Boltzmann and hydrodynamic description for self-propelled particles

TL;DR

This paper derives hydrodynamic equations from microscopic models of self-propelled particles, revealing conditions for spontaneous collective motion and its instability, providing a theoretical foundation for biological group dynamics.

Contribution

It introduces a microscopic derivation of hydrodynamic equations for self-propelled particles, linking individual behavior to collective motion phenomena.

Findings

Spontaneous collective motion emerges below a critical noise-density threshold.

Homogeneous motion state is unstable to spatial perturbations.

The model provides a microscopic basis for phenomenological equations.

Abstract

We study analytically the emergence of spontaneous collective motion within large bidimensional groups of self-propelled particles with noisy local interactions, a schematic model for assemblies of biological organisms. As a central result, we derive from the individual dynamics the hydrodynamic equations for the density and velocity fields, thus giving a microscopic foundation to the phenomenological equations used in previous approaches. A homogeneous spontaneous motion emerges below a transition line in the noise-density plane. Yet, this state is shown to be unstable against spatial perturbations, suggesting that more complicated structures should eventually appear.