Mathematical modeling and quantitative study of biological motility (in particular, of motility at microscopic scales) is producing new biophysical insight and is offering opportunities for new discoveries at the level of both fundamental science and technology. These range from the explanation of how complex behavior at the level of a single organism emerges from body architecture, to the understanding of collective phenomena in groups of organisms and tissues, and of how these forms of swarm intelligence can be controlled and harnessed in engineering applications, to the elucidation of processes of fundamental biological relevance at the cellular and sub-cellular level. In this paper, some of the most exciting new developments in the fields of locomotion of unicellular organisms, of soft adhesive locomotion across scales, of the study of pore translocation properties of knotted DNA, of the development of synthetic active solid sheets, of the mechanics of the unjamming transition in dense cell collectives, of the mechanics of cell sheet folding in volvocalean algae, and of the self-propulsion of topological defects in active matter are discussed. For each of these topics, we provide a brief state of the art, an example of recent achievements, and some directions for future research.

10aactive matter10aadhesive locomotion10acell motility10acell sheet folding10aknotted DNA10atopological defects10aunicellular swimmers10aunjamming transition1 aAgostinelli, Daniele1 aCerbino, Roberto1 aDel Alamo, Juan, C1 aDeSimone, Antonio1 aHöhn, Stephanie1 aMicheletti, Cristian1 aNoselli, Giovanni1 aSharon, Eran1 aYeomans, Julia uhttp://dx.doi.org/10.3934/mine.202001102383nas a2200205 4500008004100000022001400041245007400055210006900129300001100198490000800209520174300217653001301960653001801973653002201991653002702013653002002040100002302060700002302083856007102106 2020 eng d a0022-509600aSurface tension controls the onset of gyrification in brain organoids0 aSurface tension controls the onset of gyrification in brain orga a1037450 v1343 aUnderstanding the mechanics of brain embryogenesis can provide insights on pathologies related to brain development, such as lissencephaly, a genetic disease which causes a reduction of the number of cerebral sulci. Recent experiments on brain organoids have confirmed that gyrification, i.e. the formation of the folded structures of the brain, is triggered by the inhomogeneous growth of the peripheral region. However, the rheology of these cellular aggregates and the mechanics of lissencephaly are still matter of debate. In this work, we develop a mathematical model of brain organoids based on the theory of morpho-elasticity. We describe them as non-linear elastic bodies, composed of a disk surrounded by a growing layer called cortex. The external boundary is subjected to a tissue surface tension due the intercellular adhesion forces. We show that the resulting surface energy is relevant at the small length scales of brain organoids and affects the mechanics of cellular aggregates. We perform a linear stability analysis of the radially symmetric configuration and we study the post-buckling behaviour through finite element simulations. We find that the process of gyrification is triggered by the cortex growth and modulated by the competition between two length scales: the radius of the organoid and the capillary length generated by surface tension. We show that a solid model can reproduce the results of the in-vitro experiments. Furthermore, we prove that the lack of brain sulci in lissencephaly is caused by a reduction of the cell stiffness: the softening of the organoid strengthens the role of surface tension, delaying or even inhibiting the onset of a mechanical instability at the free boundary.

10aBuckling10aEmbryogenesis10aMorpho-elasticity10aPost-buckling analysis10aSurface tension1 aRiccobelli, Davide1 aBevilacqua, Giulia uhttp://www.sciencedirect.com/science/article/pii/S002250961930406500478nas a2200133 4500008004100000245006600041210006600107260001600173300001200189490000700201100002300208700001600231856009700247 2019 eng d00aActivation of a muscle as a mapping of stress–strain curves0 aActivation of a muscle as a mapping of stress–strain curves bElsevier BV a37–420 v281 aRiccobelli, Davide1 aAmbrosi, D. uhttps://www.math.sissa.it/publication/activation-muscle-mapping-stress%E2%80%93strain-curves01451nas a2200133 4500008004100000022001400041245008500055210007100140260000800211520101400219100001801233700001901251856004701270 2019 eng d a1432-206400aBenamou–Brenier and duality formulas for the entropic cost on RCD*(K,N) spaces0 aBenamou–Brenier and duality formulas for the entropic cost on RC cApr3 aIn this paper we prove that, within the framework of $\textsf{RCD}^\star(K,N)$ spaces with $N<\infty$, the entropic cost (i.e. the minimal value of the Schrödinger problem) admits:A threefold dynamical variational representation, in the spirit of the Benamou–Brenier formula for the Wasserstein distance; A Hamilton–Jacobi–Bellman dual representation, in line with Bobkov–Gentil–Ledoux and Otto–Villani results on the duality between Hamilton–Jacobi and continuity equation for optimal transport;A Kantorovich-type duality formula, where the Hopf–Lax semigroup is replaced by a suitable `entropic' counterpart.We thus provide a complete and unifying picture of the equivalent variational representations of the Schrödinger problem as well as a perfect parallelism with the analogous formulas for the Wasserstein distance. Riemannian manifolds with Ricci curvature bounded from below are a relevant class of $\textsf{RCD}^*(K,N)$ spaces and our results are new even in this setting.

1 aGigli, Nicola1 aTamanini, Luca uhttps://doi.org/10.1007/s00440-019-00909-102204nas a2200229 4500008004100000022001400041245009200055210006900147300001400216490000800230520153700238653000801775653001801783653000801801653001501809653000801824653002501832653001701857653000801874100002101882856007101903 2019 eng d a0010-465500aBlackNUFFT: Modular customizable black box hybrid parallelization of type 3 NUFFT in 3D0 aBlackNUFFT Modular customizable black box hybrid parallelization a324 - 3350 v2353 aMany applications benefit from an efficient Discrete Fourier Transform (DFT) between arbitrarily spaced points. The Non Uniform Fast Fourier Transform reduces the computational cost of such operation from O(N2) to O(NlogN) exploiting gridding algorithms and a standard Fast Fourier Transform on an equi-spaced grid. The parallelization of the NUFFT of type 3 (between arbitrary points in space and frequency) still poses some challenges: we present a novel and flexible hybrid parallelization in a MPI-multithreaded environment exploiting existing HPC libraries on modern architectures. To ensure the reliability of the developed library, we exploit continuous integration strategies using Travis CI. We present performance analyses to prove the effectiveness of our implementation, possible extensions to the existing library, and an application of NUFFT type 3 to MRI image processing. Program summary Program Title: BlackNUFFT Program Files doi: http://dx.doi.org/10.17632/vxfj6x2p8x.1 Licensing provisions: LGPL Programming language: C++ External routines/libraries: deal.II , FFTW, PFFT Nature of problem: Provide a modular and extensible implementation of a parallel Non Uniform Fast Fourier Transform of type 3. Solution method: Use of hybrid shared distributed memory paradigm to achieve high level of efficiency. We exploit existing HPC library following best practices in scientific computing (as continuous integration via TravisCI) to reach higher complexities and guarantee the accuracy of the solution proposed.

10aC++10aExtensibility10aFFT10aModularity10aMPI10aMRI image processing10aNUFFT type 310aTBB1 aGiuliani, Nicola uhttp://www.sciencedirect.com/science/article/pii/S001046551830353902120nas a2200133 4500008004100000245013800041210006900179520154400248100001701792700001901809700001701828700002101845856012001866 2019 eng d00aA complete data-driven framework for the efficient solution of parametric shape design and optimisation in naval engineering problems0 acomplete datadriven framework for the efficient solution of para3 aIn the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples of the ROM application, in the naval field, can be found in [31, 24]. Mandatory ingredient for the ROM methods is the relation between the high-fidelity solutions and the parameters. Dealing with geometrical parameters, especially in the industrial context, this relation may be unknown and not trivial (simulations over hand morphed geometries) or very complex (high number of parameters or many nested morphing techniques). To overcome these scenarios, we propose in this contribution an efficient and complete data-driven framework involving ROM techniques for shape design and optimization, extending the pipeline presented in [7]. By applying the singular value decomposition (SVD) to the points coordinates defining the hull geometry –- assuming the topology is inaltered by the deformation –-, we are able to compute the optimal space which the deformed geometries belong to, hence using the modal coefficients as the new parameters we can reconstruct the parametric formulation of the domain. Finally the output of interest is approximated using the proper orthogonal decomposition with interpolation technique. To conclude, we apply this framework to a naval shape design problem where the bulbous bow is morphed to reduce the total resistance of the ship advancing in calm water.

1 aDemo, Nicola1 aTezzele, Marco1 aMola, Andrea1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/complete-data-driven-framework-efficient-solution-parametric-shape-design-and00896nas a2200109 4500008004100000245008200041210006900123260001000192520051200202100001800714856005400732 2019 en d00aA continuous dependence result for a dynamic debonding model in dimension one0 acontinuous dependence result for a dynamic debonding model in di bSISSA3 aIn this paper we address the problem of continuous dependence on initial and boundary data for a one-dimensional debonding model describing a thin ﬁlm peeled away from a substrate. The system underlying the process couples the weakly damped wave equation with a Griﬃth’s criterion which rules the evolution of the debonded region. We show that under general convergence assumptions on the data the corresponding solutions converge to the limit one with respect to diﬀerent natural topologies.

1 aRiva, Filippo uhttp://preprints.sissa.it/xmlui/handle/1963/3532900784nas a2200157 4500008004100000022001400041245006600055210006600121520024700187653002800434653002100462653003000483100001800513700002400531856007100555 2019 eng d a0723-086900aDifferential structure associated to axiomatic Sobolev spaces0 aDifferential structure associated to axiomatic Sobolev spaces3 aThe 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/S072308691830097500912nas a2200109 4500008004100000245007800041210006900119520051500188100001900703700002100722856005900743 2019 eng d00aA dynamic model for viscoelastic materials with prescribed growing cracks0 adynamic model for viscoelastic materials with prescribed growing3 aIn this paper we prove the existence of solutions for a class of viscoelastic dynamic systems on time-dependent cracked domains, with possibly degenerate viscosity coefficients. Under stronger regularity assumptions we also show a uniqueness result. Finally, we exhibit an example where the energy-dissipation balance is not satisfied, showing there is an additional dissipation due to the crack growth.

1 aCaponi, Maicol1 aSapio, Francesco uhttp://preprints.sissa.it:8180/xmlui/handle/1963/3533402567nas 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-design01140nas a2200205 4500008004100000022001400041245005800055210005500113520049400168653002800662653002300690653002100713653002500734653002500759100001700784700002400801700001900825700001900844856007100863 2019 eng d a0304-414900aAn entropic interpolation proof of the HWI inequality0 aentropic interpolation proof of the HWI inequality3 aThe HWI inequality is an “interpolation”inequality between the Entropy H, the Fisher information I and the Wasserstein distance W. We present a pathwise proof of the HWI inequality which is obtained through a zero noise limit of the Schrödinger problem. Our approach consists in making rigorous the Otto–Villani heuristics in Otto and Villani (2000) taking advantage of the entropic interpolations, which are regular both in space and time, rather than the displacement ones.

10aEntropic interpolations10aFisher information10aRelative entropy10aSchrödinger problem10aWasserstein distance1 aGentil, Ivan1 aLéonard, Christian1 aRipani, Luigia1 aTamanini, Luca uhttp://www.sciencedirect.com/science/article/pii/S030441491830345400512nas a2200133 4500008004100000245007600041210006900117260002200186490000800208100002300216700001500239700002400254856010000278 2019 eng d00aOn the existence of elastic minimizers for initially stressed materials0 aexistence of elastic minimizers for initially stressed materials bThe Royal Society0 v3771 aRiccobelli, Davide1 aAgosti, A.1 aCiarletta, Pasquale uhttps://www.math.sissa.it/publication/existence-elastic-minimizers-initially-stressed-materials01292nas a2200145 4500008004100000245004900041210004900090300001200139490000700151520086800158100002901026700002101055700002401076856004601100 2019 eng d00aGround state energy of mixture of Bose gases0 aGround state energy of mixture of Bose gases a19500050 v313 aWe consider the asymptotic behavior of a system of multi-component trapped bosons, when the total particle number N becomes large. In the dilute regime, when the interaction potentials have the length scale of order O(N−1), we show that the leading order of the ground state energy is captured correctly by the Gross–Pitaevskii energy functional and that the many-body ground state fully condensates on the Gross–Pitaevskii minimizers. In the mean-field regime, when the interaction length scale is O(1), we are able to verify Bogoliubov’s approximation and obtain the second order expansion of the ground state energy. While such asymptotic results have several precursors in the literature on one-component condensates, the adaptation to the multi-component setting is non-trivial in various respects and the analysis will be presented in detail.

1 aMichelangeli, Alessandro1 aNam, Phan, Thanh1 aOlgiati, Alessandro uhttps://doi.org/10.1142/S0129055X1950005302145nas a2200157 4500008004100000245008600041210006900127260003000196300001500226490000800241520163000249100002001879700002001899700002101919856004701940 2019 eng d00aIsomonodromy deformations at an irregular singularity with coalescing eigenvalues0 aIsomonodromy deformations at an irregular singularity with coale bDuke University Pressc04 a967–11080 v1683 aWe consider an n×n linear system of ODEs with an irregular singularity of Poincar\'e rank 1 at z=∞, holomorphically depending on parameter t within a polydisc in Cn centred at t=0. The eigenvalues of the leading matrix at z=∞ coalesce along a locus Δ contained in the polydisc, passing through t=0. Namely, z=∞ is a resonant irregular singularity for t∈Δ. We analyse the case when the leading matrix remains diagonalisable at Δ. We discuss the existence of fundamental matrix solutions, their asymptotics, Stokes phenomenon and monodromy data as t varies in the polydisc, and their limits for t tending to points of Δ. When the deformation is isomonodromic away from Δ, it is well known that a fundamental matrix solution has singularities at Δ. When the system also has a Fuchsian singularity at z=0, we show under minimal vanishing conditions on the residue matrix at z=0 that isomonodromic deformations can be extended to the whole polydisc, including Δ, in such a way that the fundamental matrix solutions and the constant monodromy data are well defined in the whole polydisc. These data can be computed just by considering the system at fixed t=0. Conversely, if the t-dependent system is isomonodromic in a small domain contained in the polydisc not intersecting Δ, if the entries of the Stokes matrices with indices corresponding to coalescing eigenvalues vanish, then we show that Δ is not a branching locus for the fundamental matrix solutions. The importance of these results for the analytic theory of Frobenius Manifolds is explained. An application to Painlev\'e equations is discussed.

1 aCotti, Giordano1 aDubrovin, Boris1 aGuzzetti, Davide uhttps://doi.org/10.1215/00127094-2018-005901167nas a2200217 4500008004100000022001400041245008300055210006900138300001400207490000700221520048300228653002500711653001800736653002400754653000800778653003100786653002200817100001900839700002000858856007100878 2019 eng d a0294-144900aLocal well-posedness for quasi-linear NLS with large Cauchy data on the circle0 aLocal wellposedness for quasilinear NLS with large Cauchy data o a119 - 1640 v363 aWe prove local in time well-posedness for a large class of quasilinear Hamiltonian, or parity preserving, Schrödinger equations on the circle. After a paralinearization of the equation, we perform several paradifferential changes of coordinates in order to transform the system into a paradifferential one with symbols which, at the positive order, are constant and purely imaginary. This allows to obtain a priori energy estimates on the Sobolev norms of the solutions.

10aDispersive equations10aEnergy method10aLocal wellposedness10aNLS10aPara-differential calculus10aQuasi-linear PDEs1 aFeola, Roberto1 aIandoli, Felice uhttp://www.sciencedirect.com/science/article/pii/S029414491830042800404nas a2200097 4500008004100000245006600041210006600107100002500173700002000198856008800218 2019 eng d00aMinimality of the ball for a model of charged liquid droplets0 aMinimality of the ball for a model of charged liquid droplets1 aMukoseeva, Ekaterina1 aVescovo, Giulia uhttps://www.math.sissa.it/publication/minimality-ball-model-charged-liquid-droplets00513nas a2200157 4500008004100000245008400041210006900125300000800194490000700202100001900209700002200228700002000250700001900270700002400289856004200313 2019 eng d00aN=2 gauge theories on unoriented/open four-manifolds and their AGT counterparts0 aN2 gauge theories on unorientedopen fourmanifolds and their AGT a0400 v071 aBawane, Aditya1 aBenvenuti, Sergio1 aBonelli, Giulio1 aMuteeb, Nouman1 aTanzini, Alessandro uhttp://inspirehep.net/record/1631219/00644nas a2200145 4500008004100000245006000041210005800101260003400159300001400193490000700207520015800214100001800372700001900390856008900409 2019 eng d00aA Note About the Strong Maximum Principle on RCD Spaces0 aNote About the Strong Maximum Principle on RCD Spaces bCanadian Mathematical Society a259–2660 v623 aWe give a direct proof of the strong maximum principle on finite dimensional RCD spaces based on the Laplacian comparison of the squared distance.

1 aGigli, Nicola1 aRigoni, Chiara uhttps://www.math.sissa.it/publication/note-about-strong-maximum-principle-rcd-spaces00424nas a2200121 4500008004100000022001400041245007800055210006900133260000800202100002400210700002100234856004700255 2019 eng d a1432-044400aOn the Number of Flats Tangent to Convex Hypersurfaces in Random Position0 aNumber of Flats Tangent to Convex Hypersurfaces in Random Positi cMar1 aKozhasov, Khazhgali1 aLerario, Antonio uhttps://doi.org/10.1007/s00454-019-00067-002026nas a2200205 4500008004100000022001400041245009500055210006900150300001100219520136500230653002001595653002401615653001701639653002101656100002501677700002701702700002201729700002201751856004701773 2019 eng d a0022-509600aNutations in growing plant shoots: The role of elastic deformations due to gravity loading0 aNutations in growing plant shoots The role of elastic deformatio a1037023 aThe effect of elastic deformations induced by gravity loading on the active circumnutation movements of growing plant shoots is investigated. We consider first a discrete model (a gravitropic spring-pendulum system) and then a continuous rod model which is analyzed both analytically (under the assumption of small deformations) and numerically (in the large deformation regime). We find that, for a choice of material parameters consistent with values reported in the available literature on plant shoots, rods of sufficient length may exhibit lateral oscillations of increasing amplitude, which eventually converge to limit cycles. This behavior strongly suggests the occurrence of a Hopf bifurcation, just as for the gravitropic spring-pendulum system, for which this result is rigorously established. At least in this restricted set of material parameters, our analysis supports a view of Darwin’s circumnutations as a biological analogue to structural systems exhibiting flutter instabilities, i.e., spontaneous oscillations away from equilibrium configurations driven by non-conservative loads. Here, in the context of nutation movements of growing plant shoots, the energy needed to sustain oscillations is continuously supplied to the system by the internal biochemical machinery presiding the capability of plants to maintain a vertical pose.

10aCircumnutations10aFlutter instability10aGravitropism10aHopf bifurcation1 aAgostinelli, Daniele1 aLucantonio, Alessandro1 aNoselli, Giovanni1 aDeSimone, Antonio uhttps://doi.org/10.1016/j.jmps.2019.10370201079nas a2200133 4500008004100000022001400041245009200055210006900147260000800216520062200224100002900846700002300875856004700898 2019 eng d a1661-826200aPoint-Like Perturbed Fractional Laplacians Through Shrinking Potentials of Finite Range0 aPointLike Perturbed Fractional Laplacians Through Shrinking Pote cMay3 aWe construct the rank-one, singular (point-like) perturbations of the d-dimensional fractional Laplacian in the physically meaningful norm-resolvent limit of fractional Schrödinger operators with regular potentials centred around the perturbation point and shrinking to a delta-like shape. We analyse both possible regimes, the resonance-driven and the resonance-independent limit, depending on the power of the fractional Laplacian and the spatial dimension. To this aim, we also qualify the notion of zero-energy resonance for Schrödinger operators formed by a fractional Laplacian and a regular potential.

1 aMichelangeli, Alessandro1 aScandone, Raffaele uhttps://doi.org/10.1007/s11785-019-00927-w00394nas 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-spaces00731nas a2200133 4500008004100000022001400041245007800055210006900133260000800202520029500210100002100505700002400526856004700550 2019 eng d a1615-338300aThe Real Polynomial Eigenvalue Problem is Well Conditioned on the Average0 aReal Polynomial Eigenvalue Problem is Well Conditioned on the Av cMay3 aWe study the average condition number for polynomial eigenvalues of collections of matrices drawn from some random matrix ensembles. In particular, we prove that polynomial eigenvalue problems defined by matrices with random Gaussian entries are very well conditioned on the average.

1 aBeltrán, Carlos1 aKozhasov, Khazhgali uhttps://doi.org/10.1007/s10208-019-09414-201637nas 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/s12215-018-0366-602455nas a2200121 4500008004100000245014200041210006900183520189700252100001902149700001702168700002102185856012702206 2019 eng d00aShape optimization through proper orthogonal decomposition with interpolation and dynamic mode decomposition enhanced by active subspaces0 aShape optimization through proper orthogonal decomposition with 3 aWe propose a numerical pipeline for shape optimization in naval engineering involving two different non-intrusive reduced order method (ROM) techniques. Such methods are proper orthogonal decomposition with interpolation (PODI) and dynamic mode decomposition (DMD). The ROM proposed will be enhanced by active subspaces (AS) as a pre-processing tool that reduce the parameter space dimension and suggest better sampling of the input space. We will focus on geometrical parameters describing the perturbation of a reference bulbous bow through the free form deformation (FFD) technique. The ROM are based on a finite volume method (FV) to simulate the multi-phase incompressible flow around the deformed hulls. In previous works we studied the reduction of the parameter space in naval engineering through AS [38, 10] focusing on different parts of the hull. PODI and DMD have been employed for the study of fast and reliable shape optimization cycles on a bulbous bow in [9]. The novelty of this work is the simultaneous reduction of both the input parameter space and the output fields of interest. In particular AS will be trained computing the total drag resistance of a hull advancing in calm water and its gradients with respect to the input parameters. DMD will improve the performance of each simulation of the campaign using only few snapshots of the solution fields in order to predict the regime state of the system. Finally PODI will interpolate the coefficients of the POD decomposition of the output fields for a fast approximation of all the fields at new untried parameters given by the optimization algorithm. This will result in a non-intrusive data-driven numerical optimization pipeline completely independent with respect to the full order solver used and it can be easily incorporated into existing numerical pipelines, from the reference CAD to the optimal shape.

1 aTezzele, Marco1 aDemo, Nicola1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/shape-optimization-through-proper-orthogonal-decomposition-interpolation-and-dynamic00406nas a2200109 4500008004100000245005200041210004800093100002400141700002000165700002500185856008600210 2019 eng d00aThe sharp quantitative isocapacitary inequality0 asharp quantitative isocapacitary inequality1 aDe Philippis, Guido1 aMarini, Michele1 aMukoseeva, Ekaterina uhttps://www.math.sissa.it/publication/sharp-quantitative-isocapacitary-inequality00668nas a2200109 4500008004100000245006600041210005900107520027500166100002500441700002100466856007100487 2019 eng d00aOn the square distance function from a manifold with boundary0 asquare distance function from a manifold with boundary3 aWe characterize arbitrary codimensional smooth manifolds $\mathcal{M}$ with boundary embedded in $\mathbb{R}^n$ using the square distance function and the signed distance function from $\mathcal{M}$ and from its boundary. The results are localized in an open set.

1 aBellettini, Giovanni1 aElshorbagy, Alaa uhttp://cvgmt.sns.it/media/doc/paper/4260/manif_with_bound_dist.pdf01020nas a2200181 4500008004100000245008500041210006900126260000800195300002100203520034100224653004000565653003600605100002000641700001800661700002100679700002000700856011800720 2019 eng d00aStrong Novikov conjecture for low degree cohomology and exotic group C*-algebras0 aStrong Novikov conjecture for low degree cohomology and exotic g cMay aarXiv:1905.077303 aWe strengthen a result of Hanke–Schick about the strong Novikov conjecture for low degree cohomology by showing that their non-vanishing result for the maximal group $C^*$-algebra even holds for the reduced group $C^*$-algebra. To achieve this we provide a Fell absorption principle for certain exotic crossed product functors.

10aMathematics - K-Theory and Homology10aMathematics - Operator Algebras1 aAntonini, Paolo1 aBuss, Alcides1 aEngel, Alexander1 aSiebenand, Timo uhttps://www.math.sissa.it/publication/strong-novikov-conjecture-low-degree-cohomology-and-exotic-group-c-algebras00814nas a2200121 4500008004100000245006700041210006000108260001000168520042500178100002200603700001900625856004800644 2019 en d00aOn the topological degree of planar maps avoiding normal cones0 atopological degree of planar maps avoiding normal cones bSISSA3 aThe classical Poincaré–Bohl theorem provides the exis-tence of a zero for a function avoiding external rays. When the do-main is convex, the same holds true when avoiding normal cones. We consider here the possibility of dealing with nonconvex sets having in-ward corners or cusps, in which cases the normal cone vanishes. This allows us to deal with situations where the topological degree may be di˙erent from ±1.1 aFonda, Alessandro1 aKlun, Giuliano uhttp://preprints.sissa.it/handle/1963/3533001187nas a2200133 4500008004100000022001400041245009900055210007100154260000800225520074000233100002000973700001300993856004701006 2019 eng d a1432-091600aTwo-Dimensional Yang–Mills Theory on Surfaces with Corners in Batalin–Vilkovisky Formalism0 aTwoDimensional Yang–Mills Theory on Surfaces with Corners in Bat cMar3 aIn this paper we recover the non-perturbative partition function of 2D Yang–Mills theory from the perturbative path integral. To achieve this goal, we study the perturbative path integral quantization for 2D Yang–Mills theory on surfaces with boundaries and corners in the Batalin–Vilkovisky formalism (or, more precisely, in its adaptation to the setting with boundaries, compatible with gluing and cutting–-the BV-BFV formalism). We prove that cutting a surface (e.g. a closed one) into simple enough pieces–-building blocks–-and choosing a convenient gauge-fixing on the pieces, and assembling back the partition function on the surface, one recovers the known non-perturbative answers for 2D Yang–Mills theory.

1 aIraso, Riccardo1 aMnev, P. uhttps://doi.org/10.1007/s00220-019-03392-w00374nas a2200085 4500008004100000245011800041210006900159100002300228856003700251 2019 eng d00aZero modes and low-energy resolvent expansion for three dimensional Schrodinger operators with point interactions0 aZero modes and lowenergy resolvent expansion for three dimension1 aScandone, Raffaele uhttps://arxiv.org/abs/1901.0244900414nas 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/1807.0946701047nas a2200133 4500008004100000245007000041210006900111300001400180490000700194520062800201100002400829700002100853856003900874 2018 eng d00aAnalysis of a Dynamic Peeling Test with Speed-Dependent Toughness0 aAnalysis of a Dynamic Peeling Test with SpeedDependent Toughness a1206-12270 v783 aWe analyse a one-dimensional model of dynamic debonding for a thin film, where the local toughness of the glue between the film and the substrate also depends on the debonding speed. The wave equation on the debonded region is strongly coupled with Griffith's criterion for the evolution of the debonding front. We provide an existence and uniqueness result and find explicitly the solution in some concrete examples. We study the limit of solutions as inertia tends to zero, observing phases of unstable propagation, as well as time discontinuities, even though the toughness diverges at a limiting debonding speed.

1 aLazzaroni, Giuliano1 aNardini, Lorenzo uhttps://doi.org/10.1137/17M114735400579nas a2200145 4500008004100000245010500041210006900146300001600215490000700231100001500238700001600253700001700269700001800286856012900304 2018 eng d00aAn authenticated theoretical modeling of electrified fluid jet in core–shell nanofibers production0 aauthenticated theoretical modeling of electrified fluid jet in c a1791–18110 v471 aRafiei, S.1 aNoroozi, B.1 aHeltai, Luca1 aHaghi, A., K. uhttps://www.math.sissa.it/publication/authenticated-theoretical-modeling-electrified-fluid-jet-core%E2%80%93shell-nanofibers00657nas a2200181 4500008004100000245008300041210007100124653001000195653001000205653001000215653001000225653004000235653003600275100002000311700001500331700001800346856011100364 2018 eng d00aThe Baum–Connes conjecture localised at the unit element of a discrete group0 aBaum–Connes conjecture localised at the unit element of a discre10a19K3510a46L8010a46L8510a58J2210aMathematics - K-Theory and Homology10aMathematics - Operator Algebras1 aAntonini, Paolo1 aAzzali, S.1 aSkandalis, G. uhttps://www.math.sissa.it/publication/baum%E2%80%93connes-conjecture-localised-unit-element-discrete-group00307nas a2200085 4500008004100000245006200041210006200103100001900165856003700184 2018 eng d00aCanonical Surfaces and Hypersurfaces in Abelian Varieties0 aCanonical Surfaces and Hypersurfaces in Abelian Varieties1 aCesarano, Luca uhttps://arxiv.org/abs/1808.0530200682nas a2200121 4500008004100000245007400041210006600115260001000181520028100191100002100472700001900493856004800512 2018 en d00aOn the Cauchy problem for the wave equation on time-dependent domains0 aCauchy problem for the wave equation on timedependent domains bSISSA3 aWe introduce a notion of solution to the wave equation on a suitable class of time-dependent domains and compare it with a previous de nition. We prove an existence result for the solution of the Cauchy problem and present some additional conditions which imply uniqueness.1 aDal Maso, Gianni1 aToader, Rodica uhttp://preprints.sissa.it/handle/1963/3531400586nas a2200133 4500008004100000245010800041210006900149300001200218490000700230100002200237700002200259700002100281856015000302 2018 eng d00aCertified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models0 aCertified Reduced Basis Approximation for the Coupling of Viscou a197-2190 v741 aMartini, Immanuel1 aHaasdonk, Bernard1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85017156114&doi=10.1007%2fs10915-017-0430-y&partnerID=40&md5=023ef0bb95713f4442d1fa374c92a96401398nas a2200121 4500008004100000245014300041210006900184260001000253520092300263100002301186700001901209856004801228 2018 en d00aCharacteristic boundary layers for mixed hyperbolic systems in one space dimension and applications to the Navier-Stokes and MHD equations0 aCharacteristic boundary layers for mixed hyperbolic systems in o bSISSA3 aWe provide a detailed analysis of the boundary layers for mixed hyperbolic-parabolic systems in one space dimension and small amplitude regimes. As an application of our results, we describe the solution of the so-called boundary Riemann problem recovered as the zero viscosity limit of the physical viscous approximation. In particular, we tackle the so called doubly characteristic case, which is considerably more demanding from the technical viewpoint and occurs when the boundary is characteristic for both the mixed hyperbolic-parabolic system and for the hyperbolic system obtained by neglecting the second order terms. Our analysis applies in particular to the compressible Navier-Stokes and MHD equations in Eulerian coordinates, with both positive and null conductivity. In these cases, the doubly characteristic case occurs when the velocity is close to 0. The analysis extends to non-conservative systems.1 aBianchini, Stefano1 aSpinolo, Laura uhttp://preprints.sissa.it/handle/1963/3532501651nas a2200145 4500008004100000245009700041210006900138300001400207490000700221520116600228100001901394700002401413700002201437856004601459 2018 eng d00aCohesive fracture with irreversibility: Quasistatic evolution for a model subject to fatigue0 aCohesive fracture with irreversibility Quasistatic evolution for a1371-14120 v283 aIn this paper we prove the existence of quasistatic evolutions for a cohesive fracture on a prescribed crack surface, in small-strain antiplane elasticity. The main feature of the model is that the density of the energy dissipated in the fracture process depends on the total variation of the amplitude of the jump. Thus, any change in the crack opening entails a loss of energy, until the crack is complete. In particular this implies a fatigue phenomenon, i.e. a complete fracture may be produced by oscillation of small jumps. The first step of the existence proof is the construction of approximate evolutions obtained by solving discrete-time incremental minimum problems. The main difficulty in the passage to the continuous-time limit is that we lack of controls on the variations of the jump of the approximate evolutions. Therefore we resort to a weak formulation where the variation of the jump is replaced by a Young measure. Eventually, after proving the existence in this weak formulation, we improve the result by showing that the Young measure is concentrated on a function and coincides with the variation of the jump of the displacement.

1 aCrismale, Vito1 aLazzaroni, Giuliano1 aOrlando, Gianluca uhttps://doi.org/10.1142/S021820251850037900587nas a2200133 4500008004100000245012400041210006900165260001300234300001400247100001900261700002400280700002100304856012800325 2018 eng d00aCombined parameter and model reduction of cardiovascular problems by means of active subspaces and POD-Galerkin methods0 aCombined parameter and model reduction of cardiovascular problem bSpringer a185–2071 aTezzele, Marco1 aBallarin, Francesco1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/combined-parameter-and-model-reduction-cardiovascular-problems-means-active-subspaces00556nas a2200121 4500008004100000245010600041210006900147260002000216100002200236700002400258700002300282856012900305 2018 eng d00aA Comparison Between Active Strain and Active Stress in Transversely Isotropic Hyperelastic Materials0 aComparison Between Active Strain and Active Stress in Transverse bSpringer Nature1 aGiantesio, Giulia1 aMusesti, Alessandro1 aRiccobelli, Davide uhttps://www.math.sissa.it/publication/comparison-between-active-strain-and-active-stress-transversely-isotropic-hyperelastic01813nas a2200205 4500008004100000245005400041210005400095260001400149300000700163520117300170100002601343700001901369700002001388700002101408700002201429700002101451700002601472700002501498856008401523 2018 eng d00aComputational methods in cardiovascular mechanics0 aComputational methods in cardiovascular mechanics bCRC Press a543 aThe introduction of computational models in cardiovascular sciences has been progressively bringing new and unique tools for the investigation of the physiopathology. Together with the dramatic improvement of imaging and measuring devices on one side, and of computational architectures on the other one, mathematical and numerical models have provided a new, clearly noninvasive, approach for understanding not only basic mechanisms but also patient-specific conditions, and for supporting the design and the development of new therapeutic options. The terminology in silico is, nowadays, commonly accepted for indicating this new source of knowledge added to traditional in vitro and in vivo investigations. The advantages of in silico methodologies are basically the low cost in terms of infrastructures and facilities, the reduced invasiveness and, in general, the intrinsic predictive capabilities based on the use of mathematical models. The disadvantages are generally identified in the distance between the real cases and their virtual counterpart required by the conceptual modeling that can be detrimental for the reliability of numerical simulations.

1 aAuricchio, Ferdinando1 aConti, Michele1 aLefieux, Adrian1 aMorganti, Simone1 aReali, Alessandro1 aRozza, Gianluigi1 aVeneziani, Alessandro1 aLabrosse, Michel, F. uhttps://www.taylorfrancis.com/books/e/9781315280288/chapters/10.1201%2Fb21917-500773nas a2200097 4500008004100000245007100041210006000112520043500172100002000607856004800627 2018 en d00aOn the continuity of the trace operator in GSBV (Ω) and GSBD (Ω)0 acontinuity of the trace operator in GSBV Ω and GSBD Ω3 aIn this paper we present a new result of continuity for the trace operator acting on functions that might jump on a prescribed (n−1)-dimensional set Г, with the only hypothesis of being rectifiable and of finite measure. We also show an application of our result in relation to the variational model of elasticity with cracks, when the associated minimum problems are coupled with Dirichlet and Neumann boundary conditions.1 aTasso, Emanuele uhttp://preprints.sissa.it/handle/1963/3532400540nas a2200145 4500008004100000245007700041210006900118300001400187490000600201100002100207700002100228700002200249700001700271856010600288 2018 eng d00adeal2lkit: A toolkit library for high performance programming in deal.II0 adeal2lkit A toolkit library for high performance programming in a318–3270 v71 aSartori, Alberto1 aGiuliani, Nicola1 aBardelloni, Mauro1 aHeltai, Luca uhttps://www.math.sissa.it/publication/deal2lkit-toolkit-library-high-performance-programming-dealii-000702nas 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-maps00493nas a2200097 4500008004100000245012200041210006900163100001900232700001900251856012500270 2018 eng d00aDimension reduction for thin films with transversally varying prestrain: the oscillatory and the non-oscillatory case0 aDimension reduction for thin films with transversally varying pr1 aLewicka, Marta1 aLučić, Danka uhttps://www.math.sissa.it/publication/dimension-reduction-thin-films-transversally-varying-prestrain-oscillatory-and-non02307nas a2200169 4500008004100000245011900041210006900160260000800229300000700237490000600244520167500250100001901925700002501944700001701969700002101986856013002007 2018 eng d00aDimension reduction in heterogeneous parametric spaces with application to naval engineering shape design problems0 aDimension reduction in heterogeneous parametric spaces with appl cSep a250 v53 aWe present the results of the first application in the naval architecture field of a methodology based on active subspaces properties for parameters space reduction. The physical problem considered is the one of the simulation of the hydrodynamic flow past the hull of a ship advancing in calm water. Such problem is extremely relevant at the preliminary stages of the ship design, when several flow simulations are typically carried out by the engineers to assess the dependence of the hull total resistance on the geometrical parameters of the hull, and others related with flows and hull properties. Given the high number of geometric and physical parameters which might affect the total ship drag, the main idea of this work is to employ the active subspaces properties to identify possible lower dimensional structures in the parameter space. Thus, a fully automated procedure has been implemented to produce several small shape perturbations of an original hull CAD geometry, in order to exploit the resulting shapes to run high fidelity flow simulations with different structural and physical parameters as well, and then collect data for the active subspaces analysis. The free form deformation procedure used to morph the hull shapes, the high fidelity solver based on potential flow theory with fully nonlinear free surface treatment, and the active subspaces analysis tool employed in this work have all been developed and integrated within SISSA mathLab as open source tools. The contribution will also discuss several details of the implementation of such tools, as well as the results of their application to the selected target engineering problem.

1 aTezzele, Marco1 aSalmoiraghi, Filippo1 aMola, Andrea1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/dimension-reduction-heterogeneous-parametric-spaces-application-naval-engineering-shape00444nas a2200133 4500008004100000022001400041245008800055210006900143300001400212490000800226100001900234700002100253856003600274 2018 eng d a0564-616200aDiscriminant circle bundles over local models of Strebel graphs and Boutroux curves0 aDiscriminant circle bundles over local models of Strebel graphs a163–2070 v1971 aBertola, Marco1 aKorotkin, D., A. uhttps://doi.org/10.4213/tmf951300547nas a2200145 4500008004100000245013400041210006900175260004400244300001100288490000700299100001900306700002000325700001700345856003900362 2018 eng d00aA distributed lagrange formulation of the finite element immersed boundary method for fluids interacting with compressible solids0 adistributed lagrange formulation of the finite element immersed aChambSpringer International Publishing a1–210 v161 aBoffi, Daniele1 aGastaldi, Lucia1 aHeltai, Luca uhttps://arxiv.org/abs/1712.02545v101371nas a2200145 4500008004100000245008000041210007100121260002400192300001100216490000700227520088900234100002901123700002401152856004901176 2018 eng d00aEffective non-linear spinor dynamics in a spin-1 Bose–Einstein condensate0 aEffective nonlinear spinor dynamics in a spin1 Bose–Einstein con bIOP Publishingcsep a4052010 v513 aWe derive from first principles the experimentally observed effective dynamics of a spinor Bose gas initially prepared as a Bose–Einstein condensate and then left free to expand ballistically. In spinor condensates, which represent one of the recent frontiers in the manipulation of ultra-cold atoms, particles interact with a two-body spatial interaction and a spin–spin interaction. The effective dynamics is well-known to be governed by a system of coupled semi-linear Schrödinger equations: we recover this system, in the sense of marginals in the limit of infinitely many particles, with a mean-field re-scaling of the many-body Hamiltonian. When the resulting control of the dynamical persistence of condensation is quantified with the parameters of modern observations, we obtain a bound that remains quite accurate for the whole typical duration of the experiment.

1 aMichelangeli, Alessandro1 aOlgiati, Alessandro uhttps://doi.org/10.1088%2F1751-8121%2Faadbc202869nas a2200241 4500008004100000022002200041245016200063210006900225260007400294520193000368653002102298653002802319653003102347653003202378653002602410653003002436653002602466100001702492700001902509700001702528700002102545856006102566 2018 eng d a978-1-880653-87-600aAn efficient shape parametrisation by free-form deformation enhanced by active subspace for hull hydrodynamic ship design problems in open source environment0 aefficient shape parametrisation by freeform deformation enhanced aSapporo, JapanbInternational Society of Offshore and Polar Engineers3 aIn this contribution, we present the results of the application of a parameter space reduction methodology based on active subspaces to the hull hydrodynamic design problem. Several parametric deformations of an initial hull shape are considered to assess the influence of the shape parameters considered on the hull total drag. The hull resistance is typically computed by means of numerical simulations of the hydrodynamic flow past the ship. Given the high number of parameters involved - which might result in a high number of time consuming hydrodynamic simulations - assessing whether the parameters space can be reduced would lead to considerable computational cost reduction. Thus, the main idea of this work is to employ the active subspaces to identify possible lower dimensional structures in the parameter space, or to verify the parameter distribution in the position of the control points. To this end, a fully automated procedure has been implemented to produce several small shape perturbations of an original hull CAD geometry which are then used to carry out high-fidelity flow simulations and collect data for the active subspaces analysis. To achieve full automation of the open source pipeline described, both the free form deformation methodology employed for the hull perturbations and the solver based on unsteady potential flow theory, with fully nonlinear free surface treatment, are directly interfaced with CAD data structures and operate using IGES vendor-neutral file formats as input files. The computational cost of the fluid dynamic simulations is further reduced through the application of dynamic mode decomposition to reconstruct the steady state total drag value given only few initial snapshots of the simulation. The active subspaces analysis is here applied to the geometry of the DTMB-5415 naval combatant hull, which is which is a common benchmark in ship hydrodynamics simulations.10aActive subspaces10aBoundary element method10aDynamic mode decomposition10aFluid structure interaction10aFree form deformation10aFully nonlinear potential10aNumerical towing tank1 aDemo, Nicola1 aTezzele, Marco1 aMola, Andrea1 aRozza, Gianluigi uhttps://www.onepetro.org/conference-paper/ISOPE-I-18-48100590nas a2200133 4500008004100000245012000041210006900161100001900230700001700249700002200266700002400288700002100312856012300333 2018 eng d00aThe Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: from Laminar to Turbulent Flows0 aEffort of Increasing Reynolds Number in ProjectionBased Reduced 1 aHijazi, Saddam1 aAli, Shafqat1 aStabile, Giovanni1 aBallarin, Francesco1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/effort-increasing-reynolds-number-projection-based-reduced-order-methods-laminar00754nas a2200121 4500008004100000245005600041210005500097520037100152100001900523700002200542700002000564856004800584 2018 en d00aEnergy-dissipation balance of a smooth moving crack0 aEnergydissipation balance of a smooth moving crack3 aIn this paper we provide necessary and sufficient conditions in order to guarantee the energy-dissipation balance of a Mode III crack, growing on a prescribed smooth path. Moreover, we characterize the singularity of the displacement near the crack tip, generalizing the result in [S. Nicaise, A.M. Sandig - J. Math. Anal. Appl., 2007] valid for straight fractures.1 aCaponi, Maicol1 aLucardesi, Ilaria1 aTasso, Emanuele uhttp://preprints.sissa.it/handle/1963/3532000945nas a2200109 4500008004100000245010200041210006900143520053000212100002100742700001800763856005400781 2018 en d00aExistence and uniqueness of dynamic evolutions for a one dimensional debonding model with damping0 aExistence and uniqueness of dynamic evolutions for a one dimensi3 aIn this paper we analyse a one-dimensional debonding model for a thin film peeled from a substrate when friction is taken into account. It is described by the weakly damped wave equation whose domain, the debonded region, grows according to a Griffth's criterion. Firstly we prove that the equation admits a unique solution when the evolution of the debonding front is assigned. Finally we provide an existence and uniqueness result for the coupled problem given by the wave equation together with Griffth's criterion.

1 aNardini, Lorenzo1 aRiva, Filippo uhttp://preprints.sissa.it/xmlui/handle/1963/3531900762nas a2200121 4500008004100000245009200041210006900133520032400202100002100526700002600547700001900573856004800592 2018 en d00aExistence for elastodynamic Griffith fracture with a weak maximal dissipation condition0 aExistence for elastodynamic Griffith fracture with a weak maxima3 aWe consider a model of elastodynamics with fracture evolution, based on energy-dissipation balance and a maximal dissipation condition. We prove an existence result in the case of planar elasticity with a free crack path, where the maximal dissipation condition is satisfied among suitably regular competitor cracks.1 aDal Maso, Gianni1 aLarsen, Cristopher J.1 aToader, Rodica uhttp://preprints.sissa.it/handle/1963/3530800904nas a2200097 4500008004100000245010500041210006900146520052400215100001900739856004800758 2018 en d00aExistence of solutions to a phase field model of dynamic fracture with a crack dependent dissipation0 aExistence of solutions to a phase field model of dynamic fractur3 aWe propose a phase-field model of dynamic crack propagation based on the Ambrosio-Tortorelli approximation, which takes in account dissipative effects due to the speed of the crack tips. In particular, adapting the time discretization scheme contained in [Bourdin et al., Int. J. Fracture 168 (2011), 133-143] and [Larsen et al., Math. Models Methods Appl. Sci. 20 (2010), 1021-1048], we show the existence of a dynamic crack evolution satisfying an energy dissipation balance, according to Griffith's criterion.1 aCaponi, Maicol uhttp://preprints.sissa.it/handle/1963/3530700373nas a2200133 4500008004100000245003700041210003600078300000800114490000600122100001700128700001900145700002100164856005400185 2018 eng d00aEZyRB: Easy Reduced Basis method0 aEZyRB Easy Reduced Basis method a6610 v31 aDemo, Nicola1 aTezzele, Marco1 aRozza, Gianluigi uhttps://joss.theoj.org/papers/10.21105/joss.0066100528nas a2200145 4500008004100000020002200041245007200063210006900135260004400204300001200248100002300260700002100283700003000304856004800334 2018 eng d a978-3-319-89800-100aFailure of the Chain Rule in the Non Steady Two-Dimensional Setting0 aFailure of the Chain Rule in the Non Steady TwoDimensional Setti aChambSpringer International Publishing a33–601 aBianchini, Stefano1 aBonicatto, Paolo1 aRassias, Themistocles, M. uhttps://doi.org/10.1007/978-3-319-89800-1_200462nas a2200109 4500008004100000245012400041210006900165260002300234100002200257700002100279856005200300 2018 eng d00aFinite volume POD-Galerkin stabilised reduced order methods for the parametrised incompressible Navier-Stokes equations0 aFinite volume PODGalerkin stabilised reduced order methods for t bElsevier {BV}cfeb1 aStabile, Giovanni1 aRozza, Gianluigi uhttps://doi.org/10.1016/j.compfluid.2018.01.03500442nas a2200121 4500008004100000245005000041210005000091100002600141700002200167700002700189700001900216856008500235 2018 eng d00aFoldable structures made of hydrogel bilayers0 aFoldable structures made of hydrogel bilayers1 aAgostiniani, Virginia1 aDeSimone, Antonio1 aLucantonio, Alessandro1 aLučić, Danka uhttps://www.math.sissa.it/publication/foldable-structures-made-hydrogel-bilayers00971nas a2200145 4500008004100000245008600041210006900127300001100196490000700207520050000214100002900714700002100743700002300764856003800787 2018 eng d00aFractional powers and singular perturbations of quantum differential Hamiltonians0 aFractional powers and singular perturbations of quantum differen a0721060 v593 aWe consider the fractional powers of singular (point-like) perturbations of the Laplacian and the singular perturbations of fractional powers of the Laplacian, and we compare two such constructions focusing on their perturbative structure for resolvents and on the local singularity structure of their domains. In application to the linear and non-linear Schrödinger equations for the corresponding operators, we outline a programme of relevant questions that deserve being investigated.

1 aMichelangeli, Alessandro1 aOttolini, Andrea1 aScandone, Raffaele uhttps://doi.org/10.1063/1.503385601226nas a2200193 4500008004100000022001400041245006800055210006500123300001600188490000800204520054000212653002300752653006700775653004400842100002300886700002900909700002300938856007100961 2018 eng d a0022-123600aOn fractional powers of singular perturbations of the Laplacian0 afractional powers of singular perturbations of the Laplacian a1551 - 16020 v2753 aWe qualify a relevant range of fractional powers of the so-called Hamiltonian of point interaction in three dimensions, namely the singular perturbation of the negative Laplacian with a contact interaction supported at the origin. In particular we provide an explicit control of the domain of such a fractional operator and of its decomposition into regular and singular parts. We also qualify the norms of the resulting singular fractional Sobolev spaces and their mutual control with the corresponding classical Sobolev norms.

10aPoint interactions10aRegular and singular component of a point-interaction operator10aSingular perturbations of the Laplacian1 aGeorgiev, Vladimir1 aMichelangeli, Alessandro1 aScandone, Raffaele uhttp://www.sciencedirect.com/science/article/pii/S002212361830104600893nas a2200121 4500008004100000245004200041210004200083300001200125490000700137520055100144100003000695856004600725 2018 eng d00aFramed symplectic sheaves on surfaces0 aFramed symplectic sheaves on surfaces a18500070 v293 aA framed symplectic sheaf on a smooth projective surface $X$ is a torsion-free sheaf $E$ together with a trivialization on a divisor $D \subset X$ and a morphism $\Lambda^2 E \rightarrow \mathcal{O}_X$ satisfying some additional conditions. We construct a moduli space for framed symplectic sheaves on a surface, and present a detailed study for $X =\mathbb{P}_\mathbb{C}^2$. In this case, the moduli space is irreducible and admits an ADHM-type description and a birational proper map onto the space of framed symplectic ideal instantons.

1 aScalise, Jacopo, Vittorio uhttps://doi.org/10.1142/S0129167X1850007601597nas a2200169 4500008004100000245012200041210006900163260002100232300001200253490000700265520094600272100002501218700002201243700001801265700002101283856012301304 2018 eng d00aFree-form deformation, mesh morphing and reduced-order methods: enablers for efficient aerodynamic shape optimisation0 aFreeform deformation mesh morphing and reducedorder methods enab bTaylor & Francis a233-2470 v323 aIn this work, we provide an integrated pipeline for the model-order reduction of turbulent flows around parametrised geometries in aerodynamics. In particular, free-form deformation is applied for geometry parametrisation, whereas two different reduced-order models based on proper orthogonal decomposition (POD) are employed in order to speed-up the full-order simulations: the first method exploits POD with interpolation, while the second one is based on domain decomposition. For the sampling of the parameter space, we adopt a Greedy strategy coupled with Constrained Centroidal Voronoi Tessellations, in order to guarantee a good compromise between space exploration and exploitation. The proposed framework is tested on an industrially relevant application, i.e. the front-bumper morphing of the DrivAer car model, using the finite-volume method for the full-order resolution of the Reynolds-Averaged Navier–Stokes equations.

1 aSalmoiraghi, Filippo1 aScardigli, Angela1 aTelib, Haysam1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/free-form-deformation-mesh-morphing-and-reduced-order-methods-enablers-efficient00581nas a2200133 4500008004100000245004900041210004600090260000900136300001400145490000600159520020400165100002400369856005400393 2018 eng d00aOn fully real eigenconfigurations of tensors0 afully real eigenconfigurations of tensors bSIAM a339–3470 v23 aWe construct generic real symmetric tensors with only real eigenvectors or, equivalently, real homogeneous polynomials with the maximum possible finite number of critical points on the sphere.

1 aKozhasov, Khazhgali uhttps://epubs.siam.org/doi/pdf/10.1137/17M114590200800nas 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/1963/3532201283nas a2200169 4500008004100000022001400041245010100055210006900156260000800225300000700233490000700240520074700247100002100994700002901015700002301044856004601067 2018 eng d a1420-903900aGlobal, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials0 aGlobal finite energy weak solutions for the NLS with rough timed cMar a460 v693 aWe prove the existence of weak solutions in the space of energy for a class of nonlinear Schrödinger equations in the presence of a external, rough, time-dependent magnetic potential. Under our assumptions, it is not possible to study the problem by means of usual arguments like resolvent techniques or Fourier integral operators, for example. We use a parabolic regularisation, and we solve the approximating Cauchy problem. This is achieved by obtaining suitable smoothing estimates for the dissipative evolution. The total mass and energy bounds allow to extend the solution globally in time. We then infer sufficient compactness properties in order to produce a global-in-time finite energy weak solution to our original problem.

1 aAntonelli, Paolo1 aMichelangeli, Alessandro1 aScandone, Raffaele uhttps://doi.org/10.1007/s00033-018-0938-500570nas a2200121 4500008004100000245011800041210006900159260001700228100002600245700002700271700001900298856013100317 2018 eng d00aHeterogeneous elastic plates with in-plane modulation of the target curvature and applications to thin gel sheets0 aHeterogeneous elastic plates with inplane modulation of the targ bEDP Sciences1 aAgostiniani, Virginia1 aLucantonio, Alessandro1 aLučić, Danka uhttps://www.math.sissa.it/publication/heterogeneous-elastic-plates-plane-modulation-target-curvature-and-applications-thin-gel01340nas a2200109 4500008004100000245005100041210005100092520099000143100002001133700002901153856004801182 2018 en d00aHydrogenoid Spectra with Central Perturbations0 aHydrogenoid Spectra with Central Perturbations3 aThrough the Kreĭn-Višik-Birman extension scheme, unlike the previous classical analysis based on von Neumann's theory, we reproduce the construction and classification of all self-adjoint realisations of two intimately related models: the three-dimensional hydrogenoid-like Hamiltonians with singular perturbation supported at the centre (the nucleus), and the Schördinger operators on the halfline with Coulomb potentials centred at the origin. These two problems are technically equivalent, albeit sometimes treated by their own in the the literature. Based on such scheme, we then recover the formula to determine the eigenvalues of each self-adjoint extension, which are corrections to the non-relativistic hydrogenoid energy levels.We discuss in which respect the Kreĭn-Višik-Birman scheme is somehow more natural in yielding the typical boundary condition of self-adjointness at the centre of the perturbation and in identifying the eigenvalues of each extension.1 aGallone, Matteo1 aMichelangeli, Alessandro uhttp://preprints.sissa.it/handle/1963/3532100612nas 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/1801.0893700840nas a2200133 4500008004100000245007200041210006800113260001000181520040400191100001600595700002900611700001800640856004800658 2018 en d00aOn Krylov solutions to infinite-dimensional inverse linear problems0 aKrylov solutions to infinitedimensional inverse linear problems bSISSA3 aWe discuss, in the context of inverse linear problems in Hilbert space, the notion of the associated infinite-dimensional Krylov subspace and we produce necessary and sufficient conditions for the Krylov-solvability of the considered inverse problem. The presentation is based on theoretical results together with a series of model examples, and it is corroborated by specific numerical experiments.1 aCaruso, Noe1 aMichelangeli, Alessandro1 aNovati, Paolo uhttp://preprints.sissa.it/handle/1963/3532701258nas a2200133 4500008004100000245006300041210006300104260001000167520083800177100002001015700002001035700002101055856004801076 2018 en d00aLocal moduli of semisimple Frobenius coalescent structures0 aLocal moduli of semisimple Frobenius coalescent structures bSISSA3 aThere is a conjectural relation, formulated by the second author, between the enumerative geometry of a wide class of smooth projective varieties and their derived category of coherent sheaves. In particular, there is an increasing interest for an explicit description of certain local invariants, called monodromy data, of semisimple quantum cohomologies in terms of characteristic classes of exceptional collections in the derived categories. Being intentioned to address this problem, which, to our opinion, is still not well understood, we have realized that some issues in the theory of Frobenius manifolds need to be preliminarily clarified, and that an extension of the theory itself is necessary, in view of the fact that quantum cohomologies of certain classes of homogeneous spaces may show a coalescence phenomenon.

1 aCotti, Giordano1 aDubrovin, Boris1 aGuzzetti, Davide uhttp://preprints.sissa.it/handle/1963/3530400583nas a2200145 4500008004100000245008400041210006900125653003700194100002100231700001300252700002100265700002100286700001900307856011100326 2018 eng d00aA Localized Reduced-Order Modeling Approach for PDEs with Bifurcating Solutions0 aLocalized ReducedOrder Modeling Approach for PDEs with Bifurcati10aMathematics - Numerical Analysis1 aHess, Martin, W.1 aAlla, A.1 aQuaini, Annalisa1 aRozza, Gianluigi1 aGunzburger, M. uhttps://www.math.sissa.it/publication/localized-reduced-order-modeling-approach-pdes-bifurcating-solutions00439nas a2200097 4500008004100000245008500041210006900126100001900195700002000214856010700234 2018 eng d00aLong time existence for fully nonlinear NLS with small Cauchy data on the circle0 aLong time existence for fully nonlinear NLS with small Cauchy da1 aRoberto, Feola1 aIandoli, Felice uhttps://www.math.sissa.it/publication/long-time-existence-fully-nonlinear-nls-small-cauchy-data-circle00806nas a2200181 4500008004100000022001400041245009400055210006900149260000800218300001400226490000700240520023200247100002900479700002900508700002300537700001800560856004600578 2018 eng d a1424-066100aLp-Boundedness of Wave Operators for the Three-Dimensional Multi-Centre Point Interaction0 aLpBoundedness of Wave Operators for the ThreeDimensional MultiCe cJan a283–3220 v193 aWe prove that, for arbitrary centres and strengths, the wave operators for three-dimensional Schrödinger operators with multi-centre local point interactions are bounded in Lp(R3)for 1<p<3 and unbounded otherwise.

1 aDell'Antonio, Gianfausto1 aMichelangeli, Alessandro1 aScandone, Raffaele1 aYajima, Kenji uhttps://doi.org/10.1007/s00023-017-0628-400694nas a2200121 4500008004100000245007500041210006900116260001000185520028900195100002100484700001900505856004800524 2018 en d00aA minimization approach to the wave equation on time-dependent domains0 aminimization approach to the wave equation on timedependent doma bSISSA3 aWe prove the existence of weak solutions to the homogeneous wave equation on a suitable class of time-dependent domains. Using the approach suggested by De Giorgi and developed by Serra and Tilli, such solutions are approximated by minimizers of suitable functionals in space-time.1 aDal Maso, Gianni1 aDe Luca, Lucia uhttp://preprints.sissa.it/handle/1963/3531801671nas a2200205 4500008004100000022001400041245009100055210006900146300001100215490000800226520095800234653002501192653005401217653002501271653002901296100002501325700001901350700002501369856007101394 2018 eng d a0021-782400aMinimizing movements for mean curvature flow of droplets with prescribed contact angle0 aMinimizing movements for mean curvature flow of droplets with pr a1 - 580 v1173 aWe study the mean curvature motion of a droplet flowing by mean curvature on a horizontal hyperplane with a possibly nonconstant prescribed contact angle. Using the solutions constructed as a limit of an approximation algorithm of Almgren–Taylor–Wang and Luckhaus–Sturzenhecker, we show the existence of a weak evolution, and its compatibility with a distributional solution. We also prove various comparison results. Résumé Nous étudions le mouvement par courbure moyenne d'une goutte qui glisse par courbure moyenne sur un hyperplan horizontal avec un angle de contact prescrit éventuellement non constant. En utilisant les solutions construites comme limites d'un algorithme d'approximation dû à Almgren, Taylor et Wang et Luckhaus et Sturzenhecker, nous montrons l'existence d'une évolution faible, et sa compatibilité avec une solution au sens des distributions. Nous démontrons également plusieurs résultats de comparaison.

10aCapillary functional10aMean curvature flow with prescribed contact angle10aMinimizing movements10aSets of finite perimeter1 aBellettini, Giovanni1 aNovaga, Matteo1 aKholmatov, Shokhrukh uhttp://www.sciencedirect.com/science/article/pii/S002178241830082501065nas a2200133 4500008004100000245006300041210006300104300001400167490000700181520065400188100002500842700002500867856003900892 2018 eng d00aMinimizing Movements for Mean Curvature Flow of Partitions0 aMinimizing Movements for Mean Curvature Flow of Partitions a4117-41480 v503 aWe prove the existence of a weak global in time mean curvature flow of a bounded partition of space using the method of minimizing movements. The result is extended to the case when suitable driving forces are present. We also prove some consistency results for a minimizing movement solution with smooth and viscosity solutions when the evolution starts from a partition made by a union of bounded sets at a positive distance. In addition, the motion starting from the union of convex sets at a positive distance agrees with the classical mean curvature flow and is stable with respect to the Hausdorff convergence of the initial partitions.

1 aBellettini, Giovanni1 aKholmatov, Shokhrukh uhttps://doi.org/10.1137/17M115929401777nas a2200157 4500008004100000245013300041210006900174260003000243520120300273100001901476700001701495700002101512700001701533700002101550856004801571 2018 eng d00aModel Order Reduction by means of Active Subspaces and Dynamic Mode Decomposition for Parametric Hull Shape Design Hydrodynamics0 aModel Order Reduction by means of Active Subspaces and Dynamic M aTrieste, ItalybIOS Press3 aWe present the results of the application of a parameter space reduction methodology based on active subspaces (AS) to the hull hydrodynamic design problem. Several parametric deformations of an initial hull shape are considered to assess the influence of the shape parameters on the hull wave resistance. Such problem is relevant at the preliminary stages of the ship design, when several flow simulations are carried out by the engineers to establish a certain sensibility with respect to the parameters, which might result in a high number of time consuming hydrodynamic simulations. The main idea of this work is to employ the AS to identify possible lower dimensional structures in the parameter space. The complete pipeline involves the use of free form deformation to parametrize and deform the hull shape, the full order solver based on unsteady potential flow theory with fully nonlinear free surface treatment directly interfaced with CAD, the use of dynamic mode decomposition to reconstruct the final steady state given only few snapshots of the simulation, and the reduction of the parameter space by AS, and shared subspace. Response surface method is used to minimize the total drag.1 aTezzele, Marco1 aDemo, Nicola1 aGadalla, Mahmoud1 aMola, Andrea1 aRozza, Gianluigi uhttp://ebooks.iospress.nl/publication/4927000512nas a2200145 4500008004100000245011100041210006900152300001600221490000700237100002200244700002400266700001600290700002100306856003900327 2018 eng d00aModel Reduction for Parametrized Optimal Control Problems in Environmental Marine Sciences and Engineering0 aModel Reduction for Parametrized Optimal Control Problems in Env aB1055-B10790 v401 aStrazzullo, Maria1 aBallarin, Francesco1 aMosetti, R.1 aRozza, Gianluigi uhttps://doi.org/10.1137/17M115059100454nas a2200133 4500008004100000245005600041210005500097260001600152300001000168490000800178100002300186700002400209856008700233 2018 eng d00aMorpho-elastic model of the tortuous tumour vessels0 aMorphoelastic model of the tortuous tumour vessels bElsevier BV a1–90 v1071 aRiccobelli, Davide1 aCiarletta, Pasquale uhttps://www.math.sissa.it/publication/morpho-elastic-model-tortuous-tumour-vessels00449nas a2200109 4500008004100000245006800041210006800109100001900177700002000196700001600216856010700232 2018 eng d00aNoncommutative Painlevé Equations and Systems of Calogero Type0 aNoncommutative Painlevé Equations and Systems of Calogero Type1 aBertola, Marco1 aCafasso, Mattia1 aRubtsov, V. uhttps://www.math.sissa.it/publication/noncommutative-painlev%C3%A9-equations-and-systems-calogero-type00730nas 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-spaces00508nas a2200145 4500008004100000245008900041210006900130260002300199300001400222490000800236100002200244700002600266700001900292856005100311 2018 eng d00aA novel reduced order model for vortex induced vibrations of long flexible cylinders0 anovel reduced order model for vortex induced vibrations of long bElsevier {BV}cmay a191–2070 v1561 aStabile, Giovanni1 aMatthies, Hermann, G.1 aBorri, Claudio uhttps://doi.org/10.1016/j.oceaneng.2018.02.06401177nas 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/1804.0827100359nas a2200121 4500008004100000245004300041210004200084100001600126700001900142700002000161700001900181856003700200 2018 eng d00aObservables in the equivariant A-model0 aObservables in the equivariant Amodel1 aBonechi, F.1 aCattaneo, A.S.1 aIraso, Riccardo1 aZabzine, Maxim uhttps://arxiv.org/abs/1807.0865901288nas a2200145 4500008004100000245008600041210007000127260004400197490000700241520070800248100001900956700003200975700001801007856011701025 2018 eng d00aPainlevé IV Critical Asymptotics for Orthogonal Polynomials in the Complex Plane0 aPainlevé IV Critical Asymptotics for Orthogonal Polynomials in t bNational Academy of Sciences of Ukraine0 v143 aWe study the asymptotic behaviour of orthogonal polynomials in the complex plane that are associated to a certain normal matrix model. The model depends on a parameter and the asymptotic distribution of the eigenvalues undergoes a transition for a special value of the parameter, where it develops a corner-type singularity. In the double scaling limit near the transition we determine the asymptotic behaviour of the orthogonal polynomials in terms of a solution of the Painlev´e IV equation. We determine the Fredholm determinant associated to such solution and we compute it numerically on the real line, showing also that the corresponding Painlev´e transcendent is pole-free on a semiaxis.

1 aBertola, Marco1 aElias Rebelo, José Gustavo1 aGrava, Tamara uhttps://www.math.sissa.it/publication/painlev%C3%A9-iv-critical-asymptotics-orthogonal-polynomials-complex-plane02205nas a2200253 4500008004100000022001400041245007200055210006900127260001200196490000600208520146100214653002201675653002201697653002501719653002101744653001701765653001601782653002001798653001801818100002501836700002301861700002201884856004501906 2018 eng d a2296-914400aPeristaltic Waves as Optimal Gaits in Metameric Bio-Inspired Robots0 aPeristaltic Waves as Optimal Gaits in Metameric BioInspired Robo c09/20180 v53 a*Peristalsis*, i.e., a motion pattern arising from the propagation of muscle contraction and expansion waves along the body, is a common locomotion strategy for limbless animals. Mimicking peristalsis in bio-inspired robots has attracted considerable attention in the literature. It has recently been observed that maximal velocity in a metameric earthworm-like robot is achieved by actuating the segments using a “phase coordination” principle. This paper shows that, in fact, peristalsis (which requires not only phase coordination, but also that all segments oscillate at same frequency and amplitude) emerges from optimization principles. More precisely, basing our analysis on the assumption of small deformations, we show that peristaltic waves provide the optimal actuation solution in the ideal case of a periodic infinite system, and that this is approximately true, modulo edge effects, for the real, finite length system. Therefore, this paper confirms the effectiveness of mimicking peristalsis in bio-inspired robots, at least in the small-deformation regime. Further research will be required to test the effectiveness of this strategy if large deformations are allowed.

We study the periodic boundary value problem associated with the second order nonlinear equation u''+(λa+(t)−μa−(t))g(u)=0, where g(u) has superlinear growth at zero and sublinear growth at infinity. For λ,μ positive and large, we prove the existence of 3^m−1 positive T-periodic solutions when the weight function a(t) has m positive humps separated by m negative ones (in a T-periodicity interval). As a byproduct of our approach we also provide abundance of positive subharmonic solutions and symbolic dynamics. The proof is based on coincidence degree theory for locally compact operators on open unbounded sets and also applies to Neumann and Dirichlet boundary conditions. Finally, we deal with radially symmetric positive solutions for the Neumann and the Dirichlet problems associated with elliptic PDEs.

1 aBoscaggin, Alberto1 aFeltrin, Guglielmo1 aZanolin, Fabio uhttp://urania.sissa.it/xmlui/handle/1963/3526401233nas a2200133 4500008004100000245007600041210006900117300001200186490000700198520080200205100002301007700002301030856004601053 2018 eng d00aPositive subharmonic solutions to nonlinear ODEs with indefinite weight0 aPositive subharmonic solutions to nonlinear ODEs with indefinite a17500210 v203 aWe prove that the superlinear indefinite equation u″ + a(t)up = 0, where p > 1 and a(t) is a T-periodic sign-changing function satisfying the (sharp) mean value condition ∫0Ta(t)dt < 0, has positive subharmonic solutions of order k for any large integer k, thus providing a further contribution to a problem raised by Butler in its pioneering paper [Rapid oscillation, nonextendability, and the existence of periodic solutions to second order nonlinear ordinary differential equations, J. Differential Equations 22 (1976) 467–477]. The proof, which applies to a larger class of indefinite equations, combines coincidence degree theory (yielding a positive harmonic solution) with the Poincaré–Birkhoff fixed point theorem (giving subharmonic solutions oscillating around it).

1 aBoscaggin, Alberto1 aFeltrin, Guglielmo uhttps://doi.org/10.1142/S021919971750021300509nas a2200133 4500008004100000245012700041210006900168300001400237490000600251100002100257700001700278700002200295856005800317 2018 eng d00aPredicting and Optimizing Microswimmer Performance from the Hydrodynamics of Its Components: The Relevance of Interactions0 aPredicting and Optimizing Microswimmer Performance from the Hydr a410–4240 v51 aGiuliani, Nicola1 aHeltai, Luca1 aDeSimone, Antonio uhttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC6094362/00402nas a2200133 4500008004100000245004500041210004400086300000800130490000600138100001700144700001900161700002100180856006700201 2018 eng d00aPyDMD: Python Dynamic Mode Decomposition0 aPyDMD Python Dynamic Mode Decomposition a5300 v31 aDemo, Nicola1 aTezzele, Marco1 aRozza, Gianluigi uhttps://joss.theoj.org/papers/734e4326edd5062c6e8ee98d03df9e1d01019nas a2200157 4500008004100000022001400041245008700055210006900142260000800211300001400219490000700233520053000240100002400770700002100794856004600815 2018 eng d a1432-146700aOn the Quasistatic Limit of Dynamic Evolutions for a Peeling Test in Dimension One0 aQuasistatic Limit of Dynamic Evolutions for a Peeling Test in Di cFeb a269–3040 v283 aThe aim of this paper is to study the quasistatic limit of a one-dimensional model of dynamic debonding. We start from a dynamic problem that strongly couples the wave equation in a time-dependent domain with Griffith's criterion for the evolution of the domain. Passing to the limit as inertia tends to zero, we find that the limit evolution satisfies a stability condition; however, the activation rule in Griffith's (quasistatic) criterion does not hold in general, thus the limit evolution is not rate-independent.

1 aLazzaroni, Giuliano1 aNardini, Lorenzo uhttps://doi.org/10.1007/s00332-017-9407-000448nas a2200097 4500008004100000245008100041210006900122100002900191700002300220856010700243 2018 eng d00aOn real resonances for the three-dimensional, multi-centre point interaction0 areal resonances for the threedimensional multicentre point inter1 aMichelangeli, Alessandro1 aScandone, Raffaele uhttps://www.math.sissa.it/publication/real-resonances-three-dimensional-multi-centre-point-interaction00849nas a2200157 4500008004100000022001400041245009800055210006900153260000800222300000800230490000700238520036300245100001800608700001900626856004600645 2018 eng d a1432-083500aRecognizing the flat torus among RCD*(0,N) spaces via the study of the first cohomology group0 aRecognizing the flat torus among RCD0N spaces via the study of t cJun a1040 v573 aWe prove that if the dimension of the first cohomology group of a $\mathsf{RCD}^\star (0,N)$ space is $N$, then the space is a flat torus. This generalizes a classical result due to Bochner to the non-smooth setting and also provides a first example where the study of the cohomology groups in such synthetic framework leads to geometric consequences.

1 aGigli, Nicola1 aRigoni, Chiara uhttps://doi.org/10.1007/s00526-018-1377-z00631nas a2200133 4500008004100000245015100041210006900192100002800261700002200289700001700311700002400328700002100352856012400373 2018 eng d00aA Reduced Basis approach for PDEs on parametrized geometries based on the Shifted Boundary Finite Element Method and application to fluid dynamics0 aReduced Basis approach for PDEs on parametrized geometries based1 aKaratzas, Efthymios, N.1 aStabile, Giovanni1 aNouveau, Leo1 aScovazzi, Guglielmo1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduced-basis-approach-pdes-parametrized-geometries-based-shifted-boundary-finite00596nas a2200133 4500008004100000245012100041210006900162100002800231700002200259700001600281700002400297700002100321856012000342 2018 eng d00aA Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries0 aReduced Order Approach for the Embedded Shifted Boundary FEM and1 aKaratzas, Efthymios, N.1 aStabile, Giovanni1 aAtallah, N.1 aScovazzi, Guglielmo1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduced-order-approach-embedded-shifted-boundary-fem-and-heat-exchange-system00517nas 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-procesi01236nas a2200121 4500008004100000245007700041210006900118300001200187490000700199520084400206100001801050856004601068 2018 eng d00aRegularity estimates for scalar conservation laws in one space dimension0 aRegularity estimates for scalar conservation laws in one space d a623-6910 v153 aWe deal with the regularizing effect that, in scalar conservation laws in one space dimension, the nonlinearity of the flux function f has on the entropy solution. More precisely, if the set w : f″(w)≠0 is dense, the regularity of the solution can be expressed in terms of BVΦ spaces, where Φ depends on the nonlinearity of f. If moreover the set w : f″(w) = 0 is finite, under the additional polynomial degeneracy condition at the inflection points, we prove that f′∘ u(t) ∈BV loc(ℝ) for every t > 0 and that this can be improved to SBVloc(ℝ) regularity except an at most countable set of singular times. Finally, we present some examples that show the sharpness of these results and counterexamples to related questions, namely regularity in the kinetic formulation and a property of the fractional BV spaces.

1 aMarconi, Elio uhttps://doi.org/10.1142/S021989161850020000433nas a2200121 4500008004100000245006100041210005800102300001400160490000700174100001800181700001900199856009300218 2018 eng d00aSecond order differentiation formula on RCD(K, N) spaces0 aSecond order differentiation formula on RCDK N spaces a377–3860 v291 aGigli, Nicola1 aTamanini, Luca uhttps://www.math.sissa.it/publication/second-order-differentiation-formula-rcdk-n-spaces00386nas a2200097 4500008004100000245006100041210005700102100001800159700001900177856009200196 2018 eng d00aSecond order differentiation formula on RCD*(K,N) spaces0 aSecond order differentiation formula on RCDKN spaces1 aGigli, Nicola1 aTamanini, Luca uhttps://www.math.sissa.it/publication/second-order-differentiation-formula-rcdkn-spaces01912nas a2200157 4500008004100000245009800041210006900139260003000208520136800238100001701606700001901623700002101642700002201663700002101685856004801706 2018 eng d00aShape Optimization by means of Proper Orthogonal Decomposition and Dynamic Mode Decomposition0 aShape Optimization by means of Proper Orthogonal Decomposition a aTrieste, ItalybIOS Press3 aShape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling, applied to a naval hull design problem. The advantage introduced by this method is that the solution for a specific parameter can be expressed as the combination of few numerical solutions computed at properly chosen parametric points. The reduced model is built using the proper orthogonal decomposition with interpolation (PODI) method. We use the free form deformation (FFD) for an automated perturbation of the shape, and the finite volume method to simulate the multiphase incompressible flow around the deformed hulls. Further computational reduction is done by the dynamic mode decomposition (DMD) technique: from few high dimensional snapshots, the system evolution is reconstructed and the final state of the simulation is faithfully approximated. Finally the global optimization algorithm iterates over the reduced space: the approximated drag and lift coefficients are projected to the hull surface, hence the resistance is evaluated for the new hulls until the convergence to the optimal shape is achieved. We will present the results obtained applying the described procedure to a typical Fincantieri cruise ship.1 aDemo, Nicola1 aTezzele, Marco1 aGustin, Gianluca1 aLavini, Gianpiero1 aRozza, Gianluigi uhttp://ebooks.iospress.nl/publication/4922900543nas a2200133 4500008004100000245007700041210006900118260004700187300001600234490000700250100002300257700002400280856010500304 2018 eng d00aShape transitions in a soft incompressible sphere with residual stresses0 aShape transitions in a soft incompressible sphere with residual bSAGE Publications Sage UK: London, England a1507–15240 v231 aRiccobelli, Davide1 aCiarletta, Pasquale uhttps://www.math.sissa.it/publication/shape-transitions-soft-incompressible-sphere-residual-stresses01292nas a2200157 4500008004100000245006900041210006900110260002100179300001200200490000700212520078900219100002901008700002401037700002301061856005001084 2018 eng d00aSingular Hartree equation in fractional perturbed Sobolev spaces0 aSingular Hartree equation in fractional perturbed Sobolev spaces bTaylor & Francis a558-5880 v253 aWe establish the local and global theory for the Cauchy problem of the singular Hartree equation in three dimensions, that is, the modification of the non-linear Schrödinger equation with Hartree non-linearity, where the linear part is now given by the Hamiltonian of point interaction. The latter is a singular, self-adjoint perturbation of the free Laplacian, modelling a contact interaction at a fixed point. The resulting non-linear equation is the typical effective equation for the dynamics of condensed Bose gases with fixed point-like impurities. We control the local solution theory in the perturbed Sobolev spaces of fractional order between the mass space and the operator domain. We then control the global solution theory both in the mass and in the energy space.

1 aMichelangeli, Alessandro1 aOlgiati, Alessandro1 aScandone, Raffaele uhttps://doi.org/10.1080/14029251.2018.150342300361nas a2200109 4500008004100000245005600041210005300097100002100150700001900171700002400190856003700214 2018 eng d00aOn some rigorous aspects of fragmented condensation0 asome rigorous aspects of fragmented condensation1 aDimonte, Daniele1 aFalconi, Marco1 aOlgiati, Alessandro uhttps://arxiv.org/abs/1809.0358600348nas a2200121 4500008004100000245004500041210004400086300001100130490000700141100001800148700002200166856003800188 2018 eng d00aSpectral triples on the Jiang-Su algebra0 aSpectral triples on the JiangSu algebra a0535070 v591 aBassi, Jacopo1 aDabrowski, Ludwik uhttps://doi.org/10.1063/1.502631101002nas a2200133 4500008004100000245006100041210006000102520056900162100002200731700002100753700001900774700002700793856004800820 2018 en d00aStochastic homogenisation of free-discontinuity problems0 aStochastic homogenisation of freediscontinuity problems3 aIn this paper we study the stochastic homogenisation of free-discontinuity functionals. Assuming stationarity for the random volume and surface integrands, we prove the existence of a homogenised random free-discontinuity functional, which is deterministic in the ergodic case. Moreover, by establishing a connection between the deterministic convergence of the functionals at any fixed realisation and the pointwise Subadditive Ergodic Theorem by Akcoglou and Krengel, we characterise the limit volume and surface integrands in terms of asymptotic cell formulas.1 aCagnetti, Filippo1 aDal Maso, Gianni1 aScardia, Lucia1 aZeppieri, Caterina Ida uhttp://preprints.sissa.it/handle/1963/3530901093nas a2200145 4500008004100000245009200041210006900133300001300202490000800215520058600223100002100809700002300830700002400853856007000877 2018 eng d00aSymplectic invariants for parabolic orbits and cusp singularities of integrable systems0 aSymplectic invariants for parabolic orbits and cusp singularitie a201704240 v3763 aWe discuss normal forms and symplectic invariants of parabolic orbits and cuspidal tori in integrable Hamiltonian systems with two degrees of freedom. Such singularities appear in many integrable systems in geometry and mathematical physics and can be considered as the simplest example of degenerate singularities. We also suggest some new techniques which apparently can be used for studying symplectic invariants of degenerate singularities of more general type. This article is part of the theme issue ‘Finite dimensional integrable systems: new trends and methods’.

1 aBolsinov, Alexey1 aGuglielmi, Lorenzo1 aKudryavtseva, Elena uhttps://royalsocietypublishing.org/doi/abs/10.1098/rsta.2017.042401022nas a2200121 4500008004100000245005500041210005500096520063900151100002100790700002300811700001800834856004800852 2018 en d00aTransmission conditions obtained by homogenisation0 aTransmission conditions obtained by homogenisation3 aWe study the asymptotic behaviour of solutions to variational problems in perforated domains with Neumann boundary conditions. We consider perforations that in the limit concentrate on a smooth manifold. We characterise the limits of the solutions and show that they solve a variational problem with a transmission condition across the manifold. This is expressed through a measure on the manifold, vanishing on sets of capacity zero. Then, we prove that every such measure can be obtained by homogenising suitable perforations. Eventually, we provide an asymptotic formula for this measure by using some auxiliary minimum problems.1 aDal Maso, Gianni1 aFranzina, Giovanni1 aZucco, Davide uhttp://preprints.sissa.it/handle/1963/3531001137nas a2200133 4500008004100000245009100041210006900132260001000201520068100211100001600892700002900908700001800937856004800955 2018 en d00aTruncation and convergence issues for bounded linear inverse problems in Hilbert space0 aTruncation and convergence issues for bounded linear inverse pro bSISSA3 aWe present a general discussion of the main features and issues that (bounded) inverse linear problems in Hilbert space exhibit when the dimension of the space is infinite. This includes the set-up of a consistent notation for inverse problems that are genuinely infinite-dimensional, the analysis of the finite-dimensional truncations, a discussion of the mechanisms why the error or the residual generically fail to vanish in norm, and the identification of practically plausible sufficient conditions for such indicators to be small in some weaker sense. The presentation is based on theoretical results together with a series of model examples and numerical tests.1 aCaruso, Noe1 aMichelangeli, Alessandro1 aNovati, Paolo uhttp://preprints.sissa.it/handle/1963/3532600568nas a2200145 4500008004100000020002200041245008900063210006900152260004400221300001400265100002100279700002700300700002800327856006700355 2018 eng d a978-3-319-91545-600aOn Uniqueness of Weak Solutions to Transport Equation with Non-smooth Velocity Field0 aUniqueness of Weak Solutions to Transport Equation with Nonsmoot aChambSpringer International Publishing a191–2031 aBonicatto, Paolo1 aKlingenberg, Christian1 aWestdickenberg, Michael uhttps://link.springer.com/chapter/10.1007/978-3-319-91545-6_1501054nas a2200109 4500008004100000245007000041210006900111260001000180520068600190100002000876856004800896 2018 en d00aWeak formulation of elastodynamics in domains with growing cracks0 aWeak formulation of elastodynamics in domains with growing crack bSISSA3 aIn this paper we formulate and study the system of elastodynamics on domains with arbitrary growing cracks. This includes homogeneous Neumann conditions on the crack sets and mixed general Dirichlet-Neumann conditions on the boundary. The only assumptions on the crack sets are to be (n − 1)-rectifiable with finite surface measure, and increasing in the sense of set inclusions. In particular they might be dense, hence the weak formulation must fall outside the usual context of Sobolev spaces and Korn's inequality. We prove existence of a solution both for the damped and undamped systems, while in the damped case we are also able to prove uniqueness and an energy balance.1 aTasso, Emanuele uhttp://preprints.sissa.it/handle/1963/3532800574nas a2200133 4500008004100000245012000041210007000161300001200231490000800243100002100251700001700272700001700289856013400306 2018 eng d00aπ-BEM : A flexible parallel implementation for adaptive , geometry aware , and high order boundary element methods0 aπBEM A flexible parallel implementation for adaptive geometry aw a39–580 v1211 aGiuliani, Nicola1 aMola, Andrea1 aHeltai, Luca uhttps://www.math.sissa.it/publication/%CF%80-bem-flexible-parallel-implementation-adaptive-geometry-aware-and-high-order-boundary00999nas a2200121 4500008004100000245009100041210006900132260001000201520057300211100002400784700002100808856004800829 2017 en d00aOn the 1D wave equation in time-dependent domains and the problem of debond initiation0 a1D wave equation in timedependent domains and the problem of deb bSISSA3 aMotivated by a debonding model for a thin film peeled from a substrate, we analyse the one-dimensional wave equation, in a time-dependent domain which is degenerate at the initial time. In the first part of the paper we prove existence for the wave equation when the evolution of the domain is given; in the second part of the paper, the evolution of the domain is unknown and is governed by an energy criterion coupled with the wave equation. Our existence result for such coupled problem is a contribution to the study of crack initiation in dynamic fracture.

1 aLazzaroni, Giuliano1 aNardini, Lorenzo uhttp://preprints.sissa.it/handle/1963/3530201821nas a2200181 4500008004100000024003700041245012000078210006900198520118600267653002301453653002601476100002201502700001901524700002101543700001701564700002101581856003701602 2017 eng d ahttps://arxiv.org/abs/1701.0342400aAdvances in Reduced order modelling for CFD: vortex shedding around a circular cylinder using a POD-Galerkin method0 aAdvances in Reduced order modelling for CFD vortex shedding arou3 aVortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. In this work a Reduced Order Model (ROM) of the incompressible flow around a circular cylinder, built performing a Galerkin projection of the governing equations onto a lower dimensional space is presented. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pressure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) for this purpose the projection of the Governing equations (momentum equation and Poisson equation for pressure) is performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework are presented. The accuracy of the reduced order model is assessed against full order results.

10afinite volume, CFD10aReduced order methods1 aStabile, Giovanni1 aHijazi, Saddam1 aLorenzi, Stefano1 aMola, Andrea1 aRozza, Gianluigi uhttps://arxiv.org/abs/1701.0342402169nas a2200109 4500008004100000245012900041210006900170520172600239100002401965700002201989856004802011 2017 en d00aAlmost global existence of solutions for capillarity-gravity water waves equations with periodic spatial boundary conditions0 aAlmost global existence of solutions for capillaritygravity wate3 aThe goal of this monograph is to prove that any solution of the Cauchy problem for the capillarity-gravity water waves equations, in one space dimension, with periodic, even in space, initial data of small size ϵ, is almost globally defined in time on Sobolev spaces, i.e. it exists on a time interval of length of magnitude ϵ−N for any N, as soon as the initial data are smooth enough, and the gravity-capillarity parameters are taken outside an exceptional subset of zero measure. In contrast to the many results known for these equations on the real line, with decaying Cauchy data, one cannot make use of dispersive properties of the linear flow. Instead, our method is based on a normal forms procedure, in order to eliminate those contributions to the Sobolev energy that are of lower degree of homogeneity in the solution. Since the water waves equations are a quasi-linear system, usual normal forms approaches would face the well known problem of losses of derivatives in the unbounded transformations. In this monograph, to overcome such a difficulty, after a paralinearization of the capillarity-gravity water waves equations, necessary to obtain energy estimates, and thus local existence of the solutions, we first perform several paradifferential reductions of the equations to obtain a diagonal system with constant coefficients symbols, up to smoothing remainders. Then we may start with a normal form procedure where the small divisors are compensated by the previous paradifferential regularization.The reversible structure of the water waves equations, and the fact that we look for solutions even in x, guarantees a key cancellation which prevents the growth of the Sobolev norms of the solutions.1 aBerti, Massimiliano1 aDelort, Jean-Marc uhttp://preprints.sissa.it/handle/1963/3528501295nas a2200133 4500008004100000245006800041210006800109300001200177490000700189520087800196100002001074700002101094856004601115 2017 eng d00aAnalytic geometry of semisimple coalescent Frobenius structures0 aAnalytic geometry of semisimple coalescent Frobenius structures a17400040 v063 aWe present some results of a joint paper with Dubrovin (see references), as exposed at the Workshop “Asymptotic and Computational Aspects of Complex Differential Equations” at the CRM in Pisa, in February 2017. The analytical description of semisimple Frobenius manifolds is extended at semisimple coalescence points, namely points with some coalescing canonical coordinates although the corresponding Frobenius algebra is semisimple. After summarizing and revisiting the theory of the monodromy local invariants of semisimple Frobenius manifolds, as introduced by Dubrovin, it is shown how the definition of monodromy data can be extended also at semisimple coalescence points. Furthermore, a local Isomonodromy theorem at semisimple coalescence points is presented. Some examples of computation are taken from the quantum cohomologies of complex Grassmannians.

1 aCotti, Giordano1 aGuzzetti, Davide uhttps://doi.org/10.1142/S201032631740004400564nas a2200133 4500008004100000245012900041210006900170260008500239300001400324490000700338100002300345700001900368856004300387 2017 eng d00aAn application of coincidence degree theory to cyclic feedback type systems associated with nonlinear differential operators0 aapplication of coincidence degree theory to cyclic feedback type bNicolaus Copernicus University, Juliusz P. Schauder Centre for Nonlinear Studies a683–7260 v501 aFeltrin, Guglielmo1 aZanolin, Fabio uhttps://doi.org/10.12775/TMNA.2017.03801212nas 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-dynamics00875nas a2200193 4500008004100000022001400041245006900055210006600124300001600190490000800206520024700214653002900461653002400490653002300514653003300537100002200570700001800592856007100610 2017 eng d a0022-039600aAn avoiding cones condition for the Poincaré–Birkhoff Theorem0 aavoiding cones condition for the Poincaré–Birkhoff Theorem a1064 - 10840 v2623 aWe provide a geometric assumption which unifies and generalizes the conditions proposed in [11], [12], so to obtain a higher dimensional version of the Poincaré–Birkhoff fixed point Theorem for Poincaré maps of Hamiltonian systems.

10aAvoiding cones condition10aHamiltonian systems10aPeriodic solutions10aPoincaré–Birkhoff theorem1 aFonda, Alessandro1 aGidoni, Paolo uhttp://www.sciencedirect.com/science/article/pii/S002203961630327802454nas a2200169 4500008004100000020002200041024003400063245010200097210006900199250004300268260002500311490000900336520177800345100001802123700002102141856012202162 2017 eng d a978-3-319-65869-8 aDOI 10.1007/978-3-319-65870-400aCertified Reduced Basis Method for Affinely Parametric Isogeometric Analysis NURBS Approximation0 aCerti fied Reduced Basis Method for Affinely Parametric Isogeome aBittencourt, Dumont, Hesthaven. (Eds). aHeildebergbSpringer0 v 1193 aIn this work we apply reduced basis methods for parametric PDEs to an isogeometric formulation based on

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

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

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

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

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

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

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

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

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

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

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

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

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

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

10aCahn–Hilliard equation10aClifford Torus10aLyapunov–Schmidt reduction10aWillmore surface1 aRizzi, Matteo uhttp://www.sciencedirect.com/science/article/pii/S002203961730053001282nas a2200133 4500008004100000245004800041210004800089520088200137100002001019700002301039700001801062700001701080856005101097 2017 en d00aComplex Friedrichs systems and applications0 aComplex Friedrichs systems and applications3 aWe provide a suitable extension of the theory of abstract Friedrichs systems from real Hilbert spaces to the complex Hilbert space setting, which allows for applications to partial differential equations with complex coeffcients. We also provide examples where the involved Hilbert space is not the space of square integrable functions, as it was the case in previous works, but rather its closed subspace or the space Hs(Rd;Cr), for real s. This setting appears to be suitable for particular systems of partial differential equations, such as the Dirac system, the Dirac-Klein-Gordon system, the Dirac-Maxwell system, and the time-harmonic Maxwell system, which are all addressed in the paper. Moreover, for the time-harmonic Maxwell system we also applied a suitable version of the two-field theory with partial coercivity assumption which is developed in the paper.1 aAntonić, Nenad1 aBurazin, Krešimir1 aCrnjac, Ivana1 aErceg, Marko uhttp://urania.sissa.it/xmlui/handle/1963/3527002413nas 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 present a novel quasi-Newton continuation procedure that efficiently solves the system of nonlinear equations arising from the discretization of a phase field model for wetting phenomena. We perform a comparative numerical analysis that shows the improved speed of convergence gained with respect to other numerical schemes. Moreover, we discuss the conditions that, on a theoretical level, guarantee the convergence of this method. At each iterative step, a suitable continuation procedure develops and passes to the nonlinear solver an accurate initial guess. Discretization performs through cell-centered finite differences. The resulting system of equations is solved on a composite grid that uses dynamic mesh refinement and multi-grid techniques. The final code achieves three-dimensional, realistic computer experiments comparable to those produced in laboratory settings. This code offers not only new insights into the phenomenology of super-hydrophobicity, but also serves as a reliable predictive tool for the study of hydrophobic surfaces.

10aMultigrid10aPhase field10aQuasi-Newton10aSuper-hydrophobicity1 aFedeli, Livio uhttp://www.sciencedirect.com/science/article/pii/S002199911730356X00871nas a2200109 4500008004100000245005900041210005600100520051100156100001700667700002900684856004800713 2017 en d00aOn contact interactions realised as Friedrichs systems0 acontact interactions realised as Friedrichs systems3 aWe realise the Hamiltonians of contact interactions in quantum mechanics within the framework of abstract Friedrichs systems. In particular, we show that the construction of the self-adjoint (or even only closed) operators of contact interaction supported at a fixed point can be associated with the construction of the bijective realisations of a suitable pair of abstract Friedrich operators. In this respect, the Hamiltonians of contact interaction provide novel examples of abstract Friedrich systems.1 aErceg, Marko1 aMichelangeli, Alessandro uhttp://preprints.sissa.it/handle/1963/3529801069nas a2200181 4500008004100000022001400041245011100055210006900166300001400235490000800249520044900257653001400706653003100720653002700751100002100778700001700799856007100816 2017 eng d a0362-546X00aCurvature terms in small time heat kernel expansion for a model class of hypoelliptic Hörmander operators0 aCurvature terms in small time heat kernel expansion for a model a118 - 1340 v1643 aWe 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/S0362546X1730229800424nas a2200145 4500008004100000245005000041210004700091260002500138300001400163490000700177100001800184700001700202700001300219856004600232 2017 eng d00aCurvature-adapted remeshing of {CAD} surfaces0 aCurvatureadapted remeshing of CAD surfaces bSpringer Naturecdec a565–5760 v341 aDassi, Franco1 aMola, Andrea1 aSi, Hang uhttps://doi.org/10.1007/s00366-017-0558-200585nas 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/1963/3526901132nas a2200109 4500008004100000245006100041210006000102520076300162100002000925700002900945856004800974 2017 en d00aDiscrete spectra for critical Dirac-Coulomb Hamiltonians0 aDiscrete spectra for critical DiracCoulomb Hamiltonians3 aThe one-particle Dirac Hamiltonian with Coulomb interaction is known to be realised, in a regime of large (critical) couplings, by an infinite multiplicity of distinct self-adjoint operators, including a distinguished physically most natural one. For the latter, Sommerfeld’s celebrated fine structure formula provides the well-known expression for the eigenvalues in the gap of the continuum spectrum. Exploiting our recent general classification of all other self-adjoint realisations, we generalise Sommerfeld’s formula so as to determine the discrete spectrum of all other self-adjoint versions of the Dirac-Coulomb Hamiltonian. Such discrete spectra display naturally a fibred structure, whose bundle covers the whole gap of the continuum spectrum.1 aGallone, Matteo1 aMichelangeli, Alessandro uhttp://preprints.sissa.it/handle/1963/3530001416nas a2200169 4500008004100000020002200041245008400063210007000147260004400217300001400261520082100275100002001096700002301116700002901139700002901168856004901197 2017 eng d a978-3-319-58904-600aDispersive Estimates for Schrödinger Operators with Point Interactions in ℝ30 aDispersive Estimates for Schrödinger Operators with Point Intera aChambSpringer International Publishing a187–1993 aThe study of dispersive properties of Schrödinger operators with point interactions is a fundamental tool for understanding the behavior of many body quantum systems interacting with very short range potential, whose dynamics can be approximated by non linear Schrödinger equations with singular interactions. In this work we proved that, in the case of one point interaction in $\mathbb{R}^3$, the perturbed Laplacian satisfies the same $L^p$−$L^q$ estimates of the free Laplacian in the smaller regime $q \in [2,3)$. These estimates are implied by a recent result concerning the Lpboundedness of the wave operators for the perturbed Laplacian. Our approach, however, is more direct and relatively simple, and could potentially be useful to prove optimal weighted estimates also in the regime $q \geq 3$.

