A mean-field theory for self-propelled particles interacting by velocity alignment mechanisms
Max-Planck-Institute for Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany
2 Center for Information Services and High Performance Computing, Technische Universität Dresden, Zellescher Weg 12, 01069 Dresden, Germany
3 Physikalisch-Technische Bundesanstalt, Abbestr. 2-12, 10587 Berlin, Germany
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. ηLCC<ηFC. 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.
© EDP Sciences, Springer-Verlag, 2008