004300000245006300043210006000106520044300166100002000609700002200629856003600651 2008 en_Ud 00aExistence of conformal metrics with constant $Q$-curvature0 aExistence of conformal metrics with constant Qcurvature3 aGiven a compact four dimensional manifold, we prove existence of conformal metrics with constant $Q$-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure. Since the corresponding Euler functional is in general unbounded from above and from below, we employ topological methods and minimax schemes, jointly with a compactness result by the second author.1 aDjadli, Zindine1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/230800503nas a2200121 4500008004100000022001400041245008200055210006900137300002300206100001900229700001700248856011600265 2007 eng d a1073-792800aEffective inverse spectral problem for rational Lax matrices and applications0 aEffective inverse spectral problem for rational Lax matrices and aArt. ID rnm103, 391 aBertola, Marco1 aGekhtman, M. uhttps://www.math.sissa.it/publication/effective-inverse-spectral-problem-rational-lax-matrices-and-applications01323nas a2200133 4500008004300000245010700043210006900150520085200219100001901071700001801090700002001108700002501128856003601153 2007 en_Ud 00aEquilibrium configurations of epitaxially strained crystalline films: existence and regularity results0 aEquilibrium configurations of epitaxially strained crystalline f3 aStrained epitaxial films grown on a relatively thick substrate are considered in the context of plane linear elasticity. The total free energy of the system is assumed to be the sum of the energy of the free surface of the film and the strain energy. Because of the lattice mismatch between film and substrate, flat configurations are in general energetically unfavorable and a corrugated or islanded morphology is the preferred growth mode of the strained film. After specifying the functional setup in which the existence problem can be properly framed, a study of the qualitative properties of the solutions is undertaken. New regularity results for volume-constrained local minimizers of the total free energy are established, leading, as a byproduct, to a rigorous proof of the zero-contact-angle condition between islands and wetting layers.1 aFonseca, Irene1 aFusco, Nicola1 aLeoni, Giovanni1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/235000302nas a2200085 4500008004300000245006100043210005300104100002300157856003600180 2007 en_Ud 00aOn the Euler-Lagrange equation for a variational problem0 aEulerLagrange equation for a variational problem1 aBianchini, Stefano uhttp://hdl.handle.net/1963/179200974nas a2200109 4500008004300000245009300043210006900136520057600205100002500781700002200806856003600828 2006 en_Ud 00aAn estimation of the controllability time for single-input systems on compact Lie Groups0 aestimation of the controllability time for singleinput systems o3 aGeometric control theory and Riemannian techniques are used to describe the reachable set at time t of left invariant single-input control systems on semi-simple compact Lie groups and to estimate the minimal time needed to reach any point from identity. This method provides an effective way to give an upper and a lower bound for the minimal time needed to transfer a controlled quantum system with a drift from a given initial position to a given final position. The bounds include diameters of the flag manifolds; the latter are also explicitly computed in the paper.1 aAgrachev, Andrei, A.1 aChambrion, Thomas uhttp://hdl.handle.net/1963/213502436nas a2200169 4500008004100000245007600041210006900117260007200186520184400258100002002102700002202122700001802144700002502162700001902187700002402206856003602230 2006 en d00aExperimental and modeling studies of desensitization of P2X3 receptors.0 aExperimental and modeling studies of desensitization of P2X3 rec bthe American Society for Pharmacology and Experimental Therapeutics3 aThe function of ATP-activated P2X3 receptors