Boltzmann and hydrodynamic description for self-propelled particles.
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.
Bertin
Eric
E
Department of Theoretical Physics, University of Geneva, CH-1211 Geneva 4, Switzerland.
Droz
Michel
M
Grégoire
Guillaume
G