Propagating wave in the flock of self-propelled particles

TL;DR

This paper analyzes the hydrodynamic equations of self-propelled particles, revealing wave solutions that explain flocking behavior and band formation, with implications for understanding collective motion.

Contribution

It provides an analytical solution to the wave propagation in self-propelled particle systems, linking theoretical predictions with experimental observations.

Findings

Traveling wave solutions exist in the hydrodynamic model.

Two wave patterns depend on noise strength: single band and multiple bands.

Flocking transition involves transient vortex and wave-driven ordering.

Abstract

We investigate the linearized hydrodynamic equations of interacting self-propelled particles in two dimensional space. It is found that the small perturbations of density and polarization fields satisfy the hyperbolic partial differential equations---that admit analytical propagating wave solutions. These solutions uncover the questionable traveling band formation in the flocking state of self-propelled particles. Below the critical noise strength, an unstable disordered state (random motion) undergoes a transient vortex and evolves to an ordered state (flocking motion) as unidirectional traveling waves. There appear two possible longitudinal wave patterns depending on the noise strength, including single band in stable state and multiplebands in unstable state. A comparison of theoretical and experimental studies is presented.