The aim of this note is to explain in which sense an axiomatic Sobolev space over a general metric measure space (à la Gol’dshtein–Troyanov) induces – under suitable locality assumptions – a first-order differential structure.

10aAxiomatic Sobolev space10aCotangent module10aLocality of differentials1 aGigli, Nicola1 aPasqualetto, Enrico uhttp://www.sciencedirect.com/science/article/pii/S072308691830097502567nas a2200169 4500008004100000245009100041210006900132520193100201100001702132700001902149700002102168700002502189700001902214700002102233700002102254856012202275 2019 eng d00aEfficient Reduction in Shape Parameter Space Dimension for Ship Propeller Blade Design0 aEfficient Reduction in Shape Parameter Space Dimension for Ship 3 aIn this work, we present the results of a ship propeller design optimization campaign carried out in the framework of the research project PRELICA, funded by the Friuli Venezia Giulia regional government. The main idea of this work is to operate on a multidisciplinary level to identify propeller shapes that lead to reduced tip vortex-induced pressure and increased efficiency without altering the thrust. First, a specific tool for the bottom-up construction of parameterized propeller blade geometries has been developed. The algorithm proposed operates with a user defined number of arbitrary shaped or NACA airfoil sections, and employs arbitrary degree NURBS to represent the chord, pitch, skew and rake distribution as a function of the blade radial coordinate. The control points of such curves have been modified to generate, in a fully automated way, a family of blade geometries depending on as many as 20 shape parameters. Such geometries have then been used to carry out potential flow simulations with the Boundary Element Method based software PROCAL. Given the high number of parameters considered, such a preliminary stage allowed for a fast evaluation of the performance of several hundreds of shapes. In addition, the data obtained from the potential flow simulation allowed for the application of a parameter space reduction methodology based on active subspaces (AS) property, which suggested that the main propeller performance indices are, at a first but rather accurate approximation, only depending on a single parameter which is a linear combination of all the original geometric ones. AS analysis has also been used to carry out a constrained optimization exploiting response surface method in the reduced parameter space, and a sensitivity analysis based on such surrogate model. The few selected shapes were finally used to set up high fidelity RANS simulations and select an optimal shape.

1 aMola, Andrea1 aTezzele, Marco1 aGadalla, Mahmoud1 aValdenazzi, Federica1 aGrassi, Davide1 aPadovan, Roberta1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/efficient-reduction-shape-parameter-space-dimension-ship-propeller-blade-design00394nas a2200109 4500008004100000245004900041210004800090100002000138700001800158700002400176856008400200 2019 eng d00aQuasi-continuous vector fields on RCD spaces0 aQuasicontinuous vector fields on RCD spaces1 aDebin, Clément1 aGigli, Nicola1 aPasqualetto, Enrico uhttps://www.math.sissa.it/publication/quasi-continuous-vector-fields-rcd-spaces01637nas a2200217 4500008004100000022001400041245007700055210006900132300001400201490000800215520097100223653002001194653001501214653001701229653001701246100001901263700002201282700002301304700002101327856007101348 2019 eng d a0022-123600aReducibility of first order linear operators on tori via Moser's theorem0 aReducibility of first order linear operators on tori via Mosers a932 - 9700 v2763 aIn this paper we prove reducibility of a class of first order, quasi-linear, quasi-periodic time dependent PDEs on the torus∂tu+ζ⋅∂xu+a(ωt,x)⋅∂xu=0,x∈Td,ζ∈Rd,ω∈Rν. As a consequence we deduce a stability result on the associated Cauchy problem in Sobolev spaces. By the identification between first order operators and vector fields this problem can be formulated as the problem of finding a change of coordinates which conjugates a weakly perturbed constant vector field on Tν+d to a constant diophantine flow. For this purpose we generalize Moser's straightening theorem: considering smooth perturbations we prove that the corresponding straightening torus diffeomorphism is smooth, under the assumption that the perturbation is small only in some given Sobolev norm and that the initial frequency belongs to some Cantor-like set. In view of applications in KAM theory for PDEs we provide also tame estimates on the change of variables.

10aHyperbolic PDEs10aKAM theory10aNash–Moser10aReducibility1 aFeola, Roberto1 aGiuliani, Filippo1 aMontalto, Riccardo1 aProcesi, Michela uhttp://www.sciencedirect.com/science/article/pii/S002212361830379301650nas a2200157 4500008004100000022001400041245013600055210006900191260000800260520108900268100002501357700002101382700002201403700002001425856004701445 2019 eng d a1618-189100aOn the relaxed area of the graph of discontinuous maps from the plane to the plane taking three values with no symmetry assumptions0 arelaxed area of the graph of discontinuous maps from the plane t cJul3 aIn this paper, we estimate from above the area of the graph of a singular map u taking a disk to three vectors, the vertices of a triangle, and jumping along three $\mathcal{C}^2$-embedded curves that meet transversely at only one point of the disk. We show that the singular part of the relaxed area can be estimated from above by the solution of a Plateau-type problem involving three entangled nonparametric area-minimizing surfaces. The idea is to ``fill the hole'' in the graph of the singular map with a sequence of approximating smooth two-codimensional surfaces of graph-type, by imagining three minimal surfaces, placed vertically over the jump of u, coupled together via a triple point in the target triangle. Such a construction depends on the choice of a target triple point, and on a connection passing through it, which dictate the boundary condition for the three minimal surfaces. We show that the singular part of the relaxed area of u cannot be larger than what we obtain by minimizing over all possible target triple points and all corresponding connections.

1 aBellettini, Giovanni1 aElshorbagy, Alaa1 aPaolini, Maurizio1 aScala, Riccardo uhttps://doi.org/10.1007/s10231-019-00887-000411nas a2200145 4500008004100000022001400041245004800055210004400103260000800147300001400155490000700169100001900176700002400195856004600219 2019 eng d a1973-440900aThe Serre–Swan theorem for normed modules0 aSerre–Swan theorem for normed modules cAug a385–4040 v681 aLučić, Danka1 aPasqualetto, Enrico uhttps://doi.org/10.1007/s12215-018-0366-600414nas a2200109 4500008004100000245010800041210006900149300001100218100002100229700001700250856003700267 2018 eng d00aAccelerating the iterative solution of convection-diffusion problems using singular value decomposition0 aAccelerating the iterative solution of convectiondiffusion probl a1–211 aPitton, Giuseppe1 aHeltai, Luca uhttps://arxiv.org/abs/1807.0946700702nas a2200253 4500008004100000245003700041210003000078100002200108700001800130700001700148700001800165700002100183700001900204700002200223700001800245700001700263700002300280700002400303700002000327700002400347700001700371700001700388856004300405 2018 eng d00aThe deal.II Library, Version 9.00 adealII Library Version 901 aAlzetta, Giovanni1 aArndt, Daniel1 aBangerth, W.1 aBoddu, Vishal1 aBrands, Benjamin1 aDavydov, Denis1 aGassmöller, Rene1 aHeister, Timo1 aHeltai, Luca1 aKormann, Katharina1 aKronbichler, Martin1 aMaier, Matthias1 aPelteret, Jean-Paul1 aTurcksin, B.1 aWells, David uhttps://doi.org/10.1515/jnma-2018-005400395nas a2200109 4500008004100000245004700041210004700088100001800135700002400153700002600177856008200203 2018 eng d00aDifferential of metric valued Sobolev maps0 aDifferential of metric valued Sobolev maps1 aGigli, Nicola1 aPasqualetto, Enrico1 aSoultanis, Elefterios uhttps://www.math.sissa.it/publication/differential-metric-valued-sobolev-maps00800nas a2200121 4500008004100000245006300041210005900104520039700163100002000560700002900580700002100609856004800630 2018 en d00aOn Geometric Quantum Confinement in Grushin-Like Manifolds0 aGeometric Quantum Confinement in GrushinLike Manifolds3 aWe study the problem of so-called geometric quantum confinement in a class of two-dimensional incomplete Riemannian manifold with metric of Grushin type. We employ a constant-fibre direct integral scheme, in combination with Weyl's analysis in each fibre, thus fully characterising the regimes of presence and absence of essential self-adjointness of the associated Laplace-Beltrami operator.1 aGallone, Matteo1 aMichelangeli, Alessandro1 aPozzoli, Eugenio uhttp://preprints.sissa.it/handle/1963/3532200612nas a2200169 4500008004100000245015500041210006900196300001100265490000800276100002200284700002000306700002000326700002300346700001700369700001900386856003700405 2018 eng d00aIterative map-making with two-level preconditioning for polarized cosmic microwave background data sets. A worked example for ground-based experiments0 aIterative mapmaking with twolevel preconditioning for polarized a1–140 v6181 aPuglisi, Giuseppe1 aPoletti, Davide1 aFabbian, Giulio1 aBaccigalupi, Carlo1 aHeltai, Luca1 aStompor, Radek uhttps://arxiv.org/abs/1801.0893700730nas a2200109 4500008004100000245008900041210006900130520032300199100002900522700002100551856004800572 2018 en d00aNon-linear Gross-Pitaevskii dynamics of a 2D binary condensate: a numerical analysis0 aNonlinear GrossPitaevskii dynamics of a 2D binary condensate a n3 aWe present a numerical study of the two-dimensional Gross-Pitaevskii systems in a wide range of relevant regimes of population ratios and intra-species and inter-species interactions. Our numerical method is based on a Fourier collocation scheme in space combined with a fourth order integrating factor scheme in time.1 aMichelangeli, Alessandro1 aPitton, Giuseppe uhttp://preprints.sissa.it/handle/1963/3532300361nas a2200097 4500008004100000245005400041210004700095100001800142700002400160856007900184 2018 eng d00aOn the notion of parallel transport on RCD spaces0 anotion of parallel transport on RCD spaces1 aGigli, Nicola1 aPasqualetto, Enrico uhttps://www.math.sissa.it/publication/notion-parallel-transport-rcd-spaces01177nas a2200145 4500008004100000245008600041210006900127300001300196490000800209520068400217100001800901700002100919700002100940856007000961 2018 eng d00aNumerical study of the Kadomtsev-Petviashvili equation and dispersive shock waves0 aNumerical study of the KadomtsevPetviashvili equation and disper a201704580 v4743 aA detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev–Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For the description of dispersive shock waves, Whitham modulation equations for KP are obtained. It is shown that the modulation equations near the soliton line are hyperbolic for the KPII equation while they are elliptic for the KPI equation leading to a focusing effect and the formation of lumps. Such a behaviour is similar to the appearance of breathers for the focusing nonlinear Schrödinger equation in the semiclassical limit.

1 aGrava, Tamara1 aKlein, Christian1 aPitton, Giuseppe uhttps://royalsocietypublishing.org/doi/abs/10.1098/rspa.2017.045800437nas a2200121 4500008004100000245010800041210006900149300001400218490000800232100002100240700001700261856003700278 2018 eng d00aNURBS-SEM: A hybrid spectral element method on NURBS maps for the solution of elliptic PDEs on surfaces0 aNURBSSEM A hybrid spectral element method on NURBS maps for the a440–4620 v3381 aPitton, Giuseppe1 aHeltai, Luca uhttps://arxiv.org/abs/1804.0827100517nas a2200109 4500008004100000245011200041210006900153100001900222700002200241700002100263856012300284 2018 eng d00aReducibility for a class of weakly dispersive linear operators arising from the Degasperis Procesi equation0 aReducibility for a class of weakly dispersive linear operators a1 aFeola, Roberto1 aGiuliani, Filippo1 aProcesi, Michela uhttps://www.math.sissa.it/publication/reducibility-class-weakly-dispersive-linear-operators-arising-degasperis-procesi01212nas a2200109 4500008004100000245010500041210006900146520071800215100002100933700002100954856012700975 2017 eng d00aOn the Application of Reduced Basis Methods to Bifurcation Problems in Incompressible Fluid Dynamics0 aApplication of Reduced Basis Methods to Bifurcation Problems in 3 aIn this paper we apply a reduced basis framework for the computation of flow bifurcation (and stability) problems in fluid dynamics. The proposed method aims at reducing the complexity and the computational time required for the construction of bifurcation and stability diagrams. The method is quite general since it can in principle be specialized to a wide class of nonlinear problems, but in this work we focus on an application in incompressible fluid dynamics at low Reynolds numbers. The validation of the reduced order model with the full order computation for a benchmark cavity flow problem is promising.

1 aPitton, Giuseppe1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/application-reduced-basis-methods-bifurcation-problems-incompressible-fluid-dynamics02413nas a2200205 4500008004100000245015800041210006900199260001200268300000800280490000800288520159500296653004301891653002501934653002301959653003401982100002102016700002102037700002102058856012802079 2017 eng d00aComputational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: Applications to Coanda effect in cardiology0 aComputational reduction strategies for the detection of steady b c09/2017 a5570 v3443 aWe focus on reducing the computational costs associated with the hydrodynamic stability of solutions of the incompressible Navier–Stokes equations for a Newtonian and viscous fluid in contraction–expansion channels. In particular, we are interested in studying steady bifurcations, occurring when non-unique stable solutions appear as physical and/or geometric control parameters are varied. The formulation of the stability problem requires solving an eigenvalue problem for a partial differential operator. An alternative to this approach is the direct simulation of the flow to characterize the asymptotic behavior of the solution. Both approaches can be extremely expensive in terms of computational time. We propose to apply Reduced Order Modeling (ROM) techniques to reduce the demanding computational costs associated with the detection of a type of steady bifurcations in fluid dynamics. The application that motivated the present study is the onset of asymmetries (i.e., symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the regurgitant mitral valve orifice shape.

We consider the heat equation associated with a class of second order hypoelliptic Hörmander operators with constant second order term and linear drift. We completely describe the small time heat kernel expansions on the diagonal giving a geometric characterization of the coefficients in terms of the divergence of the drift field and the curvature-like invariants of the optimal control problem associated with the diffusion operator.

10aCurvature10aHypoelliptic heat equation10aSmall time asymptotics1 aBarilari, Davide1 aPaoli, Elisa uhttp://www.sciencedirect.com/science/article/pii/S0362546X1730229800585nas a2200217 4500008004100000245003700041210003000078300001400108490000700122100001800129700001700147700001900164700001800183700001700201700002400218700002000242700002400262700001700286700001700303856004700320 2017 eng d00aThe deal.II Library, Version 8.50 adealII Library Version 85 a137–1450 v251 aArndt, Daniel1 aBangerth, W.1 aDavydov, Denis1 aHeister, Timo1 aHeltai, Luca1 aKronbichler, Martin1 aMaier, Matthias1 aPelteret, Jean-Paul1 aTurcksin, B.1 aWells, David uhttps://www.dealii.org/deal85-preprint.pdf00906nas a2200121 4500008004100000245009600041210006900137520045600206100002300662700002400685700002400709856005100733 2017 en d00aDerivation of a rod theory from lattice systems with interactions beyond nearest neighbours0 aDerivation of a rod theory from lattice systems with interaction3 aWe study continuum limits of discrete models for (possibly heterogeneous) nanowires. The lattice energy includes at least nearest and next-to-nearest neighbour interactions: the latter have the role of penalising changes of orientation. In the heterogeneous case, we obtain an estimate on the minimal energy spent to match different equilibria. This gives insight into the nucleation of dislocations in epitaxially grown heterostructured nanowires.1 aAlicandro, Roberto1 aLazzaroni, Giuliano1 aPalombaro, Mariapia uhttp://urania.sissa.it/xmlui/handle/1963/3526901090nas 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/1963/3526801406nas a2200133 4500008004100000245004000041210004000081520101100121100002301132700002101155700002401176700002401200856004801224 2017 en d00aLinearisation of multiwell energies0 aLinearisation of multiwell energies3 aLinear elasticity can be rigorously derived from finite elasticity under the assumption of small loadings in terms of Gamma-convergence. This was first done in the case of one-well energies with super-quadratic growth and later generalised to different settings, in particular to the case of multi-well energies where the distance between the wells is very small (comparable to the size of the load). In this paper we study the case when the distance between the wells is independent of the size of the load. In this context linear elasticity can be derived by adding to the multi-well energy a singular higher order term which penalises jumps from one well to another. The size of the singular term has to satisfy certain scaling assumptions whose optimality is shown in most of the cases. Finally, the derivation of linear elasticty from a two-well discrete model is provided, showing that the role of the singular perturbation term is played in this setting by interactions beyond nearest neighbours.1 aAlicandro, Roberto1 aDal Maso, Gianni1 aLazzaroni, Giuliano1 aPalombaro, Mariapia uhttp://preprints.sissa.it/handle/1963/3528801239nas a2200169 4500008004100000022001400041245003900055210003900094260000800133300000700141490000900148520080000157100001900957700002500976700002401001856004401025 2017 eng d a1029-847900aReal topological string amplitudes0 aReal topological string amplitudes cMar a800 v20173 aWe discuss the physical superstring correlation functions in type I theory (or equivalently type II with orientifold) that compute real topological string amplitudes. We consider the correlator corresponding to holomorphic derivative of the real topological amplitude $\mathcal{G_\chi}$, at fixed worldsheet Euler characteristic $\chi$. This corresponds in the low-energy effective action to $\mathcal{N}=2$ Weyl multiplet, appropriately reduced to the orientifold invariant part, and raised to the power $g'= −\chi+ 1$. We show that the physical string correlator gives precisely the holomorphic derivative of topological amplitude. Finally, we apply this method to the standard closed oriented case as well, and prove a similar statement for the topological amplitude $\mathcal{F}_g$.

