We consider the asymptotic behavior of a system of multi-component trapped bosons, when the total particle number N becomes large. In the dilute regime, when the interaction potentials have the length scale of order O(N−1), we show that the leading order of the ground state energy is captured correctly by the Gross–Pitaevskii energy functional and that the many-body ground state fully condensates on the Gross–Pitaevskii minimizers. In the mean-field regime, when the interaction length scale is O(1), we are able to verify Bogoliubov’s approximation and obtain the second order expansion of the ground state energy. While such asymptotic results have several precursors in the literature on one-component condensates, the adaptation to the multi-component setting is non-trivial in various respects and the analysis will be presented in detail.

%B Reviews in Mathematical Physics %V 31 %P 1950005 %G eng %U https://doi.org/10.1142/S0129055X19500053 %R 10.1142/S0129055X19500053 %0 Report %D 2018 %T On Geometric Quantum Confinement in Grushin-Like Manifolds %A Matteo Gallone %A Alessandro Michelangeli %A Eugenio Pozzoli %X We study the problem of so-called geometric quantum confinement in a class of two-dimensional incomplete Riemannian manifold with metric of Grushin type. We employ a constant-fibre direct integral scheme, in combination with Weyl's analysis in each fibre, thus fully characterising the regimes of presence and absence of essential self-adjointness of the associated Laplace-Beltrami operator. %G en %U http://preprints.sissa.it/handle/1963/35322 %1 35632 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-09-19T07:05:15Z No. of bitstreams: 1 GMP-Grushin-SISSApreprint.pdf: 390608 bytes, checksum: c4bbb299a3b07668840d185c315c1a29 (MD5) %0 Journal Article %J Zeitschrift für angewandte Mathematik und Physik %D 2018 %T Global, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials %A Paolo Antonelli %A Alessandro Michelangeli %A Raffaele Scandone %XWe prove the existence of weak solutions in the space of energy for a class of nonlinear Schrödinger equations in the presence of a external, rough, time-dependent magnetic potential. Under our assumptions, it is not possible to study the problem by means of usual arguments like resolvent techniques or Fourier integral operators, for example. We use a parabolic regularisation, and we solve the approximating Cauchy problem. This is achieved by obtaining suitable smoothing estimates for the dissipative evolution. The total mass and energy bounds allow to extend the solution globally in time. We then infer sufficient compactness properties in order to produce a global-in-time finite energy weak solution to our original problem.

%B Zeitschrift für angewandte Mathematik und Physik %V 69 %P 46 %8 Mar %G eng %U https://doi.org/10.1007/s00033-018-0938-5 %R 10.1007/s00033-018-0938-5 %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 Journal of Geometry and Physics %D 2017 %T Gauge theories on compact toric surfaces, conformal field theories and equivariant Donaldson invariants %A Mikhail Bershtein %A Giulio Bonelli %A Massimiliano Ronzani %A Alessandro Tanzini %K AGT %K Donaldson invariants %K Equivariant localization %K Exact partition function %K Supersymmetry %K Virasoro conformal blocks %XWe show that equivariant Donaldson polynomials of compact toric surfaces can be calculated as residues of suitable combinations of Virasoro conformal blocks, by building on AGT correspondence between $\mathcal{N}=2$ supersymmetric gauge theories and two-dimensional conformal field theory. Talk presented by A.T. at the conference Interactions between Geometry and Physics — in honor of Ugo Bruzzo’s 60th birthday 17–22 August 2015, Guarujá, São Paulo, Brazil, mostly based on Bawane et al. (0000) and Bershtein et al. (0000).

%B Journal of Geometry and Physics %V 118 %P 40 - 50 %G eng %U http://www.sciencedirect.com/science/article/pii/S0393044017300165 %R https://doi.org/10.1016/j.geomphys.2017.01.012 %0 Journal Article %J ESAIM: COCV %D 2017 %T On the genesis of directional friction through bristle-like mediating elements %A Paolo Gidoni %A Antonio DeSimone %XWe propose an explanation of the genesis of directional dry friction, as emergent property of the oscillations produced in a bristle-like mediating element by the interaction with microscale fluctuations on the surface. Mathematically, we extend a convergence result by Mielke, for Prandtl–Tomlinson-like systems, considering also non-homothetic scalings of a wiggly potential. This allows us to apply the result to some simple mechanical models, that exemplify the interaction of a bristle with a surface having small fluctuations. We find that the resulting friction is the product of two factors: a geometric one, depending on the bristle angle and on the fluctuation profile, and a energetic one, proportional to the normal force exchanged between the bristle-like element and the surface. Finally, we apply our result to discuss the with the nap/against the nap asymmetry.

%B ESAIM: COCV %V 23 %P 1023-1046 %G eng %U https://doi.org/10.1051/cocv/2017030 %R 10.1051/cocv/2017030 %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 Journal of Nonlinear Mathematical Physics %D 2017 %T Gross-Pitaevskii non-linear dynamics for pseudo-spinor condensates %A Alessandro Michelangeli %A Alessandro Olgiati %XWe derive the equations for the non-linear effective dynamics of a so called pseudo-spinor Bose-Einstein condensate, which emerges from the linear many-body Schrödinger equation at the leading order in the number of particles. The considered system is a three-dimensional diluted gas of identical bosons with spin, possibly confined in space, and coupled with an external time-dependent magnetic field; particles also interact among themselves through a short-scale repulsive interaction. The limit of infinitely many particles is monitored in the physically relevant Gross-Pitaevskii scaling. In our main theorem, if at time zero the system is in a phase of complete condensation (at the level of the reduced one-body marginal) and with energy per particle fixed by the Gross-Pitaevskii functional, then such conditions persist also at later times, with the one-body orbital of the condensate evolving according to a system of non-linear cubic Schrödinger equations coupled among themselves through linear (Rabi) terms. The proof relies on an adaptation to the spinor setting of Pickl’s projection counting method developed for the scalar case. Quantitative rates of convergence are available, but not made explicit because evidently non-optimal. In order to substantiate the formalism and the assumptions made in the main theorem, in an introductory section we review the mathematical formalisation of modern typical experiments with pseudo-spinor condensates.

%B Journal of Nonlinear Mathematical Physics %I Taylor & Francis %V 24 %P 426-464 %G eng %U https://doi.org/10.1080/14029251.2017.1346348 %R 10.1080/14029251.2017.1346348 %0 Journal Article %J Annali di Matematica Pura ed Applicata (1923 -) %D 2016 %T Generalizing the Poincaré–Miranda theorem: the avoiding cones condition %A Alessandro Fonda %A Paolo Gidoni %XAfter proposing a variant of the Poincaré–Bohl theorem, we extend the Poincaré–Miranda theorem in several directions, by introducing an avoiding cones condition. We are thus able to deal with functions defined on various types of convex domains, and situations where the topological degree may be different from \$\$\backslashpm \$\$±1. An illustrative application is provided for the study of functionals having degenerate multi-saddle points.