involved in pain sensation is modulated by desensitization, a phenomenon poorly understood. The present study used patch-clamp recording from cultured rat or mouse sensory neurons and kinetic modeling to clarify the properties of P2X3 receptor desensitization. Two types of desensitization were observed, a fast process (t1/2 = 50 ms; 10 microM ATP) following the inward current evoked by micromolar agonist concentrations, and a slow process (t1/2 = 35 s; 10 nM ATP) that inhibited receptors without activating them. We termed the latter high-affinity desensitization (HAD). Recovery from fast desensitization or HAD was slow and agonist-dependent. When comparing several agonists, there was analogous ranking order for agonist potency, rate of desensitization and HAD effectiveness, with 2-methylthioadenosine triphosphate the strongest and beta,gamma-methylene-ATP the weakest. HAD was less developed with recombinant (ATP IC50 = 390 nM) than native P2X3 receptors (IC50 = 2.3 nM). HAD could also be induced by nanomolar ATP when receptors seemed to be nondesensitized, indicating that resting receptors could express high-affinity binding sites. Desensitization properties were well accounted for by a cyclic model in which receptors could be desensitized from either open or closed states. Recovery was assumed to be a multistate process with distinct kinetics dependent on the agonist-dependent dissociation rate from desensitized receptors. Thus, the combination of agonist-specific mechanisms such as desensitization onset, HAD, and resensitization could shape responsiveness of sensory neurons to P2X3 receptor agonists. By using subthreshold concentrations of an HAD-potent agonist, it might be possible to generate sustained inhibition of P2X3 receptors for controlling chronic pain.1 aSokolova, Elena1 aSkorinkin, Andrei1 aMoiseev, Igor1 aAgrachev, Andrei, A.1 aNistri, Andrea1 aGiniatullin, Rashid uhttp://hdl.handle.net/1963/497400687nas a2200121 4500008004300000245006200043210005900105520031100164100002000475700001800495700001600513856003600529 2006 en_Ud 00aExtended affine Weyl groups and Frobenius manifolds -- II0 aExtended affine Weyl groups and Frobenius manifolds II3 aFor the root system of type $B_l$ and $C_l$, we generalize the result of \\\\cite{DZ1998} by showing the existence of a Frobenius manifold structure on the orbit space of the extended affine Weyl group that corresponds to any vertex of the Dynkin diagram instead of a particular choice of \\\\cite{DZ1998}.1 aDubrovin, Boris1 aYoujin, Zhang1 aDafeng, Zuo uhttp://hdl.handle.net/1963/178700427nas a2200133 4500008004100000022001400041245007500055210006900130300001600199490000700215100002100222700001400243856003600257 2005 eng d a0271-209100aEnhanced residual-free bubble method for convection-diffusion problems0 aEnhanced residualfree bubble method for convectiondiffusion prob a1307–13130 v471 aCangiani, Andrea1 aSüli, E. uhttps://doi.org/10.1002/fld.85900343nas a2200133 4500008004100000022001400041245002400055210002400079300001400103490000800117100002100125700001700146856004600163 2005 eng d a0029-599X00aEnhanced RFB method0 aEnhanced RFB method a273–3080 v1011 aCangiani, Andrea1 aSüli, Endre uhttps://doi.org/10.1007/s00211-005-0620-700739nas a2200109 4500008004100000245008000041210007100121260001300192520036600205100002200571856003600593 2005 en d00aExplicit Wei–Norman formulae for matrix Lie groups via Putzer\\\'s method0 aExplicit Wei–Norman formulae for matrix Lie groups via Putzers m bElsevier3 aThe Wei–Norman formula locally relates the Magnus solution of a system of linear time-varying ODEs with the solution expressed in terms of products of exponentials by means of a set of nonlinear differential equations in the parameters of the two types of solutions. A closed form expression of such formula is proposed based on the use of Putzer\\\'s method.