1 aNarain, K., S.1 aPiazzalunga, Nicolò1 aTanzini, Alessandro uhttps://doi.org/10.1007/JHEP03(2017)08001246nas a2200205 4500008004100000245008100041210006900122260003800191300001400229520059600243100002400839700002100863700001600884700001800900700002100918700002000939700002100959700001900980856004100999 2017 eng d00aReduced-order semi-implicit schemes for fluid-structure interaction problems0 aReducedorder semiimplicit schemes for fluidstructure interaction bSpringer International Publishing a149–1673 aPOD–Galerkin reduced-order models (ROMs) for fluid-structure interaction problems (incompressible fluid and thin structure) are proposed in this paper. Both the high-fidelity and reduced-order methods are based on a Chorin-Temam operator-splitting approach. Two different reduced-order methods are proposed, which differ on velocity continuity condition, imposed weakly or strongly, respectively. The resulting ROMs are tested and compared on a representative haemodynamics test case characterized by wave propagation, in order to assess the capabilities of the proposed strategies.

1 aBallarin, Francesco1 aRozza, Gianluigi1 aMaday, Yvon1 aBenner, Peter1 aOhlberger, Mario1 aPatera, Anthony1 aRozza, Gianluigi1 aUrban, Karsten uhttps://www.math.sissa.it/node/1294801212nas a2200145 4500008004100000022001400041245008800055210007000143260000800213300001400221490000700235520076100242100001701003856004601020 2017 eng d a1573-869800aSmall Time Asymptotics on the Diagonal for Hörmander's Type Hypoelliptic Operators0 aSmall Time Asymptotics on the Diagonal for Hörmanders Type Hypoe cJan a111–1430 v233 aWe compute the small time asymptotics of the fundamental solution of Hörmander's type hypoelliptic operators with drift, on the diagonal at a point x0. We show that the order of the asymptotics depends on the controllability of an associated control problem and of its approximating system. If the control problem of the approximating system is controllable at x0, then so is also the original control problem, and in this case we show that the fundamental solution blows up as t−N/2\$\backslashphantom {\backslashdot {i}\backslash!}t^{-\backslashmathcal {N}/2}\$, where N\$\backslashphantom {\backslashdot {i}\backslash!}\backslashmathcal {N}\$is a number determined by the Lie algebra at x0 of the fields, that define the hypoelliptic operator.

1 aPaoli, Elisa uhttps://doi.org/10.1007/s10883-016-9321-z00623nas a2200169 4500008004100000245008300041210006900124260002500193300001400218490000800232100001600240700001600256700002300272700002300295700002400318856011100342 2017 eng d00aSolid tumors are poroelastic solids with a chemo-mechanical feedback on growth0 aSolid tumors are poroelastic solids with a chemomechanical feedb bSpringer Netherlands a107–1240 v1291 aAmbrosi, D.1 aPezzuto, S.1 aRiccobelli, Davide1 aStylianopoulos, T.1 aCiarletta, Pasquale uhttps://www.math.sissa.it/publication/solid-tumors-are-poroelastic-solids-chemo-mechanical-feedback-growth02112nas a2200217 4500008004100000245018600041210006900227260003600296520123100332100002501563700002401588700002001612700001701632700001901649700002101668700002101689700002101710700001701731700001601748856013001764 2016 en d00aAdvances in geometrical parametrization and reduced order models and methods for computational fluid dynamics problems in applied sciences and engineering: overview and perspectives0 aAdvances in geometrical parametrization and reduced order models aCrete, GreecebECCOMASc06/20163 aSeveral problems in applied sciences and engineering require reduction techniques in order to allow computational tools to be employed in the daily practice, especially in iterative procedures such as optimization or sensitivity analysis. Reduced order methods need to face increasingly complex problems in computational mechanics, especially into a multiphysics setting. Several issues should be faced: stability of the approximation, efficient treatment of nonlinearities, uniqueness or possible bifurcations of the state solutions, proper coupling between fields, as well as offline-online computing, computational savings and certification of errors as measure of accuracy. Moreover, efficient geometrical parametrization techniques should be devised to efficiently face shape optimization problems, as well as shape reconstruction and shape assimilation problems. A related aspect deals with the management of parametrized interfaces in multiphysics problems, such as fluid-structure interaction problems, and also a domain decomposition based approach for complex parametrized networks. We present some illustrative industrial and biomedical problems as examples of recent advances on methodological developments.

1 aSalmoiraghi, Filippo1 aBallarin, Francesco1 aCorsi, Giovanni1 aMola, Andrea1 aTezzele, Marco1 aRozza, Gianluigi1 aPapadrakakis, M.1 aPapadopoulos, V.1 aStefanou, G.1 aPlevris, V. uhttps://www.math.sissa.it/publication/advances-geometrical-parametrization-and-reduced-order-models-and-methods-computational01524nas a2200157 4500008004100000245011100041210006900152300001000221490000700231520095900238653002001197100002501217700001801242700002201260856008401282 2016 en d00aOn the area of the graph of a piecewise smooth map from the plane to the plane with a curve discontinuity0 aarea of the graph of a piecewise smooth map from the plane to th a29-630 v223 aIn this paper we provide an estimate from above for the value of the relaxed area functional for a map defined on a bounded domain of the plane with values in the plane and discontinuous on a regular simple curve with two endpoints. We show that, under suitable assumptions, the relaxed area does not exceed the area of the regular part of the map, with the addition of a singular term measuring the area of a disk type solution of the Plateau's problem spanning the two traces of the map on the jump. The result is valid also when the area minimizing surface has self intersections. A key element in our argument is to show the existence of what we call a semicartesian parametrization of this surface, namely a conformal parametrization defined on a suitable parameter space, which is the identity in the first component. To prove our result, various tools of parametric minimal surface theory are used, as well as some result from Morse theory.

10aArea functional1 aBellettini, Giovanni1 aTealdi, Lucia1 aPaolini, Maurizio uhttps://www.esaim-cocv.org/articles/cocv/abs/2016/01/cocv140065/cocv140065.html00407nas a2200097 4500008004100000245006600041210006600107100001800173700002400191856009400215 2016 eng d00aBehaviour of the reference measure on RCD spaces under charts0 aBehaviour of the reference measure on RCD spaces under charts1 aGigli, Nicola1 aPasqualetto, Enrico uhttps://www.math.sissa.it/publication/behaviour-reference-measure-rcd-spaces-under-charts01478nas a2200169 4500008004100000022001400041245008500055210006900140260000800209300001200217490000700229520096100236100002301197700002101220700002101241856004601262 2016 eng d a1424-066100aConstruction of Real-Valued Localized Composite Wannier Functions for Insulators0 aConstruction of RealValued Localized Composite Wannier Functions cJan a63–970 v173 aWe consider a real periodic Schrödinger operator and a physically relevant family of $m \geq 1$ Bloch bands, separated by a gap from the rest of the spectrum, and we investigate the localization properties of the corresponding composite Wannier functions. To this aim, we show that in dimension $d\leq 3$, there exists a global frame consisting of smooth quasi-Bloch functions which are both periodic and time-reversal symmetric. Aiming to applications in computational physics, we provide a constructive algorithm to obtain such a Bloch frame. The construction yields the existence of a basis of composite Wannier functions which are real-valued and almost-exponentially localized. The proof of the main result exploits only the fundamental symmetries of the projector on the relevant bands, allowing applications, beyond the model specified above, to a broad range of gapped periodic quantum systems with a time-reversal symmetry of bosonic type.

1 aFiorenza, Domenico1 aMonaco, Domenico1 aPanati, Gianluca uhttps://doi.org/10.1007/s00023-015-0400-600471nas 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-spaces01002nas a2200109 4500008004100000245009900041210007000140520058100210100002900791700002100820856005100841 2016 en d00aNon-linear Schrödinger system for the dynamics of a binary condensate: theory and 2D numerics0 aNonlinear Schrödinger system for the dynamics of a binary conden3 aWe present a comprehensive discussion of the mathematical framework for binary Bose-Einstein condensates and for the rigorous derivation of their effective dynamics, governed by a system of coupled non-linear Gross-Pitaevskii equations. We also develop in the 2D case a systematic numerical study of the Gross-Pitaevskii systems in a wide range of relevant regimes of population ratios and intra-species and inter-species interactions. Our numerical method is based on a Fourier collocation scheme in space combined with a fourth order integrating factor scheme in time.1 aMichelangeli, Alessandro1 aPitton, Giuseppe uhttp://urania.sissa.it/xmlui/handle/1963/3526601230nas a2200157 4500008004100000245009000041210006900131260002100200300001000221490000700231520073600238100001700974700001800991700001301009856005001022 2016 eng d00aSpectral analysis and the Aharonov-Bohm effect on certain almost-Riemannian manifolds0 aSpectral analysis and the AharonovBohm effect on certain almostR bTaylor & Francis a32-500 v413 aWe study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. This operator contains first order diverging terms caused by the divergence of the volume. We get explicit descriptions of the spectrum and the eigenfunctions. In particular in both cases we get a Weyl's law with leading term Elog E. We then study the drastic effect of Aharonov-Bohm magnetic potentials on the spectral properties. Other generalized Riemannian structures including conic and anti-conic type manifolds are also studied. In this case, the Aharonov-Bohm magnetic potential may affect the self-adjointness of the Laplace-Beltrami operator.

1 aBoscain, Ugo1 aPrandi, Dario1 aSeri, M. uhttps://doi.org/10.1080/03605302.2015.109576601454nas a2200157 4500008004100000245007300041210006900114260003500183300001100218490000700229520093500236100002201171700002501193700002201218856005601240 2016 eng d00aTowards a gauge theory interpretation of the real topological string0 aTowards a gauge theory interpretation of the real topological st bAmerican Physical SocietycMar a0660010 v933 aWe consider the real topological string on certain noncompact toric Calabi-Yau three-folds $\mathbb{X}$, in its physical realization describing an orientifold of type IIA on $\mathbb{X}$ with an O4-plane and a single D4-brane stuck on top. The orientifold can be regarded as a new kind of surface operator on the gauge theory with 8 supercharges arising from the singular geometry. We use the M-theory lift of this system to compute the real Gopakumar-Vafa invariants (describing wrapped M2-brane Bogomol’nyi-Prasad-Sommerfield (BPS) states) for diverse geometries. We show that the real topological string amplitudes pick up certain signs across flop transitions, in a well-defined pattern consistent with continuity of the real BPS invariants. We further give some preliminary proposals of an intrinsically gauge theoretical description of the effect of the surface operator in the gauge theory partition function.

1 aHayashi, Hirotaka1 aPiazzalunga, Nicolò1 aUranga, Angel, M. uhttps://link.aps.org/doi/10.1103/PhysRevD.93.06600100469nas a2200109 4500008004100000245007600041210006900117100002500186700002100211700001700232856011000249 2016 eng d00aVolume geodesic distortion and Ricci curvature for Hamiltonian dynamics0 aVolume geodesic distortion and Ricci curvature for Hamiltonian d1 aAgrachev, Andrei, A.1 aBarilari, Davide1 aPaoli, Elisa uhttps://www.math.sissa.it/publication/volume-geodesic-distortion-and-ricci-curvature-hamiltonian-dynamics01400nas a2200169 4500008004100000022001400041245007000055210006900125260000800194300001600202490000800218520089300226100002301119700002101142700002101163856004601184 2016 eng d a1432-091600aZ2 Invariants of Topological Insulators as Geometric Obstructions0 aZ2 Invariants of Topological Insulators as Geometric Obstruction cMay a1115–11570 v3433 aWe consider a gapped periodic quantum system with time-reversal symmetry of fermionic (or odd) type, i.e. the time-reversal operator squares to $-\mathbb{1}$. We investigate the existence of periodic and time-reversal invariant Bloch frames in dimensions 2 and 3. In 2d, the obstruction to the existence of such a frame is shown to be encoded in a $\mathbb{Z}_2$-valued topological invariant, which can be computed by a simple algorithm. We prove that the latter agrees with the Fu-Kane index. In 3d, instead, four $\mathbb{Z}_2$ invariants emerge from the construction, again related to the Fu-Kane-Mele indices. When no topological obstruction is present, we provide a constructive algorithm yielding explicitly a periodic and time-reversal invariant Bloch frame. The result is formulated in an abstract setting, so that it applies both to discrete models and to continuous ones.

1 aFiorenza, Domenico1 aMonaco, Domenico1 aPanati, Gianluca uhttps://doi.org/10.1007/s00220-015-2552-001202nas a2200133 4500008004100000245004900041210004800090300001200138490000700150520084200157100001300999700001801012856003801030 2015 eng d00aComplexity of Control-Affine Motion Planning0 aComplexity of ControlAffine Motion Planning a816-8440 v533 aIn this paper we study the complexity of the motion planning problem for control-affine systems. Such complexities are already defined and rather well understood in the particular case of nonholonomic (or sub-Riemannian) systems. Our aim is to generalize these notions and results to systems with a drift. Accordingly, we present various definitions of complexity, as functions of the curve that is approximated, and of the precision of the approximation. Due to the lack of time-rescaling invariance of these systems, we consider geometric and parametrized curves separately. Then, we give some asymptotic estimates for these quantities. As a byproduct, we are able to treat the long time local controllability problem, giving quantitative estimates on the cost of stabilizing the system near a nonequilibrium point of the drift.

1 aJean, F.1 aPrandi, Dario uhttps://doi.org/10.1137/13095079301209nas a2200121 4500008004300000245007700043210006900120520072500189100001900914700002500933700002200958856010700980 2015 en_Ud 00aConstrained BV functions on double coverings for Plateau's type problems0 aConstrained BV functions on double coverings for Plateaus type p3 aWe link Brakke's "soap films" covering construction with the theory of finite perimeter sets, in order to study Plateau's problem without fixing a priori the topology of the solution. The minimization is set up in the class of $BV$ functions defined on a double covering space of the complement of an $(n − 2)$-dimensional smooth compact manifold $S$ without boundary. The main novelty of our approach stands in the presence of a suitable constraint on the fibers, which couples together the covering sheets. The model allows to avoid all issues concerning the presence of the boundary $S$. The constraint is lifted in a natural way to Sobolev spaces, allowing also an approach based on $Γ$-convergence theory.

1 aAmato, Stefano1 aBellettini, Giovanni1 aPaolini, Maurizio uhttps://www.math.sissa.it/publication/constrained-bv-functions-double-coverings-plateaus-type-problems00678nas a2200169 4500008004100000245013400041210006900175300001400244490000700258100001800265700002100283700002000304700002100324700001900345700001900364856012500383 2015 eng d00aModel order reduction of parameterized systems ({MoRePaS}): Preface to the special issue of advances in computational mathematics0 aModel order reduction of parameterized systems MoRePaS Preface t a955–9600 v411 aBenner, Peter1 aOhlberger, Mario1 aPatera, Anthony1 aRozza, Gianluigi1 aSorensen, D.C.1 aUrban, Karsten uhttps://www.math.sissa.it/publication/model-order-reduction-parameterized-systems-morepas-preface-special-issue-advances01086nas a2200133 4500008004100000245009800041210006900139300001400208490000800222520055000230100001900780700002100799856013200820 2015 eng d00aReduced basis approximation of parametrized advection-diffusion PDEs with high Péclet number0 aReduced basis approximation of parametrized advectiondiffusion P a419–4260 v1033 aIn this work we show some results about the reduced basis approximation of advection dominated parametrized problems, i.e. advection-diffusion problems with high Péclet number. These problems are of great importance in several engineering applications and it is well known that their numerical approximation can be affected by instability phenomena. In this work we compare two possible stabilization strategies in the framework of the reduced basis method, by showing numerical results obtained for a steady advection-diffusion problem.