1 aIandoli, Felice1 aScandone, Raffaele1 aMichelangeli, Alessandro1 aDell'Antonio, Gianfausto uhttps://doi.org/10.1007/978-3-319-58904-6_1101090nas a2200121 4500008004100000245009000041210006900131520064600200100002300846700002400869700002400893856005100917 2017 en d00aOn the effect of interactions beyond nearest neighbours on non-convex lattice systems0 aeffect of interactions beyond nearest neighbours on nonconvex la3 aWe analyse the rigidity of non-convex discrete energies where at least nearest and next-to-nearest neighbour interactions are taken into account. Our purpose is to show that interactions beyond nearest neighbours have the role of penalising changes of orientation and, to some extent, they may replace the positive-determinant constraint that is usually required when only nearest neighbours are accounted for. In a discrete to continuum setting, we prove a compactness result for a family of surface-scaled energies and we give bounds on its possible Gamma-limit in terms of interfacial energies that penalise changes of orientation.1 aAlicandro, Roberto1 aLazzaroni, Giuliano1 aPalombaro, Mariapia uhttp://urania.sissa.it/xmlui/handle/1963/3526801139nas a2200157 4500008004100000020002200041245007400063210006900137260004400206300001400250520058600264100002400850700002900874700002900903856004900932 2017 eng d a978-3-319-58904-600aEffective Non-linear Dynamics of Binary Condensates and Open Problems0 aEffective Nonlinear Dynamics of Binary Condensates and Open Prob aChambSpringer International Publishing a239–2563 aWe report on a recent result concerning the effective dynamics for a mixture of Bose-Einstein condensates, a class of systems much studied in physics and receiving a large amount of attention in the recent literature in mathematical physics; for such models, the effective dynamics is described by a coupled system of non-linear Schödinger equations. After reviewing and commenting our proof in the mean-field regime from a previous paper, we collect the main details needed to obtain the rigorous derivation of the effective dynamics in the Gross-Pitaevskii scaling limit.

1 aOlgiati, Alessandro1 aMichelangeli, Alessandro1 aDell'Antonio, Gianfausto uhttps://doi.org/10.1007/978-3-319-58904-6_1400333nas a2200097 4500008004100000245005500041210005400096100002600150700001800176856004100194 2017 eng d00aElliptic diffeomorphisms of symplectic 4-manifolds0 aElliptic diffeomorphisms of symplectic 4manifolds1 aShevchishin, Vsevolod1 aSmirnov, Gleb uhttps://arxiv.org/pdf/1708.01518.pdf00962nas a2200133 4500008004100000245012600041210006900167260002600236300001400262490000700276520044200283100001800725856008500743 2017 eng d00aEnergy release rate and quasi-static evolution via vanishing viscosity in a fracture model depending on the crack opening0 aEnergy release rate and quasistatic evolution via vanishing visc bEDP Sciencesc05/2017 a791–8260 v233 aIn the setting of planar linearized elasticity, we study a fracture model depending on the crack opening. Assuming that the crack path is known a priori and sufficiently smooth, we prove that the energy release rate is well defined. Then, we consider the problem of quasi-static evolution for our model. Thanks to a vanishing viscosity approach, we show the existence of such an evolution satisfying a weak Griffith’s criterion.

1 aAlmi, Stefano uhttps://www.esaim-cocv.org/component/article?access=doi&doi=10.1051/cocv/201601401281nas a2200121 4500008004100000245008200041210006900123520085300192100002001045700001701065700002901082856004801111 2017 en d00aFriedrichs systems in a Hilbert space framework: solvability and multiplicity0 aFriedrichs systems in a Hilbert space framework solvability and 3 aThe Friedrichs (1958) theory of positive symmetric systems of first order partial differential equations encompasses many standard equations of mathematical physics, irrespective of their type. This theory was recast in an abstract Hilbert space setting by Ern, Guermond and Caplain (2007), and by Antonić and Burazin (2010). In this work we make a further step, presenting a purely operator-theoretic description of abstract Friedrichs systems, and proving that any pair of abstract Friedrichs operators admits bijective extensions with a signed boundary map. Moreover, we provide suffcient and necessary conditions for existence of infinitely many such pairs of spaces, and by the universal operator extension theory (Grubb, 1968) we get a complete identification of all such pairs, which we illustrate on two concrete one-dimensional examples.1 aAntonić, Nenad1 aErceg, Marko1 aMichelangeli, Alessandro uhttp://preprints.sissa.it/handle/1963/3528001393nas a2200145 4500008004100000245005300041210005100094260001000145520095500155100002201110700002101132700001901153700002701172856004801199 2017 en d00aGamma-Convergence of Free-discontinuity problems0 aGammaConvergence of Freediscontinuity problems bSISSA3 aWe study the Gamma-convergence of sequences of free-discontinuity functionals depending on vector-valued functions u which can be discontinuous across hypersurfaces whose shape and location are not known a priori. The main novelty of our result is that we work under very general assumptions on the integrands which, in particular, are not required to be periodic in the space variable. Further, we consider the case of surface integrands which are not bounded from below by the amplitude of the jump of u. We obtain three main results: compactness with respect to Gamma-convergence, representation of the Gamma-limit in an integral form and identification of its integrands, and homogenisation formulas without periodicity assumptions. In particular, the classical case of periodic homogenisation follows as a by-product of our analysis. Moreover, our result covers also the case of stochastic homogenisation, as we will show in a forthcoming paper.1 aCagnetti, Filippo1 aDal Maso, Gianni1 aScardia, Lucia1 aZeppieri, Caterina Ida uhttp://preprints.sissa.it/handle/1963/3527601348nas a2200241 4500008004100000022001400041245010800055210006900163300001200232490000800244520055100252653000800803653002500811653002900836653002900865653001800894653003000912100002300942700002000965700002600985700002401011856007101035 2017 eng d a0393-044000aGauge theories on compact toric surfaces, conformal field theories and equivariant Donaldson invariants0 aGauge theories on compact toric surfaces conformal field theorie a40 - 500 v1183 aWe show that equivariant Donaldson polynomials of compact toric surfaces can be calculated as residues of suitable combinations of Virasoro conformal blocks, by building on AGT correspondence between $\mathcal{N}=2$ supersymmetric gauge theories and two-dimensional conformal field theory. Talk presented by A.T. at the conference Interactions between Geometry and Physics — in honor of Ugo Bruzzo’s 60th birthday 17–22 August 2015, Guarujá, São Paulo, Brazil, mostly based on Bawane et al. (0000) and Bershtein et al. (0000).

10aAGT10aDonaldson invariants10aEquivariant localization10aExact partition function10aSupersymmetry10aVirasoro conformal blocks1 aBershtein, Mikhail1 aBonelli, Giulio1 aRonzani, Massimiliano1 aTanzini, Alessandro uhttp://www.sciencedirect.com/science/article/pii/S039304401730016501320nas a2200133 4500008004100000245008300041210006900124300001400193490000700207520089100214100001801105700002201123856004101145 2017 eng d00aOn the genesis of directional friction through bristle-like mediating elements0 agenesis of directional friction through bristlelike mediating el a1023-10460 v233 aWe propose an explanation of the genesis of directional dry friction, as emergent property of the oscillations produced in a bristle-like mediating element by the interaction with microscale fluctuations on the surface. Mathematically, we extend a convergence result by Mielke, for Prandtl–Tomlinson-like systems, considering also non-homothetic scalings of a wiggly potential. This allows us to apply the result to some simple mechanical models, that exemplify the interaction of a bristle with a surface having small fluctuations. We find that the resulting friction is the product of two factors: a geometric one, depending on the bristle angle and on the fluctuation profile, and a energetic one, proportional to the normal force exchanged between the bristle-like element and the surface. Finally, we apply our result to discuss the with the nap/against the nap asymmetry.

1 aGidoni, Paolo1 aDeSimone, Antonio uhttps://doi.org/10.1051/cocv/201703001385nas a2200145 4500008004100000022001400041245009300055210006900148260000800217300001400225490000800239520092700247100001901174856004601193 2017 eng d a1618-189100aGlobally stable quasistatic evolution for strain gradient plasticity coupled with damage0 aGlobally stable quasistatic evolution for strain gradient plasti cApr a641–6850 v1963 aWe consider evolutions for a material model which couples scalar damage with strain gradient plasticity, in small strain assumptions. For strain gradient plasticity, we follow the Gurtin–Anand formulation (J Mech Phys Solids 53:1624–1649, 2005). The aim of the present model is to account for different phenomena: On the one hand, the elastic stiffness reduces and the plastic yield surface shrinks due to material's degradation, on the other hand the dislocation density affects the damage growth. The main result of this paper is the existence of a globally stable quasistatic evolution (in the so-called energetic formulation). Furthermore, we study the limit model as the strain gradient terms tend to zero. Under stronger regularity assumptions, we show that the evolutions converge to the ones for the coupled elastoplastic damage model studied in Crismale (ESAIM Control Optim Calc Var 22:883-912, 2016).

1 aCrismale, Vito uhttps://doi.org/10.1007/s10231-016-0590-701947nas a2200145 4500008004100000245007100041210006800112260002100180300001200201490000700213520147800220100002901698700002401727856005001751 2017 eng d00aGross-Pitaevskii non-linear dynamics for pseudo-spinor condensates0 aGrossPitaevskii nonlinear dynamics for pseudospinor condensates bTaylor & Francis a426-4640 v243 aWe derive the equations for the non-linear effective dynamics of a so called pseudo-spinor Bose-Einstein condensate, which emerges from the linear many-body Schrödinger equation at the leading order in the number of particles. The considered system is a three-dimensional diluted gas of identical bosons with spin, possibly confined in space, and coupled with an external time-dependent magnetic field; particles also interact among themselves through a short-scale repulsive interaction. The limit of infinitely many particles is monitored in the physically relevant Gross-Pitaevskii scaling. In our main theorem, if at time zero the system is in a phase of complete condensation (at the level of the reduced one-body marginal) and with energy per particle fixed by the Gross-Pitaevskii functional, then such conditions persist also at later times, with the one-body orbital of the condensate evolving according to a system of non-linear cubic Schrödinger equations coupled among themselves through linear (Rabi) terms. The proof relies on an adaptation to the spinor setting of Pickl’s projection counting method developed for the scalar case. Quantitative rates of convergence are available, but not made explicit because evidently non-optimal. In order to substantiate the formalism and the assumptions made in the main theorem, in an introductory section we review the mathematical formalisation of modern typical experiments with pseudo-spinor condensates.

1 aMichelangeli, Alessandro1 aOlgiati, Alessandro uhttps://doi.org/10.1080/14029251.2017.134634800440nas a2200157 4500008004100000022001400041245004400055210004400099260000800143300000800151490000700159100002500166700002400191700002100215856004600236 2017 eng d a1432-083500aHomotopically invisible singular curves0 aHomotopically invisible singular curves cJul a1050 v561 aAgrachev, Andrei, A.1 aBoarotto, Francesco1 aLerario, Antonio uhttps://doi.org/10.1007/s00526-017-1203-z00569nas a2200133 4500008004100000245009900041210006900140260003400209300001400243490000700257100002400264700002100288856012600309 2017 eng d00aHomotopy properties of horizontal path spaces and a theorem of Serre in subriemannian geometry0 aHomotopy properties of horizontal path spaces and a theorem of S bInternational Press of Boston a269–3010 v251 aBoarotto, Francesco1 aLerario, Antonio uhttps://www.math.sissa.it/publication/homotopy-properties-horizontal-path-spaces-and-theorem-serre-subriemannian-geometry00713nas a2200157 4500008004100000245004400041210004000085520026500125653001200390653001000402653004000412100002000452700002400472700001800496856004100514 2017 eng d00aThe injectivity radius of Lie manifolds0 ainjectivity radius of Lie manifolds3 aWe prove in a direct, geometric way that for any compatible Riemannian metric on a Lie manifold the injectivity radius is positive

10a(58J40)10a53C2110aMathematics - Differential Geometry1 aAntonini, Paolo1 aDe Philippis, Guido1 aGigli, Nicola uhttps://arxiv.org/pdf/1707.07595.pdf01112nas a2200157 4500008004100000245007700041210006900118260003100187300001400218490000700232520054200239100002200781700001800803700002400821856010900845 2017 eng d00aIntegrability of dominated decompositions on three-dimensional manifolds0 aIntegrability of dominated decompositions on threedimensional ma bCambridge University Press a606–6200 v373 a

We investigate the integrability of two-dimensional invariant distributions (tangent sub-bundles) which arise naturally in the context of dynamical systems on 3-manifolds. In particular, we prove unique integrability of dynamically dominated and volume-dominated Lipschitz continuous invariant decompositions as well as distributions with some other regularity conditions.

Inspired by the work of Molino, we show that the integrability obstruction for transitive Lie algebroids can be made to vanish by adding extra dimensions. In particular, we prove that the Weinstein groupoid of a non-integrable transitive and abelian Lie algebroid, is the quotient of a finite dimensional Lie groupoid. Two constructions as such are given: First, explaining the counterexample to integrability given by Almeida and Molino, we see that it can be generalized to the construction of an "Almeida-Molino" integrable lift when the base manifold is simply connected. On the other hand, we notice that the classical de Rham isomorphism provides a universal integrable algebroid. Using it we construct a "de Rham" integrable lift for any given transitive Abelian Lie algebroid.

10a14F4010a58H0510aMathematics - Differential Geometry1 aAndroulidakis, I.1 aAntonini, Paolo uhttps://arxiv.org/pdf/1707.04855.pdf00428nas a2200109 4500008004100000245009800041210007000139490003400209100001900243700002000262856003600282 2017 eng d00aThe Kontsevich matrix integral: convergence to the Painlevé hierarchy and Stokes' phenomenon0 aKontsevich matrix integral convergence to the Painlevé hierarchy0 vDOI 10.1007/s00220-017-2856-31 aBertola, Marco1 aCafasso, Mattia uhttp://arxiv.org/abs/1603.0642000742nas a2200121 4500008004100000245006300041210006000104520033800164100002000502700002900522700002100551856004800572 2017 en d00aKrein-Visik-Birman self-adjoint extension theory revisited0 aKreinVisikBirman selfadjoint extension theory revisited3 aThe core results of the so-called KreIn-Visik-Birman theory of self-adjoint extensions of semi-bounded symmetric operators are reproduced, both in their original and in a more modern formulation, within a comprehensive discussion that includes missing details, elucidative steps, and intermediate results of independent interest.1 aGallone, Matteo1 aMichelangeli, Alessandro1 aOttolini, Andrea uhttp://preprints.sissa.it/handle/1963/3528600384nas a2200109 4500008004100000245006300041210006000104100002300164700002100187700001800208856004800226 2017 en d00aA Lagrangian approach for scalar multi-d conservation laws0 aLagrangian approach for scalar multid conservation laws1 aBianchini, Stefano1 aBonicatto, Paolo1 aMarconi, Elio uhttp://preprints.sissa.it/handle/1963/3529001119nas a2200157 4500008004100000245006600041210006600107260004500173300001400218490000700232520056500239100002300804700002100827700001800848856009500866 2017 eng d00aLagrangian representations for linear and nonlinear transport0 aLagrangian representations for linear and nonlinear transport bPeoples' Friendship University of Russia a418–4360 v633 aIn this note we present a unifying approach for two classes of first order partial differential equations: we introduce the notion of Lagrangian representation in the settings of continuity equation and scalar conservation laws. This yields, on the one hand, the uniqueness of weak solutions to transport equation driven by a two dimensional BV nearly incompressible vector field. On the other hand, it is proved that the entropy dissipation measure for scalar conservation laws in one space dimension is concentrated on countably many Lipschitz curves.

1 aBianchini, Stefano1 aBonicatto, Paolo1 aMarconi, Elio uhttp://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=cmfd&paperid=327&option_lang=eng01179nas a2200121 4500008004100000245009100041210006900132300001200201490000700213520077600220100002000996856004101016 2017 eng d00aLimit of viscous dynamic processes in delamination as the viscosity and inertia vanish0 aLimit of viscous dynamic processes in delamination as the viscos a593-6250 v233 aWe introduce a model of dynamic evolution of a delaminated visco-elastic body with viscous adhesive. We prove the existence of solutions of the corresponding system of PDEs and then study the behavior of such solutions when the data of the problem vary slowly. We prove that a rescaled version of the dynamic evolutions converge to a “local” quasistatic evolution, which is an evolution satisfying an energy inequality and a momentum balance at all times. In the one-dimensional case we give a more detailed description of the limit evolution and we show that it behaves in a very similar way to the limit of the solutions of the dynamic model in [T. Roubicek, SIAM J. Math. Anal. 45 (2013) 101–126], where no viscosity in the adhesive is taken into account.

1 aScala, Riccardo uhttps://doi.org/10.1051/cocv/201600601226nas a2200097 4500008004100000245006100041210006100102520089500163100001901058856005101077 2017 en d00aLinear hyperbolic systems in domains with growing cracks0 aLinear hyperbolic systems in domains with growing cracks3 aWe consider the hyperbolic system $\ddot u-{\rm div}\,(\mathbb A\nabla u)=f$ in the time varying cracked domain $\Omega\setminus\Gamma_t$, where the set $\Omega\subset\mathbb R^d$ is open, bounded, and with Lipschitz boundary, the cracks $\Gamma_t$, $t\in[0,T]$, are closed subsets of $\overline\Omega$, increasing with respect to inclusion, and $u(t):\Omega\setminus\Gamma_t\to\mathbb R^d$ for every $t\in[0,T]$. We assume the existence of suitable regular changes of variables, which reduce our problem to the transformed system $\ddot v-{\rm div}\,(\mathbb B\nabla v)+\mathbf a\nabla v -2\nabla\dot vb=g$ on the fixed domain $\Omega\setminus\Gamma_0$. Under these assumptions, we obtain existence and uniqueness of weak solutions for these two problems. Moreover, we show an energy equality for the functions $v$, which allows us to prove a continuous dependence result for both systems.1 aCaponi, Maicol uhttp://urania.sissa.it/xmlui/handle/1963/3527101406nas 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/1963/3528800988nas a2200157 4500008004100000245010900041210006900150260001500219300001400234490000700248520038700255100002100642700002200663700001900685856012600704 2017 eng d00aLower semicontinuity of a class of integral functionals on the space of functions of bounded deformation0 aLower semicontinuity of a class of integral functionals on the s bDe Gruyter a183–2070 v103 aWe study the lower semicontinuity of some free discontinuity functionals with linear growth defined on the space of functions with bounded deformation. The volume term is convex and depends only on the Euclidean norm of the symmetrized gradient. We introduce a suitable class of surface terms, which make the functional lower semicontinuous with respect to $L^1$ convergence.

1 aDal Maso, Gianni1 aOrlando, Gianluca1 aToader, Rodica uhttps://www.math.sissa.it/publication/lower-semicontinuity-class-integral-functionals-space-functions-bounded-deformation01104nas a2200145 4500008004100000245009100041210006900132300001200201490000800213520063400221100001800855700002100873700001900894856004500913 2017 en d00aA lower semicontinuity result for a free discontinuity functional with a boundary term0 alower semicontinuity result for a free discontinuity functional a952-9900 v1083 aWe study the lower semicontinuity in $GSBV^{p}(\Omega;\mathbb{R}^{m})$ of a free discontinuity functional $\mathcal{F}(u)$ that can be written as the sum of a crack term, depending only on the jump set $S_{u}$, and of a boundary term, depending on the trace of $u$ on $\partial\Omega$. We give sufficient conditions on the integrands for the lower semicontinuity of $\mathcal{F}$. Moreover, we prove a relaxation result, which shows that, if these conditions are not satisfied, the lower semicontinuous envelope of $\mathcal{F}$ can be represented by the sum of two integrals on $S_{u}$ and $\partial\Omega$, respectively.

1 aAlmi, Stefano1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/20.500.11767/1597900364nas a2200121 4500008004100000022001400041245004900055210004500104300002200149490000700171100001900178856004500197 2017 eng d a1815-065900aThe Malgrange form and Fredholm determinants0 aMalgrange form and Fredholm determinants aPaper No. 046, 120 v131 aBertola, Marco uhttp://dx.doi.org/10.3842/SIGMA.2017.04600465nas a2200133 4500008004100000022001400041245009600055210006900151300001400220490000800234100001900242700002200261856004800283 2017 eng d a0010-361600aMaximal amplitudes of finite-gap solutions for the focusing Nonlinear Schrödinger Equation0 aMaximal amplitudes of finitegap solutions for the focusing Nonli a525–5470 v3541 aBertola, Marco1 aTovbis, Alexander uhttp://dx.doi.org/10.1007/s00220-017-2895-900961nas a2200157 4500008004100000022001400041245007700055210007100132260000800203300001400211490000600225520047300231100002900704700002400733856004600757 2017 eng d a1664-235X00aMean-field quantum dynamics for a mixture of Bose–Einstein condensates0 aMeanfield quantum dynamics for a mixture of Bose–Einstein conden cDec a377–4160 v73 aWe study the effective time evolution of a large quantum system consisting of a mixture of different species of identical bosons in interaction. If the system is initially prepared so as to exhibit condensation in each component, we prove that condensation persists at later times and we show quantitatively that the many-body Schrödinger dynamics is effectively described by a system of coupled cubic non-linear Schrödinger equations, one for each component.

1 aMichelangeli, Alessandro1 aOlgiati, Alessandro uhttps://doi.org/10.1007/s13324-016-0147-301160nas a2200205 4500008004100000022001400041245006400055210006400119300000900183490000700192520049200199653003500691653001800726653003600744653002900780100002500809700001900834700002500853856007600878 2017 eng d a1534-039200aMinimizers of anisotropic perimeters with cylindrical norms0 aMinimizers of anisotropic perimeters with cylindrical norms a14270 v163 aWe study various regularity properties of minimizers of the Φ–perimeter, where Φ is a norm. Under suitable assumptions on Φ and on the dimension of the ambient space, we prove that the boundary of a cartesian minimizer is locally a Lipschitz graph out of a closed singular set of small Hausdorff dimension. Moreover, we show the following anisotropic Bernstein-type result: any entire cartesian minimizer is the subgraph of a monotone function depending only on one variable.

10aanisotropic Bernstein problem;10aminimal cones10aNon parametric minimal surfaces10aSets of finite perimeter1 aBellettini, Giovanni1 aNovaga, Matteo1 aKholmatov, Shokhrukh uhttp://aimsciences.org//article/id/47054f15-00c7-40b7-9da1-4c0b1d0a103d01991nas a2200157 4500008004100000245002800041210002800069260002200097300000900119520158000128100002401708700002001732700002101752700001901773856004101792 2017 eng d00aModel Reduction Methods0 aModel Reduction Methods bJohn Wiley & Sons a1-363 aThis chapter presents an overview of model order reduction – a new paradigm in the field of simulation-based engineering sciences, and one that can tackle the challenges and leverage the opportunities of modern ICT technologies. Despite the impressive progress attained by simulation capabilities and techniques, a number of challenging problems remain intractable. These problems are of different nature, but are common to many branches of science and engineering. Among them are those related to high-dimensional problems, problems involving very different time scales, models defined in degenerate domains with at least one of the characteristic dimensions much smaller than the others, model requiring real-time simulation, and parametric models. All these problems represent a challenge for standard mesh-based discretization techniques; yet the ability to solve these problems efficiently would open unexplored routes for real-time simulation, inverse analysis, uncertainty quantification and propagation, real-time optimization, and simulation-based control – critical needs in many branches of science and engineering. Model order reduction offers new simulation alternatives by circumventing, or at least alleviating, otherwise intractable computational challenges. In the present chapter, we revisit three of these model reduction techniques: proper orthogonal decomposition, proper generalized decomposition, and reduced basis methodologies.} preprint = {http://preprints.sissa.it/xmlui/bitstream/handle/1963/35194/ECM_MOR.pdf?sequence=1&isAllowed=y

1 aChinesta, Francisco1 aHuerta, Antonio1 aRozza, Gianluigi1 aWillcox, Karen uhttps://www.math.sissa.it/node/1294904754nas a2200097 4500008004100000245005000041210005000091520445700141100002104598856003704619 2017 eng d00aModuli of semistable sheaves as quiver moduli0 aModuli of semistable sheaves as quiver moduli3 aIn the 1980s Drézet and Le Potier realized moduli spaces of Gieseker-semistable sheaves on P2 as what are now called quiver moduli spaces. We discuss how this construction can be understood using t-structures and exceptional collections on derived categories, and how it can be extended to a similar result on P1×P1.

1 aMaiorana, Andrea uhttps://arxiv.org/abs/1709.0555501736nas a2200181 4500008004100000022001400041245010800055210006900163300000900232490000700241520106900248653003901317653002301356653004001379653003601419100002301455856007601478 2017 eng d a1534-039200aMultiple positive solutions of a sturm-liouville boundary value problem with conflicting nonlinearities0 aMultiple positive solutions of a sturmliouville boundary value p a10830 v163 aWe study the second order nonlinear differential equation

\begindocument $ u'' + \sum\limits_i = 1^m α_ia_i(x)g_i(u) - \sum\limits_j = 1^m + 1 β_jb_j(x)k_j(u) = 0,\rm $ \enddocument

where $\alpha_i, \beta_j>0$, $a_i(x), b_j(x)$ are non-negative Lebesgue integrable functions defined in $\mathopen[0, L\mathclose]$, and the nonlinearities $g_i(s), k_j(s)$ are continuous, positive and satisfy suitable growth conditions, as to cover the classical superlinear equation $u"+a(x)u.p = 0$, with $p>1$.When the positive parameters $\beta_j$ are sufficiently large, we prove the existence of at least $2.m-1$positive solutions for the Sturm-Liouville boundary value problems associated with the equation.The proof is based on the Leray-Schauder topological degree for locally compact operators on open and possibly unbounded sets.Finally, we deal with radially symmetric positive solutions for the Dirichlet problems associated with elliptic PDEs.

10aLeray-Schauder topological degree;10apositive solutions10aSturm-Liouville boundary conditions10aSuperlinear indefinite problems1 aFeltrin, Guglielmo uhttp://aimsciences.org//article/id/1163b042-0c64-4597-b25c-3494b268e5a101598nas a2200217 4500008004100000022001400041245010600055210006900161300001600230490000800246520083500254653002301089653002501112653003601137653003201173653002601205653003601231100002301267700001901290856007101309 2017 eng d a0022-039600aMultiplicity of positive periodic solutions in the superlinear indefinite case via coincidence degree0 aMultiplicity of positive periodic solutions in the superlinear i a4255 - 42910 v2623 aWe study the periodic boundary value problem associated with the second order nonlinear differential equationu″+cu′+(a+(t)−μa−(t))g(u)=0, where g(u) has superlinear growth at zero and at infinity, a(t) is a periodic sign-changing weight, c∈R and μ>0 is a real parameter. Our model includes (for c=0) the so-called nonlinear Hill's equation. We prove the existence of 2m−1 positive solutions when a(t) has m positive humps separated by m negative ones (in a periodicity interval) and μ is sufficiently large, thus giving a complete solution to a problem raised by G.J. Butler in 1976. The proof is based on Mawhin's coincidence degree defined in open (possibly unbounded) sets and applies also to Neumann boundary conditions. Our method also provides a topological approach to detect subharmonic solutions.

10aCoincidence degree10aMultiplicity results10aNeumann boundary value problems10aPositive periodic solutions10asubharmonic solutions10aSuperlinear indefinite problems1 aFeltrin, Guglielmo1 aZanolin, Fabio uhttp://www.sciencedirect.com/science/article/pii/S002203961730021900506nas a2200145 4500008004100000245009700041210006900138300001400207490000800221100001700229700001500246700002200261700002200283856005500305 2017 eng d00aA natural framework for isogeometric fluid-structure interaction based on BEM-shell coupling0 anatural framework for isogeometric fluidstructure interaction ba a522–5460 v3161 aHeltai, Luca1 aKiendl, J.1 aDeSimone, Antonio1 aReali, Alessandro uhttp://cdsads.u-strasbg.fr/abs/2017CMAME.316..522H00849nas a2200109 4500008004100000245006100041210005900102260002000161520048400181100002300665856005100688 2017 en d00aA note on a fixed point theorem on topological cylinders0 anote on a fixed point theorem on topological cylinders bSpringer Verlag3 aWe present a fixed point theorem on topological cylinders in normed linear spaces for maps satisfying a property of stretching a space along paths. This result is a generalization of a similar theorem obtained by D. Papini and F. Zanolin. In view of the main result, we discuss the existence of fixed points for maps defined on different types of domains and we propose alternative proofs for classical fixed point theorems, as Brouwer, Schauder and Krasnosel’skii ones.

1 aFeltrin, Guglielmo uhttp://urania.sissa.it/xmlui/handle/1963/3526300446nas a2200133 4500008004100000022001400041245009200055210006900147260000800216300001400224490000700238100002100245856004600266 2017 eng d a1572-922200aA Note on the Convergence of Singularly Perturbed Second Order Potential-Type Equations0 aNote on the Convergence of Singularly Perturbed Second Order Pot cJun a783–7970 v291 aNardini, Lorenzo uhttps://doi.org/10.1007/s10884-015-9461-y00711nas a2200181 4500008004100000245009900041210006900140300001400209490000700223100002400230700002000254700002000274700002200294700002100316700002000337700002200357856015000379 2017 eng d00aNumerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts0 aNumerical modeling of hemodynamics scenarios of patientspecific a1373-13990 v161 aBallarin, Francesco1 aFaggiano, Elena1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi1 aIppolito, Sonia1 aScrofani, Roberto uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85015065851&doi=10.1007%2fs10237-017-0893-7&partnerID=40&md5=c388f20bd5de14187bad9ed7d9affbd000603nas a2200169 4500008004100000245012600041210006900167260003400236300001400270490000600284100002200290700001900312700001700331700002100348700002100369856004300390 2017 eng d00aPOD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder0 aPODGalerkin reduced order methods for CFD using Finite Volume Di bWalter de Gruyter {GmbH}cdec a210–2360 v81 aStabile, Giovanni1 aHijazi, Saddam1 aMola, Andrea1 aLorenzi, Stefano1 aRozza, Gianluigi uhttps://doi.org/10.1515/caim-2017-001101350nas a2200193 4500008004100000022001400041245007200055210006900127300001600196490000800212520074100220653001800961653000800979653002400987653002301011653002901034100002201063856007101085 2017 eng d a0022-039600aQuasi-periodic solutions for quasi-linear generalized KdV equations0 aQuasiperiodic solutions for quasilinear generalized KdV equation a5052 - 51320 v2623 aWe prove the existence of Cantor families of small amplitude, linearly stable, quasi-periodic solutions of quasi-linear autonomous Hamiltonian generalized KdV equations. We consider the most general quasi-linear quadratic nonlinearity. The proof is based on an iterative Nash–Moser algorithm. To initialize this scheme, we need to perform a bifurcation analysis taking into account the strongly perturbative effects of the nonlinearity near the origin. In particular, we implement a weak version of the Birkhoff normal form method. The inversion of the linearized operators at each step of the iteration is achieved by pseudo-differential techniques, linear Birkhoff normal form algorithms and a linear KAM reducibility scheme.

10aKAM for PDE's10aKdV10aNash–Moser theory10aQuasi-linear PDE's10aQuasi-periodic solutions1 aGiuliani, Filippo uhttp://www.sciencedirect.com/science/article/pii/S002203961730048700824nas a2200157 4500008004100000022001400041245009600055210006900151260000800220300000600228490000700234520033600241100001900577700002400596856004600620 2017 eng d a1420-900400aQuasistatic crack growth based on viscous approximation: a model with branching and kinking0 aQuasistatic crack growth based on viscous approximation a model cJan a70 v243 aEmploying the technique of vanishing viscosity and time rescaling, we show the existence of quasistatic evolutions of cracks in brittle materials in the setting of antiplane shear. The crack path is not prescribed a priori and is chosen in an admissible class of piecewise regular sets that allows for branching and kinking.

1 aCrismale, Vito1 aLazzaroni, Giuliano uhttps://doi.org/10.1007/s00030-016-0426-600325nas a2200109 4500008004100000245002400041210002400065100001900089700002400108700002100132856006200153 2017 eng d00aRandom spectrahedra0 aRandom spectrahedra1 aBreiding, Paul1 aKozhasov, Khazhgali1 aLerario, Antonio uhttps://www.math.sissa.it/publication/random-spectrahedra00452nas a2200121 4500008004100000245005700041210005700098260002200155490000800177100002300185700002400208856009800232 2017 eng d00aRayleigh–Taylor instability in soft elastic layers0 aRayleigh–Taylor instability in soft elastic layers bThe Royal Society0 v3751 aRiccobelli, Davide1 aCiarletta, Pasquale uhttps://www.math.sissa.it/publication/rayleigh%E2%80%93taylor-instability-soft-elastic-layers01239nas 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)08002504nas a2200157 4500008004100000245005700041210005700098260001200155300000800167490000600175520201600181100001502197700002202212700002102234856009102255 2017 eng d00aReduced Basis Methods for Uncertainty Quantification0 aReduced Basis Methods for Uncertainty Quantification c08/2017 a8690 v53 aIn this work we review a reduced basis method for the solution of uncertainty quantification problems. Based on the basic setting of an elliptic partial differential equation with random input, we introduce the key ingredients of the reduced basis method, including proper orthogonal decomposition and greedy algorithms for the construction of the reduced basis functions, a priori and a posteriori error estimates for the reduced basis approximations, as well as its computational advantages and weaknesses in comparison with a stochastic collocation method [I. Babuška, F. Nobile, and R. Tempone, *SIAM Rev.*, 52 (2010), pp. 317--355]. We demonstrate its computational efficiency and accuracy for a benchmark problem with parameters ranging from a few to a few hundred dimensions. Generalizations to more complex models and applications to uncertainty quantification problems in risk prediction, evaluation of statistical moments, Bayesian inversion, and optimal control under uncertainty are also presented to illustrate how to use the reduced basis method in practice. Further challenges, advancements, and research opportunities are outlined.

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

1 aBallarin, Francesco1 aRozza, Gianluigi1 aMaday, Yvon1 aBenner, Peter1 aOhlberger, Mario1 aPatera, Anthony1 aRozza, Gianluigi1 aUrban, Karsten uhttps://www.math.sissa.it/node/1294801221nas a2200097 4500008004100000245007700041210006900118520087000187100001801057856004801075 2017 en d00aRegularity estimates for scalar conservation laws in one space dimension0 aRegularity estimates for scalar conservation laws in one space d3 aIn this paper we deal with the regularizing effect that, in a scalar conservation laws in one space dimension, the nonlinearity of the flux function ƒ has on the entropy solution. More precisely, if the set ⟨w : ƒ " (w) ≠ 0⟩ is dense, the regularity of the solution can be expressed in terms of BV Ф spaces, where Ф depends on the nonlinearity of ƒ. If moreover the set ⟨w : ƒ " (w) = 0⟩ is finite, under the additional polynomial degeneracy condition at the inflection points, we prove that ƒ' 0 u(t) ∈ BVloc (R) for every t > 0 and that this can be improved to SBVloc (R) regularity except an at most countable set of singular times. Finally we present some examples that shows the sharpness of these results and counterexamples to related questions, namely regularity in the kinetic formulation and a property of the fractional BV spaces.1 aMarconi, Elio uhttp://preprints.sissa.it/handle/1963/3529100917nas a2200157 4500008004100000020002200041245008300063210006900146260004400215300001400259520035500273100002400628700002900652700002900681856004900710 2017 eng d a978-3-319-58904-600aRemarks on the Derivation of Gross-Pitaevskii Equation with Magnetic Laplacian0 aRemarks on the Derivation of GrossPitaevskii Equation with Magne aChambSpringer International Publishing a257–2663 aThe effective dynamics for a Bose-Einstein condensate in the regime of high dilution and subject to an external magnetic field is governed by a magnetic Gross-Pitaevskii equation. We elucidate the steps needed to adapt to the magnetic case the proof of the derivation of the Gross-Pitaevskii equation within the ``projection counting'' scheme.

1 aOlgiati, Alessandro1 aMichelangeli, Alessandro1 aDell'Antonio, Gianfausto uhttps://doi.org/10.1007/978-3-319-58904-6_1500410nas a2200097 4500008004100000245006900041210006500110100001800175700001900193856010000212 2017 eng d00aSecond order differentiation formula on compact RCD*(K,N) spaces0 aSecond order differentiation formula on compact RCDKN spaces1 aGigli, Nicola1 aTamanini, Luca uhttps://www.math.sissa.it/publication/second-order-differentiation-formula-compact-rcdkn-spaces00941nas a2200109 4500008004100000245006900041210006800110260001000178520057200188100002000760856005100780 2017 en d00aSelf-Adjoint Extensions of Dirac Operator with Coulomb Potential0 aSelfAdjoint Extensions of Dirac Operator with Coulomb Potential bSISSA3 aIn this note we give a concise review of the present state-of-art for the problem of self-adjoint realisations for the Dirac operator with a Coulomb-like singular scalar potential V(x) = Ø(x)I4. We try to follow the historical and conceptual path that leads to the present understanding of the problem and to highlight the techniques employed and the main ideas. In the final part we outline a few major open questions that concern the topical problem of the multiplicity of self-adjoint realisations of the model, and which are worth addressing in the future.1 aGallone, Matteo uhttp://urania.sissa.it/xmlui/handle/1963/3527301120nas a2200109 4500008004100000245008000041210006900121520072300190100002000913700002900933856004800962 2017 en d00aSelf-adjoint realisations of the Dirac-Coulomb Hamiltonian for heavy nuclei0 aSelfadjoint realisations of the DiracCoulomb Hamiltonian for hea3 aWe derive a classification of the self-adjoint extensions of the three-dimensional Dirac-Coulomb operator in the critical regime of the Coulomb coupling. Our approach is solely based upon the KreĬn-Višik- Birman extension scheme, or also on Grubb's universal classification theory, as opposite to previous works within the standard von Neu- mann framework. This let the boundary condition of self-adjointness emerge, neatly and intrinsically, as a multiplicative constraint between regular and singular part of the functions in the domain of the exten- sion, the multiplicative constant giving also immediate information on the invertibility property and on the resolvent and spectral gap of the extension.1 aGallone, Matteo1 aMichelangeli, Alessandro uhttp://preprints.sissa.it/handle/1963/3528700688nas a2200121 4500008004100000245005300041210005200094520031100146100001600457700002100473700002400494856004800518 2017 en d00aSemistable Higgs Bundles on Calabi-Yau Manifolds0 aSemistable Higgs Bundles on CalabiYau Manifolds3 aWe provide a partial classification of semistable Higgs bundles over a simply connected Calabi-Yau manifold. Applications to a conjecture about a special class of semistable Higgs bundles are given. In particular, the conjecture is proved for K3 and Enriques surfaces, and some related classes of surfaces.1 aBruzzo, Ugo1 aLanza, Valeriano1 aLo Giudice, Alessio uhttp://preprints.sissa.it/handle/1963/3529501212nas 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-growth00400nas a2200097 4500008004100000245006400041210006000105100002100165700002100186856009500207 2017 eng d00aA Spectral Element Reduced Basis Method in Parametric {CFD}0 aSpectral Element Reduced Basis Method in Parametric CFD1 aHess, Martin, W.1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/spectral-element-reduced-basis-method-parametric-cfd01207nas a2200133 4500008004100000245006200041210006000103260001300163490000800176520080600184100002100990700002101011856004101032 2017 eng d00aA Spectral Element Reduced Basis Method in Parametric CFD0 aSpectral Element Reduced Basis Method in Parametric CFD bSpringer0 v1263 aWe consider the Navier-Stokes equations in a channel with varying Reynolds numbers. The model is discretized with high-order spectral element ansatz functions, resulting in 14 259 degrees of freedom. The steady-state snapshot solu- tions define a reduced order space, which allows to accurately evaluate the steady- state solutions for varying Reynolds number with a reduced order model within a fixed-point iteration. In particular, we compare different aspects of implementing the reduced order model with respect to the use of a spectral element discretization. It is shown, how a multilevel static condensation in the pressure and velocity boundary degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios.

1 aHess, Martin, W.1 aRozza, Gianluigi uhttps://www.math.sissa.it/node/1294601253nas a2200133 4500008004100000245007800041210006900119260001000188520080500198100001801003700002901021700002101050856004801071 2017 en d00aSpectral Properties of the 2+1 Fermionic Trimer with Contact Interactions0 aSpectral Properties of the 21 Fermionic Trimer with Contact Inte bSISSA3 aWe qualify the main features of the spectrum of the Hamiltonian of point interaction for a three-dimensional quantum system consisting of three point-like particles, two identical fermions, plus a third particle of different species, with two-body interaction of zero range. For arbitrary magnitude of the interaction, and arbitrary value of the mass parameter (the ratio between the mass of the third particle and that of each fermion) above the stability threshold, we identify the essential spectrum, localise and prove the finiteness of the discrete spectrum, qualify the angular symmetry of the eigenfunctions, and prove the monotonicity of the eigenvalues with respect to the mass parameter. We also demonstrate the existence of bound states in a physically relevant regime of masses.1 aBecker, Simon1 aMichelangeli, Alessandro1 aOttolini, Andrea uhttp://preprints.sissa.it/handle/1963/3530301538nas a2200157 4500008004100000022001400041245009300055210006900148260000800217300001400225490000700239520104800246100001801294700002201312856004601334 2017 eng d a1572-964800aStasis domains and slip surfaces in the locomotion of a bio-inspired two-segment crawler0 aStasis domains and slip surfaces in the locomotion of a bioinspi cFeb a587–6010 v523 aWe formulate and solve the locomotion problem for a bio-inspired crawler consisting of two active elastic segments (i.e., capable of changing their rest lengths), resting on three supports providing directional frictional interactions. The problem consists in finding the motion produced by a given, slow actuation history. By focusing on the tensions in the elastic segments, we show that the evolution laws for the system are entirely analogous to the flow rules of elasto-plasticity. In particular, sliding of the supports and hence motion cannot occur when the tensions are in the interior of certain convex regions (stasis domains), while support sliding (and hence motion) can only take place when the tensions are on the boundary of such regions (slip surfaces). We solve the locomotion problem explicitly in a few interesting examples. In particular, we show that, for a suitable range of the friction parameters, specific choices of the actuation strategy can lead to net displacements also in the direction of higher friction.

1 aGidoni, Paolo1 aDeSimone, Antonio uhttps://doi.org/10.1007/s11012-016-0408-000453nas a2200133 4500008004100000245009600041210006900137260000700206300001100213100001900224700002100243700001800264856003700282 2017 eng d00aSymplectic geometry of the moduli space of projective structures in homological coordinates0 aSymplectic geometry of the moduli space of projective structures c06 a1–561 aBertola, Marco1 aKorotkin, Dmitry1 aNorton, Chaya uhttps://arxiv.org/abs/1506.0791801540nas a2200133 4500008004100000245006000041210005900101520111900160100001301279700002401292700001901316700002301335856004801358 2017 en d00aTime quasi-periodic gravity water waves in finite depth0 aTime quasiperiodic gravity water waves in finite depth3 aWe prove the existence and the linear stability of Cantor families of small amplitude time quasi-periodic standing water wave solutions - namely periodic and even in the space variable x - of a bi-dimensional ocean with finite depth under the action of pure gravity. Such a result holds for all the values of the depth parameter in a Borel set of asymptotically full measure. This is a small divisor problem. The main difficulties are the quasi-linear nature of the gravity water waves equations and the fact that the linear frequencies grow just in a sublinear way at infinity. We overcome these problems by first reducing the linearized operators obtained at each approximate quasi-periodic solution along the Nash-Moser iteration to constant coefficients up to smoothing operators, using pseudo-differential changes of variables that are quasi-periodic in time. Then we apply a KAM reducibility scheme which requires very weak Melnikov non-resonance conditions (losing derivatives both in time and space), which we are able to verify for most values of the depth parameter using degenerate KAM theory arguments.1 aBaldi, P1 aBerti, Massimiliano1 aHaus, Emanuele1 aMontalto, Riccardo uhttp://preprints.sissa.it/handle/1963/3529601449nas a2200121 4500008004100000245006900041210006700110260001000177520104800187100002301235700002101258856004801279 2017 en d00aA uniqueness result for the decomposition of vector fields in Rd0 auniqueness result for the decomposition of vector fields in Rd bSISSA3 aGiven a vector field $\rho (1,\b) \in L^1_\loc(\R^+\times \R^{d},\R^{d+1})$ such that $\dive_{t,x} (\rho (1,\b))$ is a measure, we consider the problem of uniqueness of the representation $\eta$ of $\rho (1,\b) \mathcal L^{d+1}$ as a superposition of characteristics $\gamma : (t^-_\gamma,t^+_\gamma) \to \R^d$, $\dot \gamma (t)= \b(t,\gamma(t))$. We give conditions in terms of a local structure of the representation $\eta$ on suitable sets in order to prove that there is a partition of $\R^{d+1}$ into disjoint trajectories $\wp_\a$, $\a \in \A$, such that the PDE \begin{equation*} \dive_{t,x} \big( u \rho (1,\b) \big) \in \mathcal M(\R^{d+1}), \qquad u \in L^\infty(\R^+\times \R^{d}), \end{equation*} can be disintegrated into a family of ODEs along $\wp_\a$ with measure r.h.s.. The decomposition $\wp_\a$ is essentially unique. We finally show that $\b \in L^1_t(\BV_x)_\loc$ satisfies this local structural assumption and this yields, in particular, the renormalization property for nearly incompressible $\BV$ vector fields.

1 aBianchini, Stefano1 aBonicatto, Paolo uhttp://preprints.sissa.it/handle/1963/3527400463nas a2200133 4500008004100000022001400041245009600055210006900151300001600220490000600236100001900242700002000261856004800281 2017 eng d a2010-326300aUniversality of the matrix Airy and Bessel functions at spectral edges of unitary ensembles0 aUniversality of the matrix Airy and Bessel functions at spectral a1750010, 220 v61 aBertola, Marco1 aCafasso, Mattia uhttp://dx.doi.org/10.1142/S201032631750010100795nas a2200241 4500008004100000245011200041210006900153260003500222300001100257490000800268100001800276700001800294700001600312700002200328700001900350700002300369700002200392700002200414700001800436700001800454700002100472856006000493 2017 eng d00aUniversality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schrödinger Equation0 aUniversality of the Peregrine Soliton in the Focusing Dynamics o bAmerican Physical SocietycJul a0339010 v1191 aTikan, Alexey1 aBillet, Cyril1 aEl, Gennady1 aTovbis, Alexander1 aBertola, Marco1 aSylvestre, Thibaut1 aGustave, Francois1 aRandoux, Stephane1 aGenty, Goëry1 aSuret, Pierre1 aDudley, John, M. uhttps://link.aps.org/doi/10.1103/PhysRevLett.119.03390102562nas a2200145 4500008004100000245012400041210006900165300001100234490000700245520198000252100001702232700001702249700002202266856012802288 2017 eng d00aWet and Dry Transom Stern Treatment for Unsteady and Nonlinear Potential Flow Model for Naval Hydrodynamics Simulations0 aWet and Dry Transom Stern Treatment for Unsteady and Nonlinear P a1–140 v613 aWe present a model for the fast evaluation of the total drag of ship hulls operating in both wet and dry transom stern conditions, in calm or wavy water, based on the combination of an unsteady semi-Lagrangian potential flow formulation with fully nonlinear free-surface treatment, experimental correlations, and simplified viscous drag modeling. The implementation is entirely based on open source libraries. The spatial discretization is solved using a streamline upwind Petrov‐Galerkin stabilization of an iso-parametric, collocation based, boundary element method, implemented using the open source library deal.II. The resulting nonlinear differential-algebraic system is integrated in time using implicit backward differentiation formulas, implemented in the open source library SUNDIALS. The Open CASCADE library is used to interface the model directly with computer-aided design data structures. The model accounts automatically for hulls with a transom stern, both in wet and dry regimes, by using a specific treatment of the free-surface nodes on the stern edge that automatically detects when the hull advances at low speeds. In this case, the transom stern is partially immersed, and a pressure patch is applied on the water surface detaching from the transom stern, to recover the gravity effect of the recirculating water on the underlying irrotational flow domain. The parameters of the model used to impose the pressure patch are approximated from experimental relations found in the literature. The test cases considered are those of the U.S. Navy Combatant DTMB-5415 and the National Physical Laboratory hull. Comparisons with experimental data on quasi-steady test cases for both water elevation and total hull drag are presented and discussed. The quality of the results obtained on quasi-steady simulations suggests that this model can represent a promising alternative to current unsteady solvers for simulations with Froude numbers below 0.35.

1 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio uhttps://www.math.sissa.it/publication/wet-and-dry-transom-stern-treatment-unsteady-and-nonlinear-potential-flow-model-naval02112nas 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.html00479nas a2200133 4500008004100000022001400041245010000055210006900155300002800224490000700252100001900259700002200278856004500300 2016 eng d a1815-065900aOn asymptotic regimes of orthogonal polynomials with complex varying quartic exponential weight0 aasymptotic regimes of orthogonal polynomials with complex varyin aPaper No. 118, 50 pages0 v121 aBertola, Marco1 aTovbis, Alexander uhttp://dx.doi.org/10.3842/SIGMA.2016.11800407nas 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-charts00449nas a2200085 4500008004100000245010400041210006900145100002000214856012900234 2016 eng d00aCoalescence Phenomenon of Quantum Cohomology of Grassmannians and the Distribution of Prime Numbers0 aCoalescence Phenomenon of Quantum Cohomology of Grassmannians an1 aCotti, Giordano uhttps://www.math.sissa.it/publication/coalescence-phenomenon-quantum-cohomology-grassmannians-and-distribution-prime-numbers00889nas a2200169 4500008004100000022001400041245004700055210004600102260000800148300000800156490000900164520044700173100001600620700001900636700002000655856004400675 2016 eng d a1029-847900aComparing Poisson Sigma Model with A-model0 aComparing Poisson Sigma Model with Amodel cOct a1330 v20163 aWe discuss the A-model as a gauge fixing of the Poisson Sigma Model with target a symplectic structure. We complete the discussion in [4], where a gauge fixing defined by a compatible complex structure was introduced, by showing how to recover the A-model hierarchy of observables in terms of the AKSZ observables. Moreover, we discuss the off-shell supersymmetry of the A-model as a residual BV symmetry of the gauge fixed PSM action.

1 aBonechi, F.1 aCattaneo, A.S.1 aIraso, Riccardo uhttps://doi.org/10.1007/JHEP10(2016)13300926nas a2200205 4500008004100000022001400041245006500055210005800120300000700178490000600185520030900191653001800500653002200518653002200540653003000562653001100592100002300603700001800626856007600644 2016 eng d a1937-163200aOn the concentration of entropy for scalar conservation laws0 aconcentration of entropy for scalar conservation laws a730 v93 aWe prove that the entropy for an $L^∞$-solution to a scalar conservation laws with continuous initial data is concentrated on a countably $1$-rectifiable set. To prove this result we introduce the notion of Lagrangian representation of the solution and give regularity estimates on the solution.

10aconcentration10aConservation laws10aentropy solutions10aLagrangian representation10ashocks1 aBianchini, Stefano1 aMarconi, Elio uhttp://aimsciences.org//article/id/ce4eb91e-9553-4e8d-8c4c-868f07a315ae01304nas a2200133 4500008004100000245008300041210006900124520084400193100002201037700002201059700002001081700001801101856005101119 2016 en d00aConfinement of dislocations inside a crystal with a prescribed external strain0 aConfinement of dislocations inside a crystal with a prescribed e3 aWe study screw dislocations in an isotropic crystal undergoing antiplane shear. In the framework of linear elasticity, by fixing a suitable boundary condition for the strain (prescribed non-vanishing boundary integral), we manage to confine the dislocations inside the material. More precisely, in the presence of an external strain with circulation equal to n times the lattice spacing, it is energetically convenient to have n distinct dislocations lying inside the crystal. The novelty of introducing a Dirichlet boundary condition for the tangential strain is crucial to the confinement: it is well known that, if Neumann boundary conditions are imposed, the dislocations tend to migrate to the boundary. The results are achieved using PDE techniques and Ƭ-convergence theory, in the framework of the so-called core radius approach.1 aLucardesi, Ilaria1 aMorandotti, Marco1 aScala, Riccardo1 aZucco, Davide uhttp://urania.sissa.it/xmlui/handle/1963/3524700867nas a2200145 4500008004100000022001400041245006500055210006500120260000800185300001400193490000700207520043700214100002400651856004600675 2016 eng d a1573-869800aConformal Equivalence of 3D Contact Structures on Lie Groups0 aConformal Equivalence of 3D Contact Structures on Lie Groups cApr a251–2830 v223 aIn this paper, a conformal classification of three dimensional left-invariant sub-Riemannian contact structures is carried out; in particular, we will prove the following dichotomy: either a structure is locally conformal to the Heisenberg group $mathbbH^3$ or its conformal classification coincides with the metric one. If a structure is locally conformally flat, then its conformal group is locally isomorphic to $SU(2,1)$.

1 aBoarotto, Francesco uhttps://doi.org/10.1007/s10883-015-9273-801478nas 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/s00023-015-0400-600506nas a2200145 4500008004100000022001400041245011400055210006900169300001200238490000800250100001900258700002000277700001300297856005000310 2016 eng d a0167-278900aCorrelation functions of the KdV hierarchy and applications to intersection numbers over $\overline\CalM_g,n$0 aCorrelation functions of the KdV hierarchy and applications to i a30–570 v3271 aBertola, Marco1 aDubrovin, Boris1 aYang, Di uhttp://dx.doi.org/10.1016/j.physd.2016.04.00800358nas a2200097 4500008004100000245008800041210006900129260000700198100001900205856003600224 2016 eng d00aCORRIGENDUM: The dependence on the monodromy data of the isomonodromic tau function0 aCORRIGENDUM The dependence on the monodromy data of the isomonod c011 aBertola, Marco uhttp://arxiv.org/abs/1601.0479000357nas a2200085 4500008004100000245006000041210005900101100001800160856009300178 2016 eng d00aCritical points of a perturbed Otha-Kawasaki functional0 aCritical points of a perturbed OthaKawasaki functional1 aRizzi, Matteo uhttps://www.math.sissa.it/publication/critical-points-perturbed-otha-kawasaki-functional01884nas a2200145 4500008004100000245005300041210005300094260003400147300001100181490000700192520140800199100002001607700002501627856008601652 2016 eng d00aCurrents and dislocations at the continuum scale0 aCurrents and dislocations at the continuum scale bInternational Press of Boston a1–340 v233 aA striking geometric property of elastic bodies with dislocations is that the deformation tensor cannot be written as the gradient of a one-to-one immersion, its curl being nonzero and equal to the density of the dislocations, a measure concentrated in the dislocation lines. In this work, we discuss the mathematical properties of such constrained deformations and study a variational problem in finite-strain elasticity, where Cartesian maps allow us to consider deformations in $L^p$ with $1\leq p<2$, as required for dislocation-induced strain singularities. Firstly, we address the problem of mathematical modeling of dislocations. It is a key purpose of the paper to build a framework where dislocations are described in terms of integral 1-currents and to extract from this theoretical setting a series of notions having a mechanical meaning in the theory of dislocations. In particular, the paper aims at classifying integral 1-currents, with modeling purposes. In the second part of the paper, two variational problems are solved for two classes of dislocations, at the mesoscopic and at the continuum scale. By continuum it is here meant that a countable family of dislocations is considered, allowing for branching and cluster formation, with possible complex geometric patterns. Therefore, modeling assumptions of the defect part of the energy must also be provided, and discussed.

1 aScala, Riccardo1 aVan Goethem, Nicolas uhttps://www.math.sissa.it/publication/currents-and-dislocations-continuum-scale-000494nas a2200181 4500008004100000245003700041210003000078300001100108490000600119100001700125700001800142700001700160700001700177700002400194700002000218700001700238856005700255 2016 eng d00aThe deal.II Library, Version 8.30 adealII Library Version 83 a1–110 v41 aBangerth, W.1 aHeister, Timo1 aHeltai, Luca1 aKanschat, G.1 aKronbichler, Martin1 aMaier, Matthias1 aTurcksin, B. uhttp://nbn-resolving.de/urn:nbn:de:bsz:16-ans-23122600573nas a2200205 4500008004100000245003700041210003000078300001400108490000700122100001700129700001900146700001800165700001700183700001700200700002400217700002000241700001700261700001700278856007200295 2016 eng d00aThe deal.II library, Version 8.40 adealII library Version 84 a135–1410 v241 aBangerth, W.1 aDavydov, Denis1 aHeister, Timo1 aHeltai, Luca1 aKanschat, G.1 aKronbichler, Martin1 aMaier, Matthias1 aTurcksin, B.1 aWells, David uhttps://www.math.clemson.edu/ heister/preprints/deal84-preprint.pdf00471nas a2200097 4500008004100000245009600041210006900137100001800206700002400224856012500248 2016 eng d00aEquivalence of two different notions of tangent bundle on rectifiable metric measure spaces0 aEquivalence of two different notions of tangent bundle on rectif1 aGigli, Nicola1 aPasqualetto, Enrico uhttps://www.math.sissa.it/publication/equivalence-two-different-notions-tangent-bundle-rectifiable-metric-measure-spaces00590nas a2200157 4500008004100000245009800041210006900139300001400208490000700222100001600229700001700245700001400262700001700276700001400293856012500307 2016 eng d00aError Estimates of B-spline based finite-element method for the wind-driven ocean circulation0 aError Estimates of Bspline based finiteelement method for the wi a430–4590 v691 aRotundo, N.1 aKim, T., -Y.1 aJiang, W.1 aHeltai, Luca1 aFried, E. uhttps://www.math.sissa.it/publication/error-estimates-b-spline-based-finite-element-method-wind-driven-ocean-circulation00434nas a2200109 4500008004100000245009700041210006900138100002200207700002300229700002100252856005100273 2016 en d00aEulerian, Lagrangian and Broad continuous solutions to a balance law with non convex flux II0 aEulerian Lagrangian and Broad continuous solutions to a balance 1 aAlberti, Giovanni1 aBianchini, Stefano1 aCaravenna, Laura uhttp://urania.sissa.it/xmlui/handle/1963/3519700458nas a2200121 4500008004100000245009600041210006900137260001300206100002200219700002300241700002100264856005100285 2016 en d00aEulerian, Lagrangian and Broad continuous solutions to a balance law with non-convex flux I0 aEulerian Lagrangian and Broad continuous solutions to a balance bElsevier1 aAlberti, Giovanni1 aBianchini, Stefano1 aCaravenna, Laura uhttp://urania.sissa.it/xmlui/handle/1963/3520701475nas a2200181 4500008004100000022001400041245012000055210006900175260000800244300000700252490000900259520088800268100002301156700002001179700002601199700002401225856004401249 2016 eng d a1029-847900aExact results for N=2 supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants0 aExact results for N2 supersymmetric gauge theories on compact to cJul a230 v20163 aWe provide a contour integral formula for the exact partition function of $\mathcal{N}=2$ supersymmetric $U(N)$ gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the contour integral for $U(2)\; \mathcal{N}=2^\star$ theory on $\mathbb{P}^2$ for all instanton numbers. In the zero mass case, corresponding to the $\mathcal{N}=4$ supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of mock-modular forms. In the decoupling limit of infinite mass we find that the generating function of local and surface observables computes equivariant Donaldson invariants, thus proving in this case a longstanding conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new.

1 aBershtein, Mikhail1 aBonelli, Giulio1 aRonzani, Massimiliano1 aTanzini, Alessandro uhttps://doi.org/10.1007/JHEP07(2016)02301307nas a2200193 4500008004100000022001400041245009500055210006900150300001600219490000800235520066200243653002900905653002400934653002600958653001600984100002001000700002201020856007101042 2016 eng d a0022-123600aExistence and non-existence results for the SU(3) singular Toda system on compact surfaces0 aExistence and nonexistence results for the SU3 singular Toda sys a3750 - 38070 v2703 aWe consider the SU(3) singular Toda system on a compact surface (Σ,g)−Δu1=2ρ1(h1eu1∫Σh1eu1dVg−1)−ρ2(h2eu2∫Σh2eu2dVg−1)−4π∑m=1Mα1m(δpm−1)−Δu2=2ρ2(h2eu2∫Σh2eu2dVg−1)−ρ1(h1eu1∫Σh1eu1dVg−1)−4π∑m=1Mα2m(δpm−1), where hi are smooth positive functions on Σ, ρi∈R+, pm∈Σ and αim>−1. We give both existence and non-existence results under some conditions on the parameters ρi and αim. Existence results are obtained using variational methods, which involve a geometric inequality of new type; non-existence results are obtained using blow-up analysis and localized Pohožaev-type identities."

10aLiouville-type equations10aMin–max solutions10aNon-existence results10aToda system1 aBattaglia, Luca1 aMalchiodi, Andrea uhttp://www.sciencedirect.com/science/article/pii/S002212361500494201120nas a2200229 4500008004100000022001400041245008700055210006900142300001600211490000800227520034000235653002200575653003200597653002100629653002500650653003400675653004400709100002100753700002400774700002100798856007100819 2016 eng d a0022-039600aExistence and uniqueness of dynamic evolutions for a peeling test in dimension one0 aExistence and uniqueness of dynamic evolutions for a peeling tes a4897 - 49230 v2613 aIn this paper we present a one-dimensional model of a dynamic peeling test for a thin film, where the wave equation is coupled with a Griffith criterion for the propagation of the debonding front. Our main results provide existence and uniqueness for the solution to this coupled problem under different assumptions on the data.

10aDynamic debonding10aDynamic energy release rate10aDynamic fracture10aGriffith's criterion10aMaximum dissipation principle10aWave equation in time-dependent domains1 aDal Maso, Gianni1 aLazzaroni, Giuliano1 aNardini, Lorenzo uhttp://www.sciencedirect.com/science/article/pii/S002203961630177201717nas a2200193 4500008004100000245011900041210006900160260001400229520106200243100002401305700002001329700002001349700002101369700002201390700002001412700002201432700001801454856005101472 2016 en d00aA fast virtual surgery platform for many scenarios haemodynamics of patient-specific coronary artery bypass grafts0 afast virtual surgery platform for many scenarios haemodynamics o bSubmitted3 aA fast computational framework is devised to the study of several configurations of patient-specific coronary artery bypass grafts. This is especially useful to perform a sensitivity analysis of the haemodynamics for different flow conditions occurring in native coronary arteries and bypass grafts, the investigation of the progression of the coronary artery disease and the choice of the most appropriate surgical procedure. A complete pipeline, from the acquisition of patientspecific medical images to fast parametrized computational simulations, is proposed. Complex surgical configurations employed in the clinical practice, such as Y-grafts and sequential grafts, are studied. A virtual surgery platform based on model reduction of unsteady Navier Stokes equations for blood dynamics is proposed to carry out sensitivity analyses in a very rapid and reliable way. A specialized geometrical parametrization is employed to compare the effect of stenosis and anastomosis variation on the outcome of the surgery in several relevant cases.1 aBallarin, Francesco1 aFaggiano, Elena1 aManzoni, Andrea1 aRozza, Gianluigi1 aQuarteroni, Alfio1 aIppolito, Sonia1 aScrofani, Roberto1 aAntona, Carlo uhttp://urania.sissa.it/xmlui/handle/1963/3524000965nas a2200169 4500008004100000022001400041245012900055210006900184260000800253300000700261490000700268520041200275100002100687700002200708700001900730856004600749 2016 eng d a1432-083500aFracture models for elasto-plastic materials as limits of gradient damage models coupled with plasticity: the antiplane case0 aFracture models for elastoplastic materials as limits of gradien cApr a450 v553 aWe study the asymptotic behavior of a variational model for damaged elasto-plastic materials in the case of antiplane shear. The energy functionals we consider depend on a small parameter $\varepsilon$, which forces damage concentration on regions of codimension one. We determine the $\Gamma$-limit as $\varepsilon$ tends to zero and show that it contains an energy term involving the crack opening.

1 aDal Maso, Gianni1 aOrlando, Gianluca1 aToader, Rodica uhttps://doi.org/10.1007/s00526-016-0981-z01114nas a2200121 4500008004100000245006200041210006200103260001000165520067200175653001800847100003000865856009700895 2016 en d00aFrames symplectic sheaves on surfaces and their ADHM data0 aFrames symplectic sheaves on surfaces and their ADHM data bSISSA3 aThis dissertation is centered on the moduli space of what we call framed symplectic sheaves on a surface, compactifying the corresponding moduli space of framed principal SP−bundles. It contains the construction of the moduli space, which is carried out for every smooth projective surface X with a big and nef framing divisor, and a study of its deformation theory. We also develop an in-depth analysis of the examples X = P2 and X = Blp (P2 ), showing that the corresponding moduli spaces enjoy an ADHM-type description. In the former case, we prove irreducibility of the space and exhibit a relation with the space of framed ideal instantons on S4 in type C.10amoduli spaces1 aScalise, Jacopo, Vittorio uhttps://www.math.sissa.it/publication/frames-symplectic-sheaves-surfaces-and-their-adhm-data00789nas a2200145 4500008004100000245009000041210006900131300001200200490000700212520031400219100002200533700001800555700002400573856004600597 2016 eng d00aA Frobenius theorem for corank-1 continuous distributions in dimensions two and three0 aFrobenius theorem for corank1 continuous distributions in dimens a16500610 v273 aWe formulate a notion of (uniform) asymptotic involutivity and show that it implies (unique) integrability of corank-1 continuous distributions in dimensions three or less. This generalizes and extends a classical Frobenius theorem, which says that an involutive C1 distribution is uniquely integrable.

1 aLuzzatto, Stefano1 aTüreli, Sina1 aWar, Khadim, Mbacke uhttps://doi.org/10.1142/S0129167X1650061000945nas a2200157 4500008004100000022001400041245007900055210007200134260000800206300001600214490000800230520046300238100002200701700001800723856004600741 2016 eng d a1618-189100aGeneralizing the Poincaré–Miranda theorem: the avoiding cones condition0 aGeneralizing the Poincaré–Miranda theorem the avoiding cones con cAug a1347–13710 v1953 aAfter proposing a variant of the Poincaré–Bohl theorem, we extend the Poincaré–Miranda theorem in several directions, by introducing an avoiding cones condition. We are thus able to deal with functions defined on various types of convex domains, and situations where the topological degree may be different from \$\$\backslashpm \$\$±1. An illustrative application is provided for the study of functionals having degenerate multi-saddle points.

1 aFonda, Alessandro1 aGidoni, Paolo uhttps://doi.org/10.1007/s10231-015-0519-600947nas a2200133 4500008004100000245008500041210006900126260001700195300001400212490000700226520047700233100001900710856008400729 2016 eng d00aGlobally stable quasistatic evolution for a coupled elastoplastic–damage model0 aGlobally stable quasistatic evolution for a coupled elastoplasti bEDP Sciences a883–9120 v223 aWe show the existence of globally stable quasistatic evolutions for a rate-independent material model with elastoplasticity and incomplete damage, in small strain assumptions. The main feature of our model is that the scalar internal variable which describes the damage affects both the elastic tensor and the plastic yield surface. It is also possible to require that the history of plastic strain up to the current state influences the future evolution of damage.

1 aCrismale, Vito uhttps://www.esaim-cocv.org/articles/cocv/abs/2016/03/cocv150037/cocv150037.html01057nas a2200145 4500008004100000245004700041210004300088300001600131490000600147520062100153100002100774700001700795700002000812856007900832 2016 eng d00aThe Gysin sequence for quantum lens spaces0 aGysin sequence for quantum lens spaces a1077–11110 v93 aWe define quantum lens spaces as ‘direct sums of line bundles’ and exhibit them as ‘total spaces’ of certain principal bundles over quantum projective spaces. For each of these quantum lens spaces we construct an analogue of the classical Gysin sequence in K-theory. We use the sequence to compute the K-theory of the quantum lens spaces, in particular to give explicit geometric representatives of their K-theory classes. These representatives are interpreted as ‘line bundles’ over quantum lens spaces and generically define ‘torsion classes’. We work out explicit examples of these classes.

1 aArici, Francesca1 aBrain, Simon1 aLandi, Giovanni uhttps://www.math.sissa.it/publication/gysin-sequence-quantum-lens-spaces-000491nas a2200145 4500008004100000022001400041245009400055210006900149300001400218490000700232100001900239700001900258700002000277856004800297 2016 eng d a0176-427600aHankel determinant approach to generalized Vorob'ev-Yablonski polynomials and their roots0 aHankel determinant approach to generalized VorobevYablonski poly a417–4530 v441 aBalogh, Ferenc1 aBertola, Marco1 aBothner, Thomas uhttp://dx.doi.org/10.1007/s00365-016-9328-402791nas a2200121 4500008004100000245004400041210004400085260001000129520243500139653001802574100002602592856005102618 2016 en d00aInstanton counting on compact manifolds0 aInstanton counting on compact manifolds bSISSA3 aIn this thesis we analyze supersymmetric gauge theories on compact manifolds and their relation with representation theory of infinite Lie algebras associated to conformal field theories, and with the computation of geometric invariants and superconformal indices. The thesis contains the work done by the candidate during the doctorate programme at SISSA under the supervision of A. Tanzini and G. Bonelli. • in Chapter 2, we consider N = 2 supersymmetric gauge theories on four manifolds admitting an isometry. Generalized Killing spinor equations are derived from the consistency of supersymmetry algebrae and solved in the case of four manifolds admitting a U(1) isometry. This is used to explicitly compute the supersymmetric path integral on S2 × S2 via equivariant localization. The building blocks of the resulting partition function are shown to contain the three point functions and the conformal blocks of Liouville Gravity. • in Chapter 3, we provide a contour integral formula for the exact partition function of N = 2 supersymmetric U(N) gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the contour integral for U(2) N = 2∗ theory on P2 for all instanton numbers. In the zero mass case, corresponding to the N = 4 supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of mock-modular forms. In the decoupling limit of infinite mass we find that the generating function of local and surface observables computes equivariant Donaldson invariants, thus proving in this case a long-standing conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new. • in Chapter 4, we explore N = (1, 0) superconformal six-dimensional theories arising from M5 branes probing a transverse Ak singularity. Upon circle compactification to five dimensions, we describe this system with a dual pq-web of five-branes and propose the spectrum of basic five-dimensional in- stanton operators driving global symmetry enhancement. For a single M5 brane, we find that the exact partition function of the 5d quiver gauge theory matches the 6d (1, 0) index, which we compute by letter counting. We finally show which relations among vertex correlators of qW algebrae are implied by the S-duality of the pq-web.10aSupersymmetry1 aRonzani, Massimiliano uhttp://urania.sissa.it/xmlui/handle/1963/3521900676nas a2200157 4500008004100000245004500041210004500086260002100131300001000152490000700162520023500169100002200404700001800426700002400444856005000468 2016 eng d00aIntegrability of C1 invariant splittings0 aIntegrability of C1 invariant splittings bTaylor & Francis a79-880 v313 aWe derive some new conditions for integrability of dynamically defined C1 invariant splittings, formulated in terms of the singular values of the iterates of the derivative of the diffeomorphism which defines the splitting.

1 aLuzzatto, Stefano1 aTüreli, Sina1 aWar, Khadim, Mbacke uhttps://doi.org/10.1080/14689367.2015.105748000539nas a2200109 4500008004100000245007800041210006900119260001000188520009700198100002400295856011000319 2016 en d00aIntegrability of continuous bundles and applications to dynamical systems0 aIntegrability of continuous bundles and applications to dynamica bSISSA3 aIn this dissertation we study the problem of integrability of bundles with low regularities.1 aWar, Khadim, Mbacke uhttps://www.math.sissa.it/publication/integrability-continuous-bundles-and-applications-dynamical-systems01409nas a2200145 4500008004100000245011900041210006900160260007700229520081900306100002501125700002401150700001701174700002101191856005101212 2016 en d00aIsogeometric analysis-based reduced order modelling for incompressible linear viscous flows in parametrized shapes0 aIsogeometric analysisbased reduced order modelling for incompres bSpringer, AMOS Advanced Modelling and Simulation in Engineering Sciences3 aIn this work we provide a combination of isogeometric analysis with reduced order modelling techniques, based on proper orthogonal decomposition, to guarantee computational reduction for the numerical model, and with free-form deformation, for versatile geometrical parametrization. We apply it to computational fluid dynamics problems considering a Stokes flow model. The proposed reduced order model combines efficient shape deformation and accurate and stable velocity and pressure approximation for incompressible viscous flows, computed with a reduced order method. Efficient offine-online computational decomposition is guaranteed in view of repetitive calculations for parametric design and optimization problems. Numerical test cases show the efficiency and accuracy of the proposed reduced order model.1 aSalmoiraghi, Filippo1 aBallarin, Francesco1 aHeltai, Luca1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3519901362nas a2200121 4500008004100000245005800041210005800099520096700157100002401124700002101148700002301169856004801192 2016 en d00aLarge KAM tori for perturbations of the dNLS equation0 aLarge KAM tori for perturbations of the dNLS equation3 aWe prove that small, semi-linear Hamiltonian perturbations of the defocusing nonlinear Schr\"odinger (dNLS) equation on the circle have an abundance of invariant tori of any size and (finite) dimension which support quasi-periodic solutions. When compared with previous results the novelty consists in considering perturbations which do not satisfy any symmetry condition (they may depend on x in an arbitrary way) and need not be analytic. The main difficulty is posed by pairs of almost resonant dNLS frequencies. The proof is based on the integrability of the dNLS equation, in particular the fact that the nonlinear part of the Birkhoff coordinates is one smoothing. We implement a Newton-Nash-Moser iteration scheme to construct the invariant tori. The key point is the reduction of linearized operators, coming up in the iteration scheme, to 2×2 block diagonal ones with constant coefficients together with sharp asymptotic estimates of their eigenvalues.1 aBerti, Massimiliano1 aKappeler, Thomas1 aMontalto, Riccardo uhttp://preprints.sissa.it/handle/1963/3528400522nas a2200133 4500008004100000245008200041210006900123300001100192490000700203100002000210700002200230700001700252856011900269 2016 eng d00aLinearOperator – a generic, high-level expression syntax for linear algebra0 aLinearOperator a generic highlevel expression syntax for linear a1–240 v721 aMaier, Matthias1 aBardelloni, Mauro1 aHeltai, Luca uhttps://www.math.sissa.it/publication/linearoperator-%E2%80%93-generic-high-level-expression-syntax-linear-algebra00690nas a2200109 4500008004100000245007500041210006900116520030100185100002100486700002200507856005100529 2016 en d00aA model for the quasistatic growth of cracks with fractional dimension0 amodel for the quasistatic growth of cracks with fractional dimen3 aWe study a variational model for the quasistatic growth of cracks with fractional dimension in brittle materials. We give a minimal set of properties of the collection of admissible cracks which ensure the existence of a quasistatic evolution. Both the antiplane and the planar cases are treated.1 aDal Maso, Gianni1 aMorandotti, Marco uhttp://urania.sissa.it/xmlui/handle/1963/3517500391nas a2200133 4500008004100000245003600041210003500077260001000112100002400122700002000146700002100166700001900187856005100206 2016 en d00aModel Order Reduction: a survey0 aModel Order Reduction a survey bWiley1 aChinesta, Francisco1 aHuerta, Antonio1 aRozza, Gianluigi1 aWillcox, Karen uhttp://urania.sissa.it/xmlui/handle/1963/3519401034nas a2200145 4500008004100000022001400041245006600055210006600121260000800187300001600195490000800211520060300219100002000822856004600842 2016 eng d a1432-182300aMoser–Trudinger inequalities for singular Liouville systems0 aMoser–Trudinger inequalities for singular Liouville systems cApr a1169–11900 v2823 aIn this paper we prove a Moser–Trudinger inequality for the Euler–Lagrange functional of general singular Liouville systems on a compact surface. We characterize the values of the parameters which yield coercivity for the functional, hence the existence of energy-minimizing solutions for the system, and we give necessary conditions for boundedness from below. We also provide a sharp inequality under assuming the coefficients of the system to be non-positive outside the diagonal. The proofs use a concentration-compactness alternative, Pohožaev-type identities and blow-up analysis.

1 aBattaglia, Luca uhttps://doi.org/10.1007/s00209-015-1584-701781nas a2200157 4500008004100000022001400041245006600055210006600121260000800187300000700195490000700202520131900209100002601528700002201554856004701576 2016 eng d a1292-895X00aMotion planning and motility maps for flagellar microswimmers0 aMotion planning and motility maps for flagellar microswimmers cJul a720 v393 aWe study two microswimmers consisting of a spherical rigid head and a passive elastic tail. In the first one the tail is clamped to the head, and the system oscillates under the action of an external torque. In the second one, head and tail are connected by a joint allowing the angle between them to vary periodically, as a result of an oscillating internal torque. Previous studies on these models were restricted to sinusoidal actuations, showing that the swimmers can propel while moving on average along a straight line, in the direction given by the symmetry axis around which beating takes place. We extend these results to motions produced by generic (non-sinusoidal) periodic actuations within the regime of small compliance of the tail. We find that modulation in the velocity of actuation can provide a mechanism to select different directions of motion. With velocity-modulated inputs, the externally actuated swimmer can translate laterally with respect to the symmetry axis of beating, while the internally actuated one is able to move along curved trajectories. The governing equations are analysed with an asymptotic perturbation scheme, providing explicit formulas, whose results are expressed through motility maps. Asymptotic approximations are further validated by numerical simulations.

1 aCicconofri, Giancarlo1 aDeSimone, Antonio uhttps://doi.org/10.1140/epje/i2016-16072-y01951nas a2200169 4500008004100000245009300041210006900134260001300203300000800216490000700224520142100231100002101652700001901673700001701692700002101709856005101730 2016 en d00aA multi-physics reduced order model for the analysis of Lead Fast Reactor single channel0 amultiphysics reduced order model for the analysis of Lead Fast R bElsevier a2080 v873 aIn this work, a Reduced Basis method, with basis functions sampled by a Proper Orthogonal Decomposition technique, has been employed to develop a reduced order model of a multi-physics parametrized Lead-cooled Fast Reactor single-channel. Being the first time that a reduced order model is developed in this context, the work focused on a methodological approach and the coupling between the neutronics and the heat transfer, where the thermal feedbacks on neutronics are explicitly taken into account, in time-invariant settings. In order to address the potential of such approach, two different kinds of varying parameters have been considered, namely one related to a geometric quantity (i.e., the inner radius of the fuel pellet) and one related to a physical quantity (i.e., the inlet lead velocity). The capabilities of the presented reduced order model (ROM) have been tested and compared with a high-fidelity finite element model (upon which the ROM has been constructed) on different aspects. In particular, the comparison focused on the system reactivity prediction (with and without thermal feedbacks on neutronics), the neutron flux and temperature field reconstruction, and on the computational time. The outcomes provided by the reduced order model are in good agreement with the high-fidelity finite element ones, and a computational speed-up of at least three orders of magnitude is achieved as well.1 aSartori, Alberto1 aCammi, Antonio1 aLuzzi, Lelio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3519101319nas a2200109 4500008004100000245011100041210006900152520088700221100002901108700002101137856005101158 2016 en d00aMultiplicity of self-adjoint realisations of the (2+1)-fermionic model of Ter-Martirosyan--Skornyakov type0 aMultiplicity of selfadjoint realisations of the 21fermionic mode3 aWe reconstruct the whole family of self-adjoint Hamiltonians of Ter-Martirosyan- Skornyakov type for a system of two identical fermions coupled with a third particle of different nature through an interaction of zero range. We proceed through an operator-theoretic approach based on the self-adjoint extension theory of Kreĭn, Višiik, and Birman. We identify the explicit `Kreĭn-Višik-Birman extension param- eter' as an operator on the `space of charges' for this model (the `Kreĭn space') and we come to formulate a sharp conjecture on the dimensionality of its kernel. Based on our conjecture, for which we also discuss an amount of evidence, we explain the emergence of a multiplicity of extensions in a suitable regime of masses and we re- produce for the first time the previous partial constructions obtained by means of an alternative quadratic form approach.1 aMichelangeli, Alessandro1 aOttolini, Andrea uhttp://urania.sissa.it/xmlui/handle/1963/3526700467nas a2200109 4500008004100000245009200041210006900133300001200202490000800214100002000222856011500242 2016 eng d00aNew existence results for the mean field equation on compact surfaces via degree theory0 aNew existence results for the mean field equation on compact sur a11–170 v1361 aJevnikar, Aleks uhttps://www.math.sissa.it/publication/new-existence-results-mean-field-equation-compact-surfaces-degree-theory01002nas 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/1963/3526600476nas a2200121 4500008004100000245008400041210006900125260001500194300001400209490000700223100002000230856010400250 2016 eng d00aA note on a multiplicity result for the mean field equation on compact surfaces0 anote on a multiplicity result for the mean field equation on com bDe Gruyter a221–2290 v161 aJevnikar, Aleks uhttps://www.math.sissa.it/publication/note-multiplicity-result-mean-field-equation-compact-surfaces00961nas a2200133 4500008004100000245014200041210006900183260003100252520042800283100002300711700002300734700001900757856005100776 2016 en d00aPairs of positive periodic solutions of nonlinear ODEs with indefinite weight: a topological degree approach for the super-sublinear case0 aPairs of positive periodic solutions of nonlinear ODEs with inde bCambridge University Press3 aWe study the periodic and Neumann boundary value problems associated with the second order nonlinear differential equation u''+cu'+λa(t)g(u)=0, where g:[0,+∞[→[0,+∞[ is a sublinear function at infinity having superlinear growth at zero. We prove the existence of two positive solutions when ∫a(t)dt 0 is sufficiently large. Our approach is based on Mawhin's coincidence degree theory and index computations.

1 aBoscaggin, Alberto1 aFeltrin, Guglielmo1 aZanolin, Fabio uhttp://urania.sissa.it/xmlui/handle/1963/3526200883nas a2200157 4500008004100000245005000041210005000091260001500141300001400156490000600170520040100176100002200577700002300599700001800622856008500640 2016 eng d00aPeriodic perturbations of Hamiltonian systems0 aPeriodic perturbations of Hamiltonian systems bDe Gruyter a367–3820 v53 aWe prove existence and multiplicity results for periodic solutions of Hamiltonian systems, by the use of a higher dimensional version of the Poincaré–Birkhoff fixed point theorem. The first part of the paper deals with periodic perturbations of a completely integrable system, while in the second part we focus on some suitable global conditions, so to deal with weakly coupled systems.

1 aFonda, Alessandro1 aGarrione, Maurizio1 aGidoni, Paolo uhttps://www.math.sissa.it/publication/periodic-perturbations-hamiltonian-systems00912nas a2200229 4500008004100000020002200041245004000063210004000103260004400143300001100187520024800198100002100446700002400467700002000491700001800511700002000529700002200549700001900571700002000590700002400610856004800634 2016 eng d a978-3-319-29116-100aPimsner Algebras and Circle Bundles0 aPimsner Algebras and Circle Bundles aChambSpringer International Publishing a1–253 aWe report on the connections between noncommutative principal circle bundles, Pimsner algebras and strongly graded algebras. We illustrate several results with examples of quantum weighted projective and lens spaces and θ-deformations.

1 aArici, Francesca1 aD'Andrea, Francesco1 aLandi, Giovanni1 aAlpay, Daniel1 aCipriani, Fabio1 aColombo, Fabrizio1 aGuido, Daniele1 aSabadini, Irene1 aSauvageot, Jean-Luc uhttps://doi.org/10.1007/978-3-319-29116-1_100454nas a2200145 4500008004100000022001400041245007100055210006900126300001200195490000700207100002100214700001500235700002000250856003800270 2016 eng d a1661-695200aPimsner algebras and Gysin sequences from principal circle actions0 aPimsner algebras and Gysin sequences from principal circle actio a29–640 v101 aArici, Francesca1 aKaad, Jens1 aLandi, Giovanni uhttp://hdl.handle.net/2066/16295102275nas a2200145 4500008004100000245009200041210006900133260006800202520165800270100002101928700001901949700001701968700002101985856012302006 2016 en d00aPOD-Galerkin Method for Finite Volume Approximation of Navier-Stokes and RANS Equations0 aPODGalerkin Method for Finite Volume Approximation of NavierStok bComputer Methods in Applied Mechanics and Engineering, Elsevier3 aNumerical simulation of fluid flows requires important computational efforts but it is essential in engineering applications. Reduced Order Model (ROM) can be employed whenever fast simulations are required, or in general, whenever a trade-off between computational cost and solution accuracy is a preeminent issue as in process optimization and control. In this work, the efforts have been put to develop a ROM for Computational Fluid Dynamics (CFD) application based on Finite Volume approximation, starting from the results available in turbulent Reynold-Averaged Navier Stokes simulations in order to enlarge the application field of Proper Orthogonal Decomposition – Reduced Order Model (POD – ROM) technique to more industrial fields. The approach is tested in the classic benchmark of the numerical simulation of the 2D lid-driven cavity. In particular, two simulations at Re = 103 and Re = 105 have been considered in order to assess both a laminar and turbulent case. Some quantities have been compared with the Full Order Model in order to assess the performance of the proposed ROM procedure i.e., the kinetic energy of the system and the reconstructed quantities of interest (velocity, pressure and turbulent viscosity). In addition, for the laminar case, the comparison between the ROM steady-state solution and the data available in literature has been presented. The results have turned out to be very satisfactory both for the accuracy and the computational times. As a major outcome, the approach turns out not to be affected by the energy blow up issue characterizing the results obtained by classic turbulent POD-Galerkin methods.1 aLorenzi, Stefano1 aCammi, Antonio1 aLuzzi, Lelio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/pod-galerkin-method-finite-volume-approximation-navier-stokes-and-rans-equations01502nas a2200121 4500008004100000245010500041210007100146260001000217520097200227100002401199700002101223856013601244 2016 en d00aPOD–Galerkin monolithic reduced order models for parametrized fluid-structure interaction problems0 aPOD–Galerkin monolithic reduced order models for parametrized fl bWiley3 aIn this paper we propose a monolithic approach for reduced order modelling of parametrized fluid-structure interaction problems based on a proper orthogonal decomposition (POD)–Galerkin method. Parameters of the problem are related to constitutive properties of the fluid or structural problem, or to geometrical parameters related to the domain configuration at the initial time. We provide a detailed description of the parametrized formulation of the multiphysics problem in its components, together with some insights on how to obtain an offline-online efficient computational procedure through the approximation of parametrized nonlinear tensors. Then, we present the monolithic POD–Galerkin method for the online computation of the global structural displacement, fluid velocity and pressure of the coupled problem. Finally, we show some numerical results to highlight the capabilities of the proposed reduced order method and its computational performances1 aBallarin, Francesco1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/pod%E2%80%93galerkin-monolithic-reduced-order-models-parametrized-fluid-structure-interaction01116nas a2200109 4500008004100000245007800041210006900119520071700188100002900905700002100934856005100955 2016 en d00aOn point interactions realised as Ter-Martirosyan-Skornyakov Hamiltonians0 apoint interactions realised as TerMartirosyanSkornyakov Hamilton3 aFor quantum systems of zero-range interaction we discuss the mathematical scheme within which modelling the two-body interaction by means of the physically relevant ultra-violet asymptotics known as the ``Ter-Martirosyan--Skornyakov condition'' gives rise to a self-adjoint realisation of the corresponding Hamiltonian. This is done within the self-adjoint extension scheme of Krein, Visik, and Birman. We show that the Ter-Martirosyan--Skornyakov asymptotics is a condition of self-adjointness only when is imposed in suitable functional spaces, and not just as a point-wise asymptotics, and we discuss the consequences of this fact on a model of two identical fermions and a third particle of different nature.1 aMichelangeli, Alessandro1 aOttolini, Andrea uhttp://urania.sissa.it/xmlui/handle/1963/3519502865nas a2200121 4500008004100000245007000041210006900111260001000180520240500190653002302595100002302618856010202641 2016 en d00aPositive solutions to indefinite problems: a topological approach0 aPositive solutions to indefinite problems a topological approach bSISSA3 aThe present Ph.D. thesis is devoted to the study of positive solutions to indefinite problems. In particular, we deal with the second order nonlinear differential equation u'' + a(t) g(u) = 0, where g : [0,+∞[→[0,+∞[ is a continuous nonlinearity and a : [0,T]→R is a Lebesgue integrable sign-changing weight. We analyze the Dirichlet, Neumann and periodic boundary value problems on [0,T] associated with the equation and we provide existence, nonexistence and multiplicity results for positive solutions. In the first part of the manuscript, we investigate nonlinearities g(u) with a superlinear growth at zero and at infinity (including the classical superlinear case g(u)=u^p, with p>1). In particular, we prove that there exist 2^m-1 positive solutions when a(t) has m positive humps separated by negative ones and the negative part of a(t) is sufficiently large. Then, for the Dirichlet problem, we solve a conjecture by Gómez‐Reñasco and López‐Gómez (JDE, 2000) and, for the periodic problem, we give a complete answer to a question raised by Butler (JDE, 1976). In the second part, we study the super-sublinear case (i.e. g(u) is superlinear at zero and sublinear at infinity). If a(t) has m positive humps separated by negative ones, we obtain the existence of 3^m-1 positive solutions of the boundary value problems associated with the parameter-dependent equation u'' + λ a(t) g(u) = 0, when both λ>0 and the negative part of a(t) are sufficiently large. We propose a new approach based on topological degree theory for locally compact operators on open possibly unbounded sets, which applies for Dirichlet, Neumann and periodic boundary conditions. As a byproduct of our method, we obtain infinitely many subharmonic solutions and globally defined positive solutions with complex behavior, and we deal with chaotic dynamics. Moreover, we study positive radially symmetric solutions to the Dirichlet and Neumann problems associated with elliptic PDEs on annular domains. Furthermore, this innovative technique has the potential and the generality needed to deal with indefinite problems with more general differential operators. Indeed, our approach apply also for the non-Hamiltonian equation u'' + cu' + a(t) g(u) = 0. Meanwhile, more general operators in the one-dimensional case and problems involving PDEs will be subjects of future investigations.10apositive solutions1 aFeltrin, Guglielmo uhttps://www.math.sissa.it/publication/positive-solutions-indefinite-problems-topological-approach00997nas a2200145 4500008004100000022001400041245010200055210006900157260000800226300001400234490000700248520053000255100002000785856004600805 2016 eng d a1678-771400aA quadratic interaction estimate for conservation laws: motivations, techniques and open problems0 aquadratic interaction estimate for conservation laws motivations cJun a589–6040 v473 aIn a series of joint works with S. Bianchini [3, 4, 5], we proved a quadratic interaction estimate for general systems of conservation laws. Aim of this paper is to present the results obtained in the three cited articles [3, 4, 5], discussing how they are related with the general theory of hyperbolic conservation laws. To this purpose, first we explain why this quadratic estimate is interesting, then we give a brief overview of the techniques we used to prove it and finally we present some related open problems.

1 aModena, Stefano uhttps://doi.org/10.1007/s00574-016-0171-900510nas a2200121 4500008004100000245008100041210006900122260004500191300001400236490000700250100002000257856011100277 2016 eng d00aQuadratic interaction estimate for hyperbolic conservation laws, an overview0 aQuadratic interaction estimate for hyperbolic conservation laws bPeoples' Friendship University of Russia a148–1720 v591 aModena, Stefano uhttps://www.math.sissa.it/publication/quadratic-interaction-estimate-hyperbolic-conservation-laws-overview00972nas a2200121 4500008004100000245009000041210006900131260001000200520038100210653011700591100001800708856012400726 2016 en d00aQualitative properties and construction of solutions to some semilinear elliptic PDEs0 aQualitative properties and construction of solutions to some sem bSISSA3 aThis thesis is devoted to the study of elliptic equations. On the one hand, we study some qualitative properties, such as symmetry of solutions, on the other hand we explicitly construct some solutions vanishing near some fixed manifold. The main techniques are the moving planes method, in order to investigate the qualitative properties and the Lyapunov-Schmidt reduction.10amoving planes method, maximum principle, Lyapunov-Schmidt reduction, Willmore surfaces, Otha-Kawasaki functional1 aRizzi, Matteo uhttps://www.math.sissa.it/publication/qualitative-properties-and-construction-solutions-some-semilinear-elliptic-pdes-001110nas a2200097 4500008004100000245006200041210006000103520078000163100001800943856005100961 2016 en d00aQuasi-static hydraulic crack growth driven by Darcy's law0 aQuasistatic hydraulic crack growth driven by Darcys law3 aIn the framework of rate independent processes, we present a variational model of quasi-static crack growth in hydraulic fracture. We first introduce the energy functional and study the equilibrium conditions of an unbounded linearly elastic body subject to a remote strain ε ∈ R and with a sufficiently regular crack Γ filled by a volume V of incompressible fluid. In particular, we are able to find the pressure p of the fluid inside the crack as a function of Γ, V , and ε. Then, we study the problem of quasi-static evolution for our model, imposing that the fluid volume V and the fluid pressure p are related by Darcy’s law. We show the existence of such an evolution, and we prove that it satisfies a weak notion of the so-called Griffith’s criterion.

