A Quantitative Kinetic Theory of Flocking with Three-Particle-Closure

TL;DR

This paper develops a kinetic theory for flocking behavior in self-propelled particles, incorporating pair and three-particle correlations, and demonstrates improved quantitative agreement with simulations over mean field models.

Contribution

It introduces a three-particle-closure in kinetic theory, extending beyond mean field, to accurately predict flocking transition and correlations in particle systems.

Findings

Excellent agreement of pair correlations with simulations in disordered regime.

Flocking transition occurs at lower noise levels due to spatial correlations.

Three-particle closure improves prediction of flocking onset.

Abstract

We consider aligning self-propelled particles in two dimensions. Their motion is given by generalized Langevin equations and includes non-additive N-particle interactions. The qualitative behavior is as for the famous Vicsek model. We develop a kinetic theory of flocking beyond mean field. In particular, we self-consistently take into account the full pair correlation function. We find excellent quantitative agreement of the pair correlations with direct agent-based simulations within the disordered regime. Furthermore we use a closure relation to incorporate spatial correlations of three particles. In that way we achieve good quantitative agreement of the onset of flocking with direct simulations. Compared to mean field theory, the flocking transition is shifted significantly towards lower noise because directional correlations favor disorder. We compare our theory with a recently developed Landau-kinetic theory.