{"id":425,"date":"2019-02-08T16:07:34","date_gmt":"2019-02-08T14:07:34","guid":{"rendered":"http:\/\/sites.univ-tln.fr\/master-math\/?p=425"},"modified":"2020-02-05T22:22:07","modified_gmt":"2020-02-05T20:22:07","slug":"topics-2018-2019","status":"publish","type":"post","link":"https:\/\/sites.univ-tln.fr\/master-math\/en\/topics-2018-2019\/","title":{"rendered":"Topics 2018-2019"},"content":{"rendered":"
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  1. [M1\/M2] N. Boizot<\/a> et L. Sacchelli<\/a> (LIS)<\/strong> The study of fingerprints, an application of line fields.<\/em>\n
  2. [M1\/M2] F. Chittaro<\/a> (LSIS)<\/strong> Picard’s Great Theorem.<\/em>
    \nPicard’s theorems concern the behavior of analytic functions; in particular, Picard’s Great Theorem asserts that, in a neighborhood of an isolated essential singularity, an analytic function reaches all the complex values, except at most one.
    \nIn this project, the student must study the proof of the theorem, with a special regard to the role of isolatedness of the singularity.<\/li>\n
  3. [M1\/M2] F. Chittaro<\/a> (LSIS)<\/strong> Heisenberg system in sub-Riemannian and sub-Finsler geometry.<\/em>
    \nThe aim of this project is to discuss the first notions of sub-Riemannian geometry, by studying the famous problem of minimizing the L2 norm for the Heisenberg system.
    \nThe project may continue with the analysis of the problem of minimizing the Lp standard (numerically or analytically).<\/li>\n
  4. [M2] F. Chittaro<\/a> (LSIS)<\/strong> Regularity of eigenvectors in presence of eigenvalue intersections.<\/em>
    \nKato-Rellich’s Theorem asserts that the eigenvectors of a one-parameter analytic family of linear operators are analytical, even in the presence of intersections between the eigenvalues.
    \nWhat can be said about families of operators which depends on the disturbance?<\/li>\n
  5. [M1] G. Faccanoni<\/a> (IMATH)<\/strong> \u00c9tude (peu) math\u00e9matique et num\u00e9rique (avec FreeFem++) d’un probl\u00e8me d’\u00e9lasticit\u00e9.<\/em>
    \nCe TER porte sur l’approximation num\u00e9rique par \u00e9l\u00e9ments finis des \u00e9quations de l’\u00e9lasticit\u00e9 lin\u00e9aire (syst\u00e8me de Lam\u00e9). On simulera avec FreeFem++ par exemple la d\u00e9formation d’un barrage due \u00e0 la pression hydrostatique, la d\u00e9formation d’une poutre sous son poids, les vibrations d’une poutre, …<\/li>\n
  6. [M1\/M2] G. Faccanoni<\/a> (IMATH)<\/strong> \u00c9criture d’un notebook IPython pour la visualisation de la thermodynamique du sodium.<\/em>
    \nOn s\u2019int\u00e9resse \u00e0 la description pr\u00e9cise de la thermodynamique du sodium liquide et vapeur. On commencera par \u00e9tudier la thermodynamique classique du changement de phase liquide-vapeur et les relations entre les diff\u00e9rents fonctions thermodynamiques (voir par exemple cette pr\u00e9sentation). Ensuite, en partant des donn\u00e9es de l’article de Fink et Leibowitz (https:\/\/inis.iaea.org\/collection\/NCLCollectionStore\/_Public\/11\/537\/11537733.pdf), on d\u00e9veloppera un notebook IPython pour le calcul et l’affichage de toutes les quantit\u00e9s thermodynamiques classiques pour le sodium et on comparera les r\u00e9sultats obtenu avec le \u00ab\u00a0Database of thermophysical properties of liquid metal coolants for GEN-IV\u00a0\u00bb de V. Sobolev. Les lois ainsi construites seront utilis\u00e9es dans le mod\u00e8le LMNC pour la description d’un \u00e9coulement dans les r\u00e9acteurs RNR-Na.<\/li>\n
  7. [M1\/M2] G. Faccanoni<\/a> (IMATH)<\/strong> Traitement num\u00e9rique d’images avec Matlab\/Octave (ou Python) et FreeFem++.<\/em>
    \nCe TER porte sur quelques concepts de base du traitement math\u00e9matique des images num\u00e9riques. On commencera par des manipulations \u00e9l\u00e9mentaires (translation, zoom, modification du contraste par transformations d’abord affines puis quelconques). On s\u2019int\u00e9ressera ensuite au stockage des images et on abordera les notions de r\u00e9solution et de quantification puis la notion de compression par SVD. On conclura par l’application de techniques issues de l’approximation num\u00e9rique d’EDP pour la d\u00e9tection des bords et le floutage des images. Les diff\u00e9rents algorithmes seront d’abord impl\u00e9ment\u00e9s au choix en Matlab\/Octave ou Python. La derni\u00e8re partie sera aussi trait\u00e9e avec FreeFem++.<\/li>\n