%B Annali di Matematica Pura ed Applicata (1923 -) %V 195 %P 1347–1371 %8 Aug %G eng %U https://doi.org/10.1007/s10231-015-0519-6 %R 10.1007/s10231-015-0519-6 %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 Journal Article %J Journal of Noncommutative Geometry %D 2016 %T The Gysin sequence for quantum lens spaces %A Francesca Arici %A Simon Brain %A Giovanni Landi %XWe define quantum lens spaces as ‘direct sums of line bundles’ and exhibit them as ‘total spaces’ of certain principal bundles over quantum projective spaces. For each of these quantum lens spaces we construct an analogue of the classical Gysin sequence in K-theory. We use the sequence to compute the K-theory of the quantum lens spaces, in particular to give explicit geometric representatives of their K-theory classes. These representatives are interpreted as ‘line bundles’ over quantum lens spaces and generically define ‘torsion classes’. We work out explicit examples of these classes.

%B Journal of Noncommutative Geometry %V 9 %P 1077–1111 %G eng %R 10.4171/JNCG/216 %0 Journal Article %J Advances in Mathematics %D 2015 %T A general existence result for the Toda system on compact surfaces %A Luca Battaglia %A Aleks Jevnikar %A Andrea Malchiodi %A David Ruiz %K Geometric PDEs %K Min–max schemes %K Variational methods %XIn this paper we consider the following Toda system of equations on a compact surface:−Δu1=2ρ1(h1eu1∫Σh1eu1dVg−1)−ρ2(h2eu2∫Σh2eu2dVg−1)−Δu1=−4π∑j=1mα1,j(δpj−1),−Δu2=2ρ2(h2eu2∫Σh2eu2dVg−1)−ρ1(h1eu1∫Σh1eu1dVg−1)−Δu2=−4π∑j=1mα2,j(δpj−1), which is motivated by the study of models in non-abelian Chern–Simons theory. Here h1,h2 are smooth positive functions, ρ1,ρ2 two positive parameters, pi points of the surface and α1,i,α2,j non-negative numbers. We prove a general existence result using variational methods. The same analysis applies to the following mean field equation−Δu=ρ1(heu∫ΣheudVg−1)−ρ2(he−u∫Σhe−udVg−1), which arises in fluid dynamics."

%B Advances in Mathematics %V 285 %P 937 - 979 %G eng %U http://www.sciencedirect.com/science/article/pii/S0001870815003072 %R https://doi.org/10.1016/j.aim.2015.07.036 %0 Journal Article %J Geometry & Topology %D 2015 %T Geodesics and horizontal-path spaces in Carnot groups %A Andrei A. Agrachev %A Alessandro Gentile %A Antonio Lerario %XWe study properties of the space of horizontal paths joining the origin with a vertical point on a generic two-step Carnot group. The energy is a Morse-Bott functional on paths and its critical points (sub-Riemannian geodesics) appear in families (compact critical manifolds) with controlled topology. We study the asymptotic of the number of critical manifolds as the energy grows. The topology of the horizontal-path space is also investigated, and we find asymptotic results for the total Betti number of the sublevels of the energy as it goes to infinity. We interpret these results as local invariants of the sub-Riemannian structure.

%B Geometry & Topology %I Mathematical Sciences Publishers %V 19 %P 1569–1630 %G eng %R 10.2140/gt.2015.19.1569 %0 Thesis %D 2015 %T Geometric phases in graphene and topological insulators %A Domenico Monaco %K Geometric phases, graphene, topological insulators, Wannier functions, Bloch frames %X This thesis collects three of the publications that the candidate produced during his Ph.D. studies. They all focus on geometric phases in solid state physics. We first study topological phases of 2-dimensional periodic quantum systems, in absence of a spectral gap, like e.g. (multilayer) graphene. A topological invariant n_v in Z, baptized eigenspace vorticity, is attached to any intersection of the energy bands, and characterizes the local topology of the eigenprojectors around that intersection. With the help of explicit models, each associated to a value of n_v in Z, we are able to extract the decay at infinity of the single-band Wannier function w in mono- and bilayer graphene, obtaining |w(x)| <= const |x|^{-2} as |x| tends to infinity. Next, we investigate gapped periodic quantum systems, in presence of time-reversal symmetry. When the time-reversal operator Theta is of bosonic type, i.e. it satisfies Theta^2 = 1, we provide an explicit algorithm to construct a frame of smooth, periodic and time-reversal symmetric (quasi-)Bloch functions, or equivalently a frame of almost-exponentially localized, real-valued (composite) Wannier functions, in dimension d <= 3. In the case instead of a fermionic time-reversal operator, satisfying Theta^2 = -1, we show that the existence of such a Bloch frame is in general topologically obstructed in dimension d=2 and d=3. This obstruction is encoded in Z_2-valued topological invariants, which agree with the ones proposed in the solid state literature by Fu, Kane and Mele. %I SISSA %G en %1 34702 %2 Mathematics %4 1 %# MAT/07 %$ Submitted by Domenico Monaco (dmonaco@sissa.it) on 2015-09-13T00:09:51Z No. of bitstreams: 1 Monaco_PhDThesis.pdf: 1801696 bytes, checksum: 83cdd0dee2cc65cb246735d92f21c74a (MD5) %0 Thesis %D 2015 %T Gibbs-Markov-Young Structures and Decay of Correlations %A Marks Ruziboev %K Decay of Correlations, GMY-towers %X In this work we study mixing properties of discrete dynamical systems and related to them geometric structure. In the first chapter we show that the direct product of maps with Young towers admits a Young tower whose return times decay at a rate which is bounded above by the slowest of the rates of decay of the return times of the component maps. An application of this result, together with other results in the literature, yields various statistical properties for the direct product of various classes of systems, including Lorenz-like maps, multimodal maps, piecewise $C^2$ interval maps with critical points and singularities, H\'enon maps and partially hyperbolic systems. The second chapter is dedicated to the problem of decay of correlations for continuous observables. First we show that if the underlying system admits Young tower then the rate of decay of correlations for continuous observables can be estimated in terms of modulus of continuity and the decay rate of tail of Young tower. In the rest of the second chapter we study the relations between the rates of decay of correlations for smooth observables and continuous observables. We show that if the rates of decay of correlations is known for $C^r,$ observables ($r\ge 1$) then it is possible to obtain decay of correlations for continuous observables in terms of modulus of continuity. %I SISSA %G en %1 34677 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by mruziboe@sissa.it (mruziboe@sissa.it) on 2015-08-10T16:44:24Z No. of bitstreams: 1 ruziboev_thesis.pdf: 745751 bytes, checksum: 7743d9fe13df739ad5fe5dd9a0eed202 (MD5) %0 Journal Article %D 2015 %T Gli abachi: antichi strumenti precursori delle moderne macchine da calcolo %A Giuliano Klun %G eng %U http://hdl.handle.net/10077/10884 %0 Report %D 2015 %T Global well-posedness of the magnetic Hartree equation with non-Strichartz external fields %A Alessandro Michelangeli %X We study the magnetic Hartree equation with external fields to which magnetic Strichartz estimates are not necessarily applicable. We characterise the appropriate notion of energy space and in such a space we prove the global well-posedness of the associated initial value problem by means of energy methods only. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/34440 %1 34567 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-02-09T07:36:23Z No. of bitstreams: 1 SISSA_preprint_07-2015-MATE.pdf: 185909 bytes, checksum: ae723e94b4951f0092f096c72ebf14d6 (MD5) %0 Thesis %D 2014 %T Geometry and analysis of control-affine systems: motion planning, heat and Schrödinger evolution %A Dario Prandi %K control theory %X This thesis is dedicated to two problems arising from geometric control theory, regarding control-affine systems $\dot q= f_0(q)+\sum_{j=1}^m u_j f_j(q)$, where $f_0$ is called the drift. In the first part we extend the concept of complexity of non-admissible trajectories, well understood for sub-Riemannian systems, to this more general case, and find asymptotic estimates. In order to do this, we also prove a result in the same spirit as the Ball-Box theorem for sub-Riemannian systems, in the context of control-affine systems equipped with the L1 cost. Then, in the second part of the thesis, we consider a family of 2-dimensional driftless control systems. For these, we study how the set where the control vector fields become collinear affects the diffusion dynamics. More precisely, we study whether solutions to the heat and Schrödinger equations associated with this Laplace-Beltrami operator are able to cross this singularity, and how its the presence affects the spectral properties of the operator, in particular under a magnetic Aharonov–Bohm-type perturbation. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/7474 %1 7576 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by dprandi@sissa.it (dprandi@sissa.it) on 2014-10-28T17:03:22Z No. of bitstreams: 1 thesis_SISSA.pdf: 2610057 bytes, checksum: b1f6802988c3d34412407d628c7c1963 (MD5) %0 Journal Article %D 2014 %T Global Structure of Admissible BV Solutions to Piecewise Genuinely Nonlinear, Strictly Hyperbolic Conservation Laws in One Space Dimension %A Stefano Bianchini %A Lei Yu %XThe paper describes the qualitative structure of an admissible BV solution to a strictly hyperbolic system of conservation laws whose characteristic families are piecewise genuinely nonlinear. More precisely, we prove that there are a countable set of points Θ and a countable family of Lipschitz curves T{script} such that outside T{script} ∪ Θ the solution is continuous, and for all points in T{script}{set minus}Θ the solution has left and right limit. This extends the corresponding structural result in [7] for genuinely nonlinear systems. An application of this result is the stability of the wave structure of solution w.r.t. -convergence. The proof is based on the introduction of subdiscontinuities of a shock, whose behavior is qualitatively analogous to the discontinuities of the solution to genuinely nonlinear systems.