1 aPacciarini, P.1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduced-basis-approximation-parametrized-advection-diffusion-pdes-high-p%C3%A9clet-number00953nas a2200121 4500008004100000245009700041210006900138520050800207100001800715700002500733700002200758856005100780 2015 en d00aResults on the minimization of the Dirichlet functional among semicartesian parametrizations0 aResults on the minimization of the Dirichlet functional among se3 aWe start to investigate the existence of conformal minimizers for the Dirichlet functional in the setting of the so-called semicartesian parametrizations, adapting to this context some techniques used in solving the classical Plateau's problem. The final goal is to find area minimizing semicartesian parametrizations spanning a Jordan curve obtained as union of two graphs; this problem appeared in the study of the relaxed area functional for maps from the plane to the plane jumping on a line.

1 aTealdi, Lucia1 aBellettini, Giovanni1 aPaolini, Maurizio uhttp://urania.sissa.it/xmlui/handle/1963/3448801420nas a2200133 4500008004100000245009400041210006900135260001000204520094900214100002401163700002401187700002501211856005001236 2015 en d00aRigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires0 aRigidity of threedimensional lattices and dimension reduction in bSISSA3 aIn the context of nanowire heterostructures we perform a discrete to continuum limit of the corresponding free energy by means of Γ-convergence techniques. Nearest neighbours are identified by employing the notions of Voronoi diagrams and Delaunay triangulations. The scaling of the nanowire is done in such a way that we perform not only a continuum limit but a dimension reduction simultaneously. The main part of the proof is a discrete geometric rigidity result that we announced in an earlier work and show here in detail for a variety of three-dimensional lattices. We perform the passage from discrete to continuum twice: once for a system that compensates a lattice mismatch between two parts of the heterogeneous nanowire without defects and once for a system that creates dislocations. It turns out that we can verify the experimentally observed fact that the nanowires show dislocations when the radius of the specimen is large1 aLazzaroni, Giuliano1 aPalombaro, Mariapia1 aSchlomerkemper, Anja uhttp://urania.sissa.it/xmlui/handle/1963/749401475nas a2200121 4500008004100000245011300041210006900154520101400223100001801237700002501255700002201280856005101302 2015 en d00aSemicartesian surfaces and the relaxed area of maps from the plane to the plane with a line discontinuity0 aSemicartesian surfaces and the relaxed area of maps from the pla3 aWe address the problem of estimating the area of the graph of a map u, defined on a bounded planar domain O and taking values in the plane, jumping on a segment J, either compactly contained in O or having both the end points on the boundary of O. We define the relaxation of the area functional w.r.t. a sort of uniform convergence, and we characterize it in terms of the infimum of the area among those surfaces in the space spanning the graphs of the traces of u on the two side of J and having what we have called a semicartesian structure. We exhibit examples showing that the relaxed area functional w.r.t the L^1 convergence may depend also on the values of u far from J, and on the relative position of J w.r.t. the boundary of O; these examples confirm the non-local behaviour of the L^1 relaxed area functional, and justify the interest in studying the relaxation w.r.t. a stronger convergence. We prove also that the L^1 relaxed area functional in non-subadditive for a rather class of maps.

1 aTealdi, Lucia1 aBellettini, Giovanni1 aPaolini, Maurizio uhttp://urania.sissa.it/xmlui/handle/1963/3448301228nas a2200109 4500008004100000245007200041210006700113520083900180100002901019700001901048856005101067 2015 en d00aStability of the (2+2)-fermionic system with zero-range interaction0 aStability of the 22fermionic system with zerorange interaction3 aWe introduce a 3D model, and we study its stability, consisting of two distinct pairs of identical fermions coupled with a two-body interaction between fermions of different species, whose effective range is essentially zero (a so called (2+2)-fermionic system with zero-range interaction). The interaction is modelled by implementing the the celebrated (and ubiquitous, in the literature of this field) Bethe-Peierls contact condition with given two-body scattering length within the Krein-Visik-Birman theory of extensions of semi-bounded symmetric operators, in order to make the Hamiltonian a well-defined (self-adjoint) physical observable. After deriving the expression for the associated energy quadratic form, we show analytically and numerically that the energy of the model is bounded below, thus describing a stable system.1 aMichelangeli, Alessandro1 aPfeiffer, Paul uhttp://urania.sissa.it/xmlui/handle/1963/3447401557nas a2200121 4500008004100000245012000041210006900161260001300230520109900243100002101342700002101363856005101384 2015 en d00aSymmetry and localization in periodic crystals: triviality of Bloch bundles with a fermionic time-reversal symmetry0 aSymmetry and localization in periodic crystals triviality of Blo bSpringer3 aWe describe some applications of group- and bundle-theoretic methods in solid state physics, showing how symmetries lead to a proof of the localization of electrons in gapped crystalline solids, as e.g. insulators and semiconductors. We shortly review the Bloch-Floquet decomposition of periodic operators, and the related concepts of Bloch frames and composite Wannier functions. We show that the latter are almost-exponentially localized if and only if there exists a smooth periodic Bloch frame, and that the obstruction to the latter condition is the triviality of a Hermitian vector bundle, called the Bloch bundle. The rôle of additional Z_2-symmetries, as time-reversal and space-reflection symmetry, is discussed, showing how time-reversal symmetry implies the triviality of the Bloch bundle, both in the bosonic and in the fermionic case. Moreover, the same Z_2-symmetry allows to define a finer notion of isomorphism and, consequently, to define new topological invariants, which agree with the indices introduced by Fu, Kane and Mele in the context of topological insulators.

1 aMonaco, Domenico1 aPanati, Gianluca uhttp://urania.sissa.it/xmlui/handle/1963/3446802046nas a2200121 4500008004100000245006500041210006500106260001000171520159900181653002801780100001701808856009901825 2015 en d00aVolume variation and heat kernel for affine control problems0 aVolume variation and heat kernel for affine control problems bSISSA3 aIn this thesis we study two main problems. The first one is the small-time heat kernel expansion on the diagonal for second order hypoelliptic opeartors. We consider operators that can depend on a drift field and that satisfy only the weak Hörmander condition. In a first work we use perturbation techniques to determine the exact order of decay of the heat kernel, that depends on the Lie algebra generated by the fields involved in the hypoelliptic operator. We generalize in particular some results already obtained in the sub-Riemannian setting. In a second work we consider a model class of hypoelliptic operators and we characterize geometrically all the coefficients in the on-the diagonal asymptotics at the equilibrium points of the drift field. The class of operators that we consider contains the linear hypoelliptic operators with constant second order part on the Euclidean space. We describe the coefficients in terms only of the divergence of the drift field and of curvature-like invariants, related to the minimal cost of geodesics of the associated optimal control problem. In the second part of the thesis we consider the variation of a smooth volume along a geodesic. The structure of the manifold is induced by a quadratic Hamiltonian and the geodesic in described as the projection of the Hamiltonian flow. We find an expansion similar to the classical Riemannian one. It depends on the curvature operator associated to the Hamiltonian, on the symbol of the geodesic and on a new metric-measure invariant determined by the symbol of the geodesic and by the given volume.10aHeat kernel asymptotics1 aPaoli, Elisa uhttps://www.math.sissa.it/publication/volume-variation-and-heat-kernel-affine-control-problems01482nas a2200133 4500008004100000245013000041210007100171260001300242520098000255100002401235700001701259700002101276856005101297 2014 en d00aAn Abstract Nash–Moser Theorem and Quasi-Periodic Solutions for NLW and NLS on Compact Lie Groups and Homogeneous Manifolds0 aAbstract Nash–Moser Theorem and QuasiPeriodic Solutions for NLW bSpringer3 aWe prove an abstract implicit function theorem with parameters for smooth operators defined on scales of sequence spaces, modeled for the search of quasi-periodic solutions of PDEs. The tame estimates required for the inverse linearised operators at each step of the iterative scheme are deduced via a multiscale inductive argument. The Cantor-like set of parameters where the solution exists is defined in a non inductive way. This formulation completely decouples the iterative scheme from the measure theoretical analysis of the parameters where the small divisors non-resonance conditions are verified. As an application, we deduce the existence of quasi-periodic solutions for forced NLW and NLS equations on any compact Lie group or manifold which is homogeneous with respect to a compact Lie group, extending previous results valid only for tori. A basic tool of harmonic analysis is the highest weight theory for the irreducible representations of compact Lie groups.1 aBerti, Massimiliano1 aCorsi, Livia1 aProcesi, Michela uhttp://urania.sissa.it/xmlui/handle/1963/3465102011nas a2200241 4500008004100000245013600041210006900177260002200246300000800268490000700276520123100283100002101514700001901535700001901554700001901573700001701592700002701609700002001636700002301656700002101679700001801700856005101718 2014 en d00aComparison of a Modal Method and a Proper Orthogonal Decomposition approach for multi-group time-dependent reactor spatial kinetics0 aComparison of a Modal Method and a Proper Orthogonal Decompositi bElsevierc09/2014 a2290 v713 aIn this paper, two modelling approaches based on a Modal Method (MM) and on the Proper Orthogonal Decomposition (POD) technique, for developing a control-oriented model of nuclear reactor spatial kinetics, are presented and compared. Both these methods allow developing neutronics description by means of a set of ordinary differential equations. The comparison of the outcomes provided by the two approaches focuses on the capability of evaluating the reactivity and the neutron flux shape in different reactor configurations, with reference to a TRIGA Mark II reactor. The results given by the POD-based approach are higher-fidelity with respect to the reference solution than those computed according to the MM-based approach, in particular when the perturbation concerns a reduced region of the core. If the perturbation is homogeneous throughout the core, the two approaches allow obtaining comparable accuracy results on the quantities of interest. As far as the computational burden is concerned, the POD approach ensures a better efficiency rather than direct Modal Method, thanks to the ability of performing a longer computation in the preprocessing that leads to a faster evaluation during the on-line phase.

1 aSartori, Alberto1 aBaroli, Davide1 aCammi, Antonio1 aChiesa, Davide1 aLuzzi, Lelio1 aPonciroli, Roberto, R.1 aPrevitali, Ezio1 aRicotti, Marco, E.1 aRozza, Gianluigi1 aSisti, Monica uhttp://urania.sissa.it/xmlui/handle/1963/3503901580nas a2200157 4500008004100000245009300041210006900134260002800203520103900231100001901270700001901289700002101308700002001329700002201349856005101371 2014 en d00aConformal invariants from nodal sets. I. negative eigenvalues and curvature prescription0 aConformal invariants from nodal sets I negative eigenvalues and bOxford University Press3 aIn this paper, we study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators; more specifically, the Graham, Jenne, Mason, and Sparling (GJMS) operators, which include the Yamabe and Paneitz operators. We give several applications to curvature prescription problems. We establish a version in conformal geometry of Courant's Nodal Domain Theorem. We also show that on any manifold of dimension n≥3, there exist many metrics for which our invariants are nontrivial. We prove that the Yamabe operator can have an arbitrarily large number of negative eigenvalues on any manifold of dimension n≥3. We obtain similar results for some higher order GJMS operators on some Einstein and Heisenberg manifolds. We describe the invariants arising from the Yamabe and Paneitz operators associated to left-invariant metrics on Heisenberg manifolds. Finally, in Appendix, the second named author and Andrea Malchiodi study the Q-curvature prescription problems for noncritical Q-curvatures.1 aGover, Rod, R.1 aCanzani, Yaiza1 aJakobson, Dmitry1 aPonge, Raphaël1 aMalchiodi, Andrea uhttp://urania.sissa.it/xmlui/handle/1963/3512801955nas 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/1963/3494001517nas a2200121 4500008004100000245010200041210006900143260001000212520108600222653001901308100001801327856005001345 2014 en d00aGeometry and analysis of control-affine systems: motion planning, heat and Schrödinger evolution0 aGeometry and analysis of controlaffine systems motion planning h bSISSA3 aThis thesis is dedicated to two problems arising from geometric control theory, regarding control-affine systems $\dot q= f_0(q)+\sum_{j=1}^m u_j f_j(q)$, where $f_0$ is called the drift. In the first part we extend the concept of complexity of non-admissible trajectories, well understood for sub-Riemannian systems, to this more general case, and find asymptotic estimates. In order to do this, we also prove a result in the same spirit as the Ball-Box theorem for sub-Riemannian systems, in the context of control-affine systems equipped with the L1 cost. Then, in the second part of the thesis, we consider a family of 2-dimensional driftless control systems. For these, we study how the set where the control vector fields become collinear affects the diffusion dynamics. More precisely, we study whether solutions to the heat and Schrödinger equations associated with this Laplace-Beltrami operator are able to cross this singularity, and how its the presence affects the spectral properties of the operator, in particular under a magnetic Aharonov–Bohm-type perturbation.10acontrol theory1 aPrandi, Dario uhttp://urania.sissa.it/xmlui/handle/1963/747400468nas a2200121 4500008004100000245007300041210007000114260001700184300001600201490000700217100001800224856010400242 2014 eng d00aHölder equivalence of the value function for control-affine systems0 aHölder equivalence of the value function for controlaffine syste bEDP Sciences a1224–12480 v201 aPrandi, Dario uhttps://www.math.sissa.it/publication/h%C3%B6lder-equivalence-value-function-control-affine-systems00608nas a2200157 4500008004100000245004900041210004900090260001300139300001200152490000800164520016500172100002400337700001700361700002100378856005100399 2014 en d00aKAM for Reversible Derivative Wave Equations0 aKAM for Reversible Derivative Wave Equations bSpringer a905-9550 v2123 aWe prove the existence of Cantor families of small amplitude, analytic, linearly stable quasi-periodic solutions of reversible derivative wave equations.

1 aBerti, Massimiliano1 aBiasco, Luca1 aProcesi, Michela uhttp://urania.sissa.it/xmlui/handle/1963/3464600578nas a2200145 4500008004100000245004600041210004500087260001000132520011500142653003000257100002200287700001700309700002500326856008100351 2014 en d00aLocal behavior of fractional p-minimizers0 aLocal behavior of fractional pminimizers bSISSA3 aWe extend the De Giorgi-Nash Moser theory to nonlocal, possibly degerate integro-differential operators

10afractional Sobolev spaces1 aDi Castro, Agnese1 aKuusi, Tuomo1 aPalatucci, Giampiero uhttps://www.math.sissa.it/publication/local-behavior-fractional-p-minimizers01318nas a2200157 4500008004100000022001400041245005900055210005800114260000800172300000700180490000900187520087300196100002501069700002201094856004401116 2014 eng d a1029-847900aM-theory interpretation of the real topological string0 aMtheory interpretation of the real topological string cAug a540 v20143 aWe describe the type IIA physical realization of the unoriented topological string introduced by Walcher, describe its M-theory lift, and show that it allows to compute the open and unoriented topological amplitude in terms of one-loop diagram of BPS M2-brane states. This confirms and allows to generalize the conjectured BPS integer expansion of the topological amplitude. The M-theory lift of the orientifold is freely acting on the M-theory circle, so that integer multiplicities are a weighted version of the (equivariant subsector of the) original closed oriented Gopakumar-Vafa invariants. The M-theory lift also provides new perspective on the topological tadpole cancellation conditions. We finally comment on the M-theory version of other unoriented topological strings, and clarify certain misidentifications in earlier discussions in the literature.