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/453800854nas a2200133 4500008004100000020002200041245006500063210006000128260003400188520041800222653002300640100002100663856003600684 2004 en d a978-2-85629-229-700aThe elliptic representation of the sixth Painlevé equation.0 aelliptic representation of the sixth Painlevé equation bSociete Matematique de France3 aWe find a class of solutions of the sixth Painlev´e equation corresponding\r\nto almost all the monodromy data of the associated linear system; actually, all data\r\nbut one point in the space of data. We describe the critical behavior close to the\r\ncritical points by means of the elliptic representation, and we find the relation among\r\nthe parameters at the different critical points (connection problem).10aPainlevé equation1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/652901258nas a2200145 4500008004300000245008600043210006900129260001700198520078200215100002300997700001801020700002201038700001601060856003601076 2004 en_Ud 00aEnergetics and switching of quasi-uniform states in small ferromagnetic particles0 aEnergetics and switching of quasiuniform states in small ferroma bEDP Sciences3 aWe present a numerical algorithm to solve the micromagnetic equations based on tangential-plane minimization for the magnetization update and a homothethic-layer decomposition of outer space for the computation of the demagnetization field. As a first application, detailed results on the flower-vortex transition in the cube of Micromagnetic Standard Problem number 3 are obtained, which confirm, with a different method, those already present in the literature, and validate our method and code. We then turn to switching of small cubic or almost-cubic particles, in the single-domain limit. Our data show systematic deviations from the Stoner-Wohlfarth model due to the non-ellipsoidal shape of the particle, and in particular a non-monotone dependence on the particle size.1 aAlouges, François1 aConti, Sergio1 aDeSimone, Antonio1 aPokern, Ivo uhttp://hdl.handle.net/1963/299900881nas a2200121 4500008004100000245005300041210005200094260001800146520051800164100002100682700002000703856003600723 2004 en d00aExistence of H-bubbles in a perturbative setting0 aExistence of Hbubbles in a perturbative setting bSISSA Library3 aGiven a $C^{1}$ function $H: \\\\mathbb{R}^3 \\\\to \\\\mathbb{R}$, we look for $H$-bubbles, i.e., surfaces in $\\\\mathbb{R}^3$ parametrized by the sphere $\\\\mathbb{S}^2$ with mean curvature $H$ at every regular point. Here we study the case $H(u)=H_{0}(u)+\\\\epsilon H_{1}(u)$ where $H_{0}$ is some \\\"good\\\" curvature (for which there exist $H_{0}$-bubbles with minimal energy, uniformly bounded in $L^{\\\\infty}$), $\\\\epsilon$ is the smallness parameter, and $H_{1}$ is {\\\\em any} $C^{1}$ function.1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/160600305nas a2200109 4500008004300000245003200043210002800075100001800103700002000121700001800141856003600159 2004 en_Ud 00aThe Extended Toda Hierarchy0 aExtended Toda Hierarchy1 aCarlet, Guido1 aDubrovin, Boris1 aYoujin, Zhang uhttp://hdl.handle.net/1963/254201206nas a2200133 4500008004300000245007600043210006900119260001300188520077600201100002100977700001900998700001901017856003601036 2003 en_Ud 00aEffective dynamics for Bloch electrons: Peierls substitution and beyond0 aEffective dynamics for Bloch electrons Peierls substitution and  bSpringer3 aWe consider an electron moving in a periodic potential and subject to an additional slowly varying external electrostatic potential, $\\\\phi(\\\\epsi x)$, and vector potential $A(\\\\epsi x)$, with $x \\\\in \\\\R^d$ and $\\\\epsi \\\\ll 1$. We prove that associated to an isolated family of Bloch bands there exists an almost invariant subspace of $L^2(\\\\R^d)$ and an effective Hamiltonian governing the evolution inside this subspace to all orders in $\\\\epsi$. To leading order the effective Hamiltonian is given through the Peierls substitution. We explicitly compute the first order correction. From a semiclassical analysis of this effective quantum Hamiltonian we