Landau kinetic equation for dry aligning active models

TL;DR

This paper introduces a Landau kinetic equation for dry active matter that bridges Boltzmann and Smoluchowski models, enabling analytical descriptions at moderate densities and deriving Toner-Tu parameters.

Contribution

It develops a new kinetic equation based on weak coupling approximation for alignment and noise, extending kinetic modeling of active matter beyond dilute regimes.

Findings

Derivation of a non-linear, density-dependent kinetic equation.

Identification of stable homogeneous ordered solutions.

Parameters of Toner-Tu equations obtained from microscopic dynamics.

Abstract

The Landau equation is a kinetic equation based on the weak coupling approximation of the interaction between the particles. In the framework of dry active matter this new kinetic equation relies on the weak coupling approximation of both the alignment strength and the magnitude of the angular noise, instead of the hypothesis of diluteness. Therefore, it is a kinetic equation bridging between the Boltzmann [3], and the Smoluchowski [2] approximations, and allowing analytical descriptions at moderate densities. The form of the equation presents non-linear and density dependent diffusions and advections fully derived by the microscopic equations of motions. Finally, implementing the BGL procedure [25], the parameters of the Toner-Tu equations are derived showing the appearance of linearly stable homogeneous ordered solutions and mimicking the results obtained from the Boltzmann approach.