1 aPiazzalunga, Nicolò1 aUranga, Angel, M. uhttps://doi.org/10.1007/JHEP08(2014)05400851nas a2200121 4500008004100000245009300041210006900134260001300203520042700216100001900643700001600662856005100678 2014 en d00aPseudo-automorphisms of positive entropy on the blowups of products of projective spaces0 aPseudoautomorphisms of positive entropy on the blowups of produc bSpringer3 aWe use a concise method to construct pseudo-automorphisms fn of the first dynamical degree d1(fn) > 1 on the blowups of the projective n-space for all n ≥ 2 and more generally on the blowups of products of projective spaces. These fn, for n=3 have positive entropy, and for n≥ 4 seem to be the first examples of pseudo-automorphisms with d1(fn) > 1 (and of non-product type) on rational varieties of higher dimensions.1 aPerroni, Fabio1 aZhang, Deqi uhttp://urania.sissa.it/xmlui/handle/1963/3471400707nas a2200145 4500008004100000022001400041245007900055210006900134300001400203490000700217520023000224100001700454700001900471856007100490 2014 eng d a0294-144900aSmooth approximation of bi-Lipschitz orientation-preserving homeomorphisms0 aSmooth approximation of biLipschitz orientationpreserving homeom a567 - 5890 v313 aWe show that a planar bi-Lipschitz orientation-preserving homeomorphism can be approximated in the W1,p norm, together with its inverse, with an orientation-preserving homeomorphism which is piecewise affine or smooth.

1 aDaneri, Sara1 aPratelli, Aldo uhttp://www.sciencedirect.com/science/article/pii/S029414491300071101201nas a2200133 4500008004100000245007800041210006900119300001100188490000800199520070800207100001900915700002100934856011200955 2014 eng d00aStabilized reduced basis method for parametrized advection-diffusion PDEs0 aStabilized reduced basis method for parametrized advectiondiffus a1–180 v2743 aIn this work, we propose viable and efficient strategies for the stabilization of the reduced basis approximation of an advection dominated problem. In particular, we investigate the combination of a classic stabilization method (SUPG) with the Offline-Online structure of the RB method. We explain why the stabilization is needed in both stages and we identify, analytically and numerically, which are the drawbacks of a stabilization performed only during the construction of the reduced basis (i.e. only in the Offline stage). We carry out numerical tests to assess the performances of the ``double'' stabilization both in steady and unsteady problems, also related to heat transfer phenomena.

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

1 aPacciarini, P.1 aRozza, Gianluigi uhttps://infoscience.epfl.ch/record/203327/files/ECCOMAS_PP_GR.pdf01394nas a2200133 4500008004100000245006500041210006400106260002800170520094000198100002701138700002301165700002101188856005101209 2014 en d00aSwelling-induced and controlled curving in layered gel beams0 aSwellinginduced and controlled curving in layered gel beams bRoyal Society of London3 aWe describe swelling-driven curving in originally straight and non-homogeneous beams. We present and verify a structural model of swollen beams, based on a new point of view adopted to describe swelling-induced deformation processes in bilayered gel beams, that is based on the split of the swelling-induced deformation of the beam at equilibrium into two components, both depending on the elastic properties of the gel. The method allows us to: (i) determine beam stretching and curving, once assigned the characteristics of the solvent bath and of the non-homogeneous beam, and (ii) estimate the characteristics of non-homogeneous flat gel beams in such a way as to obtain, under free-swelling conditions, three-dimensional shapes. The study was pursued by means of analytical, semi-analytical and numerical tools; excellent agreement of the outcomes of the different techniques was found, thus confirming the strength of the method.1 aLucantonio, Alessandro1 aNardinocchi, Paola1 aPezzulla, Matteo uhttp://urania.sissa.it/xmlui/handle/1963/3498701418nas a2200133 4500008004100000245010100041210006900142260003500211520074700246653011900993100002101112700002101133856013001154 2014 en d00aTopological Invariants of Eigenvalue Intersections and Decrease of Wannier Functions in Graphene0 aTopological Invariants of Eigenvalue Intersections and Decrease bJournal of Statistical Physics3 aWe investigate the asymptotic decrease of the Wannier functions for the valence and conduction band of graphene, both in the monolayer and the multilayer case. Since the decrease of the Wannier functions is characterised by the structure of the Bloch eigenspaces around the Dirac points, we introduce a geometric invariant of the family of eigenspaces, baptised eigenspace vorticity. We compare it with the pseudospin winding number. For every value n∈Z of the eigenspace vorticity, we exhibit a canonical model for the local topology of the eigenspaces. With the help of these canonical models, we show that the single band Wannier function w satisfies |w(x)|≤const |x|^{−2} as |x|→∞, both in monolayer and bilayer graphene.

10aWannier functions, Bloch bundles, conical intersections, eigenspace vorticity, pseudospin winding number, graphene1 aMonaco, Domenico1 aPanati, Gianluca uhttps://www.math.sissa.it/publication/topological-invariants-eigenvalue-intersections-and-decrease-wannier-functions-graphene00951nas a2200145 4500008004100000245009100041210006900132260001000201520045700211653003300668100002100701700002500722700002200747856003600769 2013 en d00aDislocation dynamics in crystals: a macroscopic theory in a fractional Laplace setting0 aDislocation dynamics in crystals a macroscopic theory in a fract bSISSA3 aWe consider an evolution equation arising in the Peierls-Nabarro model for crystal dislocation. We study the evolution of such dislocation function and show that, at a macroscopic scale, the dislocations have the tendency to concentrate at single points of the crystal, where the size of the slip coincides with the natural periodicity of the medium. These dislocation points evolve according to the external stress and an interior repulsive potential.10anonlocal Allen-Cahn equation1 aDipierro, Serena1 aPalatucci, Giampiero1 aValdinoci, Enrico uhttp://hdl.handle.net/1963/712401347nas 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 aThis 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-laplacian01314nas a2200181 4500008004100000245006100041210006100102260001000163520076900173653001800942653002400960653002700984653002301011100002301034700002001057700001901077856003601096 2013 en d00aGenus stabilization for moduli of curves with symmetries0 aGenus stabilization for moduli of curves with symmetries bSISSA3 aIn a previous paper, arXiv:1206.5498, we introduced a new homological\r\ninvariant $\\e$ for the faithful action of a finite group G on an algebraic\r\ncurve.\r\n We show here that the moduli space of curves admitting a faithful action of a\r\nfinite group G with a fixed homological invariant $\\e$, if the genus g\' of the\r\nquotient curve is sufficiently large, is irreducible (and non empty iff the\r\nclass satisfies the condition which we define as \'admissibility\'). In the\r\nunramified case, a similar result had been proven by Dunfield and Thurston\r\nusing the classical invariant in the second homology group of G, H_2(G, \\ZZ).\r\n We achieve our result showing that the stable classes are in bijection with\r\nthe set of admissible classes $\\e$.10agroup actions10amapping class group10aModuli space of curves10aTeichmüller space1 aCatanese, Fabrizio1 aLönne, Michael1 aPerroni, Fabio uhttp://hdl.handle.net/1963/650900759nas a2200157 4500008004100000022001300041245006000054210006000114300001200174490000700186520025600193100002400449700001700473700002100490856009000511 2013 eng d a0012959300aKAM theory for the Hamiltonian derivative wave equation0 aKAM theory for the Hamiltonian derivative wave equation a301-3730 v463 aWe prove an infinite dimensional KAM theorem which implies the existence of Can- tor families of small-amplitude, reducible, elliptic, analytic, invariant tori of Hamiltonian derivative wave equations. © 2013 Société Mathématique de France.

1 aBerti, Massimiliano1 aBiasco, Luca1 aProcesi, Michela uhttps://www.math.sissa.it/publication/kam-theory-hamiltonian-derivative-wave-equation01020nas a2200145 4500008004100000020001500041245007100056210006500127520044300192653007200635100001900707700002500726700002200751856010100773 2013 en d a887642472400aThe nonlinear multidomain model: a new formal asymptotic analysis.0 anonlinear multidomain model a new formal asymptotic analysis3 aWe study the asymptotic analysis of a singularly perturbed weakly parabolic system of m- equations of anisotropic reaction-diffusion type. Our main result formally shows that solutions to the system approximate a geometric motion of a hypersurface by anisotropic mean curvature. The anisotropy, supposed to be uniformly convex, is explicit and turns out to be the dual of the star-shaped combination of the m original anisotropies.

10abidomain model, anisotropic mean curvature, star-shaped combination1 aAmato, Stefano1 aBellettini, Giovanni1 aPaolini, Maurizio uhttps://www.math.sissa.it/publication/nonlinear-multidomain-model-new-formal-asymptotic-analysis00494nas a2200097 4500008004100000245012100041210006900162100001700231700001800248856013000266 2013 eng d00aSelf-adjoint extensions and stochastic completeness of the Laplace-Beltrami operator on conic and anticonic surfaces0 aSelfadjoint extensions and stochastic completeness of the Laplac1 aBoscain, Ugo1 aPrandi, Dario uhttps://www.math.sissa.it/publication/self-adjoint-extensions-and-stochastic-completeness-laplace-beltrami-operator-conic-and00943nas a2200121 4500008004100000245004000041210004000081260001000121520053200131653010100663100002100764856003600785 2013 en d00aSemistability and Decorated Bundles0 aSemistability and Decorated Bundles bSISSA3 aThis thesis is devoted to the study of semistability condition of type t=(a,b,c,N) decorated bundles and sheaves in order to better understand and simplify it. We approach the problem in two different ways: on one side we “enclose” the above semistability condition between a stronger semistability condition (\epsilon-semistability) and a weaker one (k-semistability), on the other side we try, and succeed for the case of a = 2, to bound the length of weighted filtrations on which one checks the semistability condition.10aDecorated sheaves, semistability, moduli space, Mehta-Ramanathan, maximal destabilizing subsheaf1 aPustetto, Andrea uhttp://hdl.handle.net/1963/713000539nas a2200157 4500008004100000022001400041245011800055210006900173300001400242490000800256100001900264700001900283700001600302700001500318856004800333 2013 eng d a0022-471500aSpectra of random Hermitian matrices with a small-rank external source: the supercritical and subcritical regimes0 aSpectra of random Hermitian matrices with a smallrank external s a654–6970 v1531 aBertola, Marco1 aBuckingham, R.1 aLee, S., Y.1 aPierce, V. uhttp://dx.doi.org/10.1007/s10955-013-0845-200868nas a2200145 4500008004100000245004700041210004400088260004800132520037400180100002100554700002100575700002500596700002200621856007900643 2012 en d00aAsymptotics of the s-perimeter as s →0 0 aAsymptotics of the sperimeter as s →0 bAmerican Institute of Mathematical Sciences3 aWe deal with the asymptotic behavior of the $s$-perimeter of a set $E$ inside a domain $\Omega$ as $s\searrow0$. We prove necessary and sufficient conditions for the existence of such limit, by also providing an explicit formulation in terms of the Lebesgue measure of $E$ and $\Omega$. Moreover, we construct examples of sets for which the limit does not exist.

1 aDipierro, Serena1 aFigalli, Alessio1 aPalatucci, Giampiero1 aValdinoci, Enrico uhttps://www.math.sissa.it/publication/asymptotics-s-perimeter-s-%E2%86%92001971nas a2200169 4500008004100000245009100041210006900132260003100201520131900232100002201551700001701573700002001590700002201610700002201632700002501654856012201679 2012 en d00aHybridization in nanostructured DNA monolayers probed by AFM: theory versus experiment0 aHybridization in nanostructured DNA monolayers probed by AFM the bRoyal Society of Chemistry3 aNanografted monolayers (NAMs) of DNA show novel physico-chemical properties that make them ideally suited for advanced biosensing applications. In comparison with alternative solid-phase techniques for diagnostic DNA detection, NAMs have the advantage of combining a small size with a high homogeneity of the DNA surface coverage. These two properties favour the extreme miniaturization and ultrasensitivity in high-throughput biosensing devices. The systematic use of NAMs for quantitative DNA (and protein) detection has so far suffered from the lack of a control on key fabrication parameters, such as the ss- or ds-DNA surface coverage. Here we report on a combined experimental-computational study that allows us to estimate the surface density of the grafted DNA by analyzing the sample mechanical response, that is the DNA patch height vs. applied tip load curves. It is shown that the same analysis scheme can be used to detect the occurrence of hybridization with complementary strands in solution and estimate its efficiency. Thanks to these quantitative relationships it is possible to use a single AFM-based setup to: (i) fabricate a DNA NAM, (ii) control the DNA surface coverage, and (iii) characterize its level of hybridization helping the design of NAMs with pre-determined fabrication parameters.1 aBosco, Alessandro1 aBano, Fouzia1 aParisse, Pietro1 aCasalis, Loredana1 aDeSimone, Antonio1 aMicheletti, Cristian uhttps://www.math.sissa.it/publication/hybridization-nanostructured-dna-monolayers-probed-afm-theory-versus-experiment00826nas a2200133 4500008004300000245007200043210006900115260002100184520038600205100002000591700002500611700002000636856003600656 2012 en_Ud 00aNonlinear thin-walled beams with a rectangular cross-section-Part I0 aNonlinear thinwalled beams with a rectangular crosssectionPart I bWorld Scientific3 aOur aim is to rigorously derive a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section, starting from three-dimensional nonlinear elasticity. The different limit models are distinguished by the different scaling of the elastic energy and of the ratio between the sides of the cross-section. In this paper we report the first part of our results.1 aFreddi, Lorenzo1 aMora, Maria Giovanna1 aParoni, Roberto uhttp://hdl.handle.net/1963/410400559nas a2200157 4500008004100000022001400041245011500055210006900170300001400239490000800253100001900261700001900280700001600299700001500315856007100330 2012 eng d a0022-471500aSpectra of random Hermitian matrices with a small-rank external source: the critical and near-critical regimes0 aSpectra of random Hermitian matrices with a smallrank external s a475–5180 v1461 aBertola, Marco1 aBuckingham, R.1 aLee, S., Y.1 aPierce, V. uhttp://0-dx.doi.org.mercury.concordia.ca/10.1007/s10955-011-0409-201012nas a2200169 4500008004100000245005500041210005400096260006700150520046800217653002100685100002400706700002400730700002000754700001900774700001300793856003600806 2011 en d00aCones of divisors of blow-ups of projective spaces0 aCones of divisors of blowups of projective spaces bUniversità degli Studi di Catania. Dipartimento di matematica3 aWe investigate Mori dream spaces obtained by blowing-up the n-dimensional complex projective space at n+1, n+2 or n+3 points in very general position. Using toric techniques we study the movable cone of the blow-up of Pn at n+1 points, its decomposition into nef chambers and the action of theWeyl group on the set of chambers. Moreover, using different methods, we explicitly write down the equations of the movable cone also for Pn blown-up at n+2 points.10aMori dream space1 aLo Giudice, Alessio1 aCacciola, Salvatore1 aDonten-Bury, M.1 aDumitrescu, O.1 aPark, J. uhttp://hdl.handle.net/1963/661300934nas a2200133 4500008004100000245007900041210006900120260001000189520050600199100002200705700001800727700001900745856003600764 2011 en d00aCrepant resolutions of weighted projective spaces and quantum deformations0 aCrepant resolutions of weighted projective spaces and quantum de bSISSA3 aWe compare the Chen-Ruan cohomology ring of the weighted projective spaces\r\n$\\IP(1,3,4,4)$ and $\\IP(1,...,1,n)$ with the cohomology ring of their crepant\r\nresolutions. In both cases, we prove that the Chen-Ruan cohomology ring is\r\nisomorphic to the quantum corrected cohomology ring of the crepant resolution\r\nafter suitable evaluation of the quantum parameters. For this, we prove a\r\nformula for the Gromov-Witten invariants of the resolution of a transversal\r\n${\\rm A}_3$ singularity.1 aBoissiere, Samuel1 aMann, Etienne1 aPerroni, Fabio uhttp://hdl.handle.net/1963/651401229nas a2200169 4500008004100000245006500041210006200106260001000168520073800178100001600916700003100932700001500963700001200978700001400990700001901004856003601023 2011 en d00aD-branes, surface operators, and ADHM quiver representations0 aDbranes surface operators and ADHM quiver representations bSISSA3 aA supersymmetric quantum mechanical model is constructed for BPS states bound to surface operators in five dimensional SU(r) gauge theories using D-brane engineering. This model represents the effective action of a certain D2-brane configuration, and is naturally obtained by dimensional reduction of a quiver $(0,2)$ gauged linear sigma model. In a special stability chamber, the resulting moduli space of quiver representations is shown to be smooth and isomorphic to a moduli space of framed quotients on the projective plane. A precise conjecture relating a K-theoretic partition function of this moduli space to refined open string invariants of toric lagrangian branes is formulated for conifold and local P^1 x P^1 geometries.1 aBruzzo, Ugo1 aDiaconescu, Duiliu-Emanuel1 aYardim, M.1 aPan, G.1 aZhang, Yi1 aWu-yen, Chuang uhttp://hdl.handle.net/1963/413300860nas a2200181 4500008004100000022001400041245007500055210007200130300001600202490000700218520024700225653004900472653002400521100002300545700002200568700001700590856007100607 2011 eng d a0362-546X00aInfinitely many positive solutions for a Schrödinger–Poisson system0 aInfinitely many positive solutions for a Schrödinger–Poisson sys a5705 - 57210 v743 aWe are interested in the existence of infinitely many positive solutions of the Schrödinger–Poisson system −Δu+u+V(|x|)ϕu=|u|p−1u,x∈R3,−Δϕ=V(|x|)u2,x∈R3, where V(|x|) is a positive bounded function, 1<p<5 and V(r

