Comptes Rendus
Physics/Mathematical physics, theoretical physics
Time-dependent transport coefficients: an effective macroscopic description of small scale dynamics?
[Coefficients de transport dépendant du temps : vers une description macroscopique des dynamiques à petite échelle]
Comptes Rendus. Physique, Volume 9 (2008) no. 7, pp. 767-772.

On considère des situations où des particules extraites d'un réservoir à l'équilibre thermique sont immergées, à un instant donné, dans un fluide. Le model utilisé est le processus d'Ornstein–Uhlenbeck. On prouve que le transport de particules dans l'espace physique peut se décrire exactement et à tout instant à l'aide de coefficients de diffusion dépendant du temps. Ce résultat est valide, en particulier, en dehors du régime hydrodynamique. On discute également l'utilisation, dans d'autres contextes, de coefficients de transport non constants.

Situations where particles taken from a thermal reservoir are immersed at some initial time in a fluid are considered. The diffusion model is the Ornstein–Uhlenbeck process. It is proven that particle transport in physical space can be described exactly at all times with the help of a time dependent diffusion coefficient; the result is, in particular, valid outside of the hydrodynamic regime. The use of time-dependent transport coefficients in other contexts in also discussed.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crhy.2008.07.011
Keywords: Diffusion, Stochastic processes, Fick's law
Mot clés : Diffusion, Processus stochastiques, Loi de Fick

Fabrice Debbasch 1 ; Jean-Pierre Rivet 2

1 Université Pierre-et-Marie-Curie-Paris 6, UMR 8112, ERGA-LERMA, 3, rue Galilée 94200 Ivry, France
2 Laboratoire Cassiopée, Université de Nice Sophia-Antipolis, CNRS, observatoire de la Côte d'Azur, 06304 Nice cedex 04, France
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Fabrice Debbasch; Jean-Pierre Rivet. Time-dependent transport coefficients: an effective macroscopic description of small scale dynamics?. Comptes Rendus. Physique, Volume 9 (2008) no. 7, pp. 767-772. doi : 10.1016/j.crhy.2008.07.011. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2008.07.011/

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