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.

%B Mathematics in Engineering %V 2 %P 230 %G eng %U http://dx.doi.org/10.3934/mine.2020011 %9 Perspective %R 10.3934/mine.2020011 %0 Report %D 2019 %T A dynamic model for viscoelastic materials with prescribed growing cracks %A Maicol Caponi %A Francesco Sapio %XIn 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.

%G eng %U http://preprints.sissa.it:8180/xmlui/handle/1963/35334 %0 Journal Article %J Phil. Trans. R. Soc. A %D 2019 %T On the existence of elastic minimizers for initially stressed materials %A Davide Riccobelli %A A. Agosti %A Pasquale Ciarletta %B Phil. Trans. R. Soc. A %I The Royal Society %V 377 %G eng %0 Journal Article %J Duke Math. J. %D 2019 %T Isomonodromy deformations at an irregular singularity with coalescing eigenvalues %A Giordano Cotti %A Boris Dubrovin %A Davide Guzzetti %XWe 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.

%B Duke Math. J. %I Duke University Press %V 168 %P 967–1108 %8 04 %G eng %U https://doi.org/10.1215/00127094-2018-0059 %R 10.1215/00127094-2018-0059 %0 Report %D 2018 %T Canonical Surfaces and Hypersurfaces in Abelian Varieties %A Luca Cesarano %G eng %U https://arxiv.org/abs/1808.05302 %0 Journal Article %J Mathematical Models and Methods in Applied Sciences %D 2018 %T Cohesive fracture with irreversibility: Quasistatic evolution for a model subject to fatigue %A Vito Crismale %A Giuliano Lazzaroni %A Gianluca Orlando %XIn 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.

%B Mathematical Models and Methods in Applied Sciences %V 28 %P 1371-1412 %G eng %U https://doi.org/10.1142/S0218202518500379 %R 10.1142/S0218202518500379 %0 Book Section %B Cardiovascular Mechanics %D 2018 %T Computational methods in cardiovascular mechanics %A Auricchio, Ferdinando %A Conti, Michele %A Lefieux, Adrian %A Morganti, Simone %A Alessandro Reali %A Gianluigi Rozza %A Veneziani, Alessandro %E Michel F. Labrosse %XThe 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.

%B Cardiovascular Mechanics %I CRC Press %P 54 %G eng %U https://www.taylorfrancis.com/books/e/9781315280288/chapters/10.1201%2Fb21917-5 %& Computational methods in cardiovascular mechanics %0 Report %D 2018 %T Energy-dissipation balance of a smooth moving crack %A Maicol Caponi %A Ilaria Lucardesi %A Emanuele Tasso %X In this paper we provide necessary and sufficient conditions in order to guarantee the energy-dissipation balance of a Mode III crack, growing on a prescribed smooth path. Moreover, we characterize the singularity of the displacement near the crack tip, generalizing the result in [S. Nicaise, A.M. Sandig - J. Math. Anal. Appl., 2007] valid for straight fractures. %G en %U http://preprints.sissa.it/handle/1963/35320 %1 35630 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-08-01T09:36:30Z No. of bitstreams: 1 CLT-preprint.pdf: 455925 bytes, checksum: 931583a37609035d6be19feceb41142d (MD5) %0 Report %D 2018 %T Existence of solutions to a phase field model of dynamic fracture with a crack dependent dissipation %A Maicol Caponi %X We 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. %G en %U http://preprints.sissa.it/handle/1963/35307 %1 35614 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-03-05T16:29:01Z No. of bitstreams: 1 PhFiMo_Caponi.pdf: 418992 bytes, checksum: 6bf6de00d58052411ec3a588e2f7933e (MD5) %0 Report %D 2018 %T On Krylov solutions to infinite-dimensional inverse linear problems %A Noe Caruso %A Alessandro Michelangeli %A Paolo Novati %X We 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. %I SISSA %G en %U http://preprints.sissa.it/handle/1963/35327 %1 35638 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-11-20T13:12:02Z No. of bitstreams: 1 krylov_InfiniteDim_sissapreprint.pdf: 472654 bytes, checksum: 54ffc66b6879cbb031453355bf6ed56b (MD5) %0 Report %D 2018 %T Local moduli of semisimple Frobenius coalescent structures %A Giordano Cotti %A Boris Dubrovin %A Davide Guzzetti %XThere 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.

%I SISSA %G en %U http://preprints.sissa.it/handle/1963/35304 %1 35610 %2 Mathematics %4 1 %# MAT/03 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-01-16T11:11:03Z No. of bitstreams: 1 Preprint_Davide.pdf: 1242726 bytes, checksum: 527d898383b9f997856370b14965bbdc (MD5) %0 Journal Article %J Int. J. Non-Linear Mech. %D 2018 %T Morpho-elastic model of the tortuous tumour vessels %A Davide Riccobelli %A Pasquale Ciarletta %B Int. J. Non-Linear Mech. %I Elsevier BV %V 107 %P 1–9 %G eng %0 Journal Article %J Comm. Math. Phys %D 2018 %T Noncommutative Painlevé Equations and Systems of Calogero Type %A Marco Bertola %A Mattia Cafasso %A V. Rubtsov %B Comm. Math. Phys %G eng %0 Report %D 2018 %T Observables in the equivariant A-model %A Bonechi, F. %A Cattaneo, A.S. %A Riccardo Iraso %A Maxim Zabzine %G eng %U https://arxiv.org/abs/1807.08659 %0 Journal Article %J Math. Mech. Solids %D 2018 %T Shape transitions in a soft incompressible sphere with residual stresses %A Davide Riccobelli %A Pasquale Ciarletta %B Math. Mech. Solids %I SAGE Publications Sage UK: London, England %V 23 %P 1507–1524 %G eng %0 Report %D 2018 %T Stochastic homogenisation of free-discontinuity problems %A Filippo Cagnetti %A Gianni Dal Maso %A Lucia Scardia %A Caterina Ida Zeppieri %X In 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. %G en %U http://preprints.sissa.it/handle/1963/35309 %1 35617 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-03-19T09:16:27Z No. of bitstreams: 1 Cag-DM-Sca-Zep-Stochastic.pdf: 427225 bytes, checksum: 758a4e21e1c47b4a34c774f5d4bff8c2 (MD5) %0 Report %D 2018 %T Truncation and convergence issues for bounded linear inverse problems in Hilbert space %A Noe Caruso %A Alessandro Michelangeli %A Paolo Novati %X We 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. %I SISSA %G en %U http://preprints.sissa.it/handle/1963/35326 %1 35637 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-11-20T13:02:23Z No. of bitstreams: 1 infinite_dim_truncation_sissapreprint.pdf: 1326956 bytes, checksum: 75a6af69b0bca0c5b9b5283e640d89be (MD5) %0 Journal Article %J Random Matrices: Theory and Applications %D 2017 %T Analytic geometry of semisimple coalescent Frobenius structures %A Giordano Cotti %A Davide Guzzetti %XWe 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.

%B Random Matrices: Theory and Applications %V 06 %P 1740004 %G eng %U https://doi.org/10.1142/S2010326317400044 %R 10.1142/S2010326317400044 %0 Report %D 2017 %T Complex Friedrichs systems and applications %A Nenad Antonić %A Krešimir Burazin %A Ivana Crnjac %A Marko Erceg %X We 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. %G en %U http://urania.sissa.it/xmlui/handle/1963/35270 %1 35576 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-01-20T12:35:16Z No. of bitstreams: 1 antonic_burazin_crnjac_erceg2016_preprint.pdf: 308035 bytes, checksum: 7c8e2264f51ab9699c6cbe9585fc047a (MD5) %0 Report %D 2017 %T Gamma-Convergence of Free-discontinuity problems %A Filippo Cagnetti %A Gianni Dal Maso %A Lucia Scardia %A Caterina Ida Zeppieri %X We 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. %I SISSA %G en %U http://preprints.sissa.it/handle/1963/35276 %1 35583 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-03-20T13:20:54Z No. of bitstreams: 1 Cag-DM-Sca-Zep-sissa.pdf: 494285 bytes, checksum: 0da567323c828153382b08fc0f967af4 (MD5) %0 Journal Article %J Annali di Matematica Pura ed Applicata (1923 -) %D 2017 %T Globally stable quasistatic evolution for strain gradient plasticity coupled with damage %A Vito Crismale %XWe 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).

%B Annali di Matematica Pura ed Applicata (1923 -) %V 196 %P 641–685 %8 Apr %G eng %U https://doi.org/10.1007/s10231-016-0590-7 %R 10.1007/s10231-016-0590-7 %0 Journal Article %J Comm. Math. Phys %D 2017 %T The Kontsevich matrix integral: convergence to the Painlevé hierarchy and Stokes' phenomenon %A Marco Bertola %A Mattia Cafasso %B Comm. Math. Phys %V DOI 10.1007/s00220-017-2856-3 %G eng %U http://arxiv.org/abs/1603.06420 %0 Report %D 2017 %T Linear hyperbolic systems in domains with growing cracks %A Maicol Caponi %X We 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. %G en %U http://urania.sissa.it/xmlui/handle/1963/35271 %1 35577 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-01-30T11:26:46Z No. of bitstreams: 1 Caponi_LinHypSys.pdf: 432435 bytes, checksum: 3b798b4c79150cf0087bc6176258ffc6 (MD5) %0 Book Section %B Encyclopedia of Computational Mechanics Second Edition %D 2017 %T Model Reduction Methods %A Francisco Chinesta %A Antonio Huerta %A Gianluigi Rozza %A Karen Willcox %XThis 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

%B Encyclopedia of Computational Mechanics Second Edition %I John Wiley & Sons %P 1-36 %G eng %& Model Reduction Methods %R 10.1002/9781119176817.ecm2110 %0 Journal Article %J Nonlinear Differential Equations and Applications NoDEA %D 2017 %T Quasistatic crack growth based on viscous approximation: a model with branching and kinking %A Vito Crismale %A Giuliano Lazzaroni %XEmploying 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.

%B Nonlinear Differential Equations and Applications NoDEA %V 24 %P 7 %8 Jan %G eng %U https://doi.org/10.1007/s00030-016-0426-6 %R 10.1007/s00030-016-0426-6 %0 Journal Article %J Phil. Trans. R. Soc. A %D 2017 %T Rayleigh–Taylor instability in soft elastic layers %A Davide Riccobelli %A Pasquale Ciarletta %B Phil. Trans. R. Soc. A %I The Royal Society %V 375 %G eng %0 Journal Article %J SIAM/ASA Journal on Uncertainty Quantification %D 2017 %T Reduced Basis Methods for Uncertainty Quantification %A Peng Chen %A Alfio Quarteroni %A Gianluigi Rozza %XIn 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.

%B Proceedings of the ECCOMAS Congress 2016, VII European Conference on Computational Methods in Applied Sciences and Engineering, %I ECCOMAS %C Crete, Greece %8 06/2016 %G en %1 35466 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2016-05-13T00:28:01Z No. of bitstreams: 1 eccomas2016_AROMA.pdf: 1846196 bytes, checksum: 9636e713df80de178d87fd2feff76f91 (MD5) %0 Report %D 2016 %T Coalescence Phenomenon of Quantum Cohomology of Grassmannians and the Distribution of Prime Numbers %A Giordano Cotti %G eng %0 Journal Article %J Journal of High Energy Physics %D 2016 %T Comparing Poisson Sigma Model with A-model %A Bonechi, F. %A Cattaneo, A.S. %A Riccardo Iraso %XWe 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.

%B Journal of High Energy Physics %V 2016 %P 133 %8 Oct %G eng %U https://doi.org/10.1007/JHEP10(2016)133 %R 10.1007/JHEP10(2016)133 %0 Report %D 2016 %T Eulerian, Lagrangian and Broad continuous solutions to a balance law with non convex flux II %A Giovanni Alberti %A Stefano Bianchini %A Laura Caravenna %G en %U http://urania.sissa.it/xmlui/handle/1963/35197 %1 35494 %2 Mathematics %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2016-06-21T11:33:07Z No. of bitstreams: 1 file2ABCottobre2015.pdf: 486411 bytes, checksum: cbdd0bce26d338707c03a61c42ec725e (MD5) %0 Journal Article %J Journal of Differential Equations, vol. 261, issue 8 (2016): 4298-4337 %D 2016 %T Eulerian, Lagrangian and Broad continuous solutions to a balance law with non-convex flux I %A Giovanni Alberti %A Stefano Bianchini %A Laura Caravenna %B Journal of Differential Equations, vol. 261, issue 8 (2016): 4298-4337 %I Elsevier %G en %U http://urania.sissa.it/xmlui/handle/1963/35207 %1 35507 %2 Mathematics %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2016-09-05T15:06:32Z No. of bitstreams: 1 1512.04863v2_Caravenna.pdf: 1192837 bytes, checksum: 15e7fc975989af0ea19654f4eafd84a7 (MD5) %R 10.1016/j.jde.2016.06.026 %0 Journal Article %J ESAIM: Control, Optimisation and Calculus of Variations %D 2016 %T Globally stable quasistatic evolution for a coupled elastoplastic–damage model %A Vito Crismale %XWe 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.

%B ESAIM: Control, Optimisation and Calculus of Variations %I EDP Sciences %V 22 %P 883–912 %G eng %U https://www.esaim-cocv.org/articles/cocv/abs/2016/03/cocv150037/cocv150037.html %R 10.1051/cocv/2015037 %0 Book Section %B Wiley Encyclopedia of Computational Mechanics, 2016 %D 2016 %T Model Order Reduction: a survey %A Francisco Chinesta %A Antonio Huerta %A Gianluigi Rozza %A Karen Willcox %B Wiley Encyclopedia of Computational Mechanics, 2016 %I Wiley %G en %U http://urania.sissa.it/xmlui/handle/1963/35194 %1 35470 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2016-05-27T00:41:12Z No. of bitstreams: 1 ECM_MOR.pdf: 746542 bytes, checksum: 93d6252fe8a175c4378b96bd4192712c (MD5) %0 Journal Article %J The European Physical Journal E %D 2016 %T Motion planning and motility maps for flagellar microswimmers %A Giancarlo Cicconofri %A Antonio DeSimone %XWe 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.

