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Theses

Application de la mécanique statistique à trois problèmes hors d'équilibre : algorithmes, épidémies, milieux granulaires

Abstract : In this PhD thesis, we study three problems using tools from the statistical mechanics. We show the existence of the phenomenon of critical universality for the dynamical phase transition of some combinatorial search algorithms. We give the exact values of the critical exponents and an analytic formula for a scaling function. We develop a formalism which enables us to compute a systematic perturbative expansion, in high space dimensions, of the large deviations function of the metastable state of the contact process. It can be reused e.g. for other models from the biology of populations. We introduce two exactly solvable 2D models for the statics of granular media. They reproduce the jamming transition and allow to discuss the different length scales of these media and to prove the Edwards hypothesis wrong in a realistic case.
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https://tel.archives-ouvertes.fr/tel-00102083
Contributor : Christophe Deroulers Connect in order to contact the contributor
Submitted on : Wednesday, October 4, 2006 - 7:36:07 PM
Last modification on : Friday, October 15, 2021 - 1:36:46 PM
Long-term archiving on: : Friday, November 25, 2016 - 12:09:51 PM

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  • HAL Id : tel-00102083, version 2
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Citation

Christophe Deroulers. Application de la mécanique statistique à trois problèmes hors d'équilibre : algorithmes, épidémies, milieux granulaires. Physique mathématique [math-ph]. Université Pierre et Marie Curie - Paris VI, 2006. Français. ⟨tel-00102083v2⟩

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