1 aAlmi, Stefano uhttp://urania.sissa.it/xmlui/handle/1963/3519801691nas a2200169 4500008004100000245008700041210006900128260001800197300000600215490000600221520116500227100002101392700001901413700001701432700002101449856005101470 2016 en d00aA Reduced Basis Approach for Modeling the Movement of Nuclear Reactor Control Rods0 aReduced Basis Approach for Modeling the Movement of Nuclear Reac bASMEc02/2016 a80 v23 aThis work presents a reduced order model (ROM) aimed at simulating nuclear reactor control rods movement and featuring fast-running prediction of reactivity and neutron flux distribution as well. In particular, the reduced basis (RB) method (built upon a high-fidelity finite element (FE) approximation) has been employed. The neutronics has been modeled according to a parametrized stationary version of the multigroup neutron diffusion equation, which can be formulated as a generalized eigenvalue problem. Within the RB framework, the centroidal Voronoi tessellation is employed as a sampling technique due to the possibility of a hierarchical parameter space exploration, without relying on a “classical” a posteriori error estimation, and saving an important amount of computational time in the offline phase. Here, the proposed ROM is capable of correctly predicting, with respect to the high-fidelity FE approximation, both the reactivity and neutron flux shape. In this way, a computational speedup of at least three orders of magnitude is achieved. If a higher precision is required, the number of employed basis functions (BFs) must be increased.1 aSartori, Alberto1 aCammi, Antonio1 aLuzzi, Lelio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3519201826nas a2200145 4500008004100000245012700041210006900168260001600237520129800253100002101551700001901572700001701591700002101608856005101629 2016 en d00aReduced basis approaches in time-dependent noncoercive settings for modelling the movement of nuclear reactor control rods0 aReduced basis approaches in timedependent noncoercive settings f bSISSAc20163 aIn this work, two approaches, based on the certified Reduced Basis method, have been developed for simulating the movement of nuclear reactor control rods, in time-dependent non-coercive settings featuring a 3D geometrical framework. In particular, in a first approach, a piece-wise affine transformation based on subdomains division has been implemented for modelling the movement of one control rod. In the second approach, a “staircase” strategy has been adopted for simulating the movement of all the three rods featured by the nuclear reactor chosen as case study. The neutron kinetics has been modelled according to the so-called multi-group neutron diffusion, which, in the present case, is a set of ten coupled parametrized parabolic equations (two energy groups for the neutron flux, and eight for the precursors). Both the reduced order models, developed according to the two approaches, provided a very good accuracy compared with high-fidelity results, assumed as “truth” solutions. At the same time, the computational speed-up in the Online phase, with respect to the fine “truth” finite element discretization, achievable by both the proposed approaches is at least of three orders of magnitude, allowing a real-time simulation of the rod movement and control.

1 aSartori, Alberto1 aCammi, Antonio1 aLuzzi, Lelio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3496301905nas a2200157 4500008004100000245012000041210006900161260002200230300000800252490000700260520128900267100002101556700002201577700002101599856012701620 2016 en d00aReduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries0 aReduced basis method and domain decomposition for elliptic probl bElsevierc01/2016 a4300 v713 aThe aim of this work is to solve parametrized partial differential equations in computational domains represented by networks of repetitive geometries by combining reduced basis and domain decomposition techniques. The main idea behind this approach is to compute once, locally and for few reference shapes, some representative finite element solutions for different values of the parameters and with a set of different suitable boundary conditions on the boundaries: these functions will represent the basis of a reduced space where the global solution is sought for. The continuity of the latter is assured by a classical domain decomposition approach. Test results on Poisson problem show the flexibility of the proposed method in which accuracy and computational time may be tuned by varying the number of reduced basis functions employed, or the set of boundary conditions used for defining locally the basis functions. The proposed approach simplifies the pre-computation of the reduced basis space by splitting the global problem into smaller local subproblems. Thanks to this feature, it allows dealing with arbitrarily complex network and features more flexibility than a classical global reduced basis approximation where the topology of the geometry is fixed.1 aIapichino, Laura1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduced-basis-method-and-domain-decomposition-elliptic-problems-networks-and-complex01201nas a2200145 4500008004100000245005000041210005000091260003400141300001400175490000700189520075600196100002200952700003100974856005001005 2016 eng d00aRefined node polynomials via long edge graphs0 aRefined node polynomials via long edge graphs bInternational Press of Boston a193–2340 v103 aThe generating functions of the Severi degrees for sufficiently ample line bundles on algebraic surfaces are multiplicative in the topological invariants of the surface and the line bundle. Recently new proofs of this fact were given for toric surfaces by Block, Colley, Kennedy and Liu, Osserman, using tropical geometry and in particular the combinatorial tool of long-edged graphs. In the first part of this paper these results are for $\mathbb{P}^2$ and rational ruled surfaces generalised to refined Severi degrees. In the second part of the paper we give a number of mostly conjectural generalisations of this result to singular surfaces, and curves with prescribed multiple points. The formulas involve modular forms and theta functions.

1 aGöttsche, Lothar1 aKikwai, Benjamin, Kipkirui uhttp://dx.doi.org/10.4310/CNTP.2016.v10.n2.a201365nas a2200145 4500008004100000245009200041210006900133300000900202490000700211520090200218100002301120700002101143700001601164856003901180 2016 eng d00aRenormalization for Autonomous Nearly Incompressible BV Vector Fields in Two Dimensions0 aRenormalization for Autonomous Nearly Incompressible BV Vector F a1-330 v483 aGiven a bounded autonomous vector field $b \colon \mathbb{R}^d \to \mathbb{R}^d$, we study the uniqueness of bounded solutions to the initial value problem for the related transport equation \begin{equation*} \partial_t u + b \cdot \nabla u= 0. \end{equation*} We are interested in the case where $b$ is of class BV and it is nearly incompressible. Assuming that the ambient space has dimension $d=2$, we prove uniqueness of weak solutions to the transport equation. The starting point of the present work is the result which has been obtained in [7] (where the steady case is treated). Our proof is based on splitting the equation onto a suitable partition of the plane: this technique was introduced in [3], using the results on the structure of level sets of Lipschitz maps obtained in [1]. Furthermore, in order to construct the partition, we use Ambrosio's superposition principle [4].

1 aBianchini, Stefano1 aBonicatto, Paolo1 aGusev, N.A. uhttps://doi.org/10.1137/15M100738000485nas a2200145 4500008004100000022001400041245008800055210006900143300001700212490000800229100001900237700001600256700002200272856004500294 2016 eng d a1364-502100aRogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation0 aRogue waves in multiphase solutions of the focusing nonlinear Sc a20160340, 120 v4721 aBertola, Marco1 aEl, Gennady1 aTovbis, Alexander uhttp://dx.doi.org/10.1098/rspa.2016.034000431nas a2200133 4500008004100000245004100041210004000082260001000122100002700132700001700159700002200176700002000198856007900218 2016 en d00aSecond-order structured deformations0 aSecondorder structured deformations bSISSA1 aBarroso, Ana, Cristina1 aMatias, Jose1 aMorandotti, Marco1 aOwen, David, R. uhttps://www.math.sissa.it/publication/second-order-structured-deformations00651nas a2200157 4500008004100000245009600041210006900137260005800206300001400264490000600278100001700284700001700301700002200318700002400340856012900364 2016 eng d00aShip Sinkage and Trim Predictions Based on a CAD Interfaced Fully Nonlinear Potential Model0 aShip Sinkage and Trim Predictions Based on a CAD Interfaced Full bInternational Society of Offshore and Polar Engineers a511–5180 v31 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio1 aBerti, Massimiliano uhttps://www.math.sissa.it/publication/ship-sinkage-and-trim-predictions-based-cad-interfaced-fully-nonlinear-potential-model00397nas a2200121 4500008004100000245004500041210004500086490000900131100001900140700002000159700001300179856008300192 2016 eng d00aSimple Lie Algebras and Topological ODEs0 aSimple Lie Algebras and Topological ODEs0 v20161 aBertola, Marco1 aDubrovin, Boris1 aYang, Di uhttps://www.math.sissa.it/publication/simple-lie-algebras-and-topological-odes00434nas a2200109 4500008004100000245006500041210006200106100001900168700002500187700002200212856009000234 2016 eng d00aOn Sobolev instability of the interior problem of tomography0 aSobolev instability of the interior problem of tomography1 aBertola, Marco1 aKatsevich, Alexander1 aTovbis, Alexander uhttps://www.math.sissa.it/publication/sobolev-instability-interior-problem-tomography00428nas a2200097 4500008004100000245008000041210006900121260001000190100001900200856011100219 2016 en d00aSome results on quasistatic evolution problems for unidirectional processes0 aSome results on quasistatic evolution problems for unidirectiona bSISSA1 aCrismale, Vito uhttps://www.math.sissa.it/publication/some-results-quasistatic-evolution-problems-unidirectional-processes01439nas a2200121 4500008004100000245010500041210006900146260001000215520093000225653002301155100001801178856012101196 2016 en d00aSome results on the mathematical analysis of crack problems with forces applied on the fracture lips0 aSome results on the mathematical analysis of crack problems with bSISSA3 aThis thesis is devoted to the study of some models of fracture growth in elastic materials, characterized by the presence of forces acting on the crack lips. Working in the general framework of rate-independent processes, we first discuss a variational formulation of the problem of quasi-static crack evolution in hydraulic fracture. Then, we investigate the crack growth process in a cohesive fracture model, showing the existence of an evolution satisfying a weak Griffith's criterion. Finally, in the last chapter of this work we investigate, in the static case, the interaction between the energy spent in order to create a new fracture and the energy spent by the applied surface forces. This leads us to study the lower semicontinuity properties of a free discontinuity functional F(u) that can be written as the sum of a crack term, depending on the jump set of u, and of a boundary term, depending on the trace of u.10aFracture mechanics1 aAlmi, Stefano uhttps://www.math.sissa.it/publication/some-results-mathematical-analysis-crack-problems-forces-applied-fracture-lips01230nas 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/10.1080/03605302.2015.109576601093nas a2200121 4500008004100000245010400041210006900145260001000214520065500224100002300879700001800902856005100920 2016 en d00aOn the structure of $L^\infty$-entropy solutions to scalar conservation laws in one-space dimension0 astructure of Linftyentropy solutions to scalar conservation laws bSISSA3 aWe prove that if $u$ is the entropy solution to a scalar conservation law in one space dimension, then the entropy dissipation is a measure concentrated on countably many Lipschitz curves. This result is a consequence of a detailed analysis of the structure of the characteristics. In particular the characteristic curves are segments outside a countably 1-rectifiable set and the left and right traces of the solution exist in a $C^0$-sense up to the degeneracy due to the segments where $f''=0$. We prove also that the initial data is taken in a suitably strong sense and we give some counterexamples which show that these results are sharp.

1 aBianchini, Stefano1 aMarconi, Elio uhttp://urania.sissa.it/xmlui/handle/1963/3520901192nas a2200181 4500008004100000022001400041245008800055210006900143260000800212300000700220490000900227520063800236100002200874700002000896700002600916700002400942856004400966 2016 eng d a1029-847900aSymmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index0 aSymmetry enhancements via 5d instantons qWalgebrae and 10 superc cSep a530 v20163 aWe explore $\mathcal{N}=(1,0)$ superconformal six-dimensional theories arising from M5 branes probing a transverse $A_k$ singularity. Upon circle compactification to 5 dimensions, we describe this system with a dual pq-web of five-branes and propose the spectrum of basic five-dimensional instanton operators driving global symmetry enhancement. For a single M5 brane, we find that the exact partition function of the 5d quiver gauge theory matches the 6d (1, 0) index, which we compute by letter counting. We finally show that S-duality of the pq-web implies new relations among vertex correlators of $q\mathcal{W}$ algebrae.

1 aBenvenuti, Sergio1 aBonelli, Giulio1 aRonzani, Massimiliano1 aTanzini, Alessandro uhttps://doi.org/10.1007/JHEP09(2016)05300553nas a2200145 4500008004100000245008000041210006900121260002200190300001600212490000700228100002000235700002200255700001800277856011200295 2016 eng d00aSymmetry properties of some solutions to some semilinear elliptic equations0 aSymmetry properties of some solutions to some semilinear ellipti bClasse di Scienze a1209–12340 v161 aFarina, Alberto1 aMalchiodi, Andrea1 aRizzi, Matteo uhttps://www.math.sissa.it/publication/symmetry-properties-some-solutions-some-semilinear-elliptic-equations01183nas a2200121 4500008004100000245007100041210006300112260001800175520077400193100002100967700002200988856005101010 2016 en d00aOn the third critical speed for rotating Bose-Einstein condensates0 athird critical speed for rotating BoseEinstein condensates bAIP Publisher3 aWe study a two-dimensional rotating Bose-Einstein condensate confined by an anharmonic trap in the framework of the Gross-Pitaevskii theory. We consider a rapid rotation regime close to the transition to a giant vortex state. It was proven in Correggi et al. [J. Math. Phys. 53, 095203 (2012)] that such a transition occurs when the angular velocity is of order ε−4, with ε−2 denoting the coefficient of the nonlinear term in the Gross-Pitaevskii functional and ε ≪ 1 (Thomas-Fermi regime). In this paper, we identify a finite value Ωc such that if Ω = Ω0/ε4 with Ω0 > Ωc, the condensate is in the giant vortex phase. Under the same condition, we prove a refined energy asymptotics and an estimate of the winding number of any Gross-Pitaevskii minimizer.1 aDimonte, Daniele1 aCorreggi, Michele uhttp://urania.sissa.it/xmlui/handle/1963/3524601454nas 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.93.06600100906nas a2200157 4500008004100000022001400041245004500055210004400100260000800144300001400152490000700166520048600173100002300659700002000682856004600702 2016 eng d a1572-909500at-Structures are Normal Torsion Theories0 atStructures are Normal Torsion Theories cApr a181–2080 v243 aWe characterize $t$-structures in stable ∞-categories as suitable quasicategorical factorization systems. More precisely we show that a $t$-structure $\mathcal{t}$ on a stable $\infty$-category $\mathbb{C}$ is equivalent to a normal torsion theory $\mathbf{F}$ on $\mathbb{C}$, i.e. to a factorization system $\mathbf{F} = (\mathcal{\epsilon}, \mathcal{M})$ where both classes satisfy the 3-for-2 cancellation property, and a certain compatibility with pullbacks/pushouts.

1 aFiorenza, Domenico1 aLoregian, Fosco uhttps://doi.org/10.1007/s10485-015-9393-z01189nas a2200121 4500008004100000245005100041210004600092260001000138520072900148653011900877100002000996856005101016 2016 en d00at-structures on stable (infinity,1)-categories0 atstructures on stable infinity1categories bSISSA3 aThe present work re-enacts the classical theory of t-structures reducing the classical definition coming from Algebraic Geometry to a rather primitive categorical gadget: suitable reflective factorization systems (defined in the work of Rosický, Tholen, and Cassidy-Hébert-Kelly), which we call "normal torsion theories" following. A relation between these two objects has previously been noticed by other authors, on the level of the triangulated homotopy categories of stable (infinity,1)-categories. The main achievement of the present thesis is to observe and prove that this relation exists genuinely when the definition is lifted to the higher-dimensional world where the notion of triangulated category comes from.10acategory theory, higher category theory, factorization system, torsion theory, homological algebra, higher algebra1 aLoregian, Fosco uhttp://urania.sissa.it/xmlui/handle/1963/3520200745nas a2200121 4500008004100000245005600041210005600097260001000153520032000163653003100483100001800514856009100532 2016 en d00aTwo explorations in Dynamical Systems and Mechanics0 aTwo explorations in Dynamical Systems and Mechanics bSISSA3 aThis thesis contains the work done by Paolo Gidoni during the doctorate programme in Matematical Analysis at SISSA, under the supervision of A. Fonda and A. DeSimone. The thesis is composed of two parts: "Avoiding cones conditions and higher dimensional twist" and "Directional friction in bio-inspired locomotion".10aPoincaré-Birkhoff Theorem1 aGidoni, Paolo uhttps://www.math.sissa.it/publication/two-explorations-dynamical-systems-and-mechanics00786nas a2200157 4500008004100000022001400041245009300055210006900148260000800217300000700225490000700232520030000239100001900539700002400558856004600582 2016 eng d a1432-083500aViscous approximation of quasistatic evolutions for a coupled elastoplastic-damage model0 aViscous approximation of quasistatic evolutions for a coupled el cJan a170 v553 aEmploying the technique of vanishing viscosity and time rescaling, we show the existence of quasistatic evolutions for elastoplastic materials with incomplete damage affecting both the elastic tensor and the plastic yield surface, in a softening framework and in small strain assumptions.

1 aCrismale, Vito1 aLazzaroni, Giuliano uhttps://doi.org/10.1007/s00526-015-0947-600469nas 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-dynamics00968nas a2200145 4500008004100000022001400041245003700055210003700092300000900129490000700138520055900145100002200704700002000726856007600746 2016 eng d a1078-094700aYoung towers for product systems0 aYoung towers for product systems a14650 v363 aWe show that the direct product of maps with Young towers admits a Young tower whose return times decay at a rate which is bounded above by the slowest of the rates of decay of the return times of the component maps. An application of this result, together with other results in the literature, yields various statistical properties for the direct product of various classes of systems, including Lorenz-like maps, multimodal maps, piecewise $C^2$ interval maps with critical points and singularities, Hénon maps and partially hyperbolic systems.

1 aLuzzatto, Stefano1 aRuziboev, Marks uhttp://aimsciences.org//article/id/18d4526e-470d-467e-967a-a0345ad4c64201400nas 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/s00220-015-2552-001380nas a2200133 4500008004300000245007200043210006900115260001500184520093400199100001901133700001801152700002501170856005101195 2015 en_Ud 00aAnisotropic mean curvature on facets and relations with capillarity0 aAnisotropic mean curvature on facets and relations with capillar bde Gruyter3 aWe discuss the relations between the anisotropic calibrability of a facet F of a solid crystal E, and the capillary problem on a capillary tube with base F. When F is parallel to a facet of the Wulff shape, calibrability is equivalent to show the existence of an anisotropic subunitary vector field in $F, with suitable normal trace on the boundary of the facet, and with constant divergence equal to the anisotropic mean curvature of F. When the Wulff shape is a cylynder, assuming E convex at F, and F (strictly) calibrable, such a vector field is obtained by solving the capillary problem on F in absence of gravity and with zero contact angle. We show some examples of facets for which it is possible, even without the strict calibrability assumption, to build one of these vector fields. The construction provides, at least for convex facets of class C^{1,1}, the solution of the total variation flow starting at 1_F.

1 aAmato, Stefano1 aTealdi, Lucia1 aBellettini, Giovanni uhttp://urania.sissa.it/xmlui/handle/1963/3448100522nas a2200133 4500008004100000022001400041245015400055210006900209300001400278490000700292100001900299700002200318856004800340 2015 eng d a0176-427600aAsymptotics of orthogonal polynomials with complex varying quartic weight: global structure, critical point behavior and the first Painlevé equation0 aAsymptotics of orthogonal polynomials with complex varying quart a529–5870 v411 aBertola, Marco1 aTovbis, Alexander uhttp://dx.doi.org/10.1007/s00365-015-9288-001510nas a2200121 4500008004100000245009300041210006900134520100200203100001701205700001701222700002401239856012501263 2015 en d00aBenchmarking the Immersed Finite Element Method for Fluid-Structure Interaction Problems0 aBenchmarking the Immersed Finite Element Method for FluidStructu3 aWe present an implementation of a fully variational formulation of an immersed methods for fluid-structure interaction problems based on the finite element method. While typical implementation of immersed methods are characterized by the use of approximate Dirac delta distributions, fully variational formulations of the method do not require the use of said distributions. In our implementation the immersed solid is general in the sense that it is not required to have the same mass density and the same viscous response as the surrounding fluid. We assume that the immersed solid can be either viscoelastic of differential type or hyperelastic. Here we focus on the validation of the method via various benchmarks for fluid-structure interaction numerical schemes. This is the first time that the interaction of purely elastic compressible solids and an incompressible fluid is approached via an immersed method allowing a direct comparison with established benchmarks.1 aSaswati, Roy1 aHeltai, Luca1 aCostanzo, Francesco uhttps://www.math.sissa.it/publication/benchmarking-immersed-finite-element-method-fluid-structure-interaction-problems-000903nas a2200133 4500008004100000245009000041210006900131260001000200520043700210100002100647700002400668700002700692856005000719 2015 en d00aA bridging mechanism in the homogenisation of brittle composites with soft inclusions0 abridging mechanism in the homogenisation of brittle composites w bSISSA3 aWe provide a homogenisation result for the energy-functional associated with a purely brittle composite whose microstructure is characterised by soft periodic inclusions embedded in a stiffer matrix. We show that the two constituents as above can be suitably arranged on a microscopic scale ε to obtain, in the limit as ε tends to zero, a homogeneous macroscopic energy-functional explicitly depending on the opening of the crack.1 aBarchiesi, Marco1 aLazzaroni, Giuliano1 aZeppieri, Caterina Ida uhttp://urania.sissa.it/xmlui/handle/1963/749201368nam a2200229 4500008004100000020002200041022001400063245008400077210006900161250000600230260002600236300000800262520053600270653003000806653002800836653004800864653004500912100002200957700002100979700002001000856011801020 2015 eng d a978-3-319-22469-5 a2191-820100aCertified Reduced Basis Methods for Parametrized Partial Differential Equations0 aCertified Reduced Basis Methods for Parametrized Partial Differe a1 aSwitzerlandbSpringer a1353 aThis book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.

10aa posteriori error bounds10aempirical interpolation10aparametrized partial differential equations10areduced basis methods, greedy algorithms1 aHesthaven, Jan, S1 aRozza, Gianluigi1 aStamm, Benjamin uhttps://www.math.sissa.it/publication/certified-reduced-basis-methods-parametrized-partial-differential-equations01837nas a2200145 4500008004100000245007900041210006900120520133000189100002201519700002901541700002001570700002901590700002101619856005101640 2015 en d00aA class of Hamiltonians for a three-particle fermionic system at unitarity0 aclass of Hamiltonians for a threeparticle fermionic system at un3 aWe consider a quantum mechanical three-particle system made of two identical fermions of mass one and a different particle of mass $m$, where each fermion interacts via a zero-range force with the different particle. In particular we study the unitary regime, i.e., the case of infinite two-body scattering length. The Hamiltonians describing the system are, by definition, self-adjoint extensions of the free Hamiltonian restricted on smooth functions vanishing at the two-body coincidence planes, i.e., where the positions of two interacting particles coincide. It is known that for $m$ larger than a critical value $m^* \simeq (13.607)^{-1}$ a self-adjoint and lower bounded Hamiltonian $H_0$ can be constructed, whose domain is characterized in terms of the standard point-interaction boundary condition at each coincidence plane. Here we prove that for $m\in(m^*,m^{**})$, where $m^{**}\simeq (8.62)^{-1}$, there is a further family of self-adjoint and lower bounded Hamiltonians $H_{0,\beta}$, $\beta \in \mathbb{R}$, describing the system. Using a quadratic form method, we give a rigorous construction of such Hamiltonians and we show that the elements of their domains satisfy a further boundary condition, characterizing the singular behavior when the positions of all the three particles coincide.1 aCorreggi, Michele1 aDell'Antonio, Gianfausto1 aFinco, Domenico1 aMichelangeli, Alessandro1 aTeta, Alessandro uhttp://urania.sissa.it/xmlui/handle/1963/3446901802nas a2200229 4500008004100000245010400041210006900145300001400214490000700228520107100235653001001306653001001316653002901326653001501355653002001370653002501390653001801415100003301433700002001466700002501486856006101511 2015 eng d00aA compatible-incompatible decomposition of symmetric tensors in Lp with application to elasticity0 acompatibleincompatible decomposition of symmetric tensors in Lp a5217-52300 v383 aIn this paper, we prove the Saint-Venant compatibility conditions in $L^p$ for $p\in(1,∞)$, in a simply connected domain of any space dimension. As a consequence, alternative, simple, and direct proofs of some classical Korn inequalities in Lp are provided. We also use the Helmholtz decomposition in $L^p$ to show that every symmetric tensor in a smooth domain can be decomposed in a compatible part, which is the symmetric part of a displacement gradient, and in an incompatible part, which is the incompatibility of a certain divergence-free tensor. Moreover, under a suitable Dirichlet boundary condition, this Beltrami-type decomposition is proved to be unique. This decomposition result has several applications, one of which being in dislocation models, where the incompatibility part is related to the dislocation density and where $1 < p < 2$. This justifies the need to generalize and prove these rather classical results in the Hilbertian case ($p = 2$), to the full range $p\in(1,∞)$. Copyright © 2015 John Wiley & Sons, Ltd.

10a35J5810a35Q7410acompatibility conditions10aelasticity10aKorn inequality10astrain decomposition10asubclass74B051 aMaggiani, Giovanni, Battista1 aScala, Riccardo1 aVan Goethem, Nicolas uhttps://onlinelibrary.wiley.com/doi/abs/10.1002/mma.345001202nas 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-problems00336nas a2200097 4500008004100000245004100041210004100082100002000123700002300143856007200166 2015 eng d00aConvergence rate of the Glimm scheme0 aConvergence rate of the Glimm scheme1 aModena, Stefano1 aBianchini, Stefano uhttps://www.math.sissa.it/publication/convergence-rate-glimm-scheme01185nas a2200121 4500008004100000245008500041210006900126260001000195520076800205100002100973700001800994856005101012 2015 en d00aConvex combinations of low eigenvalues, Fraenkel asymmetries and attainable sets0 aConvex combinations of low eigenvalues Fraenkel asymmetries and bSISSA3 aWe consider the problem of minimizing convex combinations of the first two eigenvalues of the Dirichlet-Laplacian among open set of $R^N$ of fixed measure. We show that, by purely elementary arguments, based on the minimality condition, it is possible to obtain informations on the geometry of the minimizers of convex combinations: we study, in particular, when these minimizers are no longer convex, and the optimality of balls. As an application of our results we study the boundary of the attainable set for the Dirichlet spectrum. Our techniques involve symmetry results à la Serrin, explicit constants in quantitative inequalities, as well as a purely geometrical problem: the minimization of the Fraenkel 2-asymmetry among convex sets of fixed measure.1 aMazzoleni, Dario1 aZucco, Davide uhttp://urania.sissa.it/xmlui/handle/1963/3514001640nas a2200145 4500008004100000245007700041210006900118260001000187520116500197100002101362700002101383700002201404700001701426856005101443 2015 en d00aDeal2lkit: a Toolkit Library for High Performance Programming in deal.II0 aDeal2lkit a Toolkit Library for High Performance Programming in bSISSA3 aWe present version 1.0.0 of the deal2lkit (deal.II ToolKit) library. deal2lkit is a collection of modules and classes for the general purpose finite element library deal.II. Its principal aim is to provide a high level interface, controlled via parameter files, for those steps that are common in all finite element programs: mesh generation, selection of the finite element type, application of boundary conditions and many others. Each module can be used as a building block independently on the others, and can be integrated in existing finite element codes based on deal.II, drastically reducing the size of programs, rendering their use automatically parametrised, and reducing the overall time-to-market of finite element programming. Moreover, deal2lkit features interfaces with the SUNDIALS (SUite of Nonlinear and DIfferential/ALgebraic equation Solvers) and ASSIMP (Open Asset Import Library) libraries. Some examples are provided which show the aim and scopes of deal2lkit. The deal2lkit library is released under the GNU Lesser General Public License (LGPL) and can be retrieved from the deal2lkit repository https://github.com/mathLab/deal2lkit.1 aSartori, Alberto1 aGiuliani, Nicola1 aBardelloni, Mauro1 aHeltai, Luca uhttp://urania.sissa.it/xmlui/handle/1963/3500600596nas a2200181 4500008004100000245003700041210003000078520010700108100001700215700001800232700001700250700001700267700002400284700002000308700001700328700001800345856005100363 2015 en d00aThe deal.II Library, Version 8.20 adealII Library Version 823 aThis paper provides an overview of the new features of the finite element library deal.II version 8.21 aBangerth, W.1 aHeister, Timo1 aHeltai, Luca1 aKanschat, G.1 aKronbichler, Martin1 aMaier, Matthias1 aTurcksin, B.1 aYoung, T., D. uhttp://urania.sissa.it/xmlui/handle/1963/3446400709nas a2200133 4500008004100000245007500041210007000116260002100186300001200207490000700219520027900226100002000505856005000525 2015 eng d00aDecay of correlations for invertible maps with non-Hölder observables0 aDecay of correlations for invertible maps with nonHölder observa bTaylor & Francis a341-3520 v303 aAn invertible dynamical system with some hyperbolic structure is considered. Upper estimates for the correlations of continuous observables are given in terms of modulus of continuity. The result is applied to certain Hénon maps and Solenoid maps with intermittency.

1 aRuziboev, Marks uhttps://doi.org/10.1080/14689367.2015.104681600480nas a2200133 4500008004100000022001400041245011900055210006900174300001500243490000700258100001900265700002200284856004000306 2015 eng d a0022-248800aA degeneration of two-phase solutions of the focusing nonlinear Schrödinger equation via Riemann-Hilbert problems0 adegeneration of twophase solutions of the focusing nonlinear Sch a061507, 170 v561 aBertola, Marco1 aGiavedoni, Pietro uhttp://dx.doi.org/10.1063/1.492236201006nas a2200097 4500008004100000245007800041210006900119520059600188100001900784856010500803 2015 en d00aDispersive deformations of the Hamiltonian structure of Euler's equations0 aDispersive deformations of the Hamiltonian structure of Eulers e3 aEuler's equations for a two-dimensional system can be written in Hamiltonian form, where the Poisson bracket is the Lie-Poisson bracket associated to the Lie algebra of divergence free vector fields. We show how to derive the Poisson brackets of 2d hydrodynamics of ideal fluids as a reduction from the one associated to the full algebra of vector fields. Motivated by some recent results about the deformations of Lie-Poisson brackets of vector fields, we study the dispersive deformations of the Poisson brackets of Euler's equation and show that, up to the second order, they are trivial.1 aCasati, Matteo uhttps://www.math.sissa.it/publication/dispersive-deformations-hamiltonian-structure-eulers-equations01384nas a2200133 4500008004100000245008700041210006900128260001000197520092000207100002701127700002301154700002201177856005101199 2015 en d00aDynamics of screw dislocations: a generalised minimising-movements scheme approach0 aDynamics of screw dislocations a generalised minimisingmovements bSISSA3 aThe gradient flow structure of the model introduced in [CG99] for the dynamics of screw dislocations is investigated by means of a generalised minimising-movements scheme approach. The assumption of a finite number of available glide directions, together with the "maximal dissipation criterion" that governs the equations of motion, results into solving a differential inclusion rather than an ODE. This paper addresses how the model in [CG99] is connected to a time-discrete evolution scheme which explicitly confines dislocations to move each time step along a single glide direction. It is proved that the time-continuous model in [CG99] is the limit of these time-discrete minimising-movement schemes when the time step converges to 0. The study presented here is a first step towards a generalization of the setting in [AGS08, Chap. 2 and 3] that allows for dissipations which cannot be described by a metric.1 aBonaschi, Giovanni, A.1 aVan Meurs, Patrick1 aMorandotti, Marco uhttp://urania.sissa.it/xmlui/handle/1963/3449501187nas a2200193 4500008004100000022001400041245006700055210006700122300001200189490000800201520057400209653002100783653002900804653002400833653002900857653001600886100002000902856007100922 2015 eng d a0022-247X00aExistence and multiplicity result for the singular Toda system0 aExistence and multiplicity result for the singular Toda system a49 - 850 v4243 aWe consider the Toda system on a compact surface (Σ,g)−Δu1=2ρ1(h1eu1∫Σh1eu1dVg−1)−ρ2(h2eu2∫Σh2eu2dVg−1)−4π∑j=1Jα1j(δpj−1),−Δu2=2ρ2(h2eu2∫Σh2eu2dVg−1)−ρ1(h1eu1∫Σh1eu1dVg−1)−4π∑j=1Jα2j(δpj−1), where hi are smooth positive functions, ρi are positive real parameters, pj are given points on Σ and αij are numbers greater than −1. We give existence and multiplicity results, using variational and Morse-theoretical methods. It is the first existence result when some of the αij's are allowed to be negative."

10aExistence result10aLiouville-type equations10aMultiplicity result10aPDEs on compact surfaces10aToda system1 aBattaglia, Luca uhttp://www.sciencedirect.com/science/article/pii/S0022247X1401019101267nas a2200121 4500008004100000245009800041210006900139520082000208100002101028700002601049700001901075856005101094 2015 en d00aExistence for constrained dynamic Griffith fracture with a weak maximal dissipation condition0 aExistence for constrained dynamic Griffith fracture with a weak 3 aThere are very few existence results for fracture evolution, outside of globally minimizing quasi-static evolutions. Dynamic evolutions are particularly problematic, due to the difficulty of showing energy balance, as well as of showing that solutions obey a maximal dissipation condition, or some similar condition that prevents stationary cracks from always being solutions. Here we introduce a new weak maximal dissipation condition and show that it is compatible with cracks constrained to grow smoothly on a smooth curve. In particular, we show existence of dynamic fracture evolutions satisfying this maximal dissipation condition, subject to the above smoothness constraints, and exhibit explicit examples to show that this maximal dissipation principle can indeed rule out stationary cracks as solutions.1 aDal Maso, Gianni1 aLarsen, Cristopher J.1 aToader, Rodica uhttp://urania.sissa.it/xmlui/handle/1963/3504501084nas a2200121 4500008004100000245013700041210006900178260002300247520059900270100002300869700001900892856005100911 2015 en d00aExistence of positive solutions in the superlinear case via coincidence degree: the Neumann and the periodic boundary value problems0 aExistence of positive solutions in the superlinear case via coin bKhayyam Publishing3 aWe prove the existence of positive periodic solutions for the second order nonlinear equation u'' + a(x) g(u) = 0, where g(u) has superlinear growth at zero and at infinity. The weight function a(x) is allowed to change its sign. Necessary and sufficient conditions for the existence of nontrivial solutions are obtained. The proof is based on Mawhin's coincidence degree and applies also to Neumann boundary conditions. Applications are given to the search of positive solutions for a nonlinear PDE in annular domains and for a periodic problem associated to a non-Hamiltonian equation.

1 aFeltrin, Guglielmo1 aZanolin, Fabio uhttp://projecteuclid.org/euclid.ade/143506451801364nas a2200181 4500008004100000022001400041245009900055210006900154300000800223490000900231520072700240653002700967653002300994653004101017653002501058100002301083856007601106 2015 eng d a0133-018900aExistence of positive solutions of a superlinear boundary value problem with indefinite weight0 aExistence of positive solutions of a superlinear boundary value a4360 v20153 aWe deal with the existence of positive solutions for a two-point boundary value problem associated with the nonlinear second order equation $u''+a(x)g(u)=0$. The weight $a(x)$ is allowed to change sign. We assume that the function $g\colon\mathopen[0,+∞\mathclose[\to\mathbb{R}$ is continuous, $g(0)=0$ and satisfies suitable growth conditions, including the superlinear case $g(s)=s^p$, with $p>1$. In particular we suppose that $g(s)/s$ is large near infinity, but we do not require that $g(s)$ is non-negative in a neighborhood of zero. Using a topological approach based on the Leray-Schauder degree we obtain a result of existence of at least a positive solution that improves previous existence theorems.

10aboundary value problem10aindefinite weight10aPositive solution; existence result.10asuperlinear equation1 aFeltrin, Guglielmo uhttp://aimsciences.org//article/id/b3c1c765-e8f5-416e-8130-05cc4847802600594nas a2200145 4500008004100000245009400041210006900135260001300204300001200217100001900229700001700248700003200265700002600297856012500323 2015 eng d00aExperience on vectorizing lattice Boltzmann kernels for multi-and many-core architectures0 aExperience on vectorizing lattice Boltzmann kernels for multiand bSpringer a53–621 aCalore, Enrico1 aDemo, Nicola1 aSchifano, Sebastiano, Fabio1 aTripiccione, Raffaele uhttps://www.math.sissa.it/publication/experience-vectorizing-lattice-boltzmann-kernels-multi-and-many-core-architectures02252nas a2200145 4500008004100000245009600041210006900137260001000206520175300216100002701969700001701996700002202013700002002035856005102055 2015 en d00aExplicit formulas for relaxed disarrangement densities arising from structured deformations0 aExplicit formulas for relaxed disarrangement densities arising f bSISSA3 aStructured deformations provide a multiscale geometry that captures the contributions at the macrolevel of both smooth geometrical changes and non-smooth geometrical changes (disarrangements) at submacroscopic levels. For each (first-order) structured deformation (g,G) of a continuous body, the tensor field G is known to be a measure of deformations without disarrangements, and M:=∇g−G is known to be a measure of deformations due to disarrangements. The tensor fields G and M together deliver not only standard notions of plastic deformation, but M and its curl deliver the Burgers vector field associated with closed curves in the body and the dislocation density field used in describing geometrical changes in bodies with defects. Recently, Owen and Paroni [13] evaluated explicitly some relaxed energy densities arising in Choksi and Fonseca’s energetics of structured deformations [4] and thereby showed: (1) (trM)+ , the positive part of trM, is a volume density of disarrangements due to submacroscopic separations, (2) (trM)−, the negative part of trM, is a volume density of disarrangements due to submacroscopic switches and interpenetrations, and (3) trM, the absolute value of trM, is a volume density of all three of these non-tangential disarrangements: separations, switches, and interpenetrations. The main contribution of the present research is to show that a different approach to the energetics of structured deformations, that due to Ba\'{i}a, Matias, and Santos [1], confirms the roles of (trM)+, (trM)−, and trM established by Owen and Paroni. In doing so, we give an alternative, shorter proof of Owen and Paroni’s results, and we establish additional explicit formulas for other measures of disarrangements.1 aBarroso, Ana, Cristina1 aMatias, Jose1 aMorandotti, Marco1 aOwen, David, R. uhttp://urania.sissa.it/xmlui/handle/1963/3449200912nas a2200145 4500008004100000245010700041210006900148260001000217520041300227100002000640700002400660700001800684700001600702856004800718 2015 en d00aExtended affine Weyl groups of BCD type, Frobenius manifolds and their Landau-Ginzburg superpotentials0 aExtended affine Weyl groups of BCD type Frobenius manifolds and bSISSA3 aFor the root systems of type Bl, Cl and Dl, we generalize the result of [7] by showing the existence of Frobenius manifold structures on the orbit spaces of the extended affine Weyl groups that correspond to any vertex of the Dynkin diagram instead of a particular choice made in [7]. It also depends on certain additional data. We also construct LG superpotentials for these Frobenius manifold structures.1 aDubrovin, Boris1 aStrachan, Ian, A.B.1 aZhang, Youjin1 aZuo, Dafeng uhttp://preprints.sissa.it/handle/1963/3531601820nas a2200169 4500008004100000245015600041210006900197520118400266100002401450700002001474700002001494700002001514700002201534700002101556700002201577856005101599 2015 en d00aFast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization0 aFast simulations of patientspecific haemodynamics of coronary ar3 aIn this work a reduced-order computational framework for the study of haemodynamics in three-dimensional patient-specific configurations of coronary artery bypass grafts dealing with a wide range of scenarios is proposed. We combine several efficient algorithms to face at the same time both the geometrical complexity involved in the description of the vascular network and the huge computational cost entailed by time dependent patient-specific flow simulations. Medical imaging procedures allow to reconstruct patient-specific configurations from clinical data. A centerlines-based parametrization is proposed to efficiently handle geometrical variations. POD–Galerkin reduced-order models are employed to cut down large computational costs. This computational framework allows to characterize blood flows for different physical and geometrical variations relevant in the clinical practice, such as stenosis factors and anastomosis variations, in a rapid and reliable way. Several numerical results are discussed, highlighting the computational performance of the proposed framework, as well as its capability to perform sensitivity analysis studies, so far out of reach.1 aBallarin, Francesco1 aFaggiano, Elena1 aIppolito, Sonia1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi1 aScrofani, Roberto uhttp://urania.sissa.it/xmlui/handle/1963/3462301899nas a2200133 4500008004300000245010100043210006900144520142800213100002101641700001701662700001701679700001801696856005101714 2015 en_Ud 00aFEM SUPG stabilisation of mixed isoparametric BEMs: application to linearised free surface flows0 aFEM SUPG stabilisation of mixed isoparametric BEMs application t3 aIn finite element formulations, transport dominated problems are often stabilised through the Streamline-Upwind-Petrov–Galerkin (SUPG) method. Its application is straightforward when the problem at hand is solved using Galerkin methods. Applications of boundary integral formulations often resort to collocation techniques which are computationally more tractable. In this framework, the Galerkin method and the stabilisation may still be used to successfully apply boundary conditions and resolve instabilities that are frequently observed in transport dominated problems. We apply this technique to an adaptive collocation boundary element method for the solution of stationary potential flows, where we solve a mixed Poisson problem in boundary integral form, with the addition of linearised free surface boundary conditions. We use a mixed boundary element formulation to allow for different finite dimensional spaces describing the flow potential and its normal derivative, and we validate our method simulating the flow around both a submerged body and a surface piercing body. The coupling of mixed surface finite elements and strongly consistent stabilisation techniques with boundary elements opens up the possibility to use non conformal unstructured grids with local refinement, without introducing the inconsistencies of other stabilisation techniques based on up-winding and finite difference schemes.

1 aGiuliani, Nicola1 aMola, Andrea1 aHeltai, Luca1 aFormaggia, L. uhttp://urania.sissa.it/xmlui/handle/1963/3446601381nas a2200205 4500008004100000022001400041245007100055210006900126300001400195490000800209520074400217653001900961653002200980653002401002100002001026700002001046700002201066700001601088856007101104 2015 eng d a0001-870800aA general existence result for the Toda system on compact surfaces0 ageneral existence result for the Toda system on compact surfaces a937 - 9790 v2853 aIn this paper we consider the following Toda system of equations on a compact surface:−Δu1=2ρ1(h1eu1∫Σh1eu1dVg−1)−ρ2(h2eu2∫Σh2eu2dVg−1)−Δu1=−4π∑j=1mα1,j(δpj−1),−Δu2=2ρ2(h2eu2∫Σh2eu2dVg−1)−ρ1(h1eu1∫Σh1eu1dVg−1)−Δu2=−4π∑j=1mα2,j(δpj−1), which is motivated by the study of models in non-abelian Chern–Simons theory. Here h1,h2 are smooth positive functions, ρ1,ρ2 two positive parameters, pi points of the surface and α1,i,α2,j non-negative numbers. We prove a general existence result using variational methods. The same analysis applies to the following mean field equation−Δu=ρ1(heu∫ΣheudVg−1)−ρ2(he−u∫Σhe−udVg−1), which arises in fluid dynamics."

10aGeometric PDEs10aMin–max schemes10aVariational methods1 aBattaglia, Luca1 aJevnikar, Aleks1 aMalchiodi, Andrea1 aRuiz, David uhttp://www.sciencedirect.com/science/article/pii/S000187081500307201188nas a2200157 4500008004100000245005800041210005700099260003700156300001600193490000700209520065100216100002500867700002400892700002100916856009300937 2015 eng d00aGeodesics and horizontal-path spaces in Carnot groups0 aGeodesics and horizontalpath spaces in Carnot groups bMathematical Sciences Publishers a1569–16300 v193 aWe study properties of the space of horizontal paths joining the origin with a vertical point on a generic two-step Carnot group. The energy is a Morse-Bott functional on paths and its critical points (sub-Riemannian geodesics) appear in families (compact critical manifolds) with controlled topology. We study the asymptotic of the number of critical manifolds as the energy grows. The topology of the horizontal-path space is also investigated, and we find asymptotic results for the total Betti number of the sublevels of the energy as it goes to infinity. We interpret these results as local invariants of the sub-Riemannian structure.

1 aAgrachev, Andrei, A.1 aGentile, Alessandro1 aLerario, Antonio uhttps://www.math.sissa.it/publication/geodesics-and-horizontal-path-spaces-carnot-groups02043nas a2200121 4500008004100000245006000041210006000101260001000161520154600171653008801717100002101805856009501826 2015 en d00aGeometric phases in graphene and topological insulators0 aGeometric phases in graphene and topological insulators bSISSA3 aThis thesis collects three of the publications that the candidate produced during his Ph.D. studies. They all focus on geometric phases in solid state physics. We first study topological phases of 2-dimensional periodic quantum systems, in absence of a spectral gap, like e.g. (multilayer) graphene. A topological invariant n_v in Z, baptized eigenspace vorticity, is attached to any intersection of the energy bands, and characterizes the local topology of the eigenprojectors around that intersection. With the help of explicit models, each associated to a value of n_v in Z, we are able to extract the decay at infinity of the single-band Wannier function w in mono- and bilayer graphene, obtaining |w(x)| <= const |x|^{-2} as |x| tends to infinity. Next, we investigate gapped periodic quantum systems, in presence of time-reversal symmetry. When the time-reversal operator Theta is of bosonic type, i.e. it satisfies Theta^2 = 1, we provide an explicit algorithm to construct a frame of smooth, periodic and time-reversal symmetric (quasi-)Bloch functions, or equivalently a frame of almost-exponentially localized, real-valued (composite) Wannier functions, in dimension d <= 3. In the case instead of a fermionic time-reversal operator, satisfying Theta^2 = -1, we show that the existence of such a Bloch frame is in general topologically obstructed in dimension d=2 and d=3. This obstruction is encoded in Z_2-valued topological invariants, which agree with the ones proposed in the solid state literature by Fu, Kane and Mele.10aGeometric phases, graphene, topological insulators, Wannier functions, Bloch frames1 aMonaco, Domenico uhttps://www.math.sissa.it/publication/geometric-phases-graphene-and-topological-insulators01836nas a2200121 4500008004100000245006000041210005800101260001000159520139100169653003901560100002001599856009501619 2015 en d00aGibbs-Markov-Young Structures and Decay of Correlations0 aGibbsMarkovYoung Structures and Decay of Correlations bSISSA3 aIn this work we study mixing properties of discrete dynamical systems and related to them geometric structure. In the first chapter we show that the direct product of maps with Young towers admits a Young tower whose return times decay at a rate which is bounded above by the slowest of the rates of decay of the return times of the component maps. An application of this result, together with other results in the literature, yields various statistical properties for the direct product of various classes of systems, including Lorenz-like maps, multimodal maps, piecewise $C^2$ interval maps with critical points and singularities, H\'enon maps and partially hyperbolic systems. The second chapter is dedicated to the problem of decay of correlations for continuous observables. First we show that if the underlying system admits Young tower then the rate of decay of correlations for continuous observables can be estimated in terms of modulus of continuity and the decay rate of tail of Young tower. In the rest of the second chapter we study the relations between the rates of decay of correlations for smooth observables and continuous observables. We show that if the rates of decay of correlations is known for $C^r,$ observables ($r\ge 1$) then it is possible to obtain decay of correlations for continuous observables in terms of modulus of continuity.10aDecay of Correlations, GMY-towers1 aRuziboev, Marks uhttps://www.math.sissa.it/publication/gibbs-markov-young-structures-and-decay-correlations00332nas a2200085 4500008004100000245007900041210006900120100001900189856003800208 2015 eng d00aGli abachi: antichi strumenti precursori delle moderne macchine da calcolo0 aGli abachi antichi strumenti precursori delle moderne macchine d1 aKlun, Giuliano uhttp://hdl.handle.net/10077/1088400723nas a2200109 4500008004100000245009500041210006900136260001000205520031800215100002900533856005100562 2015 en d00aGlobal well-posedness of the magnetic Hartree equation with non-Strichartz external fields0 aGlobal wellposedness of the magnetic Hartree equation with nonSt bSISSA3 aWe study the magnetic Hartree equation with external fields to which magnetic Strichartz estimates are not necessarily applicable. We characterise the appropriate notion of energy space and in such a space we prove the global well-posedness of the associated initial value problem by means of energy methods only.1 aMichelangeli, Alessandro uhttp://urania.sissa.it/xmlui/handle/1963/3444000692nas a2200109 4500008004100000245006100041210005800102260003100160520032400191100001600515856005100531 2015 en d00aHilbert schemes of points of OP1(-n) as quiver varieties0 aHilbert schemes of points of OP1n as quiver varieties barXiv:1504.02987 [math.AG]3 aRelying on a representation of framed torsion-free sheaves on Hirzebruch surfaces in terms of monads, we construct ADHM data for the Hilbert scheme of points of the total space of the line bundle $\mathcal O(-n)$ on $\mathbb P^1$. This ADHM description is then used to realize these Hilbert schemes as quiver varieties.1 aBruzzo, Ugo uhttp://urania.sissa.it/xmlui/handle/1963/3448700685nas a2200121 4500008004100000245007200041210006900113260001000182520028100192100001700473700002200490856005100512 2015 en d00aHomogenization problems in the Calculus of Variations: an overview0 aHomogenization problems in the Calculus of Variations an overvie bSISSA3 aIn this note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundamental theoretical tools, both classical and modern. We conclude by mentioning some open problems.1 aMatias, Jose1 aMorandotti, Marco uhttp://urania.sissa.it/xmlui/handle/1963/3445501024nas a2200121 4500008004100000245005200041210005100093260001000144520060600154653007300760100001800833856005100851 2015 en d00aIntegrability of Continuous Tangent Sub-bundles0 aIntegrability of Continuous Tangent Subbundles bSISSA3 aIn this thesis, the main aim is to study the integrability properties of continuous tangent sub-bundles, especially those that arise in the study of dynamical systems. After the introduction and examples part we start by studying integrability of such sub-bundles under different regularity and dynamical assumptions. Then we formulate a continuous version of the classical Frobenius theorem and state some applications to such bundles, to ODE and PDE. Finally we close of by stating some ongoing work related to interactions between integrability, sub-Riemannian geometry and contact geometry.10aDynamical Systems, Global Analysis, Frobenius Theorem, Integrability1 aTüreli, Sina uhttp://urania.sissa.it/xmlui/handle/1963/3463003404nas a2200121 4500008004100000245013600041210006900177260001000246520292200256653003303178100002003211856005103231 2015 en d00aInteraction functionals, Glimm approximations and Lagrangian structure of BV solutions for Hyperbolic Systems of Conservations Laws0 aInteraction functionals Glimm approximations and Lagrangian stru bSISSA3 aThis thesis is a contribution to the mathematical theory of Hyperbolic Conservation Laws. Three are the main results which we collect in this work. The first and the second result (denoted in the thesis by Theorem A and Theorem B respectively) deal with the following problem. The most comprehensive result about existence, uniqueness and stability of the solution to the Cauchy problem \begin{equation}\tag{$\mathcal C$} \label{E:abstract} \begin{cases} u_t + F(u)_x = 0, \\u(0, x) = \bar u(x), \end{cases} \end{equation} where $F: \R^N \to \R^N$ is strictly hyperbolic, $u = u(t,x) \in \R^N$, $t \geq 0$, $x \in \R$, $\TV(\bar u) \ll 1$, can be found in [Bianchini, Bressan 2005], where the well-posedness of \eqref{E:abstract} is proved by means of vanishing viscosity approximations. After the paper [Bianchini, Bressan 2005], however, it seemed worthwhile to develop a \emph{purely hyperbolic} theory (based, as in the genuinely nonlinear case, on Glimm or wavefront tracking approximations, and not on vanishing viscosity parabolic approximations) to prove existence, uniqueness and stability results. The reason of this interest can be mainly found in the fact that hyperbolic approximate solutions are much easier to study and to visualize than parabolic ones. Theorems A and B in this thesis are a contribution to this line of research. In particular, Theorem A proves an estimate on the change of the speed of the wavefronts present in a Glimm approximate solution when two of them interact; Theorem B proves the convergence of the Glimm approximate solutions to the weak admissible solution of \eqref{E:abstract} and provides also an estimate on the rate of convergence. Both theorems are proved in the most general setting when no assumption on $F$ is made except the strict hyperbolicity. The third result of the thesis, denoted by Theorem C, deals with the Lagrangian structure of the solution to \eqref{E:abstract}. The notion of Lagrangian flow is a well-established concept in the theory of the transport equation and in the study of some particular system of conservation laws, like the Euler equation. However, as far as we know, the general system of conservations laws \eqref{E:abstract} has never been studied from a Lagrangian point of view. This is exactly the subject of Theorem C, where a Lagrangian representation for the solution to the system \eqref{E:abstract} is explicitly constructed. The main reasons which led us to look for a Lagrangian representation of the solution of \eqref{E:abstract} are two: on one side, this Lagrangian representation provides the continuous counterpart in the exact solution of \eqref{E:abstract} to the well established theory of wavefront approximations; on the other side, it can lead to a deeper understanding of the behavior of the solutions in the general setting, when the characteristic field are not genuinely nonlinear or linearly degenerate.10aHyperbolic conservation laws1 aModena, Stefano uhttp://urania.sissa.it/xmlui/handle/1963/3454201765nas a2200217 4500008004100000022001400041245005300055210005300108300001400161490000700175520110000182653002201282653002501304653002801329653003001357653002701387100002201414700001801436700002201454856007101476 2015 eng d a0022-509600aLiquid crystal elastomer strips as soft crawlers0 aLiquid crystal elastomer strips as soft crawlers a254 - 2720 v843 aIn this paper, we speculate on a possible application of Liquid Crystal Elastomers to the field of soft robotics. In particular, we study a concept for limbless locomotion that is amenable to miniaturisation. For this purpose, we formulate and solve the evolution equations for a strip of nematic elastomer, subject to directional frictional interactions with a flat solid substrate, and cyclically actuated by a spatially uniform, time-periodic stimulus (e.g., temperature change). The presence of frictional forces that are sensitive to the direction of sliding transforms reciprocal, ‘breathing-like’ deformations into directed forward motion. We derive formulas quantifying this motion in the case of distributed friction, by solving a differential inclusion for the displacement field. The simpler case of concentrated frictional interactions at the two ends of the strip is also solved, in order to provide a benchmark to compare the continuously distributed case with a finite-dimensional benchmark. We also provide explicit formulas for the axial force along the crawler body.

10aCrawling motility10aDirectional surfaces10aFrictional interactions10aLiquid crystal elastomers10aSoft biomimetic robots1 aDeSimone, Antonio1 aGidoni, Paolo1 aNoselli, Giovanni uhttp://www.sciencedirect.com/science/article/pii/S002250961530043000496nas a2200109 4500008004100000245010000041210006900141260001000210653001300220100002600233856012700259 2015 en d00aMathematical Models of Locomotion: Legged Crawling, Snake-like Motility, and Flagellar Swimming0 aMathematical Models of Locomotion Legged Crawling Snakelike Moti bSISSA10aMotility1 aCicconofri, Giancarlo uhttps://www.math.sissa.it/publication/mathematical-models-locomotion-legged-crawling-snake-motility-and-flagellar-swimming00454nas a2200133 4500008004100000022001400041245009000055210006900145300001100214490000600225100001900231700002200250856004800272 2015 eng d a1664-236800aMeromorphic differentials with imaginary periods on degenerating hyperelliptic curves0 aMeromorphic differentials with imaginary periods on degenerating a1–220 v51 aBertola, Marco1 aTovbis, Alexander uhttp://dx.doi.org/10.1007/s13324-014-0088-700678nas 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-advances01569nas a2200181 4500008004100000022001400041245006000055210005800115300001400173490000700187520100500194653001901199653002201218653002801240100002601268700002201294856007101316 2015 eng d a0020-746200aMotility of a model bristle-bot: A theoretical analysis0 aMotility of a model bristlebot A theoretical analysis a233 - 2390 v763 aBristle-bots are legged robots that can be easily made out of a toothbrush head and a small vibrating engine. Despite their simple appearance, the mechanism enabling them to propel themselves by exploiting friction with the substrate is far from trivial. Numerical experiments on a model bristle-bot have been able to reproduce such a mechanism revealing, in addition, the ability to switch direction of motion by varying the vibration frequency. This paper provides a detailed account of these phenomena through a fully analytical treatment of the model. The equations of motion are solved through an expansion in terms of a properly chosen small parameter. The convergence of the expansion is rigorously proven. In addition, the analysis delivers formulas for the average velocity of the robot and for the frequency at which the direction switch takes place. A quantitative description of the mechanism for the friction modulation underlying the motility of the bristle-bot is also provided.

10aBristle-robots10aCrawling motility10aFrictional interactions1 aCicconofri, Giancarlo1 aDeSimone, Antonio uhttp://www.sciencedirect.com/science/article/pii/S002074621500002501808nas a2200121 4500008004100000245011400041210006900155260001000224520121600234653008901450100001901539856012801558 2015 en d00aMultidimensional Poisson Vertex Algebras and Poisson cohomology of Hamiltonian operators of hydrodynamic type0 aMultidimensional Poisson Vertex Algebras and Poisson cohomology bSISSA3 aThe Poisson brackets of hydrodynamic type, also called Dubrovin-Novikov brackets, constitute the Hamiltonian structure of a broad class of evolutionary PDEs, that are ubiquitous in the theory of Integrable Systems, ranging from Hopf equation to the principal hierarchy of a Frobenius manifold. They can be regarded as an analogue of the classical Poisson brackets, defined on an infinite dimensional space of maps Σ → M between two manifolds. Our main problem is the study of Poisson-Lichnerowicz cohomology of such space when dim Σ > 1. We introduce the notion of multidimensional Poisson Vertex Algebras, generalizing and adapting the theory by A. Barakat, A. De Sole, and V. Kac [Poisson Vertex Algebras in the theory of Hamiltonian equations, 2009]; within this framework we explicitly compute the first nontrivial cohomology groups for an arbitrary Poisson bracket of hydrodynamic type, in the case dim Σ = dim M = 2. For the case of the so-called scalar brackets, namely the ones for which dim M = 1, we give a complete description on their Poisson–Lichnerowicz cohomology. From this computations it follows, already in the particular case dim Σ = 2, that the cohomology is infinite dimensional.10aPoisson Vertex Algebras, Poisson brackets, Hamiltonian operators, Integrable Systems1 aCasati, Matteo uhttps://www.math.sissa.it/publication/multidimensional-poisson-vertex-algebras-and-poisson-cohomology-hamiltonian-operators01516nas a2200133 4500008004100000245012100041210006900162260001300231520102900244100002101273700001501294700002201309856005101331 2015 en d00aMultilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations0 aMultilevel and weighted reduced basis method for stochastic opti bSpringer3 aIn this paper we develop and analyze a multilevel weighted reduced basis method for solving stochastic optimal control problems constrained by Stokes equations. We prove the analytic regularity of the optimal solution in the probability space under certain assumptions on the random input data. The finite element method and the stochastic collocation method are employed for the numerical approximation of the problem in the deterministic space and the probability space, respectively, resulting in many large-scale optimality systems to solve. In order to reduce the unaffordable computational effort, we propose a reduced basis method using a multilevel greedy algorithm in combination with isotropic and anisotropic sparse-grid techniques. A weighted a posteriori error bound highlights the contribution stemming from each method. Numerical tests on stochastic dimensions ranging from 10 to 100 demonstrate that our method is very efficient, especially for solving high-dimensional and large-scale optimization problems.1 aRozza, Gianluigi1 aChen, Peng1 aQuarteroni, Alfio uhttp://urania.sissa.it/xmlui/handle/1963/3449101194nas a2200121 4500008004100000245008200041210006900123260001300192520077400205100002300979700001901002856005101021 2015 en d00aMultiple positive solutions for a superlinear problem: a topological approach0 aMultiple positive solutions for a superlinear problem a topologi bElsevier3 aWe study the multiplicity of positive solutions for a two-point boundary value problem associated to the nonlinear second order equation u''+f(x,u)=0. We allow x ↦ f(x,s) to change its sign in order to cover the case of scalar equations with indefinite weight. Roughly speaking, our main assumptions require that f(x,s)/s is below λ_1 as s→0^+ and above λ_1 as s→+∞. In particular, we can deal with the situation in which f(x,s) has a superlinear growth at zero and at infinity. We propose a new approach based on the topological degree which provides the multiplicity of solutions. Applications are given for u'' + a(x) g(u) = 0, where we prove the existence of 2^n-1 positive solutions when a(x) has n positive humps and a^-(x) is sufficiently large.

1 aFeltrin, Guglielmo1 aZanolin, Fabio uhttp://urania.sissa.it/xmlui/handle/1963/3514701077nas a2200181 4500008004100000022001400041245007100055210006800126260000800194300000700202490000900209520054400218100001900762700002000781700002600801700002400827856004400851 2015 eng d a1029-847900aN=2 supersymmetric gauge theories on S^2xS^2 and Liouville Gravity0 aN2 supersymmetric gauge theories on S2xS2 and Liouville Gravity cJul a540 v20153 aWe consider $\mathcal{N}=2$ supersymmetric gauge theories on four manifolds admitting an isometry. Generalized Killing spinor equations are derived from the consistency of supersymmetry algebrae and solved in the case of four manifolds admitting a $U(1)$ isometry. This is used to explicitly compute the supersymmetric path integral on $S^2 \times S^2$ via equivariant localization. The building blocks of the resulting partition function are shown to contain the three point functions and the conformal blocks of Liouville Gravity.

1 aBawane, Aditya1 aBonelli, Giulio1 aRonzani, Massimiliano1 aTanzini, Alessandro uhttps://doi.org/10.1007/JHEP07(2015)05401699nas a2200121 4500008004100000245011400041210006900155260001000224520117400234653002501408100001701433856012701450 2015 en d00aNormal matrix models and orthogonal polynomials for a class of potentials with discrete rotational symmetries0 aNormal matrix models and orthogonal polynomials for a class of p bSISSA3 aIn this thesis we are going to study normal random matrix models which generalize naturally the polynomially perturbed Ginibre ensamble, focusing in particular on their eigenvalue distribution and on the asymptotics of the associated orthogonal polynomials. \\ The main result we are going to present are the following: \begin{itemize} \item we describe the explicit derivation of the equilibrium measure for a class of potentials with discrete rotational symmetries, namely of the form \[V(z)=|z|^{2n}-t(z^{d}+\bar{z}^{d})\qquad n,d\in\mathbb{N},\ \ d\leq2n\ \ t>0 .\] \item We obtain the strong asymptotics for the orthogonal polynomials associated to the weight \[ e^{-NV(z)},\quad V(z)=|z|^{2s}-t(z^s+\bar{z}^{s}) \qquad z \in \mathbb{C},\;s\in \mathbb{N},\quad t>0,\] and we will show how the density of their zeroes is related to the eigenvalue distribution of the corresponding matrix model; \item We show how the conformal maps used to describe the support of the equilibrium measure for polynomial perturbation of the potential $V(z)=|z|^{2n}$ lead to a natural generalization of the concept of polynomial curves introduced in by Elbau. \end{itemize}10aMathematical Physics1 aMerzi, Dario uhttps://www.math.sissa.it/publication/normal-matrix-models-and-orthogonal-polynomials-class-potentials-discrete-rotational00775nas a2200133 4500008004100000245006500041210006300106300001200169490000700181520032000188100002000508700002200528856009100550 2015 en d00aA note on compactness properties of the singular Toda system0 anote on compactness properties of the singular Toda system a299-3070 v263 aIn this note, we consider blow-up for solutions of the SU(3) Toda system on compact surfaces. In particular, we give a complete proof of a compactness result stated by Jost, Lin and Wang and we extend it to the case of singular systems. This is a necessary tool to find solutions through variational methods.

1 aBattaglia, Luca1 aMancini, Gabriele uhttps://www.math.sissa.it/publication/note-compactness-properties-singular-toda-system00769nas a2200109 4500008004100000245006200041210006100103260001600164520036100180100002200541856009600563 2015 en d00aOnofri-Type Inequalities for Singular Liouville Equations0 aOnofriType Inequalities for Singular Liouville Equations bSpringer US3 aWe study the blow-up behavior of minimizing sequences for the singular Moser–Trudinger functional on compact surfaces. Assuming non-existence of minimum points, we give an estimate for the infimum value of the functional. This result can be applied to give sharp Onofri-type inequalities on the sphere in the presence of at most two singularities.

1 aMancini, Gabriele uhttps://www.math.sissa.it/publication/onofri-type-inequalities-singular-liouville-equations00453nas a2200133 4500008004100000022001400041245008800055210006900143300001500212490000700227100001900234700001300253856005300266 2015 eng d a1751-811300aThe partition function of the extended $r$-reduced Kadomtsev-Petviashvili hierarchy0 apartition function of the extended rreduced KadomtsevPetviashvil a195205, 200 v481 aBertola, Marco1 aYang, Di uhttp://dx.doi.org/10.1088/1751-8113/48/19/19520500827nas a2200193 4500008004100000022001400041245005300055210005100108300001200159490000800171520026300179653002100442653001500463653002000478653002400498100002200522700001800544856007100562 2015 eng d a0362-546X00aA permanence theorem for local dynamical systems0 apermanence theorem for local dynamical systems a73 - 810 v1213 aWe provide a necessary and sufficient condition for permanence related to a local dynamical system on a suitable topological space. We then present an illustrative application to a Lotka–Volterra predator–prey model with intraspecific competition.

10aLotka–Volterra10apermanence10aPredator–prey10aUniform persistence1 aFonda, Alessandro1 aGidoni, Paolo uhttp://www.sciencedirect.com/science/article/pii/S0362546X1400333200719nas a2200217 4500008004100000245009200041210006900133260003300202100002200235700002400257700001600281700002300297700001500320700001400335700002200349700002600371700002100397700001300418700001900431856005100450 2015 en d00aThe phototransduction machinery in the rod outer segment has a strong efficacy gradient0 aphototransduction machinery in the rod outer segment has a stron bNational Academy of Sciences1 aMazzolini, Monica1 aFacchetti, Giuseppe1 aAndolfi, L.1 aZaccaria, Proietti1 aTuccio, S.1 aTreud, J.1 aAltafini, Claudio1 aDi Fabrizio, Enzo, M.1 aLazzarino, Marco1 aRapp, G.1 aTorre, Vincent uhttp://urania.sissa.it/xmlui/handle/1963/3515700790nas a2200121 4500008004100000245007600041210006900117520031400186100001800500700001900518700002000537856011100557 2015 en d00aPoisson cohomology of scalar multidimensional Dubrovin-Novikov brackets0 aPoisson cohomology of scalar multidimensional DubrovinNovikov br3 aWe compute the Poisson cohomology of a scalar Poisson bracket of Dubrovin-Novikov type with D independent variables. We find that the second and third cohomology groups are generically non-vanishing in D>1. Hence, in contrast with the D=1 case, the deformation theory in the multivariable case is non-trivial.1 aCarlet, Guido1 aCasati, Matteo1 aShadrin, Sergey uhttps://www.math.sissa.it/publication/poisson-cohomology-scalar-multidimensional-dubrovin-novikov-brackets01307nas a2200109 4500008004100000245006700041210006600108260001000174520088800184100002101072856010401093 2015 en d00aPrincipal circle bundles, Pimsner algebras and Gysin sequences0 aPrincipal circle bundles Pimsner algebras and Gysin sequences bSISSA3 aPrincipal circle bundles and Gysin sequences play a crucial role in mathematical physics, in particular in Chern-Simons theories and T-duality. This works focuses on the noncommutative topology of principal circle bundles: we investigate the connections between noncommutative principal circle bundles, Pimsner algebras and strongly graded algebras. At the C*-algebraic level, we start from a self-Morita equivalence bimodule E for a C*-algebra B which we think of as a non commutative line bundle over the `base space’ algebra B. The corresponding Pimsner algebra O_E, is then the total space algebra of an associated circle bundle. A natural six term exact sequence, an analogue of the Gysin sequence for circle bundles, relates the KK-theories of O_E and of the base space B. We illustrate several results with the examples of quantum weighted projective and lens spaces.1 aArici, Francesca uhttps://www.math.sissa.it/publication/principal-circle-bundles-pimsner-algebras-and-gysin-sequences01121nas a2200133 4500008004100000245007800041210006900119300001600188490000800204520062100212100002300833700002000856856011100876 2015 eng d00aQuadratic Interaction Functional for General Systems of Conservation Laws0 aQuadratic Interaction Functional for General Systems of Conserva a1075–11520 v3383 aFor the Glimm scheme approximation to the solution of the system of conservation laws in one space dimension with initial data u 0 with small total variation, we prove a quadratic (w.r.t. Tot. Var. ( u 0)) interaction estimate, which has been used in the literature for stability and convergence results. No assumptions on the structure of the flux f are made (apart from smoothness), and this estimate is the natural extension of the Glimm type interaction estimate for genuinely nonlinear systems. More precisely, we obtain the following results: a new analysis of the interaction estimates of simple waves;

1 aBianchini, Stefano1 aModena, Stefano uhttps://www.math.sissa.it/publication/quadratic-interaction-functional-general-systems-conservation-laws-002042nas a2200217 4500008004100000022001400041245010200055210006900157490003500226520122900261653002501490653002101515653002501536653002701561653002501588653001601613100002201629700002101651700002201672856013001694 2015 eng d a1019-716800aReduced basis approximation and a-posteriori error estimation for the coupled Stokes-Darcy system0 aReduced basis approximation and aposteriori error estimation for0 vspecial issue for MoRePaS 20123 aThe coupling of a free flow with a flow through porous media has many potential applications in several fields related with computational science and engineering, such as blood flows, environmental problems or food technologies. We present a reduced basis method for such coupled problems. The reduced basis method is a model order reduction method applied in the context of parametrized systems. Our approach is based on a heterogeneous domain decomposition formulation, namely the Stokes-Darcy problem. Thanks to an offline/online-decomposition, computational times can be drastically reduced. At the same time the induced error can be bounded by fast evaluable a-posteriori error bounds. In the offline-phase the proposed algorithms make use of the decomposed problem structure. Rigorous a-posteriori error bounds are developed, indicating the accuracy of certain lifting operators used in the offline-phase as well as the accuracy of the reduced coupled system. Also, a strategy separately bounding pressure and velocity errors is extended. Numerical experiments dealing with groundwater flow scenarios demonstrate the efficiency of the approach as well as the limitations regarding a-posteriori error estimation.

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

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

1 aNegri, Federico1 aManzoni, Andrea1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduced-basis-approximation-parametrized-optimal-flow-control-problems-stokes-equations02449nas a2200121 4500008004100000245012900041210006900170520189900239100002002138700002502158700001702183856012702200 2015 en d00aReduced Basis Isogeometric Methods (RB-IGA) for the real-time simulation of potential flows about parametrized NACA airfoils0 aReduced Basis Isogeometric Methods RBIGA for the realtime simula3 aWe present a Reduced Basis (RB) method based on Isogeometric Analysis (IGA) for the rapid and reliable evaluation of PDE systems characterized by complex geometrical features. At the current state of the art, this is the first case of coupling between RB and IGA methods. The construction of the RB method relies on an Isogeometric Boundary Element Method (IGA-BEM) as the high-fidelity technique, allowing a direct interface with Computer Aided Design (CAD) tools. A suitable Empirical Interpolation Method (EIM) ensures an efficient offline/online decomposition between the construction and the evaluation of the RB method. We consider the real-time simulation of potential flows past airfoils, parametrized with respect to the angle of attack and the NACA number identifying their shape, and we provide a validation of our methodology with respect to experimental data and reference numerical codes, showing in both cases a very good agreement.We present a Reduced Basis (RB) method based on Isogeometric Analysis (IGA) for the rapid and reliable evaluation of PDE systems characterized by complex geometrical features. At the current state of the art, this is the first case of coupling between RB and IGA methods. The construction of the RB method relies on an Isogeometric Boundary Element Method (IGA-BEM) as the high-fidelity technique, allowing a direct interface with Computer Aided Design (CAD) tools. A suitable Empirical Interpolation Method (EIM) ensures an efficient offline/online decomposition between the construction and the evaluation of the RB method. We consider the real-time simulation of potential flows past airfoils, parametrized with respect to the angle of attack and the NACA number identifying their shape, and we provide a validation of our methodology with respect to experimental data and reference numerical codes, showing in both cases a very good agreement.1 aManzoni, Andrea1 aSalmoiraghi, Filippo1 aHeltai, Luca uhttps://www.math.sissa.it/publication/reduced-basis-isogeometric-methods-rb-iga-real-time-simulation-potential-flows-about01509nas a2200121 4500008004100000245012400041210006900165260001000234520098200244653002001226100001801246856012301264 2015 en d00aThe relaxed area of maps from the plane to the plane with a line discontinuity, and the role of semicartesian surfaces.0 arelaxed area of maps from the plane to the plane with a line dis bSISSA3 aIn this thesis we study the relaxation of the area functional w.r.t. the L^1 topology of a map from a bounded planar domain with values in the plane and jumping on a segment. We estimate from above the singular contribution of this functional due to the presence of the jump in terms of the infimum of the area among a suitable family of surfaces that we call semicartesian surfaces. In our analysis, we also introduce a different notion of area, namely the relaxation of the area w.r.t. a convergence stronger than the L^1 convergence, whose singular contribution is completely characterized in terms of suitable semicartesian area minimizing problems. We propose also some examples of maps for which the two notions of relaxation are different: these examples underline the highly non-local behaviour of the L^1-relaxation, and justify the introduction of the other functional. Some result about the existence of a semicartesian area-minimizing surface is also provided.10aArea functional1 aTealdi, Lucia uhttps://www.math.sissa.it/publication/relaxed-area-maps-plane-plane-line-discontinuity-and-role-semicartesian-surfaces00953nas 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/1963/749401018nas a2200121 4500008004100000245007900041210007000120260001000190520058700200100002900787700002900816856005100845 2015 en d00aSchödinger operators on half-line with shrinking potentials at the origin0 aSchödinger operators on halfline with shrinking potentials at th bSISSA3 aWe discuss the general model of a Schrödinger quantum particle constrained on a straight half-line with given self-adjoint boundary condition at the origin and an interaction potential supported around the origin. We study the limit when the range of the potential scales to zero and its magnitude blows up. We show that in the limit the dynamics is generated by a self-adjoint negative Laplacian on the half-line, with a possible preservation or modification of the boundary condition at the origin, depending on the magnitude of the scaling and of the strength of the potential.1 aDell'Antonio, Gianfausto1 aMichelangeli, Alessandro uhttp://urania.sissa.it/xmlui/handle/1963/3443901475nas 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/1963/3448301019nas a2200121 4500008004100000245008500041210006900126260001000195520053500205653002000740100002200760856011500782 2015 en d00aSharp Inequalities and Blow-up Analysis for Singular Moser-Trudinger Embeddings.0 aSharp Inequalities and Blowup Analysis for Singular MoserTruding bSISSA3 aWe investigate existence of solutions for a singular Liouville equation on S^2 and prove sharp Onofri-type inequalities for a Moser-Trudinger functional in the presence of singular potentials. As a consequence we obtain existence of extremal functions for the Moser-Trudinger embedding on compact surfaces with conical singularities. Finally we study the blow-up behavior for sequences of solutions Liouville-type systems and prove a compactness condition which plays an important role in the variational analysis of Toda systems.10aMoser-Trudinger1 aMancini, Gabriele uhttps://www.math.sissa.it/publication/sharp-inequalities-and-blow-analysis-singular-moser-trudinger-embeddings00685nas a2200097 4500008004100000245008200041210006900123520032200192100002200514856005100536 2015 en d00aSingular Liouville Equations on S^2: Sharp Inequalities and Existence Results0 aSingular Liouville Equations on S2 Sharp Inequalities and Existe3 aWe prove a sharp Onofri-type inequality and non-existence of extremals for a Moser-Tudinger functional on S^2 in the presence of potentials having positive order singularities. We also investigate the existence of critical points and give some sufficient conditions under symmetry or nondegeneracy assumptions.

1 aMancini, Gabriele uhttp://urania.sissa.it/xmlui/handle/1963/3448900981nas a2200121 4500008004100000245008300041210006900124260001000193520048800203653003100691100001900722856011800741 2015 en d00aSome results on anisotropic mean curvature and other phase-transition problems0 aSome results on anisotropic mean curvature and other phasetransi bSISSA3 aThe present thesis is divided into three parts. In the first part, we analyze a suitable regularization — which we call nonlinear multidomain model — of the motion of a hypersurface under smooth anisotropic mean curvature flow. The second part of the thesis deals with crystalline mean curvature of facets of a solid set of R^3 . Finally, in the third part we study a phase-transition model for Plateau’s type problems based on the theory of coverings and of BV functions.10aAnisotropic mean curvature1 aAmato, Stefano uhttps://www.math.sissa.it/publication/some-results-anisotropic-mean-curvature-and-other-phase-transition-problems01282nas a2200121 4500008004100000245007500041210006900116260001000185520086400195100002901059700002101088856005101109 2015 en d00aStability of closed gaps for the alternating Kronig-Penney Hamiltonian0 aStability of closed gaps for the alternating KronigPenney Hamilt bSISSA3 aWe consider the Kronig-Penney model for a quantum crystal with equispaced periodic delta-interactions of alternating strength. For this model all spectral gaps at the centre of the Brillouin zone are known to vanish, although so far this noticeable property has only been proved through a very delicate analysis of the discriminant of the corresponding ODE and the associated monodromy matrix. We provide a new, alternative proof by showing that this model can be approximated, in the norm resolvent sense, by a model of regular periodic interactions with finite range for which all gaps at the centre of the Brillouin zone are still vanishing. In particular this shows that the vanishing gap property is stable in the sense that it is present also for the "physical" approximants and is not only a feature of the idealised model of zero-range interactions.1 aMichelangeli, Alessandro1 aMonaco, Domenico uhttp://urania.sissa.it/xmlui/handle/1963/3446001228nas 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/1963/3447402147nas a2200157 4500008004100000245008700041210006900128260001000197300001200207490000700219520161800226653002801844100002001872700002501892856007201917 2015 en d00aStable regular critical points of the Mumford-Shah functional are local minimizers0 aStable regular critical points of the MumfordShah functional are bSISSA a533-5700 v323 aIn this paper it is shown that any regular critical point of the Mumford–Shah functional, with positive definite second variation, is an isolated local minimizer with respect to competitors which are sufficiently close in the $L^1$

-topology. A global minimality result in small tubular neighborhoods of the discontinuity set is also established.

We examine the problem of snake-like locomotion by studying a system consisting of a planar inextensible elastic rod with adjustable spontaneous curvature, which provides an internal actuation mechanism that mimics muscular action in a snake. Using a Cosserat model, we derive the equations of motion in two special cases: one in which the rod can only move along a prescribed curve, and one in which the rod is constrained to slide longitudinally without slipping laterally, but the path is not fixed a priori (free-path case). The second setting is inspired by undulatory locomotion of snakes on flat surfaces. The presence of constraints leads in both cases to non-standard boundary conditions that allow us to close and solve the equations of motion. The kinematics and dynamics of the system can be recovered from a one-dimensional equation, without any restrictive assumption on the followed trajectory or the actuation. We derive explicit formulae highlighting the role of spontaneous curvature in providing the driving force (and the steering, in the free-path case) needed for locomotion. We also provide analytical solutions for a special class of serpentine motions, which enable us to discuss the connection between observed trajectories, internal actuation and forces exchanged with the environment.

1 aCicconofri, Giancarlo1 aDeSimone, Antonio uhttps://royalsocietypublishing.org/doi/abs/10.1098/rspa.2015.005400689nas a2200145 4500008004100000245009900041210006900140260001000209520018600219100002400405700002000429700002200449700002100471856005100492 2015 en d00aSupremizer stabilization of POD-Galerkin approximation of parametrized Navier-Stokes equations0 aSupremizer stabilization of PODGalerkin approximation of paramet bWiley3 aIn this work, we present a stable proper orthogonal decomposition–Galerkin approximation for parametrized steady incompressible Navier–Stokes equations with low Reynolds number.1 aBallarin, Francesco1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3470101557nas 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/1963/3446801401nas a2200121 4500008004100000245007200041210006900113260001300182520098700195100002401182700002201206856005101228 2015 en d00aThree-sphere low-Reynolds-number swimmer with a passive elastic arm0 aThreesphere lowReynoldsnumber swimmer with a passive elastic arm bSpringer3 aOne of the simplest model swimmers at low Reynolds number is the three-sphere swimmer by Najafi and Golestanian. It consists of three spheres connected by two rods which change their lengths periodically in non-reciprocal fashion. Here we investigate a variant of this model in which one rod is periodically actuated while the other is replaced by an elastic spring. We show that the competition between the elastic restoring force and the hydrodynamic drag produces a delay in the response of the passive elastic arm with respect to the active one. This leads to non-reciprocal shape changes and self-propulsion. After formulating the equations of motion, we study their solutions qualitatively and numerically. The leading-order term of the solution is computed analytically. We then address questions of optimization with respect to both actuation frequency and swimmer's geometry. Our results can provide valuable conceptual guidance in the engineering of robotic microswimmers.1 aMontino, Alessandro1 aDeSimone, Antonio uhttp://urania.sissa.it/xmlui/handle/1963/3453000591nas a2200145 4500008004100000245009500041210006900136260003700205300001600242490000600258100002000264700001800284700002200302856012100324 2015 eng d00aA topological join construction and the Toda system on compact surfaces of arbitrary genus0 atopological join construction and the Toda system on compact sur bMathematical Sciences Publishers a1963–20270 v81 aJevnikar, Aleks1 aKallel, Sadok1 aMalchiodi, Andrea uhttps://www.math.sissa.it/publication/topological-join-construction-and-toda-system-compact-surfaces-arbitrary-genus00787nas a2200121 4500008004100000245013000041210006900171260001000240520031200250100002300562700002900585856005100614 2015 en d00aTranslation and adaptation of Birman's paper "On the theory of self-adjoint extensions of positive definite operators" (1956)0 aTranslation and adaptation of Birmans paper On the theory of sel bSISSA3 aThis is an accurate translation from Russian and adaptation to the modern mathematical jargon of a classical paper by M. Sh. Birman published in 1956, which is still today central in the theory of self-adjoint extensions of semi-bounded operators, and for which yet no English version was available so far.1 aKhotyakov, Mikhail1 aMichelangeli, Alessandro uhttp://urania.sissa.it/xmlui/handle/1963/3444300475nas a2200133 4500008004100000245009800041210006900139260000700208300001600215490000800231100001900239700002000258856006300278 2015 eng d00aUniversality Conjecture and Results for a Model of Several Coupled Positive-Definite Matrices0 aUniversality Conjecture and Results for a Model of Several Coupl c08 a1077–11410 v3371 aBertola, Marco1 aBothner, Thomas uhttp://link.springer.com/article/10.1007/s00220-015-2327-700409nas a2200109 4500008004100000245005900041210005900100260001000159653001600169100002000185856009400205 2015 en d00aVariational aspects of Liouville equations and systems0 aVariational aspects of Liouville equations and systems bSISSA10aToda system1 aJevnikar, Aleks uhttps://www.math.sissa.it/publication/variational-aspects-liouville-equations-and-systems00779nas a2200121 4500008004100000245005400041210005400095260001000149520029900159653009000458100002000548856008900568 2015 en d00aVariational aspects of singular Liouville systems0 aVariational aspects of singular Liouville systems bSISSA3 aI studied singular Liouville systems on compact surfaces from a variational point of view. I gave sufficient and necessary conditions for the existence of globally minimizing solutions, then I found min-max solutions for some particular systems. Finally, I also gave some non-existence results.10aVariational methods, Liouville systems, Moser-Trudinger inequalities, min-max methods1 aBattaglia, Luca uhttps://www.math.sissa.it/publication/variational-aspects-singular-liouville-systems02046nas 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-problems01514nas a2200109 4500008004100000245013600041210006900177520106400246100002101310700002201331856005101353 2015 en d00aThe wave equation on domains with cracks growing on a prescribed path: existence, uniqueness, and continuous dependence on the data0 awave equation on domains with cracks growing on a prescribed pat3 aGiven a bounded open set $\Omega \subset \mathbb R^d$ with Lipschitz boundary and an increasing family $\Gamma_t$, $t\in [0,T]$, of closed subsets of $\Omega$, we analyze the scalar wave equation $\ddot{u} - div (A \nabla u) = f$ in the time varying cracked domains $\Omega\setminus\Gamma_t$. Here we assume that the sets $\Gamma_t$ are contained into a prescribed $(d-1)$-manifold of class $C^2$. Our approach relies on a change of variables: recasting the problem on the reference configuration $\Omega\setminus \Gamma_0$, we are led to consider a hyperbolic problem of the form $\ddot{v} - div (B\nabla v) + a \cdot \nabla v - 2 b \cdot \nabla \dot{v} = g$ in $\Omega \setminus \Gamma_0$. Under suitable assumptions on the regularity of the change of variables that transforms $\Omega\setminus \Gamma_t$ into $\Omega\setminus \Gamma_0$, we prove existence and uniqueness of weak solutions for both formulations. Moreover, we provide an energy equality, which gives, as a by-product, the continuous dependence of the solutions with respect to the cracks.1 aDal Maso, Gianni1 aLucardesi, Ilaria uhttp://urania.sissa.it/xmlui/handle/1963/3462901482nas 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/1963/3465101483nas a2200121 4500008004100000245005900041210005900100260005900159520105100218100002201269700001901291856005101310 2014 en d00aAchieving unanimous opinions in signed social networks0 aAchieving unanimous opinions in signed social networks bInstitute of Electrical and Electronics Engineers Inc.3 aBeing able to predict the outcome of an opinion forming process is an important problem in social network theory. However, even for linear dynamics, this becomes a difficult task as soon as non-cooperative interactions are taken into account. Such interactions are naturally modeled as negative weights on the adjacency matrix of the social network. In this paper we show how the Perron-Frobenius theorem can be used for this task also beyond its standard formulation for cooperative systems. In particular we show how it is possible to associate the achievement of unanimous opinions with the existence of invariant cones properly contained in the positive orthant. These cases correspond to signed adjacency matrices having the eventual positivity property, i.e., such that in sufficiently high powers all negative entries have disappeared. More generally, we show how for social networks the achievement of a, possibily non-unanimous, opinion can be associated to the existence of an invariant cone fully contained in one of the orthants of n.1 aAltafini, Claudio1 aLini, Gabriele uhttp://urania.sissa.it/xmlui/handle/1963/3493501209nas a2200133 4500008004100000245010300041210006900144260001000213520075500223100002100978700002000999700002001019856003601039 2014 eng d00aAdler-Gelfand-Dickey approach to classical W-algebras within the theory of Poisson vertex algebras0 aAdlerGelfandDickey approach to classical Walgebras within the th bSISSA3 aWe put the Adler-Gelfand-Dickey approach to classical W-algebras in the framework of Poisson vertex algebras. We show how to recover the bi-Poisson structure of the KP hierarchy, together with its generalizations and reduction to the N-th KdV hierarchy, using the formal distribution calculus and the lambda-bracket formalism. We apply the Lenard-Magri scheme to prove integrability of the corresponding hierarchies. We also give a simple proof of a theorem of Kupershmidt and Wilson in this framework. Based on this approach, we generalize all these results to the matrix case. In particular, we find (non-local) bi-Poisson structures of the matrix KP and the matrix N-th KdV hierarchies, and we prove integrability of the N-th matrix KdV hierarchy.1 aDe Sole, Alberto1 aKac, Victor, G.1 aValeri, Daniele uhttp://hdl.handle.net/1963/724200836nas a2200121 4500008004100000245009000041210007300131260001300204520040500217100001600622700002500638856005100663 2014 en d00aApproximate Hermitian–Yang–Mills structures on semistable principal Higgs bundles0 aApproximate Hermitian–Yang–Mills structures on semistable princi bSpringer3 aWe generalize the Hitchin-Kobayashi correspondence between semistability and the existence of approximate Hermitian-Yang-Mills structures to the case of principal Higgs bundles. We prove that a principal Higgs bundle on a compact Kaehler manifold, with structure group a connected linear algebraic reductive group, is semistable if and only if it admits an approximate Hermitian-Yang-Mills structure.1 aBruzzo, Ugo1 aGrana-Otero, Beatriz uhttp://urania.sissa.it/xmlui/handle/1963/3464500747nas a2200121 4500008004100000245006900041210006700110260003200177520032200209100001600531700002700547856005100574 2014 en d00aApproximate Hitchin-Kobayashi correspondence for Higgs G-bundles0 aApproximate HitchinKobayashi correspondence for Higgs Gbundles bWorld Scientific Publishing3 aWe announce a result about the extension of the Hitchin-Kobayashi correspondence to principal Higgs bundles. A principal Higgs bundle on a compact Kähler manifold, with structure group a connected linear algebraic reductive group, is semistable if and only if it admits an approximate Hermitian-Yang-Mills structure.1 aBruzzo, Ugo1 aOtero, Beatriz, Graña uhttp://urania.sissa.it/xmlui/handle/1963/3509501081nas a2200145 4500008004100000245007400041210006900115260003100184520057600215100002700791700002100818700002300839700002200862856005100884 2014 en d00aBuckling dynamics of a solvent-stimulated stretched elastomeric sheet0 aBuckling dynamics of a solventstimulated stretched elastomeric s bRoyal Society of Chemistry3 aWhen stretched uniaxially, a thin elastic sheet may exhibit buckling. The occurrence of buckling depends on the geometrical properties of the sheet and the magnitude of the applied strain. Here we show that an elastomeric sheet initially stable under uniaxial stretching can destabilize when exposed to a solvent that swells the elastomer. We demonstrate experimentally and computationally that the features of the buckling pattern depend on the magnitude of stretching, and this observation offers a new way for controlling the shape of a swollen homogeneous thin sheet.1 aLucantonio, Alessandro1 aRoché, Matthieu1 aNardinocchi, Paola1 aStone, Howard, A. uhttp://urania.sissa.it/xmlui/handle/1963/3496700469nas a2200145 4500008004100000022001400041245007300055210006900128300001400197490000800211100001900219700001700238700002000255856004800275 2014 eng d a0010-361600aCauchy-Laguerre two-matrix model and the Meijer-G random point field0 aCauchyLaguerre twomatrix model and the MeijerG random point fiel a111–1440 v3261 aBertola, Marco1 aGekhtman, M.1 aSzmigielski, J. uhttp://dx.doi.org/10.1007/s00220-013-1833-801294nas a2200133 4500008004100000245010400041210006900145260001000214520083900224100002101063700002001084700002001104856003601124 2014 en d00aClassical W-algebras and generalized Drinfeld-Sokolov hierarchies for minimal and short nilpotents0 aClassical Walgebras and generalized DrinfeldSokolov hierarchies bSISSA3 aWe derive explicit formulas for lambda-brackets of the affine classical W-algebras attached to the minimal and short nilpotent elements of any simple Lie algebra g. This is used to compute explicitly the first non-trivial PDE of the corresponding intgerable generalized Drinfeld-Sokolov hierarchies. It turns out that a reduction of the equation corresponding to a short nilpotent is Svinolupov's equation attached to a simple Jordan algebra, while a reduction of the equation corresponding to a minimal nilpotent is an integrable Hamiltonian equation on 2h-3 functions, where h is the dual Coxeter number of g. In the case when g is sl_2 both these equations coincide with the KdV equation. In the case when g is not of type C_n, we associate to the minimal nilpotent element of g yet another generalized Drinfeld-Sokolov hierarchy.1 aDe Sole, Alberto1 aKac, Victor, G.1 aValeri, Daniele uhttp://hdl.handle.net/1963/697902162nas a2200133 4500008004100000245009400041210006900135260001300204520170200217100001501919700002201934700002101956856005101977 2014 en d00aComparison between reduced basis and stochastic collocation methods for elliptic problems0 aComparison between reduced basis and stochastic collocation meth bSpringer3 aThe stochastic collocation method (Babuška et al. in SIAM J Numer Anal 45(3):1005-1034, 2007; Nobile et al. in SIAM J Numer Anal 46(5):2411-2442, 2008a; SIAM J Numer Anal 46(5):2309-2345, 2008b; Xiu and Hesthaven in SIAM J Sci Comput 27(3):1118-1139, 2005) has recently been applied to stochastic problems that can be transformed into parametric systems. Meanwhile, the reduced basis method (Maday et al. in Comptes Rendus Mathematique 335(3):289-294, 2002; Patera and Rozza in Reduced basis approximation and a posteriori error estimation for parametrized partial differential equations Version 1.0. Copyright MIT, http://augustine.mit.edu, 2007; Rozza et al. in Arch Comput Methods Eng 15(3):229-275, 2008), primarily developed for solving parametric systems, has been recently used to deal with stochastic problems (Boyaval et al. in Comput Methods Appl Mech Eng 198(41-44):3187-3206, 2009; Arch Comput Methods Eng 17:435-454, 2010). In this work, we aim at comparing the performance of the two methods when applied to the solution of linear stochastic elliptic problems. Two important comparison criteria are considered: (1), convergence results of the approximation error; (2), computational costs for both offline construction and online evaluation. Numerical experiments are performed for problems from low dimensions O (1) to moderate dimensions O (10) and to high dimensions O (100). The main result stemming from our comparison is that the reduced basis method converges better in theory and faster in practice than the stochastic collocation method for smooth problems, and is more suitable for large scale and high dimensional stochastic problems when considering computational costs.1 aChen, Peng1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3472702011nas a2200241 4500008004100000245013600041210006900177260002200246300000800268490000700276520123100283100002101514700001901535700001901554700001901573700001701592700002701609700002001636700002301656700002101679700001801700856005101718 2014 en d00aComparison of a Modal Method and a Proper Orthogonal Decomposition approach for multi-group time-dependent reactor spatial kinetics0 aComparison of a Modal Method and a Proper Orthogonal Decompositi bElsevierc09/2014 a2290 v713 aIn this paper, two modelling approaches based on a Modal Method (MM) and on the Proper Orthogonal Decomposition (POD) technique, for developing a control-oriented model of nuclear reactor spatial kinetics, are presented and compared. Both these methods allow developing neutronics description by means of a set of ordinary differential equations. The comparison of the outcomes provided by the two approaches focuses on the capability of evaluating the reactivity and the neutron flux shape in different reactor configurations, with reference to a TRIGA Mark II reactor. The results given by the POD-based approach are higher-fidelity with respect to the reference solution than those computed according to the MM-based approach, in particular when the perturbation concerns a reduced region of the core. If the perturbation is homogeneous throughout the core, the two approaches allow obtaining comparable accuracy results on the quantities of interest. As far as the computational burden is concerned, the POD approach ensures a better efficiency rather than direct Modal Method, thanks to the ability of performing a longer computation in the preprocessing that leads to a faster evaluation during the on-line phase.