10aNon-autonomous Schrödinger–Poisson system10aPerturbation method1 ad’Avenia, Pietro1 aPomponio, Alessio1 aVaira, Giusi uhttp://www.sciencedirect.com/science/article/pii/S0362546X1100351800923nas a2200145 4500008004100000245010600041210006900147260001300216520043000229653002300659100002000682700001700702700002200719856003600741 2011 en d00aLinearly degenerate Hamiltonian PDEs and a new class of solutions to the WDVV associativity equations0 aLinearly degenerate Hamiltonian PDEs and a new class of solution bSpringer3 aWe define a new class of solutions to the WDVV associativity equations. This class is determined by the property that one of the commuting PDEs associated with such a WDVV solution is linearly degenerate. We reduce the problem of classifying such solutions of the WDVV equations to the particular case of the so-called algebraic Riccati equation and, in this way, arrive at a complete classification of irreducible solutions.10aFrobenius manifold1 aDubrovin, Boris1 aPavlov, M.V.1 aZykov, Sergei, A. uhttp://hdl.handle.net/1963/643001120nas a2200133 4500008004300000245010500043210006900148260001300217520065000230100001900880700002500899700002600924856003600950 2011 en_Ud 00aThe matching property of infinitesimal isometries on elliptic surfaces and elasticity on thin shells0 amatching property of infinitesimal isometries on elliptic surfac bSpringer3 aUsing the notion of Γ-convergence, we discuss the limiting behavior of the three-dimensional nonlinear elastic energy for thin elliptic shells, as their thickness h converges to zero, under the assumption that the elastic energy of deformations scales like h β with 2 < β < 4. We establish that, for the given scaling regime, the limiting theory reduces to linear pure bending. Two major ingredients of the proofs are the density of smooth infinitesimal isometries in the space of W 2,2 first order infinitesimal isometries, and a result on matching smooth infinitesimal isometries with exact isometric immersions on smooth elliptic surfaces.1 aLewicka, Marta1 aMora, Maria Giovanna1 aPakzad, Mohammad Reza uhttp://hdl.handle.net/1963/339200668nas a2200145 4500008004100000245007500041210006900116260001000185520019000195653003600385100002000421700002500441700002000466856003600486 2011 en d00aNonlinear thin-walled beams with a rectangular cross-section - Part II0 aNonlinear thinwalled beams with a rectangular crosssection Part bSISSA3 aIn this paper we report the second part of our results concerning the rigorous derivation of a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section..10aThin-walled cross-section beams1 aFreddi, Lorenzo1 aMora, Maria Giovanna1 aParoni, Roberto uhttp://hdl.handle.net/1963/416901454nas a2200145 4500008004100000022001400041245009100055210007000146260000900216490000800225520090000233100002401133700002101157856013001178 2011 eng d a0012-709400aNonlinear wave and Schrödinger equations on compact Lie groups and homogeneous spaces0 aNonlinear wave and Schrödinger equations on compact Lie groups a c20110 v1593 aWe develop linear and nonlinear harmonic analysis on compact Lie groups and homogeneous spaces relevant for the theory of evolutionary Hamiltonian PDEs. A basic tool is the theory of the highest weight for irreducible representations of compact Lie groups. This theory provides an accurate description of the eigenvalues of the Laplace-Beltrami operator as well as the multiplication rules of its eigenfunctions. As an application, we prove the existence of Cantor families of small amplitude time-periodic solutions for wave and Schr¨odinger equations with differentiable nonlinearities. We apply an abstract Nash-Moser implicit function theorem to overcome the small divisors problem produced by the degenerate eigenvalues of the Laplace operator. We provide a new algebraic framework to prove the key tame estimates for the inverse linearized operators on Banach scales of Sobolev functions.1 aBerti, Massimiliano1 aProcesi, Michela uhttps://www.math.sissa.it/publication/nonlinear-wave-and-schr%C3%B6dinger-equations-compact-lie-groups-and-homogeneous-spaces00295nas a2200097 4500008004100000245004400041210004100085100001700126700001900143856003500162 2011 eng d00aA planar bi-Lipschitz extension Theorem0 aplanar biLipschitz extension Theorem1 aDaneri, Sara1 aPratelli, Aldo uhttp://arxiv.org/abs/1110.612400961nas a2200121 4500008004300000245005200043210005100095260001300146520059700159100002200756700002500778856003600803 2011 en_Ud 00aPoincaré covariance and κ-Minkowski spacetime0 aPoincaré covariance and κMinkowski spacetime bElsevier3 aA fully Poincaré covariant model is constructed out of the k-Minkowski spacetime. Covariance is implemented by a unitary representation of the Poincaré group, and thus complies with the original Wigner approach to quantum symmetries. This provides yet another example (besides the DFR model), where Poincaré covariance is realised á la Wigner in the presence of two characteristic dimensionful parameters: the light speed and the Planck length. In other words, a Doubly Special Relativity (DSR) framework may well be realised without deforming the meaning of \\\"Poincaré covariance\\\".1 aDabrowski, Ludwik1 aPiacitelli, Gherardo uhttp://hdl.handle.net/1963/389301388nas a2200157 4500008004300000245009200043210007000135260002200205300001200227490000800239520088500247100001601132700002201148700002401170856003601194 2011 en_Ud 00aPoincaré polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces0 aPoincaré polynomial of moduli spaces of framed sheaves on stacky bSpringerc06/2011 a395-4090 v3043 aWe perform a study of the moduli space of framed torsion-free sheaves on Hirzebruch surfaces by using localization techniques. We discuss some general properties of this moduli space by studying it in the framework of Huybrechts-Lehn theory of framed modules. We classify the fixed points under a toric action on the moduli space, and use this to compute the Poincare polynomial of the latter. This will imply that the moduli spaces we are considering are irreducible. We also consider fractional first Chern classes, which means that we are extending our computation to a stacky deformation of a Hirzebruch surface. From the physical viewpoint, our results provide the partition function of N=4 Vafa-Witten theory on total spaces of line bundles on P1, which is relevant in black hole entropy counting problems according to a conjecture due to Ooguri, Strominger and Vafa.

1 aBruzzo, Ugo1 aPoghossian, Rubik1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/373802121nas a2200145 4500008004100000245007900041210006900120260001300189520164700202100002001849700002201869700002301891700002501914856003601939 2011 en d00aQuantum Geometry on Quantum Spacetime: Distance, Area and Volume Operators0 aQuantum Geometry on Quantum Spacetime Distance Area and Volume O bSpringer3 aWe develop the first steps towards an analysis of geometry on the quantum\\r\\nspacetime proposed in Doplicher et al. (Commun Math Phys 172:187–220, 1995). The homogeneous elements of the universal differential algebra are naturally identified with operators living in tensor powers of Quantum Spacetime; this allows us to compute their spectra. In particular, we consider operators that can be interpreted as distances, areas, 3- and 4-volumes. The Minkowski distance operator between two independent events is shown to have pure Lebesgue spectrum with infinite multiplicity. The Euclidean distance operator is shown to have spectrum bounded below by a constant of the order of the Planck length. The corresponding statement is proved also for both the space-space and space-time area operators, as well as for the Euclidean length of the vector representing the 3-volume operators. However, the space 3-volume operator (the time component of that vector) is shown to have spectrum equal to the whole complex plane. All these operators are normal, while the distance operators are also selfadjoint. The Lorentz invariant spacetime volume operator, representing the 4- volume spanned by five\\r\\nindependent events, is shown to be normal. Its spectrum is pure point with a\\r\\nfinite distance (of the order of the fourth power of the Planck length) away\\r\\nfrom the origin. The mathematical formalism apt to these problems is developed and its relation to a general formulation of Gauge Theories on Quantum Spaces is outlined. As a byproduct, a Hodge Duality between the absolute differential and the Hochschild boundary is pointed out.1 aBahns, Dorothea1 aDoplicher, Sergio1 aFredenhagen, Klaus1 aPiacitelli, Gherardo uhttp://hdl.handle.net/1963/520302010nas a2200385 4500008004100000022001300041245007600054210006900130300001200199490000700211520082800218653001601046653002101062653002301083653002101106653003001127653001901157653002201176653002501198653002701223653001801250653001801268653002401286653002801310653002201338653002201360653002401382653001901406653001201425653001901437100002401456700002001480700002101500856010301521 2010 eng d a0294144900aAn abstract Nash-Moser theorem with parameters and applications to PDEs0 aabstract NashMoser theorem with parameters and applications to P a377-3990 v273 aWe prove an abstract Nash-Moser implicit function theorem with parameters which covers the applications to the existence of finite dimensional, differentiable, invariant tori of Hamiltonian PDEs with merely differentiable nonlinearities. The main new feature of the abstract iterative scheme is that the linearized operators, in a neighborhood of the expected solution, are invertible, and satisfy the "tame" estimates, only for proper subsets of the parameters. As an application we show the existence of periodic solutions of nonlinear wave equations on Riemannian Zoll manifolds. A point of interest is that, in presence of possibly very large "clusters of small divisors", due to resonance phenomena, it is more natural to expect solutions with only Sobolev regularity. © 2009 Elsevier Masson SAS. All rights reserved.10aAbstracting10aAircraft engines10aFinite dimensional10aHamiltonian PDEs10aImplicit function theorem10aInvariant tori10aIterative schemes10aLinearized operators10aMathematical operators10aMoser theorem10aNon-Linearity10aNonlinear equations10aNonlinear wave equation10aPeriodic solution10aPoint of interest10aResonance phenomena10aSmall divisors10aSobolev10aWave equations1 aBerti, Massimiliano1 aBolle, Philippe1 aProcesi, Michela uhttps://www.math.sissa.it/publication/abstract-nash-moser-theorem-parameters-and-applications-pdes00564nas a2200109 4500008004100000245005700041210005700098260001000155520022800165100002500393856003600418 2010 en d00aAspects of Quantum Field Theory on Quantum Spacetime0 aAspects of Quantum Field Theory on Quantum Spacetime bSISSA3 aWe provide a minimal, self-contained introduction to the covariant DFR flat\\r\\nquantum spacetime, and to some partial results for the corresponding quantum field theory. Explicit equations are given in the Dirac notation.1 aPiacitelli, Gherardo uhttp://hdl.handle.net/1963/417101351nas a2200109 4500008004300000245003600043210003500079520104400114100002501158700002201183856003601205 2010 en_Ud 00aCanonical k-Minkowski Spacetime0 aCanonical kMinkowski Spacetime3 aA complete classification of the regular representations of the relations [T,X_j] = (i/k)X_j, j=1,...,d, is given. The quantisation of RxR^d canonically (in the sense of Weyl) associated with the universal representation of the above relations is intrinsically \\\"radial\\\", this meaning that it only involves the time variable and the distance from the origin; angle variables remain classical. The time axis through the origin is a spectral singularity of the model: in the large scale limit it is topologically disjoint from the rest. The symbolic calculus is developed; in particular there is a trace functional on symbols. For suitable choices of states localised very close to the origin, the uncertainties of all spacetime coordinates can be made simultaneously small at wish. On the contrary, uncertainty relations become important at \\\"large\\\" distances: Planck scale effects should be visible at LHC energies, if processes are spread in a region of size 1mm (order of peak nominal beam size) around the origin of spacetime.1 aPiacitelli, Gherardo1 aDabrowski, Ludwik uhttp://hdl.handle.net/1963/386300912nas a2200133 4500008004300000245011700043210006900160520042800229100002600657700002200683700001900705700001800724856003600742 2010 en_Ud 00aConcentration of solutions for some singularly perturbed mixed problems: Asymptotics of minimal energy solutions0 aConcentration of solutions for some singularly perturbed mixed p3 aIn this paper we carry on the study of asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions, started in the first paper. Here we are mainly interested in the analysis of the location and shape of least energy solutions when the singular perturbation parameter tends to zero. We show that in many cases they coincide with the new solutions produced in.1 aGarcia Azorero, Jesus1 aMalchiodi, Andrea1 aMontoro, Luigi1 aPeral, Ireneo uhttp://hdl.handle.net/1963/340900856nas a2200133 4500008004300000245010300043210006900146520038600215100002600601700002200627700001900649700001800668856003600686 2010 en_Ud 00aConcentration of solutions for some singularly perturbed mixed problems. Part I: existence results0 aConcentration of solutions for some singularly perturbed mixed p3 aIn this paper we study the asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions. We prove that, under suitable geometric conditions on the boundary of the domain, there exist solutions which approach the intersection of the Neumann and the Dirichlet parts as the singular perturbation parameter tends to zero.1 aGarcia Azorero, Jesus1 aMalchiodi, Andrea1 aMontoro, Luigi1 aPeral, Ireneo uhttp://hdl.handle.net/1963/340600807nas a2200157 4500008004300000245008900043210006900132260002800201520027900229100002200508700002100530700002100551700002200572700001900594856003600613 2010 en_Ud 00aOn the geometric origin of the bi-Hamiltonian structure of the Calogero-Moser system0 ageometric origin of the biHamiltonian structure of the CalogeroM bOxford University Press3 aWe show that the bi-Hamiltonian structure of the rational n-particle (attractive) Calogero-Moser system can be obtained by means of a double projection from a very simple Poisson pair on the cotangent bundle of gl(n,R). The relation with the Lax formalism is also discussed.1 aBartocci, Claudio1 aFalqui, Gregorio1 aMencattini, Igor1 aOrtenzi, Giovanni1 aPedroni, Marco uhttp://hdl.handle.net/1963/380001140nas a2200109 4500008004300000245006600043210006200109520077800171100002400949700002100973856003600994 2010 en_Ud 00aThe geometry emerging from the symmetries of a quantum system0 ageometry emerging from the symmetries of a quantum system3 aWe investigate the relation between the symmetries of a quantum system and its topological quantum numbers, in a general C*-algebraic framework. We prove that, under suitable assumptions on the symmetry algebra, there exists a generalization of the Bloch-Floquet transform which induces a direct-integral decomposition of the algebra of observables. Such generalized transform selects uniquely the set of \\\"continuous sections\\\" in the direct integral, thus yielding a Hilbert bundle. The emerging geometric structure provides some topological invariants of the quantum system. Two running examples provide an Ariadne\\\'s thread through the paper. For the sake of completeness, we review two related theorems by von Neumann and Maurin and compare them with our result.1 aDe Nittis, Giuseppe1 aPanati, Gianluca uhttp://hdl.handle.net/1963/383400901nas a2200121 4500008004300000245004400043210004300087520054400130100002200674700002200696700002500718856003600743 2010 en_Ud 00aLorentz Covariant k-Minkowski Spacetime0 aLorentz Covariant kMinkowski Spacetime3 aIn recent years, different views on the interpretation of Lorentz covariance of non commuting coordinates were discussed. Here, by a general procedure, we construct the minimal canonical central covariantisation of the k-Minkowski spacetime. We then show that, though the usual k-Minkowski spacetime is covariant under deformed (or twisted) Lorentz action, the resulting framework is equivalent to taking a non covariant restriction of the covariantised model. We conclude with some general comments on the approach of deformed covariance.1 aDabrowski, Ludwik1 aGodlinski, Michal1 aPiacitelli, Gherardo uhttp://hdl.handle.net/1963/382901210nas a2200097 4500008004300000245004000043210003900083520092900122100002501051856003601076 2010 en_Ud 00aQuantum Spacetime: a Disambiguation0 aQuantum Spacetime a Disambiguation3 aWe review an approach to non-commutative geometry, where models are constructed by quantisation of the coordinates. In particular we focus on the full DFR model and its irreducible components; the (arbitrary) restriction to a particular irreducible component is often referred to as the \\\"canonical quantum spacetime\\\". The aim is to distinguish and compare the approaches under various points of view, including motivations, prescriptions for quantisation, the choice of mathematical objects and concepts, approaches to dynamics and to covariance. Some incorrect statements as \\\"universality of Planck scale conflicts with Lorentz-Fitzgerald contraction and requires a modification of covariance\\\", or \\\"stability of the geometric background requires an absolute lower bound of (\\\\Delta x^\\\\mu)\\\", or \\\"violations of unitarity are due to time/space non-commutativity\\\" are put in context, and discussed.1 aPiacitelli, Gherardo uhttp://hdl.handle.net/1963/386400794nas a2200121 4500008004300000245008000043210006900123520037400192100001900566700002500585700002600610856003600636 2010 en_Ud 00aShell theories arising as low energy Gamma-limit of 3d nonlinear elasticity0 aShell theories arising as low energy Gammalimit of 3d nonlinear 3 aWe discuss the limiting behavior (using the notion of gamma-limit) of the 3d nonlinear elasticity for thin shells around an arbitrary smooth 2d surface. In particular, under the assumption that the elastic energy of deformations scales like h4, h being the thickness of a shell, we derive a limiting theory which is a generalization of the von Karman theory for plates.1 aLewicka, Marta1 aMora, Maria Giovanna1 aPakzad, Mohammad Reza uhttp://hdl.handle.net/1963/260101005nas a2200121 4500008004300000245005700043210005600100520062300156100002000779700002400799700002400823856003600847 2010 en_Ud 00aTaming open/closed string duality with a Losev trick0 aTaming openclosed string duality with a Losev trick3 aA target space string field theory formulation for open and closed B-model is provided by giving a Batalin-Vilkovisky quantization of the holomorphic Chern-Simons theory with off-shell gravity background. The target space expression for the coefficients of the holomorphic anomaly equation for open strings are obtained. Furthermore, open/closed string duality is proved from a judicious integration over the open string fields. In particular, by restriction to the case of independence on continuous open moduli, the shift formulas of [7] are reproduced and shown therefore to encode the data of a closed string dual.1 aBonelli, Giulio1 aPrudenziati, Andrea1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/385501029nas a2200157 4500008004100000245008100041210006900122300001000191490000800201520055000209100001800759700001700777700001600794700001800810856004300828 2010 eng d00aA three-dimensional model for the dynamics and hydrodynamics of rowing boats0 athreedimensional model for the dynamics and hydrodynamics of row a51-610 v2243 aThis paper proposes a new model describing the dynamics of a rowing boat for general three-dimensional motions. The complex interaction between the different components of the rowers–-oars–-boat system is analysed and reduced to a set of ordinary differential equations governing the rigid motion along the six degrees of freedom. To treat the unstable nature of the physical problem, a rather simple (but effective) control model is included, which mimics the main active control techniques adopted by the rowers during their action.

