Pattern formation in active particle systems due to competing alignment interactions

TL;DR

This paper investigates pattern formation in active particle systems with competing alignment interactions, revealing diverse macroscopic structures and analyzing their instabilities through mean-field and hydrodynamic approaches.

Contribution

It extends previous numerical studies to low densities and provides analytical insights into pattern-forming instabilities using simplified hydrodynamic models.

Findings

Emergence of vortex arrays, turbulence, and polar clusters.

Identification of instabilities leading to pattern formation.

Hydrodynamic equations effectively describe high-density regimes.

Abstract

Recently, we proposed a self-propelled particle model with competing alignment interactions: nearby particles tend to align their velocities whereas they anti-align their direction of motion with particles which are further away [R. Grossmann et al., Phys. Rev. Lett. 113, 258104 (2014)]. Here, we extend our previous numerical analysis of the high density regime considering low particle densities too. We report on the emergence of various macroscopic patterns such as vortex arrays, mesoscale turbulence as well as the formation of polar clusters, polar bands and nematically ordered states. Furthermore, we study analytically the instabilities leading to pattern formation in mean-field approximation. We argue that these instabilities are well described by a reduced set of hydrodynamic equations in the limit of high density.