Journal title
SIAM Journal on Applied Mathematics
DOI
10.1137/17M1118543
Issue
6
Volume
77
Last updated
2023-12-15T04:38:15.72+00:00
Page
2294-2316
Abstract
A system of interacting Brownian particles subject to short-range repulsive potentials is considered. A continuum description in the form of a nonlinear diffusion equation is derived systematically in the dilute limit using the method of matched asymptotic expansions. Numerical simulations are performed to compare the results of the model with those of the commonly used mean-field and Kirkwood-superposition approximations, as well as with Monte Carlo simulation of the stochastic particle system, for various interaction potentials. Our approach works best for very repulsive short-range potentials, while the mean-field approximation is suitable for long-range interactions. The Kirkwood superposition approximation provides an accurate description for both short- and long-range potentials, but is considerably more computationally intensive.
Symplectic ID
736970
Submitted to ORA
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Publication type
Journal Article
Publication date
21 Dec 2017