establish the first order correction to the standard semiclassical model of solid state physics.1 aPanati, Gianluca1 aSpohn, Herbert1 aTeufel, Stefan uhttp://hdl.handle.net/1963/304000651nas a2200109 4500008004100000245006800041210006400109260001000173520030100183100002100484856003600505 2002 en d00aThe Elliptic Representation of the General Painlevé 6 Equation0 aElliptic Representation of the General Painlevé 6 Equation bSISSA3 aWe study the analytic properties and the critical behavior of the elliptic\r\nrepresentation of solutions of the Painlev\\\'e 6 equation. We solve the\r\nconnection problem for elliptic representation in the generic case and in a\r\nnon-generic case equivalent to WDVV equations of associativity.1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/652300515nas a2200121 4500008004100000245005900041210005500100260006700155520009100222653002300313100002100336856003600357 2002 en d00aThe Elliptic Representation of the Painleve 6 Equation0 aElliptic Representation of the Painleve 6 Equation bKyoto University, Research Institute for Mathematical Sciences3 aWe review our results on the elliptic representation of the sixth Painleve’ equation10aPainleve equations1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/653000315nas a2200109 4500008004100000245003500041210003400076260001800110100002100128700002000149856003600169 2002 en d00aExistence of minimal H-bubbles0 aExistence of minimal Hbubbles bSISSA Library1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/152500415nas a2200109 4500008004100000245010000041210006900141260001800210100002100228700002000249856003600269 2001 en d00aExistence and nonexistence results for a class of nonlinear, singular Sturm-Liouville equations0 aExistence and nonexistence results for a class of nonlinear sing bSISSA Library1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/131900345nas a2200109 4500008004100000245005000041210005000091260001800141100001700159700002300176856003600199 2001 en d00aExtremal synthesis for generic planar systems0 aExtremal synthesis for generic planar systems bSISSA Library1 aBoscain, Ugo1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/150300863nas a2200145 4500008004300000245008500043210006900128260001300197520039100210100002100601700001800622700001900640700002200659856003600681 2000 en_Ud 00aAn elementary approach to the polynomial $\\\\tau$-functions of the KP Hierarchy0 aelementary approach to the polynomial taufunctions of the KP Hie bSpringer3 aWe give an elementary construction of the solutions of the KP hierarchy associated with polynomial τ-functions starting with a geometric approach to soliton equations based on the concept of a bi-Hamiltonian system. As a consequence, we establish a Wronskian formula for the polynomial τ-functions of the KP hierarchy. This formula, known in the literature, is obtained very directly.1 aFalqui, Gregorio1 aMagri, Franco1 aPedroni, Marco1 aZubelli, Jorge P. uhttp://hdl.handle.net/1963/322300420nas a2200121 4500008004100000245007100041210006400112260001800176100002400194700002600218700001800244856003600262 2000 en d00aElliptic variational problems in $ R\\\\sp N$ with critical growth0 aElliptic variational problems in Rsp N with critical growth bSISSA Library1 aAmbrosetti, Antonio1 aGarcia Azorero, Jesus1 aPeral, Ireneo uhttp://hdl.handle.net/1963/125800442nas a2200121 4500008004100000245008800041210006900129260001800198100002400216700002600240700001800266856003600284 2000 en d00aExistence and multiplicity results for some nonlinear elliptic equations: a survey.0 aExistence and multiplicity results for some nonlinear elliptic e bSISSA Library1 aAmbrosetti, Antonio1 aGarcia Azorero, Jesus1 aPeral, Ireneo uhttp://hdl.handle.net/1963/146200387nas a2200109 4500008004100000245008000041210006900121260001000190653001900200100002200219856003600241 2000 en d00aExistence and multiplicity results for some problems in Riemannian geometry0 aExistence and multiplicity results for some problems in Riemanni