%I Taylor & Francis %G en %U http://urania.sissa.it/xmlui/handle/1963/34694 %1 34908 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-10-22T09:34:23Z No. of bitstreams: 1 global structure of solutions to PWGN hyperbolic conservation laws.pdf: 452219 bytes, checksum: 85bd51fc08fa53a087cee8aec2b9544a (MD5) %R 10.1080/03605302.2013.775153 %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 %J Topol. Methods Nonlinear Anal. %D 2013 %T Generalized Sturm-Liouville boundary conditions for first order differential systems in the plane %A Alessandro Fonda %A Maurizio Garrione %XWe study asymptotically positively homogeneous first order systems in the plane, with boundary conditions which are positively homogeneous, as well. Defining a generalized concept of Fučík spectrum which extends the usual one for the scalar second order equation, we prove existence and multiplicity of solutions. In this way, on one hand we extend to the plane some known results for scalar second order equations (with Dirichlet, Neumann or Sturm-Liouville boundary conditions), while, on the other hand, we investigate some other kinds of boundary value problems, where the boundary points are chosen on a polygonal line, or in a cone. Our proofs rely on the shooting method.

%B Topol. Methods Nonlinear Anal. %I Nicolaus Copernicus University, Juliusz P. Schauder Centre for Nonlinear Studies %V 42 %P 293–325 %G eng %U https://projecteuclid.org:443/euclid.tmna/1461248981 %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 de Mathématiques Pures et Appliquées, Available online 12 September 2012 %D 2012 %T Gamma-convergence and H-convergence of linear elliptic operators %A Nadia Ansini %A Gianni Dal Maso %A Caterina Ida Zeppieri %K Linear elliptic operators %B Journal de Mathématiques Pures et Appliquées, Available online 12 September 2012 %I Elsevier %G en %U http://hdl.handle.net/1963/5878 %1 5746 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-05-30T13:02:32Z\\r\\nNo. of bitstreams: 1\\r\\n04M_2012_Ansini.pdf: 226441 bytes, checksum: 789582b685e552b522a3e8a896e091f8 (MD5) %R 10.1016/j.matpur.2012.09.004 %0 Journal Article %J Lett. Math. Phys. 101 (2012) 103-124 %D 2012 %T Gauge Theories on ALE Space and Super Liouville Correlation Functions %A Giulio Bonelli %A Kazunobu Maruyoshi %A Alessandro Tanzini %X We present a relation between N=2 quiver gauge theories on the ALE space O_{P^1}(-2) and correlators of N=1 super Liouville conformal field theory, providing checks in the case of punctured spheres and tori. We derive a blow-up formula for the full Nekrasov partition function and show that, up to a U(1) factor, the N=2^* instanton partition function is given by the product of the character of \\\\hat{SU}(2)_2 times the super Virasoro conformal block on the torus with one puncture. %B Lett. Math. Phys. 101 (2012) 103-124 %I SISSA %G en %U http://hdl.handle.net/1963/4305 %1 4068 %2 Physics %3 Elementary Particle Theory %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-28T07:00:50Z\\r\\nNo. of bitstreams: 1\\r\\n1107.4609v1.pdf: 256160 bytes, checksum: f34c8fc8ed919adff7b4d65312b81db1 (MD5) %R 10.1007/s11005-012-0553-x %0 Journal Article %J Journal of Differential Equations %D 2012 %T A general method for the existence of periodic solutions of differential systems in the plane %A Alessandro Fonda %A Andrea Sfecci %K Nonlinear dynamics %K Periodic solutions %XWe propose a general method to prove the existence of periodic solutions for planar systems of ordinary differential equations, which can be used in many different circumstances. Applications are given to some nonresonant cases, even for systems with superlinear growth in some direction, or with a singularity. Systems “at resonance” are also considered, provided a Landesman–Lazer type of condition is assumed.

