Fluctuation-induced collective motion: a single-particle density analysis.
In a system of noisy self-propelled particles with interactions that favor directional alignment, collective motion will appear if the density of particles increases beyond a certain threshold. In this paper, we argue that such a threshold may depend also on the profiles of the perturbation in the particle directions. Specifically, we perform mean-field, linear stability, perturbative, and numerical analyses on an approximated form of the Fokker-Planck equation describing the system. We find that if an angular perturbation to an initially homogeneous system is large in magnitude and highly localized in space, it will be amplified and thus serves as an indication of the onset of collective motion. Our results also demonstrate that high particle speed promotes collective motion.
Lee
Chiu Fan
CF
Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str 38, 01187 Dresden, Germany. cflee@pks.mpg.de
D003198:Computer Simulation; D008956:Models, Chemical; D015233:Models, Statistical; D010316:Particle Size