Cluster dynamics and cluster size distributions in systems of self-propelled particles

TL;DR

This paper investigates the clustering behavior of self-propelled particles, develops a kinetic model for cluster size distribution, and validates it through simulations, revealing insights into cluster dynamics and steady-state distributions.

Contribution

It introduces a Smoluchowski-type kinetic model for cluster size distribution in self-propelled particles and demonstrates its qualitative agreement with simulation results.

Findings

The model predicts steady-state cluster size distributions.

Simulations show asymmetric cluster spreading.

The kinetic model captures the transition to aggregation.

Abstract

Systems of self-propelled particles (SPP) interacting by a velocity alignment mechanism in the presence of noise exhibit a rich clustering dynamics. It can be argued that clusters are responsible for the distribution of (local) information in these systems. Here, we investigate the statistical properties of single clusters in SPP systems, like the asymmetric spreading of clusters with respect to their moving direction. In addition, we formulate a Smoluchowski-type kinetic model to describe the evolution of the cluster size distribution (CSD). This model predicts the emergence of steady-state CSDs in SPP systems. We test our theoretical predictions in simulations of SPP with nematic interactions and find that our simple kinetic model reproduces qualitatively the transition to aggregation observed in simulations.