Event-Driven Brownian Dynamics for Hard Spheres

TL;DR

This paper introduces an event-driven Brownian dynamics algorithm specifically designed for simulating hard-sphere systems, addressing the challenge of accurately modeling steep interactions in long-time simulations.

Contribution

It presents a novel event-driven approach for overdamped Brownian dynamics of hard spheres, validated against exact two-body collision solutions.

Findings

Accurately reproduces two-body collision dynamics

Effective in low-density regimes

Addresses limitations of traditional numerical integrators

Abstract

Brownian dynamics algorithms integrate numerically Langevin equations and allow to probe long time scales in simulations. A common requirement for such algorithms is that interactions in the system should vary little during an integration time step: therefore, computational efficiency worsens as the interactions become steeper. In the extreme case of hard-body interactions, standard numerical integrators become ill defined. Several approximate schemes have been invented to handle such cases with little emphasis on testing the correctness of the integration scheme. Starting from the two-body Smoluchowsky equation, we discuss a general method for the overdamped Brownian dynamics of hard-spheres, recently developed by one of us. We test the accuracy of the algorithm with the exact solution of the Smoluchowsky equation in the case of twobody collisions and in the low-density limit.