Event Driven Langevin simulations of Hard Spheres

TL;DR

This paper introduces two novel algorithms for simulating Langevin dynamics of hard-sphere systems, addressing the challenge of accurately modeling their complex interactions without slow-varying assumptions.

Contribution

The authors develop and test new algorithms based on operator splitting and Green's function approximation for better simulation of hard-sphere Langevin dynamics.

Findings

Algorithms effectively handle hard-sphere interactions

Improved accuracy over standard methods

Applicable to colloids and nano-particles simulations

Abstract

The blossoming of interest in colloids and nano-particles has given renewed impulse to the study of hard-body systems. In particular, hard spheres have become a real test system for theories and experiments. It is therefore necessary to study the complex dynamics of such systems in presence of a solvent; disregarding hydrodynamic interactions, the simplest model is the Langevin equation. Unfortunately, standard algorithms for the numerical integration of the Langevin equation require that interactions are slowly varying during an integration timestep. This in not the case for hard-body systems, where there is no clearcut between the correlation time of the noise and the timescale of the interactions. Starting first from a splitting of the Fokker-Plank operator associated with the Langevin dynamics, and then from an approximation of the two-body Green's function, we introduce and test two new algorithms for the simulation of the Langevin dynamics of hard-spheres.