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Boltzmann and hydrodynamic description for self-propelled particles

Eric Bertin·Michel Droz·Guillaume Gregoire
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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.

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Eric Bertin, Michel Droz, Guillaume Gregoire. 2006-08-03. Boltzmann and hydrodynamic description for self-propelled particles. https://doi.org/10.1103/physreve.74.022101

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