Pair-distribution function of active Brownian spheres in two spatial dimensions: simulation results and analytic representation

TL;DR

This paper provides detailed simulation data and an analytic approximation for the pair-distribution function of active Brownian spheres in two dimensions, aiding theoretical modeling of their collective behavior.

Contribution

It introduces the first comprehensive simulation-based pair-distribution function for active Brownian particles in 2D and offers an analytic expression for practical use.

Findings

The pair-distribution function depends on positions, orientations, activity, and density.

The analytic approximation agrees well with simulation data.

Results facilitate theoretical studies of active matter and nonequilibrium physics.

Abstract

We investigate the full pair-distribution function of a homogeneous suspension of spherical active Brownian particles interacting by a Weeks-Chandler-Andersen potential in two spatial dimensions. The full pair-distribution function depends on three coordinates describing the relative positions and orientations of two particles, the P\'eclet number specifying the activity of the particles, and their mean packing density. This five-dimensional function is obtained from Brownian dynamics simulations. We discuss its structure taking into account all of its degrees of freedom. In addition, we present an approximate analytic expression for the product of the full pair-distribution function and the interparticle force. We find that the analytic expression, which is typically needed when deriving analytic models for the collective dynamics of active Brownian particles, is in good agreement with the simulation results. The results of this work can thus be expected to be helpful for the further theoretical investigation of active Brownian particles as well as nonequilibrium statistical physics in general.