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Étude probabiliste de systèmes de particules en interaction : applications à la simulation moléculaire

Abstract : This work presents some results on stochastically interacting particle systems and probabilistic interpretations of partial differential equations with applications to molecular dynamics and quantum chemistry. We present a particle method allowing to analyze the adaptive biasing force process, used in molecular dynamics for the computation of free energy differences. We also study the sensitivity of stochastic dynamics with respect to some parameter, aiming at the computation of forces in the Born-Oppenheimer approximation for determining the fundamental quantum state of molecules. Finally, we present a numerical scheme based on a particle system for the resolution of scalar conservation laws with an anomalous diffusion term, corresponding to a jump dynamics on the particles
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Submitted on : Wednesday, June 1, 2011 - 9:48:10 AM
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Raphaël Roux. Étude probabiliste de systèmes de particules en interaction : applications à la simulation moléculaire. Mathématiques générales [math.GM]. Université Paris-Est, 2010. Français. ⟨NNT : 2010PEST1040⟩. ⟨tel-00597479⟩

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