Self-Organized Hydrodynamics with nonconstant velocity

TL;DR

This paper investigates a self-organized hydrodynamic model with density-dependent velocity, revealing how velocity changes influence stability and clustering in self-propelled particle systems, supported by theoretical analysis and numerical simulations.

Contribution

It introduces a hydrodynamic model incorporating density-dependent velocity and alignment, analyzing stability and cluster formation, validated by simulations and modal analysis.

Findings

Stability depends on the condition $( ho v( ho))'> 0$.

Velocity decrease rate affects cluster stability.

Numerical simulations confirm theoretical predictions.

Abstract

Motivated by recent experimental and computational results that show a motility-induced clustering transition in self-propelled particle systems, we study an individual model and its corresponding Self-Organized Hydrodynamic model for collective behaviour that incorporates a density-dependent velocity, as well as inter-particle alignment. The modal analysis of the hydrodynamic model elucidates the relationship between the stability of the equilibria and the changing velocity, and the formation of clusters. We find, in agreement with earlier results for non-aligning particles, that the key criterion for stability is $(\rho v(\rho))'> 0$, i.e. a non-rapid decrease of velocity with density. Numerical simulation for both the individual and hydrodynamic models with a velocity function inspired by experiment demonstrates the validity of the theoretical results.