Hard-sphere interactions in velocity jump models

TL;DR

This paper investigates how hard-sphere interactions affect the collective behavior of particles undergoing velocity jumps, deriving transport equations and comparing approximations with simulations to understand diffusion properties.

Contribution

It introduces $N$-particle transport equations incorporating collisions and compares approximation methods with numerical simulations for velocity jump particles.

Findings

Theoretical approximations match Monte Carlo simulations when excluded volume is small.

Derived expressions relate diffusion coefficients to particle number and size.

The study enhances understanding of particle interactions in velocity jump models.

Abstract

Group-level behaviour of particles undergoing a velocity jump process with hard-sphere interactions is investigated. We derive $N$-particle transport equations that include the possibility of collisions between particles and apply different approximation techniques to get expressions for the dependence of the collective diffusion coefficient on the number of particles and their diameter. The derived approximations are compared with numerical results obtained from individual-based simulations. The theoretical results compare well with Monte Carlo simulations providing the excluded volume fraction is small.