%B The European Physical Journal E %V 39 %P 72 %8 Jul %G eng %U https://doi.org/10.1140/epje/i2016-16072-y %R 10.1140/epje/i2016-16072-y %0 Journal Article %J Annals of Nuclear Energy, 87, 2 (2016): pp. 198-208 %D 2016 %T A multi-physics reduced order model for the analysis of Lead Fast Reactor single channel %A Alberto Sartori %A Antonio Cammi %A Lelio Luzzi %A Gianluigi Rozza %X In 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. %B Annals of Nuclear Energy, 87, 2 (2016): pp. 198-208 %I Elsevier %V 87 %P 208 %G en %U http://urania.sissa.it/xmlui/handle/1963/35191 %1 35471 %2 Mathematics %4 1 %# MAT/08 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2016-06-16T11:08:05Z (GMT) No. of bitstreams: 0 %& 198 %R doi:10.1016/j.anucene.2015.09.002 %0 Book Section %B Noncommutative Analysis, Operator Theory and Applications %D 2016 %T Pimsner Algebras and Circle Bundles %A Francesca Arici %A Francesco D'Andrea %A Giovanni Landi %E Alpay, Daniel %E Cipriani, Fabio %E Colombo, Fabrizio %E Guido, Daniele %E Sabadini, Irene %E Sauvageot, Jean-Luc %XWe 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.

%B Noncommutative Analysis, Operator Theory and Applications %I Springer International Publishing %C Cham %P 1–25 %@ 978-3-319-29116-1 %G eng %U https://doi.org/10.1007/978-3-319-29116-1_1 %R 10.1007/978-3-319-29116-1_1 %0 Journal Article %D 2016 %T POD-Galerkin Method for Finite Volume Approximation of Navier-Stokes and RANS Equations %A Stefano Lorenzi %A Antonio Cammi %A Lelio Luzzi %A Gianluigi Rozza %X Numerical 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. %I Computer Methods in Applied Mechanics and Engineering, Elsevier %G en %1 35502 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2016-08-06T00:39:18Z No. of bitstreams: 1 Manuscript_second_rev.pdf: 6749813 bytes, checksum: 08833a58f5485216e08c0597a7c13975 (MD5) %0 Journal Article %J NERS-14-1062; ASME J of Nuclear Rad Sci, 2, 2 (2016) 021019 %D 2016 %T A Reduced Basis Approach for Modeling the Movement of Nuclear Reactor Control Rods %A Alberto Sartori %A Antonio Cammi %A Lelio Luzzi %A Gianluigi Rozza %X This 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. %B NERS-14-1062; ASME J of Nuclear Rad Sci, 2, 2 (2016) 021019 %I ASME %V 2 %P 8 %8 02/2016 %G en %U http://urania.sissa.it/xmlui/handle/1963/35192 %N 2 %1 35473 %2 Mathematics %4 1 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2016-05-30T00:18:10Z No. of bitstreams: 1 sartori_post-icone.pdf: 1377810 bytes, checksum: 5c09a1296518bbbd4b61b709ced8dbca (MD5) %R 10.1115/1.4031945 %0 Journal Article %J Communications in Computational Physics %D 2016 %T Reduced basis approaches in time-dependent noncoercive settings for modelling the movement of nuclear reactor control rods %A Alberto Sartori %A Antonio Cammi %A Lelio Luzzi %A Gianluigi Rozza %XIn 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.

%B Communications in Computational Physics %I SISSA %8 2016 %G en %U http://urania.sissa.it/xmlui/handle/1963/34963 %N in press %1 35188 %2 Mathematics %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2015-11-05T15:06:51Z No. of bitstreams: 1 manuscript.pdf: 2056729 bytes, checksum: 2a2fad22dc931e8c4094642e21c479cd (MD5) %0 Thesis %D 2016 %T Some results on quasistatic evolution problems for unidirectional processes %A Vito Crismale %I SISSA %G en %1 35522 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by vcrisma@sissa.it (vcrisma@sissa.it) on 2016-09-18T20:26:55Z No. of bitstreams: 1 TesiPHD.pdf: 1721272 bytes, checksum: 95ef69bafc860616d3cdb08901da7ffb (MD5) %0 Journal Article %J Correggi, M., Dimonte, D., 2016. On the third critical speed for rotating Bose-Einstein condensates. J. Math. Phys. 57, 71901 %D 2016 %T On the third critical speed for rotating Bose-Einstein condensates %A Daniele Dimonte %A Michele Correggi %X We 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. %B Correggi, M., Dimonte, D., 2016. On the third critical speed for rotating Bose-Einstein condensates. J. Math. Phys. 57, 71901 %I AIP Publisher %G en %U http://urania.sissa.it/xmlui/handle/1963/35246 %1 35557 %2 Mathematics %$ Submitted by ddimonte@sissa.it (ddimonte@sissa.it) on 2016-10-19T16:34:31Z No. of bitstreams: 1 1508.07235v4.pdf: 520340 bytes, checksum: e987bbeef8fe09e31b8ea970c4ae4b4b (MD5) %R 10.1063/1.4954805 %0 Journal Article %J Calculus of Variations and Partial Differential Equations %D 2016 %T Viscous approximation of quasistatic evolutions for a coupled elastoplastic-damage model %A Vito Crismale %A Giuliano Lazzaroni %XEmploying 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.

%B Calculus of Variations and Partial Differential Equations %V 55 %P 17 %8 Jan %G eng %U https://doi.org/10.1007/s00526-015-0947-6 %R 10.1007/s00526-015-0947-6 %0 Journal Article %J Computers and Mathematics with Applications 69 (2015) 1167–1188 %D 2015 %T Benchmarking the Immersed Finite Element Method for Fluid-Structure Interaction Problems %A Roy Saswati %A Luca Heltai %A Francesco Costanzo %X We 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. %B Computers and Mathematics with Applications 69 (2015) 1167–1188 %G en %1 34633 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Luca Heltai (heltai@sissa.it) on 2015-04-20T15:26:58Z No. of bitstreams: 1 rhc_feibm_validation-v3.pdf: 7039131 bytes, checksum: 705f28e17037504f00766fc4e84a10a4 (MD5) %R 10.1016/j.camwa.2015.03.012 %0 Report %D 2015 %T A class of Hamiltonians for a three-particle fermionic system at unitarity %A Michele Correggi %A Gianfausto Dell'Antonio %A Domenico Finco %A Alessandro Michelangeli %A Alessandro Teta %X We 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. %G en %U http://urania.sissa.it/xmlui/handle/1963/34469 %1 34644 %2 Mathematics %4 1 %$ Submitted by Alessandro Michelangeli (alemiche@sissa.it) on 2015-05-21T06:33:20Z No. of bitstreams: 1 SISSA_preprint_22-2015-MATE.pdf: 438261 bytes, checksum: ca05e5e2c5d78d87225a11073cb09d47 (MD5) %0 Journal Article %D 2015 %T Dispersive deformations of the Hamiltonian structure of Euler's equations %A Matteo Casati %X Euler'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. %G en %1 34700 %2 Mathematics %4 1 %# MAT/07 %$ Submitted by Matteo Casati (mcasati@sissa.it) on 2015-09-09T13:27:08Z No. of bitstreams: 1 defoHD.pdf: 195202 bytes, checksum: 9ee41e73fc37dd79f1659dda2e742b57 (MD5) %0 Conference Paper %B International Conference on Parallel Processing and Applied Mathematics %D 2015 %T Experience on vectorizing lattice Boltzmann kernels for multi-and many-core architectures %A Calore, Enrico %A Nicola Demo %A Schifano, Sebastiano Fabio %A Tripiccione, Raffaele %B International Conference on Parallel Processing and Applied Mathematics %I Springer %P 53–62 %G eng %0 Thesis %D 2015 %T Mathematical Models of Locomotion: Legged Crawling, Snake-like Motility, and Flagellar Swimming %A Giancarlo Cicconofri %K Motility %I SISSA %G en %1 34743 %2 Mathematics %4 1 %# FIS/02 %$ Submitted by cicconof@sissa.it (cicconof@sissa.it) on 2015-09-24T20:39:35Z No. of bitstreams: 1 TESI_Cicconofri.pdf: 4716549 bytes, checksum: 708afb866eb4c106392495f2a8e7c6a8 (MD5) %0 Journal Article %J International Journal of Non-Linear Mechanics %D 2015 %T Motility of a model bristle-bot: A theoretical analysis %A Giancarlo Cicconofri %A Antonio DeSimone %K Bristle-robots %K Crawling motility %K Frictional interactions %XBristle-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.

%B International Journal of Non-Linear Mechanics %V 76 %P 233 - 239 %G eng %U http://www.sciencedirect.com/science/article/pii/S0020746215000025 %R https://doi.org/10.1016/j.ijnonlinmec.2014.12.010 %0 Thesis %D 2015 %T Multidimensional Poisson Vertex Algebras and Poisson cohomology of Hamiltonian operators of hydrodynamic type %A Matteo Casati %K Poisson Vertex Algebras, Poisson brackets, Hamiltonian operators, Integrable Systems %X The 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. %I SISSA %G en %1 34902 %2 Mathematics %4 1 %# MAT/07 %$ Submitted by Matteo Casati (mcasati@sissa.it) on 2015-10-22T07:27:52Z No. of bitstreams: 1 PhDThesis_Casati.pdf: 1027291 bytes, checksum: 49f551db40603ca035f2515ccb6ec7a2 (MD5) %0 Journal Article %J Numerische Mathematik, (2015), 36 p. Article in Press %D 2015 %T Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations %A Gianluigi Rozza %A Peng Chen %A Alfio Quarteroni %X In 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. %B Numerische Mathematik, (2015), 36 p. Article in Press %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34491 %1 34680 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2015-08-25T23:32:48Z No. of bitstreams: 1 06August2014_wRBM4SOC.pdf: 531409 bytes, checksum: d1a2f18b0de17872919c430779f7180c (MD5) %R 10.1007/s00211-015-0743-4 %0 Report %D 2015 %T Poisson cohomology of scalar multidimensional Dubrovin-Novikov brackets %A Guido Carlet %A Matteo Casati %A Sergey Shadrin %X We 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. %G en %1 35389 %2 Mathematics %4 1 %# MAT/03 %0 Journal Article %J Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences %D 2015 %T A study of snake-like locomotion through the analysis of a flexible robot model %A Giancarlo Cicconofri %A Antonio DeSimone %XWe 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.

%B Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences %V 471 %P 20150054 %G eng %U https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2015.0054 %R 10.1098/rspa.2015.0054 %0 Journal Article %D 2014 %T An Abstract Nash–Moser Theorem and Quasi-Periodic Solutions for NLW and NLS on Compact Lie Groups and Homogeneous Manifolds %A Massimiliano Berti %A Livia Corsi %A Michela Procesi %X We 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. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34651 %1 34858 %2 Mathematics %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-10-20T12:19:54Z No. of bitstreams: 1 preprint2014.pdf: 549502 bytes, checksum: 4896c2df9fba6a09abb33941adb07837 (MD5) %R 10.1007/s00220-014-2128-4 %0 Journal Article %D 2014 %T Comparison between reduced basis and stochastic collocation methods for elliptic problems %A Peng Chen %A Alfio Quarteroni %A Gianluigi Rozza %X The 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. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34727 %1 34916 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-10-26T11:39:14Z (GMT) No. of bitstreams: 0 %R 10.1007/s10915-013-9764-2 %0 Journal Article %J Annals of Nuclear Energy %D 2014 %T Comparison of a Modal Method and a Proper Orthogonal Decomposition approach for multi-group time-dependent reactor spatial kinetics %A Alberto Sartori %A Davide Baroli %A Antonio Cammi %A Davide Chiesa %A Lelio Luzzi %A Roberto R. Ponciroli %A Ezio Previtali %A Marco E. Ricotti %A Gianluigi Rozza %A Monica Sisti %XIn 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.

%B Annals of Nuclear Energy %I Elsevier %V 71 %P 229 %8 09/2014 %G en %U http://urania.sissa.it/xmlui/handle/1963/35039 %1 35270 %2 Physics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-11-18T12:07:02Z (GMT) No. of bitstreams: 0 %& 217 %R 10.1016/j.anucene.2014.03.043 %0 Journal Article %D 2014 %T Conformal invariants from nodal sets. I. negative eigenvalues and curvature prescription %A Rod R. Gover %A Yaiza Canzani %A Dmitry Jakobson %A Raphaël Ponge %A Andrea Malchiodi %X In 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. %I Oxford University Press %G en %U http://urania.sissa.it/xmlui/handle/1963/35128 %1 35366 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-12-02T16:09:57Z No. of bitstreams: 1 preprint2014.pdf: 356671 bytes, checksum: 20e817f9f20d9c72d717e04f94f86bd9 (MD5) %R 10.1093/imrn/rns295 %0 Journal Article %J IMRN %D 2014 %T Darboux Transformations and Random Point Processes %A Marco Bertola %A Mattia Cafasso %B IMRN %V rnu122 %P 56 %G eng %0 Journal Article %D 2014 %T Editorial %A Ciro Ciliberto %A Gianni Dal Maso %A Pasquale Vetro %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34712 %1 34926 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-10-26T10:50:12Z (GMT) No. of bitstreams: 0 %R 10.1007/s12215-014-0172-8 %0 Journal Article %D 2014 %T An effective model for nematic liquid crystal composites with ferromagnetic inclusions %A Maria Carme Calderer %A Antonio DeSimone %A Dmitry Golovaty %A Alexander Panchenko %X Molecules 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. %I Society for Industrial and Applied Mathematics Publications %G en %U http://urania.sissa.it/xmlui/handle/1963/34940 %1 35194 %2 Physics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-11-09T09:28:26Z No. of bitstreams: 1 preprint2014.pdf: 284611 bytes, checksum: ef4123b4aefb1a36fa198c1207a6f021 (MD5) %R 10.1137/130910348 %0 Journal Article %J SIAM Journal on Mathematical Analysis %D 2014 %T Local and global minimality results for a nonlocal isoperimetric problem on R^N %A Marco Bonacini %A Riccardo Cristoferi %K Nonlocal isoperimetric problem %XWe 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.

