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.202001100912nas 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/1963/3533400512nas 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-materials02145nas 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/10.1215/00127094-2018-005900307nas a2200085 4500008004100000245006200041210006200103100001900165856003700184 2018 eng d00aCanonical Surfaces and Hypersurfaces in Abelian Varieties0 aCanonical Surfaces and Hypersurfaces in Abelian Varieties1 aCesarano, Luca uhttps://arxiv.org/abs/1808.0530201651nas 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/S021820251850037901813nas 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%2Fb21917-500754nas 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/1963/3532000904nas 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/1963/3530700840nas 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/1963/3530400454nas 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-type00359nas 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/1807.0865900543nas 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-stresses01002nas 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/1963/3530901137nas 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/1963/3532601295nas 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/S201032631740004401282nas 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/1963/3527001393nas 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/1963/3527601385nas 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/s10231-016-0590-700428nas 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/1603.0642001226nas 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/1963/3527101991nas 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/1294900824nas 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/s00030-016-0426-600452nas a2200121 4500008004100000245005700041210005700098260002200155490000800177100002300185700002400208856009800232 2017 eng d00aRayleigh–Taylor instability in soft elastic layers0 aRayleigh–Taylor instability in soft elastic layers bThe Royal Society0 v3751 aRiccobelli, Davide1 aCiarletta, Pasquale uhttps://www.math.sissa.it/publication/rayleigh%E2%80%93taylor-instability-soft-elastic-layers02504nas a2200157 4500008004100000245005700041210005700098260001200155300000800167490000600175520201600181100001502197700002202212700002102234856009102255 2017 eng d00aReduced Basis Methods for Uncertainty Quantification0 aReduced Basis Methods for Uncertainty Quantification c08/2017 a8690 v53 aIn this work we review a reduced basis method for the solution of uncertainty quantification problems. Based on the basic setting of an elliptic partial differential equation with random input, we introduce the key ingredients of the reduced basis method, including proper orthogonal decomposition and greedy algorithms for the construction of the reduced basis functions, a priori and a posteriori error estimates for the reduced basis approximations, as well as its computational advantages and weaknesses in comparison with a stochastic collocation method [I. Babuška, F. Nobile, and R. Tempone, *SIAM Rev.*, 52 (2010), pp. 317--355]. We demonstrate its computational efficiency and accuracy for a benchmark problem with parameters ranging from a few to a few hundred dimensions. Generalizations to more complex models and applications to uncertainty quantification problems in risk prediction, evaluation of statistical moments, Bayesian inversion, and optimal control under uncertainty are also presented to illustrate how to use the reduced basis method in practice. Further challenges, advancements, and research opportunities are outlined.

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

Several 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-computational00449nas 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)13300434nas 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/1963/3520700947nas 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.html00391nas 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/1963/3519401781nas 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/1963/3519100912nas 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_102275nas 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-equations01691nas 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/1963/3496300428nas 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-processes01183nas 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/1963/3524600786nas 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/s00526-015-0947-601510nas 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-001837nas 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/1963/3446901006nas 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-equations00594nas 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-architectures00496nas 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-swimming01569nas 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/1963/3449100790nas 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-brackets01791nas a2200133 4500008004100000245008400041210006900125300001300194490000800207520132400215100002601539700002201565856007001587 2015 eng d00aA study of snake-like locomotion through the analysis of a flexible robot model0 astudy of snakelike locomotion through the analysis of a flexible a201500540 v4713 aWe 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.2015.005401482nas 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/1963/3465102162nas 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/1963/3512800423nas 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-processes00316nas 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/1963/3494001060nas 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/1963/698400800nas 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/1963/3469501688nas 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 aIn 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/1963/656201769nas 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/1963/3507301084nas 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/1963/3469201557nas 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/1963/3502100784nas 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/1963/644101138nas 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/1963/723500809nas 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/1963/738300476nas 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/S201032631350003201314nas 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/1963/650901360nas 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-and01330nas 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/s00220-013-1663-800784nas 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-coefficients01509nas 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-elliptic01375nas 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-data01737nas 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/1963/693301152nas 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/1963/655602153nas 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/1963/650600484nas 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-x01763nas 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/1963/625501971nas 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-experiment01113nas 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/1963/692100591nas 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/s00526-011-0452-501861nas 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/1963/693400376nas 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/10.1137/10080143300516nas 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/S016727891200011500431nas 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/1963/409101580nas 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-hemodynamics01607nas 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/1963/606902171nas 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/1963/646201567nas 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/1963/521800981nas 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/1963/579301012nas 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/1963/661300524nas 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/1963/435800770nas 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/1963/358401064nas 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-spaces00842nas 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/1963/296700673nas 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/1963/235501135nas 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/1963/385800991nas 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/1963/465700558nas 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-approach00413nas 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/1963/466300984nas a2200109 4500008004300000245008100043210006900124520060700193100002100800700001700821856003600838 2010 en_Ud 00aThe disintegration of the Lebesgue measure on the faces of a convex function0 adisintegration of the Lebesgue measure on the faces of a convex 3 aWe 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/1963/410601347nas 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/1963/438402590nas 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/1963/448001051nas a2200169 4500008004300000245007900043210006900122260003000191520049800221100001800719700002600737700002300763700001800786700002200804700001900826856003600845 2010 en_Ud 00aHomogeneous binary trees as ground states of quantum critical Hamiltonians0 aHomogeneous binary trees as ground states of quantum critical Ha bAmerican Physical Society3 aMany-body states whose wave-function admits a representation in terms of a uniform binary-tree tensor decomposition are shown to obey to power-law two-body correlations functions. Any such state can be associated with the ground state of a translational invariant Hamiltonian which, depending on the dimension of the systems sites, involve at most couplings between third-neighboring sites. A detailed analysis of their spectra shows that they admit an exponentially large ground space.

