Collective motion of active Brownian particles in one dimension

TL;DR

This paper investigates the collective behavior of one-dimensional active Brownian particles with non-linear friction, deriving mean-field equations, analyzing phase stability, and validating findings through numerical simulations.

Contribution

It introduces a mean-field framework for active Brownian particles with non-linear friction, revealing phase transitions between disordered and ordered motion.

Findings

Identification of two distinct motion phases

Derivation of mean-field equations from microscopic models

Validation of analytical results with simulations

Abstract

We analyze a model of active Brownian particles with non-linear friction and velocity coupling in one spatial dimension. The model exhibits two modes of motion observed in biological swarms: A disordered phase with vanishing mean velocity and an ordered phase with finite mean velocity. Starting from the microscopic Langevin equations, we derive mean-field equations of the collective dynamics. We identify the fixed points of the mean-field equations corresponding to the two modes and analyze their stability with respect to the model parameters. Finally, we compare our analytical findings with numerical simulations of the microscopic model.