%B SIAM Journal on Mathematical Analysis %I SIAM Publications %V 46 %P 2310-2349 %G en %U http://hdl.handle.net/1963/6984 %N 4 %1 6976 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Marco Bonacini (mbonacin@sissa.it) on 2013-07-19T15:56:58Z No. of bitstreams: 1 boncri_fin.pdf: 567997 bytes, checksum: a24d4e9e6bbd6f176558b4d007dba6e3 (MD5) %R 10.1137/130929898 %0 Journal Article %D 2014 %T On the Lp-differentiability of certain classes of functions %A Giovanni Alberti %A Stefano Bianchini %A Gianluca Crippa %X We 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. %I European Mathematical Society %G en %U http://urania.sissa.it/xmlui/handle/1963/34695 %1 34909 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-10-22T09:44:25Z No. of bitstreams: 1 Alberti_Bianchini_50_M.pdf: 253000 bytes, checksum: 06381747f80814ced325966adefdec91 (MD5) %R 10.4171/rmi/782 %0 Conference Proceedings %B 22nd International Conference on Nuclear Engineering ICONE22 %D 2014 %T A reduced order model for multi-group time-dependent parametrized reactor spatial kinetics %A Alberto Sartori %A Davide Baroli %A Antonio Cammi %A Lelio Luzzi %A Gianluigi Rozza %XIn 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.

%B 22nd International Conference on Nuclear Engineering ICONE22 %7 American Society Mechanical Engineering %I American Society of Mechanical Engineers (ASME) %C Prague, Czech Republic %P V005T17A048-V005T17A048 %8 07/2014 %@ 978-079184595-0 %G en %U http://urania.sissa.it/xmlui/handle/1963/35123 %1 35360 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-12-03T10:06:02Z (GMT) No. of bitstreams: 0 %R 10.1115/ICONE22-30707 %0 Book Section %B AIMS Series on Applied Mathematics, vol. 8 (2014): 399 - 406 %D 2014 %T Reduction on characteristics for continuous of a scalar balance law %A Giovanni Alberti %A Stefano Bianchini %A Laura Caravenna %K Method of characteristics %B AIMS Series on Applied Mathematics, vol. 8 (2014): 399 - 406 %I SISSA %G en %U http://hdl.handle.net/1963/6562 %1 6516 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-04-03T07:48:04Z No. of bitstreams: 1 Alberti_11.pdf: 330968 bytes, checksum: a5f69e2a1d0afcfe139cf17ebcaf0f2d (MD5) %0 Journal Article %D 2014 %T Some remarks on the seismic behaviour of embedded cantilevered retaining walls %A Riccardo Conti %A F. Burali D'Arezzo %A Giulia M.B. Viggiani %X This 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. %I Thomas Telford %G en %U http://urania.sissa.it/xmlui/handle/1963/35073 %1 35308 %2 Physics %4 2 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-11-30T17:34:56Z No. of bitstreams: 1 art2014.pdf: 1304935 bytes, checksum: 2618504941effc8eed6dddb1077d8916 (MD5) %R 10.1680/geot.13.P.031 %0 Journal Article %D 2014 %T A uniqueness result for the continuity equation in two dimensions: dedicated to constantine dafermos on the occasion of his 70th birthday %A Giovanni Alberti %A Stefano Bianchini %A Gianluca Crippa %X We 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. %I European Mathematical Society; Springer Verlag %G en %U http://urania.sissa.it/xmlui/handle/1963/34692 %1 34906 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-10-22T09:07:51Z No. of bitstreams: 1 Alberti_Bianchini_Crippa_52M.pdf: 318780 bytes, checksum: 556a1d21b44c58d90201b25b2c104744 (MD5) %R 10.4171/JEMS/431 %0 Journal Article %D 2014 %T A weighted empirical interpolation method: A priori convergence analysis and applications %A Peng Chen %A Alfio Quarteroni %A Gianluigi Rozza %X We 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. %I EDP Sciences %G en %U http://urania.sissa.it/xmlui/handle/1963/35021 %1 35253 %2 Mathematics %4 1 %# MAT/05 %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2015-11-17T10:26:06Z (GMT) No. of bitstreams: 0 %R 10.1051/m2an/2013128 %0 Journal Article %J Journal of Geometric Analysis 23, nr.2 (2013), pages 812-854 %D 2013 %T Connected Sum Construction for σk-Yamabe Metrics %A Giovanni Catino %A Lorenzo Mazzieri %X In 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. %B Journal of Geometric Analysis 23, nr.2 (2013), pages 812-854 %I Springer %G en %U http://hdl.handle.net/1963/6441 %1 6366 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-01-29T10:41:53Z No. of bitstreams: 1 0910.5353v2.pdf: 355177 bytes, checksum: 0fa7b4a369607d617c4c167617460165 (MD5) %R 10.1007/s12220-011-9265-1 %0 Report %D 2013 %T On deformations of multidimensional Poisson brackets of hydrodynamic type %A Matteo Casati %K Hamiltonian operator %X The 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. %I SISSA %G en %U http://hdl.handle.net/1963/7235 %1 7271 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Matteo Casati (mcasati@sissa.it) on 2013-12-09T15:48:14Z No. of bitstreams: 1 1312.1878v1.pdf: 416883 bytes, checksum: d561f4d57afd0607190ba24368e563ae (MD5) %] 1. Introduction 1.1 Poisson Vertex Algebras 1.2 Poisson brackets of hydrodynamic type and their deformations 2. Multidimensional Poisson Vertex Algebras 2.1 Formal map space 2.2 Poisson bivector and Poisson brackets 2.3 Poisson Vertex Algebras 2.4 Proof of Master formula 2.5 Cohomology of Poisson Vertex Algebras 3. Multidimensional Poisson brackets of hydrodynamic type 3.1 Deformation of Lie-Poisson bracket of hydrodynamic type 3.2 Proof of Theorem 5 4. Concluding remarks %0 Journal Article %J Communications in Algebra. Volume 41, Issue 6, May 2013, Pages 2346-2386 %D 2013 %T Expanded degenerations and pairs %A Dan Abramovich %A Charles Cadman %A Barbara Fantechi %A Jonathan Wise %K Expanded pairs %X Since 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. %B Communications in Algebra. Volume 41, Issue 6, May 2013, Pages 2346-2386 %I Taylor and Francis %G en %U http://hdl.handle.net/1963/7383 %1 7431 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-06-18T09:55:33Z No. of bitstreams: 1 1110.2976v1.pdf: 418919 bytes, checksum: 61308c478c1e11ea1c389bd98e227cd2 (MD5) %R 10.1080/00927872.2012.658589 %0 Journal Article %J Random Matrices: Theory and Applications %D 2013 %T The gap probabilities of the tacnode, Pearcey and Airy point processes, their mutual relationship and evaluation %A Marco Bertola %A Mattia Cafasso %B Random Matrices: Theory and Applications %V 02 %P 1350003 %G eng %U http://www.worldscientific.com/doi/abs/10.1142/S2010326313500032 %R 10.1142/S2010326313500032 %0 Journal Article %D 2013 %T Genus stabilization for moduli of curves with symmetries %A Fabrizio Catanese %A Michael Lönne %A Fabio Perroni %K group actions %K mapping class group %K Moduli space of curves %K Teichmüller space %X In 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 $\\e$. %I SISSA %G en %U http://hdl.handle.net/1963/6509 %1 6461 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Fabio Perroni (perroni@sissa.it) on 2013-02-27T21:38:16Z\nNo. of bitstreams: 1\n1301.4409v1.pdf: 515958 bytes, checksum: 378f14240b070b5bc840d1cd9ca8e6a0 (MD5) %0 Journal Article %J Journal of Geometric Analysis %D 2013 %T Lipschitz Classification of Almost-Riemannian Distances on Compact Oriented Surfaces %A Ugo Boscain %A Grégoire Charlot %A Roberta Ghezzi %A Mario Sigalotti %XTwo-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.

%B Journal of Geometric Analysis %V 23 %P 438–455 %8 Jan %G eng %U https://doi.org/10.1007/s12220-011-9262-4 %R 10.1007/s12220-011-9262-4 %0 Journal Article %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %T Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations %A Cacace, S. %A Antonin Chambolle %A Antonio DeSimone %A Livio Fedeli %B ESAIM: Mathematical Modelling and Numerical Analysis %I EDP Sciences %V 47 %P 837–858 %G eng %R 10.1051/m2an/2012048 %0 Journal Article %J Communications in Mathematical Physics %D 2013 %T The Monge Problem for Distance Cost in Geodesic Spaces %A Stefano Bianchini %A Fabio Cavalletti %XWe 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.

%B Communications in Mathematical Physics %V 318 %P 615–673 %8 Mar %G eng %U https://doi.org/10.1007/s00220-013-1663-8 %R 10.1007/s00220-013-1663-8 %0 Journal Article %D 2013 %T A note on non-homogeneous hyperbolic operators with low-regularity coefficients %A Ferruccio Colombini %A Francesco Fanelli %XIn 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 $t$.

%G eng %0 Journal Article %J SIAM Journal on Numerical Analysis %D 2013 %T Stochastic optimal robin boundary control problems of advection-dominated elliptic equations %A Peng Chen %A Alfio Quarteroni %A Gianluigi Rozza %X In 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. %B SIAM Journal on Numerical Analysis %V 51 %P 2700–2722 %G eng %R 10.1137/120884158 %0 Journal Article %J SIAM Journal on Numerical Analysis %D 2013 %T A weighted reduced basis method for elliptic partial differential equations with random input data %A Peng Chen %A Alfio Quarteroni %A Gianluigi Rozza %X In 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. %B SIAM Journal on Numerical Analysis %V 51 %P 3163–3185 %G eng %R 10.1137/130905253 %0 Journal Article %J Geotechnique, Volume 62, Issue 12, December 2012, Pages 1081-1094 %D 2012 %T On the behaviour of flexible retaining walls under seismic actions %A Riccardo Conti %A G.S.P. Madabhushi %A Giulia M.B. Viggiani %K Centrifuge modelling %X This 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. %B Geotechnique, Volume 62, Issue 12, December 2012, Pages 1081-1094 %I ICE Publishing %G en %U http://hdl.handle.net/1963/6933 %1 6912 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-05-30T10:11:44Z No. of bitstreams: 0 %R 10.1680/geot.11.P.029 %0 Journal Article %J Journal fur die Reine und Angewandte Mathematik, Issue 671, October 2012, Pages 131-198 %D 2012 %T A Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group. %A Andrea Malchiodi %A Paul Yang %A Jih-Hsin Cheng %A JennFang Hwang %X In 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 1 %B Journal fur die Reine und Angewandte Mathematik, Issue 671, October 2012, Pages 131-198 %I SISSA %G en %U http://hdl.handle.net/1963/6556 %1 6490 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-03-25T14:33:32Z (GMT) No. of bitstreams: 0 %R 10.1515/CRELLE.2011.159 %0 Journal Article %J Nucleic Acids Research, Volume 40, Issue 15, August 2012, Pages 7132-7149 %D 2012 %T Detection of transcriptional triggers in the dynamics of microbial growth: application to the respiratory-versatile bacterium Shewanella oneidensis %A Q Beg %A Mattia Zampieri %A N Klitgord %A S Collins %A M Serres %A Daniel Segrè %A Claudio Altafini %X The 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 systems %B Nucleic Acids Research, Volume 40, Issue 15, August 2012, Pages 7132-7149 %I SISSA %G en %U http://hdl.handle.net/1963/6506 %1 6452 %2 Mathematics %4 1 %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-02-27T15:39:07Z (GMT) No. of bitstreams: 0 %R 10.1093/nar/gks467 %0 Journal Article %J Comm. Math. Phys. %D 2012 %T Fredholm determinants and pole-free solutions to the noncommutative Painlevé II equation %A Marco Bertola %A Mattia Cafasso %B Comm. Math. Phys. %V 309 %P 793–833 %G eng %U http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00220-011-1383-x %R 10.1007/s00220-011-1383-x %0 Report %D 2012 %T A Fully Coupled Immersed Finite Element Method for Fluid Structure Interaction via the Deal.II Library %A Luca Heltai %A Saswati Roy %A Francesco Costanzo %K Finite Element Method %K Immersed Boundary Method %K Immersed Finite Element Method %X We 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. %I SISSA %G en %U http://hdl.handle.net/1963/6255 %1 6172 %2 Mathematics %3 Functional Analysis and Applications %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Luca Heltai (heltai@sissa.it) on 2012-09-28T11:06:13Z\\nNo. of bitstreams: 1\\n1209.2811v1.pdf: 4766431 bytes, checksum: a46803f7f8daf3195359f65c9161b944 (MD5) %0 Journal Article %J Nanoscale. 2012 Mar; 4(5):1734-41 %D 2012 %T Hybridization in nanostructured DNA monolayers probed by AFM: theory versus experiment %A Alessandro Bosco %A Fouzia Bano %A Pietro Parisse %A Loredana Casalis %A Antonio DeSimone %A Cristian Micheletti %X Nanografted 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. %B Nanoscale. 2012 Mar; 4(5):1734-41 %I Royal Society of Chemistry %G en %1 6998 %2 Physics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-08-08T07:48:55Z No. of bitstreams: 0 %R 10.1039/c2nr11662f %0 Journal Article %J International Mathematics Research Notices, vol. 22 (2012) , page 5063-5099 %D 2012 %T The KdV hierarchy: universality and a Painleve transcendent %A Tom Claeys %A Tamara Grava %K Small-Dispersion limit %X We 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. %B International Mathematics Research Notices, vol. 22 (2012) , page 5063-5099 %I Oxford University Press %G en %U http://hdl.handle.net/1963/6921 %1 6902 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-05-29T08:08:55Z No. of bitstreams: 1 1101.2602v1.pdf: 327994 bytes, checksum: 5b5bbc9f9b74ce97c2bf5ae794698819 (MD5) %0 Journal Article %J Calculus of Variations and Partial Differential Equations %D 2012 %T The Monge problem in Wiener space %A Fabio Cavalletti %XWe 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.

