Kinetic Theory of Flocking: Derivation of Hydrodynamic Equations

TL;DR

This paper derives hydrodynamic equations from the microscopic Vicsek model using kinetic theory, providing explicit transport coefficients and analyzing the phase transition to flocking both numerically and analytically.

Contribution

It presents a novel derivation of macroscopic flocking equations from microscopic dynamics using an Enskog-type kinetic approach.

Findings

Explicit expressions for transport coefficients at high particle speeds

Numerical and analytical analysis of the flocking phase transition

Derivation of hydrodynamic equations from microscopic models

Abstract

It is shown how to explicitly coarse-grain the microscopic dynamics of the Vicsek model for self-propelled agents. The macroscopic transport equations are derived by means of an Enskog-type kinetic theory. Expressions for all transport coefficients at large particle speed are given. The phase transition from a disordered to a flocking state is studied numerically and analytically.