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Boltzmann and hydrodynamic description for self-propelled particles

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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https://hal.archives-ouvertes.fr/hal-00910408
Contributor : Eric Bertin <>
Submitted on : Thursday, November 28, 2013 - 9:12:15 AM
Last modification on : Tuesday, April 21, 2020 - 10:29:58 AM

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Eric Bertin, Michel Droz, Guillaume Gregoire. Boltzmann and hydrodynamic description for self-propelled particles. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2006, 74, pp.022101. ⟨10.1103/PhysRevE.74.022101⟩. ⟨hal-00910408⟩

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