1 aSilvi, Pietro1 aGiovannetti, Vittorio1 aMontangero, Simone1 aRizzi, Matteo1 aCirac, J. Ignacio1 aFazio, Rosario uhttp://hdl.handle.net/1963/390900781nas 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/1963/239300493nas 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-point01159nas 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/1963/402300900nas 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/1963/379900526nas 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-systems00741nas 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/1963/384600906nas 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/1963/383901439nas 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/1963/387000355nas 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/1963/365901061nas 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/1963/339601885nas 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/1963/172400318nas 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/1963/369202238nas 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/1963/373600893nas 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/1963/270001175nas 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/1963/263600301nas a2200097 4500008004300000245004300043210003900086260002100125100002100146856003600167 2008 en_Ud 00aAn entropy based Glimm-type functional0 aentropy based Glimmtype functional bWorld Scientific1 aCaravenna, Laura uhttp://hdl.handle.net/1963/405101559nas 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/1963/269401845nas 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/1963/186200444nas 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/1963/195500611nas 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/1963/217500905nas 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/1963/525401450nas a2200169 4500008004300000245007300043210006900116520092200185100001801107700001801125700001801143700001901161700001901180700002601199700001901225856003601244 2007 en_Ud 00aLuther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas0 aLutherEmery Phase and AtomicDensity Waves in a Trapped Fermion G3 aThe Luther-Emery liquid is a state of matter that is predicted to occur in one-dimensional systems of interacting fermions and is characterized by a gapless charge spectrum and a gapped spin spectrum. In this Letter we discuss a realization of the Luther-Emery phase in a trapped cold-atom gas. We study by means of the density-matrix renormalization-group technique a two-component atomic Fermi gas with attractive interactions subject to parabolic trapping inside an optical lattice. We demonstrate how this system exhibits compound phases characterized by the coexistence of spin pairing and atomic-density waves. A smooth crossover occurs with increasing magnitude of the atom-atom attraction to a state in which tightly bound spin-singlet dimers occupy the center of the trap. The existence of atomic-density waves could be detected in the elastic contribution to the light-scattering diffraction pattern.

1 aXianlong, Gao1 aRizzi, Matteo1 aPolini, Marco1 aFazio, Rosario1 aTosi, Mario P.1 aCampo, Vivaldo L. Jr.1 aCapelle, Klaus uhttp://hdl.handle.net/1963/205600522nas 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-universe00408nas 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/1963/183500311nas a2200097 4500008004300000245005000043210005000093100001800143700001600161856003600177 2007 en_Ud 00aParametrized curves in Lagrange Grassmannians0 aParametrized curves in Lagrange Grassmannians1 aZelenko, Igor1 aChengbo, Li uhttp://hdl.handle.net/1963/256000945nas 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/1963/181100537nas 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/1963/182100630nas 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/1963/199101073nas a2200121 4500008004300000245008500043210006900128260002100197520064400218100002800862700002500890856003600915 2007 en_Ud 00aViscosity solutions of Hamilton-Jacobi equations with discontinuous coefficients0 aViscosity solutions of HamiltonJacobi equations with discontinuo bWorld Scientific3 aWe consider Hamilton--Jacobi equations, where the Hamiltonian depends discontinuously on both the spatial and temporal location. Our main results are the existence and well--posedness of a viscosity solution to the Cauchy problem. We define a viscosity solution by treating the discontinuities in the coefficients analogously to \\\"internal boundaries\\\". By defining an appropriate penalization function, we prove that viscosity solutions are unique. The existence of viscosity solutions is established by showing that a sequence of front tracking approximations is compact in $L^\\\\infty$, and that the limits are viscosity solutions.1 aCoclite, Giuseppe Maria1 aRisebro, Nils Henrik uhttp://hdl.handle.net/1963/290701031nas a2200121 4500008004300000245007500043210006900118520062400187100001800811700002500829700001900854856003600873 2006 en_Ud 00a4e-condensation in a fully frustrated Josephson junction diamond chain0 a4econdensation in a fully frustrated Josephson junction diamond 3 aFully frustrated one-dimensional diamond Josephson chains have been shown [B. Dou\\\\c{c}ot and J. Vidal, Phys. Rev. Lett. {\\\\bf 88}, 227005 (2002)] to posses a remarkable property: The superfluid phase occurs through the condensation of pairs of Cooper pairs. By means of Monte Carlo simulations we analyze quantitatively the Insulator to $4e$-Superfluid transition. We determine the location of the critical point and discuss the behaviour of the phase-phase correlators. For comparison we also present the case of a diamond chain at zero and 1/3 frustration where the standard $2e$-condensation is observed.