%B Calculus of Variations and Partial Differential Equations %V 45 %P 101–124 %8 Sep %G eng %U https://doi.org/10.1007/s00526-011-0452-5 %R 10.1007/s00526-011-0452-5 %0 Journal Article %J Acta Geotechnica, Volume 7, Issue 3, September 2012, Pages 219-237 %D 2012 %T Numerical modelling of installation effects for diaphragm walls in sand %A Riccardo Conti %A Luca de Sanctis %A Giulia M.B. Viggiani %K Constitutive relations %X The 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. %B Acta Geotechnica, Volume 7, Issue 3, September 2012, Pages 219-237 %I Springer %G en %U http://hdl.handle.net/1963/6934 %1 6916 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-05-30T10:23:32Z No. of bitstreams: 0 %R 10.1007/s11440-011-0157-0 %0 Journal Article %J SIAM Journal on Mathematical Analysis %D 2012 %T Optimal Transport with Branching Distance Costs and the Obstacle Problem %A Fabio Cavalletti %B SIAM Journal on Mathematical Analysis %V 44 %P 454-482 %G eng %U https://doi.org/10.1137/100801433 %R 10.1137/100801433 %0 Journal Article %J Physica D: Nonlinear Phenomena %D 2012 %T Riemann–Hilbert approach to multi-time processes: The Airy and the Pearcey cases %A Marco Bertola %A Mattia Cafasso %K Integrable kernels %B Physica D: Nonlinear Phenomena %V 241 %P 2237 - 2245 %G eng %U http://www.sciencedirect.com/science/article/pii/S0167278912000115 %R 10.1016/j.physd.2012.01.003 %0 Journal Article %J Communications in Mathematical Physics 313 (2012) 1-33 %D 2012 %T SBV regularity for genuinely nonlinear, strictly hyperbolic systems of conservation laws in one space dimension %A Stefano Bianchini %A Laura Caravenna %B Communications in Mathematical Physics 313 (2012) 1-33 %I Springer %G en_US %U http://hdl.handle.net/1963/4091 %1 313 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-10-19T09:31:49Z\\r\\nNo. of bitstreams: 1\\r\\nBianchini_Caravenna_71M_2010.pdf: 591519 bytes, checksum: 388c1d8be60af95097574c718b4708b2 (MD5) %R 10.1007/s00220-012-1480-5 %0 Journal Article %J International Journal Numerical Methods Biomedical Engineering %D 2012 %T Simulation-based uncertainty quantification of human arterial network hemodynamics %A Peng Chen %A Alfio Quarteroni %A Gianluigi Rozza %K uncertainty quantification, mathematical modelling of the cardiovascular system, fluid-structure interaction %X This 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. %B International Journal Numerical Methods Biomedical Engineering %I Wiley %G en %1 6467 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2013-03-07T12:33:02Z\nNo. of bitstreams: 1\nreport.pdf: 1605405 bytes, checksum: bb12cf074ce32a80567a0cde0c0861db (MD5) %0 Journal Article %J Rev. Math. Phys. 24 (2012), 1250017 %D 2012 %T Stability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions %A Michele Correggi %A Gianfausto Dell'Antonio %A Domenico Finco %A Alessandro Michelangeli %A Alessandro Teta %X We 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. %B Rev. Math. Phys. 24 (2012), 1250017 %I World Scientific %G en %U http://hdl.handle.net/1963/6069 %1 5955 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-08-02T07:19:59Z\\nNo. of bitstreams: 1\\n1201.5740v1.pdf: 303047 bytes, checksum: eb2df0afd547514c235422e82f494584 (MD5) %R 10.1142/S0129055X12500171 %0 Journal Article %J Computer Methods in Applied Mechanics and Engineering. Volume 229-232, 1 July 2012, Pages 110-127 %D 2012 %T Variational implementation of immersed finite element methods %A Luca Heltai %A Francesco Costanzo %K Turbulent flow %XDirac-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.

%B Computer Methods in Applied Mechanics and Engineering. Volume 229-232, 1 July 2012, Pages 110-127 %I Elsevier %G en %U http://hdl.handle.net/1963/6462 %1 6389 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Lucio Lubiana (lubiana@sissa.it) on 2013-02-04T16:21:56Z\\nNo. of bitstreams: 0 %R 10.1016/j.cma.2012.04.001 %0 Journal Article %J Journal of Functional Analysis 262 (2012) 409-450 %D 2012 %T Weighted barycentric sets and singular Liouville equations on compact surfaces %A Alessandro Carlotto %A Andrea Malchiodi %X Given 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]). %B Journal of Functional Analysis 262 (2012) 409-450 %I Elsevier %G en %U http://hdl.handle.net/1963/5218 %1 5040 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-01-10T11:49:50Z\\nNo. of bitstreams: 1\\n1105.2363v2.pdf: 793763 bytes, checksum: 4996db876d03946c03fa0d4766801974 (MD5) %R 10.1016/j.jfa.2011.09.012 %0 Journal Article %J Comptes Rendus Mathematique 349 (2011) 161-166 %D 2011 %T A class of existence results for the singular Liouville equation %A Alessandro Carlotto %A Andrea Malchiodi %X We 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. %B Comptes Rendus Mathematique 349 (2011) 161-166 %I Elsevier %G en %U http://hdl.handle.net/1963/5793 %1 5648 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-05-07T07:37:16Z\\nNo. of bitstreams: 0 %R 10.1016/j.crma.2010.12.016 %0 Journal Article %J Le Matematiche (Catania), volume 66, Issue no.2, (2011), pages : 153-187 %D 2011 %T Cones of divisors of blow-ups of projective spaces %A Alessio Lo Giudice %A Salvatore Cacciola %A M. Donten-Bury %A O. Dumitrescu %A J. Park %K Mori dream space %X We 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. %B Le Matematiche (Catania), volume 66, Issue no.2, (2011), pages : 153-187 %I Università degli Studi di Catania. Dipartimento di matematica %G en %U http://hdl.handle.net/1963/6613 %1 6462 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Alessio Lo Giudice (logiudic@sissa.it) on 2013-03-01T08:45:50Z No. of bitstreams: 1 CONES OF DIVISORS OF BLOW-UPS OF PROJECTIVE SPACES: 409758 bytes, checksum: 15d01ca131c41cf5f244bb4621177e36 (MD5) %R 10.4418/2011.66.2.13 %0 Journal Article %J PNAS 108 (2011) 13978 %D 2011 %T Cytoskeletal actin networks in motile cells are critically self-organized systems synchronized by mechanical interactions %A Luca Cardamone %A Alessandro Laio %A Rajesh Shahapure %A Antonio DeSimone %B PNAS 108 (2011) 13978 %I National Academy of Sciences %G en %U http://hdl.handle.net/1963/4358 %1 4066 %2 Physics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-28T06:31:24Z\\nNo. of bitstreams: 0 %R 10.1073/pnas.1100549108 %0 Journal Article %J Matematische Annalen 349 (2011) 75-115 %D 2011 %T Infinite-dimensional Frobenius manifolds for 2 + 1 integrable systems %A Guido Carlet %A Boris Dubrovin %A Luca Philippe Mertens %X We 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. %B Matematische Annalen 349 (2011) 75-115 %I Springer %G en_US %U http://hdl.handle.net/1963/3584 %1 716 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-03-09T09:29:31Z\\r\\nNo. of bitstreams: 1\\r\\n0902.1245.pdf: 343930 bytes, checksum: 421342a05bb8986c1bf542d6446f5792 (MD5) %R 10.1007/s00208-010-0509-3 %0 Conference Paper %B Nonlinear Conservation Laws and Applications %D 2011 %T The Monge Problem in Geodesic Spaces %A Stefano Bianchini %A Fabio Cavalletti %E Alberto Bressan %E Chen, Gui-Qiang G. %E Marta Lewicka %E Wang, Dehua %XWe 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.

%B Nonlinear Conservation Laws and Applications %I Springer US %C Boston, MA %P 217–233 %@ 978-1-4419-9554-4 %G eng %0 Journal Article %J Mathematische Zeitschrift 268 (2011) 371-407 %D 2011 %T A proof of Sudakov theorem with strictly convex norms %A Laura Caravenna %X We 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. %B Mathematische Zeitschrift 268 (2011) 371-407 %I Springer %G en_US %U http://hdl.handle.net/1963/2967 %1 1733 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-24T10:14:57Z\\r\\nNo. of bitstreams: 1\\r\\nsudStrConv.pdf: 432852 bytes, checksum: 0c4df310f125711293cef790005abc33 (MD5) %R 10.1007/s00209-010-0677-6 %0 Journal Article %J Journal of the Mechanics and Physics of Solids 59 (2011) 787-803 %D 2011 %T Quasiconvex envelopes of energies for nematic elastomers in the small strain regime and applications %A Pierluigi Cesana %A Antonio DeSimone %X We 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. %B Journal of the Mechanics and Physics of Solids 59 (2011) 787-803 %G en_US %U http://hdl.handle.net/1963/4065 %1 337 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-09-15T10:43:52Z\\r\\nNo. of bitstreams: 1\\r\\nCesana_DeSimone_62M.pdf: 1146834 bytes, checksum: 514b1b282763c0351f234702f96e73f4 (MD5) %0 Journal Article %J ESAIM: COCV 17 (2011) 1-27 %D 2011 %T Quasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a Young measures approach %A Filippo Cagnetti %A Rodica Toader %X A 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. %B ESAIM: COCV 17 (2011) 1-27 %I Cambridge University Press / EDP Sciences %G en_US %U http://hdl.handle.net/1963/2355 %1 1662 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-11-07T13:38:16Z\\r\\nNo. of bitstreams: 1\\r\\nQuasCrack.pdf: 298737 bytes, checksum: 127034af65efce0ab97317eccb47e76c (MD5) %R 10.1051/cocv/2009037 %0 Journal Article %J Indiana Univ. Math. J. 60 (2011) 367-409 %D 2011 %T Singular perturbation models in phase transitions for second order materials %A Milena Chermisi %A Gianni Dal Maso %A Irene Fonseca %A Giovanni Leoni %X A 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. %B Indiana Univ. Math. J. 60 (2011) 367-409 %I Indiana University %G en_US %U http://hdl.handle.net/1963/3858 %1 851 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-04-27T10:47:12Z\\r\\nNo. of bitstreams: 1\\r\\nCheDMaFonLeo_2010.pdf: 350746 bytes, checksum: b384a4d0b82dd9713e1849ad3ef6a2be (MD5) %R 10.1512/iumj.2011.60.4346 %0 Journal Article %J Journal of Dynamical and Control Systems %D 2011 %T The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry %A Bernard Bonnard %A Grégoire Charlot %A Roberta Ghezzi %A Gabriel Janin %XWe 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.

%B Journal of Dynamical and Control Systems %I Springer %V 17 %P 141-161 %G en %U http://hdl.handle.net/1963/4914 %1 4692 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-25T09:38:15Z\\nNo. of bitstreams: 1\\n1009.2612v1.pdf: 263401 bytes, checksum: 0ddf4bcfd9663ee3c0da870233d119bb (MD5) %R 10.1007/s10883-011-9113-4 %0 Report %D 2011 %T Structure of level sets and Sard-type properties of Lipschitz maps %A Giovanni Alberti %A Stefano Bianchini %A Gianluca Crippa %I SISSA %G en %U http://hdl.handle.net/1963/4657 %1 4424 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-10-10T12:07:33Z\\nNo. of bitstreams: 1\\nAlberti_Bianchini_Crippa_51_M.pdf: 361735 bytes, checksum: b3f27bce1ab515dca94a6ad93d822160 (MD5) %0 Journal Article %J International Mathematics Research Notices %D 2011 %T The Transition between the Gap Probabilities from the Pearcey to the Airy Process–a Riemann-Hilbert Approach %A Marco Bertola %A Mattia Cafasso %B International Mathematics Research Notices %V doi: 10.1093/imrn/rnr066 %P 1-50 %G eng %0 Report %D 2011 %T A uniqueness result for the continuity equation in two dimensions %A Giovanni Alberti %A Stefano Bianchini %A Gianluca Crippa %I SISSA %G en %U http://hdl.handle.net/1963/4663 %1 4425 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-10-10T12:10:26Z\\nNo. of bitstreams: 1\\nAlberti_Bianchini_Crippa_52M.pdf: 318780 bytes, checksum: 556a1d21b44c58d90201b25b2c104744 (MD5) %0 Journal Article %J J. Funct. Anal. 258 (2010) 3604-3661 %D 2010 %T The disintegration of the Lebesgue measure on the faces of a convex function %A Laura Caravenna %A Sara Daneri %XWe 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.

%B J. Funct. Anal. 258 (2010) 3604-3661 %G en_US %U http://hdl.handle.net/1963/3622 %1 682 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-04-24T15:53:31Z\\nNo. of bitstreams: 1\\ndisconvCaravDaneri.pdf: 759110 bytes, checksum: e22e069339fc07c3bde1855b76e61d1e (MD5) %R 10.1016/j.jfa.2010.01.024 %0 Journal Article %J Journal of Dynamical and Control Systems. Volume 16, Issue 2, April 2010, Pages :149-162 %D 2010 %T Dynamics control by a time-varying feedback %A Andrei A. Agrachev %A Marco Caponigro %K Discrete-time dynamics %X We 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. %B Journal of Dynamical and Control Systems. Volume 16, Issue 2, April 2010, Pages :149-162 %I SISSA %G en %U http://hdl.handle.net/1963/6461 %1 6407 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-02-06T09:37:23Z (GMT) No. of bitstreams: 0 %R 10.1007/s10883-010-9087-7 %0 Journal Article %J J. Phys. A 43 (2010) 474014 %D 2010 %T Effective Schroedinger dynamics on $ ε$-thin Dirichlet waveguides via Quantum Graphs I: star-shaped graphs %A Gianfausto Dell'Antonio %A Emanuele Costa %X We describe the boundary conditions at the vertex that one must choose to obtain a dynamical system that best describes the low-energy part of the evolution of a quantum system confined to a very small neighbourhood of a star-shaped metric graph. %B J. Phys. A 43 (2010) 474014 %I IOP Publishing %G en_US %U http://hdl.handle.net/1963/4106 %1 298 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-12-06T13:09:12Z\\nNo. of bitstreams: 1\\n1004.4750v2.pdf: 273649 bytes, checksum: ff34b6647ba206615715d6c764115064 (MD5) %R 10.1088/1751-8113/43/47/474014 %0 Journal Article %J Proc. Steklov Inst. Math. 270 (2010) 43-56 %D 2010 %T Existence of planar curves minimizing length and curvature %A Ugo Boscain %A Grégoire Charlot %A Francesco Rossi %X In 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. %B Proc. Steklov Inst. Math. 270 (2010) 43-56 %I Springer %G en_US %U http://hdl.handle.net/1963/4107 %1 297 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-12-06T13:30:01Z\\nNo. of bitstreams: 1\\n0906.5290v2.pdf: 305594 bytes, checksum: 3966f5a798b69743ce88a29bf73edc47 (MD5) %R 10.1134/S0081543810030041 %0 Journal Article %J Systems and Control Letters, 59 (12):782-786, 2010 %D 2010 %T Feedback schemes for radiation damping suppression in NMR: a control-theoretical perspective %A Claudio Altafini %A Paola Cappellaro %A David Cory %X In 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. %B Systems and Control Letters, 59 (12):782-786, 2010 %I Elsevier %G en %U http://hdl.handle.net/1963/4384 %1 4132 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-09-30T10:33:33Z\\nNo. of bitstreams: 1\\nAlCaCo09.pdf: 172729 bytes, checksum: b8f2ae1517b057b5f24fd2d8b3666002 (MD5) %R 10.1016/j.sysconle.2010.09.004 %0 Journal Article %J The European journal of neuroscience. 2010 Oct; 32(8):1364-79 %D 2010 %T Gene expression analysis of the emergence of epileptiform activity after focal injection of kainic acid into mouse hippocampus. %A Dario Motti %A Caroline Le Duigou %A Nicole Chemaly %A Lucia Wittner %A Dejan Lazarevic %A Helena Krmac %A Troels Torben Marstrand %A Eivind Valen %A Remo Sanges %A Elia Stupka %A Albin Sandelin %A Enrico Cherubini %A Stefano Gustincich %A Richard Miles %XWe 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.