1 aSartori, Alberto1 aBaroli, Davide1 aCammi, Antonio1 aChiesa, Davide1 aLuzzi, Lelio1 aPonciroli, Roberto, R.1 aPrevitali, Ezio1 aRicotti, Marco, E.1 aRozza, Gianluigi1 aSisti, Monica uhttp://urania.sissa.it/xmlui/handle/1963/3503901580nas 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/1963/3512801122nas a2200145 4500008004100000245005400041210005100095260001300146520066000159653006000819100002500879700001600904700002000920856003600940 2014 en d00aOn conjugate times of LQ optimal control problems0 aconjugate times of LQ optimal control problems bSpringer3 aMotivated by the study of linear quadratic optimal control problems, we consider a dynamical system with a constant, quadratic Hamiltonian, and we characterize the number of conjugate times in terms of the spectrum of the Hamiltonian vector field $\vec{H}$. We prove the following dichotomy: the number of conjugate times is identically zero or grows to infinity. The latter case occurs if and only if $\vec{H}$ has at least one Jordan block of odd dimension corresponding to a purely imaginary eigenvalue. As a byproduct, we obtain bounds from below on the number of conjugate times contained in an interval in terms of the spectrum of $\vec{H}$.10aOptimal control, Lagrange Grassmannian, Conjugate point1 aAgrachev, Andrei, A.1 aRizzi, Luca1 aSilveira, Pavel uhttp://hdl.handle.net/1963/722700720nas a2200109 4500008004100000245007700041210006900118260003100187520031700218100002400535856005100559 2014 en d00aA correction and an extension of Stampacchia's work on the geometric BVP0 acorrection and an extension of Stampacchias work on the geometri bAdvanced Nonlinear Studies3 aG. Stampacchia introduced the geometric boundary value problem for ODEs in his doctoral thesis and published four papers related to it. Here we point out that the proof of his last theorem on the subject is incorrect and we provide a substitute for it as well as a generalizations of some of his earlier results.1 aVidossich, Giovanni uhttp://urania.sissa.it/xmlui/handle/1963/3502301733nas a2200217 4500008004100000022001400041245003700055210003700092300001200129490000700141520111900148653002901267653001901296653002201315653002501337653002001362100001801382700002201400700002201422856007101444 2014 eng d a0020-746200aCrawling on directional surfaces0 aCrawling on directional surfaces a65 - 730 v613 aIn this paper we study crawling locomotion based on directional frictional interactions, namely, frictional forces that are sensitive to the sign of the sliding velocity. Surface interactions of this type are common in biology, where they arise from the presence of inclined hairs or scales at the crawler/substrate interface, leading to low resistance when sliding ‘along the grain’, and high resistance when sliding ‘against the grain’. This asymmetry can be exploited for locomotion, in a way analogous to what is done in cross-country skiing (classic style, diagonal stride). We focus on a model system, namely, a continuous one-dimensional crawler and provide a detailed study of the motion resulting from several strategies of shape change. In particular, we provide explicit formulae for the displacements attainable with reciprocal extensions and contractions (breathing), or through the propagation of extension or contraction waves. We believe that our results will prove particularly helpful for the study of biological crawling motility and for the design of bio-mimetic crawling robots.

10aBio-mimetic micro-robots10aCell migration10aCrawling motility10aDirectional surfaces10aSelf-propulsion1 aGidoni, Paolo1 aNoselli, Giovanni1 aDeSimone, Antonio uhttp://www.sciencedirect.com/science/article/pii/S002074621400021301111nas a2200121 4500008004100000245006400041210006300105260003400168520070800202100002200910700002100932856003600953 2014 en d00aCritical points of the Moser-Trudinger functional on a disk0 aCritical points of the MoserTrudinger functional on a disk bEuropean Mathematical Society3 aOn the 2-dimensional unit disk $B_1$ we study the Moser-Trudinger functional $$E(u)=\int_{B_1}(e^{u^2}-1)dx, u\in H^1_0(B_1)$$ and its restrictions to $M_\Lambda:=\{u \in H^1_0(B_1):\|u\|^2_{H^1_0}=\Lambda\}$ for $\Lambda>0$. We prove that if a sequence $u_k$ of positive critical points of $E|_{M_{\Lambda_k}}$ (for some $\Lambda_k>0$) blows up as $k\to\infty$, then $\Lambda_k\to 4\pi$, and $u_k\to 0$ weakly in $H^1_0(B_1)$ and strongly in $C^1_{\loc}(\bar B_1\setminus\{0\})$. Using this we also prove that when $\Lambda$ is large enough, then $E|_{M_\Lambda}$ has no positive critical point, complementing previous existence results by Carleson-Chang, M. Struwe and Lamm-Robert-Struwe.1 aMalchiodi, Andrea1 aMartinazzi, Luca uhttp://hdl.handle.net/1963/656001220nas a2200121 4500008004100000245009100041210006900132260001000201520080700211653002801018100001601046856003601062 2014 en d00aThe curvature of optimal control problems with applications to sub-Riemannian geometry0 acurvature of optimal control problems with applications to subRi bSISSA3 aOptimal control theory is an extension of the calculus of variations, and deals with the optimal behaviour of a system under a very general class of constraints. This field has been pioneered by the group of mathematicians led by Lev Pontryagin in the second half of the 50s and nowadays has countless applications to the real worlds (robotics, trains, aerospace, models for human behaviour, human vision, image reconstruction, quantum control, motion of self-propulsed micro-organism). In this thesis we introduce a novel definition of curvature for an optimal control problem. In particular it works for any sub-Riemannian and sub-Finsler structure. Related problems, such as comparison theorems for sub-Riemannian manifolds, LQ optimal control problem and Popp's volume and are also investigated.10aSub-Riemannian geometry1 aRizzi, Luca uhttp://hdl.handle.net/1963/732101482nas a2200157 4500008004100000245004800041210004700089260001300136300001400149490000700163520105700170100001801227700001701245700001301262856004901275 2014 en d00aCurvature-adapted remeshing of CAD surfaces0 aCurvatureadapted remeshing of CAD surfaces bElsevier a253–2650 v823 aA common representation of surfaces with complicated topology and geometry is through composite parametric surfaces as is the case for most CAD modelers. A challenging problem is how to generate a mesh of such a surface that well approximates the geometry of the surface, preserves its topology and important geometric features, and contains nicely shaped elements. In this work, we present an optimization-based surface remeshing method that is able to satisfy many of these requirements simultaneously. This method is inspired by the recent work of Lévy and Bonneel (Proc. 21th International Meshing Roundtable, October 2012), which embeds a smooth surface into a high-dimensional space and remesh it uniformly in that embedding space. Our method works directly in the 3d spaces and uses an embedding space in R6 to evaluate mesh size and mesh quality. It generates a curvatureadapted anisotropic surface mesh that well represents the geometry of the surface with a low number of elements. We illustrate our approach through various examples.

1 aDassi, Franco1 aMola, Andrea1 aSi, Hang uhttps://doi.org/10.1016/j.proeng.2014.10.38800423nas a2200121 4500008004100000245005500041210005500096300000700151490001100158100001900169700002000188856009300208 2014 eng d00aDarboux Transformations and Random Point Processes0 aDarboux Transformations and Random Point Processes a560 vrnu1221 aBertola, Marco1 aCafasso, Mattia uhttps://www.math.sissa.it/publication/darboux-transformations-and-random-point-processes00403nas a2200109 4500008004100000245007400041210006900115260001000184653002700194100002200221856005000243 2014 en d00aThe decomposition of optimal transportation problems with convex cost0 adecomposition of optimal transportation problems with convex cos bSISSA10aOptimal Transportation1 aBardelloni, Mauro uhttp://urania.sissa.it/xmlui/handle/1963/747500387nas a2200109 4500008004300000245007400043210006900117260001000186100002300196700002200219856003600241 2014 en_Ud 00aThe decomposition of optimal transportation problems with convex cost0 adecomposition of optimal transportation problems with convex cos bSISSA1 aBianchini, Stefano1 aBardelloni, Mauro uhttp://hdl.handle.net/1963/743300921nas a2200109 4500008004100000245010000041210006900141260001300210520051500223100002200738856005100760 2014 en d00aA density result for GSBD and its application to the approximation of brittle fracture energies0 adensity result for GSBD and its application to the approximation bSpringer3 aWe present an approximation result for functions u: Ω → ℝ^n belonging to the space GSBD(Ω) ∩ L2(Ω, ℝn) with e(u) square integrable and Hn-1(Ju) finite. The approximating functions uk are piecewise continuous functions such that uk → u in (Formula Presented). As an application, we provide the extension to the vector-valued case of the Γ-convergence result in GSBV(Ω) proved by Ambrosio and Tortorelli (Commun Pure Appl Math 43:999-1036, 1990; Boll. Un. Mat. Ital. B (7) 6:105-123, 1992).

1 aIurlano, Flaviana uhttp://urania.sissa.it/xmlui/handle/1963/3464701079nas a2200133 4500008004100000245006300041210006300104260003200167520063100199100002000830700002200850700002200872856005100894 2014 en d00aDirac operators on noncommutative principal circle bundles0 aDirac operators on noncommutative principal circle bundles bWorld Scientific Publishing3 aWe study spectral triples over noncommutative principal U(1)-bundles of arbitrary dimension and a compatibility condition between the connection and the Dirac operator on the total space and on the base space of the bundle. Examples of low-dimensional noncommutative tori are analyzed in more detail and all connections found that are compatible with an admissible Dirac operator. Conversely, a family of new Dirac operators on the noncommutative tori, which arise from the base-space Dirac operator and a suitable connection is exhibited. These examples are extended to the theta-deformed principal U(1)-bundle S 3 θ → S2.1 aSitarz, Andrzej1 aZucca, Alessandro1 aDabrowski, Ludwik uhttp://urania.sissa.it/xmlui/handle/1963/3512500706nas a2200133 4500008004100000245004800041210004800089260001000137520032800147100002100475700002000496700002000516856003600536 2014 en d00aDirac reduction for Poisson vertex algebras0 aDirac reduction for Poisson vertex algebras bSISSA3 aWe construct an analogue of Dirac's reduction for an arbitrary local or non-local Poisson bracket in the general setup of non-local Poisson vertex algebras. This leads to Dirac's reduction of an arbitrary non-local Poisson structure. We apply this construction to an example of a generalized Drinfeld-Sokolov hierarchy.1 aDe Sole, Alberto1 aKac, Victor, G.1 aValeri, Daniele uhttp://hdl.handle.net/1963/698001213nas a2200145 4500008004100000245011200041210006900153260001300222520069800235653001900933100002200952700002000974700002200994856005101016 2014 en d00aDiscrete one-dimensional crawlers on viscous substrates: achievable net displacements and their energy cost0 aDiscrete onedimensional crawlers on viscous substrates achievabl bElsevier3 aWe study model one-dimensional crawlers, namely, model mechanical systems that can achieve self-propulsion by controlled shape changes of their body (extension or contraction of portions of the body), thanks to frictional interactions with a rigid substrate. We evaluate the achievable net displacement and the related energetic cost for self-propulsion by discrete crawlers (i.e., whose body is made of a discrete number of contractile or extensile segments) moving on substrates with either a Newtonian (linear) or a Bingham-type (stick-slip) rheology. Our analysis is aimed at constructing the basic building blocks towards an integrative, multi-scale description of crawling cell motility.10aCell migration1 aNoselli, Giovanni1 aTatone, Amabile1 aDeSimone, Antonio uhttp://urania.sissa.it/xmlui/handle/1963/3444900376nas a2200097 4500008004100000245008700041210006900128100002000197700002500217856003600242 2014 eng d00aDislocations at the continuum scale: functional setting and variational properties0 aDislocations at the continuum scale functional setting and varia1 aScala, Riccardo1 aVan Goethem, Nicolas uhttp://cvgmt.sns.it/paper/2294/00943nas a2200121 4500008004100000245006300041210006200104520045300166653013100619100001600750700001900766856003600785 2014 en d00aDonagi–Markman cubic for the generalised Hitchin system0 aDonagi–Markman cubic for the generalised Hitchin system3 aDonagi and Markman (1993) have shown that the infinitesimal period map for an algebraic completely integrable Hamiltonian system (ACIHS) is encoded in a section of the third symmetric power of the cotangent bundle to the base of the system. For the ordinary Hitchin system the cubic is given by a formula of Balduzzi and Pantev. We show that the Balduzzi–Pantev formula holds on maximal rank symplectic leaves of the G-generalised Hitchin system.10aGeneralized Hitchin system, Donagi-Markman cubic, algebraically completely integrable systems, moduli space of Higgs G-bundles1 aBruzzo, Ugo1 aDalakov, Peter uhttp://hdl.handle.net/1963/725301107nas a2200121 4500008004300000245007000043210006800113260001000181520068600191100002900877700002900906856005000935 2014 en_Ud 00aDynamics on a graph as the limit of the dynamics on a "fat graph"0 aDynamics on a graph as the limit of the dynamics on a fat graph bSISSA3 aWe discuss how the vertex boundary conditions for the dynamics of a quantum particle constrained on a graph emerge in the limit of the dynamics of a particle in a tubular region around the graph (\fat graph") when the transversal section of this region shrinks to zero. We give evidence of the fact that if the limit dynamics exists and is induced by the Laplacian on the graph with certain self-adjoint boundary conditions, such conditions are determined by the possible presence of a zero energy resonance on the fat graph. Pictorially, one may say that in the shrinking limit the resonance acts as a bridge connecting the boundary values at the vertex along the different rays.1 aDell'Antonio, Gianfausto1 aMichelangeli, Alessandro uhttp://urania.sissa.it/xmlui/handle/1963/748500316nas a2200121 4500008004100000245001400041210001400055260001300069100002000082700002100102700002000123856005100143 2014 en d00aEditorial0 aEditorial bSpringer1 aCiliberto, Ciro1 aDal Maso, Gianni1 aVetro, Pasquale uhttp://urania.sissa.it/xmlui/handle/1963/3471201955nas a2200145 4500008004100000245009100041210006900132260006400201520139800265100002701663700002201690700002101712700002501733856005101758 2014 en d00aAn effective model for nematic liquid crystal composites with ferromagnetic inclusions0 aeffective model for nematic liquid crystal composites with ferro bSociety for Industrial and Applied Mathematics Publications3 aMolecules of a nematic liquid crystal respond to an applied magnetic field by reorienting themselves in the direction of the field. Since the dielectric anisotropy of a nematic is small, it takes relatively large fields to elicit a significant liquid crystal response. The interaction may be enhanced in colloidal suspensions of ferromagnetic particles in a liquid crystalline matrix- ferronematics-as proposed by Brochard and de Gennes in 1970. The ability of these particles to align with the field and simultaneously cause reorientation of the nematic molecules greatly increases the magnetic response of the mixture. Essentially the particles provide an easy axis of magnetization that interacts with the liquid crystal via surface anchoring. We derive an expression for the effective energy of ferronematic in the dilute limit, that is, when the number of particles tends to infinity while their total volume fraction tends to zero. The total energy of the mixture is assumed to be the sum of the bulk elastic liquid crystal contribution, the anchoring energy of the liquid crystal on the surfaces of the particles, and the magnetic energy of interaction between the particles and the applied magnetic field. The homogenized limiting ferronematic energy is obtained rigorously using a variational approach. It generalizes formal expressions previously reported in the physical literature.1 aCalderer, Maria, Carme1 aDeSimone, Antonio1 aGolovaty, Dmitry1 aPanchenko, Alexander uhttp://urania.sissa.it/xmlui/handle/1963/3494001997nas a2200109 4500008004100000245014300041210006900184520134000253653014901593100002001742856012501762 2014 en d00aAn efficient computational framework for reduced basis approximation and a posteriori error estimation of parametrized Navier-Stokes flows0 aefficient computational framework for reduced basis approximatio3 aWe present the current Reduced Basis framework for the efficient numerical approximation of parametrized steady Navier-Stokes equations. We have extended the existing setting developed in the last decade (see e.g. [Deparis, Veroy & Patera, Quarteroni & Rozza] to more general affine and nonaffine parametrizations (such as volume-based techniques), to a simultaneous velocity-pressure error estimates and to a fully decoupled Offline/Online procedure in order to speedup the solution of the reduced-order problem. This is particularly suitable for real-time and many-query contexts, which are both part of our final goal. Furthermore, we present an efficient numerical implementation for treating nonlinear advection terms in a convenient way. A residual-based a posteriori error estimation with respect to a truth, full-order Finite Element approximation is provided for joint pressure/velocity errors, according to the Brezzi-Rappaz-Raviart stability theory. To do this, we take advantage of an extension of the Successive Constraint Method for the estimation of stability factors and of a suitable fixed-point algorithm for the approximation of Sobolev embedding constants. Finally, we present some numerical test cases, in order to show both the approximation properties and the computational efficiency of the derived framework.10aReduced Basis Method, parametrized Navier-Stokes equations, steady incompressible fluids, a posteriori error estimation, approximation stability1 aManzoni, Andrea uhttps://www.math.sissa.it/publication/efficient-computational-framework-reduced-basis-approximation-and-posteriori-error01443nas a2200133 4500008004100000245015900041210006900200300001400269490000700283520085800290100001401148700002101162856012601183 2014 eng d00aEfficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems0 aEfficient geometrical parametrisation techniques of interfaces f a158–1690 v283 aWe present some recent advances and improvements in shape parametrisation techniques of interfaces for reduced-order modelling with special attention to fluid–structure interaction problems and the management of structural deformations, namely, to represent them into a low-dimensional space (by control points). This allows to reduce the computational effort, and to significantly simplify the (geometrical) deformation procedure, leading to more efficient and fast reduced-order modelling applications in this kind of problems. We propose an efficient methodology to select the geometrical control points for the radial basis functions based on a modal greedy algorithm to improve the computational efficiency in view of more complex fluid–structure applications in several fields. The examples provided deal with aeronautics and wind engineering.1 aForti, D.1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/efficient-geometrical-parametrisation-techniques-interfaces-reduced-order-modelling00833nas a2200121 4500008004100000245010200041210006900143260003900212520036100251100002300612700002500635856005100660 2014 en d00aExistence and uniqueness of the gradient flow of the Entropy in the space of probability measures0 aExistence and uniqueness of the gradient flow of the Entropy in bEUT Edizioni Universita di Trieste3 aAfter a brief introduction on gradient flows in metric spaces and on geodesically convex functionals, we give an account of the proof (following the outline of [3, 7]) of the existence and uniqueness of the gradient flow of the Entropy in the space of Borel probability measures over a compact geodesic metric space with Ricci curvature bounded from below.1 aBianchini, Stefano1 aDabrowski, Alexander uhttp://urania.sissa.it/xmlui/handle/1963/3469301126nas a2200169 4500008004100000022001400041245009000055210006900145260000800214300001400222490000800236520060400244100001800848700002000866700002400886856004600910 2014 eng d a1432-180700aExistence of immersed spheres minimizing curvature functionals in compact 3-manifolds0 aExistence of immersed spheres minimizing curvature functionals i cJun a379–4250 v3593 aWe study curvature functionals for immersed 2-spheres in a compact, three-dimensional Riemannian manifold $M$. Under the assumption that the sectional curvature $K^M$ is strictly positive, we prove the existence of a smooth immersion $f:{\mathbb{S}}^2 \rightarrow M$ minimizing the $L^2$ integral of the second fundamental form. Assuming instead that $K^M \leq 2 $ and that there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})>6$, we obtain a smooth minimizer $f:{\mathbb{S}}^2 \rightarrow M$ for the functional $\int \frac{1}{4}|H|^2+1$, where $H$ is the mean curvature.

1 aKuwert, Ernst1 aMondino, Andrea1 aSchygulla, Johannes uhttps://doi.org/10.1007/s00208-013-1005-303135nas a2200205 4500008004100000022001400041245009400055210006900149300001400218490000700232520242200239653004902661653002302710653002902733653002802762653002402790100002002814700002402834856007102858 2014 eng d a0294-144900aExistence of immersed spheres minimizing curvature functionals in non-compact 3-manifolds0 aExistence of immersed spheres minimizing curvature functionals i a707 - 7240 v313 aWe study curvature functionals for immersed 2-spheres in non-compact, three-dimensional Riemannian manifold $(M,h)$ without boundary. First, under the assumption that $(M,h)$ is the euclidean 3-space endowed with a semi-perturbed metric with perturbation small in $C^1$ norm and of compact support, we prove that if there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})>0$ then there exists a smooth embedding $ f:\mathbb{S}^2 \hookrightarrow M$ minimizing the Willmore functional $\frac{1}{4}\int |H|^2$, where $H$ is the mean curvature. Second, assuming that $(M,h)$ is of bounded geometry (i.e. bounded sectional curvature and strictly positive injectivity radius) and asymptotically euclidean or hyperbolic we prove that if there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})>6$ then there exists a smooth immersion $f:\mathbb{S}^2\hookrightarrow M$ minimizing the functional $\int (\frac{1}{2}|A|^2+1)$, where $A$ is the second fundamental form. Finally, adding the bound $K^M \leq 2$ to the last assumptions, we obtain a smooth minimizer $f:\mathbb{S}^2 \hookrightarrow M$ for the functional $\int \frac{1}{4}(|H|^2+1)$. The assumptions of the last two theorems are satisfied in a large class of 3-manifolds arising as spacelike timeslices solutions of the Einstein vacuum equation in case of null or negative cosmological constant.

10aDirect methods in the calculus of variations10aGeneral Relativity10aGeometric measure theory10asecond fundamental form10aWillmore functional1 aMondino, Andrea1 aSchygulla, Johannes uhttp://www.sciencedirect.com/science/article/pii/S029414491300085101095nas a2200145 4500008004100000022001400041245011100055210006900166260000800235300001400243490000700257520061900264100002000883856004600903 2014 eng d a1432-083500aExistence of integral m-varifolds minimizing $\int |A|^p $ and $\int |H|^p$ , p>m, in Riemannian manifolds0 aExistence of integral mvarifolds minimizing int Ap and int Hp pm cJan a431–4700 v493 aWe prove existence of integral rectifiable $m$-dimensional varifolds minimizing functionals of the type $\int |H|^p$ and $\int |A|^p$ in a given Riemannian $n$-dimensional manifold $(N,g)$, $2 \leq m<n$ and $p>m$ under suitable assumptions on $N$ (in the end of the paper we give many examples of such ambient manifolds). To this aim we introduce the following new tools: some monotonicity formulas for varifolds in ${\mathbb{R }^S}$ involving $\int |H|^p$to avoid degeneracy of the minimizer, and a sort of isoperimetric inequality to bound the mass in terms of the mentioned functionals.

1 aMondino, Andrea uhttps://doi.org/10.1007/s00526-012-0588-y01351nas a2200133 4500008004100000245008400041210007000125260003900195520087300234100001901107700001901126700002101145856005101166 2014 en d00aFinite dimensional Kadomtsev-Petviashvili τ-functions. I. Finite Grassmannians0 aFinite dimensional KadomtsevPetviashvili τfunctions I Finite Gra bAmerican Institute of Physics Inc.3 aWe study τ-functions of the Kadomtsev-Petviashvili hierarchy in terms of abelian group actions on finite dimensional Grassmannians, viewed as subquotients of the Hilbert space Grassmannians of Sato, Segal, and Wilson. A determinantal formula of Gekhtman and Kasman involving exponentials of finite dimensional matrices is shown to follow naturally from such reductions. All reduced flows of exponential type generated by matrices with arbitrary nondegenerate Jordan forms are derived, both in the Grassmannian setting and within the fermionic operator formalism. A slightly more general determinantal formula involving resolvents of the matrices generating the flow, valid on the big cell of the Grassmannian, is also derived. An explicit expression is deduced for the Plücker coordinates appearing as coefficients in the Schur function expansion of the τ-function.1 aBalogh, Ferenc1 aFonseca, Tiago1 aHarnad, John, P. uhttp://urania.sissa.it/xmlui/handle/1963/3495201202nas a2200145 4500008004100000245010600041210006900147260001000216520062900226653002300855100001700878700001700895700002200912856012200934 2014 en d00aA fully nonlinear potential model for ship hydrodynamics directly interfaced with CAD data structures0 afully nonlinear potential model for ship hydrodynamics directly bSISSA3 aWe present a model for ship hydrodynamics simulations currently under development at SISSA. The model employs potential flow theory and fully nonlinear free surface boundary conditions. The spatial discretization of the equations is performed by means of a collocation BEM. This gives rise to a Differential Algbraic Equations (DAE) system, solved using an implicit BDF scheme to time advance the solution. The model has been implemented into a C++ software able to automatically generate the computational grids from the CAD geometry of the hull. Numerical results on Kriso KCS and KVLCC2 hulls are presented and discussed.10aship hydrodynamics1 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio uhttps://www.math.sissa.it/publication/fully-nonlinear-potential-model-ship-hydrodynamics-directly-interfaced-cad-data01604nas a2200133 4500008004100000245010100041210006900142260001900211490000800230520099000238653009201228100002101320856012901341 2014 eng d00aFundamentals of Reduced Basis Method for problems governed by parametrized PDEs and applications0 aFundamentals of Reduced Basis Method for problems governed by pa aWienbSpringer0 v5543 aIn this chapter we consider Reduced Basis (RB) approximations of parametrized Partial Differential Equations (PDEs). The the idea behind RB is to decouple the generation and projection stages (Offline/Online computational procedures) of the approximation process in order to solve parametrized PDEs in a fast, inexpensive and reliable way. The RB method, especially applied to 3D problems, allows great computational savings with respect to the classical Galerkin Finite Element (FE) Method. The standard FE method is typically ill suited to (i) iterative contexts like optimization, sensitivity analysis and many-queries in general, and (ii) real time evaluation. We consider for simplicity coercive PDEs. We discuss all the steps to set up a RB approximation, either from an analytical and a numerical point of view. Then we present an application of the RB method to a steady thermal conductivity problem in heat transfer with emphasis on geometrical and physical parameters.

10areduced basis method, linear elasticity, heat transfer, error bounds, parametrized PDEs1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/fundamentals-reduced-basis-method-problems-governed-parametrized-pdes-and-applications01517nas 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/1963/747401332nas a2200121 4500008004100000245014300041210006900184260002100253520085000274100002301124700001201147856005101159 2014 en d00aGlobal Structure of Admissible BV Solutions to Piecewise Genuinely Nonlinear, Strictly Hyperbolic Conservation Laws in One Space Dimension0 aGlobal Structure of Admissible BV Solutions to Piecewise Genuine bTaylor & Francis3 aThe paper describes the qualitative structure of an admissible BV solution to a strictly hyperbolic system of conservation laws whose characteristic families are piecewise genuinely nonlinear. More precisely, we prove that there are a countable set of points Θ and a countable family of Lipschitz curves T{script} such that outside T{script} ∪ Θ the solution is continuous, and for all points in T{script}{set minus}Θ the solution has left and right limit. This extends the corresponding structural result in [7] for genuinely nonlinear systems. An application of this result is the stability of the wave structure of solution w.r.t. -convergence. The proof is based on the introduction of subdiscontinuities of a shock, whose behavior is qualitatively analogous to the discontinuities of the solution to genuinely nonlinear systems.

1 aBianchini, Stefano1 aYu, Lei uhttp://urania.sissa.it/xmlui/handle/1963/3469400468nas 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-systems01342nas a2200121 4500008004100000245007300041210006900114260001000183520091400193653004101107100002201148856005001170 2014 en d00aHolomorphically symplectic varieties with Prym Lagrangian fibrations0 aHolomorphically symplectic varieties with Prym Lagrangian fibrat bSISSA3 aThe thesis presents a construction of singular holomorphically symplectic varieties as Lagrangian fibrations. They are relative compactified Prym varieties associated to curves on symplectic surfaces with an antisymplectic involution. They are identified with the fixed locus of a symplectic involution on singular moduli spaces of sheaves of dimension 1. An explicit example, giving a singular irreducible symplectic 6-fold without symplectic resolutions, is described for a K3 surface which is the double cover of a cubic surface. In the case of abelian surfaces, a variation of this construction is studied to get irreducible symplectic varieties: relative compactified 0-Prym varieties. A partial classification result is obtained for involutions without fixed points: either the 0-Prym variety is birational to an irreducible symplectic variety of K3[n]-type, or it does not admit symplectic resolutions.10aHolomorphically symplectic varieties1 aMatteini, Tommaso uhttp://urania.sissa.it/xmlui/handle/1963/743400862nas a2200133 4500008004100000245008700041210006900128260001000197520041000207100001700617700002200634700002200656856005000678 2014 en d00aHomogenization of functional with linear growth in the context of A-quasiconvexity0 aHomogenization of functional with linear growth in the context o bSISSA3 aThis work deals with the homogenization of functionals with linear growth in the context of A-quasiconvexity. A representation theorem is proved, where the new integrand function is obtained by solving a cell problem where the coupling between homogenization and the A-free condition plays a crucial role. This result extends some previous work to the linear case, thus allowing for concentration effects.1 aMatias, Jose1 aMorandotti, Marco1 aSantos, Pedro, M. uhttp://urania.sissa.it/xmlui/handle/1963/743600620nas a2200121 4500008004100000245006500041210006500106260001300171520022300184100001800407700002200425856005100447 2014 en d00aHomology computation for a class of contact structures on T30 aHomology computation for a class of contact structures on T3 bSpringer3 aWe consider a family of tight contact forms on the three-dimensional torus and we compute the relative Contact Homology by using the variational theory of critical points at infinity. We will also show local stability.1 aMaalaoui, Ali1 aMartino, Vittorio uhttp://urania.sissa.it/xmlui/handle/1963/3464901082nas a2200145 4500008004100000245007200041210006900113300001400182490000800196520057300204100001600777700002100793700002100814856010100835 2014 eng d00aAn improvement on geometrical parameterizations by transfinite maps0 aimprovement on geometrical parameterizations by transfinite maps a263–2680 v3523 aWe present a method to generate a non-affine transfinite map from a given reference domain to a family of deformed domains. The map is a generalization of the Gordon-Hall transfinite interpolation approach. It is defined globally over the reference domain. Once we have computed some functions over the reference domain, the map can be generated by knowing the parametric expressions of the boundaries of the deformed domain. Being able to define a suitable map from a reference domain to a desired deformation is useful for the management of parameterized geometries.1 aJäggli, C.1 aIapichino, Laura1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/improvement-geometrical-parameterizations-transfinite-maps00921nas a2200121 4500008004100000245008300041210006900124260001300193520050800206100001800714700001600732856005100748 2014 en d00aInfinite-dimensional Frobenius manifolds underlying the Toda lattice hierarchy0 aInfinitedimensional Frobenius manifolds underlying the Toda latt bElsevier3 aFollowing the approach of Carlet et al. (2011) [9], we construct a class of infinite-dimensional Frobenius manifolds underlying the Toda lattice hierarchy, which are defined on the space of pairs of meromorphic functions with possibly higher-order poles at the origin and at infinity. We also show a connection between these infinite-dimensional Frobenius manifolds and the finite-dimensional Frobenius manifolds on the orbit space of extended affine Weyl groups of type A defined by Dubrovin and Zhang.1 aWu, Chaozhong1 aZuo, Dafeng uhttp://urania.sissa.it/xmlui/handle/1963/3502600754nas a2200133 4500008004100000245006000041210005900101260001000160520035300170100002100523700002000544700002000564856003600584 2014 en d00aIntegrability of Dirac reduced bi-Hamiltonian equations0 aIntegrability of Dirac reduced biHamiltonian equations bSISSA3 aFirst, we give a brief review of the theory of the Lenard-Magri scheme for a non-local bi-Poisson structure and of the theory of Dirac reduction. These theories are used in the remainder of the paper to prove integrability of three hierarchies of bi-Hamiltonian PDE's, obtained by Dirac reduction from some generalized Drinfeld-Sokolov hierarchies.1 aDe Sole, Alberto1 aKac, Victor, G.1 aValeri, Daniele uhttp://hdl.handle.net/1963/724700974nas a2200109 4500008004100000245008800041210006900129520042300198653010900621100002200730856011200752 2014 en d00aAn irreducible symplectic orbifold of dimension 6 with a Lagrangian Prym fibration0 airreducible symplectic orbifold of dimension 6 with a Lagrangian3 aA new example of an irreducible symplectic variety of dimension 6, with only finite quotient singularities, is described as a relative compactified Prymian of a family of genus 4 curves with involution. It is associated to a K3 surface which is a double cover of a cubic surface. It has a natural Lagrangian fibration in abelian 3-folds with polarization type (1,1,2). It does not admit any symplectic resolution.10aIrreducible symplectic variety, Lagrangian fibration, Prym variety, automorphism of symplectic varieties1 aMatteini, Tommaso uhttps://www.math.sissa.it/publication/irreducible-symplectic-orbifold-dimension-6-lagrangian-prym-fibration00957nas a2200121 4500008004100000245007500041210006900116260004100185520053400226100002000760700001900780856003600799 2014 en d00aOn an isomonodromy deformation equation without the Painlevé property0 aisomonodromy deformation equation without the Painlevé property bMaik Nauka-Interperiodica Publishing3 aWe show that the fourth order nonlinear ODE which controls the pole dynamics in the general solution of equation $P_I^2$ compatible with the KdV equation exhibits two remarkable properties: 1) it governs the isomonodromy deformations of a $2\times2$ matrix linear ODE with polynomial coefficients, and 2) it does not possesses the Painlev\'e property. We also study the properties of the Riemann--Hilbert problem associated to this ODE and find its large $t$ asymptotic solution for the physically interesting initial data.1 aDubrovin, Boris1 aKapaev, Andrey uhttp://hdl.handle.net/1963/646601519nas a2200145 4500008004100000022001300041245008300054210006900137300000900206520098400215100001301199700002401212700002301236856011401259 2014 eng d a0025583100aKAM for quasi-linear and fully nonlinear forced perturbations of Airy equation0 aKAM for quasilinear and fully nonlinear forced perturbations of a1-663 aWe prove the existence of small amplitude quasi-periodic solutions for quasi-linear and fully nonlinear forced perturbations of the linear Airy equation. For Hamiltonian or reversible nonlinearities we also prove their linear stability. The key analysis concerns the reducibility of the linearized operator at an approximate solution, which provides a sharp asymptotic expansion of its eigenvalues. For quasi-linear perturbations this cannot be directly obtained by a KAM iteration. Hence we first perform a regularization procedure, which conjugates the linearized operator to an operator with constant coefficients plus a bounded remainder. These transformations are obtained by changes of variables induced by diffeomorphisms of the torus and pseudo-differential operators. At this point we implement a Nash-Moser iteration (with second order Melnikov non-resonance conditions) which completes the reduction to constant coefficients. © 2014 Springer-Verlag Berlin Heidelberg.1 aBaldi, P1 aBerti, Massimiliano1 aMontalto, Riccardo uhttps://www.math.sissa.it/publication/kam-quasi-linear-and-fully-nonlinear-forced-perturbations-airy-equation00376nas a2200097 4500008004100000245008500041210006900126260001000195100002300205856005000228 2014 en d00aKAM for quasi-linear and fully nonlinear perturbations of Airy and KdV equations0 aKAM for quasilinear and fully nonlinear perturbations of Airy an bSISSA1 aMontalto, Riccardo uhttp://urania.sissa.it/xmlui/handle/1963/747600573nas a2200157 4500008004100000245002900041210002800070260001300098300001200111490000800123520017300131100001300304700002400317700002300341856005100364 2014 en d00aKAM for quasi-linear KdV0 aKAM for quasilinear KdV bElsevier a603-6070 v3523 aWe prove the existence and stability of Cantor families of quasi-periodic, small-amplitude solutions of quasi-linear autonomous Hamiltonian perturbations of KdV.

1 aBaldi, P1 aBerti, Massimiliano1 aMontalto, Riccardo uhttp://urania.sissa.it/xmlui/handle/1963/3506700608nas 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/1963/3464601118nas a2200145 4500008004100000245013100041210006900172260001000241520052100251653010200772100002100874700002200895700001900917856003600936 2014 en d00aLaplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length0 aLaplace equation in a domain with a rectilinear crack higher ord bSISSA3 aWe consider the weak solution of the Laplace equation in a planar domain with a straight crack, prescribing a homogeneous Neumann condition on the crack and a nonhomogeneous Dirichlet condition on the rest of the boundary. For every k we express the k-th derivative of the energy with respect to the crack length in terms of a finite number of coefficients of the asymptotic expansion of the solution near the crack tip and of a finite number of other parameters, which only depend on the shape of the domain.

10acracked domains, energy release rate, higher order derivatives, asymptotic expansion of solutions1 aDal Maso, Gianni1 aOrlando, Gianluca1 aToader, Rodica uhttp://hdl.handle.net/1963/727100830nas a2200121 4500008004100000245005800041210005800099260003100157520043000188100001700618700002200635856005100657 2014 en d00aLecture notes on gradient flows and optimal transport0 aLecture notes on gradient flows and optimal transport bCambridge University Press3 aWe present a short overview on the strongest variational formulation for gradient flows of geodesically λ-convex functionals in metric spaces, with applications to diffusion equations in Wasserstein spaces of probability measures. These notes are based on a series of lectures given by the second author for the Summer School "Optimal transportation: Theory and applications" in Grenoble during the week of June 22-26, 2009.1 aDaneri, Sara1 aSavarè, Giuseppe uhttp://urania.sissa.it/xmlui/handle/1963/3509300818nas a2200109 4500008004100000245005900041210005900100260003000159520044600189100002200635856005100657 2014 en d00aLegendre duality on hypersurfaces in Kähler manifolds0 aLegendre duality on hypersurfaces in Kähler manifolds bWalter de Gruyter and Co.3 aWe give a sufficient condition on real strictly Levi-convex hypersurfaces M, embedded in four-dimensional Kähler manifolds V , such that Legendre duality can be performed. We consider the contact form onM whose kernel is the restriction of the holomorphic tangent space of V and show that if there exists a Legendrian Killing vector field v, then the dual form β(̇) := d(v, ̇) is a contact form on M with the same orientation than theta.1 aMartino, Vittorio uhttp://urania.sissa.it/xmlui/handle/1963/3477701077nas a2200133 4500008004100000245007900041210007000120260001700190300001400207490000700221520058200228100001800810856011500828 2014 eng d00aLinearized plastic plate models as Γ-limits of 3D finite elastoplasticity0 aLinearized plastic plate models as Γlimits of 3D finite elastopl bEDP Sciences a725–7470 v203 aThe subject of this paper is the rigorous derivation of reduced models for a thin plate by means of $\Gamma$-convergence, in the framework of finite plasticity. Denoting by $\epsilon$ the thickness of the plate, we analyse the case where the scaling factor of the elasto-plastic energy per unit volume is of order $\epsilon^{2 \alpha -2}$, with $\alpha \geq 3$. According to the value of $\alpha$, partially or fully linearized models are deduced, which correspond, in the absence of plastic deformation, to the Von Kármán plate theory and the linearized plate theory.

1 aDavoli, Elisa uhttps://www.math.sissa.it/publication/linearized-plastic-plate-models-%CE%B3-limits-3d-finite-elastoplasticity00762nas a2200121 4500008004100000245010000041210006900141260001300210520031900223100002200542700002500564856005100589 2014 en d00aLipschitz continuous viscosity solutions for a class of fully nonlinear equations on lie groups0 aLipschitz continuous viscosity solutions for a class of fully no bSpringer3 aIn this paper, we prove existence and uniqueness of Lipschitz continuous viscosity solutions for Dirichlet problems involving a class a fully non-linear operators on Lie groups. In particular, we consider the elementary symmetric functions of the eigenvalues of the Hessian built with left-invariant vector fields.1 aMartino, Vittorio1 aMontanari, Annamaria uhttp://urania.sissa.it/xmlui/handle/1963/3469901060nas a2200157 4500008004100000245008400041210006900125260002200194300001400216490000700230520054900237653003500786100002000821700002500841856003600866 2014 en d00aLocal and global minimality results for a nonlocal isoperimetric problem on R^N0 aLocal and global minimality results for a nonlocal isoperimetric bSIAM Publications a2310-23490 v463 aWe consider a nonlocal isoperimetric problem defined in the whole space R^N, whose nonlocal part is given by a Riesz potential with exponent $\alpha\in(0, N-1)$. We show that critical configurations with positive second variation are local minimizers and satisfy a quantitative inequality with respect to the L^1-norm. This criterion provides the existence of a (explicitly determined) critical threshold determining the interval of volumes for which the ball is a local minimizer, and allows to address several global minimality issues.

10aNonlocal isoperimetric problem1 aBonacini, Marco1 aCristoferi, Riccardo uhttp://hdl.handle.net/1963/698400578nas 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-minimizers00800nas a2200133 4500008004100000245006400041210005600105260003400161520035400195100002200549700002300571700002100594856005100615 2014 en d00aOn the Lp-differentiability of certain classes of functions0 aLpdifferentiability of certain classes of functions bEuropean Mathematical Society3 aWe prove the Lp-differentiability at almost every point for convolution products on ℝd of the form K*μ, where μ is bounded measure and K is a homogeneous kernel of degree 1-d. From this result we derive the Lp-differentiability for vector fields on R d whose curl and divergence are measures, and also for vector fields with bounded deformation.1 aAlberti, Giovanni1 aBianchini, Stefano1 aCrippa, Gianluca uhttp://urania.sissa.it/xmlui/handle/1963/3469500683nas a2200109 4500008004100000245005300041210005300094260001300147520034200160100002000502856005100522 2014 en d00aMaximal generalized solution of eikonal equation0 aMaximal generalized solution of eikonal equation bElsevier3 aWe study the Dirichlet problem for the eikonal equation: 1/2 |∇u(x)|^2-a(x)=0 in Ω u(x)=(x) on Ω, without continuity assumptions on the map a(.). We find a class of maps a(.) contained in the space L∞(Ω) for which the problem admits a (maximal) generalized solution, providing a generalization of the notion of viscosity solution.1 aZagatti, Sandro uhttp://urania.sissa.it/xmlui/handle/1963/3464201625nas a2200133 4500008004100000245007900041210006900120260001300189520117000202100002301372700002001395700002501415856005101440 2014 en d00aMinimal Liouville gravity correlation numbers from Douglas string equation0 aMinimal Liouville gravity correlation numbers from Douglas strin bSpringer3 aWe continue the study of $(q,p)$ Minimal Liouville Gravity with the help of Douglas string equation. We generalize the results of \cite{Moore:1991ir}, \cite{Belavin:2008kv}, where Lee-Yang series $(2,2s+1)$ was studied, to $(3,3s+p_0)$ Minimal Liouville Gravity, where $p_0=1,2$. We demonstrate that there exist such coordinates $\tau_{m,n}$ on the space of the perturbed Minimal Liouville Gravity theories, in which the partition function of the theory is determined by the Douglas string equation. The coordinates $\tau_{m,n}$ are related in a non-linear fashion to the natural coupling constants $\lambda_{m,n}$ of the perturbations of Minimal Lioville Gravity by the physical operators $O_{m,n}$. We find this relation from the requirement that the correlation numbers in Minimal Liouville Gravity must satisfy the conformal and fusion selection rules. After fixing this relation we compute three- and four-point correlation numbers when they are not zero. The results are in agreement with the direct calculations in Minimal Liouville Gravity available in the literature \cite{Goulian:1990qr}, \cite{Zamolodchikov:2005sj}, \cite{Belavin:2006ex}.1 aBelavin, Alexander1 aDubrovin, Boris1 aMukhametzhanov, Baur uhttp://urania.sissa.it/xmlui/handle/1963/3458801687nas a2200145 4500008004100000245005600041210005400097260001000151300001100161490000700172520119700179653007701376100001801453856007001471 2014 en d00aA model for crack growth with branching and kinking0 amodel for crack growth with branching and kinking bSISSA a63-1100 v893 aWe study an evolution model for fractured elastic materials in the 2-dimensional case, for which the crack path is not assumed to be known a priori. We introduce some general assumptions on the structure of the fracture sets suitable to remove the restrictions on the regularity of the crack sets and to allow for kinking and branching to develop. In addition we define the front of the fracture and its velocity. By means of a time-discretization approach, we prove the existence of a continuous-time evolution that satisfies an energy inequality and a stability criterion. The energy balance also takes into account the energy dissipated at the front of the fracture. The stability criterion is stated in the framework of Griffith's theory, in terms of the energy release rate, when the crack grows at least at one point of its front.

10aquasistatic crack evolution, branching, kinking, Griffith\\\'s criterion1 aRacca, Simone uhttps://content.iospress.com/articles/asymptotic-analysis/asy123301650nas a2200145 4500008004100000245007300041210006900114260001300183520112000196100001801316700002001334700002201354700002101376856010701397 2014 en d00aModel Order Reduction in Fluid Dynamics: Challenges and Perspectives0 aModel Order Reduction in Fluid Dynamics Challenges and Perspecti bSpringer3 aThis chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities - which are mainly related either to nonlinear convection terms and/or some geometric variability - that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration. We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of inf-sup stability, certification through error estimation, computational issues and-in the unsteady case - long-time stability of the reduced model. Moreover, we provide an extensive list of literature references.1 aLassila, Toni1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/model-order-reduction-fluid-dynamics-challenges-and-perspectives01391nas a2200109 4500008004100000245005300041210005000094260001300144520105400157100001901211856005101230 2014 en d00aA modular spectral triple for κ-Minkowski space0 amodular spectral triple for κMinkowski space bElsevier3 aWe present a spectral triple for κ-Minkowski space in two dimensions. Starting from an algebra naturally associated to this space, a Hilbert space is built using a weight which is invariant under the κ-Poincaré algebra. The weight satisfies a KMS condition and its associated modular operator plays an important role in the construction. This forces us to introduce two ingredients which have a modular flavour: the first is a twisted commutator, used to obtain a boundedness condition for the Dirac operator, and the second is a weight replacing the usual operator trace, used to measure the growth of the resolvent of the Dirac operator. We show that, under some assumptions related to the symmetries and the classical limit, there is a unique Dirac operator and automorphism such that the twisted commutator is bounded. Then, using the weight mentioned above, we compute the spectral dimension associated to the spectral triple and find that is equal to the classical dimension. Finally we briefly discuss the introduction of a real structure.1 aMatassa, Marco uhttp://urania.sissa.it/xmlui/handle/1963/3489500433nas a2200121 4500008004100000245006200041210005900103300001100162490000600173100002000179700002200199856009000221 2014 eng d00aA Moser-Trudinger inequality for the singular Toda system0 aMoserTrudinger inequality for the singular Toda system a1–230 v91 aBattaglia, Luca1 aMalchiodi, Andrea uhttps://www.math.sissa.it/publication/moser-trudinger-inequality-singular-toda-system01318nas 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)05401308nas a2200133 4500008004100000245005300041210005000094260001300144520090800157100001601065700002001081700002201101856005101123 2014 en d00aN = 2 Quiver Gauge Theories on A-type ALE Spaces0 aN 2 Quiver Gauge Theories on Atype ALE Spaces bSpringer3 aWe survey and compare recent approaches to the computation of the partition functions and correlators of chiral BPS observables in N = 2 gauge theories on ALE spaces based on quiver varieties and the minimal resolution Xk of the Ak-1 toric singularity C2/Zk, in light of their recently conjectured duality with two-dimensional coset conformal field theories. We review and elucidate the rigorous constructions of gauge theories for a particular family of ALE spaces, using their relation to the cohomology of moduli spaces of framed torsion-free sheaves on a suitable orbifold compactification of Xk. We extend these computations to generic N = 2 superconformal quiver gauge theories, obtaining in these instances new constraints on fractional instanton charges, a rigorous proof of the Nekrasov master formula, and new quantizations of Hitchin systems based on the underlying Seiberg–Witten geometry.1 aBruzzo, Ugo1 aSala, Francesco1 aSzabo, Richard J. uhttp://urania.sissa.it/xmlui/handle/1963/3471900423nas a2200133 4500008004100000245005600041210005500097260001300152653002200165100001800187700002100205700002700226856003600253 2014 en d00aNew results on Gamma-limits of integral functionals0 aNew results on Gammalimits of integral functionals bElsevier10aGamma-convergence1 aAnsini, Nadia1 aDal Maso, Gianni1 aZeppieri, Caterina Ida uhttp://hdl.handle.net/1963/588000656nas a2200121 4500008004100000245008200041210006900123260001000192520017100202653002900373100001900402856011300421 2014 en d00aNon-commutative integration for spectral triples associated to quantum groups0 aNoncommutative integration for spectral triples associated to qu bSISSA3 aThis thesis is dedicated to the study of non-commutative integration, in the sense of spectral triples, for some non-commutative spaces associated to quantum groups.10aNon-commutative geometry1 aMatassa, Marco uhttps://www.math.sissa.it/publication/non-commutative-integration-spectral-triples-associated-quantum-groups02051nas a2200145 4500008004100000245007600041210006900117260001300186520158600199653002601785100001701811700001901828700002201847856003601869 2014 en d00aNonsingular Isogeometric Boundary Element Method for Stokes Flows in 3D0 aNonsingular Isogeometric Boundary Element Method for Stokes Flow bElsevier3 aIsogeometric analysis (IGA) is emerging as a technology bridging Computer Aided Geometric Design (CAGD), most commonly based on Non-Uniform Rational B-Splines (NURBS) surfaces, and engineering analysis. In finite element and boundary element isogeometric methods (FE-IGA and IGA-BEM), the NURBS basis functions that de- scribe the geometry define also the approximation spaces. In the FE-IGA approach, the surfaces generated by the CAGD tools need to be extended to volumetric descriptions, a major open problem in 3D. This additional passage can be avoided in principle when the partial differential equations to be solved admit a formulation in terms of bound- ary integral equations, leading to Boundary Element Isogeometric Analysis (IGA-BEM). The main advantages of such an approach are given by the dimensionality reduction of the problem (from volumetric-based to surface-based), by the fact that the interface with CAGD tools is direct, and by the possibility to treat exterior problems, where the computational domain is infinite. By contrast, these methods produce system matrices which are full, and require the integration of singular kernels. In this paper we address the second point and propose a nonsingular formulation of IGA-BEM for 3D Stokes flows, whose convergence is carefully tested numerically. Standard Gaussian quadrature rules suffice to integrate the boundary integral equations, and carefully chosen known exact solutions of the interior Stokes problem are used to correct the resulting matrices, extending the work by Klaseboer et al. [27] to IGA-BEM.10aIsogeometric Analysis1 aHeltai, Luca1 aArroyo, Marino1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/632600908nas a2200109 4500008004100000245004700041210004700088260001300135520057900148100002000727856005100747 2014 en d00aPfaffian representations of cubic surfaces0 aPfaffian representations of cubic surfaces bSpringer3 aLet K be a field of characteristic zero. We describe an algorithm which requires a homogeneous polynomial F of degree three in K[x0,x1,x2,x3] and a zero a of F in P3 K and ensures a linear Pfaffian representation of V(F) with entries in K[x0,x1,x2,x3], under mild assumptions on F and a. We use this result to give an explicit construction of (and to prove the existence of) a linear Pfaffian representation of V (F), with entries in K′[x0,x1,x2,x3], being K′ an algebraic extension of K of degree at most six. An explicit example of such a construction is given.

1 aTanturri, Fabio uhttp://urania.sissa.it/xmlui/handle/1963/3468800655nas a2200157 4500008004100000245010000041210006900141260005800210300001400268490000600282100001700288700001700305700002200322700002400344856012900368 2014 eng d00aPotential Model for Ship Hydrodynamics Simulations Directly Interfaced with CAD Data Structures0 aPotential Model for Ship Hydrodynamics Simulations Directly Inte bInternational Society of Offshore and Polar Engineers a815–8220 v41 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio1 aBerti, Massimiliano uhttps://www.math.sissa.it/publication/potential-model-ship-hydrodynamics-simulations-directly-interfaced-cad-data-structures00851nas 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/1963/3471400713nas a2200145 4500008004100000245005900041210005400100260003200154300001200186490000700198520028400205100002300489700002000512856003500532 2014 en d00aOn a quadratic functional for scalar conservation laws0 aquadratic functional for scalar conservation laws bWorld Scientific Publishing a355-4350 v113 aWe prove a quadratic interaction estimate for approximate solutions to scalar conservation laws obtained by the wavefront tracking approximation or the Glimm scheme. This quadratic estimate has been used in the literature to prove the convergence rate of the Glimm scheme.

1 aBianchini, Stefano1 aModena, Stefano uhttp://arxiv.org/abs/1311.292900441nas a2200121 4500008004100000245008400041210006900125300001200194490000600206100002300212700002000235856006400255 2014 eng d00aQuadratic interaction functional for systems of conservation laws: a case study0 aQuadratic interaction functional for systems of conservation law a487-5460 v91 aBianchini, Stefano1 aModena, Stefano uhttps://w3.math.sinica.edu.tw/bulletin_ns/20143/2014308.pdf00844nas a2200109 4500008004100000245005200041210005200093260002900145520049000174100001900664856005100683 2014 en d00aQuantum dimension and quantum projective spaces0 aQuantum dimension and quantum projective spaces bInstitute of Mathematics3 aWe show that the family of spectral triples for quantum projective spaces introduced by D'Andrea and Dbrowski, which have spectral dimension equal to zero, can be reconsidered as modular spectral triples by taking into account the action of the element K2por its inverse. The spectral dimension computed in this sense coincides with the dimension of the classical projective spaces. The connection with the well known notion of quantum dimension of quantum group theory is pointed out.1 aMatassa, Marco uhttp://urania.sissa.it/xmlui/handle/1963/3476401462nas a2200145 4500008004100000245005600041210005600097260005100153520096300204100002501167700002401192700002701216700002201243856005101265 2014 en d00aQuantum gauge symmetries in noncommutative geometry0 aQuantum gauge symmetries in noncommutative geometry bEuropean Mathematical Society Publishing House3 aWe discuss generalizations of the notion of i) the group of unitary elements of a (real or complex) finite-dimensional C*-algebra, ii) gauge transformations and iii) (real) automorphisms in the framework of compact quantum group theory and spectral triples. The quantum analogue of these groups are defined as universal (initial) objects in some natural categories. After proving the existence of the universal objects, we discuss several examples that are of interest to physics, as they appear in the noncommutative geometry approach to particle physics: in particular, the C*-algebras M n(R), Mn(C) and Mn(H), describing the finite noncommutative space of the Einstein-Yang-Mills systems, and the algebras A F = C H M3 (C) and Aev = H H M4(C), that appear in Chamseddine-Connes derivation of the Standard Model of particle physics coupled to gravity. As a byproduct, we identify a "free" version of the symplectic group Sp.n/ (quaternionic unitary group).1 aBhowmick, Jyotishman1 aD'Andrea, Francesco1 aDas, Biswarup, Krishna1 aDabrowski, Ludwik uhttp://urania.sissa.it/xmlui/handle/1963/3489700712nas a2200157 4500008004100000245005200041210005100093260001300144300001200157490000800169520027400177100001800451700002100469700001900490856004500509 2014 en d00aQuasi-static crack growth in hydraulic fracture0 aQuasistatic crack growth in hydraulic fracture bElsevier a301-3180 v1093 aWe present a variational model for the quasi-static crack growth in hydraulic fracture in the framework of the energy formulation of rate-independent processes. The cracks are assumed to lie on a prescribed plane and to satisfy a very weak regularity assumption.

1 aAlmi, Stefano1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/20.500.11767/1735000819nas a2200157 4500008004100000022001400041245007800055210006900133260000800202300001400210490000700224520034300231100002100574700002000595856004600615 2014 eng d a1572-922200aQuasistatic Evolution in Perfect Plasticity as Limit of Dynamic Processes0 aQuasistatic Evolution in Perfect Plasticity as Limit of Dynamic cDec a915–9540 v263 aWe introduce a model of dynamic visco-elasto-plastic evolution in the linearly elastic regime and prove an existence and uniqueness result. Then we study the limit of (a rescaled version of) the solutions when the data vary slowly. We prove that they converge, up to a subsequence, to a quasistatic evolution in perfect plasticity.

1 aDal Maso, Gianni1 aScala, Riccardo uhttps://doi.org/10.1007/s10884-014-9409-701155nas a2200121 4500008004100000245010200041210006900143300001400212490000700226520073600233100001800969856004600987 2014 eng d00aQuasistatic evolution models for thin plates arising as low energy Γ-limits of finite plasticity0 aQuasistatic evolution models for thin plates arising as low ener a2085-21530 v243 aIn this paper we deduce by $\Gamma$-convergence some partially and fully linearized quasistatic evolution models for thin plates, in the framework of finite plasticity. Denoting by $\epsilon$ the thickness of the plate, we study the case where the scaling factor of the elasto-plastic energy is of order $\epsilon^{2 \alpha -2}$, with $\alpha\geq 3$. These scalings of the energy lead, in the absence of plastic dissipation, to the Von Kármán and linearized Von Kármán functionals for thin plates. We show that solutions to the three-dimensional quasistatic evolution problems converge, as the thickness of the plate tends to zero, to a quasistatic evolution associated to a suitable reduced model depending on $\alpha$.

1 aDavoli, Elisa uhttps://doi.org/10.1142/S021820251450016X01353nas a2200145 4500008004100000245007400041210006900115260001000184520088100194100002401075700002001099700001901119700001901138856005001157 2014 en d00aRate-independent damage in thermo-viscoelastic materials with inertia0 aRateindependent damage in thermoviscoelastic materials with iner bSISSA3 aWe present a model for rate-independent, unidirectional, partial damage in visco-elastic materials with inertia and thermal effects. The damage process is modeled by means of an internal variable, governed by a rate-independent flow rule. The heat equation and the momentum balance for the displacements are coupled in a highly nonlinear way. Our assumptions on the corresponding energy functional also comprise the case of the Ambrosio-Tortorelli phase-field model (without passage to the brittle limit). We discuss a suitable weak formulation and prove an existence theorem obtained with the aid of a (partially) decoupled time-discrete scheme and variational convergence methods. We also carry out the asymptotic analysis for vanishing viscosity and inertia and obtain a fully rate-independent limit model for displacements and damage, which is Independent of temperature.1 aLazzaroni, Giuliano1 aRossi, Riccarda1 aThomas, Marita1 aToader, Rodica uhttp://urania.sissa.it/xmlui/handle/1963/744401330nas a2200121 4500008004100000245006100041210006000102260001900162520091900181653003501100100002301135856005001158 2014 en d00aRational curves and instantons on the Fano threefold Y_50 aRational curves and instantons on the Fano threefold Y5 barXiv preprint3 aThis thesis is an investigation of the moduli spaces of instanton bundles on the Fano threefold Y_5 (a linear section of Gr(2,5)). It contains new proofs of classical facts about lines, conics and cubics on Y_5, and about linear sections of Y_5. The main original results are a Grauert-Mülich theorem for the splitting type of instantons on conics, a bound to the splitting type of instantons on lines and an SL_2-equivariant description of the moduli space in charge 2 and 3. Using these results we prove the existence of a unique SL_2-equivariant instanton of minimal charge and we show that for all instantons of charge 2 the divisor of jumping lines is smooth. In charge 3, we provide examples of instantons with reducible divisor of jumping lines. Finally, we construct a natural compactification for the moduli space of instantons of charge 3, together with a small resolution of singularities for it.10aModuli space of vector bundles1 aSanna, Giangiacomo uhttp://urania.sissa.it/xmlui/handle/1963/748200566nas a2200133 4500008004100000245010000041210006900141300001000210100002100220700002200241700002100263700002100284856012700305 2014 eng d00aReduced basis method for the Stokes equations in decomposable domains using greedy optimization0 aReduced basis method for the Stokes equations in decomposable do a1–71 aIapichino, Laura1 aQuarteroni, Alfio1 aRozza, Gianluigi1 aVolkwein, Stefan uhttps://www.math.sissa.it/publication/reduced-basis-method-stokes-equations-decomposable-domains-using-greedy-optimization01878nam a2200181 4500008004100000022002200041245006700063210006700130250000600197260002100203300000800224490000600232520123600238653007801474100002201552700002101574856010101595 2014 eng d a978-3-319-02089-100aReduced Order Methods for Modeling and Computational Reduction0 aReduced Order Methods for Modeling and Computational Reduction a1 aMilanobSpringer a3340 v93 aThis monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics.

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

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

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

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

1 aSartori, Alberto1 aBaroli, Davide1 aCammi, Antonio1 aLuzzi, Lelio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3512300458nas a2200133 4500008004100000245007200041210006900113260001000182653003000192100002200222700002300244700002100267856003600288 2014 en d00aReduction on characteristics for continuous of a scalar balance law0 aReduction on characteristics for continuous of a scalar balance bSISSA10aMethod of characteristics1 aAlberti, Giovanni1 aBianchini, Stefano1 aCaravenna, Laura uhttp://hdl.handle.net/1963/656200545nas a2200109 4500008004100000245004500041210004300086260001300129520022100142100002100363856005100384 2014 en d00aA Review of the Sixth Painlevé Equation0 aReview of the Sixth Painlevé Equation bSpringer3 aFor the Painlevé VI transcendents, we provide a unitary description of the critical behaviours, the connection formulae, their complete tabulation, and the asymptotic distribution of poles close to a critical point.1 aGuzzetti, Davide uhttp://urania.sissa.it/xmlui/handle/1963/3465801083nas a2200121 4500008004100000245012700041210006900168260002900237520052100266100002200787700002200809856013000831 2014 en d00aA robotic crawler exploiting directional frictional interactions: experiments, numerics, and derivation of a reduced model0 arobotic crawler exploiting directional frictional interactions e bRoyal Society Publishing3 aWe present experimental and numerical results for a model crawler which is able to extract net positional changes from reciprocal shape changes, i.e. ‘breathing-like’ deformations, thanks to directional, frictional interactions with a textured solid substrate, mediated by flexible inclined feet. We also present a simple reduced model that captures the essential features of the kinematics and energetics of the gait, and compare its predictions with the results from experiments and from numerical simulations.1 aNoselli, Giovanni1 aDeSimone, Antonio uhttps://www.math.sissa.it/publication/robotic-crawler-exploiting-directional-frictional-interactions-experiments-numerics-and00632nas a2200109 4500008004100000245008300041210007100124260001300195520024000208100002300448856005100471 2014 en d00aSBV Regularity of Systems of Conservation Laws and Hamilton–Jacobi Equations0 aSBV Regularity of Systems of Conservation Laws and Hamilton–Jaco bSpringer3 aWe review the SBV regularity for solutions to hyperbolic systems of conservation laws and Hamilton-Jacobi equations. We give an overview of the techniques involved in the proof, and a collection of related problems concludes the paper.1 aBianchini, Stefano uhttp://urania.sissa.it/xmlui/handle/1963/3469101169nas a2200145 4500008004100000245008500041210006900126260001000195520065500205653006700860100002100927700001900948700002000967856003600987 2014 en d00aSecond Order Asymptotic Development for the Anisotropic Cahn-Hilliard Functional0 aSecond Order Asymptotic Development for the Anisotropic CahnHill bSISSA3 aThe asymptotic behavior of an anisotropic Cahn-Hilliard functional with prescribed mass and Dirichlet boundary condition is studied when the parameter $\varepsilon$ that determines the width of the transition layers tends to zero. The double-well potential is assumed to be even and equal to $|s-1|^\beta$ near $s=1$, with $1<\beta<2$. The first order term in the asymptotic development by $\Gamma$-convergence is well-known, and is related to a suitable anisotropic perimeter of the interface. Here it is shown that, under these assumptions, the second order term is zero, which gives an estimate on the rate of convergence of the minimum values.10aGamma-convergence, Cahn-Hilliard functional, phase transitions1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni uhttp://hdl.handle.net/1963/739001605nas a2200121 4500008004100000245008400041210006900125260002200194520117200216100002001388700002401408856005101432 2014 en d00aSemiclassical limit of focusing NLS for a family of square barrier initial data0 aSemiclassical limit of focusing NLS for a family of square barri bWiley Periodicals3 aThe small dispersion limit of the focusing nonlinear Schrödinger equation (NLS) exhibits a rich structure of sharply separated regions exhibiting disparate rapid oscillations at microscopic scales. The non-self-adjoint scattering problem and ill-posed limiting Whitham equations associated to focusing NLS make rigorous asymptotic results difficult. Previous studies have focused on special classes of analytic initial data for which the limiting elliptic Whitham equations are wellposed. In this paper we consider another exactly solvable family of initial data,the family of square barriers,ψ 0(x) = qχ[-L,L] for real amplitudes q. Using Riemann-Hilbert techniques, we obtain rigorous pointwise asymptotics for the semiclassical limit of focusing NLS globally in space and up to an O(1) maximal time. In particular, we show that the discontinuities in our initial data regularize by the immediate generation of genus-one oscillations emitted into the support of the initial data. To the best of our knowledge, this is the first case in which the genus structure of the semiclassical asymptotics for focusing NLS have been calculated for nonanalytic initial data.1 aJenkins, Robert1 aMcLaughlin, Kenneth uhttp://urania.sissa.it/xmlui/handle/1963/3506601649nas a2200121 4500008004100000245007500041210006900116260001300185520123700198100001901435700002201454856005101476 2014 en d00aShape control of active surfaces inspired by the movement of euglenids0 aShape control of active surfaces inspired by the movement of eug bElsevier3 aWe examine a novel mechanism for active surface morphing inspired by the cell body deformations of euglenids. Actuation is accomplished through in-plane simple shear along prescribed slip lines decorating the surface. Under general non-uniform actuation, such local deformation produces Gaussian curvature, and therefore leads to shape changes. Geometrically, a deformation that realizes the prescribed local shear is an isometric embedding. We explore the possibilities and limitations of this bio-inspired shape morphing mechanism, by first characterizing isometric embeddings under axisymmetry, understanding the limits of embeddability, and studying in detail the accessibility of surfaces of zero and constant curvature. Modeling mechanically the active surface as a non-Euclidean plate (NEP), we further examine the mechanism beyond the geometric singularities arising from embeddability, where mechanics and buckling play a decisive role. We also propose a non-axisymmetric actuation strategy to accomplish large amplitude bending and twisting motions of elongated cylindrical surfaces. Besides helping understand how euglenids delicately control their shape, our results may provide the background to engineer soft machines.1 aArroyo, Marino1 aDeSimone, Antonio uhttp://urania.sissa.it/xmlui/handle/1963/3511801626nas a2200145 4500008004100000245010700041210006900148260001300217520111600230100002401346700002001370700002101390700001801411856005101429 2014 en d00aShape Optimization by Free-Form Deformation: Existence Results and Numerical Solution for Stokes Flows0 aShape Optimization by FreeForm Deformation Existence Results and bSpringer3 aShape optimization problems governed by PDEs result from many applications in computational fluid dynamics. These problems usually entail very large computational costs and require also a suitable approach for representing and deforming efficiently the shape of the underlying geometry, as well as for computing the shape gradient of the cost functional to be minimized. Several approaches based on the displacement of a set of control points have been developed in the last decades, such as the so-called free-form deformations. In this paper we present a new theoretical result which allows to recast free-form deformations into the general class of perturbation of identity maps, and to guarantee the compactness of the set of admissible shapes. Moreover, we address both a general optimization framework based on the continuous shape gradient and a numerical procedure for solving efficiently three-dimensional optimal design problems. This framework is applied to the optimal design of immersed bodies in Stokes flows, for which we consider the numerical solution of a benchmark case study from literature.1 aBallarin, Francesco1 aManzoni, Andrea1 aRozza, Gianluigi1 aSalsa, Sandro uhttp://urania.sissa.it/xmlui/handle/1963/3469800581nas a2200109 4500008004100000245016900041210006900210100001900279700002500298700002200323856012600345 2014 eng d00aSingular Value Decomposition of a Finite Hilbert Transform Defined on Several Intervals and the Interior Problem of Tomography: The Riemann-Hilbert Problem Approach0 aSingular Value Decomposition of a Finite Hilbert Transform Defin1 aBertola, Marco1 aKatsevich, Alexander1 aTovbis, Alexander uhttps://www.math.sissa.it/publication/singular-value-decomposition-finite-hilbert-transform-defined-several-intervals-and01519nas a2200145 4500008004100000245015300041210006900194260001300263520096300276100002001239700002301259700002401282700001601306856005101322 2014 en d00aSix-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics0 aSixdimensional supersymmetric gauge theories quantum cohomology bSpringer3 aWe show that the exact partition function of U(N) six-dimensional gauge theory with eight supercharges on C^2 x S^2 provides the quantization of the integrable system of hydrodynamic type known as gl(N) periodic Intermediate Long Wave (ILW). We characterize this system as the hydrodynamic limit of elliptic Calogero-Moser integrable system. We compute the Bethe equations from the effective gauged linear sigma model on S^2 with target space the ADHM instanton moduli space, whose mirror computes the Yang-Yang function of gl(N) ILW. The quantum Hamiltonians are given by the local chiral ring observables of the six-dimensional gauge theory. As particular cases, these provide the gl(N) Benjamin-Ono and Korteweg-de Vries quantum Hamiltonians. In the four dimensional limit, we identify the local chiral ring observables with the conserved charges of Heisenberg plus W_N algebrae, thus providing a gauge theoretical proof of AGT correspondence.1 aBonelli, Giulio1 aSciarappa, Antonio1 aTanzini, Alessandro1 aVasko, Petr uhttp://urania.sissa.it/xmlui/handle/1963/3454600707nas 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/S029414491300071100987nas a2200145 4500008004100000245008700041210006900128260001000197520050200207100002400709700002000733700001900753700001900772856005000791 2014 en d00aSome remarks on a model for rate-independent damage in thermo-visco-elastodynamics0 aSome remarks on a model for rateindependent damage in thermovisc bSISSA3 aThis note deals with the analysis of a model for partial damage, where the rateindependent, unidirectional flow rule for the damage variable is coupled with the rate-dependent heat equation, and with the momentum balance featuring inertia and viscosity according to Kelvin-Voigt rheology. The results presented here combine the approach from Roubicek [1] with the methods from Lazzaroni/Rossi/Thomas/Toader [2] and extend the analysis to the setting of inhomogeneous time-dependent Dirichlet data.1 aLazzaroni, Giuliano1 aRossi, Riccarda1 aThomas, Marita1 aToader, Rodica uhttp://urania.sissa.it/xmlui/handle/1963/746301769nas a2200133 4500008004100000245008300041210006900124260001900193520130400212100002001516700002101536700002701557856005101584 2014 en d00aSome remarks on the seismic behaviour of embedded cantilevered retaining walls0 aSome remarks on the seismic behaviour of embedded cantilevered r bThomas Telford3 aThis paper is a numerical investigation of the physical phenomena that control the dynamic behaviour of embedded cantilevered retaining walls. Recent experimental observations obtained from centrifuge tests have shown that embedded cantilevered retaining walls experience permanent displacements even before the acceleration reaches its critical value, corresponding to full mobilisation of the soil strength. The motivation for this work stems from the need to incorporate these observations in simplified design procedures. A parametric study was carried out on a pair of embedded cantilevered walls in dry sand, subjected to real earthquakes scaled at different values of the maximum acceleration. The results of these analyses indicate that, for the geotechnical design of the wall, the equivalent acceleration to be used in pseudo-static calculations can be related to the maximum displacement that the structure can sustain, and can be larger than the maximum acceleration expected at the site. For the structural design of the wall, it is suggested that the maximum bending moments of the wall can be computed using a realistic distribution of contact stress and a conservative value of the pseudo-static acceleration, taking into account two-dimensional amplification effects near the walls.1 aConti, Riccardo1 aD'Arezzo, Burali1 aViggiani, Giulia, M.B. uhttp://urania.sissa.it/xmlui/handle/1963/3507300993nas a2200121 4500008004100000245006500041210006500106260003000171520058100201100001600782700002200798856005100820 2014 en d00aSpontaneous division and motility in active nematic droplets0 aSpontaneous division and motility in active nematic droplets bAmerican Physical Society3 aWe investigate the mechanics of an active droplet endowed with internal nematic order and surrounded by an isotropic Newtonian fluid. Using numerical simulations we demonstrate that, due to the interplay between the active stresses and the defective geometry of the nematic director, this system exhibits two of the fundamental functions of living cells: spontaneous division and motility, by means of self-generated hydrodynamic flows. These behaviors can be selectively activated by controlling a single physical parameter, namely, an active variant of the capillary number.1 aGiomi, Luca1 aDeSimone, Antonio uhttp://urania.sissa.it/xmlui/handle/1963/3490200979nas a2200157 4500008004100000022004000041245009000081210006900171260001900240300001200259490000600271520039700277653003900674100002000713856008800733 2014 en d aOnline: 1864-8266; Print: 1864-825800aStability of equilibrium configurations for elastic films in two and three dimensions0 aStability of equilibrium configurations for elastic films in two bSISSAc01/2014 a117-1530 v83 aWe establish a local minimality sufficiency criterion, based on the strict positivity of the second variation, in the context of a variational model for the epitaxial growth of elastic films. Our result holds also in the three-dimensional case and for a general class of nonlinear elastic energies. Applications to the study of the local minimality of flat morphologies are also shown.

10aEpitaxially strained elastic films1 aBonacini, Marco uhttps://www.degruyter.com/view/j/acv.2015.8.issue-2/acv-2013-0018/acv-2013-0018.xml01201nas 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.pdf00470nas a2200109 4500008004100000245008400041210006900125260001000194100002300204700001600227856011700243 2014 en d00aSteady nearly incompressible vector elds in 2D: chain rule and renormalization0 aSteady nearly incompressible vector elds in 2D chain rule and re bSISSA1 aBianchini, Stefano1 aGusev, N.A. uhttps://www.math.sissa.it/publication/steady-nearly-incompressible-vector-elds-2d-chain-rule-and-renormalization01412nas a2200145 4500008004100000245004500041210004100086260001300127520099200140100002001132700002301152700002401175700001601199856005101215 2014 en d00aThe stringy instanton partition function0 astringy instanton partition function bSpringer3 aWe perform an exact computation of the gauged linear sigma model associated to a D1-D5 brane system on a resolved A_1 singularity. This is accomplished via supersymmetric localization on the blown-up two-sphere. We show that in the blow-down limit C^2/Z_2 the partition function reduces to the Nekrasov partition function evaluating the equivariant volume of the instanton moduli space. For finite radius we obtain a tower of world-sheet instanton corrections, that we identify with the equivariant Gromov-Witten invariants of the ADHM moduli space. We show that these corrections can be encoded in a deformation of the Seiberg-Witten prepotential. From the mathematical viewpoint, the D1-D5 system under study displays a twofold nature: the D1-branes viewpoint captures the equivariant quantum cohomology of the ADHM instanton moduli space in the Givental formalism, and the D5-branes viewpoint is related to higher rank equivariant Donaldson-Thomas invariants of P^1 x C^2.1 aBonelli, Giulio1 aSciarappa, Antonio1 aTanzini, Alessandro1 aVasko, Petr uhttp://urania.sissa.it/xmlui/handle/1963/3458901002nas a2200133 4500008004100000245005800041210005500099260001000154520060700164100002100771700002000792700002000812856003600832 2014 en d00aStructure of classical (finite and affine) W-algebras0 aStructure of classical finite and affine Walgebras bSISSA3 aFirst, we derive an explicit formula for the Poisson bracket of the classical finite W-algebra W^{fin}(g,f), the algebra of polynomial functions on the Slodowy slice associated to a simple Lie algebra g and its nilpotent element f. On the other hand, we produce an explicit set of generators and we derive an explicit formula for the Poisson vertex algebra structure of the classical affine W-algebra W(g,f). As an immediate consequence, we obtain a Poisson algebra isomorphism between W^{fin}(g,f) and the Zhu algebra of W(g,f). We also study the generalized Miura map for classical W-algebras.1 aDe Sole, Alberto1 aKac, Victor, G.1 aValeri, Daniele uhttp://hdl.handle.net/1963/731400484nas a2200133 4500008004100000245009400041210006900135260001900204300001200223490000800235100002300243700001200266856007200278 2014 en d00aStructure of entropy solutions to general scalar conservation laws in one space dimension0 aStructure of entropy solutions to general scalar conservation la bSISSAc08/2015 a356-3860 v4281 aBianchini, Stefano1 aYu, Lei uhttps://www.sciencedirect.com/science/article/pii/S0022247X1500221801169nas a2200133 4500008004100000245007700041210006900118260003400187520069100221100002700912700002300939700002200962856005100984 2014 en d00aSwelling dynamics of a thin elastomeric sheet under uniaxial pre-stretch0 aSwelling dynamics of a thin elastomeric sheet under uniaxial pre bAmerican Institute of Physics3 aIt has been demonstrated experimentally that pre-stretch affects the swelling of an elastomeric membrane when it is exposed to a solvent. We study theoretically the one-dimensional swelling of a pre-stretched thin elastomeric sheet, bonded to an impermeable rigid substrate, to quantify the influence of pre-stretch. We show that the solvent uptake increases when pre-stretch increases, both at equilibrium and during the swelling transient, where it exhibits two different scaling regimes. The coupling between the solvent uptake and pre-stretch may be practically exploited to design soft actuators where the swelling-induced deformations can be controlled by varying the pre-stretch.1 aLucantonio, Alessandro1 aNardinocchi, Paola1 aStone, Howard, A. uhttp://urania.sissa.it/xmlui/handle/1963/3511301394nas 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-graphene00781nas a2200121 4500008004100000245008700041210006900128260003100197520034000228100001800568700002200586856005100608 2014 en d00aThe topology of a subspace of the Legendrian curves on a closed contact 3-manifold0 atopology of a subspace of the Legendrian curves on a closed cont bAdvanced Nonlinear Studies3 aIn this paper we study a subspace of the space of Legendrian loops and we show that the injection of this space into the full loop space is an S 1-equivariant homotopy equivalence. This space can be also seen as the space of zero Maslov index Legendrian loops and it shows up as a suitable space of variations in contact form geometry.1 aMaalaoui, Ali1 aMartino, Vittorio uhttp://urania.sissa.it/xmlui/handle/1963/3501601084nas a2200133 4500008004100000245014200041210006900183260005100252520053000303100002200833700002300855700002100878856005100899 2014 en d00aA uniqueness result for the continuity equation in two dimensions: dedicated to constantine dafermos on the occasion of his 70th birthday0 auniqueness result for the continuity equation in two dimensions bEuropean Mathematical Society; Springer Verlag3 aWe characterize the autonomous, divergence-free vector fields b on the plane such that the Cauchy problem for the continuity equation ∂tu +div(bu) = 0 admits a unique bounded solution (in the weak sense) for every bounded initial datum; the characterization is given in terms of a property of Sard type for the potential f associated to b. As a corollary we obtain uniqueness under the assumption that the curl of b is a measure. This result can be extended to certain nonautonomous vector fields b with bounded divergence.1 aAlberti, Giovanni1 aBianchini, Stefano1 aCrippa, Gianluca uhttp://urania.sissa.it/xmlui/handle/1963/3469200850nas a2200121 4500008004300000245007700043210006900120260001000189520044200199653001700641100002000658856005000678 2014 en_Ud 00aA variational approach to statics and dynamics of elasto-plastic systems0 avariational approach to statics and dynamics of elastoplastic sy bSISSA3 aWe prove some existence results for dynamic evolutions in elasto-plasticity and delamination. We study the limit as the data vary very slowly and prove convergence results to quasistatic evolutions. We model dislocations by mean of currents, we introduce the space of deformations in the presence of dislocations and study the graphs of these maps. We prove existence results for minimum problems. We study the properties of minimizers.10adelamination1 aScala, Riccardo uhttp://urania.sissa.it/xmlui/handle/1963/747100848nas a2200133 4500008004100000245009600041210006900137260003400206520037800240653002300618100001800641700001900659856003600678 2014 en d00aA variational model for the quasi-static growth of fractional dimensional brittle fractures0 avariational model for the quasistatic growth of fractional dimen bEuropean Mathematical Society3 aWe propose a variational model for the irreversible quasi-static evolution of brittle fractures having fractional Hausdorff dimension in the setting of two-dimensional antiplane and plane elasticity. The evolution along such irregular crack paths can be obtained as $\Gamma$-limit of evolutions along one-dimensional cracks when the fracture toughness tends to zero.

10aVariational models1 aRacca, Simone1 aToader, Rodica uhttp://hdl.handle.net/1963/698301601nas a2200145 4500008004100000245008900041210007100130260001300201520110700214100002001321700002301341700002401364700001601388856005101404 2014 en d00aVortex Partition Functions, Wall Crossing and Equivariant Gromov–Witten Invariants0 aVortex Partition Functions Wall Crossing and Equivariant Gromov– bSpringer3 aIn this paper we identify the problem of equivariant vortex counting in a (2,2) supersymmetric two dimensional quiver gauged linear sigma model with that of computing the equivariant Gromov–Witten invariants of the GIT quotient target space determined by the quiver. We provide new contour integral formulae for the I and J-functions encoding the equivariant quantum cohomology of the target space. Its chamber structure is shown to be encoded in the analytical properties of the integrand. This is explained both via general arguments and by checking several key cases. We show how several results in equivariant Gromov–Witten theory follow just by deforming the integration contour. In particular, we apply our formalism to compute Gromov–Witten invariants of the C3/Zn orbifold, of the Uhlembeck (partial) compactification of the moduli space of instantons on C2, and of An and Dn singularities both in the orbifold and resolved phases. Moreover, we analyse dualities of quantum cohomology rings of holomorphic vector bundles over Grassmannians, which are relevant to BPS Wilson loop algebrae.1 aBonelli, Giulio1 aSciarappa, Antonio1 aTanzini, Alessandro1 aVasko, Petr uhttp://urania.sissa.it/xmlui/handle/1963/3465201557nas a2200133 4500008004100000245009400041210006900135260001700204520109300221100001501314700002201329700002101351856005101372 2014 en d00aA weighted empirical interpolation method: A priori convergence analysis and applications0 aweighted empirical interpolation method A priori convergence ana bEDP Sciences3 aWe extend the classical empirical interpolation method [M. Barrault, Y. Maday, N.C. Nguyen and A.T. Patera, An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations. Compt. Rend. Math. Anal. Num. 339 (2004) 667-672] to a weighted empirical interpolation method in order to approximate nonlinear parametric functions with weighted parameters, e.g. random variables obeying various probability distributions. A priori convergence analysis is provided for the proposed method and the error bound by Kolmogorov N-width is improved from the recent work [Y. Maday, N.C. Nguyen, A.T. Patera and G.S.H. Pau, A general, multipurpose interpolation procedure: the magic points. Commun. Pure Appl. Anal. 8 (2009) 383-404]. We apply our method to geometric Brownian motion, exponential Karhunen-Loève expansion and reduced basis approximation of non-affine stochastic elliptic equations. We demonstrate its improved accuracy and efficiency over the empirical interpolation method, as well as sparse grid stochastic collocation method.1 aChen, Peng1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3502100917nas a2200121 4500008004100000245006300041210006300104260002500167520051500192100001900707700001800726856005100744 2014 en d00aWeighted quantile correlation test for the logistic family0 aWeighted quantile correlation test for the logistic family bUniversity of Szeged3 aWe summarize the results of investigating the asymptotic behavior of the weighted quantile correlation tests for the location-scale family associated to the logistic distribution. Explicit representations of the limiting distribution are given in terms of integrals of weighted Brownian bridges or alternatively as infinite series of independent Gaussian random variables. The power of this test and the test for the location logistic family against some alternatives are demonstrated by numerical simulations.1 aBalogh, Ferenc1 aKrauczi, Éva uhttp://urania.sissa.it/xmlui/handle/1963/3502500995nas a2200121 4500008004300000245007400043210006900117260001000186520059200196100001700788700001800805856005000823 2014 en_Ud 00aWhere best to place a Dirichlet condition in an anisotropic membrane?0 aWhere best to place a Dirichlet condition in an anisotropic memb bSISSA3 aWe study a shape optimization problem for the first eigenvalue of an elliptic operator in divergence form, with non constant coefficients, over a fixed domain $\Omega$. Dirichlet conditions are imposed along $\partial\Omega$ and, in addition, along a set $\Sigma$ of prescribed length ($1$-dimensional Hausdorff measure). We look for the best shape and position for the supplementary Dirichlet region $\Sigma$ in order to maximize the first eigenvalue. We characterize the limit distribution of the optimal sets, as their prescribed length tends to infinity, via $\Gamma$-convergence.1 aTilli, Paolo1 aZucco, Davide uhttp://urania.sissa.it/xmlui/handle/1963/748100480nas a2200109 4500008004100000245009100041210006900132490001100201100001900212700002000231856011900251 2014 eng d00aZeros of Large Degree Vorob'ev-Yablonski Polynomials via a Hankel Determinant Identity0 aZeros of Large Degree VorobevYablonski Polynomials via a Hankel 0 vrnu2391 aBertola, Marco1 aBothner, Thomas uhttps://www.math.sissa.it/publication/zeros-large-degree-vorobev-yablonski-polynomials-hankel-determinant-identity01521nas a2200133 4500008004100000245009100041210006900132260001000201520106100211653003701272100002001309700002201329856003601351 2013 en d00aAmbrosio-Tortorelli approximation of cohesive fracture models in linearized elasticity0 aAmbrosioTortorelli approximation of cohesive fracture models in bSISSA3 aWe provide an approximation result in the sense of $\Gamma$-convergence for cohesive fracture energies of the form \[ \int_\Omega \mathscr{Q}_1(e(u))\,dx+a\,\mathcal{H}^{n-1}(J_u)+b\,\int_{J_u}\mathscr{Q}_0^{1/2}([u]\odot\nu_u)\,d\mathcal{H}^{n-1}, \] where $\Omega\subset{\mathbb R}^n$ is a bounded open set with Lipschitz boundary, $\mathscr{Q}_0$ and $\mathscr{Q}_1$ are coercive quadratic forms on ${\mathbb M}^{n\times n}_{sym}$, $a,\,b$ are positive constants, and $u$ runs in the space of fields $SBD^2(\Omega)$ , i.e., it's a special field with bounded deformation such that its symmetric gradient $e(u)$ is square integrable, and its jump set $J_u$ has finite $(n-1)$-Hausdorff measure in ${\mathbb R}^n$. The approximation is performed by means of Ambrosio-Tortorelli type elliptic regularizations, the prototype example being \[ \int_\Omega\Big(v|e(u)|^2+\frac{(1-v)^2}{\varepsilon}+{\gamma\,\varepsilon}|\nabla v|^2\Big)\,dx, \] where $(u,v)\in H^1(\Omega,{\mathbb R}^n){\times} H^1(\Omega)$, $\varepsilon\leq v\leq 1$ and $\gamma>0$.

10aFunctions of bounded deformation1 aFocardi, Matteo1 aIurlano, Flaviana uhttp://hdl.handle.net/1963/661501048nas a2200145 4500008004100000245010400041210006900145260001300214520050500227653007400732100002100806700001900827700002000846856003600866 2013 en d00aAnalytical validation of a continuum model for epitaxial growth with elasticity on vicinal surfaces0 aAnalytical validation of a continuum model for epitaxial growth bSpringer3 aIn this paper it is shown existence of weak solutions of a variational inequality derived from the continuum model introduced by Xiang [7, formula (3.62)] (see also the work of Xiang and E [8] and Xu and Xiang [9]) to describe the self-organization of terraces and steps driven by misfit elasticity between a film and a substrate in heteroepitaxial growth. This model is obtained as a continuum limit of discrete theories of Duport, Politi, and Villain [3] and Tersoff, Phang, Zhang, and Lagally[6].10asingular nonlinear parabolic equations, Hilbert transform, thin films1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni uhttp://hdl.handle.net/1963/724500531nas a2200109 4500008004100000245011300041210006900154260001000223653003700233100002200270856012900292 2013 en d00aAn Approximation Result for Generalised Functions of Bounded Deformation and Applications to Damage Problems0 aApproximation Result for Generalised Functions of Bounded Deform bSISSA10aFunctions of bounded deformation1 aIurlano, Flaviana uhttps://www.math.sissa.it/publication/approximation-result-generalised-functions-bounded-deformation-and-applications-damage01539nas a2200121 4500008004100000245009200041210006900133260005100202520107800253100001701331700001801348856005101366 2013 en d00aAsymptotics of the first Laplace eigenvalue with Dirichlet regions of prescribed length0 aAsymptotics of the first Laplace eigenvalue with Dirichlet regio bSociety for Industrial and Applied Mathematics3 aWe consider the problem of maximizing the first eigenvalue of the $p$-Laplacian (possibly with nonconstant coefficients) over a fixed domain $\Omega$, with Dirichlet conditions along $\partial\Omega$ and along a supplementary set $\Sigma$, which is the unknown of the optimization problem. The set $\Sigma$, which plays the role of a supplementary stiffening rib for a membrane $\Omega$, is a compact connected set (e.g., a curve or a connected system of curves) that can be placed anywhere in $\overline{\Omega}$ and is subject to the constraint of an upper bound $L$ to its total length (one-dimensional Hausdorff measure). This upper bound prevents $\Sigma$ from spreading throughout $\Omega$ and makes the problem well-posed. We investigate the behavior of optimal sets $\Sigma_L$ as $L\to\infty$ via $\Gamma$-convergence, and we explicitly construct certain asymptotically optimal configurations. We also study the behavior as $p\to\infty$ with $L$ fixed, finding connections with maximum-distance problems related to the principal frequency of the $\infty$-Laplacian.1 aTilli, Paolo1 aZucco, Davide uhttp://urania.sissa.it/xmlui/handle/1963/3514100882nas a2200133 4500008004100000245004600041210004600087260001000133520050000143100002600643700002100669700002200690856003600712 2013 en d00aAttainment results for nematic elastomers0 aAttainment results for nematic elastomers bSISSA3 aWe consider a class of non-quasiconvex frame indifferent energy densities which includes Ogden-type energy densities for nematic elastomers. For the corresponding geometrically linear problem we provide an explicit minimizer of the energy functional satisfying a nontrivial boundary condition. Other attainment results, both for the nonlinear and the linearized model, are obtained by using the theory of convex integration introduced by Mueller and Sverak in the context of crystalline solids.1 aAgostiniani, Virginia1 aDal Maso, Gianni1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/717401444nas a2200121 4500008004100000245006100041210006100102260001000163520093500173653009701108100002101205856009601226 2013 en d00aBiregular and Birational Geometry of Algebraic Varieties0 aBiregular and Birational Geometry of Algebraic Varieties bSISSA3 aEvery area of mathematics is characterized by a guiding problem. In algebraic geometry such problem is the classification of algebraic varieties. In its strongest form it means to classify varieties up to biregular morphisms. However, birationally equivalent varieties share many interesting properties. Therefore for any birational equivalence class it is natural to work out a variety, which is the simplest in a suitable sense, and then study these varieties. This is the aim of birational geometry. In the first part of this thesis we deal with the biregular geometry of moduli spaces of curves, and in particular with their biregular automorphisms. However, in doing this we will consider some aspects of their birational geometry. The second part is devoted to the birational geometry of varieties of sums of powers and to some related problems which will lead us to computational geometry and geometric complexity theory.10aModuli spaces of curves, automorphisms, Hassett's moduli spaces, varieties of sums of powers1 aMassarenti, Alex uhttps://www.math.sissa.it/publication/biregular-and-birational-geometry-algebraic-varieties01065nas a2200133 4500008004100000245012700041210006900168260001300237520058400250100002100834700002000855700002000875856003600895 2013 en d00aClassical W-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras0 aClassical Walgebras and generalized DrinfeldSokolov biHamiltonia bSpringer3 aWe provide a description of the Drinfeld-Sokolov Hamiltonian reduction for the construction of classical W-algebras within the framework of Poisson vertex algebras. In this context, the gauge group action on the phase space is translated in terms of (the exponential of) a Lie conformal algebra action on the space of functions. Following the ideas of Drinfeld and Sokolov, we then establish under certain sufficient conditions the applicability of the Lenard-Magri scheme of integrability and the existence of the corresponding integrable hierarchy of bi-Hamiltonian equations.1 aDe Sole, Alberto1 aKac, Victor, G.1 aValeri, Daniele uhttp://hdl.handle.net/1963/697801890nas a2200145 4500008004100000245011800041210006900159260001300228520137300241653003501614100001801649700002001667700002101687856003601708 2013 en d00aA combination between the reduced basis method and the ANOVA expansion: On the computation of sensitivity indices0 acombination between the reduced basis method and the ANOVA expan bElsevier3 aWe consider a method to efficiently evaluate in a real-time context an output based on the numerical solution of a partial differential equation depending on a large number of parameters. We state a result allowing to improve the computational performance of a three-step RB-ANOVA-RB method. This is a combination of the reduced basis (RB) method and the analysis of variations (ANOVA) expansion, aiming at compressing the parameter space without affecting the accuracy of the output. The idea of this method is to compute a first (coarse) RB approximation of the output of interest involving all the parameter components, but with a large tolerance on the a posteriori error estimate; then, we evaluate the ANOVA expansion of the output and freeze the least important parameter components; finally, considering a restricted model involving just the retained parameter components, we compute a second (fine) RB approximation with a smaller tolerance on the a posteriori error estimate. The fine RB approximation entails lower computational costs than the coarse one, because of the reduction of parameter dimensionality. Our result provides a criterion to avoid the computation of those terms in the ANOVA expansion that are related to the interaction between parameters in the bilinear form, thus making the RB-ANOVA-RB procedure computationally more feasible.

10aPartial differential equations1 aDevaud, Denis1 aManzoni, Andrea1 aRozza, Gianluigi uhttp://hdl.handle.net/1963/738901565nas a2200169 4500008004100000245010100041210006900142260001000211520092400221100002201145700002401167700002201191700001701213700001901230700002201249856012401271 2013 en d00aCommon dynamical features of sensory adaptation in photoreceptors and olfactory sensory neurons.0 aCommon dynamical features of sensory adaptation in photoreceptor bSISSA3 aSensory systems adapt, i.e., they adjust their sensitivity to external stimuli according to the ambient level. In this paper we show that single cell electrophysiological responses of vertebrate olfactory receptors and of photoreceptors to different input protocols exhibit several common features related to adaptation, and that these features can be used to investigate the dynamical structure of the feedback regulation responsible for the adaptation. In particular, we point out that two different forms of adaptation can be observed, in response to steps and to pairs of pulses. These two forms of adaptation appear to be in a dynamical trade-off: the more adaptation to a step is close to perfect, the slower is the recovery in adaptation to pulse pairs and viceversa. Neither of the two forms is explained by the dynamical models currently used to describe adaptation, such as the integral feedback model.

1 aDe Palo, Giovanna1 aFacchetti, Giuseppe1 aMazzolini, Monica1 aMenini, Anna1 aTorre, Vincent1 aAltafini, Claudio uhttps://www.math.sissa.it/publication/common-dynamical-features-sensory-adaptation-photoreceptors-and-olfactory-sensory01080nas a2200169 4500008004100000022001400041245009400055210006900149300001200218490000800230520048300238653003400721653002000755653004300775100002100818856007100839 2013 eng d a0022-039600aConcentration of solutions for a singularly perturbed mixed problem in non-smooth domains0 aConcentration of solutions for a singularly perturbed mixed prob a30 - 660 v2543 aWe consider a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^n$ whose boundary has an $(n−2)$-dimensional singularity. Assuming $1<p<\frac{n+2}{n−2}$, 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.

10aFinite-dimensional reductions10aLocal inversion10aSingularly perturbed elliptic problems1 aDipierro, Serena uhttp://www.sciencedirect.com/science/article/pii/S002203961200331200887nas a2200145 4500008004100000022001400041245006300055210005800118260000800176300001400184490000700198520047000205100002000675856004600695 2013 eng d a1559-002X00aThe Conformal Willmore Functional: A Perturbative Approach0 aConformal Willmore Functional A Perturbative Approach cApr a764–8110 v233 aThe conformal Willmore functional (which is conformal invariant in general Riemannian manifolds $(M,g)$ is studied with a perturbative method: the Lyapunov–Schmidt reduction. Existence of critical points is shown in ambient manifolds $(\mathbb{R}^3,g_\epsilon)$ – where $g_\epsilon$ is a metric close and asymptotic to the Euclidean one. With the same technique a non-existence result is proved in general Riemannian manifolds $(M,g)$ of dimension three.

