Vortex arrays and meso-scale turbulence of self-propelled particles

TL;DR

This paper introduces a simple self-propelled particle model inspired by Turing patterns, capable of generating vortex arrays, meso-scale turbulence, and ordered states, with analysis supported by kinetic theory, hydrodynamics, and simulations.

Contribution

It presents a novel particle model with short-range alignment and long-range anti-alignment, systematically deriving continuum equations and analyzing pattern formation.

Findings

Model reproduces vortex arrays and turbulence observed in bacterial suspensions.

Phase diagram shows regions of order, disorder, and pattern formation.

Simulations agree with theoretical predictions from stability analysis.

Abstract

Inspired by the Turing mechanism for pattern formation, we propose a simple self-propelled particle model with short-ranged alignment and anti-alignment at larger distances. It is able to produce orientationally ordered states, periodic vortex patterns as well as meso-scale turbulence. The latter phase resembles observations in dense bacterial suspensions. The model allows a systematic derivation and analysis of a kinetic theory as well as hydrodynamic equations for density and momentum fields. A phase diagram with regions of such pattern formation as well as spatially homogeneous orientational order and disorder is obtained from a linear stability analysis of these continuum equations. Microscopic Langevin simulations of the self-propelled particle system are in agreement with these findings.