Nonequilibrium statistical mechanics of swarms of driven particles

TL;DR

This paper develops a statistical mechanics framework for swarms of self-propelled particles, analyzing their collective behaviors and dynamics under various confinement and interaction conditions, including simulations of different swarm modes.

Contribution

It introduces a novel approach combining active Brownian motion and dissipative systems theory to model swarm dynamics with new analytical and simulation results.

Findings

Identification of attractors and distribution functions for particle pairs

Analysis of swarm behaviors such as rotation, drift, and clustering

Simulation results demonstrating various dynamical modes of active particle swarms

Abstract

As a rough model for the collective motions of cells and organisms we develop here the statistical mechanics of swarms of self-propelled particles. Our approach is closely related to the recently developed theory of active Brownian motion and the theory of canonical-dissipative systems. Free motion and motion of a swarms confined in an external field is studied. Briefly the case of particles confined on a ring and interacting by repulsive forces is studied. In more detail we investigate self-confinement by Morse-type attracting forces. We begin with pairs N = 2; the attractors and distribution functions are discussed, then the case N > 2 is discussed. Simulations for several dynamical modes of swarms of active Brownian particles interacting by Morse forces are presented. In particular we study rotations, drift, fluctuations of shape and cluster formation.