1 aRizzi, Matteo1 aCataudella, Vittorio1 aFazio, Rosario uhttp://hdl.handle.net/1963/240000487nas 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/1963/214901052nas 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/1963/218100395nas a2200097 4500008004300000245010800043210006900151100002100220700002000241856003600261 2006 en_Ud 00aThe Dirichlet problem for H-systems with small boundary data: blowup phenomena and nonexistence results0 aDirichlet problem for Hsystems with small boundary data blowup p1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/225200974nas a2200109 4500008004300000245009300043210006900136520057600205100002500781700002200806856003600828 2006 en_Ud 00aAn estimation of the controllability time for single-input systems on compact Lie Groups0 aestimation of the controllability time for singleinput systems o3 aGeometric control theory and Riemannian techniques are used to describe the reachable set at time t of left invariant single-input control systems on semi-simple compact Lie groups and to estimate the minimal time needed to reach any point from identity. This method provides an effective way to give an upper and a lower bound for the minimal time needed to transfer a controlled quantum system with a drift from a given initial position to a given final position. The bounds include diameters of the flag manifolds; the latter are also explicitly computed in the paper.1 aAgrachev, Andrei, A.1 aChambrion, Thomas uhttp://hdl.handle.net/1963/213500673nas a2200109 4500008004300000245005900043210005300102520033100155100002100486700002000507856003600527 2006 en_Ud 00aOn Palais-Smale sequences for H-systems: some examples0 aPalaisSmale sequences for Hsystems some examples3 aWe exhibit a series of examples of Palais-Smale sequences for the Dirichlet problem associated to the mean curvature equation with null boundary condition, and we show that in the case of nonconstant mean curvature functions different kinds of blow up phenomena appear and Palais-Smale sequences may have quite wild behaviour.1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/215700968nas a2200121 4500008004300000245005100043210005100094520060400145100001700749700002300766700002100789856003600810 2006 en_Ud 00aStability of planar nonlinear switched systems0 aStability of planar nonlinear switched systems3 aWe consider the time-dependent nonlinear system ˙ q(t) = u(t)X(q(t)) + (1 − u(t))Y (q(t)), where q ∈ R2, X and Y are two smooth vector fields, globally asymptotically stable at the origin and u : [0,∞) → {0, 1} is an arbitrary measurable function. Analysing the topology of the set where X and Y are parallel, we give some sufficient and some necessary conditions for global asymptotic stability, uniform with respect to u(.). Such conditions can be verified without any integration or construction of a Lyapunov function, and they are robust under small perturbations of the vector fields.1 aBoscain, Ugo1 aCharlot, Grégoire1 aSigalotti, Mario uhttp://hdl.handle.net/1963/171000897nas a2200121 4500008004300000245008900043210006900132260002400201520047200225100002000697700002200717856003600739 2005 en_Ud 00aAsymptotic Morse theory for the equation $\\\\Delta v=2v\\\\sb x\\\\wedge v\\\\sb y$0 aAsymptotic Morse theory for the equation Delta v2vsb xwedge vsb bInternational Press3 aGiven a smooth bounded domain ${\\\\O}\\\\subseteq \\\\R^2$, we consider the equation $\\\\D v = 2 v_x \\\\wedge v_y$ in $\\\\O$, where $v: {\\\\O}\\\\to \\\\R^3$. We prescribe Dirichlet boundary datum, and consider the case in which this datum converges to zero. An asymptotic study of the corresponding Euler functional is performed, analyzing multiple-bubbling phenomena. This allows us to settle a particular case of a question raised by H. Brezis and J.M. Coron.1 aChanillo, Sagun1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/353301579nas a2200121 4500008004100000245007400041210006700115260001800182520117500200100001801375700002801393856003601421 2005 en d00aOn the attainable set for Temple class systems with boundary controls0 aattainable set for Temple class systems with boundary controls bSISSA Library3 aConsider the initial-boundary value problem for a strictly hyperbolic, genuinely nonlinear, Temple class system of conservation laws % $$ u_t+f(u)_x=0, \\\\qquad u(0,x)=\\\\ov u(x), \\\\qquad {{array}{ll} &u(t,a)=\\\\widetilde u_a(t), \\\\noalign{\\\\smallskip} &u(t,b)=\\\\widetilde u_b(t), {array}. \\\\eqno(1) $$ on the domain $\\\\Omega =\\\\{(t,x)\\\\in\\\\R^2 : t\\\\geq 0, a \\\\le x\\\\leq b\\\\}.$ We study the mixed problem (1) from the point of view of control theory, taking the initial data $\\\\bar u$ fixed, and regarding the boundary data $\\\\widetilde u_a, \\\\widetilde u_b$ as control functions that vary in prescribed sets $\\\\U_a, \\\\U_b$, of $\\\\li$ boundary controls. In particular, we consider the family of configurations $$ \\\\A(T) \\\\doteq \\\\big\\\\{u(T,\\\\cdot); ~ u {\\\\rm is a sol. to} (1), \\\\quad \\\\widetilde u_a\\\\in \\\\U_a, \\\\widetilde u_b \\\\in \\\\U_b \\\\big\\\\} $$ that can be attained by the system at a given time $T>0$, and we give a description of the attainable set $\\\\A(T)$ in terms of suitable Oleinik-type conditions. We also establish closure and compactness of the set $\\\\A(T)$ in the $lu$ topology.1 aAncona, Fabio1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/158100982nas a2200121 4500008004100000245006900041210006900110260001800179520057400197100002800771700002500799856003600824 2005 en d00aConservation laws with time dependent discontinuous coefficients0 aConservation laws with time dependent discontinuous coefficients bSISSA Library3 aWe consider scalar conservation laws where the flux function depends discontinuously on both the spatial and temporal location. Our main results are the existence and well-posedness of an entropy solution to the Cauchy problem. The existence is established by showing that a sequence of front tracking approximations is compact in L1, and that the limits are entropy solutions. Then, using the definition of an entropy solution taken form [11], we show that the solution operator is L1 contractive. These results generalize the corresponding results from [16] and [11].1 aCoclite, Giuseppe Maria1 aRisebro, Nils Henrik uhttp://hdl.handle.net/1963/166602094nas a2200121 4500008004300000245013000043210006900173520162100242100002501863700003001888700001801918856003601936 2005 en_Ud 00aOn curvatures and focal points of distributions of