%B Journal of Differential Equations %V 252 %P 1369 - 1391 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022039611003196 %R https://doi.org/10.1016/j.jde.2011.08.005 %0 Book Section %B Springer, Indam Series, Vol. 4, 2012 %D 2012 %T Generalized reduced basis methods and n-width estimates for the approximation of the solution manifold of parametric PDEs %A Toni Lassila %A Andrea Manzoni %A Alfio Quarteroni %A Gianluigi Rozza %K solution manifold %X The set of solutions of a parameter-dependent linear partial di fferential equation with smooth coe fficients typically forms a compact manifold in a Hilbert space. In this paper we review the generalized reduced basis method as a fast computational tool for the uniform approximation of the solution manifold. We focus on operators showing an affi ne parametric dependence, expressed as a linear combination of parameter-independent operators through some smooth, parameter-dependent scalar functions. In the case that the parameter-dependent operator has a dominant term in its affi ne expansion, one can prove the existence of exponentially convergent uniform approximation spaces for the entire solution manifold. These spaces can be constructed without any assumptions on the parametric regularity of the manifold \\r\\nonly spatial regularity of the solutions is required. The exponential convergence rate is then inherited by the generalized reduced basis method. We provide a numerical example related to parametrized elliptic\\r\\nequations con rming the predicted convergence rates. %B Springer, Indam Series, Vol. 4, 2012 %I Springer %G en %U http://hdl.handle.net/1963/6340 %1 6270 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2012-12-13T17:47:45Z\\nNo. of bitstreams: 1\\nqlmr-bumi_FINAL_SISSAreport.pdf: 377397 bytes, checksum: ecaf5713afa6a6f68992f6331631aff4 (MD5) %0 Journal Article %J Russian Journal of Mathematical Physics. Volume 19, Issue 3, September 2012, Pages 273-298 %D 2012 %T On the genus two free energies for semisimple Frobenius manifolds %A Boris Dubrovin %A Si-Qi Liu %A Youjin Zhang %X We represent the genus two free energy of an arbitrary semisimple Frobenius\\r\\nmanifold as a sum of contributions associated with dual graphs of certain\\r\\nstable algebraic curves of genus two plus the so-called \\\"genus two G-function\\\".\\r\\nConjecturally the genus two G-function vanishes for a series of important\\r\\nexamples of Frobenius manifolds associated with simple singularities as well as\\r\\nfor ${\\\\bf P}^1$-orbifolds with positive Euler characteristics. We explain the\\r\\nreasons for such Conjecture and prove it in certain particular cases. %B Russian Journal of Mathematical Physics. Volume 19, Issue 3, September 2012, Pages 273-298 %I SISSA %G en %U http://hdl.handle.net/1963/6464 %1 6411 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-08T11:35:38Z\\nNo. of bitstreams: 1\\n1205.5990v1.pdf: 547320 bytes, checksum: 9c9d894fbe3241c632b6cab13379f9c9 (MD5) %R 10.1134/S1061920812030028 %0 Journal Article %J Continuum. Mech. Therm. %D 2011 %T Gamma-convergence of energies for nematic elastomers in the small strain limit %A Virginia Agostiniani %A Antonio DeSimone %K Liquid crystals %XWe study two variational models recently proposed in the literature to describe the mechanical behaviour of nematic elastomers either in the fully nonlinear regime or in the framework of a geometrically linear theory. We show that, in the small strain limit, the energy functional of the first one I\\\"-converges to the relaxation of the second one, a functional for which an explicit representation formula is available.

%B Continuum. Mech. Therm. %I Springer %V 23 %G en %U http://hdl.handle.net/1963/4141 %1 3882 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-15T13:10:38Z\\nNo. of bitstreams: 1\\nAgost_DeSim07M.pdf: 348761 bytes, checksum: b9b69eb7da7ca6962e4a46e904646a6b (MD5) %& 257 %R 10.1007/s00161-011-0180-2 %0 Journal Article %J J. Eur. Math. Soc. (JEMS), to appear %D 2011 %T Generalised functions of bounded deformation %A Gianni Dal Maso %K free discontinuity problems, special functions of bounded deformation, jump set, rec- tifiability, slicing, approximate differentiability %XWe introduce the space GBD of generalized functions of bounded deformation and study the structure properties of these functions: the rectifiability and the slicing properties of their jump sets, and the existence of their approximate symmetric gradients. We conclude by proving a compactness results for GBD, which leads to a compactness result for the space GSBD of generalized special functions of bounded deformation. The latter is connected to the existence of solutions to a weak formulation of some variational problems arising in fracture mechanics in the framework of linearized elasticity.

%B J. Eur. Math. Soc. (JEMS), to appear %I SISSA %G en %U http://hdl.handle.net/1963/6374 %1 6309 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-10T18:54:48Z\\nNo. of bitstreams: 1\\nDM-11.pdf: 413971 bytes, checksum: eca2a953ba1b97755da281bca4e099e4 (MD5) %0 Journal Article %J JHEP, Volume 2011, Issue 7, 2011, Article number055 %D 2011 %T Generalized matrix models and AGT correspondence at all genera %A Giulio Bonelli %A Kazunobu Maruyoshi %A Alessandro Tanzini %A Futoshi Yagib %X We study generalized matrix models corresponding to n-point Virasoro\r\nconformal blocks on Riemann surfaces with arbitrary genus g. Upon AGT\r\ncorrespondence, these describe four dimensional N=2 SU(2)^{n+3g-3} gauge\r\ntheories with generalized quiver diagrams. We obtain the generalized matrix\r\nmodels from the perturbative evaluation of the Liouville correlation functions\r\nand verify the consistency of the description with respect to degenerations of\r\nthe Riemann surface. Moreover, we derive the Seiberg-Witten curve for the N=2\r\ngauge theory as the spectral curve of the generalized matrix model, thus\r\nproviding a check of AGT correspondence at all genera. %B JHEP, Volume 2011, Issue 7, 2011, Article number055 %I SISSA %G en %U http://hdl.handle.net/1963/6568 %1 6530 %2 Mathematics %4 1 %$ Submitted by Alessandro Tanzini (tanzini@sissa.it) on 2013-04-04T10:07:44Z\nNo. of bitstreams: 1\n1011.5417v2.pdf: 288213 bytes, checksum: 4ffb3884bb05de0280c0f8a0dc7847ab (MD5) %R 10.1007/JHEP07(2011)055 %0 Journal Article %D 2011 %T Generalized Ricci Curvature Bounds for Three Dimensional Contact Subriemannian manifolds %A Andrei A. Agrachev %A Paul Lee %I SISSA %G en %U http://hdl.handle.net/1963/6507 %1 6454 %2 Mathematics %4 1 %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-02-27T15:07:16Z\nNo. of bitstreams: 2\n0903.2550v3.pdf: 413981 bytes, checksum: 6f08d5002703670b5985e13d642ef755 (MD5)\n0903.2550v3.pdf: 413981 bytes, checksum: 6f08d5002703670b5985e13d642ef755 (MD5) %0 Journal Article %J Proceedings of the Steklov Institute of mathematics. vol. 273 (2011), page: 5-27 ; ISSN: 0081-5438 %D 2011 %T The geometry of Maximum Principle %A Andrei A. Agrachev %A Revaz Gamkrelidze %X An invariant formulation of the maximum principle in optimal control is presented, and some second-order invariants are discussed. %B Proceedings of the Steklov Institute of mathematics. vol. 273 (2011), page: 5-27 ; ISSN: 0081-5438 %G en %U http://hdl.handle.net/1963/6456 %1 6401 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-02-05T14:28:16Z\\nNo. of bitstreams: 0 %0 Journal Article %J Rend. Istit. Mat. Univ. Trieste 42 (2010) 103-128 %D 2010 %T Gauge theory: from physics to geometry %A Ugo Bruzzo %X Maxwell theory may be regarded as a prototype of gauge theory and generalized to nonabelian gauge theory. We briey sketch the history of the gauge theories, from Maxwell to Yang-Mills theory, and the identification of gauge fields with connections on fibre bundles. We introduce the notion of instanton and consider the moduli spaces of such objects. Finally, we discuss some modern techniques for studying the topology of these moduli spaces. %B Rend. Istit. Mat. Univ. Trieste 42 (2010) 103-128 %I Istituto di matematica. Universita\\\' di Trieste %G en_US %U http://hdl.handle.net/1963/4105 %1 299 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-11-17T09:12:32Z\\r\\nNo. of bitstreams: 1\\r\\nBruzzo_80FM.pdf: 651780 bytes, checksum: 65c68609e094a11090d91cf1207e2c2b (MD5) %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 Journal of Functional Analysis %D 2010 %T Generic multiplicity for a scalar field equation on compact surfaces %A Francesca De Marchis %K Generic multiplicity %K Geometric PDE's %K Morse inequalities %K Scalar field equations %XWe prove generic multiplicity of solutions for a scalar field equation on compact surfaces via Morse inequalities. In particular our result improves significantly the multiplicity estimate which can be deduced from the degree-counting formula in Chen and Lin (2003) [12]. Related results are derived for the prescribed Q-curvature equation.

