Eur. Phys. J. Special Topics 191, 173-185 (2010)
https://doi.org/10.1140/epjst/e2010-01349-1

Regular article

Cluster dynamics and cluster size distributions in systems of self-propelled particles

¹ Max-Planck-Institute for Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany
² Institute of Physics, Humboldt University Berlin, Newtonstr. 15, 12489 Berlin, Germany
³ Physikalisch-Technische Bundesanstalt, Abbestr. 2-12, 10587 Berlin, Germany

Received: 22 November 2010
Revised: 23 December 2010
Published online: 18 February 2011

Abstract

Systems of self-propelled particles (SPP) interacting by a velocity alignment mechanism in the presence of noise exhibit rich clustering dynamics. Often, clusters are responsible for the distribution of (local) information in these systems. Here, we investigate the properties of individual clusters in SPP systems, in particular the asymmetric spreading behavior of clusters with respect to their direction of motion. In addition, we formulate a Smoluchowski-type kinetic model to describe the evolution of the cluster size distribution (CSD). This model predicts the emergence of steady-state CSDs in SPP systems. We test our theoretical predictions in simulations of SPP with nematic interactions and find that our simple kinetic model reproduces qualitatively the transition to aggregation observed in simulations.