Effect of the orientational relaxation on the collective motion of patterns formed by self-propelled particles

¹ Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster - 48149 Münster, Germany
² Departamento de Metodos Matematicos, Universidade da Coruna, Campus de A Coruna - 15071, A Coruna, Spain
³ Center of Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster - 48149 Münster, Germany

^(a) chervany@uni-muenster.de

Received: 14 July 2016
Accepted: 4 October 2016

Abstract

We investigate the collective behavior of self-propelled particles (SPPs) undergoing competitive processes of pattern formation and rotational relaxation of their self-propulsion velocities. In full accordance with previous work, we observe transitions between different steady states of the SPPs caused by the intricate interplay among the involved effects of pattern formation, orientational order, and coupling between the SPP density and orientation fields. Based on rigorous analytical and numerical calculations, we prove that the rate of the orientational relaxation of the SPP velocity field is the main factor determining the steady states of the SPP system. Further, we determine the boundaries between domains in the parameter plane that delineate qualitatively different resting and moving states. In addition, we analytically calculate the collective velocity of the SPPs and show that it perfectly agrees with our numerical results. We quantitatively demonstrate that does not vanish upon approaching the transition boundary between the moving pattern and homogeneous steady states.