%B Journal of Functional Analysis %V 259 %P 2165 - 2192 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022123610002697 %R https://doi.org/10.1016/j.jfa.2010.07.003 %0 Journal Article %J Int. Math. Res. Not. (2010) 2010:279-296 %D 2010 %T On the geometric origin of the bi-Hamiltonian structure of the Calogero-Moser system %A Claudio Bartocci %A Gregorio Falqui %A Igor Mencattini %A Giovanni Ortenzi %A Marco Pedroni %X We show that the bi-Hamiltonian structure of the rational n-particle (attractive) Calogero-Moser system can be obtained by means of a double projection from a very simple Poisson pair on the cotangent bundle of gl(n,R). The relation with the Lax formalism is also discussed. %B Int. Math. Res. Not. (2010) 2010:279-296 %I Oxford University Press %G en_US %U http://hdl.handle.net/1963/3800 %1 8 %2 LISNU %3 Interdisciplinary Laboratory for Advanced Studies %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-11-26T17:50:52Z\\nNo. of bitstreams: 1\\n0902.0953v2.pdf: 202665 bytes, checksum: 95f41e27482c7e7a0d598e06ea7e7763 (MD5) %R 10.1093/imrn/rnp130 %0 Report %D 2010 %T The geometry emerging from the symmetries of a quantum system %A Giuseppe De Nittis %A Gianluca Panati %X We investigate the relation between the symmetries of a quantum system and its topological quantum numbers, in a general C*-algebraic framework. We prove that, under suitable assumptions on the symmetry algebra, there exists a generalization of the Bloch-Floquet transform which induces a direct-integral decomposition of the algebra of observables. Such generalized transform selects uniquely the set of \\\"continuous sections\\\" in the direct integral, thus yielding a Hilbert bundle. The emerging geometric structure provides some topological invariants of the quantum system. Two running examples provide an Ariadne\\\'s thread through the paper. For the sake of completeness, we review two related theorems by von Neumann and Maurin and compare them with our result. %G en_US %U http://hdl.handle.net/1963/3834 %1 493 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-01-26T16:38:34Z\\nNo. of bitstreams: 1\\n0911.5270v2.pdf: 578198 bytes, checksum: a06ef54ebf418d5d7b6d0a7c3410c054 (MD5) %0 Journal Article %J Discrete & Continuous Dynamical Systems-A %D 2010 %T A global compactness result for the p-Laplacian involving critical nonlinearities %A Mercuri, Carlo %A Willem, Michel %XWe prove a representation theorem for Palais-Smale sequences involving the p-Laplacian and critical nonlinearities. Applications are given to a critical problem.

