Derivation of Langevin dynamics in a nonzero background flow field

Matthew Dobson; Frédéric Legoll; Tony Lelièvre; Gabriel Stoltz

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2013)

  • Volume: 47, Issue: 6, page 1583-1626
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Dobson, Matthew, et al. "Derivation of Langevin dynamics in a nonzero background flow field." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.6 (2013): 1583-1626. <http://eudml.org/doc/273269>.

@article{Dobson2013,
abstract = {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.},
author = {Dobson, Matthew, Legoll, Frédéric, Lelièvre, Tony, Stoltz, Gabriel},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {nonequilibrium; Langevin dynamics; multiscale; molecular simulation},
language = {eng},
number = {6},
pages = {1583-1626},
publisher = {EDP-Sciences},
title = {Derivation of Langevin dynamics in a nonzero background flow field},
url = {http://eudml.org/doc/273269},
volume = {47},
year = {2013},
}

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 - Modélisation Mathématique et Analyse Numérique
PY - 2013
PB - EDP-Sciences
VL - 47
IS - 6
SP - 1583
EP - 1626
AB - 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.
LA - eng
KW - nonequilibrium; Langevin dynamics; multiscale; molecular simulation
UR - http://eudml.org/doc/273269
ER -

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