Dresden 2017 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 37: Aktive Matter I (joint session DY/BP/CPP)

DY 37.15: Talk

Wednesday, March 22, 2017, 18:45–19:00, HÜL 186

Kinetic theory of self-propelled particles: von Mises distribution and Chapman-Enskog expansion — •Rüdiger Kürsten and Thomas Ihle — Institut für Physik, Ernst-Moritz-Arndt Universität Greifswald

We consider Vicsek-type models [1] with multi-particle interactions and discrete time dynamics. Starting from the exact evolution equation for the N-particle probability distribution, an Enskog-like kinetic equation is derived. Recently, the von Mises distribution and an geometric series ansatz were proposed to treat this nonlinear integral equation [2,3]. We critically assess them for a Vicsek-model with bounded-confidence interactions. Both approaches recover the qualitative behavior of the system but the von Mises distribution causes large deviations in certain parameter regions [4]. We extend the von Mises approximation by an additional term that leads to much better agreement. The geometric series ansatz for the Fourier modes of the probability density is typically very accurate but fails for very weak noise. We therefore suggest an alternative approach -- a Gaussian ansatz -- for the higher modes, which is robust at all noises. Furthermore, we present a non-standard Chapman-Enskog expansion with a fast time scale. This expansion is used to derive the macroscopic transport equations from the microscopic collision rules. We discuss the expressions for the transport coefficients, which become simple in the limit of infinite density.

[1] Phys. Rev. Lett. 75 (1995) 1226 [2] J. Stat. Mech. (2015) P10017

[3] Phys. Rev. E 90 (2014) 063315 [4] arXiv:1611.00624