%B Discrete & Continuous Dynamical Systems-A %V 28 %P 469–493 %G eng %U http://www.aimsciences.org/journals/displayArticles.jsp?paperID=5097 %R 10.3934/dcds.2010.28.469 %0 Journal Article %J Comm. Math. Phys. 287 (2009) 179-209 %D 2009 %T Gauged Laplacians on quantum Hopf bundles %A Giovanni Landi %A Cesare Reina %A Alessandro Zampini %X We study gauged Laplacian operators on line bundles on a quantum 2-dimensional sphere. Symmetry under the (co)-action of a quantum group allows for their complete diagonalization. These operators describe `excitations moving on the quantum sphere\\\' in the field of a magnetic monopole. The energies are not invariant under the exchange monopole/antimonopole, that is under inverting the direction of the magnetic field. There are potential applications to models of quantum Hall effect. %B Comm. Math. Phys. 287 (2009) 179-209 %I Springer %G en_US %U http://hdl.handle.net/1963/3540 %1 1161 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-24T09:35:24Z\\nNo. of bitstreams: 1\\n0801.3376v2.pdf: 353792 bytes, checksum: 1153ca993428f38ef95f7d31cd727743 (MD5) %R 10.1007/s00220-008-0672-5 %0 Journal Article %J Discrete Contin. Dyn. Syst. 20 (2008) 801-822 %D 2008 %T A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds %A Andrei A. Agrachev %A Ugo Boscain %A Mario Sigalotti %X We consider a generalization of Riemannian geometry that naturally arises in the framework of control theory. Let $X$ and $Y$ be two smooth vector fields on a two-dimensional manifold $M$. If $X$ and $Y$ are everywhere linearly independent, then they define a classical Riemannian metric on $M$ (the metric for which they are orthonormal) and they give to $M$ the structure of metric space. If $X$ and $Y$ become linearly dependent somewhere on $M$, then the corresponding Riemannian metric has singularities, but under generic conditions the metric structure is still well defined. Metric structures that can be defined locally in this way are called almost-Riemannian structures. They are special cases of rank-varying sub-Riemannian structures, which are naturally defined in terms of submodules of the space of smooth vector fields on $M$. Almost-Riemannian structures show interesting phenomena, in particular for what concerns the relation between curvature, presence of conjugate points, and topology of the manifold. The main result of the paper is a generalization to almost-Riemannian structures of the Gauss-Bonnet formula. %B Discrete Contin. Dyn. Syst. 20 (2008) 801-822 %G en_US %U http://hdl.handle.net/1963/1869 %1 2353 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-10-11T07:14:06Z\\nNo. of bitstreams: 1\\nmath.oc0609566.pdf: 920147 bytes, checksum: c6f020bc9676ee3966b64f4135e4ce52 (MD5) %R 10.3934/dcds.2008.20.801 %0 Journal Article %J Netw. Heterog. Media 3 (2008) 567-614 %D 2008 %T Globally stable quasistatic evolution in plasticity with softening %A Gianni Dal Maso %A Antonio DeSimone %A Maria Giovanna Mora %A Massimiliano Morini %X We study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is characterized by the following properties: global stability at each time and energy balance on each\\ntime interval. An example developed in detail compares the solutions obtained by this method with the ones provided by a vanishing viscosity approximation, and shows that only the latter capture a decreasing branch in the stress-strain response. %B Netw. Heterog. Media 3 (2008) 567-614 %G en_US %U http://hdl.handle.net/1963/1965 %1 2228 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-05-15T11:03:21Z\\nNo. of bitstreams: 1\\nDM-DeS-Mor-Mor-05-3-final.pdf: 395475 bytes, checksum: 5789494df44986207d416d5d1ea15d22 (MD5) %0 Journal Article %J Calc. Var. Partial Differential Equations 31 (2008) 137-145 %D 2008 %T Gradient bounds for minimizers of free discontinuity problems related to cohesive zone models in fracture mechanics %A Gianni Dal Maso %A Adriana Garroni %X In this note we consider a free discontinuity problem for a scalar function, whose energy depends also on the size of the jump. We prove that the gradient of every smooth local minimizer never exceeds a constant, determined only by the data of the problem. %B Calc. Var. Partial Differential Equations 31 (2008) 137-145 %G en_US %U http://hdl.handle.net/1963/1723 %1 2428 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-01-26T12:52:13Z\\nNo. of bitstreams: 1\\nmath.AP0507088.pdf: 132125 bytes, checksum: 444c743b7852d0f6e97bb318f49b4467 (MD5) %R 10.1007/s00526-006-0084-3 %0 Journal Article %J Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 333-342 %D 2007 %T Gaussian estimates for hypoelliptic operators via optimal control %A Ugo Boscain %A Sergio Polidoro %X We obtain Gaussian lower bounds for the fundamental solution of a class of hypoelliptic equations, by using repeatedly an invariant Harnack inequality. Our main result is given in terms of the value function of a suitable optimal control problem. %B Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 333-342 %G en_US %U http://hdl.handle.net/1963/1994 %1 2202 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-08-09T13:14:42Z\\nNo. of bitstreams: 1\\n45-2007M.pdf: 181670 bytes, checksum: 6f262dccd2b3004cfd0b0b711bd011b2 (MD5) %R 10.4171/RLM/499 %0 Journal Article %J J. Math. Sci. 135 (2006) 3168-3194 %D 2006 %T On geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on distributions of corank 1 %A Igor Zelenko %X The present paper is devoted to the problem of (local) geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on generic corank 1 distributions. Using Pontryagin Maximum Principle, we treat Riemannian and sub-Riemannian cases in an unified way and obtain some algebraic necessary conditions for the geodesic equivalence of (sub-)Riemannian metrics. In this way first we obtain a new elementary proof of classical Levi-Civita\\\'s Theorem about the classification of all Riemannian geodesically equivalent metrics in a neighborhood of so-called regular (stable) point w.r.t. these metrics. Secondly we prove that sub-Riemannian metrics on contact distributions are geodesically equivalent iff they are constantly proportional. Then we describe all geodesically equivalent sub-Riemannian metrics on quasi-contact distributions. Finally we make the classification of all pairs of geodesically equivalent Riemannian metrics on a surface, which proportional in an isolated point. This is the simplest case, which was not covered by Levi-Civita\\\'s Theorem. %B J. Math. Sci. 135 (2006) 3168-3194 %G en_US %U http://hdl.handle.net/1963/2205 %1 2039 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-11T13:59:27Z\\nNo. of bitstreams: 1\\n0406111v1.pdf: 375215 bytes, checksum: cc4213e75a28857f98f01a294abff5e0 (MD5) %R 10.1007/s10958-006-0151-5 %0 Report %D 2006 %T Glimm interaction functional for BGK schemes %A Stefano Bianchini %G en_US %U http://hdl.handle.net/1963/1770 %1 2774 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-28T10:37:13Z\\nNo. of bitstreams: 1\\n69M.pdf: 213784 bytes, checksum: 597991852480bdc1aed7ed05ecc610c5 (MD5) %0 Report %D 2005 %T Gel\\\'fand-Zakharevich Systems and Algebraic Integrability: the Volterra Lattice Revisited %A Gregorio Falqui %A Marco Pedroni %X In this paper we will discuss some features of the bi-Hamiltonian method for solving the Hamilton-Jacobi (H-J) equations by Separation of Variables, and make contact with the theory of Algebraic Complete Integrability and, specifically, with the Veselov-Novikov notion of algebro-geometric (AG) Poisson brackets. %B Regul. Chaotic Dyn. 10 (2005) 399-412 %G en_US %U http://hdl.handle.net/1963/1689 %1 2444 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2005-06-20T13:56:39Z\\nNo. of bitstreams: 1\\nnlin.SI0505018.pdf: 230177 bytes, checksum: 9f91c8fd8d698b1a0a0ad018661f1d34 (MD5) %R 10.1070/RD2005v010n04ABEH000322 %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 J. Eur. Math. Soc. 7 (2005) 117-144 %D 2005 %T Ground states of nonlinear Schroedinger equations with potentials vanishing at infinity %A Antonio Ambrosetti %A Veronica Felli %A Andrea Malchiodi %X We deal with a class on nonlinear Schr\\\\\\\"odinger equations \\\\eqref{eq:1} with potentials $V(x)\\\\sim |x|^{-\\\\a}$, $0<\\\\a<2$, and $K(x)\\\\sim |x|^{-\\\\b}$, $\\\\b>0$. Working in weighted Sobolev spaces, the existence of ground states $v_{\\\\e}$ belonging to $W^{1,2}(\\\\Rn)$ is proved under the assumption that $p$ satisfies \\\\eqref{eq:p}. Furthermore, it is shown that $v_{\\\\e}$ are {\\\\em spikes} concentrating at a minimum of ${\\\\cal A}=V^{\\\\theta}K^{-2/(p-1)}$, where $\\\\theta= (p+1)/(p-1)-1/2$. %B J. Eur. Math. Soc. 7 (2005) 117-144 %G en_US %U http://hdl.handle.net/1963/2352 %1 1664 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-11-07T08:16:53Z\\nNo. of bitstreams: 1\\nGround states.pdf: 901500 bytes, checksum: 741c3d55677b872a40e8e3ff2df2a5d2 (MD5) %0 Journal Article %J Differential Geom. Appl. 21 (2004) 349-360 %D 2004 %T A geometric approach to the separability of the Neumann-Rosochatius system %A Claudio Bartocci %A Gregorio Falqui %A Marco Pedroni %X We study the separability of the Neumann-Rosochatius system on the n-dimensional sphere using the geometry of bi-Hamiltonian manifolds. Its well-known separation variables are recovered by means of a separability condition relating the Hamiltonian with a suitable (1,1) tensor field on the sphere. This also allows us to iteratively construct the integrals of motion of the system. %B Differential Geom. Appl. 21 (2004) 349-360 %G en_US %U http://hdl.handle.net/1963/2541 %1 1578 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-21T11:58:45Z\\nNo. of bitstreams: 1\\n0307021v1.pdf: 200686 bytes, checksum: 8df72df9ec62154c01c13bf79577d97c (MD5) %R 10.1016/j.difgeo.2004.07.001 %0 Journal Article %J J. Phys. A: Math. Gen. 36 (2003) 11655-11676 %D 2003 %T Gaudin models and bending flows: a geometrical point of view %A Gregorio Falqui %A Fabio Musso %X In this paper we discuss the bihamiltonian formulation of the (rational XXX) Gaudin models of spin-spin interaction, generalized to the case of sl(r)-valued spins. In particular, we focus on the homogeneous models. We find a pencil of Poisson brackets that recursively define a complete set of integrals of the motion, alternative to the set of integrals associated with the \\\'standard\\\' Lax representation of the Gaudin model. These integrals, in the case of su(2), coincide wih the Hamiltonians of the \\\'bending flows\\\' in the moduli space of polygons in Euclidean space introduced by Kapovich and Millson. We finally address the problem of separability of these flows and explicitly find separation coordinates and separation relations for the r=2 case. %B J. Phys. A: Math. Gen. 36 (2003) 11655-11676 %I IOP Publishing %G en_US %U http://hdl.handle.net/1963/2884 %1 1816 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-10T09:56:34Z\\nNo. of bitstreams: 1\\n0306005v1.pdf: 262369 bytes, checksum: 4563b661b4ec9bfabee142962f7d9279 (MD5) %R 10.1088/0305-4470/36/46/009 %0 Journal Article %J J. Robotic Syst. 20 (2003) 211-227 %D 2003 %T Geometric motion control for a kinematically redundant robotic chain: application to a holonomic mobile manipulator %A Claudio Altafini %X For kinematically redundant robotic manipulators, the extra degrees of freedom available allows freedom in the generation of the trajectories of the end-effector. In this paper, for this scope, we use techniques for motion control of rigid bodies on Riemannian manifolds (and Lie groups in particular) to design workspace control algorithms for the end-effector of the robotic chain and then to pull them back to joint space, all respecting the different geometric structures of the two underlying model spaces. The trajectory planner makes use of geometric splines. Examples of the different kinds of curves that are obtained via the De Casteljau algorithm in correspondence of different metric structures in SE(3) are reported. The feedback module, instead, consists of a Lyapunov based PD controller defined from a suitable notion of error distance on the Lie group. The motivating application of our work is a holonomic mobile manipulator for which simulation results are described in detail. %B J. Robotic Syst. 20 (2003) 211-227 %I Wiley %G en_US %U http://hdl.handle.net/1963/3019 %1 1314 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-02T14:53:17Z\\nNo. of bitstreams: 1\\ngeometric.pdf: 355957 bytes, checksum: 4ef01346a7567eb489c48c1bc40cb9c5 (MD5) %R 10.1002/rob.10084 %0 Journal Article %J Quantum Inf.Process. 1 (2002),no.3,207 %D 2002 %T On the generation of sequential unitary gates from continuous time Schrodinger equations driven by external fields %A Claudio Altafini %B Quantum Inf.Process. 1 (2002),no.3,207 %I SISSA Library %G en %U http://hdl.handle.net/1963/1614 %1 2504 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:20Z (GMT). No. of bitstreams: 1\\nquant-ph0203005.pdf: 180528 bytes, checksum: e67198980430d8f35b340c0aa590096c (MD5)\\n Previous issue date: 2002 %R 10.1023/A:1019825109040 %0 Journal Article %J J. Dynam. Control Systems 8 (2002) 93-140 %D 2002 %T Geometry of Jacobi Curves I %A Andrei A. Agrachev %A Igor Zelenko %X Jacobi curves are deep generalizations of the spaces of \\\"Jacobi fields\\\" along Riemannian geodesics. Actually, Jacobi curves are curves in the Lagrange Grassmannians. In our paper we develop differential geometry of these curves which provides basic feedback or gauge invariants for a wide class of smooth control systems and geometric structures. Two principal invariants are the generalized Ricci curvature, which is an invariant of the parametrized curve in the Lagrange Grassmannian endowing the curve with a natural projective structure, and a fundamental form, which is a fourth-order differential on the curve. The so-called rank 1 curves are studied in more detail. Jacobi curves of this class are associated with systems with scalar controls and with rank 2 vector distributions.\\nIn the forthcoming second part of the paper we will present the comparison theorems (i.e., the estimates for the conjugate points in terms of our invariants( for rank 1 curves an introduce an important class of \\\"flat curves\\\". %B J. Dynam. Control Systems 8 (2002) 93-140 %I Springer %G en_US %U http://hdl.handle.net/1963/3110 %1 1223 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-15T09:36:40Z\\nNo. of bitstreams: 1\\nJacobicurves.pdf: 365662 bytes, checksum: 23c0d55e84f95c2c8f386ea136ef18d0 (MD5) %R 10.1023/A:1013904801414 %0 Journal Article %J J. Dynam. Control Systems 8 (2002), no. 2, 167--215 %D 2002 %T Geometry of Jacobi curves II %A Andrei A. Agrachev %A Igor Zelenko %B J. Dynam. Control Systems 8 (2002), no. 2, 167--215 %I SISSA Library %G en %U http://hdl.handle.net/1963/1589 %1 2529 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:58Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002 %R 10.1023/A:1015317426164 %0 Journal Article %J Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 1 (2002) 603-648 %D 2002 %T Global calibrations for the non-homogeneous Mumford-Shah functional %A Massimiliano Morini %X Using a calibration method we prove that, if $\\\\Gamma\\\\subset \\\\Omega$ is a closed regular hypersurface and if the function $g$ is discontinuous along $\\\\Gamma$ and regular outside, then the function $u_{\\\\beta}$ which solves $$ \\\\begin{cases} \\\\Delta u_{\\\\beta}=\\\\beta(u_{\\\\beta}-g)& \\\\text{in $\\\\Omega\\\\setminus\\\\Gamma$} \\\\partial_{\\\\nu} u_{\\\\beta}=0 & \\\\text{on $\\\\partial\\\\Omega\\\\cup\\\\Gamma$} \\\\end{cases} $$ is in turn discontinuous along $\\\\Gamma$ and it is the unique absolute minimizer of the non-homogeneous Mumford-Shah functional $$ \\\\int_{\\\\Omega\\\\setminus S_u}|\\\\nabla u|^2 dx +{\\\\cal H}^{n-1}(S_u)+\\\\beta\\\\int_{\\\\Omega\\\\setminus S_u}(u-g)^2 dx, $$ over $SBV(\\\\Omega)$, for $\\\\beta$ large enough. Applications of the result to the study of the gradient flow by the method of minimizing movements are shown. %B Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 1 (2002) 603-648 %I Scuola Normale Superiore di Pisa %G en_US %U http://hdl.handle.net/1963/3089 %1 1244 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-13T15:10:43Z\\nNo. of bitstreams: 1\\n0105141v1.pdf: 402689 bytes, checksum: 50ca626f4a7fc3ff76a466c506ca755b (MD5) %0 Journal Article %J Acta Appl. Math., 2001, 65, 