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We propose a derivation of a nonequilibrium Langevin dynamics for a large particle immersed in a background flow field. A single large particle is placed in an ideal gas heat bath composed of point particles that are distributed consistently with the background flow field and that interact with the large particle through elastic collisions. In the limit of small bath atom mass, the large particle dynamics converges in law to a stochastic dynamics. This derivation follows the ideas of [P. Calderoni, D. Dürr and S. Kusuoka, J. Stat. Phys. 55 (1989) 649-693. D. Dürr, S. Goldstein and J. Lebowitz, Z. Wahrscheinlichkeit 62 (1983) 427-448. D. Dürr, S. Goldstein and J.L. Lebowitz. Comm. Math. Phys. 78 (1981) 507-530.] and provides extensions to handle the nonzero background flow. The derived nonequilibrium Langevin dynamics is similar to the dynamics in [M. McPhie, P. Daivis, I. Snook, J. Ennis and D. Evans, Phys. A 299 (2001) 412-426]. Some numerical experiments illustrate the use of the obtained dynamic to simulate homogeneous liquid materials under shear flow.
@article{M2AN_2013__47_6_1583_0,
author = {Dobson, Matthew and Legoll, Fr\'ed\'eric and Leli\`evre, Tony and Stoltz, Gabriel},
title = {Derivation of {Langevin} dynamics in a nonzero background flow field},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1583--1626},
publisher = {EDP-Sciences},
volume = {47},
number = {6},
year = {2013},
doi = {10.1051/m2an/2013077},
mrnumber = {3110489},
zbl = {1287.82017},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013077/}
}
TY - JOUR AU - Dobson, Matthew AU - Legoll, Frédéric AU - Lelièvre, Tony AU - Stoltz, Gabriel TI - Derivation of Langevin dynamics in a nonzero background flow field JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2013 SP - 1583 EP - 1626 VL - 47 IS - 6 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013077/ DO - 10.1051/m2an/2013077 LA - en ID - M2AN_2013__47_6_1583_0 ER -
%0 Journal Article %A Dobson, Matthew %A Legoll, Frédéric %A Lelièvre, Tony %A Stoltz, Gabriel %T Derivation of Langevin dynamics in a nonzero background flow field %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %P 1583-1626 %V 47 %N 6 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013077/ %R 10.1051/m2an/2013077 %G en %F M2AN_2013__47_6_1583_0
Dobson, Matthew; Legoll, Frédéric; Lelièvre, Tony; Stoltz, Gabriel. Derivation of Langevin dynamics in a nonzero background flow field. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 6, pp. 1583-1626. doi: 10.1051/m2an/2013077
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