%B The European journal of neuroscience. 2010 Oct; 32(8):1364-79 %I Wiley %G en %U http://hdl.handle.net/1963/4480 %1 4244 %2 Neuroscience %3 Neurobiology %4 -1 %$ Approved for entry into archive by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-05T07:58:51Z (GMT) No. of bitstreams: 0 %R 10.1111/j.1460-9568.2010.07403.x %0 Journal Article %J Phys. Rev. A 81 (2010) 062335 %D 2010 %T Homogeneous binary trees as ground states of quantum critical Hamiltonians %A Pietro Silvi %A Vittorio Giovannetti %A Simone Montangero %A Matteo Rizzi %A J. Ignacio Cirac %A Rosario Fazio %XMany-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.

%B Phys. Rev. A 81 (2010) 062335 %I American Physical Society %G en_US %U http://hdl.handle.net/1963/3909 %1 800 %2 Physics %3 Condensed Matter Theory %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-07-27T07:32:21Z\\nNo. of bitstreams: 1\\n0912.0466v1.pdf: 336415 bytes, checksum: 7220d67cfb58f794aa50037140db23e6 (MD5) %R 10.1103/PhysRevA.81.062335 %0 Journal Article %J Mathematical Biosciences and Engineering 7(2):301-312, 2010 %D 2010 %T A kinetic mechanism inducing oscillations in simple chemical reactions networks %A Julien Coatleven %A Claudio Altafini %X It 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. %B Mathematical Biosciences and Engineering 7(2):301-312, 2010 %I American Institute of Mathematical Sciences %G en_US %U http://hdl.handle.net/1963/2393 %1 2304 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-11-12T13:08:42Z\\r\\nNo. of bitstreams: 1\\r\\nCoAl07.pdf: 254781 bytes, checksum: 0906fef8209903070cd78781f52b13b1 (MD5) %R 10.3934/mbe.2010.7.301 %0 Journal Article %J arXiv preprint arXiv:1008.5036 %D 2010 %T A normal form for generic 2-dimensional almost-Riemannian structures at a tangency point %A Ugo Boscain %A Grégoire Charlot %A Roberta Ghezzi %B arXiv preprint arXiv:1008.5036 %G eng %0 Journal Article %J Comptes Rendus Mathematique 348 (2010) 613-618 %D 2010 %T On optimality of c-cyclically monotone transference plans %A Stefano Bianchini %A Laura Caravenna %X Abstract. 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. %B Comptes Rendus Mathematique 348 (2010) 613-618 %I Elsevier %G en_US %U http://hdl.handle.net/1963/4023 %1 379 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-09-02T09:13:11Z\\nNo. of bitstreams: 1\\ncmonoNoteCRM.pdf: 154086 bytes, checksum: f2efc74ccfedd2e335ff99ff279b5cfd (MD5) %R 10.1016/j.crma.2010.03.022 %0 Journal Article %J Comm. Pure Appl. Math. 63 (2010) 203-232 %D 2010 %T Painlevé II asymptotics near the leading edge of the oscillatory zone for the Korteweg-de Vries equation in the small-dispersion limit %A Tom Claeys %A Tamara Grava %X In 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. %B Comm. Pure Appl. Math. 63 (2010) 203-232 %I Wiley %G en_US %U http://hdl.handle.net/1963/3799 %1 527 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-11-26T16:48:15Z\\nNo. of bitstreams: 1\\n0812.4142v1.pdf: 343118 bytes, checksum: 4bf2fa3751076c18466f29e1163acc09 (MD5) %R 10.1002/cpa.20277 %0 Journal Article %J Journal of Differential Equations %D 2010 %T Positive solutions for some non-autonomous Schrödinger–Poisson systems %A Giovanna Cerami %A Giusi Vaira %B Journal of Differential Equations %I Academic Press %V 248 %P 521–543 %G eng %0 Journal Article %J J. Phys. A 43 (2010) 045201 %D 2010 %T The reductions of the dispersionless 2D Toda hierarchy and their Hamiltonian structures %A Guido Carlet %A Paolo Lorenzoni %A Andrea Raimondo %X We 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. %B J. Phys. A 43 (2010) 045201 %I IOP Publishing %G en_US %U http://hdl.handle.net/1963/3846 %1 863 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-02-17T09:13:18Z\\nNo. of bitstreams: 1\\n0910.1210v1.pdf: 183431 bytes, checksum: 90f5253ca8e81822f6ffb26ece621075 (MD5) %R 10.1088/1751-8113/43/4/045201 %0 Journal Article %J SIAM J. Math. Anal. 42 (2010) 2132-2154 %D 2010 %T Solitonic asymptotics for the Korteweg-de Vries equation in the small dispersion limit %A Tamara Grava %A Tom Claeys %X We 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. %B SIAM J. Math. Anal. 42 (2010) 2132-2154 %G en_US %U http://hdl.handle.net/1963/3839 %1 488 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-02-05T10:12:44Z\\nNo. of bitstreams: 1\\n0911.5686v1.pdf: 311708 bytes, checksum: bfe41688febbfb066ebaae202e1e93b6 (MD5) %R 10.1137/090779103 %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire %D 2010 %T Two-dimensional almost-Riemannian structures with tangency points %A Andrei A. Agrachev %A Ugo Boscain %A Grégoire Charlot %A Roberta Ghezzi %A Mario Sigalotti %XTwo-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.

%B Ann. Inst. H. Poincare Anal. Non Lineaire %I Elsevier %V 27 %P 793-807 %G en_US %U http://hdl.handle.net/1963/3870 %1 839 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-05-31T14:15:39Z\\nNo. of bitstreams: 1\\n0908.2564v1.pdf: 302590 bytes, checksum: 15369151ee10bb886dc6678350dee7f5 (MD5) %R 10.1016/j.anihpc.2009.11.011 %0 Report %D 2009 %T Bubbles with prescribed mean curvature: the variational approach %A Paolo Caldiroli %A Roberta Musina %G en_US %U http://hdl.handle.net/1963/3659 %1 646 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-07-08T13:03:07Z\\nNo. of bitstreams: 1\\nSISSA 35-2009-M.pdf: 294313 bytes, checksum: cf6b1d87612220dc9238502f59175615 (MD5) %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire 26 (2009) 329-349 %D 2009 %T Controllability of the discrete-spectrum Schrodinger equation driven by an external field %A Thomas Chambrion %A Paolo Mason %A Mario Sigalotti %A Ugo Boscain %X We 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. %B Ann. Inst. H. Poincare Anal. Non Lineaire 26 (2009) 329-349 %G en_US %U http://hdl.handle.net/1963/2547 %1 1572 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-01-10T13:32:19Z\\nNo. of bitstreams: 1\\n2008-ttinger.pdf: 270196 bytes, checksum: e706dbae08d996576cefe55f53d7284e (MD5) %R 10.1016/j.anihpc.2008.05.001 %0 Journal Article %J Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009) 2503-2509 %D 2009 %T Controllability on the group of diffeomorphisms %A Andrei A. Agrachev %A Marco Caponigro %X Given 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. %B Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009) 2503-2509 %G en_US %U http://hdl.handle.net/1963/3396 %1 936 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-12-11T12:06:43Z\\nNo. of bitstreams: 1\\nAgrachev_Caponigro.pdf: 145136 bytes, checksum: 90eebd9912f15c33d1d93f5108ab93aa (MD5) %R 10.1016/j.anihpc.2009.07.003 %0 Journal Article %J Differential Geom. Appl. 27 (2009) 723-742 %D 2009 %T Differential geometry of curves in Lagrange Grassmannians with given Young diagram %A Igor Zelenko %A Li Chengbo %X Curves 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. %B Differential Geom. Appl. 27 (2009) 723-742 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3819 %1 508 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-01-18T16:06:20Z\\nNo. of bitstreams: 1\\n0708.1100v1.pdf: 330722 bytes, checksum: 31be09831ca0758a658e2fc9fe6a900f (MD5) %R 10.1016/j.difgeo.2009.07.002 %0 Journal Article %J Netw. Heterog. Media 4 (2009) 667-708 %D 2009 %T Discrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers %A Marco Cicalese %A Antonio DeSimone %A Caterina Ida Zeppieri %X In 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. %B Netw. Heterog. Media 4 (2009) 667-708 %I American Institute of Mathematical Sciences %G en_US %U http://hdl.handle.net/1963/3788 %1 538 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-11-25T10:31:11Z\\nNo. of bitstreams: 1\\nCDSZ08.pdf: 390765 bytes, checksum: 2b3fcd3668352c286200e0a3b7e12c1a (MD5) %R 10.3934/nhm.2009.4.667 %0 Thesis %D 2009 %T The Disintegration Theorem and Applications to Optimal Mass Transportation %A Laura Caravenna %I SISSA %G en %U http://hdl.handle.net/1963/5900 %1 5750 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-06-08T09:44:06Z\\nNo. of bitstreams: 1\\nPhDThesisCaravenna.pdf: 1700326 bytes, checksum: 9638dd5ad25fc3e1fb91399b1b12c293 (MD5) %0 Journal Article %J Funct. Anal. Appl. 43 (2009) 18-29 %D 2009 %T Equivariant cohomology and localization for Lie algebroids %A Ugo Bruzzo %A Lucio Cirio %A Paolo Rossi %A Vladimir Rubtsov %X Let 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. %B Funct. Anal. Appl. 43 (2009) 18-29 %@ 978-981-270-377-4 %G en_US %U http://hdl.handle.net/1963/1724 %1 2427 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-01-26T15:10:18Z\\nNo. of bitstreams: 1\\nmathDG0506392.pdf: 223181 bytes, checksum: bb9437e12cfd3d7cc5c14904aaeebe7d (MD5) %R 10.1007/s10688-009-0003-4 %0 Report %D 2009 %T An existence result for the Monge problem in R^n with norm cost %A Laura Caravenna %G en_US %U http://hdl.handle.net/1963/3647 %1 657 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-06-10T13:31:00Z\\nNo. of bitstreams: 1\\nMonge.sel.pdf: 1037029 bytes, checksum: 3f852fb5f7d74223ddee50818368c3f5 (MD5) %0 Journal Article %J Bull. Inst. Math. Acad. Sin. (N.S.) 4 (2009) 353-458 %D 2009 %T On the extremality, uniqueness and optimality of transference plans %A Stefano Bianchini %A Laura Caravenna %X We 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. %B Bull. Inst. Math. Acad. Sin. (N.S.) 4 (2009) 353-458 %G en_US %U http://hdl.handle.net/1963/3692 %1 613 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-07-24T11:10:18Z\\nNo. of bitstreams: 1\\n46M2009.pdf: 485239 bytes, checksum: ebe15dc163dd6bdffcbe875730432b12 (MD5) %0 Report %D 2009 %T Jacobi Equations and Comparison Theorems for Corank 1 Sub-Riemannian structures with symmetries %A Li Chengbo %A Igor Zelenko %X The 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. %G en_US %U http://hdl.handle.net/1963/3736 %1 581 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-09-08T13:36:18Z\\nNo. of bitstreams: 1\\njacompfin.pdf: 329060 bytes, checksum: 48bb88c074e19b86902a553f2055ddea (MD5) %0 Journal Article %J Math. Models Methods Appl. Sci. 19 (2009) 601-630 %D 2009 %T Strain-order coupling in nematic elastomers: equilibrium configurations %A Pierluigi Cesana %A Antonio DeSimone %X We 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. %B Math. Models Methods Appl. Sci. 19 (2009) 601-630 %G en_US %U http://hdl.handle.net/1963/2700 %1 1400 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-07-25T15:04:59Z\\nNo. of bitstreams: 1\\nprprCdS.pdf: 504721 bytes, checksum: 2ef9aff006dbc9353a50a122cb98d381 (MD5) %0 Journal Article %J Comm. Math. Phys. 286 (2009) 979-1009 %D 2009 %T Universality of the break-up profile for the KdV equation in the small dispersion limit using the Riemann-Hilbert approach %A Tamara Grava %A Tom Claeys %X We 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. %B Comm. Math. Phys. 286 (2009) 979-1009 %G en_US %U http://hdl.handle.net/1963/2636 %1 1487 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-04-22T10:17:48Z\\nNo. of bitstreams: 1\\n0801.2326v1.pdf: 375000 bytes, checksum: b00b6e0d823d47a002430b4fdecf8c7c (MD5) %R 10.1007/s00220-008-0680-5 %0 Journal Article %J J. Hyperbolic Differ. Equ. 5 (2008) 643-662 %D 2008 %T An entropy based Glimm-type functional %A Laura Caravenna %B J. Hyperbolic Differ. Equ. 5 (2008) 643-662 %I World Scientific %G en_US %U http://hdl.handle.net/1963/4051 %1 351 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-09-09T11:15:30Z\\nNo. of bitstreams: 1\\nglimm.potential.pdf: 405855 bytes, checksum: e2a5f3fed36ffe727c6d43240482aa6d (MD5) %R 10.1142/S0219891608001635 %0 Journal Article %J Phys. Rev. B 77 (2008) 245105 %D 2008 %T Fulde-Ferrell-Larkin-Ovchinnikov pairing in one-dimensional optical lattices %A Matteo Rizzi %A Marco Polini %A Miguel A. Cazalilla %A M.R. Bakhtiari %A Mario P. Tosi %A Rosario Fazio %XSpin-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.

