A mean field theory for the collective motion of self-propelled particles interacting by velocity alignment mechanisms

Fernando Peruani (1) , Andreas Deutsch (2) , Markus Baer (3)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 Center for Information Services and High Performance Computing
3 PTB - Physikalisch-Technische Bundesanstalt [Berlin]

A mean-field approach (MFA) is proposed for the analysis of orientational order in a two-dimensional system of stochastic self-propelled particles interacting by local velocity alignment mechanism. The treatment is applied to the cases of ferromagnetic (F) and liquid-crystal (LC) alignment. In both cases, MFA yields a second order phase transition for a critical noise strength and a scaling exponent of 1/2 for the respective order parameters. We find that the critical noise amplitude ηc at which orientational order emerges in the LC case is smaller than in the F-alignment case, i.e. ηLC C<ηF C. A comparison with simulations of individual-based models with F- resp. LC-alignment shows that the predictions about the critical behavior and the qualitative relation between the respective critical noise amplitudes are correct.

Domaines: Biophysique [physics.bio-ph]

Fernando Peruani, Andreas Deutsch, Markus Baer. A mean field theory for the collective motion of self-propelled particles interacting by velocity alignment mechanisms. The European Physical Journal. Special Topics, 2008, 157 (1), pp.111-122. ⟨10.1140/epjst/e2008-00634-x⟩. ⟨hal-00905153⟩