{"id":210,"date":"2017-02-09T16:56:47","date_gmt":"2017-02-09T14:56:47","guid":{"rendered":"http:\/\/sites.univ-tln.fr\/master-math\/?p=210"},"modified":"2017-12-20T15:32:19","modified_gmt":"2017-12-20T13:32:19","slug":"sujets-ter-2016-2017","status":"publish","type":"post","link":"https:\/\/sites.univ-tln.fr\/master-math\/fr\/sujets-ter-2016-2017\/","title":{"rendered":"Sujets TER 2016-2017"},"content":{"rendered":"
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  1. [M1\/2] J. Asch<\/a> (CPT)<\/strong> Occurrence of conical eigenvalue crossings.<\/em>
    \nThe object is to study the occurrence of conical eigenvalue intersections in a basic model of solid state quantum theory. In reference [1] these are shown to occur for the family of operators (-id_x-k)^2+V(x) on L^2(T) where T is a torus, V belongs to a certain class of functions, k varies in the dual torus which is related to a honeycomb lattice. The work to be done is to study reference [1] and to exhibit a way to prove stability of the result under deformations of the honeycomb structure.
    \nPrerequisites: Basic Functional Analysis, Operator and Spectral Perturbation theory.
    \nReferences:
    \n[1] C.L. Fefferman, M.L. Weinstein, Honeycomb lattice potentials and Dirac points, Journal of the American Mathematical Society, 25 (4), 2012, 1160-1220<\/li>\n
  2. [M1] N. Boizot<\/a>, A. Feddaoui<\/a> (LSIS)<\/strong> Observateurs pour les syst\u00e8mes lin\u00e9aires continu-discrets : observabilit\u00e9 et preuve de convergence du filtre de Kalman d\u00e9terministe.<\/em>
    \nCe sujet propose une introduction \u00e0 la th\u00e9orie du contr\u00f4le \u00e0 travers l’un de ses algorithmes classiques, le filtre de Kalman vu dans un cadre d\u00e9terministe. On se propose de pr\u00e9senter les grands principes de cette discipline ainsi que quelque r\u00e9sultats classiques : syst\u00e8mes lin\u00e9aires continus-discrets, observabilit\u00e9, Grammien, filtre de Kalman. L’\u00e9tudiant pourra alors \u00e9tudier quelque th\u00e9or\u00e8mes classiques ainsi que leurs preuves, et en fonction de sa sensibilit\u00e9 ainsi que du temps disponible, de programmer un filtre de Kalman sur un exemple.<\/li>\n
  3. [M1] G. Bouchitt\u00e9<\/a> (IMATH)<\/strong> Calcul des variations : forme optimale d\u2019une poutre en torsion.<\/em>
    \nCf     ici<\/a>.<\/li>\n
  4. [M2] G. Bouchitt\u00e9<\/a> (IMATH)<\/strong> Study of some variants of the Monge-Kantorovich optimal transport problem.<\/em>
    \nCf     ici<\/a>.<\/li>\n
  5. [M2] E.Busvelle<\/a> (LSIS)<\/strong> Optimal syntheses and observers.<\/em>
    \nIn linear control theory with quadratic cost, the separation principle is a theorem which is applied in order to split the output feedback control problem into two more simpler problems : state feedback control and observer. In more complex cases (nonlinear, time-optimal control), this separation principle does not apply. However, it is usual to split the problem in control and observation problems. We want to study whats happen when an exponential observer is used with an optimal synthesis (from Pontryagin maximum principle) with bang-bang trajectories. Filippov solutions are introduced to study the sub-optimality of the closed-loop control.<\/li>\n
  6. [M1\/2] T. Champion<\/a>, M. Ersoy<\/a> (IMATH)<\/strong> La m\u00e9thode de Nesterov et son interpr\u00e9tation en terme d’\u00e9quations diff\u00e9rentielles \/ Nesterov’s method and an differential equation modelling.<\/em>
    \n– Le m\u00e9thode de Nesterov (1983) est une m\u00e9thode de gradient acc\u00e9l\u00e9r\u00e9 qui a des propri\u00e9t\u00e9s optimales de convergence (en termes de rapidit\u00e9) pour la minimisation d’une fonction convexe. R\u00e9cemment, l’efficacit\u00e9 de cette m\u00e9thode a \u00e9t\u00e9 expliqu\u00e9e par divers auteurs via une interpr\u00e9tation comme diff\u00e9renciation d’une EDO d’ordre 2. On \u00e9tudiera cette interpr\u00e9tation et on programmera cette m\u00e9thode sur un probl\u00e8me de mod\u00e9lisation.
