Abstract.
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.
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Peruani, F., Deutsch, A. & Bär, M. A mean-field theory for self-propelled particles interacting by velocity alignment mechanisms. Eur. Phys. J. Spec. Top. 157, 111–122 (2008). https://doi.org/10.1140/epjst/e2008-00634-x
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DOI: https://doi.org/10.1140/epjst/e2008-00634-x