dynamical Lagrangian distributions and their reductions by first integrals0 acurvatures and focal points of distributions of dynamical Lagran3 aPairs (Hamiltonian system, Lagrangian distribution), called dynamical Lagrangian distributions, appear naturally in Differential Geometry, Calculus of Variations and Rational Mechanics. The basic differential invariants of a dynamical Lagrangian distribution w.r.t. the action of the group of symplectomorphisms of the ambient symplectic manifold are the curvature operator and the curvature form. These invariants can be seen as generalizations of the classical curvature tensor in Riemannian Geometry. In particular, in terms of these invariants one can localize the focal points along extremals of the corresponding variational problems. In the present paper we study the behavior of the curvature operator, the curvature form and the focal points of a dynamical Lagrangian distribution after its reduction by arbitrary first integrals in involution. The interesting phenomenon is that the curvature form of so-called monotone increasing Lagrangian dynamical distributions, which appear naturally in mechanical systems, does not decrease after reduction. It also turns out that the set of focal points to the given point w.r.t. the monotone increasing dynamical Lagrangian distribution and the corresponding set of focal points w.r.t. its reduction by one integral are alternating sets on the corresponding integral curve of the Hamiltonian system of the considered dynamical distributions. Moreover, the first focal point corresponding to the reduced Lagrangian distribution comes before any focal point related to the original dynamical distribution. We illustrate our results on the classical $N$-body problem.1 aAgrachev, Andrei, A.1 aChtcherbakova, Natalia N.1 aZelenko, Igor uhttp://hdl.handle.net/1963/225400818nas a2200109 4500008004300000245007400043210006900117520043500186100002200621700002900643856003600672 2005 en_Ud 00aDecay of a bound state under a time-periodic perturbation: a toy case0 aDecay of a bound state under a timeperiodic perturbation a toy c3 aWe study the time evolution of a three dimensional quantum particle, initially in a bound state, under the action of a time-periodic zero range interaction with ``strength\\\'\\\' (\\\\alpha(t)). Under very weak generic conditions on the Fourier coefficients of (\\\\alpha(t)), we prove complete ionization as (t \\\\to \\\\infty). We prove also that, under the same conditions, all the states of the system are scattering states.1 aCorreggi, Michele1 aDell'Antonio, Gianfausto uhttp://hdl.handle.net/1963/229800651nas a2200109 4500008004300000245005100043210005000094520031700144100002100461700002300482856003600505 2005 en_Ud 00aGlobal solutions of the Hunter-Saxton equation0 aGlobal solutions of the HunterSaxton equation3 aWe construct a continuous semigroup of weak, dissipative solutions to a nonlinear partial differential equations modeling nematic liquid crystals. A new distance functional, determined by a problem of optimal transportation, yields sharp estimates on the continuity of solutions with respect to the initial data.1 aBressan, Alberto1 aConstantin, Adrian uhttp://hdl.handle.net/1963/225601006nas a2200133 4500008004300000245007100043210006900114520056200183100002200745700002900767700002000796700002000816856003600836 2005 en_Ud 00aIonization for Three Dimensional Time-dependent Point Interactions0 aIonization for Three Dimensional Timedependent Point Interaction3 aWe study the time evolution of a three dimensional quantum particle under the action of a time-dependent point interaction fixed at the origin. We assume that the ``strength\\\'\\\' of the interaction (\\\\alpha(t)) is a periodic function with an arbitrary mean. Under very weak conditions on the Fourier coefficients of (\\\\alpha(t)), we prove that there is complete ionization as (t \\\\to \\\\infty), starting from a bound state at time (t = 0). Moreover we prove also that, under the same conditions, all the states of the system are scattering states.1 aCorreggi, Michele1 aDell'Antonio, Gianfausto1 aFigari, Rodolfo1 aMantile, Andrea uhttp://hdl.handle.net/1963/229701933nas a2200145 4500008004100000245004900041210004900090260002900139520150600168100002001674700002001694700002201714700001501736856003601751 2005 en d00aMinimal surfaces in pseudohermitian geometry0 aMinimal surfaces in pseudohermitian geometry bScuola Normale Superiore3 aWe consider surfaces immersed in three-dimensional pseudohermitian manifolds. We define the notion of (p-)mean curvature and of the associated (p-)minimal surfaces, extending some concepts previously given for the (flat) Heisenberg group. We interpret the p-mean curvature not only as the tangential sublaplacian of a defining function, but also as the curvature of a characteristic curve, and as a quantity in terms of calibration geometry. As a differential equation, the p-minimal surface equation is degenerate (hyperbolic and elliptic). To analyze the singular set, we formulate some {\em extension} theorems, which describe how the characteristic curves meet the singular set. This allows us to classify the entire solutions to this equation and to solve a Bernstein-type problem (for graphs over the $xy$-plane) in the Heisenberg group $H_1$. In $H_{1}$, identified with the Euclidean space $R^{3}$, the p-minimal surfaces are classical ruled surfaces with the rulings generated by Legendrian lines. We also prove a uniqueness theorem for the Dirichlet problem under a condition on the size of the singular set in two dimensions, and generalize to higher dimensions without any size control condition. We also show that there are no closed, connected, $C^{2}$ smoothly immersed constant p-mean curvature or p-minimal surfaces of genus greater than one in the standard $S^{3}.