Ringkinetic Theory of Vicsek-like Systems of Self-Propelled Particles

We consider aligning self-propelled point particles in two dimensions.

There motion is given by Langevin equations, however, the qualitative behavior is as for the famous Vicsek model.

We develop a kinetic theory of flocking beyond mean field.

In particular, we take into account the full pair correlation function.

We find excellent quantitative agreement of those pair correlations with direct agent-based simulations within the disordered regime.

Furthermore we use a closure relation to incorporate at least the 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.