%B Phys. Rev. B 77 (2008) 245105 %G en_US %U http://hdl.handle.net/1963/2694 %1 1406 %2 Physics %3 Condensed Matter Theory %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-07-14T09:46:14Z\\nNo. of bitstreams: 1\\n0712.3364v1.pdf: 305409 bytes, checksum: 13081c375909264afc4c0282b9de9f68 (MD5) %R 10.1103/PhysRevB.77.245105 %0 Journal Article %J SIAM J. Control Optim. 47 (2008) 111-143 %D 2008 %T Limit Time Optimal Syntheses for a control-affine system on S² %A Paolo Mason %A Rebecca Salmoni %A Ugo Boscain %A Yacine Chitour %X For $\\\\alpha \\\\in ]0,\\\\pi/2[$, 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 $U_\\\\alpha$. %B SIAM J. Control Optim. 47 (2008) 111-143 %G en_US %U http://hdl.handle.net/1963/1862 %1 2360 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-09-28T11:24:18Z\\nNo. of bitstreams: 1\\n48-M.pdf: 5823285 bytes, checksum: 7f66cf9d280da78b56a423c415d9078c (MD5) %R 10.1137/060675988 %0 Journal Article %J Math. Models Methods Appl. Sci. 18 (2008) 1-20 %D 2008 %T Relaxation of some transversally isotropic energies and applications to smectic A elastomers %A James Adams %A Sergio Conti %A Antonio DeSimone %A Georg Dolzmann %B Math. Models Methods Appl. Sci. 18 (2008) 1-20 %G en_US %U http://hdl.handle.net/1963/1912 %1 2325 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-02-02T14:15:25Z\\nNo. of bitstreams: 1\\nsma_Preprint_SISSA.pdf: 271875 bytes, checksum: eb0cf2c367021718506356a73bda219a (MD5) %R 10.1142/S0218202508002693 %0 Journal Article %J Calc. Var. Partial Differential Equations 33 (2008) 37-74 %D 2008 %T A second order minimality condition for the Mumford-Shah functional %A Filippo Cagnetti %A Maria Giovanna Mora %A Massimiliano Morini %X A 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. %B Calc. Var. Partial Differential Equations 33 (2008) 37-74 %G en_US %U http://hdl.handle.net/1963/1955 %1 2318 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-03-02T12:54:00Z\\nNo. of bitstreams: 1\\nCMM.pdf: 358759 bytes, checksum: c414c0080a17971ecba1251a5890b94f (MD5) %R 10.1007/s00526-007-0152-3 %0 Journal Article %J J. Funct. Anal. 254 (2008) 2816-2845 %D 2008 %T Solitons of linearly coupled systems of semilinear non-autonomous equations on Rn %A Antonio Ambrosetti %A Giovanna Cerami %A David Ruiz %X Using 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. %B J. Funct. Anal. 254 (2008) 2816-2845 %G en_US %U http://hdl.handle.net/1963/2175 %1 2069 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-04T08:29:15Z\\nNo. of bitstreams: 1\\nambceruiz.pdf: 305881 bytes, checksum: f00a4a8078e5c5d78d4309cceb317906 (MD5) %R 10.1016/j.jfa.2007.11.013 %0 Thesis %D 2008 %T Symmetries of noncommutative spaces and equivariant cohomology %A Lucio Cirio %K Noncommutative spaces %X As 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. %I SISSA %G en %U http://hdl.handle.net/1963/5254 %1 5077 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-01-23T08:57:48Z\\nNo. of bitstreams: 1\\nPhD_Cirio.pdf: 579480 bytes, checksum: 59e7b02846b913cd48e3c84e1e9a2bea (MD5) %0 Journal Article %J Phys. Rev. Lett. 98 (2007) 030404 %D 2007 %T Luther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas %A Gao Xianlong %A Matteo Rizzi %A Marco Polini %A Rosario Fazio %A Mario P. Tosi %A Vivaldo L. Jr. Campo %A Klaus Capelle %XThe 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.

%B Phys. Rev. Lett. 98 (2007) 030404 %G en_US %U http://hdl.handle.net/1963/2056 %1 2140 %2 Physics %3 Condensed Matter Theory %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-06T11:46:28Z\\nNo. of bitstreams: 1\\ncond-mat0609346v1.pdf: 218755 bytes, checksum: 06a409d540e05ece03bbac85198ee19c (MD5) %R 10.1103/PhysRevLett.98.030404 %0 Book Section %B Rigorous quantum field theory %D 2007 %T Massless scalar field in a two-dimensional de Sitter universe %A Marco Bertola %A Corbetta, Francesco %A Moschella, Ugo %B Rigorous quantum field theory %S Progr. Math. %I Birkhäuser %C Basel %V 251 %P 27–38 %G eng %0 Report %D 2007 %T Multi-bump solitons to linearly coupled systems of nonlinear Schrödinger equations %A Antonio Ambrosetti %A Eduardo Colorado %A David Ruiz %B Calc. Var. Partial Differential Equations 30 (2007) 85-112 %G en_US %U http://hdl.handle.net/1963/1835 %1 2381 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-06-13T09:30:35Z\\nNo. of bitstreams: 1\\n29M-2006.pdf: 394371 bytes, checksum: de96976aa35a5289ec5ab93a664b9be5 (MD5) %R 10.1007/s00526-006-0079-0 %0 Journal Article %J C. R. Math. 345 (2007) 647-652 %D 2007 %T Parametrized curves in Lagrange Grassmannians %A Igor Zelenko %A Li Chengbo %B C. R. Math. 345 (2007) 647-652 %G en_US %U http://hdl.handle.net/1963/2560 %1 1559 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-01-17T13:49:21Z\\nNo. of bitstreams: 1\\n0708.1100v1.pdf: 336234 bytes, checksum: d04e21a2139ddd8622a28c31cd370eed (MD5) %R 10.1016/j.crma.2007.10.034 %0 Report %D 2007 %T Soft elasticity and microstructure in smectic C elastomers %A Antonio DeSimone %A James Adams %A Sergio Conti %X Smectic 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. %B Contin. Mech. Thermodyn. 18 (2007) 319-334 %G en_US %U http://hdl.handle.net/1963/1811 %1 2403 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-04-12T09:42:24Z\\nNo. of bitstreams: 1\\nsissa05M-06.pdf: 394760 bytes, checksum: 95c4183d6cb1210bf2a689ae083a3cb7 (MD5) %R 10.1007/s00161-006-0031-8 %0 Report %D 2007 %T Standing waves of some coupled Nonlinear Schrödinger Equations %A Antonio Ambrosetti %A Eduardo Colorado %X We 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. %B J. Lond. Math. Soc. 75 (2007) 67-82 %G en_US %U http://hdl.handle.net/1963/1821 %1 2393 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-04-18T14:55:22Z\\nNo. of bitstreams: 1\\nsissa,2_2006_M.pdf: 431407 bytes, checksum: 0e294e77a4423c4b41ce178df2187dd3 (MD5) %R 10.1112/jlms/jdl020 %0 Report %D 2007 %T Twisted noncommutative equivariant %A Lucio Cirio %X We 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. %G en_US %U http://hdl.handle.net/1963/1991 %1 2205 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-08-09T12:36:58Z\\nNo. of bitstreams: 1\\nmathQA0706.3602v2.pdf: 303765 bytes, checksum: 74571e1a7df81268457a3ae54726fd75 (MD5) %0 Journal Article %J J. Hyperbolic Differ. Equ. 4 (2007) 771-795 %D 2007 %T Viscosity solutions of Hamilton-Jacobi equations with discontinuous coefficients %A Giuseppe Maria Coclite %A Nils Henrik Risebro %X We 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. %B J. Hyperbolic Differ. Equ. 4 (2007) 771-795 %I World Scientific %G en_US %U http://hdl.handle.net/1963/2907 %1 1793 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T10:55:33Z\\nNo. of bitstreams: 1\\nmath.AP0303288.pdf: 286583 bytes, checksum: ec274415af1f87dc1406bdc76cab8159 (MD5) %R 10.1142/S0219891607001355 %0 Journal Article %J Phys. Rev. B 73 (2006) 100502(R) %D 2006 %T 4e-condensation in a fully frustrated Josephson junction diamond chain %A Matteo Rizzi %A Vittorio Cataudella %A Rosario Fazio %XFully 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.