$ This fact continues to hold when $S^{3}$ is replaced by a general spherical pseudohermitian 3-manifold.1 aCheng, Jih-Hsin1 aHwang, JennFang1 aMalchiodi, Andrea1 aYang, Paul uhttp://hdl.handle.net/1963/457901293nas a2200121 4500008004300000245009700043210006900140520086400209100001701073700002201090700002301112856003601135 2005 en_Ud 00aNonisotropic 3-level quantum systems: complete solutions for minimum time and minimum energy0 aNonisotropic 3level quantum systems complete solutions for minim3 aWe apply techniques of subriemannian geometry on Lie groups and of optimal synthesis on 2-D manifolds to the population transfer problem in a three-level quantum system driven by two laser pulses, of arbitrary shape and frequency. In the rotating wave approximation, we consider a nonisotropic model i.e. a model in which the two coupling constants of the lasers are different. The aim is to induce transitions from the first to the third level, minimizing 1) the time of the transition (with bounded laser amplitudes),\\n2) the energy of lasers (with fixed final time). After reducing the problem to real variables, for the purpose 1) we develop a theory of time optimal syntheses for distributional problem on 2-D-manifolds, while for the purpose 2) we use techniques of subriemannian geometry on 3-D Lie groups. The complete optimal syntheses are computed.1 aBoscain, Ugo1 aChambrion, Thomas1 aCharlot, Grégoire uhttp://hdl.handle.net/1963/225901313nas a2200133 4500008004300000245008200043210006900125260001300194520087600207100001801083700002201101700002001123856003601143 2005 en_Ud 00aSelf-similar folding patterns and energy scaling in compressed elastic sheets0 aSelfsimilar folding patterns and energy scaling in compressed el bElsevier3 aThin elastic sheets under isotropic compression, such as for example blisters formed by thin films which debonded from the substrate, can exhibit remarkably complex folding patterns. We discuss the scaling of the elastic energy with respect to the film thickness, and show that in certain regimes the optimal energy scaling can be reached\\nby self-similar folding patterns that refine towards the boundary, in agreement with experimental observations. We then extend the analysis\\nto anisotropic compression, and discuss a simplified scalar model which suggests the presence of a transition between a regime where\\nthe deformation is governed by global properties of the domain and another one where the direction of maximal compression dominates and the scale of the folds is mainly determined by the distance to the boundary in the direction of the folds themselves.1 aConti, Sergio1 aDeSimone, Antonio1 aMüller, Stefan uhttp://hdl.handle.net/1963/300001445nas a2200121 4500008004300000245006200043210006200105260001300167520106100180100002801241700001801269856003601287 2005 en_Ud 00aStability of solutions of quasilinear parabolic equations0 aStability of solutions of quasilinear parabolic equations bElsevier3 aWe bound the difference between solutions $u$ and $v$ of $u_t = a\\\\Delta u+\\\\Div_x f+h$ and $v_t = b\\\\Delta v+\\\\Div_x g+k$ with initial data $\\\\phi$ and $ \\\\psi$, respectively, by $\\\\Vert u(t,\\\\cdot)-v(t,\\\\cdot)\\\\Vert_{L^p(E)}\\\\le A_E(t)\\\\Vert \\\\phi-\\\\psi\\\\Vert_{L^\\\\infty(\\\\R^n)}^{2\\\\rho_p}+ B(t)(\\\\Vert a-b\\\\Vert_{\\\\infty}+ \\\\Vert \\\\nabla_x\\\\cdot f-\\\\nabla_x\\\\cdot g\\\\Vert_{\\\\infty}+ \\\\Vert f_u-g_u\\\\Vert_{\\\\infty} + \\\\Vert h-k\\\\Vert_{\\\\infty})^{\\\\rho_p} \\\\abs{E}^{\\\\eta_p}$. Here all functions $a$, $f$, and $h$ are smooth and bounded, and may depend on $u$, $x\\\\in\\\\R^n$, and $t$. The functions $a$ and $h$ may in addition depend on $\\\\nabla u$. Identical assumptions hold for the functions that determine the solutions $v$. Furthermore, $E\\\\subset\\\\R^n$ is assumed to be a bounded set, and $\\\\rho_p$ and $\\\\eta_p$ are fractions that depend on $n$ and $p$. The diffusion coefficients $a$ and $b$ are assumed to be strictly positive and the initial data are smooth.1 aCoclite, Giuseppe Maria1 aHolden, Helge uhttp://hdl.handle.net/1963/289201372nas a2200109 4500008004300000245007100043210006800114520100700182100001701189700002001206856003601226 2005 en_Ud 00aTime Optimal Synthesis for Left-Invariant Control Systems on SO(3)0 aTime Optimal Synthesis for LeftInvariant Control Systems on SO33 aConsider the control system given by $\\\\dot x=x(f+ug)$, where $x\\\\in SO(3)$, $|u|\\\\leq 1$ and $f,g\\\\in so(3)$ define two perpendicular left-invariant vector fields normalized so that $\\\\|f\\\\|=\\\\cos(\\\\al)$ and $\\\\|g\\\\|=\\\\sin(\\\\al)$, $\\\\al\\\\in ]0,\\\\pi/4[$. In this paper, we provide an upper bound and a lower bound for $N(\\\\alpha)$, the maximum number of switchings for time-optimal trajectories. More precisely, we show that $N_S(\\\\al)\\\\leq N(\\\\al)\\\\leq N_S(\\\\al)+4$, where $N_S(\\\\al)$ is a suitable integer function of $\\\\al$ which for $\\\\al\\\\to 0$ is of order $\\\\pi/(4\\\\alpha).$ The result is obtained by studying the time optimal synthesis of a projected control problem on $R P^2$, where the projection is defined by an appropriate Hopf fibration. Finally, we study the projected control problem on the unit sphere $S^2$. It exhibits interesting features which will be partly rigorously derived and partially described by numerical simulations.1 aBoscain, Ugo1 aChitour, Yacine uhttp://hdl.handle.net/1963/225801069nas a2200133 4500008004100000245003500041210003500076260001800111520069800129100002800827700002300855700002100878856003600899 2005 en d00aTraffic flow on a road network0 aTraffic flow on a road network bSISSA Library3 aThis paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from conservation of the number of cars,\\ndefined on a road network that is a collection of roads with junctions. The evolution problem is underdetermined at junctions, hence we choose to have some fixed rules for the distribution of traffic plus an optimization criteria for the flux. We prove existence, uniqueness and stability of solutions to the Cauchy problem. Our method is based on wave front tracking approach, see [6], and works also for boundary data and time dependent coefficients of traffic distribution at junctions, so including traffic lights.1 aCoclite, Giuseppe Maria1 aPiccoli, Benedetto1 aGaravello, Mauro uhttp://hdl.handle.net/1963/158401258nas a2200145 4500008004300000245008600043210006900129260001700198520078200215100002300997700001801020700002201038700001601060856003601076 2004 en_Ud 00aEnergetics and switching of quasi-uniform states in small ferromagnetic particles0 aEnergetics and switching of quasiuniform states in small ferroma bEDP Sciences3 aWe present a numerical algorithm to solve the micromagnetic equations based on tangential-plane minimization for the magnetization update and a homothethic-layer decomposition of outer space for the computation of the demagnetization field. As a first application, detailed results on the flower-vortex transition in the cube of Micromagnetic Standard Problem number 3 are obtained, which confirm, with a different method, those already present in the literature, and validate our method