[Coefficients de transport dépendant du temps : vers une description macroscopique des dynamiques à petite échelle]
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.
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Mot clés : Diffusion, Processus stochastiques, Loi de Fick
Fabrice Debbasch 1 ; Jean-Pierre Rivet 2
@article{CRPHYS_2008__9_7_767_0,
author = {Fabrice Debbasch and Jean-Pierre Rivet},
title = {Time-dependent transport coefficients: an effective macroscopic description of small scale dynamics?},
journal = {Comptes Rendus. Physique},
pages = {767--772},
publisher = {Elsevier},
volume = {9},
number = {7},
year = {2008},
doi = {10.1016/j.crhy.2008.07.011},
language = {en},
}
TY - JOUR AU - Fabrice Debbasch AU - Jean-Pierre Rivet TI - Time-dependent transport coefficients: an effective macroscopic description of small scale dynamics? JO - Comptes Rendus. Physique PY - 2008 SP - 767 EP - 772 VL - 9 IS - 7 PB - Elsevier DO - 10.1016/j.crhy.2008.07.011 LA - en ID - CRPHYS_2008__9_7_767_0 ER -
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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