207-215 %D 2001 %T Gamma-limit of periodic obstacles %A Gianni Dal Maso %A Paola Trebeschi %X We compute the Gamma-limit of a sequence obstacle functionals in the case of periodic obstacles. %B Acta Appl. Math., 2001, 65, 207-215 %I SISSA Library %G en %U http://hdl.handle.net/1963/1495 %1 2668 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:12Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1023/A:1010668530972 %0 Journal Article %J Ann. Inst. H. Poincare\\\' Anal. Non Lineaire 18 (2001), no. 1, 19-42 %D 2001 %T A Glimm type functional for a special Jin-Xin relaxation model %A Stefano Bianchini %B Ann. Inst. H. Poincare\\\' Anal. Non Lineaire 18 (2001), no. 1, 19-42 %I Elsevier %G en %U http://hdl.handle.net/1963/1355 %1 3100 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:56:44Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %R 10.1016/S0294-1449(00)00124-4 %0 Journal Article %J Arch. Ration. Mech. An., 2001, 156, 89 %D 2001 %T Global continuous Riemann solver for nonlinear elasticity %A Jean-Marc Mercier %A Benedetto Piccoli %B Arch. Ration. Mech. An., 2001, 156, 89 %I SISSA Library %G en %U http://hdl.handle.net/1963/1493 %1 2670 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:11Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1007/s002050100118 %0 Journal Article %J Nuclear Phys. B %D 2000 %T A general construction of conformal field theories from scalar anti-de Sitter quantum field theories %A Marco Bertola %A Bros, Jacques %A Moschella, Ugo %A Schaeffer, Richard %B Nuclear Phys. B %V 587 %P 619–644 %G eng %0 Journal Article %J Gravit. Cosmol. %D 1998 %T Generation of primordial fluctuations in curved spaces %A Schaeffer, Richard %A Moschella, Ugo %A Marco Bertola %A Gorini, Vittorio %B Gravit. Cosmol. %V 4 %P 121–127 %G eng %0 Journal Article %J SIAM J. Control Optim. 36 (1998) 12-32 %D 1998 %T A generic classification of time-optimal planar stabilizing feedbacks %A Alberto Bressan %A Benedetto Piccoli %X Consider the problem of stabilization at the origin in minimum time for a planar control system affine with respect to the control. For a family of generic vector fields, a topological equivalence relation on the corresponding time-optimal feedback synthesis was introduced in a previous paper [Dynamics of Continuous, Discrete and Impulsive Systems, 3 (1997), pp. 335--371]. The set of equivalence classes can be put in a one-to-one correspondence with a discrete family of graphs. This provides a classification of the global structure of generic time-optimal stabilizing feedbacks in the plane, analogous to the classification of smooth dynamical systems developed by Peixoto. %B SIAM J. Control Optim. 36 (1998) 12-32 %I SISSA Library %G en %U http://hdl.handle.net/1963/998 %1 2858 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:41:28Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %R 10.1137/S0363012995291117 %0 Journal Article %J Rend. Sem. Mat. Univ. Politec. Torino 56 (1998), no. 4, 53-68 (2001) %D 1998 %T Geometric control approach to synthesis theory %A Ugo Boscain %A Benedetto Piccoli %B Rend. Sem. Mat. Univ. Politec. Torino 56 (1998), no. 4, 53-68 (2001) %I SISSA Library %G en %U http://hdl.handle.net/1963/1277 %1 3178 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:40Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %0 Book Section %B Proceedings of the International Congress of Mathematicians : Berlin 1998, August 18 - 27. II, Invited lectures. - Bielefeld : Universität Bielefeld, Fakultät für Mathematik cop. 1998. - pages : 315-326 %D 1998 %T Geometry and analytic theory of Frobenius manifolds %A Boris Dubrovin %X Main mathematical applications of Frobenius manifolds are\\r\\nin the theory of Gromov - Witten invariants, in singularity theory, in\\r\\ndifferential geometry of the orbit spaces of reflection groups and of their\\r\\nextensions, in the hamiltonian theory of integrable hierarchies. The theory\\r\\nof Frobenius manifolds establishes remarkable relationships between\\r\\nthese, sometimes rather distant, mathematical theories. %B Proceedings of the International Congress of Mathematicians : Berlin 1998, August 18 - 27. II, Invited lectures. - Bielefeld : Universität Bielefeld, Fakultät für Mathematik cop. 1998. - pages : 315-326 %G en %U http://hdl.handle.net/1963/6488 %1 6422 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T15:05:37Z\\nNo. of bitstreams: 1\\nicm98.pdf: 184775 bytes, checksum: 33db28beb5919405d7396b9f6ba40c56 (MD5) %0 Book Section %B Integrable systems and quantum groups : lectures given at the 1st session of the Centro internazionale matematico estivo (C.I.M.E.) held in Montecatini Terme, Italy, June 14-22, 1995 / R. Donagi, B. Dubrovin, E. Frenkel... [et al.] ; editors, M. Francavig %D 1995 %T Geometry of 2D topological field theories %A Boris Dubrovin %X These notes are devoted to the theory of “equations of associativity”\\r\\ndescribing geometry of moduli spaces of 2D topological field theories. %B Integrable systems and quantum groups : lectures given at the 1st session of the Centro internazionale matematico estivo (C.I.M.E.) held in Montecatini Terme, Italy, June 14-22, 1995 / R. Donagi, B. Dubrovin, E. Frenkel... [et al.] ; editors, M. Francavig %I SISSA %@ 3-540-60542-8 %G en %U http://hdl.handle.net/1963/6483 %1 6427 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T15:22:39Z\\nNo. of bitstreams: 1\\nmonte.pdf: 1437681 bytes, checksum: ecddb1d7310dbda2a35388d25609d3aa (MD5) %0 Journal Article %J Communications in Mathematical Physics. Volume 152, Issue 3, March 1993, Pages 539-564 %D 1993 %T Geometry and integrability of topological-antitopological fusion %A Boris Dubrovin %X Integrability of equations of topological-antitopological fusion (being proposed\\r\\nby Cecotti and Vafa) describing the ground state metric on a given 2D topological\\r\\nfield theory (TFT) model, is proved. For massive TFT models these equations\\r\\nare reduced to a universal form (being independent on the given TFT model) by\\r\\ngauge transformations. For massive perturbations of topological conformal field theory\\r\\nmodels the separatrix solutions of the equations bounded at infinity are found\\r\\nby the isomonodromy deformations method. Also it is shown that the ground state\\r\\nmetric together with some part of the underlined TFT structure can be parametrized\\r\\nby pluriharmonic maps of the coupling space to the symmetric space of real positive\\r\\ndefinite quadratic forms. %B Communications in Mathematical Physics. Volume 152, Issue 3, March 1993, Pages 539-564 %I SISSA %G en %U http://hdl.handle.net/1963/6481 %1 6429 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T15:28:15Z\\nNo. of bitstreams: 1\\ndubrovin_1993_cmp.pdf: 1218370 bytes, checksum: 6e082400ac3ed51e3b01ec532f9a598d (MD5) %R 10.1007/BF02096618 %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 Proc. Amer. Math. Soc. 108 (1990), no. 3, 691-702 %D 1990 %T A general chain rule for distributional derivatives %A Luigi Ambrosio %A Gianni Dal Maso %B Proc. Amer. Math. Soc. 108 (1990), no. 3, 691-702 %I SISSA Library %G en %U http://hdl.handle.net/1963/650 %1 3276 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:35:52Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1988 %0 Journal Article %J Nonlinear Anal. 15 (1990), no. 10, 897--914 %D 1990 %T A general existence theorem for boundary value problems for ordinary differential equations %A Giovanni Vidossich %B Nonlinear Anal. 15 (1990), no. 10, 897--914 %I SISSA Library %G en %U http://hdl.handle.net/1963/632 %1 3821 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:35:41Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1988 %R 10.1016/0362-546X(90)90073-P %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 Phys. Lett. B 192 (1987), no. 1-2, 81-88. %D 1987 %T Graded Chern-Simons terms %A Giovanni Landi %A Giuseppe Marmo %B Phys. Lett. B 192 (1987), no. 1-2, 81-88. %I SISSA Library %G en %U http://hdl.handle.net/1963/508 %1 3396 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:33:46Z (GMT). No. of bitstreams: 1\\n27_87.pdf: 430947 bytes, checksum: 98f993afd9ffd6652dc2751540a12c3c (MD5)\\n Previous issue date: 1987 %R 10.1016/0370-2693(87)91146-4