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Some remarks on free energy and coarse-graining

Frédéric Legoll 1, 2 Tony Lelièvre 1, 3
1 MICMAC - Methods and engineering of multiscale computing from atom to continuum
Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
2 multi-échelle - Modélisation et expérimentation multi-échelle pour les solides hétérogènes
navier umr 8205 - Laboratoire Navier
3 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
Abstract : We present recent results on coarse-graining techniques for thermodynamic quantities (canonical averages) and dynamical quantities (averages of path functionals over solutions of overdamped Langevin equations). The question is how to obtain reduced models to compute such quantities, in the specific case when the functional to be averaged only depends on a few degrees of freedom. We mainly review, numerically illustrate and extend results from [3,18], concerning the computation of the stress-strain relation for one-dimensional chains of atoms, and the construction of an effective dynamics for a scalar coarse-grained variable when the complete system evolves according to the overdamped Langevin equation.
Keywords : homogenization multiscale fast algorithms coupling methods domain decomposition
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https://hal.archives-ouvertes.fr/hal-00511221
Contributor : Tony Lelièvre Connect in order to contact the contributor
Submitted on : Tuesday, August 24, 2010 - 10:53:34 AM
Last modification on : Friday, February 4, 2022 - 3:20:18 AM

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  • HAL Id : hal-00511221, version 1
  • ARXIV : 1008.3792

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CNRS | INRIA | CERMICS | INSMI | NAVIER-STRUCTURES | ENPC | PARISTECH | UR-NAVIER | IFSTTAR | MULTI-ECHELLE | ANR | INRIA2

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Frédéric Legoll, Tony Lelièvre. Some remarks on free energy and coarse-graining. Engquist, Björn; Runborg, Olof; Tsai, Yen-Hsi R. (Eds.). Numerical analysis and multiscale computations, Springer, 420 p., 2012, Series: Lecture Notes in Computational Science and Engineering, Vol. 82. ⟨hal-00511221⟩

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