  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.
