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Boltzmann and hydrodynamic description for self-propelled particles

By Eric Bertin, Michel Droz and Guillaume Gregoire

Abstract

4 pages, 3 figuresInternational audienceWe 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

Topics: [ PHYS.COND.CM-SM ] Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech]
Publisher: American Physical Society
Year: 2006
DOI identifier: 10.1103/PhysRevE.74.022101
OAI identifier: oai:HAL:hal-00910408v1
Provided by: Hal-Diderot
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