Application of the Gillespie algorithm to a granular intruder particle

TL;DR

This paper adapts the Gillespie algorithm for simulating collisions of a granular intruder particle with bath particles, validating it against known solutions and exploring correlations in complex systems.

Contribution

It introduces a Gillespie algorithm-based method for granular collision simulations, extending its application beyond chemical reactions to granular matter.

Findings

Validated the method with a 1D system with known solutions

Demonstrated correlations between translational and rotational motion in a granular needle

Discussed the relationship with DSMC method

Abstract

We show how the Gillespie algorithm, originally developed to describe coupled chemical reactions, can be used to perform numerical simulations of a granular intruder particle colliding with thermalized bath particles. The algorithm generates a sequence of collision ``events'' separated by variable time intervals. As input, it requires the position-dependent flux of bath particles at each point on the surface of the intruder particle. We validate the method by applying it to a one-dimensional system for which the exact solution of the homogeneous Boltzmann equation is known and investigate the case where the bath particle velocity distribution has algebraic tails. We also present an application to a granular needle in bath of point particles where we demonstrate the presence of correlations between the translational and rotational degrees of freedom of the intruder particle. The relationship between the Gillespie algorithm and the commonly used Direct Simulation Monte Carlo (DSMC) method is also discussed.