    \n– Nesterov’s method (1983) is an accelerated gradient method whose convergence is proven to be optimal for the minimization of a convex function. This optimality has recently been justified by several authors via a second order differential equations approach. We shall study these works, as well as apply the method on some modelisation problem.<\/li>\n
  7. [M1] F. Chittaro<\/a> (LSIS)<\/strong> Integrable systems, Liouville’s Theorem, and action-angle variables.<\/em>
    \nThe object of this stage is to study the main points of the theory of Integrable systems, from basics definitions of integrability of vector fields to symplectic geometry, Hamiltonian systems and the Liouville-Arnold Theorem. These notions are very useful in many fields of Mathematics and Mathematical Physics (Dynamical Systems, Hamiltonian Mechanics, Control Theory, Quantum Theory). The knowledge of them could be a first step for further development in a M2 project on Control Theory.<\/li>\n
  8. [M2] F. Chittaro<\/a> (LSIS)<\/strong> Ensemble controllability: swing-up of a collection of pendula.<\/em>
    \nCf     ici<\/a><\/li>\n
  9. [M2] F. Chittaro<\/a> (LSIS)<\/strong> Schrieffer-Wolff transformation in Quantum Mechanics.<\/em>
    \nCf     ici<\/a><\/li>\n
  10. [M1] M. Ersoy<\/a>, L. Yuschenko<\/a> (IMATH)<\/strong> Sch\u00e9ma implicite MAC pour Navier-Stokes Compressible Barotrope\/  <\/span>Implicit Mac scheme for Barotropic Compressible Navier-Stokes.<\/em>\n
    – Dans un premier temps, il s\u2019agit d\u2019\u00e9tudier un sch\u00e9ma MAC (Marker And Cell) implicite pour les \u00e9quations bi-dimensionnelles de Navier-Stokes barotrope. Dans un deuxi\u00e8me temps, un code \u00e9crit en language fortran ou language C\/C++ sera d\u00e9velopp\u00e9. Enfin, les r\u00e9sultats num\u00e9riques seront valid\u00e9s via des r\u00e9sultats th\u00e9oriques et exp\u00e9rimentaux. <\/span><\/div>\n
    – In this work, we first study an implicit MAC (Marker And Cell) scheme for the two-dimensional Barotropic Compressible Navier-Stokes equations. <\/span><\/div>\n
    Then, a numerical code (written in Fortran or C\/C++ language) will be developed. The numerical results will be validated through theoretical and experimental results. <\/span><\/div>\n<\/li>\n
  11. [M2] Y. Kian<\/a> (CPT)<\/strong> Probl\u00e8mes inverses spectraux et th\u00e9or\u00e8me de Borg-Levinson.<\/em>
    \nCf.     ici<\/a><\/li>\n
  12. [M1\/2] S. Meradji<\/a> (IMATH)<\/strong> Implementation of periodic boundary conditions in the discrete ordinates method : Application to grassland fires using FireStar3D.<\/em>
    \nA 3D physics-based model referred to as \u00ab\u00a0FireStar3D\u00a0\u00bb has been developed in order to predict fire propagation in natural environment. It consists briefly in solving the conservation equations of the coupled system consisting of the vegetation and the surrounding gaseous medium. The model takes into account the phenomena of vegetation degradation (drying, pyrolysis, combustion), the interaction between an atmospheric boundary layer and a canopy (aerodynamic drag, heat transfer by convection and radiation, and mass transfer), and the transport within the fluid phase (convection, turbulence, gas-phase combustion).