1 aFormaggia, L.1 aMola, Andrea1 aParolini, N1 aPischiutta, M uhttps://doi.org/10.1243/17543371jset4601480nas a2200097 4500008004300000245008700043210006900130520112200199100002501321856003601346 2010 en_Ud 00aTwisted Covariance as a Non Invariant Restriction of the Fully Covariant DFR Model0 aTwisted Covariance as a Non Invariant Restriction of the Fully C3 aWe discuss twisted covariance over the noncommutative spacetime algebra generated by the relations [q_theta^mu,q_theta^nu]=i theta^{mu nu}, where the matrix theta is treated as fixed (not a tensor), and we refrain from using the asymptotic Moyal expansion of the twists. We show that the tensor nature of theta is only hidden in the formalism: in particular if theta fulfils the DFR conditions, the twisted Lorentz covariant model of the flat quantum spacetime may be equivalently described in terms of the DFR model, if we agree to discard a huge non invariant set of localisation states; it is only this last step which, if taken as a basic assumption, severely breaks the relativity principle. We also will show that the above mentioned, relativity breaking, ad hoc rejection of localisation states is an independent, unnecessary assumption, as far as some popular approaches to quantum field theory on the quantum Minkowski spacetime are concerned. The above should raise some concerns about speculations on possible observable consequences of arbitrary choices of theta in arbitrarily selected privileged frames.1 aPiacitelli, Gherardo uhttp://hdl.handle.net/1963/360502219nas a2200157 4500008004300000245014000043210006900183260001900252520163800271100002601909700002101935700002801956700002201984700001902006856003602025 2009 en_Ud 00aCharacterization of the time course of changes of the evoked electrical activity in a model of a chemically-induced neuronal plasticity0 aCharacterization of the time course of changes of the evoked ele bBioMed Central3 aBACKGROUND: Neuronal plasticity is initiated by transient elevations of neuronal networks activity leading to changes of synaptic properties and providing the basis for memory and learning 1. An increase of electrical activity can be caused by electrical stimulation 2 or by pharmacological manipulations: elevation of extracellular K+ 3, blockage of inhibitory pathways 4 or by an increase of second messengers intracellular concentrations 5. Neuronal plasticity is mediated by several biochemical pathways leading to the modulation of synaptic strength, density of ionic channels and morphological changes of neuronal arborisation 6. On a time scale of a few minutes, neuronal plasticity is mediated by local protein trafficking 7 while, in order to sustain modifications beyond 2-3 h, changes of gene expression are required 8. FINDINGS: In the present manuscript we analysed the time course of changes of the evoked electrical activity during neuronal plasticity and we correlated it with a transcriptional analysis of the underlying changes of gene expression. Our investigation shows that treatment for 30 min. with the GABAA receptor antagonist gabazine (GabT) causes a potentiation of the evoked electrical activity occurring 2-4 hours after GabT and the concomitant up-regulation of 342 genes. Inhibition of the ERK1/2 pathway reduced but did not abolish the potentiation of the evoked response caused by GabT. In fact not all the genes analysed were blocked by ERK1/2 inhibitors. CONCLUSION: These results are in agreement with the notion that neuronal plasticity is mediated by several distinct pathways working in unison.1 aBroccard, Frederic D.1 aPegoraro, Silvia1 aRuaro, Maria Elisabetta1 aAltafini, Claudio1 aTorre, Vincent uhttp://hdl.handle.net/1963/370601270nas a2200133 4500008004300000245010000043210006900143520080600212100002001018700002401038700002401062700001401086856003601100 2009 en_Ud 00aDecoupling A and B model in open string theory: topological adventures in the world of tadpoles0 aDecoupling A and B model in open string theory topological adven3 aIn this paper we analyze the problem of tadpole cancellation in open topological strings. We prove that the inclusion of unorientable worldsheet diagrams guarantees a consistent decoupling of A and B model for open superstring amplitudes at all genera. This is proven by direct microscopic computation in Super Conformal Field Theory. For the B-model we explicitly calculate one loop amplitudes in terms of analytic Ray-Singer torsions of appropriate vector bundles and obtain that the decoupling corresponds to the cancellation of D-brane and orientifold charges. Local tadpole cancellation on the worldsheet then guarantees the decoupling at all loops. The holomorphic anomaly equations for open topological strings at one loop are also obtained and compared with the results of the Quillen formula.1 aBonelli, Giulio1 aPrudenziati, Andrea1 aTanzini, Alessandro1 aJie, Yang uhttp://hdl.handle.net/1963/363200963nas a2200133 4500008004300000245008100043210006900124260001300193520052900206100001800735700002200753700001800775856003600793 2009 en_Ud 00aInitial value problem of the Whitham equations for the Camassa-Holm equation0 aInitial value problem of the Whitham equations for the CamassaHo bElsevier3 aWe study the Whitham equations for the Camassa-Holm equation. The equations are neither strictly hyperbolic nor genuinely nonlinear. We are interested in the initial value problem of the Whitham equations. When the initial values are given by a step function, the Whitham solution is self-similar. When the initial values are given by a smooth function, the Whitham solution exists within a cusp in the x-t plane. On the boundary of the cusp, the Whitham equation matches the Burgers solution, which exists outside the cusp.1 aGrava, Tamara1 aPierce, Virgil U.1 aTian, Fei-Ran uhttp://hdl.handle.net/1963/342900606nas a2200133 4500008004300000245006900043210006700112260002300179520017500202100002200377700001800399700001900417856003600436 2009 en_Ud 00aA model for the orbifold Chow ring of weighted projective spaces0 amodel for the orbifold Chow ring of weighted projective spaces bTaylor and Francis3 aWe construct an isomorphism of graded Frobenius algebras between the orbifold Chow ring of weighted projective spaces and graded algebras of groups of roots of the unity.1 aBoissiere, Samuel1 aMann, Etienne1 aPerroni, Fabio uhttp://hdl.handle.net/1963/358900530nas a2200121 4500008004300000245006400043210006200107520013300169100001900302700002500321700002600346856003600372 2009 en_Ud 00aA nonlinear theory for shells with slowly varying thickness0 anonlinear theory for shells with slowly varying thickness3 aWe study the Γ-limit of 3d nonlinear elasticity for shells of small, variable thickness, around an arbitrary smooth 2d surface.1 aLewicka, Marta1 aMora, Maria Giovanna1 aPakzad, Mohammad Reza uhttp://hdl.handle.net/1963/263200591nas a2200097 4500008004300000245004400043210004400087520030100131100002500432856003600457 2009 en_Ud 00aTwisted Covariance vs Weyl Quantisation0 aTwisted Covariance vs Weyl Quantisation3 aIn this letter we wish to clarify in which sense the tensor nature of the commutation relations [x^mu,x^nu]=i theta ^{mu nu} underlying Minkowski spacetime quantisation cannot be suppressed even in the twisted approach to Lorentz covariance. We then address the vexata quaestio \\\"why theta\\\"?1 aPiacitelli, Gherardo uhttp://hdl.handle.net/1963/345100454nas a2200109 4500008004300000245012300043210006900166100002100235700002600256700002600282856003600308 2009 en_Ud 00aA variational model for quasistatic crack growth in nonlinear elasticity: some qualitative properties of the solutions0 avariational model for quasistatic crack growth in nonlinear elas1 aDal Maso, Gianni1 aGiacomini, Alessandro1 aPonsiglione, Marcello uhttp://hdl.handle.net/1963/267500501nas a2200157 4500008004100000245009500041210007100136260001000207300001400217490000700231100001800238700001700256700001700273700001600290856003700306 2008 eng d00aFluid–structure interaction problems in free surface flows: Application to boat dynamics0 aFluid–structure interaction problems in free surface flows Appli bWiley a965–9780 v561 aFormaggia, L.1 aMiglio, Edie1 aMola, Andrea1 aParolini, N uhttps://doi.org/10.1002/fld.158301559nas a2200157 4500008004300000245008100043210006900124520105300193100001801246700001801264700002501282700002001307700001901327700001901346856003601365 2008 en_Ud 00aFulde-Ferrell-Larkin-Ovchinnikov pairing in one-dimensional optical lattices0 aFuldeFerrellLarkinOvchinnikov pairing in onedimensional optical 3 aSpin-polarized attractive Fermi gases in one-dimensional (1D) optical lattices are expected to be remarkably good candidates for the observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We model these systems with an attractive Hubbard model with population imbalance. By means of the density-matrix renormalization-group method we compute the pairing correlations as well as the static spin and charge structure factors in the whole range from weak to strong coupling. We demonstrate that pairing correlations exhibit quasi-long range order and oscillations at the wave number expected from FFLO theory. However, we also show by numerically computing the mixed spin-charge static structure factor that charge and spin degrees of freedom appear to be coupled already for small imbalance. We discuss the consequences of this coupling for the observation of the FFLO phase, as well as for the stabilization of the quasi-long range order into long-range order by coupling many identical 1D systems, as in quasi-1D optical lattices.

1 aRizzi, Matteo1 aPolini, Marco1 aCazalilla, Miguel A.1 aBakhtiari, M.R.1 aTosi, Mario P.1 aFazio, Rosario uhttp://hdl.handle.net/1963/269400891nas a2200121 4500008004300000245004600043210004600089520053600135100001600671700002200687700002400709856003600733 2008 en_Ud 00aInstanton counting on Hirzebruch surfaces0 aInstanton counting on Hirzebruch surfaces3 aWe perform a study of the moduli space of framed torsion free sheaves on Hirzebruch surfaces by using localization techniques. After discussing general properties of this moduli space, we classify its fixed points under the appropriate toric action and compute its Poincare\\\' polynomial. From the physical viewpoint, our results provide the partition function of N=4 Vafa-Witten theory on Hirzebruch surfaces, which is relevant in black hole entropy counting problems according to a conjecture due to Ooguri, Strominger and Vafa.1 aBruzzo, Ugo1 aPoghossian, Rubik1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/285200746nas a2200145 4500008004300000245004200043210004200085260002800127520032600155100002000481700001900501700001800520700002600538856003600564 2008 en_Ud 00aNoncommutative families of instantons0 aNoncommutative families of instantons bOxford University Press3 aWe construct $\\\\theta$-deformations of the classical groups SL(2,H) and Sp(2). Coacting on the basic instanton on a noncommutative four-sphere $S^4_\\\\theta$, we construct a noncommutative family of instantons of charge 1. The family is parametrized by the quantum quotient of $SL_\\\\theta(2,H)$ by $Sp_\\\\theta(2)$.1 aLandi, Giovanni1 aPagani, Chiara1 aReina, Cesare1 avan Suijlekom, Walter uhttp://hdl.handle.net/1963/341701700nas a2200121 4500008004300000245004200043210004200085520136200127100002101489700001601510700001601526856003601542 2007 en_Ud 00aAsymptotic variational wave equations0 aAsymptotic variational wave equations3 aWe investigate the equation $(u_t + (f(u))_x)_x = f\\\'\\\'(u) (u_x)^2/2$ where $f(u)$ is a given smooth function. Typically $f(u)= u^2/2$ or $u^3/3$. This equation models unidirectional and weakly nonlinear waves for the variational wave equation $u_{tt} - c(u) (c(u)u_x)_x =0$ which models some liquid crystals with a natural sinusoidal $c$. The equation itself is also the Euler-Lagrange equation of a variational problem. Two natural classes of solutions can be associated with this equation. A conservative solution will preserve its energy in time, while a dissipative weak solution loses energy at the time when singularities appear. Conservative solutions are globally defined, forward and backward in time, and preserve interesting geometric features, such as the Hamiltonian structure. On the other hand, dissipative solutions appear to be more natural from the physical point of view.\\nWe establish the well-posedness of the Cauchy problem within the class of conservative solutions, for initial data having finite energy and assuming that the flux function $f$ has Lipschitz continuous second-order derivative. In the case where $f$ is convex, the Cauchy problem is well-posed also within the class of dissipative solutions. However, when $f$ is not convex, we show that the dissipative solutions do not depend continuously on the initial data.1 aBressan, Alberto1 aPing, Zhang1 aYuxi, Zheng uhttp://hdl.handle.net/1963/218201185nas a2200121 4500008004100000245004600041210004500087260001000132520079900142653006700941100001901008856003601027 2007 en d00aChen-Ruan cohomology of ADE singularities0 aChenRuan cohomology of ADE singularities bSISSA3 aWe study Ruan\'s \\textit{cohomological crepant resolution conjecture} for\r\norbifolds with transversal ADE singularities. In the $A_n$-case we compute both\r\nthe Chen-Ruan cohomology ring $H^*_{\\rm CR}([Y])$ and the quantum corrected\r\ncohomology ring $H^*(Z)(q_1,...,q_n)$. The former is achieved in general, the\r\nlater up to some additional, technical assumptions. We construct an explicit\r\nisomorphism between $H^*_{\\rm CR}([Y])$ and $H^*(Z)(-1)$ in the $A_1$-case,\r\nverifying Ruan\'s conjecture. In the $A_n$-case, the family\r\n$H^*(Z)(q_1,...,q_n)$ is not defined for $q_1=...=q_n=-1$. This implies that\r\nthe conjecture should be slightly modified. We propose a new conjecture in the\r\n$A_n$-case which we prove in the $A_2$-case by constructing an explicit\r\nisomorphism.10aChen-Ruan cohomology, Ruan\'s conjecture, McKay correspondence1 aPerroni, Fabio uhttp://hdl.handle.net/1963/650200671nas a2200133 4500008004100000245006700041210005800108260001000166520026600176100002200442700001900464700001800483856003600501 2007 en d00aThe cohomological crepant resolution conjecture for P(1,3,4,4)0 acohomological crepant resolution conjecture for P1344 bSISSA3 aWe prove the cohomological crepant resolution conjecture of Ruan for the\r\nweighted projective space P(1,3,4,4). To compute the quantum corrected\r\ncohomology ring we combine the results of Coates-Corti-Iritani-Tseng on\r\nP(1,1,1,3) and our previous results.1 aBoissiere, Samuel1 aPerroni, Fabio1 aMann, Etienne uhttp://hdl.handle.net/1963/651300617nas a2200109 4500008004300000245007000043210006900113520025100182100001700433700002100450856003600471 2007 en_Ud 00aGaussian estimates for hypoelliptic operators via optimal control0 aGaussian estimates for hypoelliptic operators via optimal contro3 aWe obtain Gaussian lower bounds for the fundamental solution of a class of hypoelliptic equations, by using repeatedly an invariant Harnack inequality. Our main result is given in terms of the value function of a suitable optimal control problem.1 aBoscain, Ugo1 aPolidoro, Sergio uhttp://hdl.handle.net/1963/199401450nas a2200169 4500008004300000245007300043210006900116520092200185100001801107700001801125700001801143700001901161700001901180700002601199700001901225856003601244 2007 en_Ud 00aLuther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas0 aLutherEmery Phase and AtomicDensity Waves in a Trapped Fermion G3 aThe Luther-Emery liquid is a state of matter that is predicted to occur in one-dimensional systems of interacting fermions and is characterized by a gapless charge spectrum and a gapped spin spectrum. In this Letter we discuss a realization of the Luther-Emery phase in a trapped cold-atom gas. We study by means of the density-matrix renormalization-group technique a two-component atomic Fermi gas with attractive interactions subject to parabolic trapping inside an optical lattice. We demonstrate how this system exhibits compound phases characterized by the coexistence of spin pairing and atomic-density waves. A smooth crossover occurs with increasing magnitude of the atom-atom attraction to a state in which tightly bound spin-singlet dimers occupy the center of the trap. The existence of atomic-density waves could be detected in the elastic contribution to the light-scattering diffraction pattern.