and code. We then turn to switching of small cubic or almost-cubic particles, in the single-domain limit. Our data show systematic deviations from the Stoner-Wohlfarth model due to the non-ellipsoidal shape of the particle, and in particular a non-monotone dependence on the particle size.1 aAlouges, François1 aConti, Sergio1 aDeSimone, Antonio1 aPokern, Ivo uhttp://hdl.handle.net/1963/299900881nas a2200121 4500008004100000245005300041210005200094260001800146520051800164100002100682700002000703856003600723 2004 en d00aExistence of H-bubbles in a perturbative setting0 aExistence of Hbubbles in a perturbative setting bSISSA Library3 aGiven a $C^{1}$ function $H: \\\\mathbb{R}^3 \\\\to \\\\mathbb{R}$, we look for $H$-bubbles, i.e., surfaces in $\\\\mathbb{R}^3$ parametrized by the sphere $\\\\mathbb{S}^2$ with mean curvature $H$ at every regular point. Here we study the case $H(u)=H_{0}(u)+\\\\epsilon H_{1}(u)$ where $H_{0}$ is some \\\"good\\\" curvature (for which there exist $H_{0}$-bubbles with minimal energy, uniformly bounded in $L^{\\\\infty}$), $\\\\epsilon$ is the smallness parameter, and $H_{1}$ is {\\\\em any} $C^{1}$ function.1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/160600305nas a2200109 4500008004300000245003200043210002800075100001800103700002000121700001800141856003600159 2004 en_Ud 00aThe Extended Toda Hierarchy0 aExtended Toda Hierarchy1 aCarlet, Guido1 aDubrovin, Boris1 aYoujin, Zhang uhttp://hdl.handle.net/1963/254201254nas a2200121 4500008004100000245008600041210006900127260001800196520084100214100002101055700002001076856003601096 2004 en d00aH-bubbles in a perturbative setting: the finite-dimensional reduction\\\'s method0 aHbubbles in a perturbative setting the finitedimensional reducti bSISSA Library3 aGiven a regular function $H\\\\colon\\\\mathbb{R}^{3}\\\\to\\\\mathbb{R}$, we look for $H$-bubbles, that is, regular surfaces in $\\\\mathbb{R}^{3}$ parametrized on the sphere $\\\\mathbb{S}+^{2}$ with mean curvature $H$ at every point. Here we study the case of $H(u)=H_{0}+\\\\varepsilon H_{1}(u)=:H_{\\\\varepsilon}(u)$, where $H_{0}$ is a nonzero constant, $\\\\varepsilon$ is the smallness parameter, and $H_{1}$ is any $C^{2}$-function. We prove that if $\\\\bar p\\\\in\\\\mathbb{R}^{3}$ is a ``good\\\'\\\' stationary point for the Melnikov-type function $\\\\Gamma(p)=-\\\\int_{|q-p|<|H_{0}|^{-1}}H_{1}(q)\\\\,dq$, then for $|\\\\varepsilon|$ small there exists an $H_{\\\\varepsilon}$-bubble $\\\\omega^{\\\\varepsilon}$ that converges to a sphere of radius $|H_{0}|^{-1}$ centered at $\\\\bar p$, as $\\\\varepsilon\\\\to 0$.1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/160700956nas a2200133 4500008004100000245008400041210006900125260000900194520052900203100001700732700001700749700002000766856003600786 2004 en d00aOn the minimal degree of a common Lyapunov function for planar switched systems0 aminimal degree of a common Lyapunov function for planar switched bIEEE3 aIn this paper, we consider linear switched systems x(t) = Au(t)x(t), x ε Rn, u ε U, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching (UAS for short). We first prove that, given a UAS system, it is always possible to build a polynomial common Lyapunov function. Then our main result is that the degree of that the common polynomial Lyapunov function is not uniformly bounded over all the UAS systems. This result answers a question raised by Dayawansa and Martin.1 aMason, Paolo1 aBoscain, Ugo1 aChitour, Yacine uhttp://hdl.handle.net/1963/483401180nas a2200121 4500008004300000245007900043210006900122260001700191520077400208100001700982700002300999856003601022 2004 en_Ud 00aResonance of minimizers for n-level quantum systems with an arbitrary cost0 aResonance of minimizers for nlevel quantum systems with an arbit bEDP Sciences3 aWe consider an optimal control problem describing a laser-induced population transfer on a $n$-level quantum system.\\nFor a convex cost depending only on the moduli of controls (i.e. the lasers intensities), we prove that there always exists a minimizer in resonance. This permits to justify some strategies used in experimental physics. It is also quite important because it permits to reduce remarkably the complexity of the problem (and extend some of our previous results for $n=2$ and $n=3$): instead of looking for minimizers on the sphere $S^{2n-1}\\\\subset\\\\C^n$ one is reduced to look just for minimizers on the sphere $S^{n-1}\\\\subset \\\\R^n$. Moreover, for the reduced problem, we investigate on the question of existence of strict abnormal minimizer.1 aBoscain, Ugo1 aCharlot, Grégoire uhttp://hdl.handle.net/1963/291001012nas a2200121 4500008004300000245005300043210005300096260001300149520064100162100002200803700002900825856003600854 2004 en_Ud 00aRotating Singular Perturbations of the Laplacian0 aRotating Singular Perturbations of the Laplacian bSpringer3 aWe study a system of a quantum particle interacting with a singular time-dependent uniformly rotating potential in 2 and 3 dimensions: in particular we consider an interaction with support on a point (rotating point interaction) and on a set of codimension 1 (rotating blade). We prove the existence of the Hamiltonians of such systems as suitable self-adjoint operators and we give an explicit expression for their unitary semigroups. Moreover we analyze the asymptotic limit of large angular velocity and we prove strong convergence of the time-dependent propagator to some one-parameter unitary group as (\\\\omega \\\\to \\\\infty).1 aCorreggi, Michele1 aDell'Antonio, Gianfausto uhttp://hdl.handle.net/1963/294500759nas a2200121 4500008004100000245005300041210005300094260001800147520038500165100002800550700002300578856003600601 2004 en d00aSolitary waves for Maxwell Schrodinger equations0 aSolitary waves for Maxwell Schrodinger equations bSISSA Library3 aIn this paper we study solitary waves for the coupled system of Schrodinger-Maxwell equations in the three-dimensional space. We prove the existence of a sequence of radial solitary waves for these equations with a fixed L^2 norm. We study the asymptotic behavior and the smoothness of these solutions. We show also that the eigenvalues are negative and the first one is isolated.1 aCoclite, Giuseppe Maria1 aGeorgiev, Vladimir uhttp://hdl.handle.net/1963/158200335nas a2200109 4500008004100000245004100041210004000082260001000122653003500132100002200167856003600189 2004 en d00aTime-dependent singular interactions0 aTimedependent singular interactions bSISSA10aRotating