Derivation of Langevin Dynamics in a Nonzero Background Flow Field

TL;DR

This paper derives a nonequilibrium Langevin equation for a large particle in a background flow, extending previous models to include flow effects and validating the approach with numerical simulations.

Contribution

It introduces a derivation of Langevin dynamics in a nonzero background flow, extending prior models to nonequilibrium conditions.

Findings

Derived Langevin dynamics in flow conditions

Validated with numerical experiments on liquid materials

Extended previous equilibrium models to nonzero flow fields

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 [D. D\"urr, S. Goldstein, and J. L. Lebowitz, 1981 and 1983; P. Calderoni, D. D\"urr, and S. Kusuoka, 1989] and provides extensions to handle the nonzero background flow. The derived nonequilibrium Langevin dynamics is similar to the dynamics in [M. McPhie, et al., 2001]. Some numerical experiments illustrate the use of the obtained dynamic to simulate homogeneous liquid materials under flow.