1 aXianlong, Gao1 aRizzi, Matteo1 aPolini, Marco1 aFazio, Rosario1 aTosi, Mario P.1 aCampo, Vivaldo L. Jr.1 aCapelle, Klaus uhttp://hdl.handle.net/1963/205600512nas a2200121 4500008004300000245004900043210004800092520014900140100002500289700001700314700002300331856003600354 2007 en_Ud 00aTime optimal swing-up of the planar pendulum0 aTime optimal swingup of the planar pendulum3 aThis paper presents qualitative and numerical results on the global structure of the time optimal trajectories of the planar pendulum on a cart.1 aBroucke, Mireille E.1 aMason, Paolo1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/186700378nas a2200109 4500008004300000245006600043210006400109100001700173700001900190700002300209856003600232 2006 en_Ud 00aClassification of stable time-optimal controls on 2-manifolds0 aClassification of stable timeoptimal controls on 2manifolds1 aBoscain, Ugo1 aNikolaev, Igor1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/219601156nas a2200121 4500008004300000245007100043210006800114520075900182100002000941700001900961700001800980856003600998 2006 en_Ud 00aA Hopf bundle over a quantum four-sphere from the symplectic group0 aHopf bundle over a quantum foursphere from the symplectic group3 aWe construct a quantum version of the SU(2) Hopf bundle $S^7 \\\\to S^4$. The quantum sphere $S^7_q$ arises from the symplectic group $Sp_q(2)$ and a quantum 4-sphere $S^4_q$ is obtained via a suitable self-adjoint idempotent $p$ whose entries generate the algebra $A(S^4_q)$ of polynomial functions over it. This projection determines a deformation of an (anti-)instanton bundle over the classical sphere $S^4$. We compute the fundamental $K$-homology class of $S^4_q$ and pair it with the class of $p$ in the $K$-theory getting the value -1 for the topological charge. There is a right coaction of $SU_q(2)$ on $S^7_q$ such that the algebra $A(S^7_q)$ is a non trivial quantum principal bundle over $A(S^4_q)$ with structure quantum group $A(SU_q(2))$.1 aLandi, Giovanni1 aPagani, Chiara1 aReina, Cesare uhttp://hdl.handle.net/1963/217900794nas a2200109 4500008004300000245005500043210005500098520044900153100002100602700002500623856003600648 2006 en_Ud 00aInfinite Horizon Noncooperative Differential Games0 aInfinite Horizon Noncooperative Differential Games3 aFor a non-cooperative differential game, the value functions of the various players satisfy a system of Hamilton-Jacobi equations. In the present paper, we consider a class of infinite-horizon games with nonlinear costs exponentially discounted in time. By the analysis of the value\\nfunctions, we establish the existence of Nash equilibrium solutions in feedback form and provide results and counterexamples on their uniqueness and stability.1 aBressan, Alberto1 aPriuli, Fabio Simone uhttp://hdl.handle.net/1963/172000790nas a2200133 4500008004300000245005400043210005200097520038200149100002200531700002100553700002200574700002400596856003600620 2006 en_Ud 00aN=1 superpotentials from multi-instanton calculus0 aN1 superpotentials from multiinstanton calculus3 aIn this paper we compute gaugino and scalar condensates in N = 1 supersymmetric gauge\\ntheories with and without massive adjoint matter, using localization formulae over the multi-instanton moduli space. Furthermore we compute the chiral ring relations among the correlators of the N = 1* theory and check this result against the multi-instanton computation finding agreement.1 aFucito, Francesco1 aMorales, Jose F.1 aPoghossian, Rubik1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/177300676nas a2200109 4500008004300000245007400043210006900117520029900186100002400485700002100509856003600530 2006 en_Ud 00aQuasi-periodic solutions of completely resonant forced wave equations0 aQuasiperiodic solutions of completely resonant forced wave equat3 aWe prove existence of quasi-periodic solutions with two frequencies of completely resonant, periodically forced nonlinear wave equations with periodic spatial boundary conditions. We consider both the cases the forcing frequency is: (Case A) a rational number and (Case B) an irrational number.1 aBerti, Massimiliano1 aProcesi, Michela uhttp://hdl.handle.net/1963/223400711nas a2200109 4500008004300000245009600043210006900139520031700208100002100525700001900546856003600565 2005 en_Ud 00aGel\\\'fand-Zakharevich Systems and Algebraic Integrability: the Volterra Lattice Revisited0 aGelfandZakharevich Systems and Algebraic Integrability the Volte3 aIn this paper we will discuss some features of the bi-Hamiltonian method for solving the Hamilton-Jacobi (H-J) equations by Separation of Variables, and make contact with the theory of Algebraic Complete Integrability and, specifically, with the Veselov-Novikov notion of algebro-geometric (AG) Poisson brackets.1 aFalqui, Gregorio1 aPedroni, Marco uhttp://hdl.handle.net/1963/168900679nas a2200121 4500008004100000245003100041210003100072260000900103520036500112100002100477700002300498856003600521 2005 en d00aHybrid necessary principle0 aHybrid necessary principle bSIAM3 aWe consider a hybrid control system and general optimal control problems for this system. We suppose that the switching strategy imposes restrictions on control sets and we provide necessary conditions for an optimal hybrid trajectory, stating a hybrid necessary principle (HNP). Our result generalizes various necessary principles available in the literature.1 aGaravello, Mauro1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/164100319nas a2200109 4500008004100000245004500041210004400086260001000130653001400140100001900154856003600173 2005 en d00aOrbifold Cohomology of ADE-singularities0 aOrbifold Cohomology of ADEsingularities bSISSA10aOrbifolds1 aPerroni, Fabio uhttp://hdl.handle.net/1963/529800410nas a2200109 4500008004100000245007400041210006900115260003500184100002400219700002100243856003600264 2005 en d00aQuasi-periodic oscillations for wave equations under periodic forcing0 aQuasiperiodic oscillations for wave equations under periodic for bAccademia Nazionale dei Lincei1 aBerti, Massimiliano1 aProcesi, Michela uhttp://hdl.handle.net/1963/458300333nas a2200109 4500008004300000020001800043245004400061210004200105100001700147700002300164856003600187 2005 en_Ud a2 7056 6511 000aA short introduction to optimal control0 ashort introduction to optimal control1 aBoscain, Ugo1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/225700730nas a2200133 4500008004300000245005800043210005400101520032400155100002200479700002000501700001900521700002000540856003600560 2005 en_Ud 00aThe spectral geometry of the equatorial Podles sphere0 aspectral geometry of the equatorial Podles sphere3 aWe propose a slight modification of the properties of a spectral geometry a la Connes, which allows for some of the algebraic relations to be satisfied only modulo compact operators. On the equatorial Podles sphere we construct suq2-equivariant Dirac operator and real structure which satisfy these modified properties.1 aDabrowski, Ludwik1 aLandi, Giovanni1 aPaschke, Mario1 aSitarz, Andrzej uhttp://hdl.handle.net/1963/227501069nas a2200133 4500008004100000245003500041210003500076260001800111520069800129100002800827700002300855700002100878856003600899 2005 en d00aTraffic flow on a road network0 aTraffic flow on a road network bSISSA Library3 aThis paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from conservation of the number of cars,\\ndefined on a road network that is a collection of roads with junctions. The evolution problem is underdetermined at junctions, hence we choose to have some fixed rules for the distribution of traffic plus an optimization criteria for the flux. We prove existence, uniqueness and stability of solutions to the Cauchy problem. Our method is based on wave front tracking approach, see [6], and works also for boundary data and time dependent coefficients of traffic distribution at junctions, so including traffic lights.1 aCoclite, Giuseppe Maria1 aPiccoli, Benedetto1 aGaravello, Mauro uhttp://hdl.handle.net/1963/158401258nas 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/1963/299900797nas a2200121 4500008004300000245007900043210006900122520038600191100002200577700002100599700001900620856003600639 2004 en_Ud 00aA geometric approach to the separability of the Neumann-Rosochatius system0 ageometric approach to the separability of the NeumannRosochatius3 aWe study the separability of the Neumann-Rosochatius system on the n-dimensional sphere using the geometry of bi-Hamiltonian manifolds. Its well-known separation variables are recovered by means of a separability condition relating the Hamiltonian with a suitable (1,1) tensor field on the sphere. This also allows us to iteratively construct the integrals of motion of the system.1 aBartocci, Claudio1 aFalqui, Gregorio1 aPedroni, Marco uhttp://hdl.handle.net/1963/254101206nas 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/1963/304000868nas a2200145 4500008004300000245005900043210005800102260002300160520042200183100001800605700002100623700001900644700002300663856003600686 2003 en_Ud 00aHybrid optimal control: case study of a car with gears0 aHybrid optimal control case study of a car with gears bTaylor and Francis3 aThe purpose of this paper is to show the use of some analytical tools for hybrid optimal control. We illustrate both the hybrid maximum principle and the hybrid necessary principle at work on a simple example of a car with gears. The model is sufficiently rich to generate non-trivial optimization problems and the obtained results match with intuition. Finally, computer simulations confirm the theoretical analysis.1 aD'Apice, Ciro1 aGaravello, Mauro1 aManzo, Rosanna1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/302200998nas a2200121 4500008004100000245005500041210005400096260001800150520063200168100002100800700001900821856003600840 2003 en d00aSeparation of variables for Bi-Hamiltonian systems0 aSeparation of variables for BiHamiltonian systems bSISSA Library3 aWe address the problem of the separation of variables for the Hamilton-Jacobi equation within the theoretical scheme of bi-Hamiltonian geometry. We use the properties of a special class of bi-Hamiltonian manifolds, called omega-N manifolds, to give intrisic tests of separability (and Staeckel separability) for Hamiltonian systems. The separation variables are naturally associated with the geometrical structures of the omega-N manifold itself. We apply these results to bi-Hamiltonian systems of the Gel\\\'fand-Zakharevich type and we give explicit procedures to find the separated coordinates and the separation relations.1 aFalqui, Gregorio1 aPedroni, Marco uhttp://hdl.handle.net/1963/159801403nas a2200133 4500008004300000245004000043210003900083260002400122520102800146100002101174700001901195700001901214856003601233 2003 en_Ud 00aSpace-adiabatic perturbation theory0 aSpaceadiabatic perturbation theory bInternational Press3 aWe study approximate solutions to the Schr\\\\\\\"odinger equation $i\\\\epsi\\\\partial\\\\psi_t(x)/\\\\partial t = H(x,-i\\\\epsi\\\\nabla_x) \\\\psi_t(x)$ with the Hamiltonian given as the Weyl quantization of the symbol $H(q,p)$ taking values in the space of bounded operators on the Hilbert space $\\\\Hi_{\\\\rm f}$ of fast ``internal\\\'\\\' degrees of freedom. By assumption $H(q,p)$ has an isolated energy band. Using a method of Nenciu and Sordoni \\\\cite{NS} we prove that interband transitions are suppressed to any order in $\\\\epsi$. As a consequence, associated to that energy band there exists a subspace of $L^2(\\\\mathbb{R}^d,\\\\Hi _{\\\\rm f})$ almost invariant under the unitary time evolution. We develop a systematic perturbation scheme for the computation of effective Hamiltonians which govern approximately the intraband time evolution. As examples for the general perturbation scheme we discuss the Dirac and Born-Oppenheimer type Hamiltonians and we reconsider also the time-adiabatic theory.1 aPanati, Gianluca1 aSpohn, Herbert1 aTeufel, Stefan uhttp://hdl.handle.net/1963/304100672nas a2200133 4500008004100000245008000041210006900121260001800190520022400208100002100432700002300453700002600476856003600502 2003 en d00aA stability result for nonlinear Neumann problems under boundary variations0 astability result for nonlinear Neumann problems under boundary v bSISSA Library3 aIn this paper we study, in dimension two, the stability of the solutions of some nonlinear elliptic equations with Neumann boundary conditions, under perturbations of the domains in the Hausdorff complementary topology.1 aDal Maso, Gianni1 aEbobisse, Francois1 aPonsiglione, Marcello uhttp://hdl.handle.net/1963/161800399nas a2200109 4500008004100000245007900041210006900120260001800189100002300207700002300230856003600253 2002 en d00aAdmissible Riemann solvers for genuinely nonlinear P-systems of mixed type0 aAdmissible Riemann solvers for genuinely nonlinear Psystems of m bSISSA Library1 aMercier, Jean-Marc1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/149100398nas a2200121 4500008004300000245006200043210006100105260001300166100002100179700001800200700002200218856003600240 2002 en_Ud 00aLinearized elasticity as gamma-limit of finite elasticity0 aLinearized elasticity as gammalimit of finite elasticity bSpringer1 aDal Maso, Gianni1 aNegri, Matteo1 aPercivale, Danilo uhttp://hdl.handle.net/1963/305200365nas a2200109 4500008004100000245006500041210005500106260001800161100002100179700001900200856003600219 2002 en d00aOn a Poisson reduction for Gel\\\'fand-Zakharevich manifolds0 aPoisson reduction for GelfandZakharevich manifolds bSISSA Library1 aFalqui, Gregorio1 aPedroni, Marco uhttp://hdl.handle.net/1963/160201129nas a2200133 4500008004100000245005300041210004600094260001800140520073800158100002000896700002000916700002300936856003600959 2002 en d00aOn the reachability of quantized control systems0 areachability of quantized control systems bSISSA Library3 aIn this paper, we study control systems whose input sets are quantized, i.e., finite or regularly distributed on a mesh. We specifically focus on problems relating to the structure of the reachable set of such systems, which may turn out to be either dense or discrete. We report results on the reachable set of linear quantized systems, and on a particular but interesting class of nonlinear systems, i.e., nonholonomic chained-form systems. For such systems, we provide a complete characterization of the reachable set, and, in case the set is discrete, a computable method to completely and succinctly describe its structure. Implications and open problems in the analysis and synthesis of quantized control systems are addressed.1 aBicchi, Antonio1 aMarigo, Alessia1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/150100307nas a2200097 4500008004100000245005100041210005000092260001000142100002100152856003600173 2002 en d00aSpace-adiabatic Decoupling in Quantum Dynamics0 aSpaceadiabatic Decoupling in Quantum Dynamics bSISSA1 aPanati, Gianluca uhttp://hdl.handle.net/1963/636001131nas a2200133 4500008004100000245006000041210005900101260003000160520071200190100002100902700001900923700001900942856003600961 2002 en d00aSpace-adiabatic perturbation theory in quantum dynamics0 aSpaceadiabatic perturbation theory in quantum dynamics bAmerican Physical Society3 aA systematic perturbation scheme is developed for approximate solutions to the time-dependent Schrödinger equation with a space-adiabatic Hamiltonian. For a particular isolated energy band, the basic approach is to separate kinematics from dynamics. The kinematics is defined through a subspace of the full Hilbert space for which transitions to other band subspaces are suppressed to all orders, and the dynamics operates in that subspace in terms of an effective intraband Hamiltonian. As novel applications, we discuss the Born-Oppenheimer theory to second order and derive for the first time the nonperturbative definition of the g factor of the electron within nonrelativistic quantum electrodynamics.1 aPanati, Gianluca1 aSpohn, Herbert1 aTeufel, Stefan uhttp://hdl.handle.net/1963/598500417nas a2200121 4500008004100000245007300041210006900114260001800183100002100201700001800222700001900240856003600259 2001 en d00aBihamiltonian geometry and separation of variables for Toda lattices0 aBihamiltonian geometry and separation of variables for Toda latt bSISSA Library1 aFalqui, Gregorio1 aMagri, Franco1 aPedroni, Marco uhttp://hdl.handle.net/1963/135400661nas a2200121 4500008004300000245006900043210006900112260001300181520027600194100001600470700001700486856003600503 2001 en_Ud 00aComplex Lagrangian embeddings of moduli spaces of vector bundles0 aComplex Lagrangian embeddings of moduli spaces of vector bundles bElsevier3 aBy means of a Fourier-Mukai transform we embed moduli spaces of stable bundles on an algebraic curve C as isotropic subvarieties of moduli spaces of mu-stable bundles on the Jacobian variety J(C). When g(C)=2 this provides new examples of special Lagrangian submanifolds.1 aBruzzo, Ugo1 aPioli, Fabio uhttp://hdl.handle.net/1963/288500379nas a2200109 4500008004300000245006700043210006700110260001300177100002000190700002300210856003600233 2001 en_Ud 00aControllability for discrete systems with a finite control set0 aControllability for discrete systems with a finite control set bSpringer1 aChitour, Yacine1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/311400362nas a2200121 4500008004100000245004000041210003900081260001800120100002100138700001900159700002600178856003600204 2001 en d00aDieletric breakdown: optimal bounds0 aDieletric breakdown optimal bounds bSISSA Library1 aGarroni, Adriana1 aNesi, Vincenzo1 aPonsiglione, Marcello uhttp://hdl.handle.net/1963/156900345nas 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/1963/150300426nas a2200121 4500008004100000245008500041210006900126260001800195100001600213700002200229700001700251856003600268 2001 en d00aA Fourier transform for sheaves on real tori. I. The equivalence Sky(T)~ Loc (T)0 aFourier transform for sheaves on real tori I The equivalence Sky bSISSA Library1 aBruzzo, Ugo1 aMarelli, Giovanni1 aPioli, Fabio uhttp://hdl.handle.net/1963/152600375nas a2200109 4500008004100000245006200041210006200103260001800165100002300183700002300206856003600229 2001 en d00aGlobal continuous Riemann solver for nonlinear elasticity0 aGlobal continuous Riemann solver for nonlinear elasticity bSISSA Library1 aMercier, Jean-Marc1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/149300380nas a2200109 4500008004100000245006800041210006700109260001800176100001700194700002300211856003600234 2001 en d00aMorse properties for the minimum time function on 2-D manifolds0 aMorse properties for the minimum time function on 2D manifolds bSISSA Library1 aBoscain, Ugo1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/154100360nas a2200109 4500008004100000245005800041210005700099260001800156100001800174700002200192856003600214 2001 en d00aNumerical minimization of the Mumford-Shah functional0 aNumerical minimization of the MumfordShah functional bSISSA Library1 aNegri, Matteo1 aPaolini, Maurizio uhttp://hdl.handle.net/1963/146100436nas a2200121 4500008004300000245008800043210006900131260001300200100001700213700002500230700002300255856003600278 2001 en_Ud 00aUniqueness of classical and nonclassical solutions for nonlinear hyperbolic systems0 aUniqueness of classical and nonclassical solutions for nonlinear bElsevier1 aBaiti, Paolo1 aLeFloch, Philippe G.1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/311300351nas a2200109 4500008004100000245005300041210005300094260001800147100001700165700002300182856003600205 2000 en d00aAbnormal extremals for minimum time on the plane0 aAbnormal extremals for minimum time on the plane bSISSA Library1 aBoscain, Ugo1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/150800454nas a2200133 4500008004100000245007600041210006900117260001800186100002100204700001800225700001900243700002200262856003600284 2000 en d00aA bi-Hamiltonian theory for stationary KDV flows and their separability0 abiHamiltonian theory for stationary KDV flows and their separabi bSISSA Library1 aFalqui, Gregorio1 aMagri, Franco1 aPedroni, Marco1 aZubelli, Jorge P. uhttp://hdl.handle.net/1963/135200863nas 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/1963/146200415nas a2200133 4500008004100000020001800041245005500059210005500114260001300169100002000182700002300202700002000225856003600245 2000 en d a0-08-043658-700aQuantized control systems and discrete nonholonomy0 aQuantized control systems and discrete nonholonomy bElsevier1 aMarigo, Alessia1 aPiccoli, Benedetto1 aBicchi, Antonio uhttp://hdl.handle.net/1963/150201019nas a2200133 4500008004300000245006700043210006700110260000900177520060000186100002000786700002300806700002000829856003600849 2000 en_Ud 00aReachability Analysis for a Class of Quantized Control Systems0 aReachability Analysis for a Class of Quantized Control Systems bIEEE3 aWe study control systems whose input sets are quantized. We specifically focus on problems relating to the structure of the reachable set of such systems, which may turn out to be either dense or discrete. We report on some results on the reachable set of linear quantized systems, and study in detail an interesting class of nonlinear systems, forming the discrete counterpart of driftless nonholonomic continuous systems. For such systems, we provide a complete characterization of the reachable set, and, in the case the set is discrete, a computable method to describe its lattice structure.1 aMarigo, Alessia1 aPiccoli, Benedetto1 aBicchi, Antonio uhttp://hdl.handle.net/1963/351801450nas a2200121 4500008004300000245006400043210006400107260000900171520106500180100002301245700002401268856003601292 2000 en_Ud 00aRegular Synthesis and Sufficiency Conditions for Optimality0 aRegular Synthesis and Sufficiency Conditions for Optimality bSIAM3 aWe propose a definition of \\\"regular synthesis\\\" that is more general than those suggested by other authors such as Boltyanskii and Brunovsky, and an even more general notion of \\\"regular presynthesis.\\\" We give a complete proof of the corresponding sufficiency theorem, a slightly weaker version of which had been stated in an earlier article, with only a rough outline of the proof. We illustrate the strength of our result by showing that the optimal synthesis for the famous Fuller problem satisfies our hypotheses. We also compare our concept of synthesis with the simpler notion of a \\\"family of solutions of the closed-loop equation arising from an optimal feedback law,\\\" and show by means of examples why the latter is inadequate, and why the difficulty cannot be resolved byusing other concepts of solution--such as Filippov solutions, or the limits of sample-and-hold solutions recently proposed as feedback solutions by Clarke, Ledyaev, Subbotin and Sontag -for equations with a non-Lipschitz and possibly discontinuous right-hand side.1 aPiccoli, Benedetto1 aSussmann, Hector J. uhttp://hdl.handle.net/1963/321300449nam a2200121 4500008004300000245008000043210006900123260003400192100002100226700002100247700002300268856003600291 2000 en_Ud 00aWell-posedness of the Cauchy problem for n x n systems of conservation laws0 aWellposedness of the Cauchy problem for n x n systems of conserv bAmerican Mathematical Society1 aBressan, Alberto1 aCrasta, Graziano1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/349500585nas a2200133 4500008004300000245006900043210006700112260002100179520015700200100002100357700001800378700001900396856003600415 1999 en_Ud 00aA bihamiltonian approach to separation of variables in mechanics0 abihamiltonian approach to separation of variables in mechanics bWorld Scientific3 aThis paper is a report on a recent approach to the theory of separability of the Hamilton-Jacobi equations from the viewpoint of bihamiltonian geometry.1 aFalqui, Gregorio1 aMagri, Franco1 aPedroni, Marco uhttp://hdl.handle.net/1963/322201398nas a2200133 4500008004100000245006400041210006000105260001300165520099200178100002101170700001801191700001901209856003601228 1999 en d00aThe method of Poisson pairs in the theory of nonlinear PDEs0 amethod of Poisson pairs in the theory of nonlinear PDEs bSpringer3 aThe aim of these lectures is to show that the methods of classical Hamiltonian mechanics can be profitably used to solve certain classes of nonlinear partial differential equations. The prototype of these equations is the well-known Korteweg-de Vries (KdV) equation.\\nIn these lectures we touch the following subjects:\\ni) the birth and the role of the method of Poisson pairs inside the theory of the KdV equation;\\nii) the theoretical basis of the method of Poisson pairs;\\niii) the Gel\\\'fand-Zakharevich theory of integrable systems on bi-Hamiltonian manifolds;\\niv) the Hamiltonian interpretation of the Sato picture of the KdV flows and of its linearization on an infinite-dimensional Grassmannian manifold.\\nv) the reduction technique(s) and its use to construct classes of solutions;\\nvi) the role of the technique of separation of variables in the study of the reduced systems;\\nvii) some relations intertwining the method of Poisson pairs with the method of Lax pairs.1 aFalqui, Gregorio1 aMagri, Franco1 aPedroni, Marco uhttp://hdl.handle.net/1963/135001145nas a2200145 4500008004300000245007900043210006900122260001300191520067400204100002000878700001700898700002500915700002300940856003600963 1999 en_Ud 00aNonclassical Shocks and the Cauchy Problem for Nonconvex Conservation Laws0 aNonclassical Shocks and the Cauchy Problem for Nonconvex Conserv bElsevier3 aThe Riemann problem for a conservation law with a nonconvex (cubic) flux can be solved in a class of admissible nonclassical solutions that may violate the Oleinik entropy condition but satisfy a single entropy inequality and a kinetic relation. We use such a nonclassical Riemann solver in a front tracking algorithm, and prove that the approximate solutions remain bounded in the total variation norm. The nonclassical shocks induce an increase of the total variation and, therefore, the classical measure of total variation must be modified accordingly. We prove that the front tracking scheme converges strongly to a weak solution satisfying the entropy inequality.1 aAmadori, Debora1 aBaiti, Paolo1 aLeFloch, Philippe G.1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/331200417nas a2200121 4500008004100000245007300041210006900114260001800183100001800201700002100219700001900240856003600259 1999 en d00aA note on fractional KDV hierarchies. II. The bihamiltonian approach0 anote on fractional KDV hierarchies II The bihamiltonian approach bSISSA Library1 aCasati, Paolo1 aFalqui, Gregorio1 aPedroni, Marco uhttp://hdl.handle.net/1963/122000698nas a2200133 4500008004300000245010800043210006900151260001300220520022700233100002400460700002600484700001800510856003600528 1999 en_Ud 00aPerturbation of $\Delta u+u^{(N+2)/(N-2)}=0$, the scalar curvature problem in $R^N$, and related topics0 aPerturbation of Delta uu N2N2 0 the scalar curvature problem in bElsevier3 aSome nonlinear elliptic equations on $R^N$ which arise perturbing the problem with the critical Sobolev exponent are studied. In particular, some results dealing with the scalar curvature problem in $R^N$ are given.