    \nThe objective of this project is to evaluate using the FireStar3D source code (written in Fortran90\/95 and parallelized with OpenMP directives) the rates of spread of grassland fires for different wind speeds, and compare these rates to those obtained during experimental fires. An infinite fire front will be considered by assuming periodic boundary conditions in the horizontal direction perpendicular to the wind direction. Conducting these simulations requires first the implementation of periodic boundary conditions in the discrete ordinates method used to solve the radiative transfer equation.<\/li>\n
  13. [M1] A. Panati<\/a> (CPT)<\/strong> Th\u00e9or\u00e8me de Stone-von Neumann en M\u00e9canique Quantique.<\/em>
    \nL’objet de ce stage est l’\u00e9tude et la r\u00e9daction d’une m\u00e9moire p\u00e9dagogique sur le th\u00e9or\u00e8me de Stone-von Neumann sur l’unicit\u00e9 de repr\u00e9sentations de relations de commutation canonique, qui est l’un d\u00e8s th\u00e9or\u00e8mes fondamentales dans le cadre de la m\u00e9canique quantique.<\/li>\n
  14. [M1] A. Panati<\/a> (CPT)<\/strong> Entropie en M\u00e9canique Classique et Quantique.<\/em>
    \nL’objet de ce stage est l’\u00e9tude et la r\u00e9daction d’une m\u00e9moire p\u00e9dagogique sur le concept d’entropie et ses formulations math\u00e9matique, d’abord en m\u00e9canique classique, ensuite en m\u00e9canique quantique dans le cadre simplifi\u00e9 de syst\u00e8mes confin\u00e9s (i.e. \u00e0 dimension finie).<\/li>\n
  15. [M1] C-A. Pillet<\/a> (CPT)<\/strong> La g\u00e9om\u00e9trie Riemanienne.<\/em>
    \nCf.     ici<\/a><\/li>\n
  16. [M1] M. Rouleux<\/a> (CPT)<\/strong> Mod\u00e8le de Hubbard et spins \u00e0 sym\\’etrie continue.<\/em>
    \nL’objet de ce stage est l’\u00e9tude de la d\u00e9croissance des corr\u00e9lations (fonctions \u00e0 2 points) pour le mod\u00e8le de Hubbard sur les r\u00e9seaux Z ou Z^2, et sa g\u00e9n\u00e9ralisation possible aux syst\u00e8mes de spins \u00e0 sym\u00e9trie continue. Le mod\u00e8le de Hubbard d\u00e9crit le Hamiltonien (quantique) d’un syst\u00e8me d’\u00e9lectrons itin\u00e9rant d’un site \u00e0 l’autre du r\u00e9seau, \u00e9ventuellement soumis \u00e0 un champ magn\u00e9tique ext\u00e9rieur. Le sujet comprend une \u00e9tude analytique et \u00e9ventuellement des simulations num\u00e9riques.<\/li>\n
  17. [M1] S. Vaienti<\/a> (CPT)<\/strong> Central limit theorem via martingale techniques.<\/em>\n
    We propose to prove the central limit theorem using martingale theory. This is an alternative technique to the Levy’s approach. The student should first give an overview of martingale’s theory (not developed in the course but easily accessible with the given knowledge), and then follow the article by S. Lalley here :<\/div>\n
    http:\/\/galton.uchicago.edu\/~lalley\/Courses\/383\/Lindeberg.pdf<\/a><\/div>\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

    [M1\/2] J. Asch (CPT) Occurrence of conical eigenvalue crossings. The object is to study the occurrence of conical eigenvalue intersections in a basic model of solid state quantum theory. In reference [1] these are shown to occur for the family of operators (-id_x-k)^2+V(x) on L^2(T) where T is a torus, V belongs to a certain […]<\/p>\n","protected":false},"author":11,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[3],"tags":[],"class_list":["post-210","post","type-post","status-publish","format-standard","hentry","category-sujets-de-ter"],"_links":{"self":[{"href":"https:\/\/sites.univ-tln.fr\/master-math\/wp-json\/wp\/v2\/posts\/210","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.univ-tln.fr\/master-math\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.univ-tln.fr\/master-math\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.univ-tln.fr\/master-math\/wp-json\/wp\/v2\/users\/11"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.univ-tln.fr\/master-math\/wp-json\/wp\/v2\/comments?post=210"}],"version-history":[{"count":15,"href":"https:\/\/sites.univ-tln.fr\/master-math\/wp-json\/wp\/v2\/posts\/210\/revisions"}],"predecessor-version":[{"id":247,"href":"https:\/\/sites.univ-tln.fr\/master-math\/wp-json\/wp\/v2\/posts\/210\/revisions\/247"}],"wp:attachment":[{"href":"https:\/\/sites.univ-tln.fr\/master-math\/wp-json\/wp\/v2\/media?parent=210"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.univ-tln.fr\/master-math\/wp-json\/wp\/v2\/categories?post=210"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.univ-tln.fr\/master-math\/wp-json\/wp\/v2\/tags?post=210"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}