Boltzmann and hydrodynamic description for self-propelled particles

Details Boltzmann and hydrodynamic description for self-propelled particles Boltzmann and hydrodynamic description for self-propelled particles

2006-01-03

arxiv.org/abs/cond-mat/0601038v2

Phys. Rev. E 74, 022101 (2006)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures, final version

Scientific paper

10.1103/PhysRevE.74.022101

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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