1 aMondino, Andrea uhttps://doi.org/10.1007/s12220-011-9263-300784nas a2200121 4500008004100000245005400041210005300095260001300148520042200161100002100583700002200604856003600626 2013 en d00aConnected Sum Construction for σk-Yamabe Metrics0 aConnected Sum Construction for σkYamabe Metrics bSpringer3 aIn this paper we produce families of Riemannian metrics with positive constant $\sigma_k$-curvature equal to $2^{-k} {n \choose k}$ by performing the connected sum of two given compact {\em non degenerate} $n$--dimensional solutions $(M_1,g_1)$ and $(M_2,g_2)$ of the (positive) $\sigma_k$-Yamabe problem, provided $2 \leq 2k < n$. The problem is equivalent to solve a second order fully nonlinear elliptic equation.1 aCatino, Giovanni1 aMazzieri, Lorenzo uhttp://hdl.handle.net/1963/644101071nas a2200145 4500008004100000245006700041210006600108260001300174520054900187100002200736700002400758700002200782700002000804856010100824 2013 en d00aCrawlers in viscous environments: linear vs nonlinear rheology0 aCrawlers in viscous environments linear vs nonlinear rheology bElsevier3 aWe study model self-propelled crawlers which derive their propulsive capabilities from the tangential resistance to motion offered by the environment. Two types of relationships between tangential forces and slip velocities are considered: a linear, Newtonian one and a nonlinear one of Bingham-type. Different behaviors result from the two different rheologies. These differences and their implications in terms of motility performance are discussed. Our aim is to develop new tools and insight for future studies of cell motility by crawling.1 aDeSimone, Antonio1 aGuarnieri, Federica1 aNoselli, Giovanni1 aTatone, Amabile uhttps://www.math.sissa.it/publication/crawlers-viscous-environments-linear-vs-nonlinear-rheology01219nas a2200145 4500008004100000245008300041210006900124260001000193520068100203100002000884700001800904700002100922700001800943856011200961 2013 en d00aOn critical behaviour in systems of Hamiltonian partial differential equations0 acritical behaviour in systems of Hamiltonian partial differentia bSISSA3 aWe study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by particular solutions to the Painlev\'e-I (P$_I$) equation or its fourth order analogue P$_I^2$. As concrete examples we discuss nonlinear Schr\"odinger equations in the semiclassical limit. A numerical study of these cases provides strong evidence in support of the conjecture.

1 aDubrovin, Boris1 aGrava, Tamara1 aKlein, Christian1 aMoro, Antonio uhttps://www.math.sissa.it/publication/critical-behaviour-systems-hamiltonian-partial-differential-equations01043nas a2200145 4500008004100000245004200041210003700083260001000120520060700130653006200737100002500799700002100824700001600845856003600861 2013 en d00aThe curvature: a variational approach0 acurvature a variational approach bSISSA3 aThe curvature discussed in this paper is a rather far going generalization of the Riemannian sectional curvature. We define it for a wide class of optimal control problems: a unified framework including geometric structures such as Riemannian, sub-Riemannian, Finsler and sub-Finsler structures; a special attention is paid to the sub-Riemannian (or Carnot-Caratheodory) metric spaces. Our construction of the curvature is direct and naive, and it is similar to the original approach of Riemann. Surprisingly, it works in a very general setting and, in particular, for all sub-Riemannian spaces.10aCrurvature, subriemannian metric, optimal control problem1 aAgrachev, Andrei, A.1 aBarilari, Davide1 aRizzi, Luca uhttp://hdl.handle.net/1963/722600967nas a2200133 4500008004100000245005000041210004800091260003400139520056900173653001300742100002200755700002000777856003600797 2013 en d00aCurved noncommutative torus and Gauss--Bonnet0 aCurved noncommutative torus and GaussBonnet bAmerican Institute of Physics3 aWe study perturbations of the flat geometry of the noncommutative two-dimensional torus T^2_\theta (with irrational \theta). They are described by spectral triples (A_\theta, \H, D), with the Dirac operator D, which is a differential operator with coefficients in the commutant of the (smooth) algebra A_\theta of T_\theta. We show, up to the second order in perturbation, that the zeta-function at 0 vanishes and so the Gauss-Bonnet theorem holds. We also calculate first two terms of the perturbative expansion of the corresponding local scalar curvature.10aGeometry1 aDabrowski, Ludwik1 aSitarz, Andrzej uhttp://hdl.handle.net/1963/737600604nas a2200193 4500008004100000245003700041210003000078260001000108520010800118100001700226700001800243700001700261700001700278700002400295700002000319700001700339700001800356856003600374 2013 en d00aThe deal.II Library, Version 8.10 adealII Library Version 81 bSISSA3 aThis paper provides an overview of the new features of the finite element library deal.II version 8.0.1 aBangerth, W.1 aHeister, Timo1 aHeltai, Luca1 aKanschat, G.1 aKronbichler, Martin1 aMaier, Matthias1 aTurcksin, B.1 aYoung, T., D. uhttp://hdl.handle.net/1963/723601298nas a2200145 4500008004100000245006100041210006100102260001000163520087100173100001601044700002101060700001101081700002401092856003601116 2013 en d00aDefect annihilation and proliferation in active nematics0 aDefect annihilation and proliferation in active nematics bSISSA3 aLiquid crystals inevitably possess topological defect excitations generated\r\nthrough boundary conditions, applied fields or in quenches to the ordered\r\nphase. In equilibrium pairs of defects coarsen and annihilate as the uniform\r\nground state is approached. Here we show that defects in active liquid crystals\r\nexhibit profoundly different behavior, depending on the degree of activity and\r\nits contractile or extensile character. While contractile systems enhance the\r\nannihilation dynamics of passive systems, extensile systems act to drive\r\ndefects apart so that they swarm around in the manner of topologically\r\nwell-characterized self-propelled particles. We develop a simple analytical\r\nmodel for the defect dynamics which reproduces the key features of both the\r\nnumerical solutions and recent experiments on microtuble-kinesin assemblies.1 aGiomi, Luca1 aBowick, Mark, J.1 aMa, Xu1 aMarchetti, Cristina uhttp://hdl.handle.net/1963/656601138nas a2200121 4500008004100000245007900041210006900120260001000189520073700199653002500936100001900961856003600980 2013 en d00aOn deformations of multidimensional Poisson brackets of hydrodynamic type0 adeformations of multidimensional Poisson brackets of hydrodynami bSISSA3 aThe theory of Poisson Vertex Algebras (PVAs) is a good framework to treat Hamiltonian partial differential equations. A PVA consist of a pair $(\mathcal{A},\{\cdot_{\lambda}\cdot\})$ of a differential algebra $\mathcal{A}$ and a bilinear operation called the $\lambda$-bracket. We extend the definition to the class of algebras $\mathcal{A}$ endowed with $d\geq 1$ commuting derivations. We call this structure a multidimensional PVA: it is a suitable setting to the study of deformations of the Poisson bracket of hydrodynamic type associated to the Euler's equation of motion of $d$-dimensional incompressible fluids. We prove that for $d=2$ all the first order deformations of such class of Poisson brackets are trivial.10aHamiltonian operator1 aCasati, Matteo uhttp://hdl.handle.net/1963/723500420nas a2200097 4500008004100000245008000041210006900121260001000190100001900200856010300219 2013 en d00aOn the desingularization of Kahler orbifolds with constant scalar curvature0 adesingularization of Kahler orbifolds with constant scalar curva bSISSA1 aLena, Riccardo uhttps://www.math.sissa.it/publication/desingularization-kahler-orbifolds-constant-scalar-curvature01202nas a2200133 4500008004100000245005000041210005000091260001900141520081700160653001200977100002200989700002101011856003601032 2013 en d00aDirac operator on spinors and diffeomorphisms0 aDirac operator on spinors and diffeomorphisms bIOP Publishing3 aThe issue of general covariance of spinors and related objects is reconsidered. Given an oriented manifold $M$, to each spin structure $\sigma$ and Riemannian metric $g$ there is associated a space $S_{\sigma, g}$ of spinor fields on $M$ and a Hilbert space $\HH_{\sigma, g}= L^2(S_{\sigma, g},\vol{M}{g})$ of $L^2$-spinors of $S_{\sigma, g}$. The group $\diff{M}$ of orientation-preserving diffeomorphisms of $M$ acts both on $g$ (by pullback) and on $[\sigma]$ (by a suitably defined pullback $f^*\sigma$). Any $f\in \diff{M}$ lifts in exactly two ways to a unitary operator $U$ from $\HH_{\sigma, g} $ to $\HH_{f^*\sigma,f^*g}$. The canonically defined Dirac operator is shown to be equivariant with respect to the action of $U$, so in particular its spectrum is invariant under the diffeomorphisms.10agravity1 aDabrowski, Ludwik1 aDossena, Giacomo uhttp://hdl.handle.net/1963/737700951nas 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/1963/712401988nas a2200133 4500008004100000245010500041210006900146260003000215520151100245100002101756700002201777700001901799856003601818 2013 en d00aEarly phase of plasticity-related gene regulation and SRF dependent transcription in the hippocampus0 aEarly phase of plasticityrelated gene regulation and SRF depende bPublic Library of Science3 aHippocampal organotypic cultures are a highly reliable in vitro model for studying neuroplasticity: in this paper, we analyze the early phase of the transcriptional response induced by a 20 µM gabazine treatment (GabT), a GABA-Ar antagonist, by using Affymetrix oligonucleotide microarray, RT-PCR based time-course and chromatin-immuno-precipitation. The transcriptome profiling revealed that the pool of genes up-regulated by GabT, besides being strongly related to the regulation of growth and synaptic transmission, is also endowed with neuro-protective and pro-survival properties. By using RT-PCR, we quantified a time-course of the transient expression for 33 of the highest up-regulated genes, with an average sampling rate of 10 minutes and covering the time interval [10:90] minutes. The cluster analysis of the time-course disclosed the existence of three different dynamical patterns, one of which proved, in a statistical analysis based on results from previous works, to be significantly related with SRF-dependent regulation (p-value<0.05). The chromatin immunoprecipitation (chip) assay confirmed the rich presence of working CArG boxes in the genes belonging to the latter dynamical pattern and therefore validated the statistical analysis. Furthermore, an in silico analysis of the promoters revealed the presence of additional conserved CArG boxes upstream of the genes Nr4a1 and Rgs2. The chip assay confirmed a significant SRF signal in the Nr4a1 CArG box but not in the Rgs2 CArG box.1 aIacono, Giovanni1 aAltafini, Claudio1 aTorre, Vincent uhttp://hdl.handle.net/1963/728701025nas a2200109 4500008004100000245008100041210006900122260001700191520065100208100002000859856003600879 2013 en d00aEpitaxially strained elastic films: the case of anisotropic surface energies0 aEpitaxially strained elastic films the case of anisotropic surfa bEDP Sciences3 aIn the context of a variational model for the epitaxial growth of strained elastic films, we study the effects of the presence of anisotropic surface energies in the determination of equilibrium configurations. We show that the threshold effect that describes the stability of flat morphologies in the isotropic case remains valid for weak anisotropies, but is no longer present in the case of highly anisotropic surface energies, where we show that the flat configuration is always a local minimizer of the total energy. The main tool used to obtain these results is a minimality criterion based on the positivity of the second variation.

1 aBonacini, Marco uhttp://hdl.handle.net/1963/426801024nas a2200121 4500008004100000245008800041210006900129260001000198520062200208100001900830700001700849856003600866 2013 en d00aEquilibrium measures for a class of potentials with discrete rotational symmetries0 aEquilibrium measures for a class of potentials with discrete rot bSISSA3 aIn this note the logarithmic energy problem with external potential $|z|^{2n}+tz^d+\bar{t}\bar{z}^d$ is considered in the complex plane, where $n$ and $d$ are positive integers satisfying $d\leq 2n$. Exploiting the discrete rotational invariance of the potential, a simple symmetry reduction procedure is used to calculate the equilibrium measure for all admissible values of $n,d$ and $t$. It is shown that, for fixed $n$ and $d$, there is a critical value $|t|=t_{cr}$ such that the support of the equilibrium measure is simply connected for $|t|This paper deals with the following class of nonlocal Schr\"odinger equations $$ \displaystyle (-\Delta)^s u + u = |u|^{p-1}u \ \ \text{in} \ \mathbb{R}^N, \quad \text{for} \ s\in (0,1). $$ We prove existence and symmetry results for the solutions $u$ in the fractional Sobolev space $H^s(\mathbb{R}^N)$. Our results are in clear accordance with those for the classical local counterpart, that is when $s=1$.

1 aDipierro, Serena1 aPalatucci, Giampiero1 aValdinoci, Enrico uhttps://www.math.sissa.it/publication/existence-and-symmetry-results-schrodinger-type-problem-involving-fractional-laplacian00556nas a2200121 4500008004100000245010500041210006900146260005100215300001600266490000800282100002000290856012400310 2013 eng d00aAn existence result for the mean-field equation on compact surfaces in a doubly supercritical regime0 aexistence result for the meanfield equation on compact surfaces bRoyal Society of Edinburgh Scotland Foundation a1021–10450 v1431 aJevnikar, Aleks uhttps://www.math.sissa.it/publication/existence-result-mean-field-equation-compact-surfaces-doubly-supercritical-regime00809nas a2200157 4500008004100000245003700041210003700078260002300115520037700138653001900515100002000534700002000554700002200574700001900596856003600615 2013 en d00aExpanded degenerations and pairs0 aExpanded degenerations and pairs bTaylor and Francis3 aSince Jun Li's original definition, several other definitions of expanded pairs and expanded degenerations have appeared in the literature. We explain how these definitions are related and introduce several new variants and perspectives. Among these are the twisted expansions used by Abramovich and Fantechi as a basis for orbifold techniques in degeneation formulas.10aExpanded pairs1 aAbramovich, Dan1 aCadman, Charles1 aFantechi, Barbara1 aWise, Jonathan uhttp://hdl.handle.net/1963/738301391nas a2200109 4500008004100000245006200041210006200103260001000165520104500175100002501220856003601245 2013 en d00aFields of bounded deformation for mesoscopic dislocations0 aFields of bounded deformation for mesoscopic dislocations bSISSA3 aIn this paper we discuss the consequences of the distributional approach to dislocations in terms of the mathematical properties\\r\\nof the auxiliary model fields such as displacement and displacement gradient which are obtained directly from \\r\\nthe main model field here considered as the linear strain. We show that these fields cannot be introduced rigourously without \\r\\nthe introduction of gauge fields, or equivalently, without cuts in the Riemann foliation associated to the dislocated crystal.\\r\\nIn a second step we show that the space of bounded deformations follows from the distributional approach in a natural way and \\r\\ndiscuss the reasons why it is adequate to model dislocations. The case of dislocation clusters is also addressed, as it represents an important issue in industrial crystal growth while from a mathematical point of view, peculiar phenomena might appear at the set of accumulation points. \\r\\nThe elastic-plastic decomposition of the strain within this approach is also given a precise meaning.1 aVan Goethem, Nicolas uhttp://hdl.handle.net/1963/637800902nas a2200121 4500008004100000245005300041210005200094260004800146520050700194100002100701700002200722856003600744 2013 en d00aFracture models as Gamma-limits of damage models0 aFracture models as Gammalimits of damage models bAmerican Institute of Mathematical Sciences3 aWe analyze the asymptotic behavior of a variational model for damaged elastic materials. This model depends on two small parameters, which govern the width of the damaged regions and the minimum elasticity constant attained in the damaged regions. When these parameters tend to zero, we find that the corresponding functionals Gamma-converge to a functional related to fracture mechanics. The corresponding problem is brittle or cohesive, depending on the asymptotic ratio of the two parameters.

1 aDal Maso, Gianni1 aIurlano, Flaviana uhttp://hdl.handle.net/1963/422502234nas a2200109 4500008004100000245004000041210004000081520191700121100001602038700002002054856005002074 2013 en d00aFramed sheaves on projective stacks0 aFramed sheaves on projective stacks3 aGiven a normal projective irreducible stack $\mathscr X$ over an algebraically closed field of characteristic zero we consider {\em framed sheaves} on $\mathscr X$, i.e., pairs $(\mathcal E,\phi_{\mathcal E})$, where $\mathcal E$ is a coherent sheaf on $\mathscr X$ and $\phi_{\mathcal E}$ is a morphism from $\mathcal E$ to a fixed coherent sheaf $\mathcal F$. After introducing a suitable notion of (semi)stability, we construct a projective scheme, which is a moduli space for semistable framed sheaves with fixed Hilbert polynomial, and an open subset of it, which is a fine moduli space for stable framed sheaves. If $\mathscr X$ is a projective irreducible orbifold of dimension two and $\mathcal F$ a locally free sheaf on a smooth divisor $\mathscr D\subset \mathscr X$ satisfying certain conditions, we consider {\em $(\mathscr{D}, \mathcal{F})$-framed sheaves}, i.e., framed sheaves $(\mathcal E,\phi_{\mathcal E})$ with $\mathcal E$ a torsion-free sheaf which is locally free in a neighborhood of $\mathscr D$, and ${\phi_{\mathcal{E}}}_{\vert \mathscr{D}}$ an isomorphism. These pairs are $\mu$-stable for a suitable choice of a parameter entering the (semi)stability condition, and of the polarization of $\mathscr X$. This implies the existence of a fine moduli space parameterizing isomorphism classes of $(\mathscr{D}, \mathcal{F})$-framed sheaves on $\mathscr{X}$ with fixed Hilbert polynomial, which is a quasi-projective scheme. In an appendix we develop the example of stacky Hirzebruch surfaces. This is the first paper of a project aimed to provide an algebro-geometric approach to the study of gauge theories on a wide class of 4-dimensional Riemannian manifolds by means of framed sheaves on ``stacky" compactifications of them. In particular, in a subsequent paper \cite{art:bruzzopedrinisalaszabo2013} these results are used to study gauge theories on ALE spaces of type $A_k$.1 aBruzzo, Ugo1 aSala, Francesco uhttp://urania.sissa.it/xmlui/handle/1963/743801318nas a2200121 4500008004100000245007900041210006900120520083000189100002001019700002201039700002101061856011401082 2013 eng d00aFree Form Deformation Techniques Applied to 3D Shape Optimization Problems0 aFree Form Deformation Techniques Applied to 3D Shape Optimizatio3 aThe purpose of this work is to analyse and study an efficient parametrization technique for a 3D shape optimization problem. After a brief review of the techniques and approaches already available in literature, we recall the Free Form Deformation parametrization, a technique which proved to be efficient and at the same time versatile, allowing to manage complex shapes even with few parameters. We tested and studied the FFD technique by establishing a path, from the geometry definition, to the method implementation, and finally to the simulation and to the optimization of the shape. In particular, we have studied a bulb and a rudder of a race sailing boat as model applications, where we have tested a complete procedure from Computer-Aided-Design to build the geometrical model to discretization and mesh generation.1 aKoshakji, Anwar1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/free-form-deformation-techniques-applied-3d-shape-optimization-problems00476nas a2200121 4500008004100000245011700041210006900158300001200227490000700239100001900246700002000265856006900285 2013 eng d00aThe gap probabilities of the tacnode, Pearcey and Airy point processes, their mutual relationship and evaluation0 agap probabilities of the tacnode Pearcey and Airy point processe a13500030 v021 aBertola, Marco1 aCafasso, Mattia uhttp://www.worldscientific.com/doi/abs/10.1142/S201032631350003201258nas a2200145 4500008004100000245010200041210006900143260008500212300001400297490000700311520069200318100002201010700002301032856005701055 2013 eng d00aGeneralized Sturm-Liouville boundary conditions for first order differential systems in the plane0 aGeneralized SturmLiouville boundary conditions for first order d bNicolaus Copernicus University, Juliusz P. Schauder Centre for Nonlinear Studies a293–3250 v423 aWe study asymptotically positively homogeneous first order systems in the plane, with boundary conditions which are positively homogeneous, as well. Defining a generalized concept of Fučík spectrum which extends the usual one for the scalar second order equation, we prove existence and multiplicity of solutions. In this way, on one hand we extend to the plane some known results for scalar second order equations (with Dirichlet, Neumann or Sturm-Liouville boundary conditions), while, on the other hand, we investigate some other kinds of boundary value problems, where the boundary points are chosen on a polygonal line, or in a cone. Our proofs rely on the shooting method.

1 aFonda, Alessandro1 aGarrione, Maurizio uhttps://projecteuclid.org:443/euclid.tmna/146124898101314nas 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/1963/650900420nas a2200109 4500008004100000245011000041210006900151260001000220100002200230700002200252856003600274 2013 en d00aAn improved geometric inequality via vanishing moments, with applications to singular Liouville equations0 aimproved geometric inequality via vanishing moments with applica bSISSA1 aBardelloni, Mauro1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/656100476nas a2200145 4500008004100000022001400041245007100055210006700126300001600193490000800209100001900217700001800236700002200254856005400276 2013 eng d a0002-993900aInversion formulae for the $\romancosh$-weighted Hilbert transform0 aInversion formulae for the romancoshweighted Hilbert transform a2703–27180 v1411 aBertola, Marco1 aKatsevich, A.1 aTovbis, Alexander uhttp://dx.doi.org/10.1090/S0002-9939-2013-11642-400759nas 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-equation01360nas a2200181 4500008004100000022001400041245008900055210006900144260000800213300001400221490000700235520080900242100001701051700002301068700002001091700002101111856004601132 2013 eng d a1559-002X00aLipschitz Classification of Almost-Riemannian Distances on Compact Oriented Surfaces0 aLipschitz Classification of AlmostRiemannian Distances on Compac cJan a438–4550 v233 aTwo-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We consider the Carnot–Carathéodory distance canonically associated with an almost-Riemannian structure and study the problem of Lipschitz equivalence between two such distances on the same compact oriented surface. We analyze the generic case, allowing in particular for the presence of tangency points, i.e., points where two generators of the distribution and their Lie bracket are linearly dependent. The main result of the paper provides a characterization of the Lipschitz equivalence class of an almost-Riemannian distance in terms of a labeled graph associated with it.

1 aBoscain, Ugo1 aCharlot, Grégoire1 aGhezzi, Roberta1 aSigalotti, Mario uhttps://doi.org/10.1007/s12220-011-9262-400625nas a2200157 4500008004100000245011600041210006900157260001700226300001400243490000700257100001500264700002300279700002200302700001800324856012500342 2013 eng d00aMacroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations0 aMacroscopic contact angle and liquid drops on rough solid surfac bEDP Sciences a837–8580 v471 aCacace, S.1 aChambolle, Antonin1 aDeSimone, Antonio1 aFedeli, Livio uhttps://www.math.sissa.it/publication/macroscopic-contact-angle-and-liquid-drops-rough-solid-surfaces-homogenization-and01676nas a2200145 4500008004100000245009400041210006900135260001000204520112400214653008201338100002001420700002501440700002901465856003601494 2013 en d00aMinimal partitions and image classification using a gradient-free perimeter approximation0 aMinimal partitions and image classification using a gradientfree bSISSA3 aIn this paper a new mathematically-founded method for the optimal partitioning of domains, with applications to the classification of greyscale and color images, is proposed. Since optimal partition problems are in general ill-posed, some regularization strategy is required. Here we regularize by a non-standard approximation of the total interface length, which does not involve the gradient of approximate characteristic functions, in contrast to the classical Modica-Mortola approximation. Instead, it involves a system of uncoupled linear partial differential equations and nevertheless shows $\Gamma$-convergence properties in appropriate function spaces. This approach leads to an alternating algorithm that ensures a decrease of the objective function at each iteration, and which always provides a partition, even during the iterations. The efficiency of this algorithm is illustrated by various numerical examples. Among them we consider binary and multilabel minimal partition problems including supervised or automatic image classification, inpainting, texture pattern identification and deblurring.10aImage classification, deblurring, optimal partitions, perimeter approximation1 aAmstutz, Samuel1 aVan Goethem, Nicolas1 aNovotny, Antonio, André uhttp://hdl.handle.net/1963/697600516nas a2200109 4500008004100000245010700041210006900148260001000217653003200227100002000259856012700279 2013 en d00aMinimality and stability results for a class of free-discontinuity and nonlocal isoperimetric problems0 aMinimality and stability results for a class of freediscontinuit bSISSA10afree-discontinuity problems1 aBonacini, Marco uhttps://www.math.sissa.it/publication/minimality-and-stability-results-class-free-discontinuity-and-nonlocal-isoperimetric00733nas a2200133 4500008004100000245005300041210005300094520025800147653004800405100002200453700001600475700002400491856008400515 2013 en d00aMonads for framed sheaves on Hirzebruch surfaces0 aMonads for framed sheaves on Hirzebruch surfaces3 aWe define monads for framed torsion-free sheaves on Hirzebruch surfaces and use them to construct moduli spaces for these objects. These moduli spaces are smooth algebraic varieties, and we show that they are fine by constructing a universal monad.10aMonads, framed sheaves, Hirzebruch surfaces1 aBartocci, Claudio1 aBruzzo, Ugo1 aRava, Claudio, L.S. uhttps://www.math.sissa.it/publication/monads-framed-sheaves-hirzebruch-surfaces01330nas a2200157 4500008004100000022001400041245005900055210005500114260000800169300001400177490000800191520088200199100002301081700002201104856004601126 2013 eng d a1432-091600aThe Monge Problem for Distance Cost in Geodesic Spaces0 aMonge Problem for Distance Cost in Geodesic Spaces cMar a615–6730 v3183 aWe address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish space and dLis a geodesic Borel distance which makes (X, dL) a non branching geodesic space. We show that under the assumption that geodesics are d-continuous and locally compact, we can reduce the transport problem to 1-dimensional transport problems along geodesics. We introduce two assumptions on the transport problem π which imply that the conditional probabilities of the first marginal on each geodesic are continuous or absolutely continuous w.r.t. the 1-dimensional Hausdorff distance induced by dL. It is known that this regularity is sufficient for the construction of a transport map. We study also the dynamics of transport along the geodesic, the stability of our conditions and show that in this setting dL-cyclical monotonicity is not sufficient for optimality.

1 aBianchini, Stefano1 aCavalletti, Fabio uhttps://doi.org/10.1007/s00220-013-1663-800430nas a2200121 4500008004100000245009500041210006900136260001300205653001400218100001800232700002200250856003600272 2013 en d00aMultiplicity result for a nonhomogeneous Yamabe type equation involving the Kohn Laplacian0 aMultiplicity result for a nonhomogeneous Yamabe type equation in bElsevier10aCR-Yamabe1 aMaalaoui, Ali1 aMartino, Vittorio uhttp://hdl.handle.net/1963/737401436nas a2200145 4500008004100000245008000041210006900121260001000190520096800200100002001168700002401188700002401212700001801236856003601254 2013 en d00aN=2 gauge theories on toric singularities, blow-up formulae and W-algebrae0 aN2 gauge theories on toric singularities blowup formulae and Wal bSISSA3 aWe compute the Nekrasov partition function of gauge theories on the\r\n(resolved) toric singularities C^2/\\Gamma in terms of blow-up formulae. We\r\ndiscuss the expansion of the partition function in the \\epsilon_1,\\epsilon_2\r\n\\to 0 limit along with its modular properties and how to derive them from the\r\nM-theory perspective. On the two-dimensional conformal field theory side, our\r\nresults can be interpreted in terms of representations of the direct sum of\r\nHeisenberg plus W_N-algebrae with suitable central charges, which can be\r\ncomputed from the fan of the resolved toric variety.We provide a check of this\r\ncorrespondence by computing the central charge of the two-dimensional theory\r\nfrom the anomaly polynomial of M5-brane theory. Upon using the AGT\r\ncorrespondence our results provide a candidate for the conformal blocks and\r\nthree-point functions of a class of the two-dimensional CFTs which includes\r\nparafermionic theories.1 aBonelli, Giulio1 aMaruyoshi, Kazunobu1 aTanzini, Alessandro1 aYagi, Futoshi uhttp://hdl.handle.net/1963/657700408nas a2200109 4500008004100000245005900041210005700100490000700157100002300164700002000187856009100207 2013 eng d00aA New Quadratic Potential for Scalar Conservation Laws0 aNew Quadratic Potential for Scalar Conservation Laws0 v291 aBianchini, Stefano1 aModena, Stefano uhttps://www.math.sissa.it/publication/new-quadratic-potential-scalar-conservation-laws00840nas a2200145 4500008004100000245004000041210004000081520035300121653006200474100001600536700002100552700002100573700002200594856007800616 2013 en d00aNonabelian Lie algebroid extensions0 aNonabelian Lie algebroid extensions3 aWe classify nonabelian extensions of Lie algebroids in the holomorphic or algebraic category, and introduce and study a spectral sequence that one can attach to any such extension and generalizes the Hochschild-Serre spectral sequence associated to an ideal in a Lie algebra. We compute the differentials of the spectral sequence up to $d_2$

10aLie algebroids, nonabelian extensions, spectral sequences1 aBruzzo, Ugo1 aMencattini, Igor1 aTortella, Pietro1 aRubtsov, Vladimir uhttps://www.math.sissa.it/publication/nonabelian-lie-algebroid-extensions01090nas a2200133 4500008004100000245005800041210005800099260001300157520067800170653003000848100002200878700002000900856003600920 2013 en d00aNoncommutative circle bundles and new Dirac operators0 aNoncommutative circle bundles and new Dirac operators bSpringer3 aWe study spectral triples over noncommutative principal U(1) bundles. Basing on the classical situation and the abstract algebraic approach, we propose an operatorial definition for a connection and compatibility between the connection and the Dirac operator on the total space and on the base space of the bundle. We analyze in details the example of the noncommutative three-torus viewed as a U(1) bundle over the noncommutative two-torus and find all connections compatible with an admissible Dirac operator. Conversely, we find a family of new Dirac operators on the noncommutative tori, which arise from the base-space Dirac operator and a suitable connection.10aQuantum principal bundles1 aDabrowski, Ludwik1 aSitarz, Andrzej uhttp://hdl.handle.net/1963/738401020nas 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-analysis01376nas a2200145 4500008004100000245007300041210006900114260003400183520083400217653001701051100001301068700002401081700002301105856010201128 2013 en d00aA note on KAM theory for quasi-linear and fully nonlinear forced KdV0 anote on KAM theory for quasilinear and fully nonlinear forced Kd bEuropean Mathematical Society3 aWe present the recent results in [3] concerning quasi-periodic solutions for quasi-linear and fully nonlinear forced perturbations of KdV equations. For Hamiltonian or reversible nonlinearities the solutions are linearly stable. The proofs are based on a combination of di erent ideas and techniques: (i) a Nash-Moser iterative scheme in Sobolev scales. (ii) A regularization procedure, which conjugates the linearized operator to a di erential operator with constant coe cients plus a bounded remainder. These transformations are obtained by changes of variables induced by di eomorphisms of the torus and pseudo-di erential operators. (iii) A reducibility KAM scheme, which completes the reduction to constant coe cients of the linearized operator, providing a sharp asymptotic expansion of the perturbed eigenvalues.10aKAM for PDEs1 aBaldi, P1 aBerti, Massimiliano1 aMontalto, Riccardo uhttps://www.math.sissa.it/publication/note-kam-theory-quasi-linear-and-fully-nonlinear-forced-kdv00784nas a2200109 4500008004100000245008400041210006900125520032000194100002500514700002300539856011200562 2013 eng d00aA note on non-homogeneous hyperbolic operators with low-regularity coefficients0 anote on nonhomogeneous hyperbolic operators with lowregularity c3 aIn this paper we obtain an energy estimate for a complete strictly hyperbolic operator with second order coefficients satisfying a log-Zygmund-continuity condition with respect to $t$, uniformly with respect to $x$, and a log-Lipschitz-continuity condition with respect to $x$, uniformly with respect to $t$.

1 aColombini, Ferruccio1 aFanelli, Francesco uhttps://www.math.sissa.it/publication/note-non-homogeneous-hyperbolic-operators-low-regularity-coefficients01596nas a2200133 4500008004100000245010900041210006900150260001000219520113200229100002101361700002201382700002201404856003601426 2013 en d00aOne-dimensional swimmers in viscous fluids: dynamics, controllability, and existence of optimal controls0 aOnedimensional swimmers in viscous fluids dynamics controllabili bSISSA3 aIn this paper we study a mathematical model of one-dimensional swimmers performing a planar motion while fully immersed in a viscous fluid. The swimmers are assumed to be of small size, and all inertial effects are neglected. Hydrodynamic interactions are treated in a simplified way, using the local drag approximation of resistive force theory. We prove existence and uniqueness of the solution of the equations of motion driven by shape changes of the swimmer. Moreover, we prove a controllability result showing that given any pair of initial and final states, there exists a history of shape changes such that the resulting motion takes the swimmer from the initial to the final state. We give a constructive proof, based on the composition of elementary maneuvers (straightening and its inverse, rotation, translation), each of which represents the solution of an interesting motion planning problem. Finally, we prove the existence of solutions for the optimal control problem of finding, among the histories of shape changes taking the swimmer from an initial to a final state, the one of minimal energetic cost.

1 aDal Maso, Gianni1 aDeSimone, Antonio1 aMorandotti, Marco uhttp://hdl.handle.net/1963/646700555nas a2200133 4500008004100000245009600041210006900137260003700206300001200243490000700255100002300262700001900285856011700304 2013 eng d00aPairs of nodal solutions for a class of nonlinear problems with one-sided growth conditions0 aPairs of nodal solutions for a class of nonlinear problems with bAdvanced Nonlinear Studies, Inc. a13–530 v131 aBoscaggin, Alberto1 aZanolin, Fabio uhttps://www.math.sissa.it/publication/pairs-nodal-solutions-class-nonlinear-problems-one-sided-growth-conditions00503nas a2200133 4500008004100000245006500041210006500106260003700171300001400208490000700222100002200229700001900251856009900270 2013 eng d00aPeriodic bouncing solutions for nonlinear impact oscillators0 aPeriodic bouncing solutions for nonlinear impact oscillators bAdvanced Nonlinear Studies, Inc. a179–1890 v131 aFonda, Alessandro1 aSfecci, Andrea uhttps://www.math.sissa.it/publication/periodic-bouncing-solutions-nonlinear-impact-oscillators01133nas a2200157 4500008004100000022001400041245008000055210007300135260000800208300001400216490000700230520064600237100002300883700002300906856004600929 2013 eng d a1420-900400aPlanar Hamiltonian systems at resonance: the Ahmad–Lazer–Paul condition0 aPlanar Hamiltonian systems at resonance the Ahmad–Lazer–Paul con cJun a825–8430 v203 aWe consider the planar Hamiltonian system\$\$Ju^{\backslashprime} = \backslashnabla F(u) + \backslashnabla_u R(t,u), \backslashquad t \backslashin [0,T], \backslash,u \backslashin \backslashmathbb{R}^2,\$\$with F(u) positive and positively 2-homogeneous and \$\${\backslashnabla_{u}R(t, u)}\$\$sublinear in u. By means of an Ahmad-Lazer-Paul type condition, we prove the existence of a T-periodic solution when the system is at resonance. The proof exploits a symplectic change of coordinates which transforms the problem into a perturbation of a linear one. The relationship with the Landesman–Lazer condition is analyzed, as well.

1 aBoscaggin, Alberto1 aGarrione, Maurizio uhttps://doi.org/10.1007/s00030-012-0181-200550nas a2200109 4500008004100000245002500041210002500066260001000091520025100101100002500352856006300377 2013 en d00aQuadratic cohomology0 aQuadratic cohomology bSISSA3 aWe study homological invariants of smooth families of real quadratic forms as\r\na step towards a \"Lagrange multipliers rule in the large\" that intends to\r\ndescribe topology of smooth vector functions in terms of scalar Lagrange\r\nfunctions.1 aAgrachev, Andrei, A. uhttps://www.math.sissa.it/publication/quadratic-cohomology01345nas a2200145 4500008004100000022001300041245009800054210006900152300001200221490000700233520079700240100002401037700002001061856011801081 2013 eng d a1435985500aQuasi-periodic solutions with Sobolev regularity of NLS on Td with a multiplicative potential0 aQuasiperiodic solutions with Sobolev regularity of NLS on Td wit a229-2860 v153 aWe prove the existence of quasi-periodic solutions for Schrödinger equations with a multiplicative potential on Td , d ≥ 1, finitely differentiable nonlinearities, and tangential frequencies constrained along a pre-assigned direction. The solutions have only Sobolev regularity both in time and space. If the nonlinearity and the potential are C∞ then the solutions are C∞. The proofs are based on an improved Nash-Moser iterative scheme, which assumes the weakest tame estimates for the inverse linearized operators ("Green functions") along scales of Sobolev spaces. The key off-diagonal decay estimates of the Green functions are proved via a new multiscale inductive analysis. The main novelty concerns the measure and "complexity" estimates. © European Mathematical Society 2013.1 aBerti, Massimiliano1 aBolle, Philippe uhttps://www.math.sissa.it/publication/quasi-periodic-solutions-sobolev-regularity-nls-td-multiplicative-potential01461nas a2200217 4500008004100000022001400041245008900055210006900144300001400213490000700227520075100234653001700985653002301002653003101025653002601056653003101082653001601113100001801129700002501147856007101172 2013 eng d a0294-144900aA quasistatic evolution model for perfectly plastic plates derived by Γ-convergence0 aquasistatic evolution model for perfectly plastic plates derived a615 - 6600 v303 aThe subject of this paper is the rigorous derivation of a quasistatic evolution model for a linearly elastic–perfectly plastic thin plate. As the thickness of the plate tends to zero, we prove via Γ-convergence techniques that solutions to the three-dimensional quasistatic evolution problem of Prandtl–Reuss elastoplasticity converge to a quasistatic evolution of a suitable reduced model. In this limiting model the admissible displacements are of Kirchhoff–Love type and the stretching and bending components of the stress are coupled through a plastic flow rule. Some equivalent formulations of the limiting problem in rate form are derived, together with some two-dimensional characterizations for suitable choices of the data.

10a-convergence10aPerfect plasticity10aPrandtl–Reuss plasticity10aQuasistatic evolution10aRate-independent processes10aThin plates1 aDavoli, Elisa1 aMora, Maria Giovanna uhttp://www.sciencedirect.com/science/article/pii/S029414491200103502183nas a2200145 4500008004100000245015300041210006900194260001300263520163200276653003401908100002101942700001801963700002001981856003602001 2013 en d00aReduced basis approximation and a posteriori error estimation for Stokes flows in parametrized geometries: roles of the inf-sup stability constants0 aReduced basis approximation and a posteriori error estimation fo bSpringer3 aIn this paper we review and we extend the reduced basis approximation and a posteriori error estimation for steady Stokes flows in a ffinely parametrized geometries, focusing on the role played by the Brezzi\\\'s and Babu ska\\\'s stability constants. The crucial ingredients of the methodology are a Galerkin projection onto a low-dimensional space of basis functions properly selected, an a ne parametric dependence enabling to perform competitive Off ine-Online splitting in the computational\\r\\nprocedure and a rigorous a posteriori error estimation on eld variables.\\r\\nThe combination of these three factors yields substantial computational savings which are at the basis of an e fficient model order reduction, ideally suited for real-time simulation and many-query contexts (e.g. optimization, control or parameter identi cation). In particular, in this work we focus on i) the stability of the reduced basis approximation based on the Brezzi\\\'s saddle point theory and the introduction of a supremizer operator on the pressure terms, ii) a rigorous a posteriori error estimation procedure for velocity and pressure elds based on the Babu ska\\\'s inf-sup constant (including residuals calculations), iii) the computation of a lower bound of the stability constant, and iv) di erent options for the reduced basis spaces construction. We present some illustrative results for both\\r\\ninterior and external steady Stokes flows in parametrized geometries representing two parametrized classical Poiseuille and Couette \\r\\nflows, a channel contraction and a simple flow control problem around a curved obstacle.10aparametrized Stokes equations1 aRozza, Gianluigi1 aHuynh, Phuong1 aManzoni, Andrea uhttp://hdl.handle.net/1963/633900531nas a2200121 4500008004100000245011700041210006900158300001100227490000700238100001800245700002100263856012500284 2013 eng d00aReduced Basis Approximation for the Structural-Acoustic Design based on Energy Finite Element Analysis (RB-EFEA)0 aReduced Basis Approximation for the StructuralAcoustic Design ba a98-1150 v481 aDevaud, Denis1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduced-basis-approximation-structural-acoustic-design-based-energy-finite-element01701nas a2200157 4500008004100000245007600041210006900117300001800186490000700204520113900211100002001350700002101370700002001391700002201411856011001433 2013 eng d00aReduced basis method for parametrized elliptic optimal control problems0 aReduced basis method for parametrized elliptic optimal control p aA2316–A23400 v353 aWe propose a suitable model reduction paradigm-the certified reduced basis method (RB)-for the rapid and reliable solution of parametrized optimal control problems governed by partial differential equations. In particular, we develop the methodology for parametrized quadratic optimization problems with elliptic equations as a constraint and infinite-dimensional control variable. First, we recast the optimal control problem in the framework of saddle-point problems in order to take advantage of the already developed RB theory for Stokes-type problems. Then, the usual ingredients of the RB methodology are called into play: a Galerkin projection onto a low-dimensional space of basis functions properly selected by an adaptive procedure; an affine parametric dependence enabling one to perform competitive offline-online splitting in the computational procedure; and an efficient and rigorous a posteriori error estimate on the state, control, and adjoint variables as well as on the cost functional. Finally, we address some numerical tests that confirm our theoretical results and show the efficiency of the proposed technique.1 aNegri, Federico1 aRozza, Gianluigi1 aManzoni, Andrea1 aQuarteroni, Alfio uhttps://www.math.sissa.it/publication/reduced-basis-method-parametrized-elliptic-optimal-control-problems00548nas a2200133 4500008004100000245009200041210006900133260001000202100001800212700002000230700002200250700002100272856012100293 2013 en d00aA Reduced Computational and Geometrical Framework for Inverse Problems in Haemodynamics0 aReduced Computational and Geometrical Framework for Inverse Prob bSISSA1 aLassila, Toni1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduced-computational-and-geometrical-framework-inverse-problems-haemodynamics00568nas a2200133 4500008004100000245010500041210006900146260001000215100001800225700002000243700002200263700002100285856012800306 2013 en d00aA reduced-order strategy for solving inverse Bayesian identification problems in physiological flows0 areducedorder strategy for solving inverse Bayesian identificatio bSISSA1 aLassila, Toni1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduced-order-strategy-solving-inverse-bayesian-identification-problems-physiological00490nas a2200121 4500008004100000245007900041210006900120260001000189100001800199700002000217700002100237856011000258 2013 en d00aReduction Strategies for Shape Dependent Inverse Problems in Haemodynamics0 aReduction Strategies for Shape Dependent Inverse Problems in Hae bSISSA1 aLassila, Toni1 aManzoni, Andrea1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduction-strategies-shape-dependent-inverse-problems-haemodynamics00793nas a2200145 4500008004100000245004800041210004800089260003500137300001200172490000600184520038200190100002200572700002000594856003300614 2013 en d00aRemarks on the Moser–Trudinger inequality0 aRemarks on the Moser–Trudinger inequality bAdvances in Nonlinear Analysis a389-4250 v23 aWe extend the Moser-Trudinger inequality to any Euclidean domain satisfying Poincaré's inequality. We find out that the same equivalence does not hold in general for conformal metrics on the unit ball, showing counterexamples. We also study the existence of extremals for the Moser-Trudinger inequalities for unbounded domains, proving it for the infinite planar strip.

1 aMancini, Gabriele1 aBattaglia, Luca uhttp://edoc.unibas.ch/43974/00494nas 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/1963/713001064nas a2200109 4500008004100000245002900041210002900070260001000099520079300109100001600902856003600918 2013 en d00aSoftly Constrained Films0 aSoftly Constrained Films bSISSA3 aThe shape of materials is often subject to a number of geometric constraints\r\nthat limit the size of the system or fix the structure of its boundary. In soft\r\nand biological materials, however, these constraints are not always hard, but\r\nare due to other physical mechanisms that affect the overall force balance. A\r\ncapillary film spanning a flexible piece of wire or a cell anchored to a\r\ncompliant substrate by mean of adhesive contacts are examples of these softly\r\nconstrained systems in the macroscopic and microscopic world. In this article I\r\nreview some of the important mathematical and physical developments that\r\ncontributed to our understanding of shape formation in softly constrained films\r\nand their recent application to the mechanics of adherent cells.1 aGiomi, Luca uhttp://hdl.handle.net/1963/656300403nas a2200109 4500008004100000245005300041210005300094260001000147653003300157100001800190856008500208 2013 en d00aSome models of crack growth in brittle materials0 aSome models of crack growth in brittle materials bSISSA10aQuasi-static crack evolution1 aRacca, Simone uhttps://www.math.sissa.it/publication/some-models-crack-growth-brittle-materials00401nas a2200121 4500008004100000245002300041210002300064260001000087520010800097653001300205100002500218856003600243 2013 en d00aSome open problems0 aSome open problems bSISSA3 aWe discuss some challenging open problems in the geometric control theory and sub-Riemannian geometry.10aGeometry1 aAgrachev, Andrei, A. uhttp://hdl.handle.net/1963/707000835nas a2200145 4500008004100000245006200041210006200103260001000165490000600175520040600181653002300587100002400610700001900634856003600653 2013 en d00aSome remarks on the viscous approximation of crack growth0 aSome remarks on the viscous approximation of crack growth bSISSA0 v63 aWe describe an existence result for quasistatic evolutions of cracks in antiplane elasticity obtained in [16] by a vanishing viscosity approach, with free (but regular enough) crack path. We underline in particular the motivations for the choice of the class of admissible cracks and of the dissipation potential. Moreover, we extend the result to a model with applied forces depending on time.

10aVariational models1 aLazzaroni, Giuliano1 aToader, Rodica uhttp://hdl.handle.net/1963/420601894nas a2200121 4500008004100000245008300041210006900124260001000193520137300203653005401576100002401630856011801654 2013 en d00aSome topics on Higgs bundles over projective varieties and their moduli spaces0 aSome topics on Higgs bundles over projective varieties and their bSISSA3 aIn this thesis we study vector bundles on projective varieties and their moduli spaces. In Chapters 2, 3 and 4 we recall some basic notions as Higgs bundles, decorated bundles and generalized parabolic sheaves and introduce the problem we want to study. In chapter 5, we study Higgs bundles on nodal curves. After moving the problem on the normalization of the curve, starting from a Higgs bundle we obtain a generalized parabolic Higgs bundle. Using decorated bundles we are able to construct a projective moduli space which parametrizes equivalence classes of Higgs bundles on a nodal curve X. This chapter is an extract of a joint work with Andrea Pustetto Later on Chapter 6 is devoted to the study of holomorphic pairs (or twisted Higgs bundles) on elliptic curve. Holomorphic pairs were introduced by Nitsure and they are a natural generalization of the concept of Higgs bundles. In this Chapter we extend a result of E. Franco, O. Garc\'ia-Prada And P.E. Newstead valid for Higgs bundles to holomorphic pairs. Finally the last Chapter describes a joint work with Professor Ugo Bruzzo. We study Higgs bundles over varieties with nef tangent bundle. In particular generalizing a result of Nitsure we prove that if a Higgs bundle $(E,\phi)$ over the variety X with nef tangent remains semisatble when pulled-back to any smooth curve then it discrimiant vanishes.10aAlgebraic Geometry, Moduli spaces, Vector bundles1 aLo Giudice, Alessio uhttps://www.math.sissa.it/publication/some-topics-higgs-bundles-over-projective-varieties-and-their-moduli-spaces00539nas 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/s10955-013-0845-200744nas a2200097 4500008004100000245004800041210004300089520044800132100001800580856004800598 2013 en d00aThe splitting theorem in non-smooth context0 asplitting theorem in nonsmooth context3 aWe prove that an infinitesimally Hilbertian $CD(0,N)$ space containing a line splits as the product of $R$ and an infinitesimally Hilbertian $CD(0,N −1)$ space. By ‘infinitesimally Hilbertian’ we mean that the Sobolev space $W^{1,2}(X,d,m)$, which in general is a Banach space, is an Hilbert space. When coupled with a curvature-dimension bound, this condition is known to be stable with respect to measured Gromov-Hausdorff convergence.1 aGigli, Nicola uhttp://preprints.sissa.it/handle/1963/3530601218nas a2200121 4500008004100000245008200041210006900123520080800192100002201000700002301022700001501045856003601060 2013 en d00aStabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control0 aStabilization of Stochastic Quantum Dynamics via Open and Closed3 aIn this paper, we investigate parametrization-free solutions of the problem of quantum pure state preparation and subspace stabilization by means of Hamiltonian control, continuous measurement, and quantum feedback, in the presence of a Markovian environment. In particular, we show that whenever suitable dissipative effects are induced either by the unmonitored environment, or by non-Hermitian measurements, there is no need for feedback, as open-loop time-invariant control is sufficient to achieve stabilization of the target set in probability. Constructive necessary and sufficient conditions on the form of the control Hamiltonian can be provided in this case. When time-invariant control is not sufficient, state stabilization can be attained by the addition of filtering-based feedback control1 aAltafini, Claudio1 aTicozzi, Francesco1 aNishio, K. uhttp://hdl.handle.net/1963/650301660nas a2200145 4500008004100000245010800041210006900149260001000218520115900228653003501387100001701422700001701439700002201456856003601478 2013 en d00aA stable and adaptive semi-Lagrangian potential model for unsteady and nonlinear ship-wave interactions0 astable and adaptive semiLagrangian potential model for unsteady bSISSA3 aWe present an innovative numerical discretization of the equations of inviscid potential flow for the simulation of three dimensional unsteady and nonlinear water waves generated by a ship hull advancing in water. The equations of motion are written in a semi-Lagrangian framework, and the resulting integro-diff erential equations are discretized in space via an adaptive iso-parametric collocation Boundary Element Method, and in time via adaptive implicit Backward Di erentiation Formulas (BDF) with variable step and variable order. When the velocity of the advancing ship hull is non-negligible, the semi-Lagrangian formulation (also known as Arbitrary Lagrangian Eulerian formulation, or ALE) of the free surface equations contains dominant transport terms which are stabilized with a Streamwise Upwind Petrov-Galerkin (SUPG) method. The SUPG stabilization allows automatic and robust adaptation of the spatial discretization with unstructured quadrilateral grids. Preliminary results are presented where we compare our numerical model with experimental results on the case of a Wigley hull advancing in calm water with fi xed sink and trim.

10aUnsteady ship-wave interaction1 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/566900757nas a2200133 4500008004100000245008600041210006900127260002100196300001200217490000700229520031600236100002200552856004900574 2013 eng d00aStable determination of a body immersed in a fluid: the nonlinear stationary case0 aStable determination of a body immersed in a fluid the nonlinear bTaylor & Francis a460-4810 v923 aWe consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the stationary Navier–Stokes equations, from a single measurement of force and velocity on a portion of the boundary. We obtain an estimate of stability of log–log type.

1 aBallerini, Andrea uhttps://doi.org/10.1080/00036811.2011.62817301509nas a2200145 4500008004100000245009700041210006900138300001600207490000700223520095300230100001501183700002201198700002101220856012201241 2013 eng d00aStochastic optimal robin boundary control problems of advection-dominated elliptic equations0 aStochastic optimal robin boundary control problems of advectiond a2700–27220 v513 aIn this work we deal with a stochastic optimal Robin boundary control problem constrained by an advection-diffusion-reaction elliptic equation with advection-dominated term. We assume that the uncertainty comes from the advection field and consider a stochastic Robin boundary condition as control function. A stochastic saddle point system is formulated and proved to be equivalent to the first order optimality system for the optimal control problem, based on which we provide the existence and uniqueness of the optimal solution as well as some results on stochastic regularity with respect to the random variables. Stabilized finite element approximations in physical space and collocation approximations in stochastic space are applied to discretize the optimality system. A global error estimate in the product of physical space and stochastic space for the numerical approximation is derived. Illustrative numerical experiments are provided.1 aChen, Peng1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/stochastic-optimal-robin-boundary-control-problems-advection-dominated-elliptic00584nas a2200145 4500008004100000022001400041245010700055210006900162300001500231490000700246100001900253700001700272700002000289856012900309 2013 eng d a0022-248800aStrong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two-matrix model0 aStrong asymptotics for Cauchy biorthogonal polynomials with appl a043517, 250 v541 aBertola, Marco1 aGekhtman, M.1 aSzmigielski, J. uhttps://www.math.sissa.it/publication/strong-asymptotics-cauchy-biorthogonal-polynomials-application-cauchy-two-matrix-model00932nas a2200109 4500008004100000245011500041210006900156260001000225520044500235100001200680856013000692 2013 en d00aThe structure and regularity of admissible BV solutions to hyperbolic conservation laws in one space dimension0 astructure and regularity of admissible BV solutions to hyperboli bSISSA3 aThis thesis is devoted to the study of the qualitative properties of admissible BV solutions to the strictly hyperbolic conservation laws in one space dimension by using wave-front tracking approximation. This thesis consists of two parts: • SBV-like regularity of vanishing viscosity BV solutions to strict hyperbolic systems of conservation laws. • Global structure of admissible BV solutions to strict hyperbolic conservation laws.1 aYu, Lei uhttps://www.math.sissa.it/publication/structure-and-regularity-admissible-bv-solutions-hyperbolic-conservation-laws-one-space01092nas a2200205 4500008004100000022001400041245010400055210006900159300000700228490000700235520037600242653003000618653003400648653002300682653003700705653002600742100002300768700001900791856007600810 2013 eng d a1078-094700aSubharmonic solutions for nonlinear second order equations in presence of lower and upper solutions0 aSubharmonic solutions for nonlinear second order equations in pr a890 v333 aWe study the problem of existence and multiplicity of subharmonic solutions for a second order nonlinear ODE in presence of lower and upper solutions. We show how such additional information can be used to obtain more precise multiplicity results. Applications are given to pendulum type equations and to Ambrosetti-Prodi results for parameter dependent equations.

10alower and upper solutions10aparameter dependent equations10aPeriodic solutions10aPoincaré-Birkhoff twist theorem10asubharmonic solutions1 aBoscaggin, Alberto1 aZanolin, Fabio uhttp://aimsciences.org//article/id/3638a93e-4f3e-4146-a927-3e8a64e6863f00380nas a2200109 4500008004100000245007400041210006900115260001000184100002300194700001700217856003600234 2013 en d00aOn Sudakov's type decomposition of transference plans with norm costs0 aSudakovs type decomposition of transference plans with norm cost bSISSA1 aBianchini, Stefano1 aDaneri, Sara uhttp://hdl.handle.net/1963/720600812nas a2200133 4500008004100000245006300041210006200104260003000166520036300196100001600559700002600575700002600601856005100627 2013 en d00aSymplectic instanton bundles on P3 and 't Hooft instantons0 aSymplectic instanton bundles on P3 and t Hooft instantons barXiv:1312.5554 [math.AG]3 aWe introduce the notion of tame symplectic instantons by excluding a kind of pathological monads and show that the locus $I^*_{n,r}$ of tame symplectic instantons is irreducible and has the expected dimension, equal to $4n(r+1)-r(2r+1)$. The proof is inherently based on a relation between the spaces $I^*_{n,r}$ and the moduli spaces of 't Hooft instantons.1 aBruzzo, Ugo1 aMarkushevich, Dimitri1 aTikhomirov, Alexander uhttp://urania.sissa.it/xmlui/handle/1963/3448600364nas a2200109 4500008004100000245004800041210004800089260001000137653004600147100002500193856003600218 2013 en d00aTopology of moduli spaces of framed sheaves0 aTopology of moduli spaces of framed sheaves bSISSA10aModuli spaces, framed sheaves, instantons1 aAbdellaoui, Gharchia uhttp://hdl.handle.net/1963/715201015nas a2200133 4500008004100000245004500041210003400086260001000120520062000130100001800750700001900768700002100787856007300808 2013 en d00aOn the tritronquée solutions of P$_I^2$0 atritronquée solutions of PI2 bSISSA3 aFor equation P$_I^2$, the second member in the P$_I$ hierarchy, we prove existence of various degenerate solutions depending on the complex parameter $t$ and evaluate the asymptotics in the complex $x$ plane for $|x|\to\infty$ and $t=o(x^{2/3})$. Using this result, we identify the most degenerate solutions $u^{(m)}(x,t)$, $\hat u^{(m)}(x,t)$, $m=0,\dots,6$, called {\em tritronqu\'ee}, describe the quasi-linear Stokes phenomenon and find the large $n$ asymptotics of the coefficients in a formal expansion of these solutions. We supplement our findings by a numerical study of the tritronqu\'ee solutions.

1 aGrava, Tamara1 aKapaev, Andrey1 aKlein, Christian uhttps://www.math.sissa.it/publication/tritronqu%C3%A9e-solutions-pi200539nas a2200133 4500008004100000022001400041245017800055210007000233300001400303490000700317100001900324700002200343856004000365 2013 eng d a0010-364000aUniversality for the focusing nonlinear Schrödinger equation at the gradient catastrophe point: rational breathers and poles of the \it Tritronquée solution to Painlevé I0 aUniversality for the focusing nonlinear Schrödinger equation at a678–7520 v661 aBertola, Marco1 aTovbis, Alexander uhttp://dx.doi.org/10.1002/cpa.2144500725nas a2200121 4500008004100000245006600041210006400107260001000171520034800181100002200529700001600551856003600567 2013 en d00aA variational Analysis of the Toda System on Compact Surfaces0 avariational Analysis of the Toda System on Compact Surfaces bWiley3 aIn this paper we consider the Toda system of equations on a compact surface. We will give existence results by using variational methods in a non coercive case. A key tool in our analysis is a new Moser-Trudinger type inequality under suitable conditions on the center of mass and the scale of concentration of the two components u_1, u_2.1 aMalchiodi, Andrea1 aRuiz, David uhttp://hdl.handle.net/1963/655801375nas a2200145 4500008004100000245010300041210006900144300001600213490000700229520080500236100001501041700002201056700002101078856013001099 2013 eng d00aA weighted reduced basis method for elliptic partial differential equations with random input data0 aweighted reduced basis method for elliptic partial differential a3163–31850 v513 aIn this work we propose and analyze a weighted reduced basis method to solve elliptic partial differential equations (PDEs) with random input data. The PDEs are first transformed into a weighted parametric elliptic problem depending on a finite number of parameters. Distinctive importance of the solution at different values of the parameters is taken into account by assigning different weights to the samples in the greedy sampling procedure. A priori convergence analysis is carried out by constructive approximation of the exact solution with respect to the weighted parameters. Numerical examples are provided for the assessment of the advantages of the proposed method over the reduced basis method and the stochastic collocation method in both univariate and multivariate stochastic problems.1 aChen, Peng1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/weighted-reduced-basis-method-elliptic-partial-differential-equations-random-input-data00934nas a2200133 4500008004100000245005700041210005100098260005100149520050200200100002100702700001700723700002400740856003600764 2012 en d00aOn 2-step, corank 2 nilpotent sub-Riemannian metrics0 a2step corank 2 nilpotent subRiemannian metrics bSociety for Industrial and Applied Mathematics3 aIn this paper we study the nilpotent 2-step, corank 2 sub-Riemannian metrics\\r\\nthat are nilpotent approximations of general sub-Riemannian metrics. We exhibit optimal syntheses for these problems. It turns out that in general the cut time is not equal to the first conjugate time but has a simple explicit expression. As a byproduct of this study we get some smoothness properties of the spherical Hausdorff measure in the case of a generic 6 dimensional, 2-step corank 2 sub-Riemannian metric.1 aBarilari, Davide1 aBoscain, Ugo1 aGauthier, Jean-Paul uhttp://hdl.handle.net/1963/606500868nas 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%92001737nas a2200145 4500008004100000245007100041210006400112260001900176520126500195653002501460100002001485700002301505700002701528856003601555 2012 en d00aOn the behaviour of flexible retaining walls under seismic actions0 abehaviour of flexible retaining walls under seismic actions bICE Publishing3 aThis paper describes an experimental investigation of the behaviour of embedded retaining walls under seismic actions. Nine centrifuge tests were carried out on reduced-scale models of pairs of retaining walls in dry sand, either cantilevered or with one level of props near the top. The experimental data indicate that, for maximum accelerations that are smaller than the critical limit equilibrium value, the retaining walls experience significant permanent displacements under increasing structural loads, whereas for larger accelerations the walls rotate under constant internal forces. The critical acceleration at which the walls start to rotate increases with increasing maximum acceleration. No significant displacements are measured if the current earthquake is less severe than earthquakes previously experienced by the wall. The increase of critical acceleration is explained in terms of redistribution of earth pressures and progressive mobilisation of the passive strength in front of the wall. The experimental data for cantilevered retaining walls indicate that the permanent displacements of the wall can be reasonably predicted adopting a Newmark-type calculation with a critical acceleration that is a fraction of the limit equilibrium value.10aCentrifuge modelling1 aConti, Riccardo1 aMadabhushi, G.S.P.1 aViggiani, Giulia, M.B. uhttp://hdl.handle.net/1963/693301501nas a2200157 4500008004100000245010600041210006900147260003100216520095600247653002301203100001801226700002001244700002201264700002101286856003601307 2012 en d00aBoundary control and shape optimization for the robust design of bypass anastomoses under uncertainty0 aBoundary control and shape optimization for the robust design of bCambridge University Press3 aWe review the optimal design of an arterial bypass graft following either a (i) boundary optimal control approach, or a (ii) shape optimization formulation. The main focus is quantifying and treating the uncertainty in the residual flow when the hosting artery is not completely occluded,\\r\\nfor which the worst-case in terms of recirculation e ffects is inferred to correspond to a strong ori fice flow through near-complete occlusion. A worst-case optimal control approach is applied to the steady\\r\\nNavier-Stokes equations in 2D to identify an anastomosis angle and a cu ed shape that are robust with respect to a possible range of residual \\r\\nflows. We also consider a reduced order modelling framework\\r\\nbased on reduced basis methods in order to make the robust design problem computationally feasible. The results obtained in 2D are compared with simulations in a 3D geometry but without model\\r\\nreduction or the robust framework.10ashape optimization1 aLassila, Toni1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://hdl.handle.net/1963/633701113nas a2200145 4500008004100000245009600041210006900137260001300206300001200219490000700231520057100238100002000809700002400829856011400853 2012 en d00aOn a class of vector fields with discontinuity of divide-by-zero type and its applications0 aclass of vector fields with discontinuity of dividebyzero type a bSpringer a135-1580 v183 aWe study phase portraits and singular points of vector fields of a special type, that is, vector fields whose components are fractions with a common denominator vanishing on a smooth regular hypersurface in the phase space. We assume also some additional conditions, which are fulfilled, for instance, if the vector field is divergence-free. This problem is motivated by a large number of applications. In this paper, we consider three of them in the framework of differential geometry: singularities of geodesic flows in various singular metrics on surfaces.

1 aGhezzi, Roberta1 aRemizov, Alexey, O. uhttps://www.math.sissa.it/publication/class-vector-fields-discontinuity-divide-zero-type-and-its-applications01113nas a2200121 4500008004100000245008000041210006900121260001000190520071100200100002000911700002400931856003600955 2012 en d00aClassical double, R-operators, and negative flows of integrable hierarchies0 aClassical double Roperators and negative flows of integrable hie bSISSA3 aUsing the classical double G of a Lie algebra g equipped with the classical R-operator, we define two sets of functions commuting with respect to the initial Lie–Poisson bracket on g and its extensions. We consider examples of Lie algebras g with the “Adler–Kostant–Symes” R-operators and the two corresponding sets of mutually commuting functions in detail. Using the constructed commutative Hamiltonian flows on different extensions of g, we obtain zero-curvature equations with g-valued U–V pairs. The so-called negative flows of soliton hierarchies are among such equations. We illustrate the proposed approach with examples of two-dimensional Abelian and non-Abelian Toda field equations.1 aDubrovin, Boris1 aSkrypnyk, Taras, V. uhttp://hdl.handle.net/1963/646801152nas a2200145 4500008004100000245009700041210006900138260001000207520067600217100002200893700001500915700002000930700002000950856003600970 2012 en d00aA Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group.0 aCodazzilike equation and the singular set for C1 smooth surfaces bSISSA3 aIn this paper, we study the structure of the singular set for a C 1 smooth surface in the 3-dimensional Heisenberg group ℍ 1. We discover a Codazzi-like equation for the p-area element along the characteristic curves on the surface. Information obtained from this ordinary differential equation helps us to analyze the local configuration of the singular set and the characteristic curves. In particular, we can estimate the size and obtain the regularity of the singular set. We understand the global structure of the singular set through a Hopf-type index theorem. We also justify the Codazzi-like equation by proving a fundamental theorem for local surfaces in ℍ 11 aMalchiodi, Andrea1 aYang, Paul1 aCheng, Jih-Hsin1 aHwang, JennFang uhttp://hdl.handle.net/1963/655600824nas a2200169 4500008004100000020001800041245006300059210006300122260001300185520030800198653002400506100002200530700001700552700002300569700002600592856003600618 2012 en d a978146143996700aComputing optimal strokes for low reynolds number swimmers0 aComputing optimal strokes for low reynolds number swimmers bSpringer3 aWe discuss connections between low-Reynolds-number swimming and geometric control theory, and present a general algorithm for the numerical computation of energetically optimal strokes. As an illustration of our approach, we show computed motility maps and optimal strokes for two model swimmers.

10aNumerical analysis.1 aDeSimone, Antonio1 aHeltai, Luca1 aAlouges, François1 aAline, Lefebvre-Lepot uhttp://hdl.handle.net/1963/644500854nas a2200157 4500008004100000245012200041210007200163260002100235300001200256490000700268520031300275100002000588700002300608700001900631856004600650 2012 eng d00aConcentration on circles for nonlinear Schrödinger–Poisson systems with unbounded potentials vanishing at infinity0 aConcentration on circles for nonlinear Schrödinger–Poisson syste bWorld Scientific a12500090 v143 aThe present paper is devoted to weighted nonlinear Schrödinger–Poisson systems with potentials possibly unbounded and vanishing at infinity. Using a purely variational approach, we prove the existence of solutions concentrating on a circle.

1 aBonheure, Denis1 aDi Cosmo, Jonathan1 aMercuri, Carlo uhttps://doi.org/10.1142/S021919971250009501031nas a2200133 4500008004100000245009200041210006900133260002100202300001400223490000700237520058100244100002300825856004900848 2012 eng d00aConservation of Geometric Structures for Non-Homogeneous Inviscid Incompressible Fluids0 aConservation of Geometric Structures for NonHomogeneous Inviscid bTaylor & Francis a1553-15950 v373 aIn this article we get a result on propagation of geometric properties for solutions of the non-homogeneous incompressible Euler system in any dimension N ≥ 2. In particular, we investigate conservation of striated and conormal regularity, which generalize the 2-D structure of vortex patches. The results we get are only local in time, even for N = 2; however, we provide an explicit lower bound for the lifespan of the solution. In the case of physical dimension N = 2 or 3, we investigate also propagation of Hölder regularity in the interior of a bounded domain.

1 aFanelli, Francesco uhttps://doi.org/10.1080/03605302.2012.69834300925nas a2200121 4500008004100000245010900041210006900150260001300219520049100232100002500723700001900748856003600767 2012 en d00aConvergence of equilibria of thin elastic plates under physical growth conditions for the energy density0 aConvergence of equilibria of thin elastic plates under physical bElsevier3 aThe asymptotic behaviour of the equilibrium configurations of a thin elastic plate is studied, as the thickness $h$ of the plate goes to zero. More precisely, it is shown that critical points of the nonlinear elastic functional $\mathcal E^h$, whose energies (per unit thickness) are bounded by $Ch^4$, converge to critical points of the $\Gamma$-limit of $h^{-4}\mathcal E^h$. This is proved under the physical assumption that the energy density $W(F)$ blows up as $\det F\to0$.

1 aMora, Maria Giovanna1 aScardia, Lucia uhttp://hdl.handle.net/1963/346601015nas a2200109 4500008004100000245004300041210004300084260001300127520070800140100002100848856003600869 2012 en d00aConvex pencils of real quadratic forms0 aConvex pencils of real quadratic forms bSpringer3 aWe study the topology of the set X of the solutions of a system of two quadratic inequalities in the real projective space RP^n (e.g. X is the intersection of two real quadrics). We give explicit formulae for its Betti numbers and for those of its double cover in the sphere S^n; we also give similar formulae for level sets of homogeneous quadratic maps to the plane. We discuss some applications of these results, especially in classical convexity theory. We prove the sharp bound b(X)\leq 2n for the total Betti number of X; we show that for odd n this bound is attained only by a singular X. In the nondegenerate case we also prove the bound on each specific Betti number b_k(X)\leq 2(k+2).1 aLerario, Antonio uhttp://hdl.handle.net/1963/709901915nas a2200121 4500008004100000245008100041210006900122260001300191520151100204100002201715700002001737856003601757 2012 en d00aCrawling motility through the analysis of model locomotors: two case studies0 aCrawling motility through the analysis of model locomotors two c bSpringer3 aWe study model locomotors on a substrate, which derive their propulsive capabilities from the tangential (viscous or frictional) resistance offered by the substrate. Our aim is to develop new tools and insight for future studies of cellular motility by crawling and of collective bacterial motion. The purely viscous case (worm) is relevant for cellular motility by crawling of individual cells. We re-examine some recent results on snail locomotion in order to assess the role of finely regulated adhesion mechanisms in crawling motility. Our main conclusion is that such regulation, although well documented in several biological systems, is not indispensable to accomplish locomotion driven by internal deformations, provided that the crawler may execute sufficiently large body deformations. Thus, there is no snail theorem. Namely, the crawling analog of the scallop theorem of low Reynolds number hydrodynamics does not hold for snail-like crawlers. The frictional case is obtained by assuming that the viscous coefficient governing tangential resistance forces, which act parallel and in the direction opposite to the velocity of the point to which they are applied, depends on the normal force acting at that point. We combine these surface interactions with inertial effects in order to investigate the mechanisms governing the motility of a bristle-robot. This model locomotor is easily manufactured and has been proposed as an effective tool to replicate and study collective bacterial motility.1 aDeSimone, Antonio1 aTatone, Amabile uhttp://hdl.handle.net/1963/701700864nas a2200121 4500008004100000245008100041210006900122260001000191520046700201100002000668700001800688856003600706 2012 en d00aOn the critical behavior in nonlinear evolutionary PDEs with small viscocity0 acritical behavior in nonlinear evolutionary PDEs with small visc bSISSA3 aWe address the problem of general dissipative regularization of the quasilinear transport equation. We argue that the local behavior of solutions to the regularized equation near the point of gradient catastrophe for the transport equation is described by the logarithmic derivative of the Pearcey function, a statement generalizing the result of A.M.Il\\\'in \\\\cite{ilin}. We provide some analytic arguments supporting such conjecture and test it numerically.1 aDubrovin, Boris1 aElaeva, Maria uhttp://hdl.handle.net/1963/646501414nas a2200145 4500008004100000245008300041210006900124260002800193520092600221100002001147700002201167700002101189700002201210856003601232 2012 en d00aDecompositions of large-scale biological systems based on dynamical properties0 aDecompositions of largescale biological systems based on dynamic bOxford University Press3 aMOTIVATION: Given a large-scale biological network represented as an influence graph, in this article we investigate possible decompositions of the network aimed at highlighting specific dynamical properties.\\r\\nRESULTS: The first decomposition we study consists in finding a maximal directed acyclic subgraph of the network, which dynamically corresponds to searching for a maximal open-loop subsystem of the given system. Another dynamical property investigated is strong monotonicity. We propose two methods to deal with this property, both aimed at decomposing the system into strongly monotone subsystems, but with different structural characteristics: one method tends to produce a single large strongly monotone component, while the other typically generates a set of smaller disjoint strongly monotone subsystems.\\r\\nAVAILABILITY: Original heuristics for the methods investigated are described in the article.1 aSoranzo, Nicola1 aRamezani, Fahimeh1 aIacono, Giovanni1 aAltafini, Claudio uhttp://hdl.handle.net/1963/522602150nas a2200157 4500008004100000245008500041210006900126260003000195520152900225653003001754100003001784700002301814700001901837700002001856856011601876 2012 en d00aDeformed Lorentz symmetry and relative locality in a curved/expanding spacetime0 aDeformed Lorentz symmetry and relative locality in a curvedexpan bAmerican Physical Society3 aThe interest of part of the quantum-gravity community in the possibility of\r\nPlanck-scale-deformed Lorentz symmetry is also fueled by the opportunities for testing the relevant scenarios with analyses, from a signal-propagation perspective, of observations of bursts of particles from cosmological distances. In this respect the fact that so far the implications of deformed Lorentz symmetry have been investigated only for flat (Minkowskian) spacetimes represents a very significant limitation, since for propagation over cosmological distances the curvature/expansion of spacetime is evidently tangible. We here provide a significant step toward filling this gap by exhibiting an explicit example of Planck-scale-deformed relativistic symmetries of a spacetime with constant rate of expansion (deSitterian). Technically we obtain the first ever example of a relativistic theory of worldlines of particles with 3 nontrivial relativistic invariants: a large speed scale (\"speed-of-light scale\"), a large distance scale (inverse of the \"expansion-rate scale\"), and a large momentum scale (\"Planck scale\"). We address some of the challenges that had obstructed success for previous attempts by exploiting the recent understanding of the connection between deformed Lorentz symmetry and relativity of spacetime locality. We also offer a preliminary analysis of the differences between the scenario we here propose and the most studied scenario for broken (rather than deformed) Lorentz symmetry in expanding spacetimes.10aDoubly special relativity1 aAmelino-Camelia, Giovanni1 aMarciano, Antonino1 aMatassa, Marco1 aRosati, Giacomo uhttps://www.math.sissa.it/publication/deformed-lorentz-symmetry-and-relative-locality-curvedexpanding-spacetime02153nas a2200181 4500008004100000245015200041210006900193260001000262520154500272100001101817700002101828700001601849700001501865700001401880700001901894700002201913856003601935 2012 en d00aDetection of transcriptional triggers in the dynamics of microbial growth: application to the respiratory-versatile bacterium Shewanella oneidensis0 aDetection of transcriptional triggers in the dynamics of microbi bSISSA3 aThe capacity of microorganisms to respond to variable external conditions requires a coordination of environment-sensing mechanisms and decisionmaking regulatory circuits. Here, we seek to understand the interplay between these two processes by combining high-throughput measurement of time-dependent mRNA profiles with a novel computational approach that searches for key genetic triggers of transcriptional changes. Our approach helped us understand the regulatory strategies of a respiratorily versatile bacterium with promising bioenergy and bioremediation applications, Shewanella oneidensis, in minimal and rich media. By comparing expression profiles across these two conditions, we unveiled components of the transcriptional program that depend mainly on the growth phase. Conversely, by integrating our time-dependent data with a previously available large compendium of static perturbation responses, we identified transcriptional changes that cannot be explained solely by internal network dynamics, but are rather triggered by specific genes acting as key mediators of an environment-dependent response. These transcriptional triggers include known and novel regulators that respond to carbon, nitrogen and oxygen limitation. Our analysis suggests a sequence of physiological responses, including a coupling between nitrogen depletion and glycogen storage, partially recapitulated through dynamic flux balance analysis, and experimentally confirmed by metabolite measurements. Our approach is broadly applicable to other systems1 aBeg, Q1 aZampieri, Mattia1 aKlitgord, N1 aCollins, S1 aSerres, M1 aSegrè, Daniel1 aAltafini, Claudio uhttp://hdl.handle.net/1963/650601693nas a2200157 4500008004100000245008400041210006900125260003400194520117300228100002201401700002001423700001701443700001701460700002201477856003601499 2012 en d00aA dynamical feedback model for adaptation in the olfactory transduction pathway0 adynamical feedback model for adaptation in the olfactory transdu bBiophysical Society, Elsevier3 aOlfactory transduction exhibits two distinct types of adaptation, which we denote multipulse and step adaptation. In terms of measured transduction current, multipulse adaptation appears as a decrease in the amplitude of the second of two consecutive responses when the olfactory neuron is stimulated with two brief pulses. Step adaptation occurs in response to a sustained steplike stimulation and is characterized by a return to a steady-state current amplitude close to the prestimulus value, after a transient peak. In this article, we formulate a dynamical model of the olfactory transduction pathway, which includes the kinetics of the CNG channels, the concentration of Ca ions flowing through them, and the Ca-complexes responsible for the regulation. Based on this model, a common dynamical explanation for the two types of adaptation is suggested. We show that both forms of adaptation can be well described using different time constants for the kinetics of Ca ions (faster) and the kinetics of the feedback mechanisms (slower). The model is validated on experimental data collected in voltage-clamp conditions using different techniques and animal species.1 aDe Palo, Giovanna1 aBoccaccio, Anna1 aMiri, Andrew1 aMenini, Anna1 aAltafini, Claudio uhttp://hdl.handle.net/1963/701901344nas a2200109 4500008004100000245007300041210006900114260000900183520098400192100002201176856003601198 2012 en d00aDynamics of opinion forming in structurally balanced social networks0 aDynamics of opinion forming in structurally balanced social netw bPLoS3 aA structurally balanced social network is a social community that splits into two antagonistic factions (typical example being a two-party political system). The process of opinion forming on such a community is most often highly predictable, with polarized opinions reflecting the bipartition of the network. The aim of this paper is to suggest a class of dynamical systems, called monotone systems, as natural models for the dynamics of opinion forming on structurally balanced social networks. The high predictability of the outcome of a decision process is explained in terms of the order-preserving character of the solutions of this class of dynamical systems. If we represent a social network as a signed graph in which individuals are the nodes and the signs of the edges represent friendly or hostile relationships, then the property of structural balance corresponds to the social community being splittable into two antagonistic factions, each containing only friends.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/605101741nas a2200133 4500008004100000245007700041210006900118260001000187520130700197100002401504700002101528700002201549856003601571 2012 en d00aExploring the low-energy landscape of large-scale signed social networks0 aExploring the lowenergy landscape of largescale signed social ne bSISSA3 aAnalogously to a spin glass, a large-scale signed social network is characterized by the presence of disorder, expressed in this context (and in the social network literature) by the concept of structural balance. If, as we have recently shown, the signed social networks currently available have a limited amount of true disorder (or frustration), it is also interesting to investigate how this frustration is organized, by exploring the landscape of near-optimal structural balance. What we obtain in this paper is that while one of the networks analyzed shows a unique valley of minima, and a funneled landscape that gradually and smoothly worsens as we move away from the optimum, another network shows instead several distinct valleys of optimal or near-optimal structural balance, separated by energy barriers determined by internally balanced subcommunities of users, a phenomenon similar to the replica-symmetry breaking of spin glasses. Multiple, essentially isoenergetic, arrangements of these communities are possible. Passing from one valley to another requires one to destroy the internal arrangement of these balanced subcommunities and then to reform it again. It is essentially this process of breaking the internal balance of the subcommunities which gives rise to the energy barriers.1 aFacchetti, Giuseppe1 aIacono, Giovanni1 aAltafini, Claudio uhttp://hdl.handle.net/1963/650401179nas a2200133 4500008004100000245006000041210005500101260001000156520076500166653004100931100001600972700002100988856003601009 2012 en d00aA formula for Popp\'s volume in sub-Riemannian geometry0 aformula for Popps volume in subRiemannian geometry bSISSA3 aFor an equiregular sub-Riemannian manifold M, Popp\'s volume is a smooth\r\nvolume which is canonically associated with the sub-Riemannian structure, and\r\nit is a natural generalization of the Riemannian one. In this paper we prove a\r\ngeneral formula for Popp\'s volume, written in terms of a frame adapted to the\r\nsub-Riemannian distribution. As a first application of this result, we prove an\r\nexplicit formula for the canonical sub-Laplacian, namely the one associated\r\nwith Popp\'s volume. Finally, we discuss sub-Riemannian isometries, and we prove\r\nthat they preserve Popp\'s volume. We also show that, under some hypotheses on\r\nthe action of the isometry group of M, Popp\'s volume is essentially the unique\r\nvolume with such a property.10asubriemannian, volume, Popp, control1 aRizzi, Luca1 aBarilari, Davide uhttp://hdl.handle.net/1963/650100484nas a2200133 4500008004100000022001400041245009400055210006900149300001400218490000800232100001900240700002000259856007100279 2012 eng d a0010-361600aFredholm determinants and pole-free solutions to the noncommutative Painlevé II equation0 aFredholm determinants and polefree solutions to the noncommutati a793–8330 v3091 aBertola, Marco1 aCafasso, Mattia uhttp://0-dx.doi.org.mercury.concordia.ca/10.1007/s00220-011-1383-x00909nas a2200109 4500008004100000245007800041210006900119260001300188520054100201100002100742856003600763 2012 en d00aFrobenius manifold for the dispersionless Kadomtsev-Petviashvili equation0 aFrobenius manifold for the dispersionless KadomtsevPetviashvili bSpringer3 aWe consider a Frobenius structure associated with the dispersionless\\r\\nKadomtsev-Petviashvili equation. This is done, essentially, by applying a\\r\\ncontinuous analogue of the finite dimensional theory in the space of Schwartz\\r\\nfunctions on the line. The potential of the Frobenius manifold is found to be a\\r\\nlogarithmic potential with quadratic external field. Following the construction\\r\\nof the principal hierarchy, we construct a set of infinitely many commuting\\r\\nflows, which extends the classical dKP hierarchy.1 aRaimondo, Andrea uhttp://hdl.handle.net/1963/604001763nas a2200169 4500008004100000245010700041210006900148260001000217520118200227653002601409653002901435653003501464100001701499700001701516700002401533856003601557 2012 en d00aA Fully Coupled Immersed Finite Element Method for Fluid Structure Interaction via the Deal.II Library0 aFully Coupled Immersed Finite Element Method for Fluid Structure bSISSA3 aWe present the implementation of a solution scheme for fluid-structure\\r\\ninteraction problems via the finite element software library deal.II. The\\r\\nsolution scheme is an immersed finite element method in which two independent discretizations are used for the fluid and immersed deformable body. In this type of formulation the support of the equations of motion of the fluid is extended to cover the union of the solid and fluid domains. The equations of motion over the extended solution domain govern the flow of a fluid under the action of a body force field. This body force field informs the fluid of the presence of the immersed solid. The velocity field of the immersed solid is the restriction over the immersed domain of the velocity field in the extended equations of motion. The focus of this paper is to show how the determination of the motion of the immersed domain is carried out in practice. We show that our implementation is general, that is, it is not dependent on a specific choice of the finite element spaces over the immersed solid and the extended fluid domains. We present some preliminary results concerning the accuracy of the proposed method.10aFinite Element Method10aImmersed Boundary Method10aImmersed Finite Element Method1 aHeltai, Luca1 aRoy, Saswati1 aCostanzo, Francesco uhttp://hdl.handle.net/1963/625500456nas a2200133 4500008004100000245006900041210006700110260001300177653003000190100001800220700002100238700002700259856003600286 2012 en d00aGamma-convergence and H-convergence of linear elliptic operators0 aGammaconvergence and Hconvergence of linear elliptic operators bElsevier10aLinear elliptic operators1 aAnsini, Nadia1 aDal Maso, Gianni1 aZeppieri, Caterina Ida uhttp://hdl.handle.net/1963/587800922nas a2200133 4500008004100000245007400041210006900115260001000184520049000194100002000684700002400704700002400728856003600752 2012 en d00aGauge Theories on ALE Space and Super Liouville Correlation Functions0 aGauge Theories on ALE Space and Super Liouville Correlation Func bSISSA3 aWe present a relation between N=2 quiver gauge theories on the ALE space O_{P^1}(-2) and correlators of N=1 super Liouville conformal field theory, providing checks in the case of punctured spheres and tori. We derive a blow-up formula for the full Nekrasov partition function and show that, up to a U(1) factor, the N=2^* instanton partition function is given by the product of the character of \\\\hat{SU}(2)_2 times the super Virasoro conformal block on the torus with one puncture.1 aBonelli, Giulio1 aMaruyoshi, Kazunobu1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/430501004nas a2200169 4500008004100000022001400041245009800055210006900153300001600222490000800238520043000246653002300676653002300699100002200722700001900744856007100763 2012 eng d a0022-039600aA general method for the existence of periodic solutions of differential systems in the plane0 ageneral method for the existence of periodic solutions of differ a1369 - 13910 v2523 aWe propose a general method to prove the existence of periodic solutions for planar systems of ordinary differential equations, which can be used in many different circumstances. Applications are given to some nonresonant cases, even for systems with superlinear growth in some direction, or with a singularity. Systems “at resonance” are also considered, provided a Landesman–Lazer type of condition is assumed.

10aNonlinear dynamics10aPeriodic solutions1 aFonda, Alessandro1 aSfecci, Andrea uhttp://www.sciencedirect.com/science/article/pii/S002203961100319601643nas a2200157 4500008004100000245012600041210006900167260001300236520109700249653002201346100001801368700002001386700002201406700002101428856003601449 2012 en d00aGeneralized reduced basis methods and n-width estimates for the approximation of the solution manifold of parametric PDEs0 aGeneralized reduced basis methods and nwidth estimates for the a bSpringer3 aThe set of solutions of a parameter-dependent linear partial di fferential equation with smooth coe fficients typically forms a compact manifold in a Hilbert space. In this paper we review the generalized reduced basis method as a fast computational tool for the uniform approximation of the solution manifold. We focus on operators showing an affi ne parametric dependence, expressed as a linear combination of parameter-independent operators through some smooth, parameter-dependent scalar functions. In the case that the parameter-dependent operator has a dominant term in its affi ne expansion, one can prove the existence of exponentially convergent uniform approximation spaces for the entire solution manifold. These spaces can be constructed without any assumptions on the parametric regularity of the manifold \\r\\nonly spatial regularity of the solutions is required. The exponential convergence rate is then inherited by the generalized reduced basis method. We provide a numerical example related to parametrized elliptic\\r\\nequations con rming the predicted convergence rates.10asolution manifold1 aLassila, Toni1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://hdl.handle.net/1963/634000982nas a2200133 4500008004100000245007000041210006300111260001000174520057500184100002000759700001500779700001800794856003600812 2012 en d00aOn the genus two free energies for semisimple Frobenius manifolds0 agenus two free energies for semisimple Frobenius manifolds bSISSA3 aWe represent the genus two free energy of an arbitrary semisimple Frobenius\\r\\nmanifold as a sum of contributions associated with dual graphs of certain\\r\\nstable algebraic curves of genus two plus the so-called \\\"genus two G-function\\\".\\r\\nConjecturally the genus two G-function vanishes for a series of important\\r\\nexamples of Frobenius manifolds associated with simple singularities as well as\\r\\nfor ${\\\\bf P}^1$-orbifolds with positive Euler characteristics. We explain the\\r\\nreasons for such Conjecture and prove it in certain particular cases.1 aDubrovin, Boris1 aLiu, Si-Qi1 aZhang, Youjin uhttp://hdl.handle.net/1963/646401194nas a2200133 4500008004100000245005500041210004700096260001000143520080800153100002500961700002100986700001701007856003601024 2012 en d00aOn the Hausdorff volume in sub-Riemannian geometry0 aHausdorff volume in subRiemannian geometry bSISSA3 aFor a regular sub-Riemannian manifold we study the Radon-Nikodym derivative\r\nof the spherical Hausdorff measure with respect to a smooth volume. We prove\r\nthat this is the volume of the unit ball in the nilpotent approximation and it\r\nis always a continuous function. We then prove that up to dimension 4 it is\r\nsmooth, while starting from dimension 5, in corank 1 case, it is C^3 (and C^4\r\non every smooth curve) but in general not C^5. These results answer to a\r\nquestion addressed by Montgomery about the relation between two intrinsic\r\nvolumes that can be defined in a sub-Riemannian manifold, namely the Popp and\r\nthe Hausdorff volume. If the nilpotent approximation depends on the point (that\r\nmay happen starting from dimension 5), then they are not proportional, in\r\ngeneral.1 aAgrachev, Andrei, A.1 aBarilari, Davide1 aBoscain, Ugo uhttp://hdl.handle.net/1963/645401971nas 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-experiment00389nas a2200121 4500008004100000245005900041210005800100260001000158100002500168700002100193700001700214856003600231 2012 en d00aIntroduction to Riemannian and sub-Riemannian geometry0 aIntroduction to Riemannian and subRiemannian geometry bSISSA1 aAgrachev, Andrei, A.1 aBarilari, Davide1 aBoscain, Ugo uhttp://hdl.handle.net/1963/587701113nas a2200133 4500008004100000245006400041210005900105260002800164520069000192653002700882100001600909700001800925856003600943 2012 en d00aThe KdV hierarchy: universality and a Painleve transcendent0 aKdV hierarchy universality and a Painleve transcendent bOxford University Press3 aWe study the Cauchy problem for the Korteweg-de Vries (KdV) hierarchy in the small dispersion limit where $\e\to 0$. For negative analytic initial data with a single negative hump, we prove that for small times, the solution is approximated by the solution to the hyperbolic transport equation which corresponds to $\e=0$. Near the time of gradient catastrophe for the transport equation, we show that the solution to the KdV hierarchy is approximated by a particular Painlev\'e transcendent. This supports Dubrovins universality conjecture concerning the critical behavior of Hamiltonian perturbations of hyperbolic equations. We use the Riemann-Hilbert approach to prove our results.10aSmall-Dispersion limit1 aClaeys, Tom1 aGrava, Tamara uhttp://hdl.handle.net/1963/692100709nas a2200169 4500008004100000245011000041210006900151260003000220300001200250490000700262520014000269653002500409100002600434700002100460700002200481856003600503 2012 en d00aLinear elasticity obtained from finite elasticity by Gamma-convergence under weak coerciveness conditions0 aLinear elasticity obtained from finite elasticity by Gammaconver bGauthier-Villars;Elsevier a715-7350 v293 aThe energy functional of linear elasticity is obtained as G-limit of suitable rescalings of the energies of finite elasticity...

10aNonlinear elasticity1 aAgostiniani, Virginia1 aDal Maso, Gianni1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/426700646nas a2200133 4500008004100000245005800041210005500099260001300154520025200167653001900419100001600438700002200454856003600476 2012 en d00aOn localization in holomorphic equivariant cohomology0 alocalization in holomorphic equivariant cohomology bSpringer3 aWe prove a localization formula for a "holomorphic equivariant cohomology" attached to the Atiyah algebroid of an equivariant holomorphic vector bundle. This generalizes Feng-Ma, Carrell-Liebermann, Baum-Bott and K. Liu's localization formulas.10aLie algebroids1 aBruzzo, Ugo1 aRubtsov, Vladimir uhttp://hdl.handle.net/1963/658400466nas a2200121 4500008004100000022001400041245010500055210006900160300001600229490000700245100001900252856007300271 2012 eng d a0951-771500aOn the location of poles for the Ablowitz-Segur family of solutions to the second Painlevé equation0 alocation of poles for the AblowitzSegur family of solutions to t a1179–11850 v251 aBertola, Marco uhttp://0-dx.doi.org.mercury.concordia.ca/10.1088/0951-7715/25/4/117901914nas a2200145 4500008004100000020001800041245010100059210006900160260003100229520140500260653002201665100002301687700002201710856003601732 2012 en d a978160511380700aMathematical and numerical modeling of liquid crystal elastomer phase transition and deformation0 aMathematical and numerical modeling of liquid crystal elastomer bCambridge University Press3 aLiquid crystal (in particular, nematic) elastomers consist of cross-linked flexible polymer chains with embedded stiff rod molecules that allow them to behave as a rubber and a liquid crystal. Nematic elastomers are characterized by a phase transition from isotropic to nematic past a temperature threshold. They behave as rubber at high temperature and show nematic behavior below the temperature threshold. Such transition is reversible. While in the nematic phase, the rod molecules are aligned along the direction of the "nematic director". This molecular rearrangement induces a stretch in the polymer chains and hence macroscopic spontaneous deformations. The coupling between nematic order parameter and deformation gives rise to interesting phenomena with a potential for new interesting applications. In the biological field, the ability to considerably change their length makes them very promising as artificial muscles actuators. Their tunable optical properties make them suitable, for example, as lenses for new imaging systems. We present a mathematical model able to describe the behavior of nematic elastomers and numerical simulations reproducing such peculiar behavior. We use a geometrically linear version of the Warner and Terentjev model [1] and consider cooling experiments and stretching experiments in the direction perpendicular to the one of the director at cross-linking.10aArtificial muscle1 aDe Luca, Mariarita1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/702001486nas a2200121 4500008004100000245006100041210006000102260005400162520106700216100002201283700002301305856003601328 2012 en d00aModeling and control of quantum systems: An introduction0 aModeling and control of quantum systems An introduction bInstitute of Electrical and Electronics Engineers3 aThe scope of this work is to provide a self-contained introduction to a selection of basic theoretical aspects in the modeling and control of quantum mechanical systems, as well as a brief survey on the main approaches to control synthesis. While part of the existing theory, especially in the open-loop setting, stems directly from classical control theory (most notably geometric control and optimal control), a number of tools specifically tailored for quantum systems have been developed since the 1980s, in order to take into account their distinctive features: the probabilistic nature of atomic-scale physical systems, the effect of dissipation and the irreversible character of the measurements have all proved to be critical in feedback-design problems. The relevant dynamical models for both closed and open quantum systems are presented, along with the main results on their controllability and stability. A brief review of several currently available control design methods is meant to provide the interested reader with a roadmap for further studies1 aAltafini, Claudio1 aTicozzi, Francesco uhttp://hdl.handle.net/1963/650500979nas a2200133 4500008004100000245010200041210006900143260001000212520051900222100001600741700002600757700002600783856003600809 2012 en d00aModuli of symplectic instanton vector bundles of higher rank on projective space $\\mathbb{P}^3$0 aModuli of symplectic instanton vector bundles of higher rank on bSISSA3 aSymplectic instanton vector bundles on the projective space $\\mathbb{P}^3$ constitute a natural generalization of mathematical instantons of rank 2. We study the moduli space $I_{n,r}$ of rank-$2r$ symplectic instanton vector bundles on $\\mathbb{P}^3$ with $r\\ge2$ and second Chern class $n\\ge r,\\ n\\equiv r({\\rm mod}2)$. We give an explicit construction of an irreducible component $I^*_{n,r}$ of this space for each such value of $n$ and show that $I^*_{n,r}$ has the expected dimension $4n(r+1)-r(2r+1)$.1 aBruzzo, Ugo1 aMarkushevich, Dimitri1 aTikhomirov, Alexander uhttp://hdl.handle.net/1963/465601072nas a2200121 4500008004300000245008700043210006900130260002800199520065000227100001700877700002000894856003600914 2012 en_Ud 00aModuli spaces of noncommutative instantons: gauging away noncommutative parameters0 aModuli spaces of noncommutative instantons gauging away noncommu bOxford University Press3 aUsing the theory of noncommutative geometry in a braided monoidal category, we improve upon a previous construction of noncommutative families of instantons of arbitrary charge on the deformed sphere S^4_\\\\theta. We formulate a notion of noncommutative parameter spaces for families of instantons and we explore what it means for such families to be gauge equivalent, as well as showing how to remove gauge parameters using a noncommutative quotient construction. Although the parameter spaces are a priori noncommutative, we show that one may always recover a classical parameter space by making an appropriate choice of gauge transformation.1 aBrain, Simon1 aLandi, Giovanni uhttp://hdl.handle.net/1963/377700591nas a2200145 4500008004100000022001400041245003800055210003400093260000800127300001400135490000700149520022100156100002200377856004600399 2012 eng d a1432-083500aThe Monge problem in Wiener space0 aMonge problem in Wiener space cSep a101–1240 v453 aWe address the Monge problem in the abstract Wiener space and we give an existence result provided both marginal measures are absolutely continuous with respect to the infinite dimensional Gaussian measure γ.