singular interactions1 aCorreggi, Michele uhttp://hdl.handle.net/1963/531000362nas a2200109 4500008004100000245005400041210005400095260001000149653002900159100002800188856003600216 2003 en d00aControl Problems for Systems of Conservation Laws0 aControl Problems for Systems of Conservation Laws bSISSA10aAsymptotic Stabilization1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/532500338nas a2200097 4500008004100000245006000041210005700101260001800158100002800176856003600204 2003 en d00aAn interior estimate for a nonlinear parabolic equation0 ainterior estimate for a nonlinear parabolic equation bSISSA Library1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/162200426nas a2200121 4500008004100000245007300041210006900114260001800183100002100201700001800222700002800240856003600268 2003 en d00aSome results on the boundary control of systems of conservation laws0 aSome results on the boundary control of systems of conservation bSISSA Library1 aBressan, Alberto1 aAncona, Fabio1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/161500716nas a2200121 4500008004300000245006000043210005300103260000900156520034400165100002100509700002800530856003600558 2002 en_Ud 00aOn the Boundary Control of Systems of Conservation Laws0 aBoundary Control of Systems of Conservation Laws bSIAM3 aThe paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand, we give an example showing that exact controllability in finite time cannot be achieved, in general.1 aBressan, Alberto1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/307000397nas a2200109 4500008004100000245008300041210006900124260001300193100002400206700002100230856003600251 2002 en d00aChaotic dynamics for perturbations of infinite-dimensional Hamiltonian systems0 aChaotic dynamics for perturbations of infinitedimensional Hamilt bElsevier1 aBerti, Massimiliano1 aCarminati, Carlo uhttp://hdl.handle.net/1963/127900315nas a2200109 4500008004100000245003500041210003400076260001800110100002100128700002000149856003600169 2002 en d00aExistence of minimal H-bubbles0 aExistence of minimal Hbubbles bSISSA Library1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/152500435nas a2200121 4500008004100000245008600041210006900127260001800196100001700214700002200231700002400253856003600277 2002 en d00aOn the K+P problem for a three-level quantum system: optimality implies resonance0 aKP problem for a threelevel quantum system optimality implies re bSISSA Library1 aBoscain, Ugo1 aChambrion, Thomas1 aGauthier, Jean-Paul uhttp://hdl.handle.net/1963/160100546nas a2200109 4500008004300000245008800043210006900131260001000200520016200210100002800372856003600400 2002 en_Ud 00aA multiplicity result for the Schrodinger-Maxwell equations with negative potential0 amultiplicity result for the SchrodingerMaxwell equations with ne bIMPAN3 aWe prove the existence of a sequence of radial solutions with negative energy of the Schrödinger-Maxwell equations under the action of a negative potential.1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/305300411nas a2200109 4500008004100000245009300041210006900134260001800203100002200221700002200243856003600265 2002 en d00aQuantum mechanics and stochastic mechanics for compatible observables at different times0 aQuantum mechanics and stochastic mechanics for compatible observ bSISSA Library1 aCorreggi, Michele1 aMorchio, Giovanni uhttp://hdl.handle.net/1963/157700345nas a2200109 4500008004100000245005200041210005200093260001100145100002100156700002200177856003600199 2002 en d00aSingular elliptic problems with critical growth0 aSingular elliptic problems with critical growth bDekker1 aCaldiroli, Paolo1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/126800355nas a2200109 4500008004100000245005500041210004800096260001800144100002300162700002400185856003600209 2002 en d00aOn the Stability of the Standard Riemann Semigroup0 aStability of the Standard Riemann Semigroup bSISSA Library1 aBianchini, Stefano1 aColombo, Rinaldo M. uhttp://hdl.handle.net/1963/152800379nas a2200109 4500008004300000245006700043210006700110260001300177100002000190700002300210856003600233 2001 en_Ud 00aControllability for discrete systems with a finite control set0 aControllability for discrete systems with a finite control set bSpringer1 aChitour, Yacine1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/311400415nas a2200109 4500008004100000245010000041210006900141260001800210100002100228700002000249856003600269 2001 en d00aExistence and nonexistence results for a class of nonlinear, singular Sturm-Liouville equations0 aExistence and nonexistence results for a class of nonlinear sing bSISSA Library1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/131900395nas a2200109 4500008004100000245008300041210006900124260001500193100002100208700002000229856003600249 2001 en d00aS^2 type parametric surfaces with prescribed mean curvature and minimal energy0 aS2 type parametric surfaces with prescribed mean curvature and m bBirkhauser1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/160500389nas a2200109 4500008004100000245007400041210006900115260001800184100002100202700002000223856003600243 2001 en d00aStationary states for a two-dimensional singular Schrodinger equation0 aStationary states for a twodimensional singular Schrodinger equa bSISSA Library1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/124900401nas a2200109 4500008004100000245008600041210006900127260001800196100002000214700002100234856003600255 2000 en d00aOn a Steffen\\\'s result about parametric surfaces with prescribed mean curvature0 aSteffens result about parametric surfaces with prescribed mean c bSISSA Library1 aMusina, Roberta1 aCaldiroli, Paolo uhttp://hdl.handle.net/1963/155800449nam a2200121 4500008004300000245008000043210006900123260003400192100002100226700002100247700002300268856003600291 2000 en_Ud 00aWell-posedness of the Cauchy problem for n x n systems of conservation laws0 aWellposedness of the Cauchy problem for n x n systems of conserv bAmerican Mathematical Society1 aBressan, Alberto1 aCrasta, Graziano1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/349500394nas a2200109 4500008004300000245007500043210006900118260001700187100002300204700002100227856003600248 1999 en_Ud 00aDiscrete approximation of the Mumford-Shah functional in dimension two0 aDiscrete approximation of the MumfordShah functional in dimensio bEDP Sciences1 aChambolle, Antonin1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/358800417nas a2200121 