  8. [M2] G. Faccanoni<\/a> (IMATH)<\/strong> Cubic equations of state for two-phase flow LMNC model with phase transition.<\/em>
    \nWe investigate a simplified model describing the evolution of the coolant within a nuclear reactor core (e.g. of PWR type or of RNR-Na type). This model is named LMNC (for Low Mach Nuclear Core) and consists of the coupling between three PDEs together with boundary conditions specific to the nuclear framework. The fluid is modeled by an Equation of State (EoS) describing the pure liquid and vapor phases and the phase transition. We consider here some cubic EoS with the Maxwell area rule.Simulations 1d with Matlab\/Octave or Python, 2d with FreeFem++.<\/li>\n
  9. [M1] C-A. Pillet<\/a> (CPT)<\/strong> Dynamique quantique des mesures r\u00e9p\u00e9t\u00e9es.<\/em>
    \nUn processus de mesure est une op\u00e9ration permettant d’extraire de l’information d’un syst\u00e8me physique. Dans le r\u00e9gime quantique, ces processus ont un statut particulier. Bien que la m\u00e9canique quantique n’aie jamais \u00e9t\u00e9 mise en d\u00e9faut, les probl\u00e8mes conceptuels pos\u00e9s par la mesure ont de ce fait hant\u00e9 l’histoire de son d\u00e9veloppement, d\u00e8s son origine. Le raffinement des techniques exp\u00e9rimentales dont disposent aujourd’hui les physiciens pour sonder le monde quantique permettent d’acc\u00e9der au coeur des processus de mesure et de tester ainsi les pr\u00e9dictions de la th\u00e9orie (c.f. prix Nobel 2012 de S.Haroche et D. Wineland). Bien que la description d’une mesure soit tr\u00e8s simple du point de vue math\u00e9matique, la r\u00e9p\u00e9tition de cette mesure g\u00e9n\u00e8re un syst\u00e8me dynamique encore peu \u00e9tudi\u00e9 et mal compris. L’objectif de ce stage est l’\u00e9tude d’un exemple simple de mesure r\u00e9p\u00e9t\u00e9e dont les propri\u00e9t\u00e9s statistiques sont encore inconnues.<\/li>\n
  10. [M1\/M2] M. Rouleux<\/a> (CPT)<\/strong> Intrication multi-mode de syst\u00e8mes fermioniques.<\/em>
    \nSee     this file<\/a>.<\/li>\n<\/ol>\n<\/div>\n
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    Companies and other Universities
    \n<\/b><\/div>\n
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    1. [M2] A. Lisser<\/a> (Univ. Paris-Saclay)<\/strong> Optimisation stochastique appliqu\u00e9e \u00e0 la location de v\u00e9los libre-service.<\/em>
      \nSee       this file<\/a>.<\/li>\n
    2. [M2] ALTEN <\/b> Mod\u00e9lisation physico-math\u00e9matique.<\/strong><\/em>
      \nSee       this file<\/a>.<\/li>\n<\/ol>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

      [M1\/M2] N. Boizot et L. Sacchelli (LIS) The study of fingerprints, an application of line fields. See this file. [M1\/M2] F. Chittaro (LSIS) Picard’s Great Theorem. Picard’s theorems concern the behavior of analytic functions; in particular, Picard’s Great Theorem asserts that, in a neighborhood of an isolated essential singularity, an analytic function reaches all the complex values, […]<\/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":[19],"tags":[],"class_list":["post-425","post","type-post","status-publish","format-standard","hentry","category-master-thesis-topics"],"_links":{"self":[{"href":"https:\/\/sites.univ-tln.fr\/master-math\/wp-json\/wp\/v2\/posts\/425","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=425"}],"version-history":[{"count":3,"href":"https:\/\/sites.univ-tln.fr\/master-math\/wp-json\/wp\/v2\/posts\/425\/revisions"}],"predecessor-version":[{"id":455,"href":"https:\/\/sites.univ-tln.fr\/master-math\/wp-json\/wp\/v2\/posts\/425\/revisions\/455"}],"wp:attachment":[{"href":"https:\/\/sites.univ-tln.fr\/master-math\/wp-json\/wp\/v2\/media?parent=425"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.univ-tln.fr\/master-math\/wp-json\/wp\/v2\/categories?post=425"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.univ-tln.fr\/master-math\/wp-json\/wp\/v2\/tags?post=425"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}