A kinetic model and scaling properties for non-equilibrium clustering of self-propelled particles

TL;DR

This paper introduces a kinetic model that captures the clustering behavior and phase transition in self-propelled particles, linking cluster scaling exponents to observed non-equilibrium phenomena.

Contribution

It presents a simple kinetic framework that relates cluster scaling laws to phase transitions in self-propelled particles, aligning theoretical predictions with experimental and simulation data.

Findings

Identifies two distinct clustering phases in self-propelled particles.

Derives a critical power-law exponent for cluster size distribution.

Shows the critical exponent depends only on scaling parameters nd eta.

Abstract

We demonstrate that the clustering statistics and the corresponding phase transition to non-equilibrium clustering found in many experiments and simulation studies with self-propelled particles (SPPs) with alignment can be obtained from a simple kinetic model. The key elements of this approach are the scaling of the cluster cross-section with the cluster mass -- characterized by an exponent $\alpha$ -- and the scaling of the cluster perimeter with the cluster mass -- described by an exponent $\beta$. The analysis of the kinetic approach reveals that the SPPs exhibit two phases: i) an individual phase, where the cluster size distribution (CSD) is dominated by an exponential tail that defines a characteristic cluster size, and ii) a collective phase characterized by the presence of non-monotonic CSD with a local maximum at large cluster sizes. At the transition between these two phases the CSD is well described by a power-law with a critical exponent $\gamma$, which is a function of $\alpha$ and $\beta$ only. The critical exponent is found to be in the range $0.8 < \gamma < 1.5$ in line with observations in experiments and simulations.