4500008004100000245007300041210006900114260001800183100001800201700002100219700001900240856003600259 1999 en d00aA note on fractional KDV hierarchies. II. The bihamiltonian approach0 anote on fractional KDV hierarchies II The bihamiltonian approach bSISSA Library1 aCasati, Paolo1 aFalqui, Gregorio1 aPedroni, Marco uhttp://hdl.handle.net/1963/122000397nas a2200109 4500008004100000245008000041210006900121260001800190100002100208700002300229856003500252 1997 en d00aViscosity solutions and uniquenessfor systems of inhomogeneous balance laws0 aViscosity solutions and uniquenessfor systems of inhomogeneous b bSISSA Library1 aCrasta, Graziano1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/96900453nas a2200121 4500008004300000245008900043210006900132260000900201520004500210100002000255700002000275856003600295 1995 en_Ud 00aAn existence result in a problem of the vectorial case of the calculus of variations0 aexistence result in a problem of the vectorial case of the calcu bSIAM3 aSIAM J. Control Optim. 33 (1995) 960-9701 aCellina, Arrigo1 aZagatti, Sandro uhttp://hdl.handle.net/1963/351300375nas a2200121 4500008004100000245004500041210004500086260001800131100002500149700002300174700002100197856003500218 1995 en d00aSpecial functions of bounded deformation0 aSpecial functions of bounded deformation bSISSA Library1 aBellettini, Giovanni1 aCoscia, Alessandra1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/97800871nas a2200121 4500008004100000245006200041210006200103260004300165520046100208100002100669700002400690856003500714 1995 en d00aUnique solutions of 2x2 conservation laws with large data0 aUnique solutions of 2x2 conservation laws with large data bIndiana University Mathematics Journal3 aFor a 2x2 hyperbolic system of conservation laws, we first consider a Riemann problem with arbitrarily large data. A stability assumption is introduced, which yields the existence of a Lipschitz semigroup of solutions, defined on a domain containing all suitably small BV perturbations of the Riemann data. We then establish a uniqueness result for large BV solutions, valid within the same class of functions where a local existence theorem can be proved.1 aBressan, Alberto1 aColombo, Rinaldo M. uhttp://hdl.handle.net/1963/97500702nas a2200121 4500008004300000245007700043210006900120260000900189520030600198100002000504700002000524856003600544 1994 en_Ud 00aA version of Olech\\\'s lemma in a problem of the calculus of variations0 aversion of Olechs lemma in a problem of the calculus of variatio bSIAM3 aThis paper studies the solutions of the minimum problem for a functional of the gradient under linear boundary conditions. A necessary and sufficient condition, based on the facial structure of the epigraph of the integrand, is provided for the continuous dependence of the solutions on boundary data.1 aCellina, Arrigo1 aZagatti, Sandro uhttp://hdl.handle.net/1963/351400404nas a2200121 4500008004100000245006200041210006000103260001800163100002100181700002000202700002500222856003500247 1991 en d00aA class of absolute retracts of dwarf spheroidal galaxies0 aclass of absolute retracts of dwarf spheroidal galaxies bSISSA Library1 aBressan, Alberto1 aCellina, Arrigo1 aFryszkowski, Andrzej uhttp://hdl.handle.net/1963/83700376nas a2200109 4500008004100000245006600041210006300107260001800170100002100188700002200209856003500231 1990 en d00aExistence and continuous dependence for discontinuous O.D.E.s0 aExistence and continuous dependence for discontinuous ODEs bSISSA Library1 aBressan, Alberto1 aColombo, Giovanni uhttp://hdl.handle.net/1963/71600390nas a2200109 4500008004100000245007700041210006900118260001800187100001800205700002200223856003500245 1990 en d00aExistence of solutions for a class of non-convex differential inclusions0 aExistence of solutions for a class of nonconvex differential inc bSISSA Library1 aAncona, Fabio1 aColombo, Giovanni uhttp://hdl.handle.net/1963/79200370nas a2200121 4500008004100000245004000041210003900081260001800120100002600138700002100164700002800185856003500213 1990 en d00aG-convergence of monotone operators0 aGconvergence of monotone operators bSISSA Library1 aChiadò Piat, Valeria1 aDal Maso, Gianni1 aDefranceschi, Anneliese uhttp://hdl.handle.net/1963/68000424nas a2200133 4500008004100000245005700041210005600098260001800154100002100172700002200193700001900215700002100234856003500255 1989 en d00aLimits of obstacle problems for the area functional.0 aLimits of obstacle problems for the area functional bSISSA Library1 aDal Maso, Gianni1 aCarriero, Michele1 aLeaci, Antonio1 aPascali, Eduardo uhttp://hdl.handle.net/1963/57700413nas a2200121 4500008004100000245006700041210006700108260001800175100002100193700002000214700002200234856003500256 1989 en d00aUpper semicontinuous differential inclusions without convexity0 aUpper semicontinuous differential inclusions without convexity bSISSA Library1 aBressan, Alberto1 aCellina, Arrigo1 aColombo, Giovanni uhttp://hdl.handle.net/1963/67000393nas a2200109 4500008004100000245007700041210006900118260001800187100002100205700002200226856003500248 1988 en d00aGeneralized Baire category and differential inclusions in Banach spaces.0 aGeneralized Baire category and differential inclusions in Banach bSISSA Library1 aBressan, Alberto1 aColombo, Giovanni uhttp://hdl.handle.net/1963/53800402nas a2200109 4500008004100000245007900041210006900120260001800189100002400207700002600231856003500257 1987 en d00aSolutions with minimal period for Hamiltonian systems in a potential well.0 aSolutions with minimal period for Hamiltonian systems in a poten bSISSA Library1 aAmbrosetti, Antonio1 aCoti Zelati, Vittorio uhttp://hdl.handle.net/1963/46600374nas a2200121 4500008004100000245004500041210004500086260001800131100002400149700002600173700001800199856003500217 1987 en d00aSymmetry breaking in Hamiltonian systems0 aSymmetry breaking in Hamiltonian systems bSISSA Library1 aAmbrosetti, Antonio1 aCoti Zelati, Vittorio1 aEkeland, Ivar uhttp://hdl.handle.net/1963/40900605nas a2200121 4500008004100000245006100041210006000102260003200162520020700194100002700401700002000428856003500448 1985 en d00aMaximal acceleration and Sakharov's limiting temperature0 aMaximal acceleration and Sakharovs limiting temperature bSocietà Italiana di Fisica3 aIt is shown that Sakharov's maximal temperature, derived by him from astrophysical considerations, is a straightforward consequence of the maximal acceleration introduced by us in previous works.

1 aCaianiello, Eduardo R.1 aLandi, Giovanni uhttp://hdl.handle.net/1963/372