The microscopic phase density functional approach to the construction of the kinetic and hydrodynamic description for the system of self-propelled particles

TL;DR

This paper derives kinetic and hydrodynamic equations for self-propelled particles using microscopic phase density, revealing a transition from disorder to order and analyzing effects of noise on viscosity.

Contribution

It introduces a microscopic phase density approach to derive hydrodynamics for self-propelled particles with Vicsek-like rules, including noise effects.

Findings

Hydrodynamic equations resemble Euler equations for self-propelled fluids.

Dynamical transition from disordered to ordered motion observed.

Shear viscosity vanishes under local equilibrium approximation.

Abstract

We use the method of the microscopic phase density to get the kinetic equation for the system of self-propelled particles with Vicsek-like alignment rule. The hydrodynamic equations are derived for the ordered phase taking into account the mean-field force only. The equation for the hydrodynamic velocity plays the role of the Euler equation for the self-propelled Vicsek fluid. The hydrodynamics of such ideal self-propelled fluid demonstrates the dynamical transition from disordered initial state to the completely ordered motion. To take the noise into account we consider how the framework of the local equilibrium approximation affects the hydrodynamic equations and the viscous tensor and show that in such approximation the shear viscosity vanishes.