%B Phys. Rev. B 73 (2006) 100502(R) %G en_US %U http://hdl.handle.net/1963/2400 %1 2297 %2 Physics %3 Condensed Matter Theory %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-11-13T08:27:31Z\\nNo. of bitstreams: 1\\n0511423v1.pdf: 197406 bytes, checksum: 754c3576bbb6a549f4dac12eeb8fc92d (MD5) %R 10.1103/PhysRevB.73.100502 %0 Journal Article %J C. R. Acad. Sci. Paris, Ser. I 342 (2006) 453-458 %D 2006 %T Bound and ground states of coupled nonlinear Schrödinger equations %A Antonio Ambrosetti %A Eduardo Colorado %X We prove existence of bound and ground states of some systems of coupled nonlinear Schrodinger equations. %B C. R. Acad. Sci. Paris, Ser. I 342 (2006) 453-458 %G en_US %U http://hdl.handle.net/1963/2149 %1 2094 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-28T10:05:04Z\\nNo. of bitstreams: 1\\nAmbrosettiColorado05.pdf: 205538 bytes, checksum: 7ada83c882cd1488c72316a917a79c87 (MD5) %R 10.1016/j.crma.2006.01.024 %0 Journal Article %J SIAM J. Control Optim. 45 (2006) 226-245 %D 2006 %T Common Polynomial Lyapunov Functions for Linear Switched Systems %A Paolo Mason %A Ugo Boscain %A Yacine Chitour %X In 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. %B SIAM J. Control Optim. 45 (2006) 226-245 %G en_US %U http://hdl.handle.net/1963/2181 %1 2063 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-04T14:36:21Z\\nNo. of bitstreams: 1\\n0403209v2.pdf: 244831 bytes, checksum: 1762d79876f9eb915a68dbc25d9a3a21 (MD5) %R 10.1137/040613147 %0 Journal Article %J Arch. Ration. Mech. Anal. 181 (2006) 1-42 %D 2006 %T The Dirichlet problem for H-systems with small boundary data: blowup phenomena and nonexistence results %A Paolo Caldiroli %A Roberta Musina %B Arch. Ration. Mech. Anal. 181 (2006) 1-42 %G en_US %U http://hdl.handle.net/1963/2252 %1 1995 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-18T07:32:51Z\\nNo. of bitstreams: 1\\nCaldiroliMusina04.pdf: 395788 bytes, checksum: f37ad36b2fc2eb85d6430053a575ed8c (MD5) %R 10.1007/s00205-005-0398-x %0 Journal Article %J ESAIM Control Optim. Calc. Var. 12 (2006) 409-441 %D 2006 %T An estimation of the controllability time for single-input systems on compact Lie Groups %A Andrei A. Agrachev %A Thomas Chambrion %X Geometric 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. %B ESAIM Control Optim. Calc. Var. 12 (2006) 409-441 %G en_US %U http://hdl.handle.net/1963/2135 %1 2108 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-24T13:09:42Z\\nNo. of bitstreams: 1\\ncocv0452.pdf: 441157 bytes, checksum: 7c8ead7c835051e17567fe9bb8a60fbe (MD5) %R 10.1051/cocv:2006007 %0 Journal Article %J Adv. Differential Equations 11 (2006) 931-960 %D 2006 %T On Palais-Smale sequences for H-systems: some examples %A Paolo Caldiroli %A Roberta Musina %X We 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. %B Adv. Differential Equations 11 (2006) 931-960 %G en_US %U http://hdl.handle.net/1963/2157 %1 2087 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-02T07:36:26Z\\nNo. of bitstreams: 1\\n32M.pdf: 296654 bytes, checksum: 7052b4b72f783376708b6bc60c882375 (MD5) %0 Report %D 2006 %T Stability of planar nonlinear switched systems %A Ugo Boscain %A Grégoire Charlot %A Mario Sigalotti %X We 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. %B Discrete Contin. Dyn. Syst. 15 (2006) 415-432 %G en_US %U http://hdl.handle.net/1963/1710 %1 2441 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-01-18T08:35:31Z\\nNo. of bitstreams: 1\\nmath.OC0502361.pdf: 322404 bytes, checksum: e56f0d709d97e2e300e3cb9d4a629a1b (MD5) %0 Journal Article %J Comm. Anal. Geom. 13 (2005) 187-252 %D 2005 %T Asymptotic Morse theory for the equation $\\\\Delta v=2v\\\\sb x\\\\wedge v\\\\sb y$ %A Sagun Chanillo %A Andrea Malchiodi %X Given 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. %B Comm. Anal. Geom. 13 (2005) 187-252 %I International Press %G en_US %U http://hdl.handle.net/1963/3533 %1 731 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-20T10:28:24Z\\nNo. of bitstreams: 1\\n0205106v1.pdf: 508637 bytes, checksum: 9894eb1ef04ac61cd02aebdee04ff5fa (MD5) %0 Journal Article %J SIAM J. Control Optim. 43 (2005) 2166-2190 %D 2005 %T On the attainable set for Temple class systems with boundary controls %A Fabio Ancona %A Giuseppe Maria Coclite %X Consider 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. %B SIAM J. Control Optim. 43 (2005) 2166-2190 %I SISSA Library %G en %U http://hdl.handle.net/1963/1581 %1 2537 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:51Z (GMT). No. of bitstreams: 1\\nmath.AP0205167.pdf: 356214 bytes, checksum: 05474bd7744107031887816262b561b3 (MD5)\\n Previous issue date: 2002 %R 10.1137/S0363012902407776 %0 Journal Article %J SIAM J. Math. Anal. 36 (2005) 1293-1309 %D 2005 %T Conservation laws with time dependent discontinuous coefficients %A Giuseppe Maria Coclite %A Nils Henrik Risebro %X We 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]. %B SIAM J. Math. Anal. 36 (2005) 1293-1309 %I SISSA Library %G en %U http://hdl.handle.net/1963/1666 %1 2452 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:06:09Z (GMT). No. of bitstreams: 1\\n96_02.pdf: 3363466 bytes, checksum: 5ed39a522bb68737585e74668afafc5a (MD5)\\n Previous issue date: 2002 %R 10.1137/S0036141002420005 %0 Journal Article %J J. Dyn. Control Syst. 11 (2005) 297-327 %D 2005 %T On curvatures and focal points of distributions of dynamical Lagrangian distributions and their reductions by first integrals %A Andrei A. Agrachev %A Natalia N. Chtcherbakova %A Igor Zelenko %X Pairs (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. %B J. Dyn. Control Syst. 11 (2005) 297-327 %G en_US %U http://hdl.handle.net/1963/2254 %1 1993 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-18T08:53:27Z\\nNo. of bitstreams: 1\\n0409152v1.pdf: 335893 bytes, checksum: bf4dfeb39ad05ff60c2c2cc745fa0fc1 (MD5) %R 10.1007/s10883-005-6581-4 %0 Journal Article %J J. Phys. A 38 (2005) 4769-4781 %D 2005 %T Decay of a bound state under a time-periodic perturbation: a toy case %A Michele Correggi %A Gianfausto Dell'Antonio %X We 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. %B J. Phys. A 38 (2005) 4769-4781 %G en_US %U http://hdl.handle.net/1963/2298 %1 1718 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-25T08:22:58Z\\nNo. of bitstreams: 1\\n0408003v2.pdf: 207599 bytes, checksum: 256b29c96ea071184e9455fd1dd92717 (MD5) %R 10.1088/0305-4470/38/22/002 %0 Journal Article %J SIAM J. Math. Anal. 37 (2005) 996-1026 %D 2005 %T Global solutions of the Hunter-Saxton equation %A Alberto Bressan %A Adrian Constantin %X We 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. %B SIAM J. Math. Anal. 37 (2005) 996-1026 %G en_US %U http://hdl.handle.net/1963/2256 %1 1991 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-18T10:16:52Z\\nNo. of bitstreams: 1\\n0502059v1.pdf: 276204 bytes, checksum: ba0bfd37b8aa3a5ef2c0ef7358081cf9 (MD5) %R 10.1137/050623036 %0 Journal Article %J Comm. Math. Phys. 257 (2005) 169-192 %D 2005 %T Ionization for Three Dimensional Time-dependent Point Interactions %A Michele Correggi %A Gianfausto Dell'Antonio %A Rodolfo Figari %A Andrea Mantile %X We 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. %B Comm. Math. Phys. 257 (2005) 169-192 %G en_US %U http://hdl.handle.net/1963/2297 %1 1719 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-25T08:14:45Z\\nNo. of bitstreams: 1\\n0402011v2.pdf: 306766 bytes, checksum: 7efb2bcceb4c2699d662ae1af9e7dd76 (MD5) %R 10.1007/s00220-005-1293-x %0 Journal Article %J Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (5), 4 (2005) 129-177. %D 2005 %T Minimal surfaces in pseudohermitian geometry %A Jih-Hsin Cheng %A JennFang Hwang %A Andrea Malchiodi %A Paul Yang %X We 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. %B Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (5), 4 (2005) 129-177. %I Scuola Normale Superiore %G en %U http://hdl.handle.net/1963/4579 %1 4347 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-07T09:39:45Z No. of bitstreams: 1 math_0401136v3.pdf: 476553 bytes, checksum: 85c9b54a1f7e6c159e8fbc2486849a53 (MD5) %R 10.2422/2036-2145.2005.1.05 %0 Journal Article %J Discrete Contin. Dyn. Syst. Ser. B 5 (2005) 957-990 %D 2005 %T Nonisotropic 3-level quantum systems: complete solutions for minimum time and minimum energy %A Ugo Boscain %A Thomas Chambrion %A Grégoire Charlot %X We 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. %B Discrete Contin. Dyn. Syst. Ser. B 5 (2005) 957-990 %G en_US %U http://hdl.handle.net/1963/2259 %1 1988 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-18T11:55:27Z\\nNo. of bitstreams: 1\\n0409022v2.pdf: 578605 bytes, checksum: db7298996e781c3a8546c3d01ee28384 (MD5) %0 Journal Article %J Comput. Methods Appl. Mech. Engrg. 194 (2005) 2534-2549 %D 2005 %T Self-similar folding patterns and energy scaling in compressed elastic sheets %A Sergio Conti %A Antonio DeSimone %A Stefan Müller %X Thin 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. %B Comput. Methods Appl. Mech. Engrg. 194 (2005) 2534-2549 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3000 %1 1333 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-01T10:37:14Z\\nNo. of bitstreams: 1\\npreprint2004_3.pdf: 907333 bytes, checksum: 2b22c209b91ba2ddacc1a1c14a9054a2 (MD5) %R 10.1016/j.cma.2004.07.044 %0 Journal Article %J J. Math. Anal. Appl. 308 (2005) 221-239 %D 2005 %T Stability of solutions of quasilinear parabolic equations %A Giuseppe Maria Coclite %A Helge Holden %X We 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. %B J. Math. Anal. Appl. 308 (2005) 221-239 %I Elsevier %G en_US %U http://hdl.handle.net/1963/2892 %1 1808 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-10T12:48:15Z\\nNo. of bitstreams: 1\\n0306160v1.pdf: 240791 bytes, checksum: 4654ca0f7a1735bc7ee6666d37a2d57a (MD5) %R 10.1016/j.jmaa.2005.01.026 %0 Journal Article %J SIAM J. Control Optim. 44 (2005) 111-139 %D 2005 %T Time Optimal Synthesis for Left-Invariant Control Systems on SO(3) %A Ugo Boscain %A Yacine Chitour %X Consider 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. %B SIAM J. Control Optim. 44 (2005) 111-139 %G en_US %U http://hdl.handle.net/1963/2258 %1 1989 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-18T11:43:01Z\\nNo. of bitstreams: 1\\n0502483v1.pdf: 429552 bytes, checksum: 9f72f53d7031cdc7ccb2aca8b8ec16de (MD5) %R 10.1137/S0363012904441532 %0 Journal Article %J SIAM J. Math. Anal. 36 (2005) 1862-1886 %D 2005 %T Traffic flow on a road network %A Giuseppe Maria Coclite %A Benedetto Piccoli %A Mauro Garavello %X This 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. %B SIAM J. Math. Anal. 36 (2005) 1862-1886 %I SISSA Library %G en %U http://hdl.handle.net/1963/1584 %1 2534 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:54Z (GMT). No. of bitstreams: 1\\nmath.AP0202146.pdf: 256961 bytes, checksum: 51f64ff00e916dd87d3dd6df41903d23 (MD5)\\n Previous issue date: 2002 %R 10.1137/S0036141004402683 %0 Journal Article %J M2AN Math. Model. Numer. Anal. 38 (2004) 235-248 %D 2004 %T Energetics and switching of quasi-uniform states in small ferromagnetic particles %A François Alouges %A Sergio Conti %A Antonio DeSimone %A Ivo Pokern %X We 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. %B M2AN Math. Model. Numer. Anal. 38 (2004) 235-248 %I EDP Sciences %G en_US %U http://hdl.handle.net/1963/2999 %1 1334 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-01T10:25:50Z\\nNo. of bitstreams: 1\\npreprint2003_88.pdf: 297354 bytes, checksum: d907d5a9d74d0a3dcb244e26ff2af68a (MD5) %R 10.1051/m2an:2004011 %0 Journal Article %J Rev. Mat. Iberoamericana 20 (2004) 611-626 %D 2004 %T Existence of H-bubbles in a perturbative setting %A Paolo Caldiroli %A Roberta Musina %X Given 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. %B Rev. Mat. Iberoamericana 20 (2004) 611-626 %I SISSA Library %G en %U http://hdl.handle.net/1963/1606 %1 2512 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:13Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002 %0 Journal Article %J Moscow Math. J. 4 (2004)\\n313-332. %D 2004 %T The Extended Toda Hierarchy %A Guido Carlet %A Boris Dubrovin %A Zhang Youjin %B Moscow Math. J. 4 (2004)\\n313-332. %G en_US %U http://hdl.handle.net/1963/2542 %1 1577 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-21T12:22:27Z\\nNo. of bitstreams: 1\\n0306060v2.pdf: 242352 bytes, checksum: 7a4fc53dbf549eb7046e75be6c087368 (MD5) %0 Journal Article %J Duke Math. J. 122 (2004), no. 3, 457--484 %D 2004 %T H-bubbles in a perturbative setting: the finite-dimensional reduction\\\'s method %A Paolo Caldiroli %A Roberta Musina %X Given 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 $\\\\varepsilon\\\\to 0$. %B Duke Math. J. 122 (2004), no. 3, 457--484 %I SISSA Library %G en %U http://hdl.handle.net/1963/1607 %1 2511 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:13Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002 %R 10.1215/S0012-7094-04-12232-8 %0 Conference Proceedings %B 43rd IEEE Conference on Decision and Control, 2004, 2786 - 2791 Vol.3 %D 2004 %T On the minimal degree of a common Lyapunov function for planar switched systems %A Paolo Mason %A Ugo Boscain %A Yacine Chitour %X In 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. %B 43rd IEEE Conference on Decision and Control, 2004, 2786 - 2791 Vol.3 %I IEEE %G en %U http://hdl.handle.net/1963/4834 %1 4611 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-19T07:47:35Z\\nNo. of bitstreams: 0 %R 10.1109/CDC.2004.1428884 %0 Journal Article %J ESAIM COCV 10 (2004) 593-614 %D 2004 %T Resonance of minimizers for n-level quantum systems with an arbitrary cost %A Ugo Boscain %A Grégoire Charlot %X We 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. %B ESAIM COCV 10 (2004) 593-614 %I EDP Sciences %G en_US %U http://hdl.handle.net/1963/2910 %1 1790 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T12:22:45Z\\nNo. of bitstreams: 1\\n0308103v2.pdf: 290972 bytes, checksum: 2195a0a0002da9f91cbc9fff24262981 (MD5) %R 10.1051/cocv:2004022 %0 Journal Article %J Ann. Henri Poincare 5 (2004) 773-808 %D 2004 %T Rotating Singular Perturbations of the Laplacian %A Michele Correggi %A Gianfausto Dell'Antonio %X We 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). %B Ann. Henri Poincare 5 (2004) 773-808 %I Springer %G en_US %U http://hdl.handle.net/1963/2945 %1 1755 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-15T08:20:31Z\\nNo. of bitstreams: 1\\nmath-ph0307056.pdf: 360658 bytes, checksum: 16a12ce4dfd525b63e0a6e703ef9d7bf (MD5) %R 10.1007/s00023-004-0182-8 %0 Journal Article %J Electron. J. Differential Equations (2004) 94 %D 2004 %T Solitary waves for Maxwell Schrodinger equations %A Giuseppe Maria Coclite %A Vladimir Georgiev %X In 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. %B Electron. J. Differential Equations (2004) 94 %I SISSA Library %G en %U http://hdl.handle.net/1963/1582 %1 2536 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:52Z (GMT). No. of bitstreams: 1\\nmath.AP0303142.pdf: 326987 bytes, checksum: 37c172f10800ae7a41e5398f6a0a0a0e (MD5)\\n Previous issue date: 2002 %0 Thesis %D 2004 %T Time-dependent singular interactions %A Michele Correggi %K Rotating singular interactions %I SISSA %G en %U http://hdl.handle.net/1963/5310 %1 5135 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-01-31T10:36:04Z\\nNo. of bitstreams: 1\\nCorreggi_PhD.pdf: 7625881 bytes, checksum: 2f2f600f7e0b513322732b8a447ef88d (MD5) %0 Thesis %D 2003 %T Control Problems for Systems of Conservation Laws %A Giuseppe Maria Coclite %K Asymptotic Stabilization %I SISSA %G en %U http://hdl.handle.net/1963/5325 %1 5154 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Gerardina Cargnelutti (gerry@sissa.it) on 2012-02-01T11:55:57Z\\nNo. of bitstreams: 1\\nPhD_Coclite_Giuseppe_Maria.pdf: 6164510 bytes, checksum: 461d3d4a88e73be06d19b21a85ab149a (MD5) %0 Journal Article %J J.Math.Anal.Appl. 284 (2003) no.1, 49 %D 2003 %T An interior estimate for a nonlinear parabolic equation %A Giuseppe Maria Coclite %B J.Math.Anal.Appl. 284 (2003) no.1, 49 %I SISSA Library %G en %U http://hdl.handle.net/1963/1622 %1 2496 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:27Z (GMT). No. of bitstreams: 1\\nmath.AP0207193.pdf: 123937 bytes, checksum: e3147ae778a391681315f33680cefa66 (MD5)\\n Previous issue date: 2002 %R 10.1016/S0022-247X(03)00157-4 %0 Journal Article %J SIAM J.Control Optim. 