1 aCavalletti, Fabio uhttps://doi.org/10.1007/s00526-011-0452-500826nas 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/1963/410401058nas a2200181 4500008004100000022001400041245009000055210006900145300001600214490000700230520047800237653002000715653001700735653002100752653001300773100001900786856007100805 2012 eng d a0362-546X00aA nonresonance condition for radial solutions of a nonlinear Neumann elliptic problem0 anonresonance condition for radial solutions of a nonlinear Neuma a6191 - 62020 v753 aWe prove an existence result for radial solutions of a Neumann elliptic problem whose nonlinearity asymptotically lies between the first two eigenvalues. To this aim, we introduce an alternative nonresonance condition with respect to the second eigenvalue which, in the scalar case, generalizes the classical one, in the spirit of Fonda et al. (1991) [2]. Our approach also applies for nonlinearities which do not necessarily satisfy a subcritical growth assumption.

10aNeumann problem10aNonresonance10aRadial solutions10aTime-map1 aSfecci, Andrea uhttp://www.sciencedirect.com/science/article/pii/S0362546X1200265901662nas a2200121 4500008004100000245009600041210006900137260001300206520124300219100002001462700002201482856003601504 2012 en d00aNon-uniqueness results for critical metrics of regularized determinants in four dimensions0 aNonuniqueness results for critical metrics of regularized determ bSpringer3 aThe regularized determinant of the Paneitz operator arises in quantum gravity (see Connes 1994, IV.4.$\gamma$). An explicit formula for the relative determinant of two conformally related metrics was computed by Branson in Branson (1996). A similar formula holds for Cheeger's half-torsion, which plays a role in self-dual field theory (see Juhl, 2009), and is defined in terms of regularized determinants of the Hodge laplacian on $p$-forms ($p < n/2$). In this article we show that the corresponding actions are unbounded (above and below) on any conformal four-manifold. We also show that the conformal class of the round sphere admits a second solution which is not given by the pull-back of the round metric by a conformal map, thus violating uniqueness up to gauge equivalence. These results differ from the properties of the determinant of the conformal Laplacian established in Chang and Yang (1995), Branson, Chang, and Yang (1992), and Gursky (1997). We also study entire solutions of the Euler-Lagrange equation of $\log \det P$ and the half-torsion $\tau_h$ on $\mathbb{R}^4 \setminus {0}$, and show the existence of two families of periodic solutions. One of these families includes Delaunay-type solutions.1 aGursky, Matthew1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/655901861nas a2200145 4500008004100000245007600041210006900117260001300186520138500199653002701584100002001611700002101631700002701652856003601679 2012 en d00aNumerical modelling of installation effects for diaphragm walls in sand0 aNumerical modelling of installation effects for diaphragm walls bSpringer3 aThe scopes of this work are to study the mechanisms of load transfer and the deformations of the ground during slurry trenching and concreting in dry sand and to evaluate their effects on service structural loads, wall deflections and ground displacements behind the wall caused by subsequent excavation. A series of three-dimensional finite element analyses was carried out modelling the installation of diaphragm walls consisting of panels of different length. The soil was modelled as either linearly elastic-perfectly plastic or incrementally non-linear (hypoplastic) with elastic strain range. Plane strain analyses of diaphragm walls of identical cross section were also carried out in which wall installation was either modelled or the wall was wished in place (WIP). The analyses predict ground movements consistent with the experimental observations both in magnitude and trend. The results also show that the maximum horizontal wall deflections and structural loads reduce with increasing panel aspect ratio towards a minimum which is about twice the value computed for WIP analyses. Panel aspect ratios should be larger than about three to take advantage of the three-dimensional effects. The pattern and magnitude of surface vertical displacements obtained from linearly elastic-perfectly plastic analyses, no matter whether three- or two-dimensional, are unrealistic.10aConstitutive relations1 aConti, Riccardo1 ade Sanctis, Luca1 aViggiani, Giulia, M.B. uhttp://hdl.handle.net/1963/693400918nas a2200133 4500008004100000245011000041210006900151260001300220520035800233653003100591100001800622700002100640856012300661 2012 en d00aNumerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions0 aNumerical study of the small dispersion limit of the Kortewegde bElsevier3 aWe study numerically the small dispersion limit for the Korteweg-de Vries (KdV) equation $u_t+6uu_x+\epsilon^{2}u_{xxx}=0$ for $\epsilon\ll1$ and give a quantitative comparison of the numerical solution with various asymptotic formulae for small $\epsilon$ in the whole $(x,t)$-plane. The matching of the asymptotic solutions is studied numerically.10aKorteweg-de Vries equation1 aGrava, Tamara1 aKlein, Christian uhttps://www.math.sissa.it/publication/numerical-study-small-dispersion-limit-korteweg-de-vries-equation-and-asymptotic01684nas a2200157 4500008004100000245004700041210004600088260001300134300001200147490000700159520120600166653002501372100002601397700002201423856008101445 2012 en d00aOgden-type energies for nematic elastomers0 aOgdentype energies for nematic elastomers bElsevier a402-4120 v473 aOgden-type extensions of the free-energy densities currently used to model the mechanical behavior of nematic elastomers are proposed and analyzed. Based on a multiplicative decomposition of the deformation gradient into an elastic and a spontaneous or remanent part, they provide a suitable framework to study the stiffening response at high imposed stretches. Geometrically linear versions of the models (Taylor expansions at order two) are provided and discussed. These small strain theories provide a clear illustration of the geometric structure of the underlying energy landscape (the energy grows quadratically with the distance from a non-convex set of spontaneous strains or energy wells). The comparison between small strain and finite deformation theories may also be useful in the opposite direction, inspiring finite deformation generalizations of small strain theories currently used in the mechanics of active and phase-transforming materials. The energy well structure makes the free-energy densities non-convex. Explicit quasi-convex envelopes are provided, and applied to compute the stiffening response of a specimen tested in plane strain extension experiments (pure shear).

10aNonlinear elasticity1 aAgostiniani, Virginia1 aDeSimone, Antonio uhttps://www.math.sissa.it/publication/ogden-type-energies-nematic-elastomers00559nas a2200121 4500008004100000245012000041210006900161260003700230300001400267490000700281100002300288856012600311 2012 eng d00aOne-signed harmonic solutions and sign-changing subharmonic solutions to scalar second order differential equations0 aOnesigned harmonic solutions and signchanging subharmonic soluti bAdvanced Nonlinear Studies, Inc. a445–4630 v121 aBoscaggin, Alberto uhttps://www.math.sissa.it/publication/one-signed-harmonic-solutions-and-sign-changing-subharmonic-solutions-scalar-second00376nas a2200109 4500008004100000245007700041210006900118300001200187490000700199100002200206856003800228 2012 eng d00aOptimal Transport with Branching Distance Costs and the Obstacle Problem0 aOptimal Transport with Branching Distance Costs and the Obstacle a454-4820 v441 aCavalletti, Fabio uhttps://doi.org/10.1137/10080143301215nas a2200193 4500008004100000022001400041245010000055210006900155300001600224490000800240520056000248653002000808653002500828653003200853653002300885100002300908700001900931856007100950 2012 eng d a0022-039600aPairs of positive periodic solutions of second order nonlinear equations with indefinite weight0 aPairs of positive periodic solutions of second order nonlinear e a2900 - 29210 v2523 aWe study the problem of the existence and multiplicity of positive periodic solutions to the scalar ODEu″+λa(t)g(u)=0,λ>0, where g(x) is a positive function on R+, superlinear at zero and sublinear at infinity, and a(t) is a T-periodic and sign indefinite weight with negative mean value. We first show the nonexistence of solutions for some classes of nonlinearities g(x) when λ is small. Then, using critical point theory, we prove the existence of at least two positive T-periodic solutions for λ large. Some examples are also provided.

10aCritical points10aNecessary conditions10aPairs of positive solutions10aPeriodic solutions1 aBoscaggin, Alberto1 aZanolin, Fabio uhttp://www.sciencedirect.com/science/article/pii/S002203961100389500499nas a2200133 4500008004100000245010300041210006900144260003300213300001500246490000700261100002200268700001900290856005600309 2012 eng d00aPeriodic solutions of a system of coupled oscillators with one-sided superlinear retraction forces0 aPeriodic solutions of a system of coupled oscillators with onesi bKhayyam Publishing, Inc.c11 a993–10100 v251 aFonda, Alessandro1 aSfecci, Andrea uhttps://projecteuclid.org:443/euclid.die/135601224800752nas a2200133 4500008004100000245006500041210006500106260005100171300001400222490000700236520025200243100002300495856010000518 2012 eng d00aPeriodic solutions to superlinear planar Hamiltonian systems0 aPeriodic solutions to superlinear planar Hamiltonian systems bEuropean Mathematical Society Publishing House a127–1410 v693 aWe prove the existence of infinitely many periodic (harmonic and subharmonic) solutions to planar Hamiltonian systems satisfying a suitable superlinearity condition at infinity. The proof relies on the Poincare-Birkhoff fixed point theorem.

1 aBoscaggin, Alberto uhttps://www.math.sissa.it/publication/periodic-solutions-superlinear-planar-hamiltonian-systems00782nas a2200121 4500008004100000245008600041210006900127260001300196520037000209653002400579100002100603856003600624 2012 en d00aPoles Distribution of PVI Transcendents close to a Critical Point (summer 2011)0 aPoles Distribution of PVI Transcendents close to a Critical Poin bElsevier3 aThe distribution of the poles of Painlevé VI transcendents associated to semi-simple Frobenius manifolds is determined close to a critical point. It is shown that the poles accumulate at the critical point,asymptotically along two rays. As an example, the Frobenius manifold given by the quantum cohomology of CP2 is considered. The general PVI is also considered.10aPainleve' equations1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/652601126nas a2200193 4500008004100000022001400041245013400055210006900189300001600258490000800274520044900282653002100731653001800752653003200770653001700802100002300819700001900842856007100861 2012 eng d a0022-039600aPositive periodic solutions of second order nonlinear equations with indefinite weight: Multiplicity results and complex dynamics0 aPositive periodic solutions of second order nonlinear equations a2922 - 29500 v2523 aWe prove the existence of a pair of positive T-periodic solutions as well as the existence of positive subharmonic solutions of any order and the presence of chaotic-like dynamics for the scalar second order ODEu″+aλ,μ(t)g(u)=0, where g(x) is a positive function on R+, superlinear at zero and sublinear at infinity, and aλ,μ(t) is a T-periodic and sign indefinite weight of the form λa+(t)−μa−(t), with λ,μ>0 and large.

10aComplex dynamics10aPoincaré map10aPositive periodic solutions10aSubharmonics1 aBoscaggin, Alberto1 aZanolin, Fabio uhttp://www.sciencedirect.com/science/article/pii/S002203961100388302201nas a2200133 4500008004100000245010400041210006900145260001900214520173100233100002401964700002201988700002102010856003602031 2012 en d00aPredicting and characterizing selective multiple drug treatments for metabolic diseases and cancer.0 aPredicting and characterizing selective multiple drug treatments bBioMed Central3 aBackground: In the field of drug discovery, assessing the potential of multidrug therapies is a difficult task because of the combinatorial complexity (both theoretical and experimental) and because of the requirements on the selectivity of the therapy. To cope with this problem, we have developed a novel method for the systematic in silico investigation of synergistic effects of currently available drugs on genome-scale metabolic networks. The algorithm finds the optimal combination of drugs which guarantees the inhibition of an objective function, while minimizing the side effect on the overall network. Results: Two different applications are considered: finding drug synergisms for human metabolic diseases (like diabetes, obesity and hypertension) and finding antitumoral drug combinations with minimal side effect on the normal human metabolism.The results we obtain are consistent with some of the available therapeutic indications and predict some new multiple drug treatments.A cluster analysis on all possible interactions among the currently available drugs indicates a limited variety on the metabolic targets for the approved drugs. Conclusion: The in silico prediction of drug synergism can represent an important tool for the repurposing of drug in a realistic perspective which considers also the selectivty of the therapy. Moreover, for a more profitable exploitation of drug-drug interactions, also drugs which show a too low efficacy but which have a non-common mechanism of action, can be reconsider as potential ingredients of new multicompound therapeutic indications.Needless to say the clues provided by a computational study like ours need in any case to be thoroughly evaluated experimentally.1 aFacchetti, Giuseppe1 aAltafini, Claudio1 aZampieri, Mattia uhttp://hdl.handle.net/1963/651501387nas a2200133 4500008004300000245008800043210006900131260001300200520093500213100002101148700002201169700002601191856003601217 2012 en_Ud 00aQuasistatic evolution for Cam-Clay plasticity: properties of the viscosity solution0 aQuasistatic evolution for CamClay plasticity properties of the v bSpringer3 aCam-Clay plasticity is a well established model for the description of the mechanics of fine grained soils. As solutions can develop discontinuities in time, a weak notion of solution, in terms of a rescaled time s , has been proposed in [8] to give a meaning to this discontinuous evolution. In this paper we first prove that this rescaled evolution satisfies the flow-rule for the rate of plastic strain, in a suitable measure-theoretical sense. In the second part of the paper we consider the behavior of the evolution in terms of the original time variable t . We prove that the unrescaled solution satisfies an energy-dissipation balance and an evolution law for the internal variable, which can be expressed in terms of integrals depending only on the original time. Both these integral identities contain terms concentrated on the jump times, whose size can only be determined by looking at the rescaled formulation.

1 aDal Maso, Gianni1 aDeSimone, Antonio1 aSolombrino, Francesco uhttp://hdl.handle.net/1963/390000946nas a2200145 4500008004100000245007300041210006900114260000900183520047100192653002200663100002900685700002500714700002500739856003600764 2012 en d00aQuasistatic evolution in non-associative plasticity - the cap models0 aQuasistatic evolution in nonassociative plasticity the cap model bSIAM3 aNon-associative elasto-plasticity is the working model of plasticity for soil and rocks mechanics. Yet, it is usually viewed as non-variational. In this work, we prove a contrario the existence of a variational evolution for such a model under a natural capping assumption on the hydrostatic stresses and a less natural mollification of the stress admissibility constraint. The obtained elasto-plastic evolution is expressed for times that are conveniently rescaled.10aElasto-plasticity1 aBabadjian, Jean-Francois1 aFrancfort, Gilles A.1 aMora, Maria Giovanna uhttp://hdl.handle.net/1963/413901651nas a2200133 4500008004100000245008400041210006900125520120500194653002101399100002101420700002001441700002001461856003601481 2012 en d00aReduction strategies for PDE-constrained oprimization problems in Haemodynamics0 aReduction strategies for PDEconstrained oprimization problems in3 aSolving optimal control problems for many different scenarios obtained by varying a set of parameters in the state system is a computationally extensive task. In this paper we present a new reduced framework for the formulation, the analysis and the numerical solution of parametrized PDE-constrained optimization problems. This framework is based on a suitable saddle-point formulation of the optimal control problem and exploits the reduced basis method for the rapid and reliable solution of parametrized PDEs, leading to a relevant computational reduction with respect to traditional discretization techniques such as the finite element method. This allows a very efficient evaluation of state solutions and cost functionals, leading to an effective solution of repeated optimal control problems, even on domains of variable shape, for which a further (geometrical) reduction is pursued, relying on flexible shape parametrization techniques. This setting is applied to the solution of two problems arising from haemodynamics, dealing with both data reconstruction and data assimilation over domains of variable shape,\\r\\nwhich can be recast in a common PDE-constrained optimization formulation.10ainverse problems1 aRozza, Gianluigi1 aManzoni, Andrea1 aNegri, Federico uhttp://hdl.handle.net/1963/633800498nas a2200121 4500008004100000245013300041210006900174260003300243300001400276490000700290100002300297856005600320 2012 eng d00aResonance at the first eigenvalue for first-order systems in the plane: vanishing Hamiltonians and the Landesman-Lazer condition0 aResonance at the first eigenvalue for firstorder systems in the bKhayyam Publishing, Inc.c05 a505–5260 v251 aGarrione, Maurizio uhttps://projecteuclid.org:443/euclid.die/135601267602076nas a2200145 4500008004100000245004700041210004700088520166300135653001801798100001901816700001701835700002001852700002201872856003601894 2012 en d00aReverse engineering the euglenoid movement0 aReverse engineering the euglenoid movement3 aEuglenids exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large-amplitude highly concerted deformations of the entire body (euglenoid movement or metaboly). A plastic cell envelope called pellicle mediates these deformations. Unlike ciliary or flagellar motility, the biophysics of this mode is not well understood, including its efficiency and molecular machinery. We quantitatively examine video recordings of four euglenids executing such motions with statistical learning methods. This analysis reveals strokes of high uniformity in shape and pace. We then interpret the observations in the light of a theory for the pellicle kinematics, providing a precise understanding of the link between local actuation by pellicle shear and shape control. We systematically understand common observations, such as the helical conformations of the pellicle, and identify previously unnoticed features of metaboly. While two of our euglenids execute their stroke at constant body volume, the other two exhibit deviations of about 20% from their average volume, challenging current models of low Reynolds number locomotion. We find that the active pellicle shear deformations causing shape changes can reach 340%, and estimate the velocity of the molecular motors. Moreover, we find that metaboly accomplishes locomotion at hydrodynamic efficiencies comparable to those of ciliates and flagellates. Our results suggest new quantitative experiments, provide insight into the evolutionary history of euglenids, and suggest that the pellicle may serve as a model for engineered active surfaces with applications in microfluidics.10amicroswimmers1 aArroyo, Marino1 aHeltai, Luca1 aMillán, Daniel1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/644400581nas a2200121 4500008004100000245004500041210004300086260001000129520024000139653002300379100002100402856003600423 2012 en d00aA Review on The Sixth Painlevé Equation0 aReview on The Sixth Painlevé Equation bSISSA3 aFor the Painlev\\\'e 6 transcendents, we provide a unitary description of the\r\ncritical behaviours, the connection formulae, their complete tabulation, and\r\nthe asymptotic distribution of the poles close to a critical point.

10aPainlevé equation1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/652500516nas a2200145 4500008004100000022001400041245008700055210007100142300001600213490000800229653002300237100001900260700002000279856007100299 2012 eng d a0167-278900aRiemann–Hilbert approach to multi-time processes: The Airy and the Pearcey cases0 aRiemann–Hilbert approach to multitime processes The Airy and the a2237 - 22450 v24110aIntegrable kernels1 aBertola, Marco1 aCafasso, Mattia uhttp://www.sciencedirect.com/science/article/pii/S016727891200011500821nas a2200121 4500008004100000245007700041210006900118520040700187100002500594700002300619700002100642856003600663 2012 en d00aOn robust Lie-algebraic stability conditions for switched linear systems0 arobust Liealgebraic stability conditions for switched linear sys3 aThis paper presents new sufficient conditions for exponential stability of switched linear systems under arbitrary switching, which involve the commutators (Lie brackets) among the given matrices generating the switched system. The main novelty feature of these stability criteria is that, unlike their earlier counterparts, they are robust with respect to small perturbations of the system parameters.1 aAgrachev, Andrei, A.1 aBaryshnikov, Yurij1 aLiberzon, Daniel uhttp://hdl.handle.net/1963/645500431nas a2200109 4500008004300000245011600043210006900159260001300228100002300241700002100264856003600285 2012 en_Ud 00aSBV regularity for genuinely nonlinear, strictly hyperbolic systems of conservation laws in one space dimension0 aSBV regularity for genuinely nonlinear strictly hyperbolic syste bSpringer1 aBianchini, Stefano1 aCaravenna, Laura uhttp://hdl.handle.net/1963/409100447nas a2200133 4500008004100000245008500041210006900126260001000195300001400205490000700219100002300226700001900249856004500268 2012 en d00aSBV regularity for Hamilton-Jacobi equations with Hamiltonian depending on (t,x)0 aSBV regularity for HamiltonJacobi equations with Hamiltonian dep bSISSA a2179-22030 v441 aBianchini, Stefano1 aTonon, Daniela uhttp://hdl.handle.net/20.500.11767/1406600755nas a2200121 4500008004100000245010500041210006900146260001300215520032300228653002300551100002300574856003600597 2012 en d00aSBV regularity of genuinely nonlinear hyperbolic systems of conservation laws in one space dimension0 aSBV regularity of genuinely nonlinear hyperbolic systems of cons bElsevier3 aThe problem of the presence of Cantor part in the derivative of a solution to a hyperbolic system of conservation laws is considered. An overview of the techniques involved in the proof is given, and a collection of related problems concludes the paper. Key words hyperbolic systems; conservation laws; SBV; regularity10aHyperbolic systems1 aBianchini, Stefano uhttp://hdl.handle.net/1963/653500509nas a2200121 4500008004100000245009900041210006900140300001400209490000700223100002300230700001200253856012200265 2012 eng d00aSBV-like regularity for general hyperbolic systems of conservation laws in one space dimension0 aSBVlike regularity for general hyperbolic systems of conservatio a439–4720 v441 aBianchini, Stefano1 aYu, Lei uhttps://www.math.sissa.it/publication/sbv-regularity-general-hyperbolic-systems-conservation-laws-one-space-dimension00441nas a2200133 4500008004100000245008000041210006900121260001000190300001200200490000800212100002300220700001900243856004500262 2012 en d00aSBV-like regularity for Hamilton-Jacobi equations with a convex Hamiltonian0 aSBVlike regularity for HamiltonJacobi equations with a convex Ha bSISSA a190-2080 v3911 aBianchini, Stefano1 aTonon, Daniela uhttp://hdl.handle.net/20.500.11767/1390901260nas a2200193 4500008004100000022001400041245008600055210006900141300000900210490000700219520060600226653002800832653002500860653002800885653002700913653002400940100002600964856007600990 2012 eng d a1078-094700aSecond order approximations of quasistatic evolution problems in finite dimension0 aSecond order approximations of quasistatic evolution problems in a11250 v323 aIn this paper, we study the limit, as ε goes to zero, of a particular solution of the equation $\epsilon^2A\ddot u^ε(t)+εB\dot u^ε(t)+\nabla_xf(t,u^ε(t))=0$, where $f(t,x)$ is a potential satisfying suitable coerciveness conditions. The limit $u(t)$ of $u^ε(t)$ is piece-wise continuous and verifies $\nabla_xf(t,u(t))=0$. Moreover, certain jump conditions characterize the behaviour of $u(t)$ at the discontinuity times. The same limit behaviour is obtained by considering a different approximation scheme based on time discretization and on the solutions of suitable autonomous systems.

10adiscrete approximations10aperturbation methods10asaddle-node bifurcation10aSingular perturbations10avanishing viscosity1 aAgostiniani, Virginia uhttp://aimsciences.org//article/id/560b82d9-f289-498a-a619-a4b132aaf9f801314nas a2200133 4500008004100000245005400041210005200095260002100147300001100168490000600179520092400185100002201109856004901131 2012 eng d00aSelf-propelled micro-swimmers in a Brinkman fluid0 aSelfpropelled microswimmers in a Brinkman fluid bTaylor & Francis a88-1030 v63 aWe prove an existence, uniqueness, and regularity result for the motion of a self-propelled micro-swimmer in a particulate viscous medium, modelled as a Brinkman fluid. A suitable functional setting is introduced to solve the Brinkman system for the velocity field and the pressure of the fluid by variational techniques. The equations of motion are written by imposing a self-propulsion constraint, thus allowing the viscous forces and torques to be the only ones acting on the swimmer. From an infinite-dimensional control on the shape of the swimmer, a system of six ordinary differential equations for the spatial position and the orientation of the swimmer is obtained. This is dealt with standard techniques for ordinary differential equations, once the coefficients are proved to be measurable and bounded. The main result turns out to extend an analogous result previously obtained for the Stokes system.

1 aMorandotti, Marco uhttps://doi.org/10.1080/17513758.2011.61126001580nas a2200145 4500008004100000245008700041210006900128260001000197520093400207653011301141100001501254700002201269700002101291856012201312 2012 en d00aSimulation-based uncertainty quantification of human arterial network hemodynamics0 aSimulationbased uncertainty quantification of human arterial net bWiley3 aThis work aims at identifying and quantifying uncertainties from various sources in human cardiovascular\r\nsystem based on stochastic simulation of a one dimensional arterial network. A general analysis of\r\ndifferent uncertainties and probability characterization with log-normal distribution of these uncertainties\r\nis introduced. Deriving from a deterministic one dimensional fluid structure interaction model, we establish\r\nthe stochastic model as a coupled hyperbolic system incorporated with parametric uncertainties to describe\r\nthe blood flow and pressure wave propagation in the arterial network. By applying a stochastic collocation\r\nmethod with sparse grid technique, we study systemically the statistics and sensitivity of the solution with\r\nrespect to many different uncertainties in a relatively complete arterial network with potential physiological\r\nand pathological implications for the first time.10auncertainty quantification, mathematical modelling of the cardiovascular system, fluid-structure interaction1 aChen, Peng1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/simulation-based-uncertainty-quantification-human-arterial-network-hemodynamics01296nas a2200145 4500008004100000022001300041245010400054210006900158300001400227490000700241520073600248100002400984700002001008856012201028 2012 eng d a0951771500aSobolev quasi-periodic solutions of multidimensional wave equations with a multiplicative potential0 aSobolev quasiperiodic solutions of multidimensional wave equatio a2579-26130 v253 aWe prove the existence of quasi-periodic solutions for wave equations with a multiplicative potential on T d , d ≥ 1, and finitely differentiable nonlinearities, quasi-periodically forced in time. The only external parameter is the length of the frequency vector. The solutions have Sobolev regularity both in time and space. The proof is based on a Nash-Moser iterative scheme as in [5]. The key tame estimates for the inverse linearized operators are obtained by a multiscale inductive argument, which is more difficult than for NLS due to the dispersion relation of the wave equation. We prove the 'separation properties' of the small divisors assuming weaker non-resonance conditions than in [11]. © 2012 IOP Publishing Ltd.1 aBerti, Massimiliano1 aBolle, Philippe uhttps://www.math.sissa.it/publication/sobolev-quasi-periodic-solutions-multidimensional-wave-equations-multiplicative01270nas a2200109 4500008004100000245012700041210007000168260002800238520083700266100002101103856003601124 2012 en d00aSolving the Sixth Painlevé Equation: Towards the Classification of all the Critical Behaviors and the Connection Formulae0 aSolving the Sixth Painlevé Equation Towards the Classification o bOxford University Press3 aThe critical behavior of a three real parameter class of solutions of the\\r\\nsixth Painlev\\\\\\\'e equation is computed, and parametrized in terms of monodromy\\r\\ndata of the associated $2\\\\times 2$ matrix linear Fuchsian system of ODE. The\\r\\nclass may contain solutions with poles accumulating at the critical point. The\\r\\nstudy of this class closes a gap in the description of the transcendents in one\\r\\nto one correspondence with the monodromy data. These transcendents are reviewed in the paper. Some formulas that relate the monodromy data to the critical behaviors of the four real (two complex) parameter class of solutions are\\r\\nmissing in the literature, so they are computed here. A computational procedure to write the full expansion of the four and three real parameter class of solutions is proposed.1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/609300790nas a2200121 4500008004100000245014600041210006900187300001400256490000600270520032300276100001900599856005000618 2012 eng d00aSome applications of the SBV Regularity Theorem for entropy solutions of 1D scalar conservation laws to ConvectionTheory and sticky particles0 aSome applications of the SBV Regularity Theorem for entropy solu a163–1750 v33 aWe show how it is possible to apply the SBV Regularity Theorem for entropy solutions of one-dimensional scalar conservation laws, proved by Ambrosio and De Lellis, to Convection Theory and sticky particles. In the multi-dimensional case we present a counterexample which prevent us from using the same approach.

1 aTonon, Daniela uhttps://hal.archives-ouvertes.fr/hal-0091840900324nas a2200097 4500008004100000245006100041210005700102260001000159100002100169856003600190 2012 en d00aSome aspects of spinors – classical and noncommutative0 aSome aspects of spinors classical and noncommutative bSISSA1 aDossena, Giacomo uhttp://hdl.handle.net/1963/631700568nas a2200121 4500008004100000245003800041210003800079260003200117520021000149653002200359100002900381856003600410 2012 en d00aSome remarks on quantum mechanics0 aSome remarks on quantum mechanics bWorld Scientific Publishing3 aWe discuss the similarities and differences between the formalism of Hamiltonian Classical Mechanics and of Quantum Mechanics and exemplify the differences through an analysis of tracks in a cloud chamber.10aQuantum mechanics1 aDell'Antonio, Gianfausto uhttp://hdl.handle.net/1963/701800559nas 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/s10955-011-0409-201607nas a2200157 4500008004100000245009600041210006900137260002100206520106500227100002201292700002901314700002001343700002901363700002101392856003601413 2012 en d00aStability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions0 aStability for a System of N Fermions Plus a Different Particle w bWorld Scientific3 aWe study the stability problem for a non-relativistic quantum system in\\r\\ndimension three composed by $ N \\\\geq 2 $ identical fermions, with unit mass,\\r\\ninteracting with a different particle, with mass $ m $, via a zero-range\\r\\ninteraction of strength $ \\\\alpha \\\\in \\\\R $. We construct the corresponding\\r\\nrenormalised quadratic (or energy) form $ \\\\form $ and the so-called\\r\\nSkornyakov-Ter-Martirosyan symmetric extension $ H_{\\\\alpha} $, which is the\\r\\nnatural candidate as Hamiltonian of the system. We find a value of the mass $\\r\\nm^*(N) $ such that for $ m > m^*(N)$ the form $ \\\\form $ is closed and bounded from below. As a consequence, $ \\\\form $ defines a unique self-adjoint and bounded from below extension of $ H_{\\\\alpha}$ and therefore the system is stable. On the other hand, we also show that the form $ \\\\form $ is unbounded from below for $ m < m^*(2)$. In analogy with the well-known bosonic case, this suggests that the system is unstable for $ m < m^*(2)$ and the so-called Thomas effect occurs.1 aCorreggi, Michele1 aDell'Antonio, Gianfausto1 aFinco, Domenico1 aMichelangeli, Alessandro1 aTeta, Alessandro uhttp://hdl.handle.net/1963/606900518nas a2200109 4500008004100000245011900041210006900160100001700229700001700246700002200263856012300285 2012 eng d00aA stable semi-lagrangian potential method for the simulation of ship interaction with unsteady and nonlinear waves0 astable semilagrangian potential method for the simulation of shi1 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio uhttps://www.math.sissa.it/publication/stable-semi-lagrangian-potential-method-simulation-ship-interaction-unsteady-and00752nas a2200121 4500008004100000245004700041210004600088260001000134520040400144100002500548700002100573856003600594 2012 en d00aSub-Riemannian structures on 3D Lie groups0 aSubRiemannian structures on 3D Lie groups bSISSA3 aWe give a complete classification of left-invariant sub-Riemannian structures on three dimensional Lie groups in terms of the basic differential invariants. As a corollary we explicitly find a sub-Riemannian isometry between the nonisomorphic Lie groups $SL(2)$ and $A^+(\mathbb{R})\times S^1$, where $A^+(\mathbb{R})$ denotes the group of orientation preserving affine maps on the real line.

1 aAgrachev, Andrei, A.1 aBarilari, Davide uhttp://hdl.handle.net/1963/645300723nas a2200121 4500008004100000245003800041210003800079260001000117520039200127100002500519700002100544856003600565 2012 en d00aSystems of Quadratic Inequalities0 aSystems of Quadratic Inequalities bSISSA3 aWe present a spectral sequence which efficiently computes Betti numbers of a closed semi-algebraic subset of RP^n defined by a system of quadratic inequalities and the image of the homology homomorphism induced by the inclusion of this subset in RP^n. We do not restrict ourselves to the term E_2 of the spectral sequence and give a simple explicit formula for the differential d_2.1 aAgrachev, Andrei, A.1 aLerario, Antonio uhttp://hdl.handle.net/1963/707200562nas a2200109 4500008004100000245004400041210004400085260001900129520024700148100002100395856003600416 2012 en d00aTabulation of Painlevé 6 transcendents0 aTabulation of Painlevé 6 transcendents bIOP Publishing3 aThe critical and asymptotic behaviors of solutions of the sixth Painlev'e equation PVI, obtained in the framework of the monodromy preserving deformation method, and their explicit parametrization in terms of monodromy data, are tabulated.1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/652000948nas a2200121 4500008004100000245006000041210006000101260002200161520056500183100002400748700001800772856003600790 2012 en d00aThermodynamic phase transitions and shock singularities0 aThermodynamic phase transitions and shock singularities bThe Royal Society3 aWe show that under rather general assumptions on the form of the entropy\\r\\nfunction, the energy balance equation for a system in thermodynamic equilibrium is equivalent to a set of nonlinear equations of hydrodynamic type. This set of equations is integrable via the method of the characteristics and it provides the equation of state for the gas. The shock wave catastrophe set identifies the phase transition. A family of explicitly solvable models of\\r\\nnon-hydrodynamic type such as the classical plasma and the ideal Bose gas are\\r\\nalso discussed.1 aDe Nittis, Giuseppe1 aMoro, Antonio uhttp://hdl.handle.net/1963/609001511nas a2200145 4500008004100000245007100041210006900112260001000181520099600191653006801187100002001255700002901275700002501304856003601329 2012 en d00aTopological sensitivity analysis for high order elliptic operators0 aTopological sensitivity analysis for high order elliptic operato bSISSA3 aThe topological derivative is defined as the first term of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of a singular domain perturbation. It has applications in many different fields such as shape and topology optimization, inverse problems, image processing and mechanical modeling including synthesis and/or optimal design of microstructures, fracture mechanics sensitivity analysis and damage evolution modeling. The topological derivative has been fully developed for a wide range of second order differential operators. In this paper we deal with the topological asymptotic expansion of a class of shape functionals associated with elliptic differential operators of order 2m, m>=1. The general structure of the polarization tensor is derived and the concept of degenerate polarization tensor is introduced. We provide full mathematical justifications for the derived formulas, including precise estimates of remainders.10aTopological derivative, Elliptic operators, Polarization tensor1 aAmstutz, Samuel1 aNovotny, Antonio, André1 aVan Goethem, Nicolas uhttp://hdl.handle.net/1963/634302171nas a2200133 4500008004100000245006600041210006600107260001300173520175500186653001901941100001701960700002401977856003602001 2012 en d00aVariational implementation of immersed finite element methods0 aVariational implementation of immersed finite element methods bElsevier3 aDirac-delta distributions are often crucial components of the solid-fluid coupling operators in immersed solution methods for fluid-structure interaction (FSI) problems. This is certainly so for methods like the Immersed Boundary Method (IBM) or the Immersed Finite Element Method (IFEM), where Dirac-delta distributions are approximated via smooth functions. By contrast, a truly variational formulation of immersed methods does not require the use of Dirac-delta distributions, either formally or practically. This has been shown in the Finite Element Immersed Boundary Method (FEIBM), where the variational structure of the problem is exploited to avoid Dirac-delta distributions at both the continuous and the discrete level. In this paper, we generalize the FEIBM to the case where an incompressible Newtonian fluid interacts with a general hyperelastic solid. Specifically, we allow (i) the mass density to be different in the solid and the fluid, (ii) the solid to be either viscoelastic of differential type or purely elastic, and (iii) the solid to be and either compressible or incompressible. At the continuous level, our variational formulation combines the natural stability estimates of the fluid and elasticity problems. In immersed methods, such stability estimates do not transfer to the discrete level automatically due to the non- matching nature of the finite dimensional spaces involved in the discretization. After presenting our general mathematical framework for the solution of FSI problems, we focus in detail on the construction of natural interpolation operators between the fluid and the solid discrete spaces, which guarantee semi-discrete stability estimates and strong consistency of our spatial discretization.

10aTurbulent flow1 aHeltai, Luca1 aCostanzo, Francesco uhttp://hdl.handle.net/1963/646201295nas a2200133 4500008004100000245005500041210005200096260001000148520090800158100002001066700002401086700001501110856003601125 2012 en d00aVertices, vortices & interacting surface operators0 aVertices vortices interacting surface operators bSISSA3 aWe show that the vortex moduli space in non-abelian supersymmetric N=(2,2) gauge theories on the two dimensional plane with adjoint and anti-fundamental matter can be described as an holomorphic submanifold of the instanton moduli space in four dimensions. The vortex partition functions for these theories are computed via equivariant localization. We show that these coincide with the field theory limit of the topological vertex on the strip with boundary conditions corresponding to column diagrams. Moreover, we resum the field theory limit of the vertex partition functions in terms of generalized hypergeometric functions formulating their AGT dual description as interacting surface operators of simple type. Analogously we resum the topological open string amplitudes in terms of q-deformed generalized hypergeometric functions proving that they satisfy appropriate finite difference equations.1 aBonelli, Giulio1 aTanzini, Alessandro1 aJian, Zhao uhttp://hdl.handle.net/1963/413401110nas a2200109 4500008004100000245003900041210003600080260001000116520082000126100001800946856003600964 2012 en d00aA Viscosity-driven crack evolution0 aViscositydriven crack evolution bSISSA3 aWe present a model of crack growth in brittle materials which couples dissipative effects on the crack tip and viscous effects. We consider the 2 -dimensional antiplane case with pre-assigned crack path, and firstly prove an existence result for a rate-dependent evolution problem by means of time-discretization. The next goal is to describe the rate-independent evolution as limit of the rate-dependent ones when the dissipative and viscous effects vanish. The rate-independent evolution satisfies a Griffith’s criterion for the crack growth, but, in general, it does not fulfil a global minimality condition; its fracture set may exhibit jump discontinuities with respect to time. Under suitable regularity assumptions, the quasi-static crack growth is described by solving a finite-dimensional problem.

1 aRacca, Simone uhttp://hdl.handle.net/1963/513001567nas a2200121 4500008004100000245008300041210006900124260001300193520115600206100002501362700002201387856003601409 2012 en d00aWeighted barycentric sets and singular Liouville equations on compact surfaces0 aWeighted barycentric sets and singular Liouville equations on co bElsevier3 aGiven a closed two dimensional manifold, we prove a general existence result\\r\\nfor a class of elliptic PDEs with exponential nonlinearities and negative Dirac\\r\\ndeltas on the right-hand side, extending a theory recently obtained for the\\r\\nregular case. This is done by global methods: since the associated Euler\\r\\nfunctional is in general unbounded from below, we need to define a new model\\r\\nspace, generalizing the so-called space of formal barycenters and\\r\\ncharacterizing (up to homotopy equivalence) its very low sublevels. As a\\r\\nresult, the analytic problem is reduced to a topological one concerning the\\r\\ncontractibility of this model space. To this aim, we prove a new functional\\r\\ninequality in the spirit of [16] and then we employ a min-max scheme based on a cone-style construction, jointly with the blow-up analysis given in [5] (after\\r\\n[6] and [8]). This study is motivated by abelian Chern- Simons theory in\\r\\nself-dual regime, or from the problem of prescribing the Gaussian curvature in\\r\\npresence of conical singularities (hence generalizing a problem raised by\\r\\nKazdan and Warner in [26]).1 aCarlotto, Alessandro1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/521800994nas a2200133 4500008004100000245003100041210003100072260001000103520064300113100002000756700002400776700002400800856003600824 2012 en d00aWild quiver gauge theories0 aWild quiver gauge theories bSISSA3 aWe study $N=2$ supersymmetric $SU(2)$ gauge theories coupled to non-Lagrangian superconformal field theories induced by compactifying the six dimensional $A_1 (2,0)$ theory on Riemann surfaces with irregular punctures. These are naturally associated to Hitchin systems with wild ramification whose spectral curves provide the relevant Seiberg-Witten geometries. We propose that the prepotential of these gauge theories on the Omega-background can be obtained from the corresponding irregular conformal blocks on the Riemann surfaces via a generalization of the coherent state construction to the case of higher order singularities.

1 aBonelli, Giulio1 aMaruyoshi, Kazunobu1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/518401400nas a2200169 4500008004100000245009000041210006900131260005000200520083200250100001401082700001801096700001501114700002201129700002201151700002101173856003601194 2011 en d00aAdaptation as a genome-wide autoregulatory principle in the stress response of yeast.0 aAdaptation as a genomewide autoregulatory principle in the stres bThe Institution of Engineering and Technology3 aThe gene expression response of yeast to various types of stresses/perturbations shows a common functional and dynamical pattern for the vast majority of genes, characterised by a quick transient peak (affecting primarily short genes) followed by a return to the pre-stimulus level. Kinetically, this process of adaptation following the transient excursion can be modelled using a genome-wide autoregulatory mechanism by means of which yeast aims at maintaining a preferential concentration in its mRNA levels. The resulting feedback system explains well the different time constants observable in the transient response, while being in agreement with all the known experimental dynamical features. For example, it suggests that a very rapid transient can be induced also by a slowly varying concentration of the gene products.1 aEduati, F1 aDi Camillo, B1 aToffolo, G1 aAltafini, Claudio1 aDe Palo, Giovanna1 aZampieri, Mattia uhttp://hdl.handle.net/1963/510600665nas a2200109 4500008004100000245007400041210007100115260001900186520029300205100002100498856003600519 2011 en d00aAn asymptotic reduction of a Painlevé VI equation to a Painlevé III0 aasymptotic reduction of a Painlevé VI equation to a Painlevé III bIOP Publishing3 aWhen the independent variable is close to a critical point, it is shown that\\r\\nPVI can be asymptotically reduced to PIII. In this way, it is possible to\\r\\ncompute the leading term of the critical behaviors of PVI transcendents\\r\\nstarting from the behaviors of PIII transcendents.1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/512400772nas a2200157 4500008004300000245008600043210007000129260003400199520023700233653003600470100001900506700002200525700001600547700001500563856003600578 2011 en_Ud 00aAxial symmetry of some steady state solutions to nonlinear Schrödinger equations0 aAxial symmetry of some steady state solutions to nonlinear Schrö bAmerican Mathematical Society3 aIn this note, we show the axial symmetry of steady state solutions of nonlinear Schrodinger equations when the exponent of the nonlinearity is between the critical Sobolev exponent of n dimensional space and n - 1 dimensional space.10aNonlinear Schrödinger equation1 aGui, Changfeng1 aMalchiodi, Andrea1 aXu, Haoyuan1 aYang, Paul uhttp://hdl.handle.net/1963/410000585nas a2200121 4500008004100000245011300041210006900154260001000223520015500233100002500388700001400413856003600427 2011 en d00aBishop and Laplacian Comparison Theorems on Three Dimensional Contact Subriemannian Manifolds with Symmetry0 aBishop and Laplacian Comparison Theorems on Three Dimensional Co bSISSA3 aWe prove a Bishop volume comparison theorem and a Laplacian comparison\r\ntheorem for three dimensional contact subriemannian manifolds with symmetry.1 aAgrachev, Andrei, A.1 aLee, Paul uhttp://hdl.handle.net/1963/650800425nas a2200121 4500008004100000022001400041245009200055210006900147300001400216490000600230100001900236856004800255 2011 eng d a1664-236800aBoutroux curves with external field: equilibrium measures without a variational problem0 aBoutroux curves with external field equilibrium measures without a167–2110 v11 aBertola, Marco uhttp://dx.doi.org/10.1007/s13324-011-0012-301306nas a2200145 4500008004100000022001300041245007600054210006900130300001200199490000800211520079500219100002401014700001701038856010501055 2011 eng d a0010361600aBranching of Cantor Manifolds of Elliptic Tori and Applications to PDEs0 aBranching of Cantor Manifolds of Elliptic Tori and Applications a741-7960 v3053 aWe consider infinite dimensional Hamiltonian systems. We prove the existence of "Cantor manifolds" of elliptic tori-of any finite higher dimension-accumulating on a given elliptic KAM torus. Then, close to an elliptic equilibrium, we show the existence of Cantor manifolds of elliptic tori which are "branching" points of other Cantor manifolds of higher dimensional tori. We also answer to a conjecture of Bourgain, proving the existence of invariant elliptic tori with tangential frequency along a pre-assigned direction. The proofs are based on an improved KAM theorem. Its main advantages are an explicit characterization of the Cantor set of parameters and weaker smallness conditions on the perturbation. We apply these results to the nonlinear wave equation. © 2011 Springer-Verlag.1 aBerti, Massimiliano1 aBiasco, Luca uhttps://www.math.sissa.it/publication/branching-cantor-manifolds-elliptic-tori-and-applications-pdes00981nas a2200121 4500008004100000245006900041210006700110260001300177520058600190100002500776700002200801856003600823 2011 en d00aA class of existence results for the singular Liouville equation0 aclass of existence results for the singular Liouville equation bElsevier3 aWe consider a class of elliptic PDEs on closed surfaces with exponential nonlinearities and Dirac deltas on the right-hand side. The study arises from abelian Chern–Simons theory in self-dual regime, or from the problem of prescribing the Gaussian curvature in presence of conical singularities. A general existence result is proved using global variational methods: the analytic problem is reduced to a topological problem concerning the contractibility of a model space, the so-called space of formal barycenters, characterizing the very low sublevels of a suitable functional.1 aCarlotto, Alessandro1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/579300505nas a2200133 4500008004100000245010600041210007000147260004400217300001400261490000700275100001600282700001700298856005600315 2011 eng d00aCluster solutions for the Schrödinger-Poisson-Slater problem around a local minimum of the potential0 aCluster solutions for the SchrödingerPoissonSlater problem aroun bReal Sociedad Matemática Españolac01 a253–2710 v271 aRuiz, David1 aVaira, Giusi uhttps://projecteuclid.org:443/euclid.rmi/129682883400613nas a2200097 4500008004100000245003000041210003000071520034600101100002000447856004800467 2011 en d00aCompactness by maximality0 aCompactness by maximality3 aWe derive a compactness property in the Sobolev space $W^{1,1}(\O)$ in order to study the Dirichlet problem for the eikonal equation \begin{displaymath} \begin{cases} \ha |\n u(x)|^2 - a(x) = 0 & \ \textrm{in} \ \O\cr u(x)=\varphi(x) & \ \textrm{on} \ \partial \O, \end{cases} \end{displaymath} without continuity assumptions on the map $a$.1 aZagatti, Sandro uhttp://preprints.sissa.it/handle/1963/3531701286nas a2200145 4500008004100000245007900041210006900120260003300189520078400222653003101006100002401037700002101061700002201082856003601104 2011 en d00aComputing global structural balance in large-scale signed social networks.0 aComputing global structural balance in largescale signed social bNational Academy of Sciences3 aStructural balance theory affirms that signed social networks (i.e., graphs whose signed edges represent friendly/hostile interactions among individuals) tend to be organized so as to avoid conflictual situations, corresponding to cycles of negative parity. Using an algorithm for ground-state calculation in large-scale Ising spin glasses, in this paper we compute the global level of balance of very large online social networks and verify that currently available networks are indeed extremely balanced. This property is explainable in terms of the high degree of skewness of the sign distributions on the nodes of the graph. In particular, individuals linked by a large majority of negative edges create mostly \\\"apparent disorder,\\\" rather than true \\\"frustration.\\\"10aCombinatorial optimization1 aFacchetti, Giuseppe1 aIacono, Giovanni1 aAltafini, Claudio uhttp://hdl.handle.net/1963/642600435nas a2200121 4500008004100000245009600041210006900137260001300206300001200219490000700231100002100238856005400259 2011 eng d00aConcentration of solutions for a singularly perturbed Neumann problem in non-smooth domains0 aConcentration of solutions for a singularly perturbed Neumann pr bElsevier a107-1260 v281 aDipierro, Serena uhttp://www.numdam.org/item/AIHPC_2011__28_1_107_001012nas 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/1963/661300920nas a2200133 4500008004100000245005100041210005100092260007200143520047100215100002100686700002100707700002200728856003600750 2011 en d00aCovered by lines and Conic connected varieties0 aCovered by lines and Conic connected varieties bUniversita\\\' di Catania, Dipartimento di Matematica e Informatica3 aWe study some properties of an embedded variety covered by lines and give a\\r\\nnumerical criterion ensuring the existence of a singular conic through two of\\r\\nits general points. We show that our criterion is sharp. Conic-connected,\\r\\ncovered by lines, QEL, LQEL, prime Fano, defective, and dual defective\\r\\nvarieties are closely related. We study some relations between the above\\r\\nmentioned classes of objects using celebrated results by Ein and Zak.1 aMarchesi, Simone1 aMassarenti, Alex1 aTafazolian, Saeed uhttp://hdl.handle.net/1963/578800974nas a2200121 4500008004300000245009300043210006900136260004800205520051800253100002100771700002400792856003600816 2011 en_Ud 00aCrack growth with non-interpenetration : a simplified proof for the pure Neumann problem0 aCrack growth with noninterpenetration a simplified proof for the bAmerican Institute of Mathematical Sciences3 aWe present a recent existence result concerning the quasi-static evolution of cracks in hyperelastic brittle materials, in the frame-work of finite elasticity with non-interpenetration. In particular, here we consider the problem where no Dirichlet conditions are imposed, the boundary is traction-free, and the body is subject only to time-dependent volume forces. This allows us to present the main ideas of the proof in a simpler way, avoiding some of the technicalities needed in the general case, studied in.1 aDal Maso, Gianni1 aLazzaroni, Giuliano uhttp://hdl.handle.net/1963/380100934nas 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/1963/651400428nas a2200133 4500008004100000245005400041210005300095260001000148653003100158100002600189700002200215700002100237856003600258 2011 en d00aCritical points of the Moser-Trudinger functional0 aCritical points of the MoserTrudinger functional bSISSA10aMoser-Trudinger inequality1 aDe Marchis, Francesca1 aMalchiodi, Andrea1 aMartinazzi, Luca uhttp://hdl.handle.net/1963/459200524nas a2200133 4500008004100000245012600041210006900167260003300236100002000269700002100289700002200310700002200332856003600354 2011 en d00aCytoskeletal actin networks in motile cells are critically self-organized systems synchronized by mechanical interactions0 aCytoskeletal actin networks in motile cells are critically selfo bNational Academy of Sciences1 aCardamone, Luca1 aLaio, Alessandro1 aShahapure, Rajesh1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/435801229nas 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/1963/413300421nas a2200133 4500008004300000245004500043210004300088260004800131300001400179490000700193100002300200700001900223856004500242 2011 en_Ud 00aA Decomposition Theorem for BV functions0 aDecomposition Theorem for BV functions bAmerican Institute of Mathematical Sciences a1549-15660 v101 aBianchini, Stefano1 aTonon, Daniela uhttp://hdl.handle.net/20.500.11767/1459900919nas a2200157 4500008004100000022001300041245006100054210006100115300001400176490000800190520040200198100001900600700002400619700002300643856009500666 2011 eng d a0022039600aDegenerate KAM theory for partial differential equations0 aDegenerate KAM theory for partial differential equations a3379-33970 v2503 aThis paper deals with degenerate KAM theory for lower dimensional elliptic tori of infinite dimensional Hamiltonian systems, depending on one parameter only. We assume that the linear frequencies are analytic functions of the parameter, satisfy a weak non-degeneracy condition of Rüssmann type and an asymptotic behavior. An application to nonlinear wave equations is given. © 2010 Elsevier Inc.1 aBambusi, Dario1 aBerti, Massimiliano1 aMagistrelli, Elena uhttps://www.math.sissa.it/publication/degenerate-kam-theory-partial-differential-equations00653nas a2200109 4500008004100000245009700041210006900138260001000207520027300217100001700490856003600507 2011 en d00aDimensional Reduction and Approximation of Measures and Weakly Differentiable Homeomorphisms0 aDimensional Reduction and Approximation of Measures and Weakly D bSISSA3 aThis thesis is devoted to the study of two different problems: the properties of the disintegration of the Lebesgue measure on the faces of a convex function and the existence of smooth approximations of bi-Lipschitz orientation-preserving homeomorphisms in the plane.1 aDaneri, Sara uhttp://hdl.handle.net/1963/534801344nas a2200181 4500008004100000022001400041245010900055210007100164300001600235490000800251520070400259653002100963653003300984653002901017100002201046700002301068856007101091 2011 eng d a0022-039600aDouble resonance with Landesman–Lazer conditions for planar systems of ordinary differential equations0 aDouble resonance with Landesman–Lazer conditions for planar syst a1052 - 10820 v2503 aWe prove the existence of periodic solutions for first order planar systems at resonance. The nonlinearity is indeed allowed to interact with two positively homogeneous Hamiltonians, both at resonance, and some kind of Landesman–Lazer conditions are assumed at both sides. We are thus able to obtain, as particular cases, the existence results proposed in the pioneering papers by Lazer and Leach (1969) [27], and by Frederickson and Lazer (1969) [18]. Our theorem also applies in the case of asymptotically piecewise linear systems, and in particular generalizes Fabry's results in Fabry (1995) [10], for scalar equations with double resonance with respect to the Dancer–Fučik spectrum.

10aDouble resonance10aLandesman–Lazer conditions10aNonlinear planar systems1 aFonda, Alessandro1 aGarrione, Maurizio uhttp://www.sciencedirect.com/science/article/pii/S002203961000290101116nas a2200145 4500008004100000245013000041210007000171260001300241300001600254490000800270520060700278100002000885700001900905856004600924 2011 eng d00aEmbedding theorems and existence results for nonlinear Schrödinger–Poisson systems with unbounded and vanishing potentials0 aEmbedding theorems and existence results for nonlinear Schröding bElsevier a1056–10850 v2513 aMotivated by existence results for positive solutions of non-autonomous nonlinear Schrödinger–Poisson systems with potentials possibly unbounded or vanishing at infinity, we prove embedding theorems for weighted Sobolev spaces. We both consider a general framework and spaces of radially symmetric functions when assuming radial symmetry of the potentials.

1 aBonheure, Denis1 aMercuri, Carlo uhttps://doi.org/10.1016/j.jde.2011.04.01000728nas a2200121 4500008004300000245007600043210006900119260001300188520032600201100002400527700001900551856003600570 2011 en_Ud 00aEnergy release rate and stress intensity factor in antiplane elasticity0 aEnergy release rate and stress intensity factor in antiplane ela bElsevier3 aIn the setting of antiplane linearized elasticity, we show the existence of the stress intensity factor and its relation with the energy release rate when the crack path is a C1,1 curve. Finally, we show that the energy release rate is continuous with respect to the Hausdorff convergence in a class of admissible cracks.1 aLazzaroni, Giuliano1 aToader, Rodica uhttp://hdl.handle.net/1963/378000628nas a2200109 4500008004100000245003900041210003800080260004800118520029500166100002100461856003600482 2011 en d00aEnnio De Giorgi and Γ-convergence0 aEnnio De Giorgi and Γconvergence bAmerican Institute of Mathematical Sciences3 aΓ-convergence was introduced by Ennio De Giorgi in a series of papers published between 1975 and 1983. In the same years he developed many applications of this tool to a great variety of asymptotic problems in the calculus of variations and in the theory of partial differential equations.1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/530800369nas a2200109 4500008004300000245006000043210005700103260002100160100002300181700001900204856003600223 2011 en_Ud 00aAn Estimate on the Flow Generated by Monotone Operators0 aEstimate on the Flow Generated by Monotone Operators bTaylor & Francis1 aBianchini, Stefano1 aGloyer, Matteo uhttp://hdl.handle.net/1963/364601548nas a2200157 4500008004300000245008600043210006900129260005100198300001400249490000800263520101800271100002101289700002201310700002201332856003601354 2011 en_Ud 00aAn Existence and Uniqueness Result for the Motion of Self-Propelled Microswimmers0 aExistence and Uniqueness Result for the Motion of SelfPropelled bSociety for Industrial and Applied Mathematics a1345-13680 v 433 aWe present an analytical framework to study the motion of micro-swimmers in a viscous fluid. Our main result is that, under very mild regularity assumptions, the change of shape determines uniquely the motion of the swimmer. We assume that the Reynolds number is very small, so that the velocity field of the surrounding, infinite fluid is governed by the Stokes system and all inertial effects can be neglected. Moreover, we enforce the self propulsion constraint (no external forces and torques). Therefore, Newton\\\'s equations of motion reduce to the vanishing of the viscous drag force and torque acting on the body. By exploiting an integral representation of viscous force and torque, the equations of motion can be reduced to a system of six ordinary differential equations. Variational techniques are used to prove the boundedness and measurability of its coefficients, so that classical results on ordinary differential equations can be invoked to prove existence and uniqueness of the solution.

1 aDal Maso, Gianni1 aDeSimone, Antonio1 aMorandotti, Marco uhttp://hdl.handle.net/1963/389401004nas a2200133 4500008004100000245007400041210006900115260003400184520055100218653001800769100002100787700002600808856003600834 2011 en d00aExistence for wave equations on domains with arbitrary growing cracks0 aExistence for wave equations on domains with arbitrary growing c bEuropean Mathematical Society3 aIn this paper we formulate and study scalar wave equations on domains with arbitrary growing cracks. This includes a zero Neumann condition on the crack sets, and the only assumptions on these sets are that they have bounded surface measure and are growing in the sense of set inclusion. In particular, they may be dense, so the weak formulations must fall outside of the usual weak formulations using Sobolev spaces. We study both damped and undamped equations, showing existence and, for the damped equation, uniqueness and energy conservation.10aWave equation1 aDal Maso, Gianni1 aLarsen, Cristopher J. uhttp://hdl.handle.net/1963/428400878nas a2200109 4500008004100000245008900041210006900130260002200199520048900221100002200710856003600732 2011 en d00aFracture and plastic models as Gamma-limits of damage models under different regimes0 aFracture and plastic models as Gammalimits of damage models unde bWalter de Gruyter3 aWe consider a variational model for damaged elastic materials. This model depends on three small parameters, which are related to the cost of the damage, to the width of the damaged regions, and to the minimum elasticity constant attained in the damaged regions. As these parameters tend to zero, our models Gamma-converge to a model for brittle fracture, for fracture with a cohesive zone, or for perfect plasticity, depending on the asymptotic ratios of the three parameters.

1 aIurlano, Flaviana uhttp://hdl.handle.net/1963/506900898nas a2200145 4500008004100000245008300041210006900124260001300193490000800206520043400214653002000648100002600668700002200694856003600716 2011 en d00aGamma-convergence of energies for nematic elastomers in the small strain limit0 aGammaconvergence of energies for nematic elastomers in the small bSpringer0 v 233 aWe study two variational models recently proposed in the literature to describe the mechanical behaviour of nematic elastomers either in the fully nonlinear regime or in the framework of a geometrically linear theory. We show that, in the small strain limit, the energy functional of the first one I\\\"-converges to the relaxation of the second one, a functional for which an explicit representation formula is available.

10aLiquid crystals1 aAgostiniani, Virginia1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/414101081nas a2200121 4500008004100000245004900041210004900090260001000139520061100149653014200760100002100902856003600923 2011 en d00aGeneralised functions of bounded deformation0 aGeneralised functions of bounded deformation bSISSA3 aWe introduce the space GBD of generalized functions of bounded deformation and study the structure properties of these functions: the rectifiability and the slicing properties of their jump sets, and the existence of their approximate symmetric gradients. We conclude by proving a compactness results for GBD, which leads to a compactness result for the space GSBD of generalized special functions of bounded deformation. The latter is connected to the existence of solutions to a weak formulation of some variational problems arising in fracture mechanics in the framework of linearized elasticity.

10afree discontinuity problems, special functions of bounded deformation, jump set, rec- tifiability, slicing, approximate differentiability1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/637401134nas a2200145 4500008004100000245006700041210006700108260001000175520068000185100002000865700002400885700002400909700001900933856003600952 2011 en d00aGeneralized matrix models and AGT correspondence at all genera0 aGeneralized matrix models and AGT correspondence at all genera bSISSA3 aWe study generalized matrix models corresponding to n-point Virasoro\r\nconformal blocks on Riemann surfaces with arbitrary genus g. Upon AGT\r\ncorrespondence, these describe four dimensional N=2 SU(2)^{n+3g-3} gauge\r\ntheories with generalized quiver diagrams. We obtain the generalized matrix\r\nmodels from the perturbative evaluation of the Liouville correlation functions\r\nand verify the consistency of the description with respect to degenerations of\r\nthe Riemann surface. Moreover, we derive the Seiberg-Witten curve for the N=2\r\ngauge theory as the spectral curve of the generalized matrix model, thus\r\nproviding a check of AGT correspondence at all genera.1 aBonelli, Giulio1 aMaruyoshi, Kazunobu1 aTanzini, Alessandro1 aYagib, Futoshi uhttp://hdl.handle.net/1963/656800398nas a2200109 4500008004100000245009300041210006900134260001000203100002500213700001400238856003600252 2011 en d00aGeneralized Ricci Curvature Bounds for Three Dimensional Contact Subriemannian manifolds0 aGeneralized Ricci Curvature Bounds for Three Dimensional Contact bSISSA1 aAgrachev, Andrei, A.1 aLee, Paul uhttp://hdl.handle.net/1963/650700442nas a2200109 4500008004100000245003800041210003400079520013500113100002500248700002300273856003600296 2011 en d00aThe geometry of Maximum Principle0 ageometry of Maximum Principle3 aAn invariant formulation of the maximum principle in optimal control is presented, and some second-order invariants are discussed.1 aAgrachev, Andrei, A.1 aGamkrelidze, Revaz uhttp://hdl.handle.net/1963/645600395nas a2200109 4500008004300000245008700043210006900130260001300199100002100212700001600233856003600249 2011 en_Ud 00aHolomorphic Cartan geometry on manifolds with numerically effective tangent bundle0 aHolomorphic Cartan geometry on manifolds with numerically effect bElsevier1 aBiswas, Indranil1 aBruzzo, Ugo uhttp://hdl.handle.net/1963/383001189nas a2200109 4500008004100000245004200041210004200083260001000125520088700135100002101022856003601043 2011 en d00aHomology invariants of quadratic maps0 aHomology invariants of quadratic maps bSISSA3 aGiven a real projective algebraic set X we could hope that the equations describing it can give some information on its topology, e.g. on the number of its connected components. Unfortunately in the general case this hope is too vague and there is no direct way to extract such information from the algebraic description of X: Even the problem to decide whether X is empty or not is far from an easy visualization and requires some complicated algebraic machinery. A fi rst step observation is that as long as we are interested only in the topology of X, we can replace, using some Veronese embedding, the original ambient space with a much bigger RPn and assume that X is cut by quadratic equations. The price for this is the increase of the number of equations de ning our set; the advantage is that quadratic polynomials are easier to handle and our hope becomes more concrete...1 aLerario, Antonio uhttp://hdl.handle.net/1963/624500770nas a2200133 4500008004300000245007400043210006900117260001300186520033600199100001800535700002000553700002700573856003600600 2011 en_Ud 00aInfinite-dimensional Frobenius manifolds for 2 + 1 integrable systems0 aInfinitedimensional Frobenius manifolds for 2 1 integrable syste bSpringer3 aWe introduce a structure of an infinite-dimensional Frobenius manifold on a subspace in the space of pairs of functions analytic inside/outside the unit circle with simple poles at 0/infinity respectively. The dispersionless 2D Toda equations are embedded into a bigger integrable hierarchy associated with this Frobenius manifold.1 aCarlet, Guido1 aDubrovin, Boris1 aMertens, Luca Philippe uhttp://hdl.handle.net/1963/358400860nas 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/S0362546X1100351800632nas a2200133 4500008004100000245007400041210006900115260001000184520020000194100002000394700002400414700002400438856003600462 2011 en d00aInstantons on ALE spaces and Super Liouville Conformal Field Theories0 aInstantons on ALE spaces and Super Liouville Conformal Field The bSISSA3 aWe provide evidence that the conformal blocks of N=1 super Liouville\\r\\nconformal field theory are described in terms of the SU(2) Nekrasov partition\\r\\nfunction on the ALE space O_{P^1}(-2).1 aBonelli, Giulio1 aMaruyoshi, Kazunobu1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/426201512nas a2200109 4500008004100000245009500041210006900136260002200205520111900227100002001346856003601366 2011 en d00aAn Integro-Extremization Approach for Non Coercive and Evolution Hamilton-Jacobi Equations0 aIntegroExtremization Approach for Non Coercive and Evolution Ham bHeldermann Verlag3 aWe devote the \\\\textit{integro-extremization} method to the study of the Dirichlet problem for homogeneous Hamilton-Jacobi equations \\\\begin{displaymath} \\\\begin{cases} F(Du)=0 & \\\\quad \\\\textrm{in} \\\\quad\\\\O\\\\cr u(x)=\\\\varphi(x) & \\\\quad \\\\textrm{for} \\\\quad x\\\\in \\\\partial \\\\O, \\\\end{cases} \\\\end{displaymath} with a particular interest for non coercive hamiltonians $F$, and to the Cauchy-Dirichlet problem for the corresponding homogeneous time-dependent equations \\\\begin{displaymath} \\\\begin{cases} \\\\frac{\\\\partial u}{\\\\partial t}+ F(\\\\nabla u)=0 & \\\\quad \\\\textrm{in} \\\\quad ]0,T[\\\\times \\\\O\\\\cr u(0,x)=\\\\eta(x) & \\\\quad \\\\textrm{for} \\\\quad x\\\\in\\\\O \\\\cr u(t,x)=\\\\psi(x) & \\\\quad \\\\textrm{for} \\\\quad (t,x)\\\\in[0,T]\\\\times \\\\partial \\\\O. \\\\end{cases} \\\\end{displaymath} We prove existence and some qualitative results for viscosity and almost everywhere solutions, under suitably convexity conditions on the hamiltonian $F$, on the domain $\\\\O$ and on the boundary datum, without any growth assumptions on $F$.1 aZagatti, Sandro uhttp://hdl.handle.net/1963/553800383nas a2200109 4500008004300000245007000043210006900113260001300182100002300195700001900218856003600237 2011 en_Ud 00aInvariant manifolds for a singular ordinary differential equation0 aInvariant manifolds for a singular ordinary differential equatio bElsevier1 aBianchini, Stefano1 aSpinolo, Laura uhttp://hdl.handle.net/1963/255401397nas a2200121 4500008004100000245006800041210006600109260001000175520100500185653002801190100002101218856003601239 2011 en d00aInvariants, volumes and heat kernels in sub-Riemannian geometry0 aInvariants volumes and heat kernels in subRiemannian geometry bSISSA3 aSub-Riemannian geometry can be seen as a generalization of Riemannian geometry under non-holonomic constraints. From the theoretical point of view, sub-Riemannian geometry is the geometry underlying the theory of hypoelliptic operators (see [32, 57, 70, 92] and references therein) and many problems of geometric measure theory (see for instance [18, 79]). In applications it appears in the study of many mechanical problems (robotics, cars with trailers, etc.) and recently in modern elds of research such as mathematical models of human behaviour, quantum control or motion of self-propulsed micro-organism (see for instance [15, 29, 34])\\r\\nVery recently, it appeared in the eld of cognitive neuroscience to model the\\r\\nfunctional architecture of the area V1 of the primary visual cortex, as proposed by Petitot in [87, 86], and then by Citti and Sarti in [51]. In this context, the sub-Riemannian heat equation has been used as basis to new applications in image reconstruction (see [35]).10aSub-Riemannian geometry1 aBarilari, Davide uhttp://hdl.handle.net/1963/612401000nas a2200133 4500008004300000245005100043210005100094260002100145520060100166100001800767700002500785700002000810856003600830 2011 en_Ud 00aLarge Time Existence for Thin Vibrating Plates0 aLarge Time Existence for Thin Vibrating Plates bTaylor & Francis3 aWe construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence of strong solutions for large\\r\\ntimes under appropriate scaling of the initial values such that the limit system as h --> 0 is either the nonlinear von Karman plate equation or the linear fourth order Germain-Lagrange equation. In the case of the\\r\\nlinear Germain-Lagrange equation we even obtain a convergence rate of the three-dimensional solution to the solution of the two-dimensional linear plate equation.1 aAbels, Helmut1 aMora, Maria Giovanna1 aMüller, Stefan uhttp://hdl.handle.net/1963/375500923nas 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/1963/643000818nas a2200133 4500008004100000245003700041210003300078260001000111520046800121100002000589700002400609700001500633856003600648 2011 en d00aThe Liouville side of the vortex0 aLiouville side of the vortex bSISSA3 aWe analyze conformal blocks with multiple (semi-)degenerate field insertions in Liouville/Toda conformal field theories an show that their vector space is fully reproduced by the four-dimensional limit of open topological string amplitudes on the strip with generic boundary conditions associated to a suitable quiver gauge theory. As a byproduct we identify the non-abelian vortex partition function with a specific fusion channel of degenerate conformal blocks.1 aBonelli, Giulio1 aTanzini, Alessandro1 aZhao, Jian uhttp://hdl.handle.net/1963/430401120nas 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/1963/339201329nas a2200169 4500008004100000022001400041245008700055210006900142260000800211300001400219490000700233520081100240100001801051700002201069700002201091856004601113 2011 eng d a1432-095900aMetastable equilibria of capillary drops on solid surfaces: a phase field approach0 aMetastable equilibria of capillary drops on solid surfaces a pha cSep a453–4710 v233 aWe discuss a phase field model for the numerical simulation of metastable equilibria of capillary drops resting on rough solid surfaces and for the description of contact angle hysteresis phenomena in wetting. The model is able to reproduce observed transitions of drops on micropillars from Cassie–Baxter to Wenzel states. When supplemented with a dissipation potential which describes energy losses due to frictional forces resisting the motion of the contact line, the model can describe metastable states such as drops in equilibrium on vertical glass plates. The reliability of the model is assessed by a detailed comparison of its predictions with experimental data on the maximal size of water drops that can stick on vertical glass plates which have undergone different surface treatments.

1 aFedeli, Livio1 aTurco, Alessandro1 aDeSimone, Antonio uhttps://doi.org/10.1007/s00161-011-0189-601532nas a2200277 4500008004100000022001600041245006500057210006300122260009400185300001600279490000900295520056700304653002100871653002200892653002200914653002400936653003200960653002500992653002101017653002901038653002401067653002401091100002401115700001901139856009601158 2011 eng d a{0218-2025}00aA MODEL FOR CRACK PROPAGATION BASED ON VISCOUS APPROXIMATION0 aMODEL FOR CRACK PROPAGATION BASED ON VISCOUS APPROXIMATION a{5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE}b{WORLD SCIENTIFIC PUBL CO PTE LTD}c{OCT} a{2019-2047}0 v{21}3 a{In the setting of antiplane linearized elasticity, we show the existence of quasistatic evolutions of cracks in brittle materials by using a vanishing viscosity approach, thus taking into account local minimization. The main feature of our model is that the path followed by the crack need not be prescribed a priori: indeed, it is found as the limit (in the sense of Hausdorff convergence) of curves obtained by an incremental procedure. The result is based on a continuity property for the energy release rate in a suitable class of admissible cracks.}

10aBrittle fracture10aCrack propagation10aenergy derivative10aenergy release rate10afree-discontinuity problems10aGriffith's criterion10alocal minimizers10astress intensity factor}10avanishing viscosity10a{Variational models1 aLazzaroni, Giuliano1 aToader, Rodica uhttps://www.math.sissa.it/publication/model-crack-propagation-based-viscous-approximation-000841nas a2200121 4500008004100000245005200041210005200093260002600145520047000171100001600641700002600657856003600683 2011 en d00aModuli of framed sheaves on projective surfaces0 aModuli of framed sheaves on projective surfaces bDocumenta Mathematica3 aWe show that there exists a fine moduli space for torsion-free sheaves on a\\r\\nprojective surface, which have a \\\"good framing\\\" on a big and nef divisor. This\\r\\nmoduli space is a quasi-projective scheme. This is accomplished by showing that such framed sheaves may be considered as stable pairs in the sense of\\r\\nHuybrechts and Lehn. We characterize the obstruction to the smoothness of the moduli space, and discuss some examples on rational surfaces.1 aBruzzo, Ugo1 aMarkushevich, Dimitri uhttp://hdl.handle.net/1963/512601064nas a2200193 4500008004100000020002200041245004100063210003700104260002800141300001400169520049000183100002300673700002200696700002100718700002400739700001900763700001600782856007200798 2011 eng d a978-1-4419-9554-400aThe Monge Problem in Geodesic Spaces0 aMonge Problem in Geodesic Spaces aBoston, MAbSpringer US a217–2333 aWe address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish non branching geodesic space. We show that we can reduce the transport problem to 1-dimensional transport problems along geodesics. We introduce an assumption on the transport problem π which implies that the conditional probabilities of the first marginal on each geodesic are continuous. It is known that this regularity is sufficient for the construction of an optimal transport map.

1 aBianchini, Stefano1 aCavalletti, Fabio1 aBressan, Alberto1 aChen, Gui-Qiang, G.1 aLewicka, Marta1 aWang, Dehua uhttps://www.math.sissa.it/publication/monge-problem-geodesic-spaces00490nas a2200145 4500008004100000245008500041210006900126260002500195300001200220490000700232100001700239700001900256700002300275856004600298 2011 eng d00aMulti-physics modelling and sensitivity analysis of olympic rowing boat dynamics0 aMultiphysics modelling and sensitivity analysis of olympic rowin bSpringer Naturecnov a85–940 v141 aMola, Andrea1 aGhommem, Mehdi1 aHajj, Muhammad, R. uhttps://doi.org/10.1007/s12283-011-0075-200786nas a2200121 4500008004100000245007600041210006900117300001400186490000600200520033000206100002600536856010200562 2011 eng d00aMultiplicity of solutions for a mean field equation on compact surfaces0 aMultiplicity of solutions for a mean field equation on compact s a245–2570 v43 aWe consider a scalar field equation on compact surfaces which has variational structure. When the surface is a torus and a physical parameter ρ belongs to $(8\pi, 4\pi^2 )$ we show under some extra assumptions that, as conjectured in [9], the functional admits at least three saddle points other than a local minimum.

1 aDe Marchis, Francesca uhttps://www.math.sissa.it/publication/multiplicity-solutions-mean-field-equation-compact-surfaces00729nas a2200121 4500008004300000245009900043210006900142260001300211520030900224100002200533700001600555856003600571 2011 en_Ud 00aNew improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces0 aNew improved MoserTrudinger inequalities and singular Liouville bSpringer3 aWe consider a singular Liouville equation on a compact surface, arising from the study of Chern-Simons vortices in a self dual regime. Using new improved versions of the Moser-Trudinger inequalities (whose main feature is to be scaling invariant) and a variational scheme, we prove new existence results.1 aMalchiodi, Andrea1 aRuiz, David uhttp://hdl.handle.net/1963/409900992nas a2200145 4500008004100000245009400041210006900135260003700204300001400241490000700255520041000262100002200672700002300694856012900717 2011 eng d00aNonlinear resonance: a comparison between Landesman-Lazer and Ahmad-Lazer-Paul conditions0 aNonlinear resonance a comparison between LandesmanLazer and Ahma bAdvanced Nonlinear Studies, Inc. a391–4040 v113 aWe show that the Ahmad-Lazer-Paul condition for resonant problems is more general than the Landesman-Lazer one, discussing some relations with other existence conditions, as well. As a consequence, such a relation holds, for example, when considering resonant boundary value problems associated with linear elliptic operators, the p-Laplacian and, in the scalar case, with an asymmetric oscillator.

1 aFonda, Alessandro1 aGarrione, Maurizio uhttps://www.math.sissa.it/publication/nonlinear-resonance-comparison-between-landesman-lazer-and-ahmad-lazer-paul-conditions00668nas 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-spaces00897nas a2200181 4500008004100000022001400041245008800055210006900143300001400212490000800226520028400234653002200518653003800540653002300578653002000601100002300621856007100644 2011 eng d a0022-247X00aA note on a superlinear indefinite Neumann problem with multiple positive solutions0 anote on a superlinear indefinite Neumann problem with multiple p a259 - 2680 v3773 aWe prove the existence of three positive solutions for the Neumann problem associated to u″+a(t)uγ+1=0, assuming that a(t) has two positive humps and ∫0Ta−(t)dt is large enough. Actually, the result holds true for a more general class of superlinear nonlinearities.

10aIndefinite weight10aNonlinear boundary value problems10apositive solutions10aShooting method1 aBoscaggin, Alberto uhttp://www.sciencedirect.com/science/article/pii/S0022247X1000879600467nas a2200121 4500008004100000245010400041210006900145260001900214100002900233700002600262700002100288856003600309 2011 en d00aOn the number of eigenvalues of a model operator related to a system of three particles on lattices0 anumber of eigenvalues of a model operator related to a system of bIOP Publishing1 aDell'Antonio, Gianfausto1 aMuminov, Zahriddin I.1 aShermatova, Y.M. uhttp://hdl.handle.net/1963/549600977nas a2200145 4500008004300000245007900043210006900122260002100191520050000212653002100712100002300733700002200756700001700778856003600795 2011 en_Ud 00aNumerical Strategies for Stroke Optimization of Axisymmetric Microswimmers0 aNumerical Strategies for Stroke Optimization of Axisymmetric Mic bWorld Scientific3 aWe propose a computational method to solve optimal swimming problems, based on the boundary integral formulation of the hydrodynamic interaction between swimmer and surrounding fluid and direct constrained minimization of the energy consumed by the swimmer. We apply our method to axisymmetric model examples. We consider a classical model swimmer (the three-sphere swimmer of Golestanian et al.) as well as a novel axisymmetric swimmer inspired by the observation of biological micro-organisms.10aOptimal swimming1 aAlouges, François1 aDeSimone, Antonio1 aHeltai, Luca uhttp://hdl.handle.net/1963/365701547nas a2200133 4500008004100000245008700041210006900128260000900197520111200206100002001318700001801338700002101356856003601377 2011 en d00aNumerical Study of breakup in generalized Korteweg-de Vries and Kawahara equations0 aNumerical Study of breakup in generalized Kortewegde Vries and K bSIAM3 aThis article is concerned with a conjecture in [B. Dubrovin, Comm. Math. Phys., 267 (2006), pp. 117–139] on the formation of dispersive shocks in a class of Hamiltonian dispersive regularizations of the quasi-linear transport equation. The regularizations are characterized by two arbitrary functions of one variable, where the condition of integrability implies that one of these functions must not vanish. It is shown numerically for a large class of equations that the local behavior of their solution near the point of gradient catastrophe for the transport equation is described by a special solution of a Painlevé-type equation. This local description holds also for solutions to equations where blowup can occur in finite time. Furthermore, it is shown that a solution of the dispersive equations away from the point of gradient catastrophe is approximated by a solution of the transport equation with the same initial data, modulo terms of order $\\\\epsilon^2$, where $\\\\epsilon^2$ is the small dispersion parameter. Corrections up to order $\\\\epsilon^4$ are obtained and tested numerically.1 aDubrovin, Boris1 aGrava, Tamara1 aKlein, Christian uhttp://hdl.handle.net/1963/495100449nas a2200109 4500008004300000245005100043210005100094260003400145520010000179100002400279856003600303 2011 en_Ud 00aOsservazioni sui teoremi di inversione globale0 aOsservazioni sui teoremi di inversione globale bEuropean Mathematical Society3 aSome global inversion theorems with applications to semilinear elliptic equation are discussed.1 aAmbrosetti, Antonio uhttp://hdl.handle.net/1963/406800295nas a2200097 4500008004100000245004400041210004100085100001700126700001900143856003500162 2011 eng d00aA planar bi-Lipschitz extension Theorem0 aplanar biLipschitz extension Theorem1 aDaneri, Sara1 aPratelli, Aldo uhttp://arxiv.org/abs/1110.612400420nas a2200109 4500008004300000245009100043210006900134260003400203653001700237100002000254856003600274 2011 en_Ud 00aPlanar loops with prescribed curvature: existence, multiplicity and uniqueness results0 aPlanar loops with prescribed curvature existence multiplicity an bAmerican Mathematical Society10aPlane curves1 aMusina, Roberta uhttp://hdl.handle.net/1963/384200961nas 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/1963/373800741nas a2200121 4500008004100000245003700041210003700078260002100115520040400136100002200540700002100562856003600583 2011 en d00aProduct of real spectral triples0 aProduct of real spectral triples bWorld Scientific3 aWe construct the product of real spectral triples of arbitrary finite dimension (and arbitrary parity) taking into account the fact that in the even case there are two possible real structures, in the odd case there are two inequivalent representations of the gamma matrices (Clifford algebra), and in the even-even case there are two natural candidates for the Dirac operator of the product triple.1 aDabrowski, Ludwik1 aDossena, Giacomo uhttp://hdl.handle.net/1963/551000842nas a2200109 4500008004300000245005800043210005600101260001300157520050500170100002100675856003600696 2011 en_Ud 00aA proof of Sudakov theorem with strictly convex norms0 aproof of Sudakov theorem with strictly convex norms bSpringer3 aWe establish a solution to the Monge problem in Rn, with an asymmetric, strictly convex norm cost function, when the initial measure is absolutely continuous. We focus on the strategy, based on disintegration of measures, initially proposed by Sudakov. As known, there is a gap to fill. The missing step is completed when the unit ball is strictly convex, but not necessarily differentiable nor uniformly convex. The key disintegration is achieved following a similar proof for a variational problem.1 aCaravenna, Laura uhttp://hdl.handle.net/1963/296700609nas a2200121 4500008004100000245003000041210002900071260001000100520030300110100001600413700002200429856003600451 2011 en d00aQ-factorial Laurent rings0 aQfactorial Laurent rings bSISSA3 aDolgachev proved that, for any field k, the ring naturally associated to a\\r\\ngeneric Laurent polynomial in d variables, $d \\\\geq 4$, is factorial. We prove a\\r\\nsufficient condition for the ring associated to a very general complex Laurent\\r\\npolynomial in d=3 variables to be Q-factorial.1 aBruzzo, Ugo1 aGrassi, Antonella uhttp://hdl.handle.net/1963/418302121nas 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/1963/520301134nas a2200133 4500008004100000245006000041210005900101260001000160520072600170100002000896700002400916700002400940856003600964 2011 en d00aQuantum Hitchin Systems via beta-deformed Matrix Models0 aQuantum Hitchin Systems via betadeformed Matrix Models bSISSA3 aWe study the quantization of Hitchin systems in terms of beta-deformations of generalized matrix models related to conformal blocks of Liouville theory on punctured Riemann surfaces. We show that in a suitable limit, corresponding to the Nekrasov-Shatashvili one, the loop equations of the matrix model reproduce the Hamiltonians of the quantum Hitchin system on the sphere and the torus with marked points. The eigenvalues of these Hamiltonians are shown to be the epsilon1-deformation of the chiral observables of the corresponding N=2 four ndimensional gauge theory. Moreover, we find the exact wave-functions in terms of the matrix model representation of the conformal blocks with degenerate field insertions.

1 aBonelli, Giulio1 aMaruyoshi, Kazunobu1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/418100860nas a2200133 4500008004100000245008400041210006900125260001300194520041200207100002500619700002400644700002200668856003600690 2011 en d00aQuantum Isometries of the finite noncommutative geometry of the Standard Model0 aQuantum Isometries of the finite noncommutative geometry of the bSpringer3 aWe compute the quantum isometry group of the finite noncommutative geometry F describing the internal degrees of freedom in the Standard Model of particle physics. We show that this provides genuine quantum symmetries of the spectral triple corresponding to M x F where M is a compact spin manifold. We also prove that the bosonic and fermionic part of the spectral action are preserved by these symmetries.1 aBhowmick, Jyotishman1 aD'Andrea, Francesco1 aDabrowski, Ludwik uhttp://hdl.handle.net/1963/490600673nas a2200109 4500008004300000245010600043210006900149520026500218100002200483700002200505856003600527 2011 en_Ud 00aQuasiconvex envelopes of energies for nematic elastomers in the small strain regime and applications0 aQuasiconvex envelopes of energies for nematic elastomers in the 3 aWe provide some explicit formulas for the quasiconvex envelope of energy densities for nematic elastomers in the small strain regime and plane strain conditions. We then demonstrate their use as a powerful tool for the interpretation of mechanical experiments.1 aCesana, Pierluigi1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/406500919nas a2200121 4500008004300000245013400043210006900177260004600246520042800292100002200720700001900742856003600761 2011 en_Ud 00aQuasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a Young measures approach0 aQuasistatic crack evolution for a cohesive zone model with diffe bCambridge University Press / EDP Sciences3 aA new approach to irreversible quasistatic fracture growth is given, by means of Young measures. The study concerns a cohesive zone model with prescribed crack path, when the material gives different responses to loading and unloading phases. In the particular situation of constant unloading response, the result contained in [6] is recovered. In this case, the convergence of the discrete time approximations is improved.1 aCagnetti, Filippo1 aToader, Rodica uhttp://hdl.handle.net/1963/235501263nas a2200277 4500008004100000022001600041245007000057210006900127260008600196300001400282490001000296520028400306653002100590653002200611653002400633653002200657653003200679653002500711653002600736653001800762653002600780653003100806653002400837100002400861856010000885 2011 eng d a{0373-3114}00aQuasistatic crack growth in finite elasticity with Lipschitz data0 aQuasistatic crack growth in finite elasticity with Lipschitz dat a{TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY}b{SPRINGER HEIDELBERG}c{JAN} a{165-194}0 v{190}3 a{We extend the recent existence result of Dal Maso and Lazzaroni (Ann Inst H Poincare Anal Non Lineaire 27:257-290, 2010) for quasistatic evolutions of cracks in finite elasticity, allowing for boundary conditions and external forces with discontinuous first derivatives.}

10aBrittle fracture10aCrack propagation10aEnergy minimization10aFinite elasticity10afree-discontinuity problems10aGriffith's criterion10aNon-interpenetration}10aPolyconvexity10aQuasistatic evolution10aRate-independent processes10a{Variational models1 aLazzaroni, Giuliano uhttps://www.math.sissa.it/publication/quasistatic-crack-growth-finite-elasticity-lipschitz-data01427nas a2200145 4500008004300000245012100043210006900164260001300233520090600246653002401152100002101176700002201197700002601219856003601245 2011 en_Ud 00aQuasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling0 aQuasistatic evolution for CamClay plasticity a weak formulation bSpringer3 aCam-Clay nonassociative plasticity exhibits both hardening and softening behaviour, depending on the loading. For many initial data the classical formulation of the quasistatic evolution problem has no smooth solution. We propose here a notion of generalized solution, based on a viscoplastic approximation. To study the limit of the viscoplastic evolutions we rescale time, in such a way that the plastic strain is uniformly Lipschitz with respect to the rescaled time. The limit of these rescaled solutions, as the viscosity parameter tends to zero, is characterized through an energy-dissipation balance, that can be written in a natural way using the rescaled time. As shown in [4] and [6], the proposed solution may be discontinuous with respect to the original time. Our formulation allows to compute the amount of viscous dissipation occurring instantaneously at each discontinuity time.

10aCam-Clay plasticity1 aDal Maso, Gianni1 aDeSimone, Antonio1 aSolombrino, Francesco uhttp://hdl.handle.net/1963/367000823nas a2200121 4500008004100000245007200041210006900113260001300182520042600195100002200621700002200643856003600665 2011 en d00aQuasistatic evolution of sessile drops and contact angle hysteresis0 aQuasistatic evolution of sessile drops and contact angle hystere bSpringer3 aWe consider the classical model of capillarity coupled with a rate-independent dissipation mechanism due to frictional forces acting on the contact line, and prove the existence of quasistatic evolutions with prescribed initial configuration. We also discuss in detail some explicit solutions to show that the model does account for contact angle hysteresis, and to compare its predictions with experimental observations.1 aAlberti, Giovanni1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/491201079nas a2200121 4500008004100000245007600041210006900117300001400186490000700200520062100207100002300828856010600851 2011 eng d00aResonance and Landesman-Lazer conditions for first order systems in R^20 aResonance and LandesmanLazer conditions for first order systems a153–1600 v663 aThe first part of the paper surveys the concept of resonance for $T$-periodic nonlinear problems. In the second part, some new results about existence conditions for nonlinear planar systems are presented. In particular, the Landesman-Lazer conditions are generalized to systems in $\mathbbR^2$ where the nonlinearity interacts with two resonant Hamiltonians. Such results apply to second order equations, generalizing previous theorems by Fabry [4] (for the undamped case), and Frederickson-Lazer [9] (for the case with friction). The results have been obtained with A. Fonda, and have been published in [8].

1 aGarrione, Maurizio uhttps://www.math.sissa.it/publication/resonance-and-landesman-lazer-conditions-first-order-systems-r201464nas a2200193 4500008004100000022001400041245012500055210006900180300001600249490000700265520078200272653003201054653003301086653001401119653002001133100002301153700002301176856007101199 2011 eng d a0362-546X00aResonance and rotation numbers for planar Hamiltonian systems: Multiplicity results via the Poincaré–Birkhoff theorem0 aResonance and rotation numbers for planar Hamiltonian systems Mu a4166 - 41850 v743 aIn the general setting of a planar first order system (0.1)u′=G(t,u),u∈R2, with G:[0,T]×R2→R2, we study the relationships between some classical nonresonance conditions (including the Landesman–Lazer one) — at infinity and, in the unforced case, i.e. G(t,0)≡0, at zero — and the rotation numbers of “large” and “small” solutions of (0.1), respectively. Such estimates are then used to establish, via the Poincaré–Birkhoff fixed point theorem, new multiplicity results for T-periodic solutions of unforced planar Hamiltonian systems Ju′=∇uH(t,u) and unforced undamped scalar second order equations x″+g(t,x)=0. In particular, by means of the Landesman–Lazer condition, we obtain sharp conclusions when the system is resonant at infinity.

10aMultiple periodic solutions10aPoincaré–Birkhoff theorem10aResonance10aRotation number1 aBoscaggin, Alberto1 aGarrione, Maurizio uhttp://www.sciencedirect.com/science/article/pii/S0362546X1100181700804nas a2200133 4500008004100000245005600041210005400097260001300151520040700164100002300571700002300594700001700617856003600634 2011 en d00aSBV regularity for Hamilton-Jacobi equations in R^n0 aSBV regularity for HamiltonJacobi equations in Rn bSpringer3 aIn this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$ \partial_t u + H(D_{x} u)=0 \qquad \textrm{in}\quad \Omega\subset \mathbb{R}\times \mathbb{R}^{n} . $$ In particular, under the assumption that the Hamiltonian $H\in C^2(\mathbb{R}^n)$ is uniformly convex, we prove that $D_{x}u$ and $\partial_t u$ belong to the class $SBV_{loc}(\Omega)$.

1 aBianchini, Stefano1 aDe Lellis, Camillo1 aRobyr, Roger uhttp://hdl.handle.net/1963/491101465nas a2200121 4500008004300000245006700043210006500110260001300175520107800188100001601266700002501282856003601307 2011 en_Ud 00aSemistable and numerically effective principal (Higgs) bundles0 aSemistable and numerically effective principal Higgs bundles bElsevier3 aWe study Miyaoka-type semistability criteria for principal Higgs G-bundles E on complex projective manifolds of any dimension. We prove that E has the property of being semistable after pullback to any projective curve if and only if certain line bundles, obtained from some characters of the parabolic subgroups of G, are numerically effective. One also proves that these conditions are met for semistable principal Higgs bundles whose adjoint bundle has vanishing second Chern class.\\r\\n\\r\\nIn a second part of the paper, we introduce notions of numerical effectiveness and numerical flatness for principal (Higgs) bundles, discussing their main properties. For (non-Higgs) principal bundles, we show that a numerically flat principal bundle admits a reduction to a Levi factor which has a flat Hermitian–Yang–Mills connection, and, as a consequence, that the cohomology ring of a numerically flat principal bundle with coefficients in R is trivial. To our knowledge this notion of numerical effectiveness is new even in the case of (non-Higgs) principal bundles.1 aBruzzo, Ugo1 aGrana-Otero, Beatriz uhttp://hdl.handle.net/1963/363801135nas a2200145 4500008004300000245008100043210006900124260002300193520065600216100002100872700002100893700001900914700002000933856003600953 2011 en_Ud 00aSingular perturbation models in phase transitions for second order materials0 aSingular perturbation models in phase transitions for second ord bIndiana University3 aA variational model proposed in the physics literature to describe the onset of pattern formation in two-component bilayer membranes and amphiphilic monolayers leads to the analysis of a Ginzburg-Landau type energy with a negative term depending on the first derivative of the phase function. Scaling arguments motivate the study of the family of second order singular perturbed energies Fe having a negative term depending on the first derivative of the phase function. Here, the asymptotic behavior of {Fe} is studied using G-convergence techniques. In particular, compactness results and an integral representation of the limit energy are obtained.1 aChermisi, Milena1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni uhttp://hdl.handle.net/1963/385801019nas a2200133 4500008004100000020001800041245004500059210004500104260001000149520064400159653002500803100002100828856003600849 2011 en d a978311027558200aSolving PVI by Isomonodromy Deformations0 aSolving PVI by Isomonodromy Deformations bSISSA3 aThe critical and asymptotic behaviors of solutions of the sixth Painlev\\\'e\r\nequation, an their parametrization in terms of monodromy data, are\r\nsynthetically reviewed. The explicit formulas are given. This paper has been\r\nwithdrawn by the author himself, because some improvements are necessary.\r\nThis is a proceedings of the international conference \"Painlevé Equations and Related Topics\" which was taking place at the Euler International Mathematical Institute, a branch of the Saint Petersburg Department of the SteklovInstitute of Mathematicsof theRussian Academy of Sciences, in Saint Petersburg on June 17 to 23, 2011.10aPainlevé Equations1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/652200674nas a2200121 4500008004100000245006800041210006100109260001000170520028700180653002400467100002500491856003600516 2011 en d00aOn the Space of Symmetric Operators with Multiple Ground States0 aSpace of Symmetric Operators with Multiple Ground States bSISSA3 aWe study homological structure of the filtrations of the spaces of self-adjoint operators by the multiplicity of the ground state. We consider only operators acting in a finite dimensional complex or real Hilbert space but infinite dimensional generalizations are easily guessed.10aMultiple eigenvalue1 aAgrachev, Andrei, A. uhttp://hdl.handle.net/1963/706900991nas a2200169 4500008004100000245009900041210006900140260001300209300001200222490000800234520046000242100002100702700002300723700002000746700001900766856003600785 2011 en d00aThe sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry0 asphere and the cut locus at a tangency point in twodimensional a bSpringer a141-1610 v17 3 aWe study the tangential case in 2-dimensional almost-Riemannian geometry. We\\r\\nanalyse the connection with the Martinet case in sub-Riemannian geometry. We\\r\\ncompute estimations of the exponential map which allow us to describe the\\r\\nconjugate locus and the cut locus at a tangency point. We prove that this last\\r\\none generically accumulates at the tangency point as an asymmetric cusp whose branches are separated by the singular set.

