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Theses

Méthodes stochastiques en dynamique moléculaire

Abstract : This thesis presents two independent research topics. Both are related to the application of stochastic problems to molecular dynamics. In the first part, we present a work related to the probabilistic interpretation of the Poisson-Boltzmann equation. This equation describes the electrostatic potential of a molecular system. After an introduction to the Poisson-Boltzmann equation, we focus on the parabolic and linear equation. After extending an existence and uniqueness result for backward stochastic differential equations, we establish a probabilistic interpretation of the nonlinear Poisson-Boltzmann equation with backward stochastic differential equations. Finally, in a more prospective second part, we initiate a study of a slow and fast variables detection method due to Paul Malliavin.
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https://tel.archives-ouvertes.fr/tel-00833886
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Submitted on : Thursday, June 13, 2013 - 4:34:10 PM
Last modification on : Monday, October 12, 2020 - 2:28:05 PM
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Nicolas Perrin. Méthodes stochastiques en dynamique moléculaire. Mathématiques générales [math.GM]. Université Nice Sophia Antipolis, 2013. Français. ⟨NNT : 2013NICE4011⟩. ⟨tel-00833886⟩

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