41 (2003),no.2, 607 %D 2003 %T Some results on the boundary control of systems of conservation laws %A Alberto Bressan %A Fabio Ancona %A Giuseppe Maria Coclite %B SIAM J.Control Optim. 41 (2003),no.2, 607 %I SISSA Library %G en %U http://hdl.handle.net/1963/1615 %1 2503 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:20Z (GMT). No. of bitstreams: 1\\nmath.AP0205246.pdf: 155904 bytes, checksum: 294663b00a9e6b6ae91096fd628a942a (MD5)\\n Previous issue date: 2002 %R 10.1137/S0363012901392529 %0 Journal Article %J SIAM J. Control Optim. 41 (2002) 607-622 %D 2002 %T On the Boundary Control of Systems of Conservation Laws %A Alberto Bressan %A Giuseppe Maria Coclite %X The 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. %B SIAM J. Control Optim. 41 (2002) 607-622 %I SIAM %G en_US %U http://hdl.handle.net/1963/3070 %1 1263 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-10T10:05:11Z\\nNo. of bitstreams: 1\\n0108224v1.pdf: 198822 bytes, checksum: b08b507c4b17c8b48aaa3aafdc4d7360 (MD5) %R 10.1137/S0363012901392529 %0 Journal Article %J Nonlinear Anal. 48 (2002) 481-504 %D 2002 %T Chaotic dynamics for perturbations of infinite-dimensional Hamiltonian systems %A Massimiliano Berti %A Carlo Carminati %B Nonlinear Anal. 48 (2002) 481-504 %I Elsevier %G en %U http://hdl.handle.net/1963/1279 %1 3176 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:42Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %R 10.1016/S0362-546X(00)00200-5 %0 Journal Article %J Commun. Contemp. Math. 4 (2002) 177-209 %D 2002 %T Existence of minimal H-bubbles %A Paolo Caldiroli %A Roberta Musina %B Commun. Contemp. Math. 4 (2002) 177-209 %I SISSA Library %G en %U http://hdl.handle.net/1963/1525 %1 2638 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:37Z (GMT). No. of bitstreams: 1\\nmath.AP0006157.pdf: 242337 bytes, checksum: ad4f345871a0c7fb33e9c4bc361ce4d8 (MD5)\\n Previous issue date: 2000 %R 10.1142/S021919970200066X %0 Journal Article %J J.Dynam. Control Systems 8 (2002),no.4, 547 %D 2002 %T On the K+P problem for a three-level quantum system: optimality implies resonance %A Ugo Boscain %A Thomas Chambrion %A Jean-Paul Gauthier %B J.Dynam. Control Systems 8 (2002),no.4, 547 %I SISSA Library %G en %U http://hdl.handle.net/1963/1601 %1 2517 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:08Z (GMT). No. of bitstreams: 1\\nmath.OC0204233.pdf: 252630 bytes, checksum: 14283368a7848e46caf6447b4bad85d4 (MD5)\\n Previous issue date: 2002 %R 10.1023/A:1020767419671 %0 Journal Article %J Ann. Pol. Math. 79 (2002) 21-30 %D 2002 %T A multiplicity result for the Schrodinger-Maxwell equations with negative potential %A Giuseppe Maria Coclite %X We prove the existence of a sequence of radial solutions with negative energy of the Schrödinger-Maxwell equations under the action of a negative potential. %B Ann. Pol. Math. 79 (2002) 21-30 %I IMPAN %G en_US %U http://hdl.handle.net/1963/3053 %1 1280 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-09T15:31:03Z\\nNo. of bitstreams: 1\\n0109017v1.pdf: 119291 bytes, checksum: 3cab63ccaba611cce6115aa21acc9fbf (MD5) %0 Journal Article %J Ann.Physics 296 (2002), no.2, 371 %D 2002 %T Quantum mechanics and stochastic mechanics for compatible observables at different times %A Michele Correggi %A Giovanni Morchio %B Ann.Physics 296 (2002), no.2, 371 %I SISSA Library %G en %U http://hdl.handle.net/1963/1577 %1 2541 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T13:04:48Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002 %R 10.1006/aphy.2002.6236 %0 Journal Article %J Comm. Partial Differential Equations 27 (2002), no. 5-6, 847-876 %D 2002 %T Singular elliptic problems with critical growth %A Paolo Caldiroli %A Andrea Malchiodi %B Comm. Partial Differential Equations 27 (2002), no. 5-6, 847-876 %I Dekker %G en %U http://hdl.handle.net/1963/1268 %1 3187 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:34Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %R 10.1081/PDE-120004887 %0 Journal Article %J P. Am. Math. Soc., 2002, 130, 1961 %D 2002 %T On the Stability of the Standard Riemann Semigroup %A Stefano Bianchini %A Rinaldo M. Colombo %B P. Am. Math. Soc., 2002, 130, 1961 %I SISSA Library %G en %U http://hdl.handle.net/1963/1528 %1 2635 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:40Z (GMT). No. of bitstreams: 1\\nmath.AP0007055.pdf: 195640 bytes, checksum: 3708c7f60ae79e0790175863c0290b0e (MD5)\\n Previous issue date: 2000 %0 Journal Article %J Math. Control Signals Systems 14 (2001) 173-193 %D 2001 %T Controllability for discrete systems with a finite control set %A Yacine Chitour %A Benedetto Piccoli %B Math. Control Signals Systems 14 (2001) 173-193 %I Springer %G en_US %U http://hdl.handle.net/1963/3114 %1 1219 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-15T10:33:44Z\\nNo. of bitstreams: 1\\ncontrollability.pdf: 247896 bytes, checksum: 6f94f9b27348f59bb506c1e79beba6e1 (MD5) %R 10.1007/PL00009881 %0 Journal Article %J Adv. Differential Equations 6 (2001), no. 3, 303-326 %D 2001 %T Existence and nonexistence results for a class of nonlinear, singular Sturm-Liouville equations %A Paolo Caldiroli %A Roberta Musina %B Adv. Differential Equations 6 (2001), no. 3, 303-326 %I SISSA Library %G en %U http://hdl.handle.net/1963/1319 %1 3136 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:56:13Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %0 Book Section %B Nonlinear equations : methods, models and applications (Bergamo, 2001) / Daniela Lupo, Carlo D. Pagani, Bernhard Ruf, editors. - Basel : Birkhäuser, 2003. - (Progress in nonlinear differential equations and their applications; 54). - p. 61-77 %D 2001 %T S^2 type parametric surfaces with prescribed mean curvature and minimal energy %A Paolo Caldiroli %A Roberta Musina %B Nonlinear equations : methods, models and applications (Bergamo, 2001) / Daniela Lupo, Carlo D. Pagani, Bernhard Ruf, editors. - Basel : Birkhäuser, 2003. - (Progress in nonlinear differential equations and their applications; 54). - p. 61-77 %I Birkhauser %G en %U http://hdl.handle.net/1963/1605 %1 2513 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:12Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002 %0 Journal Article %J Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 4 (2001), no. 3, 609-633. %D 2001 %T Stationary states for a two-dimensional singular Schrodinger equation %A Paolo Caldiroli %A Roberta Musina %B Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 4 (2001), no. 3, 609-633. %I SISSA Library %G en %U http://hdl.handle.net/1963/1249 %1 3206 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:18Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %0 Journal Article %D 2000 %T On a Steffen\\\'s result about parametric surfaces with prescribed mean curvature %A Roberta Musina %A Paolo Caldiroli %I SISSA Library %G en %U http://hdl.handle.net/1963/1558 %1 2560 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:07Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %0 Book %B Mem. Amer. Math. Soc. 146 (2000), no. 694, 134 p. %D 2000 %T Well-posedness of the Cauchy problem for n x n systems of conservation laws %A Alberto Bressan %A Graziano Crasta %A Benedetto Piccoli %B Mem. Amer. Math. Soc. 146 (2000), no. 694, 134 p. %I American Mathematical Society %G en_US %U http://hdl.handle.net/1963/3495 %1 769 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-06T11:34:33Z\\nNo. of bitstreams: 1\\nbcpams.pdf: 323551 bytes, checksum: 9bc3f06472e13a47266da010edb58ba1 (MD5) %0 Journal Article %J M2AN 33 (1999) 651-672 %D 1999 %T Discrete approximation of the Mumford-Shah functional in dimension two %A Antonin Chambolle %A Gianni Dal Maso %B M2AN 33 (1999) 651-672 %I EDP Sciences %G en_US %U http://hdl.handle.net/1963/3588 %1 712 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-03-09T13:50:04Z\\nNo. of bitstreams: 1\\nDalMaso1999.pdf: 462659 bytes, checksum: 04dc23ba4544d5be9ebdd703da477c7e (MD5) %R 10.1051/m2an:1999156 %0 Journal Article %D 1999 %T A note on fractional KDV hierarchies. II. The bihamiltonian approach %A Paolo Casati %A Gregorio Falqui %A Marco Pedroni %I SISSA Library %G en %U http://hdl.handle.net/1963/1220 %1 2723 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:54:55Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %0 Journal Article %J Discrete Contin. Dynam. Systems 3 (1997), no. 4, 477--5 %D 1997 %T Viscosity solutions and uniquenessfor systems of inhomogeneous balance laws %A Graziano Crasta %A Benedetto Piccoli %B Discrete Contin. Dynam. Systems 3 (1997), no. 4, 477--5 %I SISSA Library %G en %U http://hdl.handle.net/1963/969 %1 3485 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:41:06Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Journal Article %D 1995 %T An existence result in a problem of the vectorial case of the calculus of variations %A Arrigo Cellina %A Sandro Zagatti %X SIAM J. Control Optim. 33 (1995) 960-970 %I SIAM %G en_US %U http://hdl.handle.net/1963/3513 %1 751 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-12T14:55:58Z\\nNo. of bitstreams: 1\\ncellina.pdf: 925141 bytes, checksum: d75c968d00d2e76a821d8ff4e31987ad (MD5) %0 Journal Article %D 1995 %T Special functions of bounded deformation %A Giovanni Bellettini %A Alessandra Coscia %A Gianni Dal Maso %I SISSA Library %G en %U http://hdl.handle.net/1963/978 %1 3476 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:41:13Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Journal Article %J Indiana Univ. Math. J. 44 (1995), no. 3, 677-725 %D 1995 %T Unique solutions of 2x2 conservation laws with large data %A Alberto Bressan %A Rinaldo M. Colombo %X For 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. %B Indiana Univ. Math. J. 44 (1995), no. 3, 677-725 %I Indiana University Mathematics Journal %G en %U http://hdl.handle.net/1963/975 %1 3479 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:41:11Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %R 10.1512/iumj.1995.44.2004 %0 Journal Article %J SIAM J. Control Optim. 32 (1994) 1114-1127 %D 1994 %T A version of Olech\\\'s lemma in a problem of the calculus of variations %A Arrigo Cellina %A Sandro Zagatti %X This 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. %B SIAM J. Control Optim. 32 (1994) 1114-1127 %I SIAM %G en_US %U http://hdl.handle.net/1963/3514 %1 750 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-12T14:59:35Z\\nNo. of bitstreams: 1\\ncellina.pdf: 1532989 bytes, checksum: a1e477c545eaaf66420216c3e5c4c153 (MD5) %R 10.1137/S0363012992234669 %0 Journal Article %J Proc.Amer.Math.Soc. 112 (1991), no.2, 413 %D 1991 %T A class of absolute retracts of dwarf spheroidal galaxies %A Alberto Bressan %A Arrigo Cellina %A Andrzej Fryszkowski %B Proc.Amer.Math.Soc. 112 (1991), no.2, 413 %I SISSA Library %G en %U http://hdl.handle.net/1963/837 %1 2954 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:38:33Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1989 %0 Journal Article %J Boll. Un. Mat. Ital. B (7) 4 (1990), no. 2, 295--311 %D 1990 %T Existence and continuous dependence for discontinuous O.D.E.s %A Alberto Bressan %A Giovanni Colombo %B Boll. Un. Mat. Ital. B (7) 4 (1990), no. 2, 295--311 %I SISSA Library %G en %U http://hdl.handle.net/1963/716 %1 3210 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:36:40Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1988 %0 Journal Article %J Rend.Sem.Mat.Univ. Padova, 83 (1990), 71-76 %D 1990 %T Existence of solutions for a class of non-convex differential inclusions %A Fabio Ancona %A Giovanni Colombo %B Rend.Sem.Mat.Univ. Padova, 83 (1990), 71-76 %I SISSA Library %G en %U http://hdl.handle.net/1963/792 %1 2999 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:38:01Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1989 %0 Journal Article %J Ann. Inst. H. Poincare\\\' Anal. Non Linére 7 (1990), no. 3, 123-160 %D 1990 %T G-convergence of monotone operators %A Valeria Chiadò Piat %A Gianni Dal Maso %A Anneliese Defranceschi %B Ann. Inst. H. Poincare\\\' Anal. Non Linére 7 (1990), no. 3, 123-160 %I SISSA Library %G en %U http://hdl.handle.net/1963/680 %1 3246 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:36:13Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1988 %0 Journal Article %J Partial differential equations and the calculus of variations : essays in honor of Ennio De Giorgi. - Boston : Birkhauser, 1989. - p. 285-309 %D 1989 %T Limits of obstacle problems for the area functional. %A Gianni Dal Maso %A Michele Carriero %A Antonio Leaci %A Eduardo Pascali %B Partial differential equations and the calculus of variations : essays in honor of Ennio De Giorgi. - Boston : Birkhauser, 1989. - p. 285-309 %I SISSA Library %G en %U http://hdl.handle.net/1963/577 %1 3327 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:34:36Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1987 %0 Journal Article %J Proc. Amer. Math. Soc. 106 (1989), no. 3, 771-775 %D 1989 %T Upper semicontinuous differential inclusions without convexity %A Alberto Bressan %A Arrigo Cellina %A Giovanni Colombo %B Proc. Amer. Math. Soc. 106 (1989), no. 3, 771-775 %I SISSA Library %G en %U http://hdl.handle.net/1963/670 %1 3256 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:36:07Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1988 %0 Journal Article %J J. Differential Equations 76 (1988), no. 1, 135-158. %D 1988 %T Generalized Baire category and differential inclusions in Banach spaces. %A Alberto Bressan %A Giovanni Colombo %B J. Differential Equations 76 (1988), no. 1, 135-158. %I SISSA Library %G en %U http://hdl.handle.net/1963/538 %1 3366 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:34:07Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1987 %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire 4 (1987), no. 3, 275-296 %D 1987 %T Solutions with minimal period for Hamiltonian systems in a potential well. %A Antonio Ambrosetti %A Vittorio Coti Zelati %B Ann. Inst. H. Poincare Anal. Non Lineaire 4 (1987), no. 3, 275-296 %I SISSA Library %G en %U http://hdl.handle.net/1963/466 %1 3437 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:32:46Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1985 %0 Journal Article %J J. Differential Equations 67 (1987), no. 2, 165-184 %D 1987 %T Symmetry breaking in Hamiltonian systems %A Antonio Ambrosetti %A Vittorio Coti Zelati %A Ivar Ekeland %B J. Differential Equations 67 (1987), no. 2, 165-184 %I SISSA Library %G en %U http://hdl.handle.net/1963/409 %1 3558 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:32:09Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1985 %0 Journal Article %J Lett. Nuovo Cim. 42 (1985) 70-72 %D 1985 %T Maximal acceleration and Sakharov's limiting temperature %A Eduardo R. Caianiello %A Giovanni Landi %XIt 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.

%B Lett. Nuovo Cim. 42 (1985) 70-72 %I Società Italiana di Fisica %G en %U http://hdl.handle.net/1963/372 %1 3595 %2 Physics %3 Elementary Particle Theory %$ Made available in DSpace on 2004-09-01T12:28:51Z (GMT). No. of bitstreams: 1\\n69_84.pdf: 77590 bytes, checksum: 43178eeeda3b943f920430cfd241f874 (MD5)\\n Previous issue date: 1984 %R 10.1007/BF02748306