1 aBonnard, Bernard1 aCharlot, Grégoire1 aGhezzi, Roberta1 aJanin, Gabriel uhttp://hdl.handle.net/1963/491400415nas a2200121 4500008004100000245007100041210006900112260001000181100002200191700002300213700002100236856003600257 2011 en d00aStructure of level sets and Sard-type properties of Lipschitz maps0 aStructure of level sets and Sardtype properties of Lipschitz map bSISSA1 aAlberti, Giovanni1 aBianchini, Stefano1 aCrippa, Gianluca uhttp://hdl.handle.net/1963/465700512nas a2200121 4500008004100000245008400041210006900125260003700194300001300231490000700244100002300251856011600274 2011 eng d00aSubharmonic solutions of planar Hamiltonian systems: a rotation number approach0 aSubharmonic solutions of planar Hamiltonian systems a rotation n bAdvanced Nonlinear Studies, Inc. a77–1030 v111 aBoscaggin, Alberto uhttps://www.math.sissa.it/publication/subharmonic-solutions-planar-hamiltonian-systems-rotation-number-approach00785nas a2200121 4500008004100000245009300041210006900134300001400203490000700217520028800224100002300512856012800535 2011 eng d00aSubharmonic solutions of planar Hamiltonian systems via the Poincaré́-Birkhoff theorem0 aSubharmonic solutions of planar Hamiltonian systems via the Poin a115–1220 v663 aWe revisit some recent results obtained in [1] about the existence of subharmonic solutions for a class of (nonautonomous) planar Hamiltonian systems, and we compare them with the existing literature. New applications to undamped second order equations are discussed, as well.

1 aBoscaggin, Alberto uhttps://www.math.sissa.it/publication/subharmonic-solutions-planar-hamiltonian-systems-poincar%C3%A9%CC%81-birkhoff-theorem00731nas a2200133 4500008004300000245007500043210006900118260002800187520027600215100002200491700002600513700002200539856003600561 2011 en_Ud 00aSupercritical conformal metrics on surfaces with conical singularities0 aSupercritical conformal metrics on surfaces with conical singula bOxford University Press3 aWe study the problem of prescribing the Gaussian curvature on surfaces with conical singularities in supercritical regimes. Using a Morse-theoretical approach we prove a general existence theorem on surfaces with positive genus, with a generic multiplicity result.

1 aBardelloni, Mauro1 aDe Marchis, Francesca1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/409501822nas a2200145 4500008004100000245009200041210006900133260002800202520132600230100002101556700002201577700001901599700002201618856003601640 2011 en d00aA system-level approach for deciphering the transcriptional response to prion infection0 asystemlevel approach for deciphering the transcriptional respons bOxford University Press3 aMOTIVATION: Deciphering the response of a complex biological system to an insulting event, at the gene expression level, requires adopting theoretical models that are more sophisticated than a one-to-one comparison (i.e. t-test). Here, we investigate the ability of a novel reverse engineering approach (System Response Inference) to unveil non-obvious transcriptional signatures of the system response induced by prion infection.\\r\\nRESULTS: To this end, we analyze previously published gene expression data, from which we extrapolate a putative full-scale model of transcriptional gene-gene dependencies in the mouse central nervous system. Then, we use this nominal model to interpret the gene expression changes caused by prion replication, aiming at selecting the genes primarily influenced by this perturbation. Our method sheds light on the mode of action of prions by identifying key transcripts that are the most likely to be responsible for the overall transcriptional rearrangement from a nominal regulatory network. As a first result of our inference, we have been able to predict known targets of prions (i.e. PrP(C)) and to unveil the potential role of previously unsuspected genes.\\r\\nCONTACT: altafini@sissa.it\\r\\nSUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.1 aZampieri, Mattia1 aLegname, Giuseppe1 aSegrè, Daniel1 aAltafini, Claudio uhttp://hdl.handle.net/1963/574501043nas a2200097 4500008004100000245013400041210006900175520055400244100001800798856012900816 2011 eng d00aThin-walled beams with a cross-section of arbitrary geometry: derivation of linear theories starting from 3D nonlinear elasticity0 aThinwalled beams with a crosssection of arbitrary geometry deriv3 aThe subject of this paper is the rigorous derivation of lower dimensional models for a nonlinearly elastic thin-walled beam whose cross-section is given by a thin tubular neighbourhood of a smooth curve. Denoting by h and δ_h, respectively, the diameter and the thickness of the cross-section, we analyse the case where the scaling factor of the elastic energy is of order ε_h^2, with ε_h/δ_h^2 \rightarrow l \in [0, +\infty). Different linearized models are deduced according to the relative order of magnitude of δ_h with respect to h.

1 aDavoli, Elisa uhttps://www.math.sissa.it/publication/thin-walled-beams-cross-section-arbitrary-geometry-derivation-linear-theories-starting00881nas a2200133 4500008004300000245008900043210007100132260001300203520043200216100001800648700002500666700002000691856003600711 2011 en_Ud 00aThe time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity0 atimedependent von Kármán plate equation as a limit of 3d nonline bSpringer3 aThe asymptotic behaviour of the solutions of three-dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness $h$ of the plate tends to zero. Under appropriate scalings of the applied force and of the initial values in terms of $h$, it is shown that three-dimensional solutions of the nonlinear elastodynamic equation converge to solutions of the time-dependent von K\\\\\\\'arm\\\\\\\'an plate equation.1 aAbels, Helmut1 aMora, Maria Giovanna1 aMüller, Stefan uhttp://hdl.handle.net/1963/383500558nas a2200121 4500008004100000245011500041210006900156300000900225490002900234100001900263700002000282856013400302 2011 eng d00aThe Transition between the Gap Probabilities from the Pearcey to the Airy Process–a Riemann-Hilbert Approach0 aTransition between the Gap Probabilities from the Pearcey to the a1-500 vdoi: 10.1093/imrn/rnr0661 aBertola, Marco1 aCafasso, Mattia uhttps://www.math.sissa.it/publication/transition-between-gap-probabilities-pearcey-airy-process%E2%80%93-riemann-hilbert-approach00843nas a2200169 4500008004100000022001400041245011600055210006900171300001600240490000700256520022700263653002300490653003700513653002500550100002700575856007100602 2011 eng d a0362-546X00aUniqueness and nondegeneracy of the ground state for a quasilinear Schrödinger equation with a small parameter0 aUniqueness and nondegeneracy of the ground state for a quasiline a1731 - 17370 v743 aWe study least energy solutions of a quasilinear Schrödinger equation with a small parameter. We prove that the ground state is nondegenerate and unique up to translations and phase shifts using bifurcation theory.

10aBifurcation theory10aNonlinear Schrödinger equations10aStationary solutions1 aSelvitella, Alessandro uhttp://www.sciencedirect.com/science/article/pii/S0362546X1000761300413nas a2200121 4500008004100000245007000041210006800111260001000179100002200189700002300211700002100234856003600255 2011 en d00aA uniqueness result for the continuity equation in two dimensions0 auniqueness result for the continuity equation in two dimensions bSISSA1 aAlberti, Giovanni1 aBianchini, Stefano1 aCrippa, Gianluca uhttp://hdl.handle.net/1963/466302515nas a2200205 4500008004100000022001400041245009600055210006900151300001400220490000700234520182300241653002202064653002402086653003502110653001302145653003502158100002202193700002302215856007102238 2011 eng d a0021-782400aThe well-posedness issue for the density-dependent Euler equations in endpoint Besov spaces0 awellposedness issue for the densitydependent Euler equations in a253 - 2780 v963 aThis work is the continuation of the recent paper (Danchin, 2010) [9] devoted to the density-dependent incompressible Euler equations. Here we concentrate on the well-posedness issue in Besov spaces of type B∞,rs embedded in the set of Lipschitz continuous functions, a functional framework which contains the particular case of Hölder spaces C1,α and of the endpoint Besov space B∞,11. For such data and under the non-vacuum assumption, we establish the local well-posedness and a continuation criterion in the spirit of that of Beale, Kato and Majda (1984) [2]. In the last part of the paper, we give lower bounds for the lifespan of a solution. In dimension two, we point out that the lifespan tends to infinity when the initial density tends to be a constant. This is, to our knowledge, the first result of this kind for the density-dependent incompressible Euler equations. Résumé Ce travail complète lʼarticle récent (Danchin, 2010) [9] consacré au système dʼEuler incompressible à densité variable. Lorsque lʼétat initial ne comporte pas de vide, on montre ici que le système est bien posé dans tous les espaces de Besov B∞,rs inclus dans lʼensemble des fonctions lipschitziennes. Ce cadre fonctionnel contient en particulier les espaces de Hölder C1,α et lʼespace de Besov limite B∞,11. On établit également un critère de prolongement dans lʼesprit de celui de Beale, Kato et Majda (1984) [2] pour le cas homogène. Dans la dernière partie de lʼarticle, on donne des minorations pour le temps de vie des solutions du système. En dimension deux, on montre que ce temps de vie tend vers lʼinfini lorsque la densité tend à être homogène. À notre connaissance, il sʼagit du premier résultat de ce type pour le système dʼEuler incompressible à densité variable.

10aBlow-up criterion10aCritical regularity10aIncompressible Euler equations10aLifespan10aNonhomogeneous inviscid fluids1 aDanchin, Raphaël1 aFanelli, Francesco uhttp://www.sciencedirect.com/science/article/pii/S002178241100051102010nas 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-pdes00340nas a2200097 4500008004100000245006800041210006700109260001000176100002000186856003600206 2010 en d00aAlmost-Riemannian Geometry from a Control Theoretical Viewpoint0 aAlmostRiemannian Geometry from a Control Theoretical Viewpoint bSISSA1 aGhezzi, Roberta uhttp://hdl.handle.net/1963/470500564nas 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/1963/386300422nas a2200145 4500008004100000022001400041245003600055210003600091300001400127490000800141100001900149700001700168700002000185856007100205 2010 eng d a0021-904500aCauchy biorthogonal polynomials0 aCauchy biorthogonal polynomials a832–8670 v1621 aBertola, Marco1 aGekhtman, M.1 aSzmigielski, J. uhttp://0-dx.doi.org.mercury.concordia.ca/10.1016/j.jat.2009.09.00801271nas a2200133 4500008004300000245007300043210006800116520083300184100001801017700001901035700002301054700002401077856003601101 2010 en_Ud 00aChern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality0 aChernSimons theory on Lpq lens spaces and GopakumarVafa duality3 aWe consider aspects of Chern-Simons theory on L(p,q) lens spaces and its relation with matrix models and topological string theory on Calabi-Yau threefolds, searching for possible new large N dualities via geometric transition for non-SU(2) cyclic quotients of the conifold. To this aim we find, on one hand, some novel matrix integral representations of the SU(N) CS partition function in a generic flat background for the whole L(p,q) family and provide a solution for its large N dynamics; on the other, we perform in full detail the construction of a family of would-be dual closed string backgrounds via conifold geometric transition from T^*L(p,q). We can then explicitly prove that Gopakumar-Vafa duality in a fixed vacuum fails in the case q>1, and briefly discuss how it could be restored in a non-perturbative setting.1 aBrini, Andrea1 aGriguolo, Luca1 aSeminara, Domenico1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/293800560nas a2200109 4500008004300000245005000043210004900093520023400142100001600376700002200392856003600414 2010 en_Ud 00aCohomology of Skew-holomorphic lie algebroids0 aCohomology of Skewholomorphic lie algebroids3 aWe introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.1 aBruzzo, Ugo1 aRubtsov, Vladimir uhttp://hdl.handle.net/1963/385300912nas 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/1963/340600703nas a2200121 4500008004100000245007900041210006900120260001000189520030700199100002500506700001400531856003600545 2010 en d00aContinuity of optimal control costs and its application to weak KAM theory0 aContinuity of optimal control costs and its application to weak bSISSA3 aWe prove continuity of certain cost functions arising from optimal control of\\r\\naffine control systems. We give sharp sufficient conditions for this\\r\\ncontinuity. As an application, we prove a version of weak KAM theorem and\\r\\nconsider the Aubry-Mather problems corresponding to these systems.1 aAgrachev, Andrei, A.1 aLee, Paul uhttp://hdl.handle.net/1963/645900908nas a2200109 4500008004300000245010700043210006900150520050000219100001800719700002500737856003600762 2010 en_Ud 00aConvergence of equilibria of thin elastic rods under physical growth conditions for the energy density0 aConvergence of equilibria of thin elastic rods under physical gr3 aThe subject of this paper is the study of the asymptotic behaviour of the equilibrium configurations of a nonlinearly elastic thin rod, as the diameter of the cross-section tends to zero. Convergence results are established assuming physical growth conditions for the elastic energy density and suitable scalings of the applied loads, that correspond at the limit to different rod models: the constrained linear theory, the analogous of von Kármán plate theory for rods, and the linear theory.1 aDavoli, Elisa1 aMora, Maria Giovanna uhttp://hdl.handle.net/1963/408600433nas a2200121 4500008004100000022001400041245007500055210006900130300001400199490000800213100001900221856007100240 2010 eng d a0010-361600aThe dependence on the monodromy data of the isomonodromic tau function0 adependence on the monodromy data of the isomonodromic tau functi a539–5790 v2941 aBertola, Marco uhttp://0-dx.doi.org.mercury.concordia.ca/10.1007/s00220-009-0961-700681nas a2200109 4500008004300000245004900043210004900092520034800141100002400489700002200513856003600535 2010 en_Ud 00aDirac Operators on Quantum Projective Spaces0 aDirac Operators on Quantum Projective Spaces3 aWe construct a family of self-adjoint operators D_N which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space CP_q(l), for any l>1 and 0We consider the disintegration of the Lebesgue measure on the graph of a convex function f:\\\\Rn-> \\\\R w.r.t. the partition into its faces, which are convex sets and therefore have a well defined linear dimension, and we prove that each conditional measure is equivalent to the k-dimensional Hausdorff measure of the k-dimensional face on which it is concentrated. The remarkable fact is that a priori the directions of the faces are just Borel and no Lipschitz regularity is known. Notwithstanding that, we also prove that a Green-Gauss formula for these directions holds on special sets.1 aCaravenna, Laura1 aDaneri, Sara uhttp://hdl.handle.net/1963/362200778nas a2200133 4500008004100000245004800041210004700089260001000136520038900146653002700535100002500562700002100587856003600608 2010 en d00aDynamics control by a time-varying feedback0 aDynamics control by a timevarying feedback bSISSA3 aWe consider a smooth bracket generating control-affine system in R^d and show that any orientation preserving diffeomorphism of R^d can be approximated, in the very strong sense, by a diffeomorphism included in the flow generated by a time-varying feedback control which is polynomial with respect to the state variables and trigonometric-polynomial with respect to the time variable.10aDiscrete-time dynamics1 aAgrachev, Andrei, A.1 aCaponigro, Marco uhttp://hdl.handle.net/1963/646100702nas a2200121 4500008004300000245011200043210007000155260001900225520025100244100002900495700002000524856003600544 2010 en_Ud 00aEffective Schroedinger dynamics on $ ε$-thin Dirichlet waveguides via Quantum Graphs I: star-shaped graphs0 aEffective Schroedinger dynamics on εthin Dirichlet waveguides vi bIOP Publishing3 aWe describe the boundary conditions at the vertex that one must choose to obtain a dynamical system that best describes the low-energy part of the evolution of a quantum system confined to a very small neighbourhood of a star-shaped metric graph.1 aDell'Antonio, Gianfausto1 aCosta, Emanuele uhttp://hdl.handle.net/1963/410601221nas a2200109 4500008004300000245005800043210005800101520086900159100002301028700002401051856003601075 2010 en_Ud 00aEstimates on path functionals over Wasserstein Spaces0 aEstimates on path functionals over Wasserstein Spaces3 aIn this paper we consider the class a functionals (introduced in [Brancolini, Buttazzo, and Santambrogio, J. Eur. Math. Soc. (JEMS), 8 (2006), pp. 415-434] $\\\\mathcal{G}_{r,p}$ defined on Lipschitz curves $\\\\gamma$ valued in the $p$-Wasserstein space. The problem considered is the following: given a measure $\\\\mu$, give conditions in order to assure the existence of a curve $\\\\gamma$ such that $\\\\gamma(0)=\\\\mu$, $\\\\gamma(1)=\\\\delta_{x_0}$, and $\\\\mathcal{G}_{r,p}(\\\\gamma)<+\\\\infty$. To this end, new estimates on $\\\\mathcal{G}_{r,p}(\\\\mu)$ are given, and a notion of dimension of a measure (called path dimension) is introduced: the path dimension specifies the values of the parameters $(r,p)$ for which the answer to the previous reachability problem is positive. Finally, we compare the path dimension with other known dimensions.1 aBianchini, Stefano1 aBrancolini, Alessio uhttp://hdl.handle.net/1963/358300371nas a2200097 4500008004300000245008300043210006900126100002300195700001900218856003600237 2010 en_Ud 00aOn the Euler-Lagrange equation for a variational problem : the general case II0 aEulerLagrange equation for a variational problem the general cas1 aBianchini, Stefano1 aGloyer, Matteo uhttp://hdl.handle.net/1963/255100773nas a2200145 4500008004300000245007900043210006900122260001300191520030200204100001900506700002000525700002100545700002500566856003600591 2010 en_Ud 00aExact reconstruction of damaged color images using a total variation model0 aExact reconstruction of damaged color images using a total varia bElsevier3 aIn this paper the reconstruction of damaged piecewice constant color images is studied using a RGB total variation based model for colorization/inpainting. In particular, it is shown that when color is known in a uniformly distributed region, then reconstruction is possible with maximal fidelity.1 aFonseca, Irene1 aLeoni, Giovanni1 aMaggi, Francesco1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/403901347nas a2200133 4500008004300000245006300043210006300106260001300169520093400182100001701116700002301133700002101156856003601177 2010 en_Ud 00aExistence of planar curves minimizing length and curvature0 aExistence of planar curves minimizing length and curvature bSpringer3 aIn this paper we consider the problem of reconstructing a curve that is partially hidden or corrupted by minimizing the functional $\\\\int \\\\sqrt{1+K_\\\\gamma^2} ds$, depending both on length and curvature $K$. We fix starting and ending points as well as initial and final directions.\\nFor this functional we discuss the problem of existence of minimizers on various functional spaces. We find non-existence of minimizers in cases in which initial and final directions are considered with orientation. In this case, minimizing sequences of trajectories can converge to curves with angles.\\nWe instead prove existence of minimizers for the \\\"time-reparameterized\\\" functional $$\\\\int \\\\| \\\\dot\\\\gamma(t) \\\\|\\\\sqrt{1+K_\\\\ga^2} dt$$ for all boundary conditions if initial and final directions are considered regardless to orientation. In this case, minimizers can present cusps (at most two) but not angles.1 aBoscain, Ugo1 aCharlot, Grégoire1 aRossi, Francesco uhttp://hdl.handle.net/1963/410701148nas a2200133 4500008004100000245009700041210006900138260001300207520069800220100002200918700002200940700001600962856003600978 2010 en d00aFeedback schemes for radiation damping suppression in NMR: a control-theoretical perspective0 aFeedback schemes for radiation damping suppression in NMR a cont bElsevier3 aIn NMR spectroscopy, the collective measurement is weakly invasive and its back-action is called radiation damping. The aim of this paper is to provide a control-theoretical analysis of the problem of suppressing this radiation damping. It is shown that the two feedback schemes commonly used in the NMR practice correspond one to a high gain oputput feedback for the simple case of maintaining the spin 1/2 in its inverted state, and the second to a 2-degree of freedom control design with a prefeedback that exactly cancels the radiation damping field. A general high gain feedback stabilization design not requiring the knowledge of the radiation damping time constant is also investigated.1 aAltafini, Claudio1 aCappellaro, Paola1 aCory, David uhttp://hdl.handle.net/1963/438400439nas a2200133 4500008004100000022001400041245006200055210006100117300001400178490000700192100001900199700001600218856007100234 2010 eng d a0176-427600aFirst colonization of a hard-edge in random matrix theory0 aFirst colonization of a hardedge in random matrix theory a231–2570 v311 aBertola, Marco1 aLee, S., Y. uhttp://0-dx.doi.org.mercury.concordia.ca/10.1007/s00365-009-9052-400792nas a2200109 4500008004300000245004300043210004200086260005400128520044800182100001600630856003600646 2010 en_Ud 00aGauge theory: from physics to geometry0 aGauge theory from physics to geometry bIstituto di matematica. Universita\\\' di Trieste3 aMaxwell theory may be regarded as a prototype of gauge theory and generalized to nonabelian gauge theory. We briey sketch the history of the gauge theories, from Maxwell to Yang-Mills theory, and the identification of gauge fields with connections on fibre bundles. We introduce the notion of instanton and consider the moduli spaces of such objects. Finally, we discuss some modern techniques for studying the topology of these moduli spaces.1 aBruzzo, Ugo uhttp://hdl.handle.net/1963/410502590nas a2200265 4500008004100000245013200041210006900173260001000242520175000252100001702002700002402019700002002043700001902063700002102082700001802103700003002121700001802151700001702169700001702186700002002203700002202223700002402245700001902269856003602288 2010 en d00aGene expression analysis of the emergence of epileptiform activity after focal injection of kainic acid into mouse hippocampus.0 aGene expression analysis of the emergence of epileptiform activi bWiley3 aWe report gene profiling data on genomic processes underlying the progression towards recurrent seizures after injection of kainic acid (KA) into the mouse hippocampus. Focal injection enabled us to separate the effects of proepileptic stimuli initiated by KA injection. Both the injected and contralateral hippocampus participated in the status epilepticus. However, neuronal death induced by KA treatment was restricted to the injected hippocampus, although there was some contralateral axonal degeneration. We profiled gene expression changes in dorsal and ventral regions of both the injected and contralateral hippocampus. Changes were detected in the expression of 1526 transcripts in samples from three time-points: (i) during the KA-induced status epilepticus, (ii) at 2 weeks, before recurrent seizures emerged, and (iii) at 6 months after seizures emerged. Grouping genes with similar spatio-temporal changes revealed an early transcriptional response, strong immune, cell death and growth responses at 2 weeks and an activation of immune and extracellular matrix genes persisting at 6 months. Immunostaining for proteins coded by genes identified from array studies provided evidence for gliogenesis and suggested that the proteoglycan biglycan is synthesized by astrocytes and contributes to a glial scar. Gene changes at 6 months after KA injection were largely restricted to tissue from the injection site. This suggests that either recurrent seizures might depend on maintained processes including immune responses and changes in extracellular matrix proteins near the injection site or alternatively might result from processes, such as growth, distant from the injection site and terminated while seizures are maintained.

1 aMotti, Dario1 aLe Duigou, Caroline1 aChemaly, Nicole1 aWittner, Lucia1 aLazarevic, Dejan1 aKrmac, Helena1 aMarstrand, Troels, Torben1 aValen, Eivind1 aSanges, Remo1 aStupka, Elia1 aSandelin, Albin1 aCherubini, Enrico1 aGustincich, Stefano1 aMiles, Richard uhttp://hdl.handle.net/1963/448000947nas a2200181 4500008004100000022001400041245007300055210006900128300001600197490000800213520035200221653002500573653002000598653002300618653002700641100002600668856007100694 2010 eng d a0022-123600aGeneric multiplicity for a scalar field equation on compact surfaces0 aGeneric multiplicity for a scalar field equation on compact surf a2165 - 21920 v2593 aWe prove generic multiplicity of solutions for a scalar field equation on compact surfaces via Morse inequalities. In particular our result improves significantly the multiplicity estimate which can be deduced from the degree-counting formula in Chen and Lin (2003) [12]. Related results are derived for the prescribed Q-curvature equation.

10aGeneric multiplicity10aGeometric PDE's10aMorse inequalities10aScalar field equations1 aDe Marchis, Francesca uhttp://www.sciencedirect.com/science/article/pii/S002212361000269700807nas 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/1963/383400848nas a2200133 4500008004100000245008600041210006900127300001400196490000700210520038600217100001900603700001900622856007300641 2010 eng d00aA global compactness result for the p-Laplacian involving critical nonlinearities0 aglobal compactness result for the pLaplacian involving critical a469–4930 v283 aWe prove a representation theorem for Palais-Smale sequences involving the p-Laplacian and critical nonlinearities. Applications are given to a critical problem.1 aMercuri, Carlo1 aWillem, Michel uhttp://www.aimsciences.org/journals/displayArticles.jsp?paperID=509700685nas a2200109 4500008004100000245006100041210005800102260001000160520034900170100002000519856003600539 2010 en d00aHamiltonian PDEs: deformations, integrability, solutions0 aHamiltonian PDEs deformations integrability solutions bSISSA3 aWe review recent classification results on the theory of systems of nonlinear\\r\\nHamiltonian partial differential equations with one spatial dimension, including\\r\\na perturbative approach to the integrability theory of such systems, and discuss\\r\\nuniversality conjectures describing critical behaviour of solutions to such\\r\\nsystems.1 aDubrovin, Boris uhttp://hdl.handle.net/1963/646900979nas a2200109 4500008004300000245005400043210005100097520064100148100002000789700002400809856003600833 2010 en_Ud 00aHitchin systems, N=2 gauge theories and W-gravity0 aHitchin systems N2 gauge theories and Wgravity3 aWe propose some arguments supporting an M-theory derivation of the duality recently discovered by Alday, Gaiotto and Tachikawa between two-dimensional conformal field theories and N=2 superconformal gauge theories in four dimensions. We find that A_{N-1} Toda field theory is the simplest two-dimensional conformal field theory quantizing the moduli of N M5-branes wrapped on a Riemann surface. This leads us to identify chiral operators of the N=2 gauge theories with W-algebra currents. As a check of this correspondence we study some relevant OPE\\\'s obtaining that Nekrasov\\\'s partition function satisfies W-geometry constraints.1 aBonelli, Giulio1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/383101051nas a2200169 4500008004300000245007900043210006900122260003000191520049800221100001800719700002600737700002300763700001800786700002200804700001900826856003600845 2010 en_Ud 00aHomogeneous binary trees as ground states of quantum critical Hamiltonians0 aHomogeneous binary trees as ground states of quantum critical Ha bAmerican Physical Society3 a

Many-body states whose wave-function admits a representation in terms of a uniform binary-tree tensor decomposition are shown to obey to power-law two-body correlations functions. Any such state can be associated with the ground state of a translational invariant Hamiltonian which, depending on the dimension of the systems sites, involve at most couplings between third-neighboring sites. A detailed analysis of their spectra shows that they admit an exponentially large ground space.

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

1 aRizzi, Matteo1 aMontangero, Simone1 aSilvi, Pietro1 aGiovannetti, Vittorio1 aFazio, Rosario uhttp://hdl.handle.net/1963/406700629nas a2200121 4500008004300000245007900043210006900122260002200191520021000213100002100423700002700444856003600471 2010 en_Ud 00aHomogenization of fiber reinforced brittle material: the intermediate case0 aHomogenization of fiber reinforced brittle material the intermed bWalter de Gruyter3 aWe derive a cohesive fracture model by homogenizing a periodic composite material whose microstructure is characterized by the presence of brittle inclusions in a reticulated unbreakable elastic structure.1 aDal Maso, Gianni1 aZeppieri, Caterina Ida uhttp://hdl.handle.net/1963/360700468nas a2200109 4500008004100000245005900041210005900100260001000159520012800169100002500297856003600322 2010 en d00aInvariant Lagrange submanifolds of dissipative systems0 aInvariant Lagrange submanifolds of dissipative systems bSISSA3 aWe study solutions of modified Hamilton-Jacobi equations H(du/dq,q) + cu(q) =\\r\\n0, q \\\\in M, on a compact manifold M .1 aAgrachev, Andrei, A. uhttp://hdl.handle.net/1963/645700781nas a2200121 4500008004300000245008400043210006900127260004800196520033500244100002200579700002200601856003600623 2010 en_Ud 00aA kinetic mechanism inducing oscillations in simple chemical reactions networks0 akinetic mechanism inducing oscillations in simple chemical react bAmerican Institute of Mathematical Sciences3 aIt is known that a kinetic reaction network in which one or more secondary substrates are acting as cofactors may exhibit an oscillatory behavior. The aim of this work is to provide a description of the functional form of such a cofactor action guaranteeing the\\r\\nonset of oscillations in sufficiently simple reaction networks.1 aCoatleven, Julien1 aAltafini, Claudio uhttp://hdl.handle.net/1963/239300901nas 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/1963/382902106nas a2200121 4500008004300000245013400043210006900177260001900246520164000265100002101905700002201926856003601948 2010 en_Ud 00aMonotonicity, frustration, and ordered response: an analysis of the energy landscape of perturbed large-scale biological networks0 aMonotonicity frustration and ordered response an analysis of the bBioMed Central3 aBackground. \\nFor large-scale biological networks represented as signed graphs, the index of frustration measures how far a network is from a monotone system, i.e., how incoherently the system responds to perturbations.\\nResults. \\nIn this paper we find that the frustration is systematically lower in transcriptional networks (modeled at functional level) than in signaling and metabolic networks (modeled at stoichiometric level). A possible interpretation of this result is in terms of energetic cost of an interaction: an erroneous or contradictory transcriptional action costs much more than a signaling/metabolic error, and therefore must be avoided as much as possible. Averaging over all possible perturbations, however, we also find that unlike for transcriptional networks, in the signaling/metabolic networks the probability of finding the system in its least frustrated configuration tends to be high also in correspondence of a moderate energetic regime, meaning that, in spite of the higher frustration, these networks can achieve a globally ordered response to perturbations even for moderate values of the strength of the interactions. Furthermore, an analysis of the energy landscape shows that signaling and metabolic networks lack energetic barriers around their global optima, a property also favouring global order.\\nConclusion. \\nIn conclusion, transcriptional and signaling/metabolic networks appear to have systematic differences in both the index of frustration and the transition to global order. These differences are interpretable in terms of the different functions of the various classes of networks.1 aIacono, Giovanni1 aAltafini, Claudio uhttp://hdl.handle.net/1963/405500928nas a2200109 4500008004300000245008500043210006900128520053800197100002300735700002400758856003600782 2010 en_Ud 00aMoore-Read Fractional Quantum Hall wavefunctions and SU(2) quiver gauge theories0 aMooreRead Fractional Quantum Hall wavefunctions and SU2 quiver g3 aWe identify Moore-Read wavefunctions, describing non-abelian statistics in fractional quantum Hall systems, with the instanton partition of N=2 superconformal quiver gauge theories at suitable values of masses and \\\\Omega-background parameters. This is obtained by extending to rational conformal field theories the SU(2) gauge quiver/Liouville field theory duality recently found by Alday-Gaiotto-Tachikawa. A direct link between the Moore-Read Hall $n$-body wavefunctions and Z_n-equivariant Donaldson polynomials is pointed out.1 aSantachiara, Raoul1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/385200369nas a2200085 4500008004100000245006200041210006200103100002200165856009600187 2010 eng d00aNew approximation results for free discontinuity problems0 aNew approximation results for free discontinuity problems1 aIurlano, Flaviana uhttps://www.math.sissa.it/publication/new-approximation-results-free-discontinuity-problems00409nas a2200109 4500008004300000245009100043210006900134100002100203700001900224700002000243856003600263 2010 en_Ud 00aNonlocal character of the reduced theory of thin films with higher order perturbations0 aNonlocal character of the reduced theory of thin films with high1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni uhttp://hdl.handle.net/1963/375400493nas a2200109 4500008004100000245009300041210006900134100001700203700002300220700002000243856012000263 2010 eng d00aA normal form for generic 2-dimensional almost-Riemannian structures at a tangency point0 anormal form for generic 2dimensional almostRiemannian structures1 aBoscain, Ugo1 aCharlot, Grégoire1 aGhezzi, Roberta uhttps://www.math.sissa.it/publication/normal-form-generic-2-dimensional-almost-riemannian-structures-tangency-point00335nas a2200085 4500008004300000245007700043210006900120100002400189856003600213 2010 en_Ud 00aOn the number of positive solutions of some semilinear elliptic problems0 anumber of positive solutions of some semilinear elliptic problem1 aAmbrosetti, Antonio uhttp://hdl.handle.net/1963/408301048nas a2200121 4500008004300000245012100043210006900164520059600233100002200829700001800851700002100869856003600890 2010 en_Ud 00aNumerical Solution of the Small Dispersion Limit of the Camassa-Holm and Whitham Equations and Multiscale Expansions0 aNumerical Solution of the Small Dispersion Limit of the CamassaH3 aThe small dispersion limit of solutions to the Camassa-Holm (CH) equation is characterized by the appearance of a zone of rapid modulated oscillations. An asymptotic description of these oscillations is given, for short times, by the one-phase solution to the CH equation, where the branch points of the corresponding elliptic curve depend on the physical coordinates via the Whitham equations. We present a conjecture for the phase of the asymptotic solution. A numerical study of this limit for smooth hump-like initial data provides strong evidence for the validity of this conjecture....1 aAbenda, Simonetta1 aGrava, Tamara1 aKlein, Christian uhttp://hdl.handle.net/1963/384001159nas a2200121 4500008004300000245006200043210005800105260001300163520078100176100002300957700002100980856003601001 2010 en_Ud 00aOn optimality of c-cyclically monotone transference plans0 aoptimality of ccyclically monotone transference plans bElsevier3 aAbstract. This note deals with the equivalence between the optimality of a transport plan for the Monge-Kantorovich problem and the condition of c-cyclical monotonicity, as an outcome of the construction in [7]. We emphasize the measurability assumption on the hidden structure of linear preorder, applied also to extremality and uniqueness problems. Resume. Dans la presente note nous decrivons brievement la construction introduite dans [7] a propos de l\\\'equivalence entre l\\\'optimalite d\\\'un plan de transport pour le probleme de Monge-Kantorovich et la condition de monotonie c-cyclique ainsi que d\\\'autres sujets que cela nous amene a aborder. Nous souhaitons mettre en evidence l\\\'hypothese de mesurabilite sur la structure sous-jacente de pre-ordre lineaire.1 aBianchini, Stefano1 aCaravenna, Laura uhttp://hdl.handle.net/1963/402301187nas a2200145 4500008004300000245004000043210004000083520078100123100002300904700002200927700001700949700002000966700001900986856003601005 2010 en_Ud 00aOptimally swimming Stokesian Robots0 aOptimally swimming Stokesian Robots3 aWe study self propelled stokesian robots composed of assemblies of balls, in dimen-\\nsions 2 and 3, and prove that they are able to control their position and orientation. This is a result of controllability, and its proof relies on applying Chow\\\'s theorem in an analytic framework, similarly to what has been done in [3] for an axisymmetric system swimming along the axis of symmetry. However, we simplify drastically\\nthe analyticity result given in [3] and apply it to a situation where more complex swimmers move either in a plane or in three-dimensional space, hence experiencing also rotations. We then focus our attention on energetically optimal strokes, which we are able to compute numerically. Some examples of computed optimal strokes are discussed in detail.1 aAlouges, François1 aDeSimone, Antonio1 aHeltai, Luca1 aLefebvre, Aline1 aMerlet, Benoit uhttp://hdl.handle.net/1963/392900900nas a2200121 4500008004300000245014000043210007000183260001000253520044500263100001600708700001800724856003600742 2010 en_Ud 00aPainlevé II asymptotics near the leading edge of the oscillatory zone for the Korteweg-de Vries equation in the small-dispersion limit0 aPainlevé II asymptotics near the leading edge of the oscillatory bWiley3 aIn the small dispersion limit, solutions to the Korteweg-de Vries equation develop an interval of fast oscillations after a certain time. We obtain a universal asymptotic expansion for the Korteweg-de Vries solution near the leading edge of the oscillatory zone up to second order corrections. This expansion involves the Hastings-McLeod solution of the Painlev\\\\\\\'e II equation. We prove our results using the Riemann-Hilbert approach.1 aClaeys, Tom1 aGrava, Tamara uhttp://hdl.handle.net/1963/379900902nas a2200169 4500008004100000020002200041245007700063210006900140260003600209300001200245520028600257100002200543700001800565700002200583700001700605856011000622 2010 eng d a978-90-481-9195-600aA Phase Field Approach to Wetting and Contact Angle Hysteresis Phenomena0 aPhase Field Approach to Wetting and Contact Angle Hysteresis Phe aDordrechtbSpringer Netherlands a51–633 aWe discuss a phase field model for the numerical simulation of contact angle hysteresis phenomena in wetting. The performance of the model is assessed by comparing its predictions with experimental data on the critical size of drops that can stick on a vertical glass plate.

1 aDeSimone, Antonio1 aFedeli, Livio1 aTurco, Alessandro1 aHackl, Klaus uhttps://www.math.sissa.it/publication/phase-field-approach-wetting-and-contact-angle-hysteresis-phenomena00671nas a2200109 4500008004300000245005300043210005300096520033800149100001600487700002200503856003600525 2010 en_Ud 00aPicard group of hypersurfaces in toric varieties0 aPicard group of hypersurfaces in toric varieties3 aWe show that the usual sufficient criterion for a generic hypersurface in a smooth projective manifold to have the same Picard number as the ambient variety can be generalized to hypersurfaces in complete simplicial toric varieties. This sufficient condition is always satisfied by generic K3 surfaces embedded in Fano toric 3-folds.1 aBruzzo, Ugo1 aGrassi, Antonella uhttp://hdl.handle.net/1963/410300784nas a2200097 4500008004300000245010500043210006900148520041300217100002000630856003600650 2010 en_Ud 00aPoles of Integrale Tritronquee and Anharmonic Oscillators. Asymptotic localization from WKB analysis0 aPoles of Integrale Tritronquee and Anharmonic Oscillators Asympt3 aPoles of integrale tritronquee are in bijection with cubic oscillators that admit the simultaneous solutions of two quantization conditions. We show that the poles lie near the solutions of a pair of Bohr-Sommerfeld quantization conditions (the Bohr-Sommerfeld-Boutroux system): the distance between a pole and the corresponding solution of the Bohr-Sommerfeld-Boutroux system vanishes asymptotically.

1 aMasoero, Davide uhttp://hdl.handle.net/1963/384100526nas a2200133 4500008004100000245007800041210007200119260001900191300001400210490000800224100002100232700001700253856012200270 2010 eng d00aPositive solutions for some non-autonomous Schrödinger–Poisson systems0 aPositive solutions for some nonautonomous Schrödinger–Poisson sy bAcademic Press a521–5430 v2481 aCerami, Giovanna1 aVaira, Giusi uhttps://www.math.sissa.it/publication/positive-solutions-some-non-autonomous-schr%C3%B6dinger%E2%80%93poisson-systems01299nas a2200109 4500008004300000245006000043210005600103520095600159100001701115700002101132856003601153 2010 en_Ud 00aProjective Reeds-Shepp car on $S^2$ with quadratic cost0 aProjective ReedsShepp car on S2 with quadratic cost3 aFix two points $x,\\\\bar{x}\\\\in S^2$ and two directions (without orientation) $\\\\eta,\\\\bar\\\\eta$ of the velocities in these points. In this paper we are interested to the problem of minimizing the cost $$ J[\\\\gamma]=\\\\int_0^T g_{\\\\gamma(t)}(\\\\dot\\\\gamma(t),\\\\dot\\\\gamma(t))+\\nK^2_{\\\\gamma(t)}g_{\\\\gamma(t)}(\\\\dot\\\\gamma(t),\\\\dot\\\\gamma(t)) ~dt$$ along all smooth curves starting from $x$ with direction $\\\\eta$ and ending in $\\\\bar{x}$ with direction $\\\\bar\\\\eta$. Here $g$ is the standard Riemannian metric on $S^2$ and $K_\\\\gamma$ is the corresponding geodesic curvature.\\nThe interest of this problem comes from mechanics and geometry of vision. It can be formulated as a sub-Riemannian problem on the lens space L(4,1).\\nWe compute the global solution for this problem: an interesting feature is that some optimal geodesics present cusps. The cut locus is a stratification with non trivial topology.1 aBoscain, Ugo1 aRossi, Francesco uhttp://hdl.handle.net/1963/266801210nas 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/1963/386400550nas a2200109 4500008004300000245008300043210006900126520016900195100002100364700001900385856003600404 2010 en_Ud 00aQuasistatic crack growth in elasto-plastic materials: the two-dimensional case0 aQuasistatic crack growth in elastoplastic materials the twodimen3 aWe study a variational model for the quasistatic evolution of elasto-plastic materials with cracks in the case of planar small strain associative elasto-plasticity.1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/1963/296400595nas a2200109 4500008004300000245007600043210006900119520021600188100002100404700002400425856003600449 2010 en_Ud 00aQuasistatic crack growth in finite elasticity with non-interpenetration0 aQuasistatic crack growth in finite elasticity with noninterpenet3 aWe present a variational model to study the quasistatic growth of brittle cracks in hyperelastic materials, in the framework of finite elasticity, taking\\ninto account the non-interpenetration condition.

1 aDal Maso, Gianni1 aLazzaroni, Giuliano uhttp://hdl.handle.net/1963/339701311nas a2200121 4500008004300000245008200043210006900125520088800194653002401082100002101106700002601127856003601153 2010 en_Ud 00aQuasistatic evolution for Cam-Clay plasticity: the spatially homogeneous case0 aQuasistatic evolution for CamClay plasticity the spatially homog3 aWe study the spatially uniform case of the problem of quasistatic evolution in small strain nonassociative elastoplasticity (Cam-Clay model). Through the introdution of a viscous approximation, the problem reduces to determine the limit behavior of the solutions of a singularly perturbed system of ODE\\\'s in a finite dimensional Banach space. Depending on the sign of two explicit scalar indicators, we see that the limit dynamics presents, under quite generic assumptions, the alternation of three possible regimes: the elastic regime, when the limit equation is just the equation of linearized elasticity, the slow dynamics, when the strain evolves smoothly on the yield surface and plastic flow is produced, and the fast dynamics, which may happen only in the softening regime, where\\nviscous solutions exhibit a jump across a heteroclinic orbit of an auxiliary system.

10aCam-Clay plasticity1 aDal Maso, Gianni1 aSolombrino, Francesco uhttp://hdl.handle.net/1963/367101168nas a2200157 4500008004100000022001400041245008800055210006900143300000900212490000700221520061900228653003000847653003100877100002600908856007600934 2010 eng d a1078-094700aQuasistatic evolution for plasticity with softening: The spatially homogeneous case0 aQuasistatic evolution for plasticity with softening The spatiall a11890 v273 aThe spatially uniform case of the problem of quasistatic evolution in small strain associative elastoplasticity with softening is studied. Through the introdution of a viscous approximation, the problem reduces to determine the limit behaviour of the solutions of a singularly perturbed system of ODE's in a finite dimensional Banach space. We see that the limit dynamics presents, for a generic choice of the initial data, the alternation of three possible regimes (elastic regime, slow dynamics, fast dynamics), which is determined by the sign of two scalar indicators, whose explicit expression is given.

10aplasticity with softening10arate independent processes1 aSolombrino, Francesco uhttp://aimsciences.org//article/id/4c2301d8-f553-493e-b672-b4f76a3ede2f00741nas a2200133 4500008004300000245009200043210006900135260001900204520028800223100001800511700002100529700002100550856003600571 2010 en_Ud 00aThe reductions of the dispersionless 2D Toda hierarchy and their Hamiltonian structures0 areductions of the dispersionless 2D Toda hierarchy and their Ham bIOP Publishing3 aWe study finite-dimensional reductions of the dispersionless 2D Toda hierarchy showing that the consistency conditions for such reductions are given by a system of radial Loewner equations. We then construct their Hamiltonian structures, following an approach proposed by Ferapontov.1 aCarlet, Guido1 aLorenzoni, Paolo1 aRaimondo, Andrea uhttp://hdl.handle.net/1963/384601121nas a2200121 4500008004300000245007400043210006900117260003700186520069600223100002200919700002200941856003600963 2010 en_Ud 00aRiemann-Roch theorems and elliptic genus for virtually smooth schemes0 aRiemannRoch theorems and elliptic genus for virtually smooth sch bMathematical Sciences Publishers3 aFor a proper scheme X with a fixed 1-perfect obstruction theory, we define virtual versions of holomorphic Euler characteristic, chi y-genus, and elliptic genus; they are deformation invariant, and extend the usual definition in the smooth case. We prove virtual versions of the Grothendieck-Riemann-Roch and Hirzebruch-Riemann-Roch theorems. We show that the virtual chi y-genus is a polynomial, and use this to define a virtual topological Euler characteristic. We prove that the virtual elliptic genus satisfies a Jacobi modularity property; we state and prove a localization theorem in the toric equivariant case. We show how some of our results apply to moduli spaces of stable sheaves.1 aFantechi, Barbara1 aGöttsche, Lothar uhttp://hdl.handle.net/1963/388801810nas a2200121 4500008004300000245007000043210006600113520141500179100001901594700002201613700001701635856003601652 2010 en_Ud 00aThe role of membrane viscosity in the dynamics of fluid membranes0 arole of membrane viscosity in the dynamics of fluid membranes3 aFluid membranes made out of lipid bilayers are the fundamental separation structure in eukaryotic cells. Many physiological processes rely on dramatic shape and topological changes (e.g. fusion, fission) of fluid membrane systems. Fluidity is key to the versatility and constant reorganization of lipid bilayers. Here, we study the role of the membrane intrinsic viscosity, arising from the friction of the lipid molecules as they rearrange to accommodate shape changes, in the dynamics of morphological changes of fluid vesicles. In particular, we analyze the competition between the membrane viscosity and the viscosity of the bulk fluid surrounding the vesicle as the dominant dissipative mechanism. We consider the relaxation dynamics of fluid vesicles put in an out-of-equilibrium state, but conclusions can be drawn regarding the kinetics or power consumption in regulated shape changes in the cell. On the basis of numerical calculations, we find that the dynamics arising from the membrane viscosity are qualitatively different from the dynamics arising from the bulk viscosity. When these two dissipation mechanisms are put in competition, we find that for small vesicles the membrane dissipation dominates, with a relaxation time that scales as the size of the vesicle to the power 2. For large vesicles, the bulk dissipation dominates, and the exponent in the relaxation time vs. size relation is 3.1 aArroyo, Marino1 aDeSimone, Antonio1 aHeltai, Luca uhttp://hdl.handle.net/1963/393000486nas a2200121 4500008004100000245011700041210006900158260003300227300001400260490000700274100002700281856005600308 2010 eng d00aSemiclassical evolution of two rotating solitons for the Nonlinear Schrödinger Equation with electric potential0 aSemiclassical evolution of two rotating solitons for the Nonline bKhayyam Publishing, Inc.c03 a315–3480 v151 aSelvitella, Alessandro uhttps://projecteuclid.org:443/euclid.ade/135585475201102nas a2200109 4500008004300000245007400043210006900117520073300186100002100919700001600940856003600956 2010 en_Ud 00aOn semistable principal bundles over complex projective manifolds, II0 asemistable principal bundles over complex projective manifolds I3 aLet (X, \\\\omega) be a compact connected Kaehler manifold of complex dimension d and E_G a holomorphic principal G-bundle on X, where G is a connected reductive linear algebraic group defined over C. Let Z (G) denote the center of G. We prove that the following three statements are equivalent: (1) There is a parabolic subgroup P of G and a holomorphic reduction of the structure group of E_G to P (say, E_P) such that the bundle obtained by extending the structure group of E_P to L(P)/Z(G) (where L(P) is the Levi quotient of P) admits a flat connection; (2) The adjoint vector bundle ad(E_G) is numerically flat; (3) The principal G-bundle E_G is pseudostable, and the degree of the charateristic class c_2(ad(E_G) is zero.1 aBiswas, Indranil1 aBruzzo, Ugo uhttp://hdl.handle.net/1963/340400622nas a2200109 4500008004300000245010100043210006900144520021400213100002900427700002000456856003600476 2010 en_Ud 00aSharp nonexistence results for a linear elliptic inequality involving Hardy and Leray potentials0 aSharp nonexistence results for a linear elliptic inequality invo3 aIn this paper we deal with nonnegative distributional supersolutions for a class of linear\\nelliptic equations involving inverse-square potentials and logarithmic weights. We prove sharp nonexistence results.1 aFall, Mouhamed Moustapha1 aMusina, Roberta uhttp://hdl.handle.net/1963/386900794nas 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/1963/260101245nas a2200145 4500008004100000022001300041245008800054210006900142300001200211490000800223520070400231100002400935700002000959856012000979 2010 eng d a0003952700aSobolev periodic solutions of nonlinear wave equations in higher spatial dimensions0 aSobolev periodic solutions of nonlinear wave equations in higher a609-6420 v1953 aWe prove the existence of Cantor families of periodic solutions for nonlinear wave equations in higher spatial dimensions with periodic boundary conditions. We study both forced and autonomous PDEs. In the latter case our theorems generalize previous results of Bourgain to more general nonlinearities of class C k and assuming weaker non-resonance conditions. Our solutions have Sobolev regularity both in time and space. The proofs are based on a differentiable Nash-Moser iteration scheme, where it is sufficient to get estimates of interpolation-type for the inverse linearized operators. Our approach works also in presence of very large "clusters of small divisors". © Springer-Verlag (2009).1 aBerti, Massimiliano1 aBolle, Philippe uhttps://www.math.sissa.it/publication/sobolev-periodic-solutions-nonlinear-wave-equations-higher-spatial-dimensions00906nas a2200109 4500008004300000245009100043210006900134520052300203100001800726700001600744856003600760 2010 en_Ud 00aSolitonic asymptotics for the Korteweg-de Vries equation in the small dispersion limit0 aSolitonic asymptotics for the Kortewegde Vries equation in the s3 aWe study the small dispersion limit for the Korteweg-de Vries (KdV) equation $u_t+6uu_x+\\\\epsilon^{2}u_{xxx}=0$ in a critical scaling regime where $x$ approaches the trailing edge of the region where the KdV solution shows oscillatory behavior. Using the Riemann-Hilbert approach, we obtain an asymptotic expansion for the KdV solution in a double scaling limit, which shows that the oscillations degenerate to sharp pulses near the trailing edge. Locally those pulses resemble soliton solutions of the KdV equation.1 aGrava, Tamara1 aClaeys, Tom uhttp://hdl.handle.net/1963/383900741nas a2200133 4500008004100000245007400041210006900115260002400184300001100208490000700219520030000226100002200526856005900548 2010 eng d00aStable determination of an immersed body in a stationary Stokes fluid0 aStable determination of an immersed body in a stationary Stokes bIOP Publishingcnov a1250150 v263 aWe consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the Stokes equations, from a single measurement of force and velocity on a portion of the boundary. We obtain an estimate of the stability of log–log type.

1 aBallerini, Andrea uhttps://doi.org/10.1088%2F0266-5611%2F26%2F12%2F12501501005nas 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/10.1243/17543371jset4601175nas a2200133 4500008004300000245008500043210006900128260001300197520072500210100002900935700002000964700002100984856003601005 2010 en_Ud 00aA time-dependent perturbative analysis for a quantum particle in a cloud chamber0 atimedependent perturbative analysis for a quantum particle in a bSpringer3 aWe consider a simple model of a cloud chamber consisting of a test particle (the alpha-particle) interacting with two other particles (the atoms of the vapour) subject to attractive potentials centered in $a_1, a_2 \\\\in \\\\mathbb{R}^3$. At time zero the alpha-particle is described by an outgoing spherical wave centered in the origin and the atoms are in their ground state. We show that, under suitable assumptions on the physical parameters of the system and up to second order in perturbation theory, the probability that both atoms are ionized is negligible unless $a_2$ lies on the line joining the origin with $a_1$. The work is a fully time-dependent version of the original analysis proposed by Mott in 1929.1 aDell'Antonio, Gianfausto1 aFigari, Rodolfo1 aTeta, Alessandro uhttp://hdl.handle.net/1963/396901480nas 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/1963/360501439nas a2200181 4500008004300000245007000043210006800113260001300181300001200194490000700206520090200213100002501115700001701140700002301157700002001180700002101200856003601221 2010 en_Ud 00aTwo-dimensional almost-Riemannian structures with tangency points0 aTwodimensional almostRiemannian structures with tangency points bElsevier a793-8070 v273 aTwo-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We study the relation between the topological invariants of an almost-Riemannian structure on a compact oriented surface and the rank-two vector bundle over the surface which defines the structure. We analyse the generic case including the presence of tangency points, i.e. points where two generators of the distribution and their Lie bracket are linearly dependent. The main result of the paper provides a classification of oriented almost-Riemannian structures on compact oriented surfaces in terms of the Euler number of the vector bundle corresponding to the structure. Moreover, we present a Gauss-Bonnet formula for almost-Riemannian structures with tangency points.

1 aAgrachev, Andrei, A.1 aBoscain, Ugo1 aCharlot, Grégoire1 aGhezzi, Roberta1 aSigalotti, Mario uhttp://hdl.handle.net/1963/387001011nas a2200121 4500008004300000245008300043210006900126520059000195100001600785700002600801700002600827856003600853 2010 en_Ud 00aUhlenbeck-Donaldson compactification for framed sheaves on projective surfaces0 aUhlenbeckDonaldson compactification for framed sheaves on projec3 aWe construct a compactification $M^{\\\\mu ss}$ of the Uhlenbeck-Donaldson type for the moduli space of slope stable framed bundles. This is a kind of a moduli space of slope semistable framed sheaves. We show that there exists a projective morphism $\\\\gamma \\\\colon M^s \\\\to M^{\\\\mu ss}$, where $M^s$ is the moduli space of S-equivalence classes of Gieseker-semistable framed sheaves. The space $M^{\\\\mu ss}$ has a natural set-theoretic stratification which allows one, via a Hitchin-Kobayashi correspondence, to compare it with the moduli spaces of framed ideal instantons.1 aBruzzo, Ugo1 aMarkushevich, Dimitri1 aTikhomirov, Alexander uhttp://hdl.handle.net/1963/404900513nas a2200121 4500008004100000022001400041245014500055210006900200300001600269100001900285700002200304856006500326 2010 eng d a1073-792800aUniversality in the profile of the semiclassical limit solutions to the focusing nonlinear Schrödinger equation at the first breaking curve0 aUniversality in the profile of the semiclassical limit solutions a2119–21671 aBertola, Marco1 aTovbis, Alexander uhttp://0-dx.doi.org.mercury.concordia.ca/10.1093/imrn/rnp19600894nas a2200109 4500008004100000245007500041210006900116260001000185520052800195100002500723856003600748 2010 en d00aWell-posed infinite horizon variational problems on a compact manifold0 aWellposed infinite horizon variational problems on a compact man bSISSA3 aWe give an effective sufficient condition for a variational problem with infinite horizon on a compact Riemannian manifold M to admit a smooth optimal synthesis, i. e., a smooth dynamical system on M whose positive semi-trajectories are solutions to the problem. To realize the synthesis, we construct an invariant Lagrangian submanifold (well-projected to M) of the flow of extremals in the cotangent bundle T*M. The construction uses the curvature of the flow in the cotangent bundle and some ideas of hyperbolic dynamics1 aAgrachev, Andrei, A. uhttp://hdl.handle.net/1963/645801174nas a2200109 4500008004300000245005400043210005300097520082800150100002900978700002101007856003601028 2009 en_Ud 00a1D periodic potentials with gaps vanishing at k=00 a1D periodic potentials with gaps vanishing at k03 aAppearance of energy bands and gaps in the dispersion relations of a periodic potential is a standard feature of Quantum Mechanics. We investigate the class of one-dimensional periodic potentials for which all gaps vanish at the center of the Brillouin zone. We characterise themthrough a necessary and sufficient condition. Potentials of the form we focus on arise in different fields of Physics, from supersymmetric Quantum Mechanics, to Korteweg-de Vries equation theory and classical diffusion problems. The O.D.E. counterpart to this problem is the characterisation of periodic potentials for which coexistence occurs of linearly independent solutions of the corresponding Schrödinger equation (Hill\\\'s equation). This result is placed in the perspective of the previous related results available in the literature.1 aMichelangeli, Alessandro1 aZagordi, Osvaldo uhttp://hdl.handle.net/1963/181800396nas a2200109 4500008004300000245007300043210006900116100002200185700002300207700002000230856003600250 2009 en_Ud 00aBiological Fluid Dynamics, Non-linear Partial Differential Equations0 aBiological Fluid Dynamics Nonlinear Partial Differential Equatio1 aDeSimone, Antonio1 aAlouges, François1 aLefebvre, Aline uhttp://hdl.handle.net/1963/263002193nas a2200109 4500008004300000245008700043210006900130520180600199100002302005700001902028856003602047 2009 en_Ud 00aThe boundary Riemann solver coming from the real vanishing viscosity approximation0 aboundary Riemann solver coming from the real vanishing viscosity3 aWe study the limit of the hyperbolic-parabolic approximation $$ \\\\begin{array}{lll} v_t + \\\\tilde{A} ( v, \\\\, \\\\varepsilon v_x ) v_x = \\\\varepsilon \\\\tilde{B}(v ) v_{xx} \\\\qquad v \\\\in R^N\\\\\\\\ \\\\tilde \\\\beta (v (t, \\\\, 0)) = \\\\bar g \\\\\\\\ v (0, \\\\, x) = \\\\bar v_0. \\\\\\\\ \\\\end{array} \\\\right. $$\\nThe function $\\\\tilde \\\\beta$ is defined in such a way to guarantee that the initial boundary value problem is well posed even if $\\\\tilde \\\\beta$ is not invertible.\\nThe data $\\\\bar g$ and $\\\\bar v_0$ are constant. When $\\\\tilde B$ is invertible, the previous problem takes the simpler form $$ \\\\left\\\\{ \\\\begin{array}{lll} v_t + \\\\tilde{A} \\\\big( v, \\\\, \\\\varepsilon v_x \\\\big) v_x = \\\\varepsilon \\\\tilde{B}(v ) v_{xx} \\\\qquad v \\\\in \\\\mathbb{R}^N\\\\\\\\ v (t, \\\\, 0) \\\\equiv \\\\bar v_b \\\\\\\\ v (0, \\\\, x) \\\\equiv \\\\bar{v}_0. \\\\\\\\ \\\\end{array} \\\\right. $$\\nAgain, the data $\\\\bar v_b$ and $\\\\bar v_0$ are constant. The conservative case is included in the previous formulations. It is assumed convergence of the v, smallness of the total variation and other technical hypotheses and it is provided a complete characterization of the limit. The most interesting points are the following two. First, the boundary characteristic case is considered, i.e. one eigenvalue of $\\\\tilde A$ can be 0.\\n Second, as pointed out before we take into account the possibility that $\\\\tilde B$ is not invertible. To deal with this case, we take as hypotheses conditions that were introduced by Kawashima and Shizuta relying on physically meaningful examples. We also introduce a new condition of block linear degeneracy. We prove that, if it is not satisfied, then pathological behaviours may occur.1 aBianchini, Stefano1 aSpinolo, Laura uhttp://hdl.handle.net/1963/183100355nas a2200097 4500008004300000245006900043210006800112100002100180700002000201856003600221 2009 en_Ud 00aBubbles with prescribed mean curvature: the variational approach0 aBubbles with prescribed mean curvature the variational approach1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/365900390nas a2200133 4500008004100000245003400041210003000075300001500105490000800120100001900128700001600147700001900163856007400182 2009 eng d00aThe Cauchy two–matrix model0 aCauchy two–matrix model a983–10140 v2871 aBertola, Marco1 aGekhtman, M1 aSzmigielski, J uhttps://www.math.sissa.it/publication/cauchy-two%E2%80%93matrix-model02219nas 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/1963/370600578nas a2200133 4500008004100000022001400041245013700055210006900192300001400261490000800275100001900283700001500302856012700317 2009 eng d a0001-870800aCommuting difference operators, spinor bundles and the asymptotics of orthogonal polynomials with respect to varying complex weights0 aCommuting difference operators spinor bundles and the asymptotic a154–2180 v2201 aBertola, Marco1 aMo, M., Y. uhttps://www.math.sissa.it/publication/commuting-difference-operators-spinor-bundles-and-asymptotics-orthogonal-polynomials00337nas a2200097 4500008004300000245006000043210005800103100002300161700001900184856003600203 2009 en_Ud 00aA connection between viscous profiles and singular ODEs0 aconnection between viscous profiles and singular ODEs1 aBianchini, Stefano1 aSpinolo, Laura uhttp://hdl.handle.net/1963/255500997nas a2200109 4500008004300000245011900043210006900162260001300231520058500244100002200829856003600851 2009 en_Ud 00aControllability and simultaneous controllability of isospectral bilinear control systems on complex flag manifolds0 aControllability and simultaneous controllability of isospectral bElsevier3 aFor isospectral bilinear control systems evolving on the so-called complex flag manifolds (i.e., on the orbits of the Hermitian matrices under unitary conjugation action) it is shown that controllability is almost always verified. Easy and generic sufficient conditions are provided. The result applies to the problem of density operator controllability of finite dimensional quantum mechanical systems. In addition, we show that systems having different drifts (corresponding for example to different Larmor frequencies) are simultaneously controllable by the same control field.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/352301061nas a2200133 4500008004300000245009500043210006900138520060700207100002200814700001700836700002100853700001700874856003600891 2009 en_Ud 00aControllability of the discrete-spectrum Schrodinger equation driven by an external field0 aControllability of the discretespectrum Schrodinger equation dri3 aWe prove approximate controllability of the bilinear Schrodinger equation in the case in which the uncontrolled Hamiltonian has discrete nonresonant\\nspectrum. The results that are obtained apply both to bounded or unbounded domains and to the case in which the control potential is bounded or unbounded. The method relies on finite-dimensional techniques applied to the\\nGalerkin approximations and permits, in addition, to get some controllability properties for the density matrix. Two examples are presented: the harmonic oscillator and the 3D well of potential controlled by suitable potentials.1 aChambrion, Thomas1 aMason, Paolo1 aSigalotti, Mario1 aBoscain, Ugo uhttp://hdl.handle.net/1963/254700583nas a2200109 4500008004300000245005200043210005200095520024400147100002500391700002100416856003600437 2009 en_Ud 00aControllability on the group of diffeomorphisms0 aControllability on the group of diffeomorphisms3 aGiven a compact manifold M, we prove that any bracket generating family of vector fields on M, which is invariant under multiplication by smooth functions, generates the connected component of identity of the group of diffeomorphisms of M.1 aAgrachev, Andrei, A.1 aCaponigro, Marco uhttp://hdl.handle.net/1963/339600806nas a2200121 4500008004300000245007400043210006700117260004800184520037100232100002100603700002400624856003600648 2009 en_Ud 00aOn the convergence of viscous approximations after shock interactions0 aconvergence of viscous approximations after shock interactions bAmerican Institute of Mathematical Sciences3 aWe consider a piecewise smooth solution to a scalar conservation law, with possibly interacting shocks. We show that, after the interactions have taken place, vanishing viscosity approximations can still be represented by a regular expansion on smooth regions and by a singular perturbation expansion near the shocks, in terms of powers of the viscosity coefficient.1 aBressan, Alberto1 aDonadello, Carlotta uhttp://hdl.handle.net/1963/341200501nas a2200145 4500008004100000022001400041245007700055210006900132300001500201490000700216100001900223700001700242700002000259856007600279 2009 eng d a1751-811300aCubic string boundary value problems and Cauchy biorthogonal polynomials0 aCubic string boundary value problems and Cauchy biorthogonal pol a454006, 130 v421 aBertola, Marco1 aGekhtman, M.1 aSzmigielski, J. uhttp://0-dx.doi.org.mercury.concordia.ca/10.1088/1751-8113/42/45/45400601270nas 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/1963/363201885nas a2200121 4500008004300000245008700043210006900130260001300199520148100212100001801693700001601711856003601727 2009 en_Ud 00aDifferential geometry of curves in Lagrange Grassmannians with given Young diagram0 aDifferential geometry of curves in Lagrange Grassmannians with g bElsevier3 aCurves in Lagrange Grassmannians appear naturally in the intrinsic study of geometric structures on manifolds. By a smooth geometric structure on a manifold we mean any submanifold of its tangent bundle, transversal to the fibers. One can consider the time-optimal problem naturally associate with a geometric structure. The Pontryagin extremals of this optimal problem are integral curves of certain Hamiltonian system in the cotangent bundle. The dynamics of the fibers of the cotangent bundle w.r.t. this system along an extremal is described by certain curve in a Lagrange Grassmannian, called Jacobi curve of the extremal. Any symplectic invariant of the Jacobi curves produces the invariant of the original geometric structure. The basic characteristic of a curve in a Lagrange Grassmannian is its Young diagram. The number of boxes in its kth column is equal to the rank of the kth derivative of the curve (which is an appropriately defined linear mapping) at a generic point. We will describe the construction of the complete system of symplectic invariants for parameterized curves in a Lagrange Grassmannian with given Young diagram. It allows to develop in a unified way local differential geometry of very wide classes of geometric structures on manifolds, including both classical geometric structures such as Riemannian and Finslerian structures and less classical ones such as sub-Riemannian and sub-Finslerian structures, defined on nonholonomic distributions.1 aZelenko, Igor1 aChengbo, Li uhttp://hdl.handle.net/1963/381901141nas a2200133 4500008004300000245014200043210006900185260004800254520060000302100002000902700002200922700002700944856003600971 2009 en_Ud 00aDiscrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers0 aDiscretetocontinuum limits for strainalignmentcoupled systems Ma bAmerican Institute of Mathematical Sciences3 aIn the framework of linear elasticity, we study the limit of a class of discrete free energies modeling strain-alignment-coupled systems by a rigorous coarse-graining procedure, as the number of molecules diverges. We focus on three paradigmatic examples: magnetostrictive solids, ferroelectric crystals and nematic elastomers, obtaining in the limit three continuum models consistent with those commonly employed in the current literature. We also derive the correspondent macroscopic energies in the presence of displacement boundary conditions and of various kinds of applied external fields.1 aCicalese, Marco1 aDeSimone, Antonio1 aZeppieri, Caterina Ida uhttp://hdl.handle.net/1963/378800354nas a2200097 4500008004100000245007900041210006900120260001000189100002100199856003600220 2009 en d00aThe Disintegration Theorem and Applications to Optimal Mass Transportation0 aDisintegration Theorem and Applications to Optimal Mass Transpor bSISSA1 aCaravenna, Laura uhttp://hdl.handle.net/1963/590000760nas a2200145 4500008004300000020002200043245006300065210006300128520031500191100001600506700001700522700001700539700002200556856003600578 2009 en_Ud a978-981-270-377-400aEquivariant cohomology and localization for Lie algebroids0 aEquivariant cohomology and localization for Lie algebroids3 aLet M be a manifold carrying the action of a Lie group G, and A a Lie algebroid on M equipped with a compatible infinitesimal G-action. Out of these data we construct an equivariant Lie algebroid cohomology and prove for compact G a related localization formula. As an application we prove a Bott-type formula.1 aBruzzo, Ugo1 aCirio, Lucio1 aRossi, Paolo1 aRubtsov, Vladimir uhttp://hdl.handle.net/1963/172400980nas a2200121 4500008004300000245005900043210005800102260002800160520059200188100002000780700002200800856003600822 2009 en_Ud 00aERNEST: a toolbox for chemical reaction network theory0 aERNEST a toolbox for chemical reaction network theory bOxford University Press3 aSummary: ERNEST Reaction Network Equilibria Study Toolbox is a MATLAB package which, by checking various different criteria on the structure of a chemical reaction network, can exclude the multistationarity of the corresponding reaction system. The results obtained are independent of the rate constants of the reactions, and can be used for model discrimination.\\nAvailability and Implementation: The software, implemented in MATLAB, is available under the GNU GPL free software license from http://people.sissa.it/~altafini/papers/SoAl09/. It requires the MATLAB Optimization Toolbox.1 aSoranzo, Nicola1 aAltafini, Claudio uhttp://hdl.handle.net/1963/382600361nas a2200097 4500008004300000245007300043210006900116100001800185700002400203856003600227 2009 en_Ud 00aExact results for topological strings on resolved Yp,q singularities0 aExact results for topological strings on resolved Ypq singularit1 aBrini, Andrea1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/263100512nas a2200097 4500008004300000245009600043210006900139520015000208100002000358856003600378 2009 en_Ud 00aExistence of extremals for the Maz\\\'ya and for the Caffarelli-Kohn-Nirenberg inequalities0 aExistence of extremals for the Mazya and for the CaffarelliKohnN3 aThis paper deals with some Sobolev-type inequalities with weights that were proved by Maz\\\'ya in 1980 and by Caffarelli-Kohn-Nirenberg in 1984.1 aMusina, Roberta uhttp://hdl.handle.net/1963/273900318nas a2200085 4500008004300000245006800043210006400111100002100175856003600196 2009 en_Ud 00aAn existence result for the Monge problem in R^n with norm cost0 aexistence result for the Monge problem in Rn with norm cost1 aCaravenna, Laura uhttp://hdl.handle.net/1963/364700624nas a2200109 4500008004300000245007200043210006400115520025500179100002300434700002100457856003600478 2009 en_Ud 00aOn the extremality, uniqueness and optimality of transference plans0 aextremality uniqueness and optimality of transference plans3 aWe consider the following standard problems appearing in optimal mass transportation theory: when a transference plan is extremal; when a transference plan is the unique transference plan concentrated on a set A,; when a transference plan is optimal.1 aBianchini, Stefano1 aCaravenna, Laura uhttp://hdl.handle.net/1963/369200938nas a2200109 4500008004300000245007800043210006900121520056500190100001700755700002000772856003600792 2009 en_Ud 00aFamilies of Monads and Instantons from a Noncommutative ADHM Construction0 aFamilies of Monads and Instantons from a Noncommutative ADHM Con3 aWe give a \\\\theta-deformed version of the ADHM construction of SU(2) instantons with arbitrary topological charge on the sphere S^4. Classically the instanton gauge fields are constructed from suitable monad data; we show that in the deformed case the set of monads is itself a noncommutative space. We use these monads to construct noncommutative `families\\\' of SU(2) instantons on the deformed sphere S^4_\\\\theta. We also compute the topological charge of each of the families. Finally we discuss what it means for such families to be gauge equivalent.1 aBrain, Simon1 aLandi, Giovanni uhttp://hdl.handle.net/1963/347800454nas a2200133 4500008004100000022001400041245006900055210006900124300001400193490000700207100001900214700001600233856007100249 2009 eng d a0176-427600aFirst colonization of a spectral outpost in random matrix theory0 aFirst colonization of a spectral outpost in random matrix theory a225–2630 v301 aBertola, Marco1 aLee, S., Y. uhttp://0-dx.doi.org.mercury.concordia.ca/10.1007/s00365-008-9026-y08321nas a2200145 4500008004100000245008100041210006900122260001300191300001600204490000700220520785400227100003008081700001908111856004508130 2009 eng d00aFoliations of small tubes in Riemannian manifolds by capillary minimal discs0 aFoliations of small tubes in Riemannian manifolds by capillary m bElsevier a4422–44400 v703 aLetting be an embedded curve in a Riemannian manifold , we prove the existence of minimal disc-type surfaces centered at inside the surface of revolution of around , having small radius, and intersecting it with constant angles. In particular we obtain that small tubular neighborhoods can be foliated by minimal discs.

1 aFall, Mouhamed, Moustapha1 aMercuri, Carlo uhttps://doi.org/10.1016/j.na.2008.10.02400873nas a2200133 4500008004300000245004600043210004600089260001300135520049300148100002000641700001800661700002400679856003600703 2009 en_Ud 00aGauged Laplacians on quantum Hopf bundles0 aGauged Laplacians on quantum Hopf bundles bSpringer3 aWe study gauged Laplacian operators on line bundles on a quantum 2-dimensional sphere. Symmetry under the (co)-action of a quantum group allows for their complete diagonalization. These operators describe `excitations moving on the quantum sphere\\\' in the field of a magnetic monopole. The energies are not invariant under the exchange monopole/antimonopole, that is under inverting the direction of the magnetic field. There are potential applications to models of quantum Hall effect.1 aLandi, Giovanni1 aReina, Cesare1 aZampini, Alessandro uhttp://hdl.handle.net/1963/354001528nas a2200121 4500008004100000020002200041245010900063210006900172260001000241520109900251100002001350856003601370 2009 en d a978-90-481-2810-500aHamiltonian perturbations of hyperbolic PDEs: from classification results to the properties of solutions0 aHamiltonian perturbations of hyperbolic PDEs from classification bSISSA3 aWe begin with presentation of classi cation results in the theory of Hamiltonian\\r\\nPDEs with one spatial dimension depending on a small parameter. Special\\r\\nattention is paid to the deformation theory of integrable hierarchies, including an\\r\\nimportant subclass of the so-called integrable hierarchies of the topological type\\r\\nassociated with semisimple Frobenius manifolds. Many well known equations of\\r\\nmathematical physics, such as KdV, NLS, Toda, Boussinesq etc., belong to this\\r\\nsubclass, but there are many new integrable PDEs, some of them being of interest\\r\\nfor applications. Connections with the theory of Gromov{Witten invariants\\r\\nand random matrices are outlined. We then address the problem of comparative\\r\\nstudy of singularities of solutions to the systems of first order quasilinear\\r\\nPDEs and their Hamiltonian perturbations containing higher derivatives. We\\r\\nformulate Universality Conjectures describing different types of critical behavior\\r\\nof perturbed solutions near the point of gradient catastrophe of the unperturbed\\r\\none.1 aDubrovin, Boris uhttp://hdl.handle.net/1963/647000381nas a2200097 4500008004300000245009500043210006900138100002000207700002000227856003600247 2009 en_Ud 00aHardy-Sobolev-Maz\\\'ja inequalities: symmetry and breaking symmetry of extremal functions0 aHardySobolevMazja inequalities symmetry and breaking symmetry of1 aGazzini, Marita1 aMusina, Roberta uhttp://hdl.handle.net/1963/256900927nas a2200133 4500008004300000245007300043210006900116520048700185100002100672700001900693700002000712700002500732856003600757 2009 en_Ud 00aA higher order model for image restoration: the one dimensional case0 ahigher order model for image restoration the one dimensional cas3 aThe higher order total variation-based model for image restoration proposed by Chan, Marquina, and Mulet in [6] is analyzed in one dimension. A suitable functional framework in which the minimization problem is well posed is being proposed and it is proved analytically that the\\nhigher order regularizing term prevents the occurrence of the staircase effect. The generalized version of the model considered here includes, as particular cases, some curvature dependent functionals.1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/317400361nas a2200097 4500008004300000245007700043210006900120100001600189700002200205856003600227 2009 en_Ud 00aHolomorphic equivariant cohomology of Atiyah algebroids and localization0 aHolomorphic equivariant cohomology of Atiyah algebroids and loca1 aBruzzo, Ugo1 aRubtsov, Vladimir uhttp://hdl.handle.net/1963/377401152nas a2200121 4500008004300000245007700043210006900120260000900189520075400198100002100952700002100973856003600994 2009 en_Ud 00aHomogenization of fiber reinforced brittle materials: the extremal cases0 aHomogenization of fiber reinforced brittle materials the extrema bSIAM3 aWe analyze the behavior of a fragile material reinforced by a reticulated elastic unbreakable structure in the case of antiplane shear. The microscopic geometry of this material is described by means of two small parameters: the period $\\\\varepsilon$ of the grid and the ratio $\\\\delta$ between the thickness of the fibers and the period $\\\\varepsilon$. We show that the asymptotic behavior as $\\\\varepsilon\\\\to0^+$ and $\\\\delta\\\\to0^+$ depends dramatically on the relative size of these parameters. Indeed, in the two cases considered, i.e., $\\\\varepsilon\\\\ll\\\\delta$ and $\\\\varepsilon\\\\gg\\\\delta$, we obtain two different limit models: a perfectly elastic model and an elastic model with macroscopic cracks, respectively.1 aBarchiesi, Marco1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/270500963nas 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/1963/342901520nas a2200133 4500008004300000245008600043210006900129520106500198100002501263700001701288700002401305700002101329856003601350 2009 en_Ud 00aThe intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups0 aintrinsic hypoelliptic Laplacian and its heat kernel on unimodul3 aWe present an invariant definition of the hypoelliptic Laplacian on sub-Riemannian structures with constant growth vector, using the Popp\\\'s volume form introduced by Montgomery. This definition generalizes the one of the Laplace-Beltrami operator in Riemannian geometry. In the case of left-invariant problems on unimodular Lie groups we prove that it coincides with the usual sum of squares.\\nWe then extend a method (first used by Hulanicki on the Heisenberg group) to compute explicitly the kernel of the hypoelliptic heat equation on any unimodular Lie group of type I. The main tool is the noncommutative Fourier transform. We then study some relevant cases: SU(2), SO(3), SL(2) (with the metrics inherited by the Killing form), and the group SE(2) of rototranslations of the plane.\\nOur study is motivated by some recent results about the cut and conjugate loci on these sub-Riemannian manifolds. The perspective is to understand how singularities of the sub-Riemannian distance reflect on the kernel of the corresponding hypoelliptic heat equation.1 aAgrachev, Andrei, A.1 aBoscain, Ugo1 aGauthier, Jean-Paul1 aRossi, Francesco uhttp://hdl.handle.net/1963/266901588nas a2200133 4500008004300000245010000043210006900143260000900212520113200221100002101353700002201374700002201396856003601418 2009 en_Ud 00aInvestigating the Conformational Stability of Prion Strains through a Kinetic Replication Model0 aInvestigating the Conformational Stability of Prion Strains thro bPLoS3 aPrion proteins are known to misfold into a range of different aggregated forms, showing different phenotypic and pathological states. Understanding strain specificities is an important problem in the field of prion disease. Little is known about which PrPSc structural properties and molecular mechanisms determine prion replication, disease progression and strain phenotype. The aim of this work is to investigate, through a mathematical model, how the structural stability of different aggregated forms can influence the kinetics of prion replication. The model-based results suggest that prion strains with different conformational stability undergoing in vivo replication are characterizable in primis by means of different rates of breakage. A further role seems to be played by the aggregation rate (i.e. the rate at which a prion fibril grows). The kinetic variability introduced in the model by these two parameters allows us to reproduce the different characteristic features of the various strains (e.g., fibrils\\\' mean length) and is coherent with all experimental observations concerning strain-specific behavior.1 aZampieri, Mattia1 aLegname, Giuseppe1 aAltafini, Claudio uhttp://hdl.handle.net/1963/398902238nas a2200109 4500008004300000245010000043210006900143520184600212100001602058700001802074856003602092 2009 en_Ud 00aJacobi Equations and Comparison Theorems for Corank 1 Sub-Riemannian structures with symmetries0 aJacobi Equations and Comparison Theorems for Corank 1 SubRiemann3 aThe Jacobi curve of an extremal of optimal control problem is a curve in a Lagrangian Grassmannian defined up to a symplectic transformation and containing all information about the solutions of the Jacobi equations along this extremal. In our previous works we constructed the canonical\\nbundle of moving frames and the complete system of symplectic invariants, called curvature maps, for\\nparametrized curves in Lagrange Grassmannians satisfying very general assumptions. The structural\\nequation for a canonical moving frame of the Jacobi curve of an extremal can be interpreted as the\\nnormal form for the Jacobi equation along this extremal and the curvature maps can be seen as the\\n\\\"coefficients\\\"of this normal form. In the case of a Riemannian metric there is only one curvature map and it is naturally related to the Riemannian sectional curvature. In the present paper we study the curvature maps for a sub-Riemannian structure on a corank 1 distribution having an additional transversal infinitesimal symmetry. After the factorization by the integral foliation of this symmetry, such sub-Riemannian structure can be reduced to a Riemannian manifold equipped with a closed 2-form(a magnetic field). We obtain explicit expressions for the curvature maps of the original sub-Riemannian structure in terms of the curvature tensor of this Riemannian manifold and the magnetic field. We also estimate the number of conjugate points along the sub-Riemannian extremals in terms of the bounds for the curvature tensor of this Riemannian manifold and the magnetic field in the case of an uniform magnetic field. The language developed for the calculation of the curvature maps can be applied to more general sub-Riemannian structures with symmetries, including sub-Riemmannian structures appearing naturally in Yang-Mills fields.1 aChengbo, Li1 aZelenko, Igor uhttp://hdl.handle.net/1963/373600554nas a2200145 4500008004100000245010200041210006900143260005400212300001400266490000800280100001700288700002500305700002300330856005500353 2009 eng d00aLow-Frequency Variations of Force Coefficients on Square Cylinders with Sharp and Rounded Corners0 aLowFrequency Variations of Force Coefficients on Square Cylinder bAmerican Society of Civil Engineers ({ASCE})cjul a828–8350 v1351 aMola, Andrea1 aBordonaro, Giancarlo1 aHajj, Muhammad, R. uhttps://doi.org/10.1061/(asce)st.1943-541x.000003400443nas a2200145 4500008004100000022001400041245004700055210004700102300001500149490000700164100001900171700001600190700001500206856007600221 2009 eng d a1751-811300aMesoscopic colonization in a spectral band0 aMesoscopic colonization in a spectral band a415204, 170 v421 aBertola, Marco1 aLee, S., Y.1 aMo, M., Y. uhttp://0-dx.doi.org.mercury.concordia.ca/10.1088/1751-8113/42/41/41520400903nas a2200145 4500008004100000245006400041210006300105260002900168300001600197490000700213520043600220100003000656700001900686856005200705 2009 eng d00aMinimal disc-type surfaces embedded in a perturbed cylinder0 aMinimal disctype surfaces embedded in a perturbed cylinder bKhayyam Publishing, Inc. a1115–11240 v223 aIn the present note we deal with small perturbations of an infinite cylinder in the 3D euclidian space. We find minimal disc-type surfaces embedded in the cylinder and intersecting its boundary perpendicularly. The existence and localization of those minimal discs is a consequence of a non-degeneracy condition for the critical points of a functional related to the oscillations of the cylinder from the flat configuration.

1 aFall, Mouhamed, Moustapha1 aMercuri, Carlo uhttps://projecteuclid.org/euclid.die/135601940700433nas a2200157 4500008004100000245004500041210004300086260001500129300001400144490000700158100001800165700001700183700001700200700002100217856003700238 2009 eng d00aA model for the dynamics of rowing boats0 amodel for the dynamics of rowing boats bWileycsep a119–1430 v611 aFormaggia, L.1 aMiglio, Edie1 aMola, Andrea1 aMontano, Antonio uhttps://doi.org/10.1002/fld.194000606nas 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/1963/358900389nas a2200109 4500008004100000245005500041210005500096300001200151490000700163100001900170856009000189 2009 eng d00aMoment determinants as isomonodromic tau functions0 aMoment determinants as isomonodromic tau functions a29–500 v221 aBertola, Marco uhttps://www.math.sissa.it/publication/moment-determinants-isomonodromic-tau-functions01344nas a2200145 4500008004300000245009700043210006900140260001900209520085100228100002001079700002101099700002001120700002201140856003601162 2009 en_Ud 00amRNA stability and the unfolding of gene expression in the long-period yeast metabolic cycle0 amRNA stability and the unfolding of gene expression in the longp bBioMed Central3 aBackground: In yeast, genome-wide periodic patterns associated with energy-metabolic oscillations have been shown recently for both short (approx. 40 min) and long (approx. 300 min) periods.\\nResults: The dynamical regulation due to mRNA stability is found to be an important aspect of the genome-wide coordination of the long-period yeast metabolic cycle. It is shown that for periodic genes, arranged in classes according either to expression profile or to function, the pulses of mRNA abundance have phase and width which are directly proportional to the corresponding turnover rates.\\nConclusion: The cascade of events occurring during the yeast metabolic cycle (and their correlation with mRNA turnover) reflects to a large extent the gene expression program observable in other dynamical contexts such as the response to stresses/stimuli.1 aSoranzo, Nicola1 aZampieri, Mattia1 aFarina, Lorenzo1 aAltafini, Claudio uhttp://hdl.handle.net/1963/363000530nas 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/1963/263200356nas a2200085 4500008004300000245010200043210006900145100002000214856003600234 2009 en_Ud 00aA note on the paper \\\"Optimizing improved Hardy inequalities\\\" by S. Filippas and A. Tertikas0 anote on the paper Optimizing improved Hardy inequalities by S Fi1 aMusina, Roberta uhttp://hdl.handle.net/1963/269801018nas a2200109 4500008004300000245005800043210005800101520067400159100002500833700001400858856003600872 2009 en_Ud 00aOptimal transportation under nonholonomic constraints0 aOptimal transportation under nonholonomic constraints3 aWe study the Monge\\\'s optimal transportation problem where the cost is given by optimal control cost. We prove the existence and uniqueness of optimal map under certain regularity conditions on the Lagrangian, absolute continuity of the measures and most importantly the absent of sharp abnormal minimizers. In particular, this result is applicable in the case of subriemannian manifolds with a 2-generating distribution and cost given by d2, where d is the subriemannian distance. Also, we discuss some properties of the optimal plan when abnormal minimizers are present. Finally, we consider some examples of displacement interpolation in the case of Grushin plane.1 aAgrachev, Andrei, A.1 aLee, Paul uhttp://hdl.handle.net/1963/217600462nas a2200133 4500008004100000022001400041245008300055210007000138300001500208490000700223100001900230700001600249856006300265 2009 eng d a0022-248800aThe partition function of the two-matrix model as an isomonodromic τ function0 apartition function of the twomatrix model as an isomonodromic τ a013529, 170 v501 aBertola, Marco1 aMarchal, O. uhttp://0-dx.doi.org.mercury.concordia.ca/10.1063/1.305486500735nas a2200109 4500008004300000245009500043210006900138520033900207100002100546700002200567856003600589 2009 en_Ud 00aQuasistatic evolution for Cam-Clay plasticity: examples of spatially homogeneous solutions0 aQuasistatic evolution for CamClay plasticity examples of spatial3 aWe study a quasistatic evolution problem for Cam-Clay plasticity under a special loading program which leads to spatially homogeneous solutions. Under some initial conditions, the solutions exhibit a softening behaviour and time discontinuities.\\nThe behavior of the solutions at the jump times is studied by a viscous approximation.1 aDal Maso, Gianni1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/339501324nas a2200121 4500008004100000245008000041210006900121300001300190490000700203520085200210100002601062856011401088 2009 eng d00aQuasistatic evolution problems for nonhomogeneous elastic plastic materials0 aQuasistatic evolution problems for nonhomogeneous elastic plasti a89–1190 v163 aThe paper studies the quasistatic evolution for elastoplastic materials when the yield surface depends on the position in the reference configuration. The main results are obtained when the yield surface is continuous with respect to the space variable. The case of piecewise constant dependence is also considered. The evolution is studied in the framework of the variational formulation for rate independent problems developed by Mielke. The results are proved by adapting the arguments introduced for a constant yield surface, using some properties of convex valued semicontinuous multifunctions. A strong formulation of the problem is also obtained, which includes a pointwise version of the plastic flow rule. Some examples are considered, which show that strain concentration may occur as a consequence of a nonconstant yield surface.

1 aSolombrino, Francesco uhttps://www.math.sissa.it/publication/quasistatic-evolution-problems-nonhomogeneous-elastic-plastic-materials00456nas a2200133 4500008004100000022001400041245006800055210006800123300001400191490000800205100001900213700001900232856007100251 2009 eng d a0021-904500aRegularity of a vector potential problem and its spectral curve0 aRegularity of a vector potential problem and its spectral curve a353–3700 v1611 aBalogh, Ferenc1 aBertola, Marco uhttp://0-dx.doi.org.mercury.concordia.ca/10.1016/j.jat.2008.10.01001411nas a2200121 4500008004300000245004300043210004300086260003000129520105300159100001901212700002201231856003601253 2009 en_Ud 00aRelaxation dynamics of fluid membranes0 aRelaxation dynamics of fluid membranes bAmerican Physical Society3 aWe study the effect of membrane viscosity in the dynamics of liquid membranes-possibly with free or internal boundaries-driven by conservative forces (curvature elasticity and line tension) and dragged by the bulk dissipation of the ambient fluid and the friction occurring when the amphiphilic molecules move relative to each other. To this end, we formulate a continuum model which includes a form of the governing equations for a two-dimensional viscous fluid moving on a curved, time-evolving surface. The effect of membrane viscosity has received very limited attention in previous continuum studies of the dynamics of fluid membranes, although recent coarse-grained discrete simulations suggest its importance. By applying our model to the study of vesiculation and membrane fusion in a simplified geometry, we conclude that membrane viscosity plays a dominant role in the relaxation dynamics of fluid membranes of sizes comparable to those found in eukaryotic cells, and is not negligible in many large synthetic systems of current interest.1 aArroyo, Marino1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/361800362nas a2200097 4500008004300000245007600043210006900119100002000188700002000208856003600228 2009 en_Ud 00aOn a Sobolev type inequality related to the weighted p-Laplace operator0 aSobolev type inequality related to the weighted pLaplace operato1 aGazzini, Marita1 aMusina, Roberta uhttp://hdl.handle.net/1963/261300857nas a2200133 4500008004100000245010700041210007200148300001200220490000700232520040100239100002000640700001700660856004600677 2009 eng d00aSolutions of the Schrödinger–Poisson problem concentrating on spheres, part I: necessary conditions0 aSolutions of the Schrödinger–Poisson problem concentrating on sp a707-7200 v193 aIn this paper we study a coupled nonlinear Schrödinger–Poisson problem with radial functions. This system has been introduced as a model describing standing waves for the nonlinear Schrödinger equations in the presence of the electrostatic field. We provide necessary conditions for concentration on sphere for the solutions of this kind of problem extending the results already known.

1 aIanni, Isabella1 aVaira, Giusi uhttps://doi.org/10.1142/S021820250900358900350nas a2200097 4500008004300000245006900043210006900112260001300181100002200194856003600216 2009 en_Ud 00aSome new entire solutions of semilinear elliptic equations on Rn0 aSome new entire solutions of semilinear elliptic equations on Rn bElsevier1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/364500893nas a2200109 4500008004300000245007600043210006900119520051500188100002200703700002200725856003600747 2009 en_Ud 00aStrain-order coupling in nematic elastomers: equilibrium configurations0 aStrainorder coupling in nematic elastomers equilibrium configura3 aWe consider models that describe liquid crystal elastomers either in a biaxial or in a uniaxial phase and in the framework of Frank\\\'s director theory. We prove existence of static equilibrium solutions in the presence of frustrations due to electro-mechanical boundary conditions and to applied loads and fields. We find explicit solutions arising in connection with special boundary conditions and the corresponding phase diagrams, leading to significant implications on possible experimental observations.1 aCesana, Pierluigi1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/270000754nas a2200121 4500008004300000245007200043210006900115520035700184100002200541700001600563700001700579856003600596 2009 en_Ud 00aStratos: a code for 3D free surface flows with floating constraints0 aStratos a code for 3D free surface flows with floating constrain3 aThis report presents a brief discussion of the theoretical aspects and practical implementation of STRATOS . STRATOS is a 3D code for the simulation\\nof hydrodynamic flows for incompressible fluids, in the presence of a free surface, capable of simulating the interaction between the free surface and a\\nfloating object via Lagrange multipliers......1 aDeSimone, Antonio1 aBianchi, B.1 aHeltai, Luca uhttp://hdl.handle.net/1963/370100841nas a2200121 4500008004300000245007600043210006900119520043200188100002200620700001700642700002400659856003600683 2009 en_Ud 00aTools for the Solution of PDEs Defined on Curved Manifolds with deal.II0 aTools for the Solution of PDEs Defined on Curved Manifolds with 3 aThe deal.II finite element library was originally designed to solve partial differential equations defined on one, two or three space dimensions, mostly\\nvia the Finite Element Method. In its versions prior to version 6.2, the user could not solve problems defined on curved manifolds embedded in two or\\nthree spacial dimensions. This infrastructure is needed if one wants to solve, for example, Boundary Integral Equations.1 aDeSimone, Antonio1 aHeltai, Luca1 aManigrasso, Cataldo uhttp://hdl.handle.net/1963/370001000nas a2200121 4500008004300000245006600043210006400109520060600173100002000779700002400799700001900823856003600842 2009 en_Ud 00aTopological branes, p-algebras and generalized Nahm equations0 aTopological branes palgebras and generalized Nahm equations3 aInspired by the recent advances in multiple M2-brane theory, we consider the generalizations of Nahm equations for arbitrary p-algebras. We construct the topological p-algebra quantum mechanics associated to them and we show that this can be obtained as a truncation of the topological p-brane theory previously studied by the authors. The resulting topological p-algebra quantum mechanics is discussed in detail and the relation with the M2-M5 system is pointed out in the p=3 case, providing a geometrical argument for the emergence of the 3-algebra structure in the Bagger-Lambert-Gustavsson theory1 aBonelli, Giulio1 aTanzini, Alessandro1 aZabzine, Maxim uhttp://hdl.handle.net/1963/270200416nas a2200133 4500008004100000022001400041245005800055210005700113300001500170490000700185100001900192700001800211856005300229 2009 eng d a1751-811300aTopological expansion for the Cauchy two-matrix model0 aTopological expansion for the Cauchy twomatrix model a335201, 280 v421 aBertola, Marco1 aFerrer, Prats uhttp://dx.doi.org/10.1088/1751-8113/42/33/33520100591nas 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/1963/345100978nas a2200121 4500008004300000245018700043210006900230520046200299100002000761700001800781700002100799856003600820 2009 en_Ud 00aOn universality of critical behaviour in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the {\\\\it tritronquée} solution to the Painlevé-I equation0 auniversality of critical behaviour in the focusing nonlinear Sch3 aWe argue that the critical behaviour near the point of ``gradient catastrophe\\\" of the solution to the Cauchy problem for the focusing nonlinear Schr\\\\\\\"odinger equation $ i\\\\epsilon \\\\psi_t +\\\\frac{\\\\epsilon^2}2\\\\psi_{xx}+ |\\\\psi|^2 \\\\psi =0$ with analytic initial data of the form $\\\\psi(x,0;\\\\epsilon) =A(x) e^{\\\\frac{i}{\\\\epsilon} S(x)}$ is approximately described by a particular solution to the Painlev\\\\\\\'e-I equation.1 aDubrovin, Boris1 aGrava, Tamara1 aKlein, Christian uhttp://hdl.handle.net/1963/252501175nas a2200109 4500008004300000245012700043210006900170520075600239100001800995700001601013856003601029 2009 en_Ud 00aUniversality of the break-up profile for the KdV equation in the small dispersion limit using the Riemann-Hilbert approach0 aUniversality of the breakup profile for the KdV equation in the 3 aWe obtain an asymptotic expansion for the solution of the Cauchy problem for the Korteweg-de Vries (KdV) equation in the small dispersion limit near the point of gradient catastrophe (x_c,t_c) for the solution of the dispersionless equation.\\nThe sub-leading term in this expansion is described by the smooth solution of a fourth order ODE, which is a higher order analogue to the Painleve I equation. This is in accordance with a conjecture of Dubrovin, suggesting that this is a universal phenomenon for any Hamiltonian perturbation of a hyperbolic equation. Using the Deift/Zhou steepest descent method applied on the Riemann-Hilbert problem for the KdV equation, we are able to prove the asymptotic expansion rigorously in a double scaling limit.1 aGrava, Tamara1 aClaeys, Tom uhttp://hdl.handle.net/1963/263600454nas 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/1963/267500547nas a2200109 4500008004300000245005600043210005200099260003400151520019600185100002000381856003600401 2009 en_Ud 00aOn viscosity solutions of Hamilton-Jacobi equations0 aviscosity solutions of HamiltonJacobi equations bAmerican Mathematical Society3 aWe consider the Dirichlet problem for Hamilton-Jacobi equations and prove existence, uniqueness and continuous dependence on boundary data of Lipschitz continuous maximal viscosity solutions.1 aZagatti, Sandro uhttp://hdl.handle.net/1963/342000988nas a2200133 4500008004100000022001400041245012300055210007000178300001600248490000800264520048400272100002700756856007100783 2008 eng d a0022-039600aAsymptotic evolution for the semiclassical nonlinear Schrödinger equation in presence of electric and magnetic fields0 aAsymptotic evolution for the semiclassical nonlinear Schrödinger a2566 - 25840 v2453 aIn this paper we study the semiclassical limit for the solutions of a subcritical focusing NLS with electric and magnetic potentials. We consider in particular the Cauchy problem for initial data close to solitons and show that, when the Planck constant goes to zero, the motion shadows that of a classical particle. Several works were devoted to the case of standing waves: differently from these we show that, in the dynamic version, the Lorentz force appears crucially.

