Fluctuations and Pattern Formation in Self-Propelled Particles

TL;DR

This paper investigates the stability and pattern formation in a system of self-propelled particles using hydrodynamic equations, revealing conditions for flocking stability, inhomogeneous stripe patterns, and large fluctuations.

Contribution

It introduces a hydrodynamic framework to analyze fluctuations and pattern formation in self-propelled particle systems, highlighting instability thresholds and inhomogeneous states.

Findings

Ordered flocking state becomes unstable beyond a velocity threshold.

System forms propagating stripe patterns in the unstable regime.

Large fluctuations occur even when the flocking state is stable.

Abstract

We consider a coarse-grained description of a system of self-propelled particles given by hydrodynamic equations for the density and polarization fields. We find that the ordered moving or flocking state of the system is unstable to spatial fluctuations beyond a threshold set by the self-propulsion velocity of the individual units. In this region, the system organizes itself into an inhomogeneous state of well-defined propagating stripes of flocking particles interspersed with low density disordered regions. Further, we find that even in the regime where the homogeneous flocking state is stable, the system exhibits large fluctuations in both density and orientational order. We study the hydrodynamic equations analytically and numerically to characterize both regimes.