Eur. Phys. J. Special Topics 224, 1325-1347 (2015)
https://doi.org/10.1140/epjst/e2015-02462-3

Regular Article

Pattern formation in active particle systems due to competing alignment interactions

¹ Physikalisch-Technische Bundesanstalt, Abbestr. 2-12, 10587 Berlin, Germany
² Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ 80544, USA
³ Thaer Institute, Humboldt-Universität zu Berlin, 10099 Berlin, Germany
⁴ Department of Physics, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany

^a e-mail: grossmann@physik.hu-berlin.de
^b e-mail: pawelr@princeton.edu

Received: 8 April 2015
Revised: 18 May 2015
Published online: 24 July 2015

Abstract

Recently, we proposed a self-propelled particle model with competing alignment interactions: nearby particles tend to align their velocities whereas they anti-align their direction of motion with particles which are further away [R. Großmann, et al., Phys. Rev. Lett. 113, 258104 (2014)]. Here, we extend our previous numerical analysis of the high density regime considering low particle densities too. We report on the emergence of various macroscopic patterns such as vortex arrays, mesoscale turbulence as well as the formation of polar clusters, polar bands and nematically ordered states. Furthermore, we study analytically the instabilities leading to pattern formation in mean-field approximation. We argue that these instabilities are well described by a reduced set of hydrodynamic equations in the limit of high density.