bSISSA10aYamabe problem1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/594800685nas 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/1963/336600336nas a2200109 4500008004100000245004800041210004700089260001000136100002100146700002300167856003600190 1999 en d00aEvans-Vasilesco theorem in Dirichlet spaces0 aEvansVasilesco theorem in Dirichlet spaces bSISSA1 aDal Maso, Gianni1 aDe Cicco, Virginia uhttp://hdl.handle.net/1963/643600360nas a2200097 4500008004300000245007800043210006900121260001300190100002300203856003600226 1999 en_Ud 00aExtremal faces of the range of a vector measure and a theorem of Lyapunov0 aExtremal faces of the range of a vector measure and a theorem of bElsevier1 aBianchini, Stefano uhttp://hdl.handle.net/1963/337000924nas a2200121 4500008004100000245006500041210006500106260001300171520054200184100001900726700002100745856003600766 1998 en d00aError bounds for a deterministic version of the Glimm scheme0 aError bounds for a deterministic version of the Glimm scheme bSpringer3 aConsider the hyperbolic system of conservation laws $u_t F(u)_x=0. Let $u$ be the unique viscosity solution with initial condition $u(0,x)=\\\\bar u(x)$ and let $u^\\\\varepsilon$ be an approximate solution constructed by the Glimm scheme, corresponding to the mesh sizes $\\\\Delta x,\\\\Delta t=O(\\\\Delta x). With a suitable choise of the sampling sequence, we prove the estimate $$ \\\\left\\\\Vert u^\\\\varepsilon(t,\\\\cdot)-u(t,\\\\cdot) \\\\right\\\\Vert_1=o(1)\\\\cdot\\\\sqrt{\\\\Delta x}\\\\vert\\\\ln\\\\Delta x\\\\vert. $$1 aMarson, Andrea1 aBressan, Alberto uhttp://hdl.handle.net/1963/104500348nas a2200109 4500008004100000245005600041210005600097260001100153100002000164700001800184856003600202 1998 en d00aExtended affine Weyl groups and Frobenius manifolds0 aExtended affine Weyl groups and Frobenius manifolds bKluwer1 aDubrovin, Boris1 aZhang, Youjin uhttp://hdl.handle.net/1963/648600381nas a2200109 4500008004100000245007600041210006900117260001000186653002200196100001700218856003600235 1997 en d00aOn Existence and Continuous Dependence for Systems of Conservation Laws0 aExistence and Continuous Dependence for Systems of Conservation  bSISSA10aConservation laws1 aBaiti, Paolo uhttp://hdl.handle.net/1963/558800453nas a2200121 4500008004300000245008900043210006900132260000900201520004500210100002000255700002000275856003600295 1995 en_Ud 00aAn existence result in a problem of the vectorial case of the calculus of variations0 aexistence result in a problem of the vectorial case of the calcu bSIAM3 aSIAM J. Control Optim. 33 (1995) 960-9701 aCellina, Arrigo1 aZagatti, Sandro uhttp://hdl.handle.net/1963/351300376nas a2200109 4500008004100000245006600041210006300107260001800170100002100188700002200209856003500231 1990 en d00aExistence and continuous dependence for discontinuous O.D.E.s0 aExistence and continuous dependence for discontinuous ODEs bSISSA Library1 aBressan, Alberto1 aColombo, Giovanni uhttp://hdl.handle.net/1963/71600390nas a2200109 4500008004100000245007700041210006900118260001800187100001800205700002200223856003500245 1990 en d00aExistence of solutions for a class of non-convex differential inclusions0 aExistence of solutions for a class of nonconvex differential inc bSISSA Library1 aAncona, Fabio1 aColombo, Giovanni uhttp://hdl.handle.net/1963/79200368nas a2200109 4500008004100000245006300041210006100104260001800165100002000183700002000203856003500223 1988 en d00aEinstein algebras and the algebraic Kaluza-Klein monopole.0 aEinstein algebras and the algebraic KaluzaKlein monopole bSISSA Library1 aLandi, Giovanni1 aMarmo, Giuseppe uhttp://hdl.handle.net/1963/60300390nas a2200109 4500008004100000245007700041210006900118260001800187100002000205700002000225856003500245 1987 en d00aExtensions of Lie superalgebras and supersymmetric Abelian gauge fields.0 aExtensions of Lie superalgebras and supersymmetric Abelian gauge bSISSA Library1 aLandi, Giovanni1 aMarmo, Giuseppe uhttp://hdl.handle.net/1963/507