Effect of the orientational relaxation on the collective motion of patterns formed by self-propelled particles

TL;DR

This paper explores how the rate of orientational relaxation influences the collective motion and pattern formation of self-propelled particles, revealing key factors that determine steady states and transitions in their behavior.

Contribution

It provides a rigorous analytical and numerical analysis showing that orientational relaxation rate is the main factor controlling steady states in self-propelled particle systems.

Findings

Orientational relaxation rate determines steady states.

Boundaries between resting and moving states are analytically identified.

Collective velocity aligns with numerical results and remains finite at transition boundaries.

Abstract

We investigate the collective behavior of self-propelled particles (SPPs) undergoing competitive processes of pattern formation and rotational relaxation of their self-propulsion velocities. In full accordance with previous work, we observe transitions between different steady states of the SPPs caused by the intricate interplay among the involved effects of pattern formation, orientational order, and coupling between the SPP density and orientation fields. Based on rigorous analytical and numerical calculations, we prove that the rate of the orientational relaxation of the SPP velocity field is the main factor determining the steady states of the SPP system. Further, we determine the boundaries between domains in the parameter plane that delineate qualitatively different resting and moving states. In addition, we analytically calculate the collective velocity $\vec{v}$ of the SPPs and show that it perfectly agrees with our numerical results. We quantitatively demonstrate that $\vec{v}$ does not vanish upon approaching the transition boundary between the moving pattern and homogeneous steady states.