1 aAmbrosetti, Antonio1 aGarcia Azorero, Jesus1 aPeral, Ireneo uhttp://hdl.handle.net/1963/325500367nas a2200109 4500008004100000245006100041210006100102260001800163100001700181700002300198856003600221 1999 en d00aProjection singularities of extremals for planar systems0 aProjection singularities of extremals for planar systems bSISSA Library1 aBoscain, Ugo1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/130400470nas a2200133 4500008004100000245007500041210006900116260003700185100002100222700002000243700001800263700001900281856003600300 1999 en d00aRenormalized solutions of elliptic equations with general measure data0 aRenormalized solutions of elliptic equations with general measur bScuola Normale Superiore di Pisa1 aDal Maso, Gianni1 aMurat, Francois1 aOrsina, Luigi1 aPrignet, Alain uhttp://hdl.handle.net/1963/123601087nas a2200121 4500008004100000245007400041210006900115260001800184520068400202100002100886700002300907856003500930 1998 en d00aA generic classification of time-optimal planar stabilizing feedbacks0 ageneric classification of timeoptimal planar stabilizing feedbac bSISSA Library3 aConsider the problem of stabilization at the origin in minimum time for a planar control system affine with respect to the control. For a family of generic vector fields, a topological equivalence relation on the corresponding time-optimal feedback synthesis was introduced in a previous paper [Dynamics of Continuous, Discrete and Impulsive Systems, 3 (1997), pp. 335--371]. The set of equivalence classes can be put in a one-to-one correspondence with a discrete family of graphs. This provides a classification of the global structure of generic time-optimal stabilizing feedbacks in the plane, analogous to the classification of smooth dynamical systems developed by Peixoto.1 aBressan, Alberto1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/99800347nas a2200109 4500008004100000245005100041210005100092260001800143100001700161700002300178856003600201 1998 en d00aGeometric control approach to synthesis theory0 aGeometric control approach to synthesis theory bSISSA Library1 aBoscain, Ugo1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/127701111nas a2200109 4500008004300000245003600043210003600079260001700115520081000132100002300942856003600965 1998 en_Ud 00aInfinite time regular synthesis0 aInfinite time regular synthesis bEDP Sciences3 aIn this paper we provide a new sufficiency theorem for regular syntheses. The concept of regular synthesis is discussed in [12], where a sufficiency theorem for finite time syntheses is proved. There are interesting examples of optimal syntheses that are very regular, but whose trajectories have time domains not necessarily bounded. The regularity assumptions of the main theorem in [12] are verified by every piecewise smooth feedback control generating extremal trajectories that reach the target in finite time with a finite number of switchings. In the case of this paper the situation is even more complicate, since we admit both trajectories with finite and infinite time. We use weak differentiability assumptions on the synthesis and weak continuity assumptions on the associated value function.1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/351700363nas a2200109 4500008004100000245005800041210005700099260001800156100002100174700002300195856003500218 1997 en d00aStructural stability for time-optimal planar sytheses0 aStructural stability for timeoptimal planar sytheses bSISSA Library1 aBressan, Alberto1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/99700397nas a2200109 4500008004100000245008000041210006900121260001800190100002100208700002300229856003500252 1997 en d00aViscosity solutions and uniquenessfor systems of inhomogeneous balance laws0 aViscosity solutions and uniquenessfor systems of inhomogeneous b bSISSA Library1 aCrasta, Graziano1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/96900558nas a2200109 4500008004100000245004300041210004300084260000900127520025400136100002300390856003500413 1995 en d00aSome control problems for the pendulum0 aSome control problems for the pendulum bIEEE3 aThe aim of this paper is to illustrate some geometric techniques for the study of nonlinear systems. The pendulum on one hand is good for its simplicity, on the other it presents many of the difficulties one can encounter treating nonlinear systems.1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/98200424nas a2200133 4500008004100000245005700041210005600098260001800154100002100172700002200193700001900215700002100234856003500255 1989 en d00aLimits of obstacle problems for the area functional.0 aLimits of obstacle problems for the area functional bSISSA Library1 aDal Maso, Gianni1 aCarriero, Michele1 aLeaci, Antonio1 aPascali, Eduardo uhttp://hdl.handle.net/1963/57700399nas a2200109 4500008004100000245008200041210006900123260001800192100002100210700002300231856003500254 1988 en d00aVariational inequalities for the biharmonic operator with variable obstacles.0 aVariational inequalities for the biharmonic operator with variab bSISSA Library1 aDal Maso, Gianni1 aPaderni, Gabriella uhttp://hdl.handle.net/1963/53100371nas a2200109 4500008004100000245006200041210006100103260001800164100002100182700002300203856003500226 1987 en d00aIntegral representation of some convex local functionals.0 aIntegral representation of some convex local functionals bSISSA Library1 aDal Maso, Gianni1 aPaderni, Gabriella uhttp://hdl.handle.net/1963/497