1 aSelvitella, Alessandro uhttp://www.sciencedirect.com/science/article/pii/S002203960800243X00787nas a2200145 4500008004100000022001300041245008100054210006900135300001200204490000600216520026300222100002400485700002000509856011200529 2008 eng d a1673345200aCantor families of periodic solutions for completely resonant wave equations0 aCantor families of periodic solutions for completely resonant wa a151-1650 v33 aWe present recent existence results of Cantor families of small amplitude periodic solutions for completely resonant nonlinear wave equations. The proofs rely on the Nash-Moser implicit function theory and variational methods. © 2008 Higher Education Press.1 aBerti, Massimiliano1 aBolle, Philippe uhttps://www.math.sissa.it/publication/cantor-families-periodic-solutions-completely-resonant-wave-equations01284nas a2200145 4500008004100000022001300041245008900054210006900143300001400212490000800226520074600234100002400980700002001004856011401024 2008 eng d a0001870800aCantor families of periodic solutions for wave equations via a variational principle0 aCantor families of periodic solutions for wave equations via a v a1671-17270 v2173 aWe prove existence of small amplitude periodic solutions of completely resonant wave equations with frequencies in a Cantor set of asymptotically full measure, via a variational principle. A Lyapunov-Schmidt decomposition reduces the problem to a finite dimensional bifurcation equation-variational in nature-defined on a Cantor set of non-resonant parameters. The Cantor gaps are due to "small divisors" phenomena. To solve the bifurcation equation we develop a suitable variational method. In particular, we do not require the typical "Arnold non-degeneracy condition" of the known theory on the nonlinear terms. As a consequence our existence results hold for new generic sets of nonlinearities. © 2007 Elsevier Inc. All rights reserved.1 aBerti, Massimiliano1 aBolle, Philippe uhttps://www.math.sissa.it/publication/cantor-families-periodic-solutions-wave-equations-variational-principle00827nas a2200145 4500008004100000022001300041245008400054210006900138300001200207490000700219520030000226100002400526700002000550856011100570 2008 eng d a1021972200aCantor families of periodic solutions of wave equations with C k nonlinearities0 aCantor families of periodic solutions of wave equations with C k a247-2760 v153 aWe prove bifurcation of Cantor families of periodic solutions for wave equations with nonlinearities of class C k . It requires a modified Nash-Moser iteration scheme with interpolation estimates for the inverse of the linearized operators and for the composition operators. © 2008 Birkhaueser.1 aBerti, Massimiliano1 aBolle, Philippe uhttps://www.math.sissa.it/publication/cantor-families-periodic-solutions-wave-equations-c-k-nonlinearities00588nas a2200097 4500008004300000245007600043210006900119520024400188100002200432856003600454 2008 en_Ud 00aConcentrating solutions of some singularly perturbed elliptic equations0 aConcentrating solutions of some singularly perturbed elliptic eq3 aWe study singularly perturbed elliptic equations arising from models in physics or biology, and investigate the asymptotic behavior of some special solutions. We also discuss some connections with problems arising in differential geometry.1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/265700915nas a2200145 4500008004100000245009900041210007000140260003700210300001400247490000600261520034300267100002000610700001700630856012200647 2008 eng d00aOn concentration of positive bound states for the Schrödinger-Poisson problem with potentials0 aconcentration of positive bound states for the SchrödingerPoisso bAdvanced Nonlinear Studies, Inc. a573–5950 v83 aWe study the existence of semiclassical states for a nonlinear Schrödinger-Poisson system that concentrate near critical points of the external potential and of the density charge function. We use a perturbation scheme in a variational setting, extending the results in [1]. We also discuss necessary conditions for concentration.

1 aIanni, Isabella1 aVaira, Giusi uhttps://www.math.sissa.it/publication/concentration-positive-bound-states-schr%C3%B6dinger-poisson-problem-potentials01160nas a2200109 4500008004300000245007000043210006900113520078700182100002500969700002000994856003601014 2008 en_Ud 00aConvergence of equilibria of three-dimensional thin elastic beams0 aConvergence of equilibria of threedimensional thin elastic beams3 aA convergence result is proved for the equilibrium configurations of a three-dimensional thin elastic beam, as the diameter $h$ of the cross-section tends to zero. More precisely, we show that stationary points of the nonlinear elastic functional $E^h$, whose energies (per unit cross-section) are bounded by $Ch^2$, converge to stationary points of the $\\\\varGamma$-limit of $E^h/h^2$. This corresponds to a nonlinear one-dimensional model for inextensible rods, describing bending and torsion effects. The proof is based on the rigidity estimate for low-energy deformations by Friesecke, James and Müller and on a compensated compactness argument in a singular geometry. In addition, possible concentration effects of the strain are controlled by a careful truncation argument.1 aMora, Maria Giovanna1 aMüller, Stefan uhttp://hdl.handle.net/1963/189600386nas a2200109 4500008004300000245006300043210006300106260003100169100002100200700001900221856003600240 2008 en_Ud 00aDecomposition results for functions with bounded variation0 aDecomposition results for functions with bounded variation bUnione Matematica Italiana1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/1963/353502210nas a2200121 4500008004300000245009000043210006900133520178700202100002101989700002002010700002202030856003602052 2008 en_Ud 00aDiscerning static and causal interactions in genome-wide reverse engineering problems0 aDiscerning static and causal interactions in genomewide reverse 3 aBackground. In the past years devicing methods for discovering gene regulatory mechanisms at a genome-wide level has become a fundamental topic in the field of system biology. The aim is to infer gene-gene interactions in a more sophisticated and reliable way through the continuously improvement of reverse engineering algorithms exploiting microarray technologies. Motivation. This work is inspired by the several studies suggesting that co-expression is mostly related to \\\"static\\\" stable binding relationships, like belonging to the same protein complex, rather than other types of interactions more of a \\\"causal\\\" and transient nature (metabolic pathway or transcription factor-binding site interaction). Discerning static relationships from causal ones on the basis of their characteristic regulatory structures and in particular identifing \\\"dense modules\\\" with protein complex, and \\\"sparse modules\\\" with causal interactions such as those between transcription factor and corresponding binding site, the performances of different network inference algorithms in artificial and real networks (derived from E.coli and S.cerevisiae) can be tested and compared. Results. Our study shows that methods that try to prune indirect interactions from the inferred gene networks may fail to retrieve genes co-participating in a protein complex. On the other hand they are more robust in the identification of transcription factor-binding sites dependences when multiple transcription factors regulate the expression of the same gene. In the end we confirm the stronger co-expression regarding genes belonging to a protein complex than transcription factor-binding site, according, also, to the effect of multiple transcription factors and a low expression variance.1 aZampieri, Mattia1 aSoranzo, Nicola1 aAltafini, Claudio uhttp://hdl.handle.net/1963/275700657nas a2200097 4500008004300000245007900043210006900122520031000191100002200501856003600523 2008 en_Ud 00aEntire solutions of autonomous equations on Rn with nontrivial asymptotics0 aEntire solutions of autonomous equations on Rn with nontrivial a3 aWe prove existence of a new type of solutions for the semilinear equation $- \\\\D u + u = u^p$ on $\\\\R^n$, with $1 < p < \\\\frac{n+2}{n-2}$. These solutions are positive, bounded, decay exponentially to zero away from three half-lines with a common origin, and at infinity are asymptotically periodic.1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/264000301nas a2200097 4500008004300000245004300043210003900086260002100125100002100146856003600167 2008 en_Ud 00aAn entropy based Glimm-type functional0 aentropy based Glimmtype functional bWorld Scientific1 aCaravenna, Laura uhttp://hdl.handle.net/1963/405100767nas a2200097 4500008004300000245005300043210004900096520045900145100002900604856003600633 2008 en_Ud 00aEquivalent definitions of asymptotic 100% B.E.C.0 aEquivalent definitions of asymptotic 100 BEC3 aIn the mathematical analysis Bose-Einstein condensates, in particular in the study of the quantum dynamics, some kind of factorisation property has been recently proposed as a convenient technical assumption of condensation. After having surveyed both the standard definition of complete Bose-Einstein condensation in the limit of infinitely many particles and some forms of asymptotic factorisation, we prove that these characterisations are equivalent.1 aMichelangeli, Alessandro uhttp://hdl.handle.net/1963/254600962nas a2200121 4500008004300000245008100043210006900124260000900193520056300202100001700765700002200782856003600804 2008 en_Ud 00aEulerian calculus for the displacement convexity in the Wasserstein distance0 aEulerian calculus for the displacement convexity in the Wasserst bSIAM3 aIn this paper we give a new proof of the (strong) displacement convexity of a class of integral functionals defined on a compact Riemannian manifold satisfying a lower Ricci curvature bound. Our approach does not rely on existence and regularity results for optimal transport maps on Riemannian manifolds, but it is based on the Eulerian point of view recently introduced by Otto and Westdickenberg [SIAM J. Math. Anal., 37 (2005), pp. 1227-1255] and on the metric characterization of the gradient flows generated by the functionals in the Wasserstein space.1 aDaneri, Sara1 aSavarè, Giuseppe uhttp://hdl.handle.net/1963/341300797nas a2200109 4500008004300000245006300043210006000106520044300166100002000609700002200629856003600651 2008 en_Ud 00aExistence of conformal metrics with constant $Q$-curvature0 aExistence of conformal metrics with constant Qcurvature3 aGiven a compact four dimensional manifold, we prove existence of conformal metrics with constant $Q$-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure. Since the corresponding Euler functional is in general unbounded from above and from below, we employ topological methods and minimax schemes, jointly with a compactness result by the second author.1 aDjadli, Zindine1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/230800501nas 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.158300637nas a2200109 4500008004300000245004900043210004900092520031300141100001300454700002400467856003600491 2008 en_Ud 00aForced Vibrations of a Nonhomogeneous String0 aForced Vibrations of a Nonhomogeneous String3 aWe prove existence of vibrations of a nonhomogeneous string under a nonlinear time periodic forcing term in the case in which the forcing frequency avoids resonances with the vibration modes of the string (nonresonant case). The proof relies on a Lyapunov-Schmidt reduction and a Nash-Moser iteration scheme.1 aBaldi, P1 aBerti, Massimiliano uhttp://hdl.handle.net/1963/264300701nas a2200121 4500008004300000245009900043210006900142520027900211100002000490700001500510700001800525856003600543 2008 en_Ud 00aFrobenius Manifolds and Central Invariants for the Drinfeld - Sokolov Bihamiltonian Structures0 aFrobenius Manifolds and Central Invariants for the Drinfeld Soko3 aThe Drinfeld - Sokolov construction associates a hierarchy of bihamiltonian integrable systems with every untwisted affine Lie algebra. We compute the complete set of invariants of the related bihamiltonian structures with respect to the group of Miura type transformations.1 aDubrovin, Boris1 aSi-Qi, Liu1 aYoujin, Zhang uhttp://hdl.handle.net/1963/252301559nas 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/1963/269401551nas a2200121 4500008004300000245007900043210006900122520113900191100002501330700001701355700002101372856003601393 2008 en_Ud 00aA Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds0 aGaussBonnetlike formula on twodimensional almostRiemannian manif3 aWe consider a generalization of Riemannian geometry that naturally arises in the framework of control theory. Let $X$ and $Y$ be two smooth vector fields on a two-dimensional manifold $M$. If $X$ and $Y$ are everywhere linearly independent, then they define a classical Riemannian metric on $M$ (the metric for which they are orthonormal) and they give to $M$ the structure of metric space. If $X$ and $Y$ become linearly dependent somewhere on $M$, then the corresponding Riemannian metric has singularities, but under generic conditions the metric structure is still well defined. Metric structures that can be defined locally in this way are called almost-Riemannian structures. They are special cases of rank-varying sub-Riemannian structures, which are naturally defined in terms of submodules of the space of smooth vector fields on $M$. Almost-Riemannian structures show interesting phenomena, in particular for what concerns the relation between curvature, presence of conjugate points, and topology of the manifold. The main result of the paper is a generalization to almost-Riemannian structures of the Gauss-Bonnet formula.1 aAgrachev, Andrei, A.1 aBoscain, Ugo1 aSigalotti, Mario uhttp://hdl.handle.net/1963/186901036nas a2200133 4500008004300000245007100043210006900114520059000183100002100773700002200794700002500816700002500841856003600866 2008 en_Ud 00aGlobally stable quasistatic evolution in plasticity with softening0 aGlobally stable quasistatic evolution in plasticity with softeni3 aWe study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is characterized by the following properties: global stability at each time and energy balance on each\\ntime interval. An example developed in detail compares the solutions obtained by this method with the ones provided by a vanishing viscosity approximation, and shows that only the latter capture a decreasing branch in the stress-strain response.1 aDal Maso, Gianni1 aDeSimone, Antonio1 aMora, Maria Giovanna1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/196500681nas a2200109 4500008004300000245012000043210006900163520026100232100002100493700002100514856003600535 2008 en_Ud 00aGradient bounds for minimizers of free discontinuity problems related to cohesive zone models in fracture mechanics0 aGradient bounds for minimizers of free discontinuity problems re3 aIn this note we consider a free discontinuity problem for a scalar function, whose energy depends also on the size of the jump. We prove that the gradient of every smooth local minimizer never exceeds a constant, determined only by the data of the problem.1 aDal Maso, Gianni1 aGarroni, Adriana uhttp://hdl.handle.net/1963/172301495nas a2200109 4500008004100000245007100041210006900112260001000181520113800191100002001329856003601349 2008 en d00aHamiltonian partial differential equations and Frobenius manifolds0 aHamiltonian partial differential equations and Frobenius manifol bSISSA3 aIn the first part of this paper the theory of Frobenius manifolds\\r\\nis applied to the problem of classification of Hamiltonian systems of partial\\r\\ndifferential equations depending on a small parameter. Also developed is\\r\\na deformation theory of integrable hierarchies including the subclass of\\r\\nintegrable hierarchies of topological type. Many well-known examples\\r\\nof integrable hierarchies, such as the Korteweg–de Vries, non-linear\\r\\nSchr¨odinger, Toda, Boussinesq equations, and so on, belong to this\\r\\nsubclass that also contains new integrable hierarchies. Some of these new\\r\\nintegrable hierarchies may be important for applications. Properties of the\\r\\nsolutions to these equations are studied in the second part. Consideration\\r\\nis given to the comparative study of the local properties of perturbed and\\r\\nunperturbed solutions near a point of gradient catastrophe. A Universality\\r\\nConjecture is formulated describing the various types of critical behaviour\\r\\nof solutions to perturbed Hamiltonian systems near the point of gradient\\r\\ncatastrophe of the unperturbed solution.1 aDubrovin, Boris uhttp://hdl.handle.net/1963/647100434nas a2200121 4500008004100000022001400041245005200055210005100107300002300158100001900181700002500200856008700225 2008 eng d a1073-792800aHarish-Chandra integrals as nilpotent integrals0 aHarishChandra integrals as nilpotent integrals aArt. ID rnn062, 151 aBertola, Marco1 aFerrer, Aleix, Prats uhttps://www.math.sissa.it/publication/harish-chandra-integrals-nilpotent-integrals00891nas 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/1963/285200870nas a2200109 4500008004300000245007800043210006900121520049600190100001700686700002100703856003600724 2008 en_Ud 00aInvariant Carnot-Caratheodory metrics on S3, SO(3), SL(2) and Lens Spaces0 aInvariant CarnotCaratheodory metrics on S3 SO3 SL2 and Lens Spac3 aIn this paper we study the invariant Carnot-Caratheodory metrics on SU(2) \\\' S3,\\nSO(3) and SL(2) induced by their Cartan decomposition. Beside computing explicitly geodesics and conjugate loci, we compute the cut loci (globally) and we give the expression of the Carnot-Caratheodory distance as the inverse of an elementary function. We then prove that the metric\\ngiven on SU(2) projects on the so called Lens Spaces L(p; q). Also for Lens Spaces, we compute\\nthe cut loci (globally).1 aBoscain, Ugo1 aRossi, Francesco uhttp://hdl.handle.net/1963/214400382nas a2200097 4500008004300000245009400043210006900137100002300206700001900229856003600248 2008 en_Ud 00aInvariant Manifolds for Viscous Profiles of a Class of Mixed Hyperbolic-Parabolic Systems0 aInvariant Manifolds for Viscous Profiles of a Class of Mixed Hyp1 aBianchini, Stefano1 aSpinolo, Laura uhttp://hdl.handle.net/1963/340001110nas a2200121 4500008004300000245008200043210006900125520069200194100002400886700002200910700002000932856003600952 2008 en_Ud 00aThe Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere0 aIsospectral Dirac Operator on the 4dimensional Orthogonal Quantu3 aEquivariance under the action of Uq(so(5)) is used to compute the left regular and (chiral) spinorial representations of the algebra of the quantum Euclidean 4-sphere S^4_q. These representations are the constituents of a spectral triple on this sphere with a Dirac operator which is isospectral to the canonical one of the spin structure of the round undeformed four-sphere and which gives metric dimension four for the noncommutative geometry. Non-triviality of the geometry is proved by pairing the associated Fredholm module with an `instanton\\\' projection. A real structure which satisfies all required properties modulo a suitable ideal of `infinitesimals\\\' is also introduced.1 aD'Andrea, Francesco1 aDabrowski, Ludwik1 aLandi, Giovanni uhttp://hdl.handle.net/1963/256701845nas a2200133 4500008004300000245006800043210006700111520142200178100001701600700002101617700001701638700002001655856003601675 2008 en_Ud 00aLimit Time Optimal Syntheses for a control-affine system on S²0 aLimit Time Optimal Syntheses for a controlaffine system on S²3 aFor $\\\\alpha \\\\in ]0,\\\\pi/2[$, let $(\\\\Sigma)_\\\\alpha$ be the control system $\\\\dot{x}=(F+uG)x$, where $x$ belongs to the two-dimensional unit sphere $S^2$, $u\\\\in [-1,1]$, and $F,G$ are $3\\\\times3$ skew-symmetric matrices generating rotations with perpendicular axes and of respective norms $\\\\cos(\\\\alpha)$ and $\\\\sin(\\\\alpha)$. In this paper, we study the time optimal synthesis (TOS) from the north pole $(0,0,1)^T$ associated to $(\\\\Sigma)_\\\\alpha$, as the parameter $\\\\alpha$ tends to zero; this problem is motivated by specific issues in the control of quantum systems. We first prove that the TOS is characterized by a \\\"two-snakes\\\" configuration on the whole $S^2$, except for a neighborhood $U_\\\\alpha$ of the south pole $(0,0,-1)^T$ of diameter at most ${\\\\cal O}(\\\\alpha)$. We next show that, inside $U_\\\\alpha$, the TOS depends on the relationship between $r(\\\\alpha):=\\\\pi/2\\\\alpha-[\\\\pi/2\\\\alpha]$ and $\\\\alpha$. More precisely, we characterize three main relationships by considering sequences $(\\\\alpha_k)_{k\\\\geq 0}$ satisfying (a) $r(\\\\alpha_k)=\\\\bar{r}$, (b) $r(\\\\alpha_k)=C\\\\alpha_k$, and (c) $r(\\\\alpha_k)=0$, where $\\\\bar{r}\\\\in (0,1)$ and $C>0$. In each case, we describe the TOS and provide, after a suitable rescaling, the limiting behavior, as $\\\\alpha$ tends to zero, of the corresponding TOS inside $U_\\\\alpha$.1 aMason, Paolo1 aSalmoni, Rebecca1 aBoscain, Ugo1 aChitour, Yacine uhttp://hdl.handle.net/1963/186200688nas a2200109 4500008004100000245008400041210006900125260001000194520031700204100002100521856003600542 2008 en d00aOn the Logarithmic Asymptotics of the Sixth Painleve\' Equation (Summer 2007)0 aLogarithmic Asymptotics of the Sixth Painleve Equation Summer 20 bSISSA3 aWe study the solutions of the sixth Painlev\'e equation with a logarithmic\r\nasymptotic behavior at a critical point. We compute the monodromy group\r\nassociated to the solutions by the method of monodromy preserving deformations\r\nand we characterize the asymptotic behavior in terms of the monodromy itself.1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/652100334nas a2200085 4500008004300000245008000043210006900123100002000192856003600212 2008 en_Ud 00aMinimization of non quasiconvex functionals by integro-extremization method0 aMinimization of non quasiconvex functionals by integroextremizat1 aZagatti, Sandro uhttp://hdl.handle.net/1963/276100355nas a2200085 4500008004300000245010100043210006900144100002000213856003600233 2008 en_Ud 00aMinimizers of non convex scalar functionals and viscosity solutions of Hamilton-Jacobi equations0 aMinimizers of non convex scalar functionals and viscosity soluti1 aZagatti, Sandro uhttp://hdl.handle.net/1963/276000352nas a2200097 4500008004300000245006500043210006500108260002300173100002200196856003600218 2008 en_Ud 00aMorse theory and a scalar field equation on compact surfaces0 aMorse theory and a scalar field equation on compact surfaces bKhayyam Publishing1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/353100342nas a2200097 4500008004300000245006300043210006200106100002400168700001600192856003600208 2008 en_Ud 00aMultiple bound states for the Schroedinger-Poisson problem0 aMultiple bound states for the SchroedingerPoisson problem1 aAmbrosetti, Antonio1 aRuiz, David uhttp://hdl.handle.net/1963/267900746nas a2200145 4500008004300000245004200043210004200085260002800127520032600155100002000481700001900501700001800520700002600538856003600564 2008 en_Ud 00aNoncommutative families of instantons0 aNoncommutative families of instantons bOxford University Press3 aWe construct $\\\\theta$-deformations of the classical groups SL(2,H) and Sp(2). Coacting on the basic instanton on a noncommutative four-sphere $S^4_\\\\theta$, we construct a noncommutative family of instantons of charge 1. The family is parametrized by the quantum quotient of $SL_\\\\theta(2,H)$ by $Sp_\\\\theta(2)$.1 aLandi, Giovanni1 aPagani, Chiara1 aReina, Cesare1 avan Suijlekom, Walter uhttp://hdl.handle.net/1963/341700576nas a2200121 4500008004300000245006400043210006000107520018500167100002400352700002200376700002000398856003600418 2008 en_Ud 00aThe Noncommutative Geometry of the Quantum Projective Plane0 aNoncommutative Geometry of the Quantum Projective Plane3 aWe study the spectral geometry of the quantum projective plane CP^2_q. In particular, we construct a Dirac operator which gives a 0^+ summable triple, equivariant under U_q(su(3)).1 aD'Andrea, Francesco1 aDabrowski, Ludwik1 aLandi, Giovanni uhttp://hdl.handle.net/1963/254800355nas a2200085 4500008004300000245009600043210006900139100002500208856003600233 2008 en_Ud 00aA note on the differentiability of Lipschitz functions and the chain rule in Sobolev spaces0 anote on the differentiability of Lipschitz functions and the cha1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/265401399nas a2200109 4500008004300000245010600043210006900149520099600218100001801214700002101232856003601253 2008 en_Ud 00aNumerical study of a multiscale expansion of the Korteweg-de Vries equation and Painlevé-II equation0 aNumerical study of a multiscale expansion of the Kortewegde Vrie3 aThe Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion of order $\\\\e^2$, $\\\\e\\\\ll 1$, is characterized by the appearance of a zone of rapid modulated oscillations. These oscillations are approximately described by the elliptic solution of KdV where the amplitude, wave-number and frequency are not constant but evolve according to the Whitham equations. Whereas the difference between the KdV and the asymptotic solution decreases as $\\\\epsilon$ in the interior of the Whitham oscillatory zone, it is known to be only of order $\\\\epsilon^{1/3}$ near the leading edge of this zone. To obtain a more accurate description near the leading edge of the oscillatory zone we present a multiscale expansion of the solution of KdV in terms of the Hastings-McLeod solution of the Painlev\\\\\\\'e-II equation. We show numerically that the resulting multiscale solution approximates the KdV solution, in the small dispersion limit, to the order $\\\\epsilon^{2/3}$.1 aGrava, Tamara1 aKlein, Christian uhttp://hdl.handle.net/1963/259201131nas a2200133 4500008004300000245006500043210006400108260001300172520071100185100002300896700002200919700002000941856003600961 2008 en_Ud 00aOptimal Strokes for Low Reynolds Number Swimmers: An Example0 aOptimal Strokes for Low Reynolds Number Swimmers An Example bSpringer3 aSwimming, i.e., being able to advance in the absence of external forces by performing cyclic shape changes, is particularly demanding at low Reynolds numbers. This is the regime of interest for micro-organisms and micro- or nano-robots. We focus in this paper on a simple yet representative example: the three-sphere swimmer of Najafi and Golestanian (Phys. Rev. E, 69, 062901-062904, 2004). For this system, we show how to cast the problem of swimming in the language of control theory, prove global controllability (which implies that the three-sphere swimmer can indeed swim), and propose a numerical algorithm to compute optimal strokes (which turn out to be suitably defined sub-Riemannian geodesics).1 aAlouges, François1 aDeSimone, Antonio1 aLefebvre, Aline uhttp://hdl.handle.net/1963/400602183nas a2200133 4500008004300000245010900043210006900152520170600221100002101927700002001948700002301968700002201991856003602013 2008 en_Ud 00aOrigin of Co-Expression Patterns in E.coli and S.cerevisiae Emerging from Reverse Engineering Algorithms0 aOrigin of CoExpression Patterns in Ecoli and Scerevisiae Emergin3 aBackground: The concept of reverse engineering a gene network, i.e., of inferring a genome-wide graph of putative genegene interactions from compendia of high throughput microarray data has been extensively used in the last few years to deduce/integrate/validate various types of \\\"physical\\\" networks of interactions among genes or gene products. Results: This paper gives a comprehensive overview of which of these networks emerge significantly when reverse engineering large collections of gene expression data for two model organisms, E.coli and S.cerevisiae, without any prior information. For the first organism the pattern of co-expression is shown to reflect in fine detail both the operonal structure of the DNA and the regulatory effects exerted by the gene products when co-participating in a protein complex. For the second organism we find that direct transcriptional control (e.g., transcription factor-binding site interactions) has little statistical significance in comparison to the other regulatory mechanisms (such as co-sharing a protein complex, colocalization on a metabolic pathway or compartment), which are however resolved at a lower level of detail than in E.coli. Conclusion: The gene co-expression patterns deduced from compendia of profiling experiments tend to unveil functional categories that are mainly associated to stable bindings rather than transient interactions. The inference power of this systematic analysis is substantially reduced when passing from E.coli to S.cerevisiae. This extensive analysis provides a way to describe the different complexity between the two organisms and discusses the critical limitations affecting this type of methodologies.1 aZampieri, Mattia1 aSoranzo, Nicola1 aBianchini, Daniele1 aAltafini, Claudio uhttp://hdl.handle.net/1963/272200666nas a2200157 4500008004100000022001300041245006000054210005700114300001200171490000600183520016900189100002400358700001400382700002200396856009000418 2008 eng d a1534039200aOn periodic elliptic equations with gradient dependence0 aperiodic elliptic equations with gradient dependence a601-6150 v73 aWe construct entire solutions of Δu = f(x, u, ∇u) which are superpositions of odd, periodic functions and linear ones, with prescribed integer or rational slope.1 aBerti, Massimiliano1 aMatzeu, M1 aValdinoci, Enrico uhttps://www.math.sissa.it/publication/periodic-elliptic-equations-gradient-dependence00618nas a2200133 4500008004100000245011000041210007000151260001300221300001400234490000700248520012200255100001900377856008800396 2008 eng d00aPositive solutions of nonlinear Schrödinger-Poisson systems with radial potentials vanishing at infinity0 aPositive solutions of nonlinear SchrödingerPoisson systems with bCiteseer a211–2270 v193 aWe deal with a weighted nonlinear Schr¨odinger-Poisson system, allowing the potentials to vanish at infinity.

1 aMercuri, Carlo uhttp://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.510.3635&rep=rep1&type=pdf00444nas a2200121 4500008004300000245009700043210006900140100001700209700001800226700002200244700002000266856003600286 2008 en_Ud 00aRelaxation of some transversally isotropic energies and applications to smectic A elastomers0 aRelaxation of some transversally isotropic energies and applicat1 aAdams, James1 aConti, Sergio1 aDeSimone, Antonio1 aDolzmann, Georg uhttp://hdl.handle.net/1963/191201111nas a2200121 4500008004300000245007200043210006900115520069700184100002200881700002500903700002500928856003600953 2008 en_Ud 00aA second order minimality condition for the Mumford-Shah functional0 asecond order minimality condition for the MumfordShah functional3 aA new necessary minimality condition for the Mumford-Shah functional is derived by means of second order variations. It is expressed in terms of a sign condition for a nonlocal quadratic form on $H^1_0(\\\\Gamma)$, $\\\\Gamma$ being a submanifold of the regular part of the discontinuity set of the critical point. Two equivalent formulations are provided: one in terms of the first eigenvalue of a suitable compact operator, the other involving a sort of nonlocal capacity of $\\\\Gamma$. A sufficient condition for minimality is also deduced. Finally, an explicit example is discussed, where a complete characterization of the domains where the second variation is nonnegative can be given.1 aCagnetti, Filippo1 aMora, Maria Giovanna1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/195501262nas a2200121 4500008004300000245007100043210006800114260002800182520085700210100002101067700001601088856003601104 2008 en_Ud 00aOn semistable principal bundles over a complex projective manifold0 asemistable principal bundles over a complex projective manifold bOxford University Press3 aLet G be a simple linear algebraic group defined over the complex numbers. Fix a proper parabolic subgroup P of G and a nontrivial antidominant character \\\\chi of P. We prove that a holomorphic principal G-bundle E over a connected complex projective manifold M is semistable and the second Chern class of its adjoint bundle vanishes in rational cohomology if and only if the line bundle over E/P defined by \\\\chi is numerically effective. Similar results remain valid for principal bundles with a reductive linear algebraic group as the structure group. These generalize an earlier work of Y. Miyaoka where he gave a characterization of semistable vector bundles over a smooth projective curve. Using these characterizations one can also produce similar criteria for the semistability of parabolic principal bundles over a compact Riemann surface.1 aBiswas, Indranil1 aBruzzo, Ugo uhttp://hdl.handle.net/1963/341800611nas a2200121 4500008004300000245008600043210006900129520019400198100002400392700002100416700001600437856003600453 2008 en_Ud 00aSolitons of linearly coupled systems of semilinear non-autonomous equations on Rn0 aSolitons of linearly coupled systems of semilinear nonautonomous3 aUsing concentration compactness type arguments, we prove some results about the existence of positive ground and bound state of linearly coupled systems of nonlinear Schrödinger equations.1 aAmbrosetti, Antonio1 aCerami, Giovanna1 aRuiz, David uhttp://hdl.handle.net/1963/217500349nas a2200097 4500008004300000245006900043210006800112100001700180700001800197856003600215 2008 en_Ud 00aStability of planar switched systems: the nondiagonalizable case0 aStability of planar switched systems the nondiagonalizable case1 aBoscain, Ugo1 aBalde, Moussa uhttp://hdl.handle.net/1963/185701518nas a2200109 4500008004300000245007900043210006900122520114200191100001701333700002201350856003601372 2008 en_Ud 00aSymmetric obstruction theories and Hilbert schemes of points on threefolds0 aSymmetric obstruction theories and Hilbert schemes of points on 3 aIn an earlier paper by one of us (Behrend), Donaldson-Thomas type invariants were expressed as certain weighted Euler characteristics of the moduli space. The Euler characteristic is weighted by a certain canonical\\nZ-valued constructible function on the moduli space. This constructible function associates to\\nany point of the moduli space a certain invariant of the singularity of the space at the point. Here we evaluate this invariant for the case of a singularity that is an isolated point of a C∗-action and that admits a symmetric obstruction theory compatible with the C∗-action. The answer is (-1)d, where d\\nis the dimension of the Zariski tangent space. We use this result to prove that for any threefold, proper or not, the weighted Euler characteristic of the Hilbert scheme of n points on the threefold is, up to sign, equal to the usual Euler characteristic. For the case of a projective Calabi-Yau threefold, we deduce that the Donaldson-Thomas invariant of the Hilbert scheme of n points is, up to sign, equal to the Euler characteristic. This proves a conjecture of Maulik, Nekrasov, Okounkov and Pandharipande.1 aBehrend, Kai1 aFantechi, Barbara uhttp://hdl.handle.net/1963/270900905nas a2200121 4500008004100000245006700041210006700108260001000175520051900185653002600704100001700730856003600747 2008 en d00aSymmetries of noncommutative spaces and equivariant cohomology0 aSymmetries of noncommutative spaces and equivariant cohomology bSISSA3 aAs the title suggests, the main subject of this thesis is the study of symmetries of noncommutative spaces and related equivariant cohomologies. We focus on deformations of classical geometries coming from the action of some symmetry. A close relation between the deformation of the symmetry and the deformation of the space on which it acts is at the heart of our approach; we will use this idea to generate noncommutative geometries, and to de¯ne algebraic models for the equivariant cohomology of such actions.10aNoncommutative spaces1 aCirio, Lucio uhttp://hdl.handle.net/1963/525401205nas a2200109 4500008004300000245008000043210006900123520082300192100002001015700002401035856003601059 2008 en_Ud 00aTopological Gauge Theories on Local Spaces and Black Hole Entropy Countings0 aTopological Gauge Theories on Local Spaces and Black Hole Entrop3 aWe study cohomological gauge theories on total spaces of holomorphic line bundles over complex manifolds and obtain their reduction to the base manifold by U(1) equivariant localization of the path integral. We exemplify this general mechanism by proving via exact path integral localization a reduction for local curves conjectured in hep-th/0411280, relevant to the calculation of black hole entropy/Gromov-Witten invariants. Agreement with the four-dimensional gauge theory is recovered by taking into account in the latter non-trivial contributions coming from one-loop fluctuations determinants at the boundary of the total space. We also study a class of abelian gauge theories on Calabi-Yau local surfaces, describing the quantum foam for the A-model, relevant to the calculation of Donaldson-Thomas invariants.1 aBonelli, Giulio1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/199200725nas a2200097 4500008004300000245008100043210006900124520037600193100002200569856003600591 2008 en_Ud 00aTopological methods for an elliptic equation with exponential nonlinearities0 aTopological methods for an elliptic equation with exponential no3 aWe consider a class of variational equations with exponential nonlinearities on compact surfaces. From considerations involving the Moser-Trudinger inequality, we characterize some sublevels of the Euler-Lagrange functional in terms of the topology of the surface and of the data of the equation. This is used together with a min-max argument to obtain existence results.1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/259401148nas a2200121 4500008004300000245006300043210006200106520076200168100002000930700002200950700001800972856003600990 2008 en_Ud 00aTransition layer for the heterogeneous Allen-Cahn equation0 aTransition layer for the heterogeneous AllenCahn equation3 aWe consider the equation $\\\\e^{2}\\\\Delta u=(u-a(x))(u^2-1)$ in $\\\\Omega$, $\\\\frac{\\\\partial u}{\\\\partial \\\\nu} =0$ on $\\\\partial \\\\Omega$, where $\\\\Omega$ is a smooth and bounded domain in $\\\\R^n$, $\\\\nu$ the outer unit normal to $\\\\pa\\\\Omega$, and $a$ a smooth function satisfying $-10} and {a<0}. Assuming $\\\\nabla a \\\\neq 0$ on $K$ and $a\\\\ne 0$ on $\\\\partial \\\\Omega$, we show that there exists a sequence $\\\\e_j \\\\to 0$ such that the above equation has a solution $u_{\\\\e_j}$ which converges uniformly to $\\\\pm 1$ on the compact sets of $\\\\O_{\\\\pm}$ as $j \\\\to + \\\\infty$.1 aMahmoudi, Fethi1 aMalchiodi, Andrea1 aWei, Juncheng uhttp://hdl.handle.net/1963/265600781nas a2200133 4500008004100000020002200041245006700063210006700130260001300197520035900210100002300569700001900592856003600611 2008 en d a978-3-642-21718-000aTransport Rays and Applications to Hamilton–Jacobi Equations0 aTransport Rays and Applications to Hamilton–Jacobi Equations bSpringer3 aThe aim of these notes is to introduce the readers to the use of the Disintegration Theorem for measures as an effective tool for reducing problems in transport equations to simpler ones. The basic idea is to partition Rd into one dimensional sets, on which the problem under consideration becomes one space dimensional (and thus much easier, hopefully).1 aBianchini, Stefano1 aGloyer, Matteo uhttp://hdl.handle.net/1963/546301276nas a2200133 4500008004300000245008900043210006900132520081200201100002101013700002201034700002501056700002501081856003601106 2008 en_Ud 00aA vanishing viscosity approach to quasistatic evolution in plasticity with softening0 avanishing viscosity approach to quasistatic evolution in plastic3 aWe deal with quasistatic evolution problems in plasticity with softening, in the framework of small strain associative elastoplasticity. The presence of a nonconvex term due to the softening phenomenon requires a nontrivial extension of the variational framework for rate-independent problems to the case of a nonconvex energy functional. We argue that, in this case, the use of global minimizers in the corresponding incremental problems is not justified from the mechanical point of view. Thus, we analize a different selection criterion for the solutions of the quasistatic evolution problem, based on a viscous approximation. This leads to a generalized formulation in terms of Young measures, developed in the first part of the paper. In the second part we apply our approach to some concrete examples.1 aDal Maso, Gianni1 aDeSimone, Antonio1 aMora, Maria Giovanna1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/184401563nas a2200133 4500008004100000020001800041022001300059245004500072210004500117300001200162520115200174100002401326856007901350 2008 eng d a9781402069628 a1874650000aVariational methods for Hamiltonian PDEs0 aVariational methods for Hamiltonian PDEs a391-4203 aWe present recent existence results of periodic solutions for completely resonant nonlinear wave equations in which both "small divisor" difficulties and infinite dimensional bifurcation phenomena occur. These results can be seen as generalizations of the classical finite-dimensional resonant center theorems of Weinstein-Moser and Fadell-Rabinowitz. The proofs are based on variational bifurcation theory: after a Lyapunov-Schmidt reduction, the small divisor problem in the range equation is overcome with a Nash-Moser implicit function theorem for a Cantor set of non-resonant parameters. Next, the infinite dimensional bifurcation equation, variational in nature, possesses minimax mountain-pass critical points. The big difficulty is to ensure that they are not in the "Cantor gaps". This is proved under weak non-degeneracy conditions. Finally, we also discuss the existence of forced vibrations with rational frequency. This problem requires variational methods of a completely different nature, such as constrained minimization and a priori estimates derivable from variational inequalities. © 2008 Springer Science + Business Media B.V.1 aBerti, Massimiliano uhttps://www.math.sissa.it/publication/variational-methods-hamiltonian-pdes00645nas a2200121 4500008004300000245011200043210006900155520019600224100002300420700002200443700002200465856003600487 2007 en_Ud 00aAsymptotic behaviour of smooth solutions for partially dissipative hyperbolic systems with a convex entropy0 aAsymptotic behaviour of smooth solutions for partially dissipati3 aWe study the asymptotic time behavior of global smooth solutions to general entropy dissipative hyperbolic systems of balance law in m space dimensions, under the Shizuta-Kawashima condition.1 aBianchini, Stefano1 aHanouzet, Bernard1 aNatalini, Roberto uhttp://hdl.handle.net/1963/178000925nas a2200121 4500008004100000245012500041210006900166260004700235520035300282100002100635700002100656856012600677 2007 en d00aThe Asymptotic Behaviour of the Fourier Transforms of Orthogonal Polynomials II: L.I.F.S. Measures and Quantum Mechanics0 aAsymptotic Behaviour of the Fourier Transforms of Orthogonal Pol b2007 Birkh¨auser Verlag Basel/Switzerland3 aWe study measures generated by systems of linear iterated functions,\r\ntheir Fourier transforms, and those of their orthogonal polynomials. We\r\ncharacterize the asymptotic behaviours of their discrete and continuous averages.\r\nFurther related quantities are analyzed, and relevance of this analysis\r\nto quantum mechanics is briefly discussed1 aGuzzetti, Davide1 aMantica, Giorgio uhttps://www.math.sissa.it/publication/asymptotic-behaviour-fourier-transforms-orthogonal-polynomials-ii-lifs-measures-and01700nas 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/1963/218200554nas a2200133 4500008004100000022001400041245011300055210007000168300001400238490000700252100001900259700001700278856012500295 2007 eng d a0176-427600aBiorthogonal Laurent polynomials, Töplitz determinants, minimal Toda orbits and isomonodromic tau functions0 aBiorthogonal Laurent polynomials Töplitz determinants minimal To a383–4300 v261 aBertola, Marco1 aGekhtman, M. uhttps://www.math.sissa.it/publication/biorthogonal-laurent-polynomials-t%C3%B6plitz-determinants-minimal-toda-orbits-and00478nas a2200121 4500008004100000022001400041245008100055210006900136300001400205490000800219100001900227856011000246 2007 eng d a0021-904500aBiorthogonal polynomials for two-matrix models with semiclassical potentials0 aBiorthogonal polynomials for twomatrix models with semiclassical a162–2120 v1441 aBertola, Marco uhttps://www.math.sissa.it/publication/biorthogonal-polynomials-two-matrix-models-semiclassical-potentials01457nas a2200133 4500008004300000245010800043210006900151520097900220100001901199700002301218700002201241700002401263856003601287 2007 en_Ud 00aBlack Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory0 aBlack Holes Instanton Counting on Toric Singularities and qDefor3 aWe study the relationship between instanton counting in N=4 Yang-Mills theory on a generic four-dimensional toric orbifold and the semi-classical expansion of q-deformed Yang-Mills theory on the blowups of the minimal resolution of the orbifold singularity, with an eye to clarifying the recent proposal of using two-dimensional gauge theories to count microstates of black holes in four dimensions. We describe explicitly the instanton contributions to the counting of D-brane bound states which are captured by the two-dimensional gauge theory. We derive an intimate relationship between the two-dimensional Yang-Mills theory and Chern-Simons theory on generic Lens spaces, and use it to show that the correct instanton counting is only reproduced when the Chern-Simons contributions are treated as non-dynamical boundary conditions in the D4-brane gauge theory. We also use this correspondence to discuss the counting of instantons on higher genus ruled Riemann surfaces.1 aGriguolo, Luca1 aSeminara, Domenico1 aSzabo, Richard J.1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/188800337nas a2200085 4500008004300000245007400043210006900117100002900186856003600215 2007 en_Ud 00aBose-Einstein condensation: analysis of problems and rigorous results0 aBoseEinstein condensation analysis of problems and rigorous resu1 aMichelangeli, Alessandro uhttp://hdl.handle.net/1963/218900318nas a2200097 4500008004300000245005100043210005000094100002200144700001800166856003600184 2007 en_Ud 00aBoundary interface for the Allen-Cahn equation0 aBoundary interface for the AllenCahn equation1 aMalchiodi, Andrea1 aWei, Juncheng uhttp://hdl.handle.net/1963/202700420nas a2200121 4500008004100000245006400041210006300105260003700168100002200205700001700227700001800244856003600262 2007 en d00aBoundary-clustered interfaces for the Allen–Cahn equation0 aBoundaryclustered interfaces for the Allen–Cahn equation bMathematical Sciences Publishers1 aMalchiodi, Andrea1 aNi, Wei-Ming1 aWei, Juncheng uhttp://hdl.handle.net/1963/508900820nas a2200121 4500008004300000245004900043210004800092520045600140100001700596700002100613700002800634856003600662 2007 en_Ud 00aBV instability for the Lax-Friedrichs scheme0 aBV instability for the LaxFriedrichs scheme3 aIt is proved that discrete shock profiles (DSPs) for the Lax-Friedrichs scheme for a system of conservation laws do not necessarily depend continuously in BV on their speed. We construct examples of $2 \\\\times 2$-systems for which there are sequences of DSPs with speeds converging to a rational number. Due to a resonance phenomenon, the difference between the limiting DSP and any DSP in the sequence will contain an order-one amount of variation.1 aBaiti, Paolo1 aBressan, Alberto1 aJenssen, Helge Kristian uhttp://hdl.handle.net/1963/233500899nas a2200109 4500008004300000245006800043210006800111520053400179100002000713700002000733856003600753 2007 en_Ud 00aCanonical structure and symmetries of the Schlesinger equations0 aCanonical structure and symmetries of the Schlesinger equations3 aThe Schlesinger equations S (n,m) describe monodromy preserving deformations of order m Fuchsian systems with n+1 poles. They can be considered as a family of commuting time-dependent Hamiltonian systems on the direct product of n copies of m×m matrix algebras equipped with the standard linear Poisson bracket. In this paper we present a new canonical Hamiltonian formulation ofthe general Schlesinger equations S (n,m) for all n, m and we compute the action of the symmetries of the Schlesinger equations in these coordinates.1 aDubrovin, Boris1 aMazzocco, Marta uhttp://hdl.handle.net/1963/199701185nas 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/1963/651302020nas a2200121 4500008004300000245013300043210006900176520155200245100002001797700002301817700002201840856003601862 2007 en_Ud 00aComparing association network algorithms for reverse engineering of large scale gene regulatory networks: synthetic vs real data0 aComparing association network algorithms for reverse engineering3 aMotivation: Inferring a gene regulatory network exclusively from microarray expression profiles is a difficult but important task. The aim of this work is to compare the predictive power of some of the most popular algorithms in different conditions (like data taken at equilibrium or time courses) and on both synthetic and real microarray data. We are in particular interested in comparing similarity measures both of linear type (like correlations and partial correlations) and of nonlinear type (mutual information and conditional mutual information), and in investigating the underdetermined case (less samples than genes). Results: In our simulations we see that all network inference algorithms obtain better performances from data produced with \\\"structural\\\" perturbations, like gene knockouts at steady state, than with any dynamical perturbation. The predictive power of all algorithms is confirmed on a reverse engineering problem from E. coli gene profiling data: the edges of the \\\"physical\\\" network of transcription factor-binding sites are significantly overrepresented among the highest weighting edges of the graph that we infer directly from the data without any structure supervision. Comparing synthetic and in vivo data on the same network graph allows us to give an indication of how much more complex a real transcriptional regulation program is with respect to an artificial model. Availability: Software and supplementary material are freely available at the URL http://people.sissa.it/~altafini/papers/SoBiAl07/1 aSoranzo, Nicola1 aBianconi, Ginestra1 aAltafini, Claudio uhttp://hdl.handle.net/1963/202800643nas a2200109 4500008004300000245006200043210005400105520029200159100002200451700002400473856003600497 2007 en_Ud 00aThe complete one-loop spin chain for N=2 Super-Yang-Mills0 acomplete oneloop spin chain for N2 SuperYangMills3 aWe show that the complete planar one-loop mixing matrix of the N=2 Super Yang--Mills theory can be obtained from a reduction of that of the N=4 theory. For composite operators of scalar fields, this yields an anisotropic XXZ spin chain, whose spectrum of excitations displays a mass gap.1 aDi Vecchia, Paolo1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/230901000nas a2200121 4500008004300000245004900043210004800092520063900140100002000779700002400799700001900823856003600842 2007 en_Ud 00aComputing Amplitudes in topological M-theory0 aComputing Amplitudes in topological Mtheory3 aWe define a topological quantum membrane theory on a seven dimensional manifold of $G_2$ holonomy. We describe in detail the path integral evaluation for membrane geometries given by circle bundles over Riemann surfaces. We show that when the target space is $CY_3\\\\times S^1$ quantum amplitudes of non-local observables of membranes wrapping the circle reduce to the A-model amplitudes. \\nIn particular for genus zero we show that our model computes the Gopakumar-Vafa invariants. Moreover, for membranes wrapping calibrated homology spheres in the $CY_3$, we find that the amplitudes of our model are related to Joyce invariants.1 aBonelli, Giulio1 aTanzini, Alessandro1 aZabzine, Maxim uhttp://hdl.handle.net/1963/190100919nas a2200109 4500008004300000245008500043210006900128520053400197100002000731700002200751856003600773 2007 en_Ud 00aConcentration on minimal submanifolds for a singularly perturbed Neumann problem0 aConcentration on minimal submanifolds for a singularly perturbed3 aWe consider the equation $- \\\\e^2 \\\\D u + u= u^p$ in $\\\\Omega \\\\subseteq \\\\R^N$, where $\\\\Omega$ is open, smooth and bounded, and we prove concentration of solutions along $k$-dimensional minimal submanifolds of $\\\\partial \\\\O$, for $N \\\\geq 3$ and for $k \\\\in \\\\{1, ..., N-2\\\\}$. We impose Neumann boundary conditions, assuming $13 or with two inputs for n=4 and n=5, up to state-feedback transformations, preserving the affine structure. First using the Poincare series of moduli numbers we introduce the intrinsic numbers of functional moduli of each prescribed number of variables on which a classification problem depends. In order to classify affine systems with scalar input we associate with such a system the canonical frame by normalizing some structural functions in a commutative relation of the vector fields, which define our control system. Then, using this canonical frame, we introduce the canonical coordinates and find a complete system of state-feedback invariants of the system. It also gives automatically the micro-local (i.e. local in state-input space) classification of the generic non-affine n-dimensional control system with scalar input for n>2. Further we show how the problem of feedback-equivalence of affine systems with two-dimensional input in state space of dimensions 4 and 5 can be reduced to the same problem for affine systems with scalar input. In order to make this reduction we distinguish the subsystem of our control system, consisting of the directions of all extremals in dimension 4 and all abnormal extremals in dimension 5 of the time optimal problem, defined by the original control system. In each classification problem under consideration we find the intrinsic numbers of functional moduli of each prescribed number of variables according to its Poincare series.1 aAgrachev, Andrei, A.1 aZelenko, Igor uhttp://hdl.handle.net/1963/218600760nas a2200097 4500008004300000245003700043210003700080520048700117100002200604856003600626 2007 en_Ud 00aFeedback control of spin systems0 aFeedback control of spin systems3 aThe feedback stabilization problem for ensembles of coupled spin 1/2 systems is discussed from a control theoretic perspective. The noninvasive nature of the bulk measurement allows for a fully unitary and deterministic closed loop. The Lyapunov-based feedback design presented does not require spins that are selectively addressable. With this method, it is possible to obtain control inputs also for difficult tasks, like suppressing undesired couplings in identical spin systems.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/180801194nas a2200097 4500008004300000245010500043210006900148520082100217100002201038856003601060 2007 en_Ud 00aFeedback stabilization of quantum ensembles: a global convergence analysis on complex flag manifolds0 aFeedback stabilization of quantum ensembles a global convergence3 aIn an N-level quantum mechanical system, the problem of unitary feedback stabilization of mixed density operators to periodic orbits admits a natural Lyapunov-based time-varying feedback design. A global description of the domain of attraction of the closed-loop system can be provided based on a \\\"root-space\\\"-like structure of the space of density operators. This convex set foliates as a complex flag manifold where each leaf is identified with the coadjoint orbit of the eigenvalues of the density operator. The converging conditions are time-independent but depend from the topology of the flag manifold: it is shown that the closed loop must have a number of equilibria at least equal to the Euler characteristic of the manifold, thus imposing obstructions of topological nature to global stabilizability.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/172900873nas a2200133 4500008004300000245009700043210006900140520040800209100002500617700001900642700002100661700002100682856003600703 2007 en_Ud 00aOn finite-dimensional projections of distributions for solutions of randomly forced PDE\\\'s0 afinitedimensional projections of distributions for solutions of 3 aThe paper is devoted to studying the image of probability measures on a Hilbert space under finite-dimensional analytic maps. We establish sufficient conditions under which the image of a measure has a density with respect to the Lebesgue measure and continuously depends on the map. The results obtained are applied to the 2D Navier-Stokes equations perturbed by various random forces of low dimension.1 aAgrachev, Andrei, A.1 aKuksin, Sergei1 aSarychev, Andrey1 aShirikyan, Armen uhttp://hdl.handle.net/1963/201200617nas 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/1963/199401180nas a2200109 4500008004300000245005200043210005000095520085100145100001700996700002101013856003601034 2007 en_Ud 00aHigh-order angles in almost-Riemannian geometry0 aHighorder angles in almostRiemannian geometry3 aLet X and Y be two smooth vector fields on a two-dimensional manifold M. If X and Y are everywhere linearly independent, then they define a Riemannian metric on M (the metric for which they are orthonormal) and they give to M the structure of metric space. If X and Y become linearly dependent somewhere on M, then the corresponding Riemannian metric has singularities, but under generic conditions the metric structure is still well defined. Metric structures that can be defined locally in this way are called almost-Riemannian structures. The main result of the paper is a generalization to almost-Riemannian structures of the Gauss-Bonnet formula for domains with piecewise-C2 boundary. The main feature of such formula is the presence of terms that play the role of high-order angles at the intersection points with the set of singularities.1 aBoscain, Ugo1 aSigalotti, Mario uhttp://hdl.handle.net/1963/199500967nas a2200109 4500008004300000245005100043210004700094520063600141100002000777700002400797856003600821 2007 en_Ud 00aThe holomorphic anomaly for open string moduli0 aholomorphic anomaly for open string moduli3 aWe complete the holomorphic anomaly equations for topological strings with their dependence on open moduli. We obtain the complete system by standard path integral arguments generalizing the analysis of BCOV (Commun. Math. Phys. 165 (1994) 311) to strings with boundaries. We study both the anti-holomorphic dependence on open moduli and on closed moduli in presence of Wilson lines. By providing the compactification a\\\' la Deligne-Mumford of the moduli space of Riemann surfaces with boundaries, we show that the open holomorphic anomaly equations are structured on the (real codimension one) boundary components of this space.1 aBonelli, Giulio1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/211301450nas 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 a

The Luther-Emery liquid is a state of matter that is predicted to occur in one-dimensional systems of interacting fermions and is characterized by a gapless charge spectrum and a gapped spin spectrum. In this Letter we discuss a realization of the Luther-Emery phase in a trapped cold-atom gas. We study by means of the density-matrix renormalization-group technique a two-component atomic Fermi gas with attractive interactions subject to parabolic trapping inside an optical lattice. We demonstrate how this system exhibits compound phases characterized by the coexistence of spin pairing and atomic-density waves. A smooth crossover occurs with increasing magnitude of the atom-atom attraction to a state in which tightly bound spin-singlet dimers occupy the center of the trap. The existence of atomic-density waves could be detected in the elastic contribution to the light-scattering diffraction pattern.

1 aXianlong, Gao1 aRizzi, Matteo1 aPolini, Marco1 aFazio, Rosario1 aTosi, Mario P.1 aCampo, Vivaldo L. Jr.1 aCapelle, Klaus uhttp://hdl.handle.net/1963/205600522nas a2200145 4500008004100000245006600041210006500107260002300172300001200195490000800207100001900215700002400234700001900258856009900277 2007 eng d00aMassless scalar field in a two-dimensional de Sitter universe0 aMassless scalar field in a twodimensional de Sitter universe aBaselbBirkhäuser a27–380 v2511 aBertola, Marco1 aCorbetta, Francesco1 aMoschella, Ugo uhttps://www.math.sissa.it/publication/massless-scalar-field-two-dimensional-de-sitter-universe00410nas a2200097 4500008004300000245012400043210006900167100002000236700002000256856003600276 2007 en_Ud 00aOn the Maz\\\'ya inequalities: existence and multiplicity results for an elliptic problem involving cylindrical weights0 aMazya inequalities existence and multiplicity results for an ell1 aGazzini, Marita1 aMusina, Roberta uhttp://hdl.handle.net/1963/252201055nas a2200109 4500008004300000245006600043210006600109520069300175100001600868700002500884856003600909 2007 en_Ud 00aMetrics on semistable and numerically effective Higgs bundles0 aMetrics on semistable and numerically effective Higgs bundles3 aWe consider fibre metrics on Higgs vector bundles on compact K\\\\\\\"ahler manifolds, providing notions of numerical effectiveness and numerical flatness in terms of such metrics. We prove several properties of bundles satisfying such conditions and in particular we show that numerically flat Higgs bundles have vanishing Chern classes, and that they admit filtrations whose quotients are stable flat Higgs bundles. We compare these definitions with those previously given in the case of projective varieties. Finally we study the relations between numerically effectiveness and semistability, providing semistability criteria for Higgs bundles on projective manifolds of any dimension.1 aBruzzo, Ugo1 aGrana-Otero, Beatriz uhttp://hdl.handle.net/1963/184000408nas a2200109 4500008004300000245008800043210006900131100002400200700002200224700001600246856003600262 2007 en_Ud 00aMulti-bump solitons to linearly coupled systems of nonlinear Schrödinger equations0 aMultibump solitons to linearly coupled systems of nonlinear Schr1 aAmbrosetti, Antonio1 aColorado, Eduardo1 aRuiz, David uhttp://hdl.handle.net/1963/183500894nas a2200109 4500008004300000245005300043210005300096520056000149100001800709700002100727856003600748 2007 en_Ud 00aNearly time optimal stabilizing patchy feedbacks0 aNearly time optimal stabilizing patchy feedbacks3 aWe consider the time optimal stabilization problem for a nonlinear control system $\\\\dot x=f(x,u)$. Let $\\\\tau(y)$ be the minimum time needed to steer the system from the state $y\\\\in\\\\R^n$ to the origin, and call $\\\\A(T)$ the set of initial states that can be steered to the origin in time $\\\\tau(y)\\\\leq T$. Given any $\\\\ve>0$, in this paper we construct a patchy feedback $u=U(x)$ such that every solution of $\\\\dot x=f(x, U(x))$, $x(0)=y\\\\in \\\\A(T)$ reaches an $\\\\ve$-neighborhood of the origin within time $\\\\tau(y)+\\\\ve$.1 aAncona, Fabio1 aBressan, Alberto uhttp://hdl.handle.net/1963/218500581nas a2200109 4500008004300000245009300043210006900136520018500205100002000390700002500410856003600435 2007 en_Ud 00aNecessary and sufficient conditions for the chainrule in W1,1loc(RN;Rd) and BVloc(RN;Rd)0 aNecessary and sufficient conditions for the chainrule in W11locR3 aIn this paper we prove necessary and sufficient conditions for the validity of the classical chain rule in Sobolev spaces and in the space of functions of bounded variation.

1 aLeoni, Giovanni1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/203701154nas a2200121 4500008004300000245004500043210004300088520080300131100002200934700002400956700001600980856003600996 2007 en_Ud 00aA new model for contact angle hysteresis0 anew model for contact angle hysteresis3 aWe present a model which explains several experimental observations relating contact angle hysteresis with surface roughness. The model is based on the balance between released energy and dissipation, and it describes the stick-slip behavior of drops on a rough surface using ideas similar to those employed in dry friction, elasto-plasticity and fracture mechanics. The main results of our analysis are formulas giving the interval of stable contact angles as a function of the surface roughness. These formulas show that the difference between advancing and receding angles is much larger for a drop in complete contact with the substrate (Wenzel drop) than for one whose cavities are filled with air (Cassie-Baxter drop). This fact is used as the key tool to interpret the experimental evidence.1 aDeSimone, Antonio1 aGruenewald, Natalie1 aOtto, Felix uhttp://hdl.handle.net/1963/184801143nas a2200121 4500008004100000245005700041210005700098260001000155520076800165653002800933100002400961856003600985 2007 en d00aNoncommutative geometry and quantum group symmetries0 aNoncommutative geometry and quantum group symmetries bSISSA3 aIt is a widespread belief that mathematics originates from the desire to understand (and eventually to formalize) some aspects of the real world. Quoting [Man07], «we are doing mathematics in order to understand, create, and handle things, and perhaps this understanding is mathematics» . Let me thus begin with a brief discussion of the physical ideas that motivated the development of Noncommutative Geometry and Quantum Group Theory - the areas of mathematics to which this dissertation belongs. Some physicists believe, and Einstein himself expressed this view in [Ein98a], that physics progresses in stages: there is no `final\\\' theory of Nature, but simply a sequence of theories which provide more and more accurate descriptions of the real world...10aNoncommutative geometry1 aD'Andrea, Francesco uhttp://hdl.handle.net/1963/526900613nas a2200109 4500008004300000245006800043210006200111520025400173100002100427700001900448856003600467 2007 en_Ud 00aOn a notion of unilateral slope for the Mumford-Shah functional0 anotion of unilateral slope for the MumfordShah functional3 aIn this paper we introduce a notion of unilateral slope for the Mumford-Shah functional, and provide an explicit formula in the case of smooth cracks. We show that the slope is not lower semicontinuous and study the corresponding relaxed functional.1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/1963/205901687nas a2200121 4500008004300000245008300043210007000126520125600196100002201452700002901474700002601503856003601529 2007 en_Ud 00aThe number of eigenvalues of three-particle Schrödinger operators on lattices0 anumber of eigenvalues of threeparticle Schrödinger operators on 3 aWe consider the Hamiltonian of a system of three quantum mechanical particles (two identical fermions and boson)on the three-dimensional lattice $\\\\Z^3$ and interacting by means of zero-range attractive potentials. We describe the location and structure of the essential spectrum of the three-particle discrete Schr\\\\\\\"{o}dinger operator $H_{\\\\gamma}(K),$ $K$ being the total quasi-momentum and $\\\\gamma>0$ the ratio of the mass of fermion and boson.\\nWe choose for $\\\\gamma>0$ the interaction $v(\\\\gamma)$ in such a way the system consisting of one fermion and one boson has a zero energy resonance.\\nWe prove for any $\\\\gamma> 0$ the existence infinitely many eigenvalues of the operator $H_{\\\\gamma}(0).$ We establish for the number $N(0,\\\\gamma; z;)$ of eigenvalues lying below $z<0$ the following asymptotics $$ \\\\lim_{z\\\\to 0-}\\\\frac{N(0,\\\\gamma;z)}{\\\\mid \\\\log \\\\mid z\\\\mid \\\\mid}={U} (\\\\gamma) .$$ Moreover, for all nonzero values of the quasi-momentum $K \\\\in T^3 $ we establish the finiteness of the number $ N(K,\\\\gamma;\\\\tau_{ess}(K))$ of eigenvalues of $H(K)$ below the bottom of the essential spectrum and we give an asymptotics for the number $N(K,\\\\gamma;0)$ of eigenvalues below zero.1 aAlbeverio, Sergio1 aDell'Antonio, Gianfausto1 aLakaev, Saidakhmat N. uhttp://hdl.handle.net/1963/257601358nas a2200109 4500008004300000245009600043210006900139520096500208100001801173700002101191856003601212 2007 en_Ud 00aNumerical solution of the small dispersion limit of Korteweg de Vries and Whitham equations0 aNumerical solution of the small dispersion limit of Korteweg de 3 aThe Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion of order $\\\\epsilon^2$, is characterized by the appearance of a zone of rapid modulated oscillations of wave-length of order $\\\\epsilon$. These oscillations are approximately described by the elliptic solution of KdV where the amplitude, wave-number and frequency are not constant but evolve according to the Whitham equations. In this manuscript we give a quantitative analysis of the discrepancy between the numerical solution of the KdV equation in the small dispersion limit and the corresponding approximate solution for values of $\\\\epsilon$ between $10^{-1}$ and $10^{-3}$. The numerical results are compatible with a difference of order $\\\\epsilon$ within the `interior\\\' of the Whitham oscillatory zone, of order $\\\\epsilon^{1/3}$ at the left boundary outside the Whitham zone and of order $\\\\epsilon^{1/2}$ at the right boundary outside the Whitham zone.1 aGrava, Tamara1 aKlein, Christian uhttp://hdl.handle.net/1963/178801084nas a2200109 4500008004300000245007900043210006900122520070800191100001800899700002100917856003600938 2007 en_Ud 00aNumerical study of a multiscale expansion of KdV and Camassa-Holm equation0 aNumerical study of a multiscale expansion of KdV and CamassaHolm3 aWe study numerically solutions to the Korteweg-de Vries and Camassa-Holm equation close to the breakup of the corresponding solution to the dispersionless equation. The solutions are compared with the properly rescaled numerical solution to a fourth order ordinary differential equation, the second member of the Painlev\\\\\\\'e I hierarchy. It is shown that this solution gives a valid asymptotic description of the solutions close to breakup. We present a detailed analysis of the situation and compare the Korteweg-de Vries solution quantitatively with asymptotic solutions obtained via the solution of the Hopf and the Whitham equations. We give a qualitative analysis for the Camassa-Holm equation1 aGrava, Tamara1 aKlein, Christian uhttp://hdl.handle.net/1963/252700810nas a2200109 4500008004300000245004200043210004200085520049600127100001600623700002500639856003600664 2007 en_Ud 00aNumerically flat Higgs vector bundles0 aNumerically flat Higgs vector bundles3 aAfter providing a suitable definition of numerical effectiveness for Higgs bundles, and a related notion of numerical flatness, in this paper we prove, together with some side results, that all Chern classes of a Higgs-numerically flat Higgs bundle vanish, and that a Higgs bundle is Higgs-numerically flat if and only if it is has a filtration whose quotients are flat stable Higgs bundles. We also study the relation between these numerical properties of Higgs bundles and (semi)stability.1 aBruzzo, Ugo1 aGrana-Otero, Beatriz uhttp://hdl.handle.net/1963/175700311nas a2200097 4500008004300000245005000043210005000093100001800143700001600161856003600177 2007 en_Ud 00aParametrized curves in Lagrange Grassmannians0 aParametrized curves in Lagrange Grassmannians1 aZelenko, Igor1 aChengbo, Li uhttp://hdl.handle.net/1963/256000408nas a2200097 4500008004100000245011900041210006900160260001000229100002300239856004800262 2007 en d00aPerturbation techniques applied to the real vanishing viscosity approximation of an initial boundary value problem0 aPerturbation techniques applied to the real vanishing viscosity bSISSA1 aBianchini, Stefano uhttp://preprints.sissa.it/handle/1963/3531500626nas a2200109 4500008004300000245008200043210006900125520024600194100002100440700001900461856003600480 2007 en_Ud 00aQuasistatic crack growth for a cohesive zone model with prescribed crack path0 aQuasistatic crack growth for a cohesive zone model with prescrib3 aIn this paper we study the quasistatic crack growth for a cohesive zone model. We assume that the crack path is prescribed and we study the time evolution of the crack in the framework of the variational theory of rate-independent processes.1 aDal Maso, Gianni1 aZanini, Chiara uhttp://hdl.handle.net/1963/168600558nas a2200121 4500008004300000245007600043210006900119520014800188100002100336700002100357700002200378856003600400 2007 en_Ud 00aQuasistatic evolution problems for pressure-sensitive plastic materials0 aQuasistatic evolution problems for pressuresensitive plastic mat3 aWe study quasistatic evolution problems for pressure-sensitive plastic materials in the context of small strain associative perfect plasticity.1 aDal Maso, Gianni1 aDemyanov, Alexey1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/196200973nas a2200109 4500008004300000245006600043210006600109520061200175100002200787700001800809856003600827 2007 en_Ud 00aReciprocal transformations and flat metrics on Hurwitz spaces0 aReciprocal transformations and flat metrics on Hurwitz spaces3 aWe consider hydrodynamic systems which possess a local Hamiltonian structure of Dubrovin-Novikov type. To such a system there are also associated an infinite number of nonlocal Hamiltonian structures. We give necessary and sufficient conditions so that, after a nonlinear transformation of the independent variables, the reciprocal system still possesses a local Hamiltonian structure of Dubrovin-Novikov type. We show that, under our hypotheses, bi-hamiltonicity is preserved by the reciprocal transformation. Finally we apply such results to reciprocal systems of genus g Whitham-KdV modulation equations.1 aAbenda, Simonetta1 aGrava, Tamara uhttp://hdl.handle.net/1963/221001299nas a2200097 4500008004300000245006000043210005900103520097400162100002901136856003601165 2007 en_Ud 00aReduced density matrices and Bose-Einstein condensation0 aReduced density matrices and BoseEinstein condensation3 aEmergence and applications of the ubiquitous tool of reduced density matrices in the rigorous analysis of Bose Einstein condensation is reviewed, and new related results are added. The need and the nature of scaling limits of infinitely many particles is discussed, which imposes that a physically meaningful and mathematically well-posed definition of asymptotic condensation is placed at the level of marginals.\\nThe topic of correlations in the condensed state is addressed in order to show their influence at this level of marginals, both in the true condensed state and in the suitable trial functions one introduces to approximate the many-body structure and energy. Complete condensation is shown to be equivalently defined at any fixed k-body level, both for pure and mixed states. Further, it is proven to be equivalent to some other characterizations in terms of asymptotic factorization of the many-body state, which are currently present in the literature.1 aMichelangeli, Alessandro uhttp://hdl.handle.net/1963/198600931nas a2200121 4500008004100000245007500041210006800116260001000184520053900194100002000733700002000753856003600773 2007 en d00aOn the reductions and classical solutions of the Schlesinger equations0 areductions and classical solutions of the Schlesinger equations bSISSA3 aThe Schlesinger equations S(n,m) describe monodromy preserving\\r\\ndeformations of order m Fuchsian systems with n+1 poles. They\\r\\ncan be considered as a family of commuting time-dependent Hamiltonian\\r\\nsystems on the direct product of n copies of m×m matrix algebras\\r\\nequipped with the standard linear Poisson bracket. In this paper we address\\r\\nthe problem of reduction of particular solutions of “more complicated”\\r\\nSchlesinger equations S(n,m) to “simpler” S(n′,m′) having n′ < n\\r\\nor m′ < m.1 aDubrovin, Boris1 aMazzocco, Marta uhttp://hdl.handle.net/1963/647200600nas a2200097 4500008004300000245005300043210004500096520030500141100002000446856003600466 2007 en_Ud 00aOn the regularity of weak solutions to H-systems0 aregularity of weak solutions to Hsystems3 aAbstract. In this paper we prove that every weak solution to the H-surface equation is locally bounded, provided the prescibed mean curvatore H is asymptotic to a constant at infinity (with a suitable decay rate). No smoothness ssumptions are required on H. We consider also the Dirichlet problem....1 aMusina, Roberta uhttp://hdl.handle.net/1963/175300981nas a2200097 4500008004300000245008200043210006900125520062400194100002900818856003600847 2007 en_Ud 00aRole of scaling limits in the rigorous analysis of Bose-Einstein condensation0 aRole of scaling limits in the rigorous analysis of BoseEinstein 3 aIn the context of the rigorous analysis of Bose-Einstein condensation, recent achievements have been obtained in the form of asymptotic results when some appropriate scaling is performed in the Hamiltonian, and the limit of infinite number of particles is taken. In particular, two modified thermodynamic limits of infinite dilution turned out to provide an insight in this analysis, the so-\\ncalled Gross-Pitaevskii limit and the related Tomas-Fermi limit. Here such scalings are discussed with respect to their physical and mathematical motivations, and to the currently known results obtained within this framework.1 aMichelangeli, Alessandro uhttp://hdl.handle.net/1963/198400296nas a2200097 4500008004300000245003900043210003900082100001600121700002500137856003600162 2007 en_Ud 00aSemistable principal Higgs bundles0 aSemistable principal Higgs bundles1 aBruzzo, Ugo1 aGrana-Otero, Beatriz uhttp://hdl.handle.net/1963/253300729nas a2200121 4500008004300000245002700043210002700070520041600097100002200513700001800535700001800553856003600571 2007 en_Ud 00aSmooth toric DM stacks0 aSmooth toric DM stacks3 aWe give a new definition of smooth toric DM stacks in the same spirit of toric varieties. We show that our definition is equivalent to the one of Borisov, Chen and Smith in terms of stacky fans. In particular, we give a geometric interpretation of the combinatorial data contained in a stacky fan. We also give a bottom up classification in terms of simplicial toric varieties and fiber products of root stacks.1 aFantechi, Barbara1 aMann, Etienne1 aNironi, Fabio uhttp://hdl.handle.net/1963/212000945nas a2200121 4500008004300000245006300043210006300106520056100169100002200730700001700752700001800769856003600787 2007 en_Ud 00aSoft elasticity and microstructure in smectic C elastomers0 aSoft elasticity and microstructure in smectic C elastomers3 aSmectic C elastomers are layered materials exhibiting a solid-like elastic response along the layer normal and a rubbery one in the plane. The set of strains minimizing the elastic energy contains a one-parameter family of simple stretches associated with an internal degree of freedom, coming from the in-plane component of the director. We investigate soft elasticity and the corresponding microstructure by determining the quasiconvex hull of the set , and use this to propose experimental tests that should make the predicted soft response observable.1 aDeSimone, Antonio1 aAdams, James1 aConti, Sergio uhttp://hdl.handle.net/1963/181100726nas a2200097 4500008004300000245009800043210006900141520036200210100002000572856003600592 2007 en_Ud 00aSolutions of vectorial Hamilton-Jacobi equations and minimizers of nonquasiconvex functionals0 aSolutions of vectorial HamiltonJacobi equations and minimizers o3 aWe provide a unified approach to prove existence results for the Dirichlet problem for Hamilton-Jacobi equations and for the minimum problem for nonquasiconvex functionals of the Calculus of Variations with affine boundary data. The idea relies on the definition of integro-extremal solutions introduced in the study of nonconvex scalar variational problem.1 aZagatti, Sandro uhttp://hdl.handle.net/1963/276301231nas a2200109 4500008004300000245012500043210006900168520080600237100002001043700002201063856003601085 2007 en_Ud 00aSolutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part II: proof of the existence result0 aSolutions to the nonlinear Schroedinger equation carrying moment3 aWe prove existence of a special class of solutions to the (elliptic) Nonlinear Schroedinger Equation $- \\\\epsilon^2 \\\\Delta \\\\psi + V(x) \\\\psi = |\\\\psi|^{p-1} \\\\psi$ on a manifold or in the Euclidean space. Here V represents the potential, p is an exponent greater than 1 and $\\\\epsilon$ a small parameter corresponding to the Planck constant. As $\\\\epsilon$ tends to zero (namely in the semiclassical limit) we prove existence of complex-valued solutions which concentrate along closed curves, and whose phase in highly oscillatory. Physically, these solutions carry quantum-mechanical momentum along the limit curves. In the first part of this work we identified the limit set and constructed approximate solutions, while here we give the complete proof of our main existence result.1 aMahmoudi, Fethi1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/211101499nas a2200121 4500008004300000245014300043210006900186520102000255100002001275700002201295700002401317856003601341 2007 en_Ud 00aSolutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part I: study of the limit set and approximate solutions0 aSolutions to the nonlinear Schroedinger equation carrying moment3 aWe prove existence of a special class of solutions to the (elliptic) Nonlinear Schroeodinger Equation $- \\\\epsilon^2 \\\\Delta \\\\psi + V(x) \\\\psi = |\\\\psi|^{p-1} \\\\psi$, on a manifold or in the Euclidean space. Here V represents the potential, p an exponent greater than 1 and $\\\\epsilon$ a small parameter corresponding to the Planck constant. As $\\\\epsilon$ tends to zero (namely in the semiclassical limit) we prove existence of complex-valued solutions which concentrate along closed curves, and whose phase is highly oscillatory. Physically, these solutions carry quantum-mechanical momentum along the limit curves. In this first part we provide the characterization of the limit set, with natural stationarity and non-degeneracy conditions. We then construct an approximate solution up to order $\\\\epsilon^2$, showing that these conditions appear naturally in a Taylor expansion of the equation in powers of $\\\\epsilon$. Based on these, an existence result will be proved in the second part.1 aMahmoudi, Fethi1 aMalchiodi, Andrea1 aMontenegro, Marcelo uhttp://hdl.handle.net/1963/211200914nas a2200109 4500008004300000245006600043210006600109520054400175100002200719700002700741856003600768 2007 en_Ud 00aSome existence results for the Toda system on closed surfaces0 aSome existence results for the Toda system on closed surfaces3 aGiven a compact closed surface $\\\\Sig$, we consider the {\\\\em generalized Toda} system of equations on $\\\\Sig$: $- \\\\D u_i = \\\\sum_{j=1}^2 \\\\rho_j a_{ij} \\\\left( \\\\frac{h_j e^{u_j}}{\\\\int_\\\\Sig h_j e^{u_j} dV_g} - 1 \\\\right)$ for $i = 1, 2$, where $\\\\rho_1, \\\\rho_2$ are real parameters and $h_1, h_2$ are smooth positive functions. Exploiting the variational structure of the problem and using a new minimax scheme we prove existence of solutions for generic values of $\\\\rho_1$ and for $\\\\rho_2 < 4 \\\\pi$.1 aMalchiodi, Andrea1 aNdiaye, Cheikh Birahim uhttp://hdl.handle.net/1963/177500406nas a2200097 4500008004300000245011700043210006900160100001900229700002400248856003600272 2007 en_Ud 00aStability of front tracking solutions to the initial and boundary value problem for systems of conservation laws0 aStability of front tracking solutions to the initial and boundar1 aMarson, Andrea1 aDonadello, Carlotta uhttp://hdl.handle.net/1963/176900537nas a2200109 4500008004300000245006800043210006800111520016600179100002400345700002200369856003600391 2007 en_Ud 00aStanding waves of some coupled Nonlinear Schrödinger Equations0 aStanding waves of some coupled Nonlinear Schrödinger Equations3 aWe deal with a class of systems of NLS equations, proving the existence of bound and ground states provided the coupling parameter is small, respectively, large.1 aAmbrosetti, Antonio1 aColorado, Eduardo uhttp://hdl.handle.net/1963/182100738nas a2200097 4500008004300000245008700043210006900130520037600199100002900575856003600604 2007 en_Ud 00aStrengthened convergence of marginals to the cubic nonlinear Schroedinger equation0 aStrengthened convergence of marginals to the cubic nonlinear Sch3 aWe rewrite a recent derivation of the cubic non-linear Schroedinger equation by Adami, Golse, and Teta in the more natural formof the asymptotic factorisation of marginals at any fixed time and in the trace norm. This is the standard form in which the emergence of the\\nnon-linear effective dynamics of a large system of interacting bosons is\\nproved in the literature.1 aMichelangeli, Alessandro uhttp://hdl.handle.net/1963/197700907nas a2200121 4500008004300000245005500043210005300098520053100151100001900682700002500701700002300726856003600749 2007 en_Ud 00aSurfactants in Foam Stability: A Phase-Field Model0 aSurfactants in Foam Stability A PhaseField Model3 aThe role of surfactants in stabilizing the formation of bubbles in foams is studied using a phase-field model. The analysis is centered on a van der Walls-Cahn-Hilliard-type energy with an added term accounting for the interplay between the presence of a surfactant density and the creation of interfaces. In particular, it is concluded that the surfactant segregates to the interfaces, and that the prescriptionof the distribution of surfactant will dictate the locus of interfaces, what is in agreement with experimentation.1 aFonseca, Irene1 aMorini, Massimiliano1 aSlastikov, Valeriy uhttp://hdl.handle.net/1963/203500512nas 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/1963/186700987nas a2200133 4500008004300000245005700043210005600100520056800156100002100724700002200745700002500767700002500792856003600817 2007 en_Ud 00aTime-dependent systems of generalized Young measures0 aTimedependent systems of generalized Young measures3 aIn this paper some new tools for the study of evolution problems in the framework of Young measures are introduced. A suitable notion of time-dependent system of generalized Young measures is defined, which allows to extend the classical notions of total variation and absolute continuity with respect to time, as well as the notion of time derivative. The main results are a Helly type theorem for sequences of systems of generalized Young measures and a theorem about the existence of the time derivative for systems with bounded variation with respect to time.1 aDal Maso, Gianni1 aDeSimone, Antonio1 aMora, Maria Giovanna1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/179500630nas a2200097 4500008004300000245003900043210003900082520035800121100001700479856003600496 2007 en_Ud 00aTwisted noncommutative equivariant0 aTwisted noncommutative equivariant3 aWe propose Weil and Cartan models for the equivariant cohomology of covariant actions on toric deformation manifolds. The construction is based on the noncommutative Weil algebra of Alekseev and Meinrenken; we show that one can implement a Drinfeld twist of their models in order to take into account the noncommutativity of the spaces we are acting on.1 aCirio, Lucio uhttp://hdl.handle.net/1963/199100718nas a2200097 4500008004300000245012400043210006900167520032800236100002000564856003600584 2007 en_Ud 00aUniqueness and continuous dependence on boundary data for integro-extremal minimizers of the functional of the gradient0 aUniqueness and continuous dependence on boundary data for integr3 aWe study some qualitative properties of the integro-extremal minimizers of the functional of the gradient defined on Sobolev spaces with Dirichlet boundary conditions. We discuss their use in the non-convex case via viscosity methods and give conditions under which they are unique and depend continuously on boundary data.1 aZagatti, Sandro uhttp://hdl.handle.net/1963/276201073nas a2200121 4500008004300000245008500043210006900128260002100197520064400218100002800862700002500890856003600915 2007 en_Ud 00aViscosity solutions of Hamilton-Jacobi equations with discontinuous coefficients0 aViscosity solutions of HamiltonJacobi equations with discontinuo bWorld Scientific3 aWe consider Hamilton--Jacobi equations, where the Hamiltonian depends discontinuously on both the spatial and temporal location. Our main results are the existence and well--posedness of a viscosity solution to the Cauchy problem. We define a viscosity solution by treating the discontinuities in the coefficients analogously to \\\"internal boundaries\\\". By defining an appropriate penalization function, we prove that viscosity solutions are unique. The existence of viscosity solutions is established by showing that a sequence of front tracking approximations is compact in $L^\\\\infty$, and that the limits are viscosity solutions.1 aCoclite, Giuseppe Maria1 aRisebro, Nils Henrik uhttp://hdl.handle.net/1963/290700572nas a2200121 4500008004300000245003600043210003500079520024300114100002200357700001900379700001600398856003600414 2006 en_Ud 00a2-d stability of the Néel wall0 a2d stability of the Néel wall3 aWe are interested in thin-film samples in micromagnetism, where the magnetization m is a 2-d unit-length vector field. More precisely we are interested in transition layers which connect two opposite magnetizations, so called Néel walls.1 aDeSimone, Antonio1 aKnuepfer, Hans1 aOtto, Felix uhttp://hdl.handle.net/1963/219401031nas a2200121 4500008004300000245007500043210006900118520062400187100001800811700002500829700001900854856003600873 2006 en_Ud 00a4e-condensation in a fully frustrated Josephson junction diamond chain0 a4econdensation in a fully frustrated Josephson junction diamond 3 aFully frustrated one-dimensional diamond Josephson chains have been shown [B. Dou\\\\c{c}ot and J. Vidal, Phys. Rev. Lett. {\\\\bf 88}, 227005 (2002)] to posses a remarkable property: The superfluid phase occurs through the condensation of pairs of Cooper pairs. By means of Monte Carlo simulations we analyze quantitatively the Insulator to $4e$-Superfluid transition. We determine the location of the critical point and discuss the behaviour of the phase-phase correlators. For comparison we also present the case of a diamond chain at zero and 1/3 frustration where the standard $2e$-condensation is observed.

1 aRizzi, Matteo1 aCataudella, Vittorio1 aFazio, Rosario uhttp://hdl.handle.net/1963/240000859nas a2200109 4500008004300000245008400043210006900127520047200196100002200668700002300690856003600713 2006 en_Ud 00aAlmost Global Stochastic Feedback Stabilization of Conditional Quantum Dynamics0 aAlmost Global Stochastic Feedback Stabilization of Conditional Q3 aWe propose several parametrization-free solutions to the problem of quantum state reduction control by means of continuous measurement and smooth quantum feedback. In particular, we design a feedback law for which almost global stochastic feedback stabilization can be proved analytically by means of Lyapunov techinques. This synthesis arises very naturally from the physics of the problem, as it relies on the variance associated with the quantum filtering process.1 aAltafini, Claudio1 aTicozzi, Francesco uhttp://hdl.handle.net/1963/172700611nas a2200109 4500008004300000245006500043210006200108520025700170100001900427700001900446856003600465 2006 en_Ud 00aAn artificial viscosity approach to quasistatic crack growth0 aartificial viscosity approach to quasistatic crack growth3 aWe introduce a new model of irreversible quasistatic crack growth in which the evolution of cracks is the limit of a suitably modified $\\\\epsilon$-gradient flow of the energy functional, as the \\\"viscosity\\\" parameter $\\\\epsilon$ tends to zero.1 aToader, Rodica1 aZanini, Chiara uhttp://hdl.handle.net/1963/185000957nas a2200109 4500008004300000245006000043210005600103520060900159100001900768700002400787856003600811 2006 en_Ud 00aA Birkhoff-Lewis-Type Theorem for Some Hamiltonian PDEs0 aBirkhoffLewisType Theorem for Some Hamiltonian PDEs3 aIn this paper we give an extension of the Birkhoff--Lewis theorem to some semilinear PDEs. Accordingly we prove existence of infinitely many periodic orbits with large period accumulating at the origin. Such periodic orbits bifurcate from resonant finite dimensional invariant tori of the fourth order normal form of the system. Besides standard nonresonance and nondegeneracy assumptions, our main result is obtained assuming a regularizing property of the nonlinearity. We apply our main theorem to a semilinear beam equation and to a nonlinear Schr\\\\\\\"odinger equation with smoothing nonlinearity.1 aBambusi, Dario1 aBerti, Massimiliano uhttp://hdl.handle.net/1963/215901209nas a2200097 4500008004300000245009800043210006900141520083600210100002901046856003601075 2006 en_Ud 00aBorn approximation in the problem of the rigorous derivation of the Gross-Pitaevskii equation0 aBorn approximation in the problem of the rigorous derivation of 3 a\\\"It has a flavour of Mathematical Physics...\\\"With these words, just few years ago, prof. Di Giacomo\\nused to introduce the topic of the Born approximation within a nonrelativistic potential theory, in his `oversize\\\' course of Theoretical Physics in Pisa. Something maybe too fictitious inside the formal theory of the scattering he was teaching us at that point of the course. Now that I\\\'m (studying to become) a Mathematical Physicist indeed, dealing with such an `exotic tasting\\\' topic, those words come back to the mind, into a new perspective. Here the very recent problem of the rigorous derivation of\\nthe cubic nonlinear Schrödinger equation (the Gross-Pitaevskiî equation) is reviewed and discussed, with respect to the role of the Born approximation that one ends up with in an appropriate scaling limit1 aMichelangeli, Alessandro uhttp://hdl.handle.net/1963/181900487nas a2200109 4500008004300000245007200043210007000115520011000185100002400295700002200319856003600341 2006 en_Ud 00aBound and ground states of coupled nonlinear Schrödinger equations0 aBound and ground states of coupled nonlinear Schrödinger equatio3 aWe prove existence of bound and ground states of some systems of coupled nonlinear Schrodinger equations.1 aAmbrosetti, Antonio1 aColorado, Eduardo uhttp://hdl.handle.net/1963/214900412nas a2200109 4500008004300000245009200043210006900135100002400204700002200228700001600250856003600266 2006 en_Ud 00aBound states of Nonlinear Schroedinger Equations with Potentials Vanishing at Infinity0 aBound states of Nonlinear Schroedinger Equations with Potentials1 aAmbrosetti, Antonio1 aMalchiodi, Andrea1 aRuiz, David uhttp://hdl.handle.net/1963/175600319nas a2200085 4500008004300000245006900043210006200112100002300174856003600197 2006 en_Ud 00aOn Bressan\\\'s conjecture on mixing properties of vector fields0 aBressans conjecture on mixing properties of vector fields1 aBianchini, Stefano uhttp://hdl.handle.net/1963/180601054nas a2200097 4500008004300000245006500043210005900108520073200167100002100899856003600920 2006 en_Ud 00aOn a Camassa-Holm type equation with two dependent variables0 aCamassaHolm type equation with two dependent variables3 aWe consider a generalization of the Camassa Holm (CH) equation with two dependent variables, called CH2, introduced in [16]. We briefly provide an alternative derivation of it based on the theory of Hamiltonian structures\\non (the dual of) a Lie Algebra. The Lie Algebra here involved is the same algebra underlying the NLS hierarchy. We study the structural properties of the CH2 hierarchy within the bihamiltonian theory of integrable PDEs, and\\nprovide its Lax representation. Then we explicitly discuss how to construct classes of solutions, both of peakon and of algebro-geometrical type. We finally sketch the construction of a class of singular solutions, defined by setting to zero one of the two dependent variables.1 aFalqui, Gregorio uhttp://hdl.handle.net/1963/172100728nas a2200109 4500008004300000245007900043210006900122520035400191100001900545700001800564856003600582 2006 en_Ud 00aA Canonical Frame for Nonholonomic Rank Two Distributions of Maximal Class0 aCanonical Frame for Nonholonomic Rank Two Distributions of Maxim3 aIn 1910 E. Cartan constructed the canonical frame and found the most symmetric case for maximally nonholonomic rank 2 distributions in R5. We solve the analogous problems for rank 2 distributions in Rn for arbitrary n > 5. Our method is a kind of symplectification of the problem and it is completely different from the Cartan method of equivalence.1 aDoubrov, Boris1 aZelenko, Igor uhttp://hdl.handle.net/1963/171201190nas a2200109 4500008004300000245009100043210006900134520079700203100002401000700002001024856003601044 2006 en_Ud 00aCantor families of periodic solutions for completely resonant nonlinear wave equations0 aCantor families of periodic solutions for completely resonant no3 aWe prove the existence of small amplitude, $2\\\\pi \\\\slash \\\\om$-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions, for any frequency $ \\\\om $ belonging to a Cantor-like set of positive measure and for a new set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem. In spite of the complete resonance of the equation we show that we can still reduce the problem to a {\\\\it finite} dimensional bifurcation equation. Moreover, a new simple approach for the inversion of the linearized operators required by the Nash-Moser scheme is developed. It allows to deal also with nonlinearities which are not odd and with finite spatial regularity.1 aBerti, Massimiliano1 aBolle, Philippe uhttp://hdl.handle.net/1963/216100378nas 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/1963/219601052nas a2200121 4500008004300000245006900043210006900112520065900181100001700840700001700857700002000874856003600894 2006 en_Ud 00aCommon Polynomial Lyapunov Functions for Linear Switched Systems0 aCommon Polynomial Lyapunov Functions for Linear Switched Systems3 aIn this paper, we consider linear switched systems $\\\\dot x(t)=A_{u(t)} x(t)$, $x\\\\in\\\\R^n$, $u\\\\in U$, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching ({\\\\bf UAS} for short). We first prove that, given a {\\\\bf UAS} system, it is always possible to build a common polynomial Lyapunov function. Then our main result is that the degree of that common polynomial Lyapunov function is not uniformly bounded over all the {\\\\bf UAS} systems. This result answers a question raised by Dayawansa and Martin. A generalization to a class of piecewise-polynomial Lyapunov functions is given.1 aMason, Paolo1 aBoscain, Ugo1 aChitour, Yacine uhttp://hdl.handle.net/1963/218100823nas a2200097 4500008004300000245007000043210006900113520048500182100002200667856003600689 2006 en_Ud 00aCompactness of solutions to some geometric fourth-order equations0 aCompactness of solutions to some geometric fourthorder equations3 aWe prove compactness of solutions to some fourth order equations with exponential nonlinearities on four manifolds. The proof is based on a refined bubbling analysis, for which the main estimates are given in integral form. Our result is used in a subsequent paper to find critical points (via minimax arguments) of some geometric functional, which give rise to conformal metrics of constant $Q$-curvature. As a byproduct of our method, we also obtain compactness of such metrics.1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/212600921nas a2200109 4500008004300000245009700043210006900140520052400209100002000733700002200753856003600775 2006 en_Ud 00aConcentration at manifolds of arbitrary dimension for a singularly perturbed Neumann problem0 aConcentration at manifolds of arbitrary dimension for a singular3 aWe consider the equation $- \\\\e^2 \\\\D u + u = u^p$ in $\\\\O \\\\subseteq \\\\R^N$, where $\\\\O$ is open, smooth and bounded, and we prove concentration of solutions along $k$-dimensional minimal submanifolds of $\\\\pa \\\\O$, for $N \\\\geq 3$ and for $k \\\\in \\\\{1, \\\\dots, N-2\\\\}$. We impose Neumann boundary conditions, assuming $1<\\\\frac{N-k+2}{N-k-2}$ and $\\\\e \\\\to 0^+$. This result settles in full generality a phenomenon previously considered only in the particular case $N = 3$ and $k = 1$.1 aMahmoudi, Fethi1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/217000638nas a2200109 4500008004300000245006800043210006800111520027600179100002100455700001600476856003600492 2006 en_Ud 00aConservative Solutions to a Nonlinear Variational Wave Equation0 aConservative Solutions to a Nonlinear Variational Wave Equation3 aWe establish the existence of a conservative weak solution to the Cauchy problem for the nonlinear variational wave equation $u_{tt} - c(u)(c(u)u_x)_x=0$, for initial data of finite energy. Here $c(\\\\cdot)$ is any smooth function with uniformly positive bounded values.1 aBressan, Alberto1 aYuxi, Zheng uhttp://hdl.handle.net/1963/218401941nas a2200133 4500008004300000245006300043210005900106520150700165100002501672700003001697700002001727700002401747856003601771 2006