title: Vortex with fourfold defect lines in a simple model of self-propelled particles.
abstract: We study the formation of a vortex with fourfold symmetry in a minimal model of self-propelled particles, confined inside a squared box, using computer simulations and also theoretical analysis. In addition to the vortex pattern, we observe five other regimes in the system: a homogeneous gaseous phase, band structures, moving clumps, moving clusters, and vibrating rings. All six regimes emerge from controlling the strength of noise and from the contribution of repulsion and alignment interactions. We study the shape of the vortex and its symmetry in detail. The pattern shows exponential defect lines where incoming and outgoing flows of particles collide. We show that alignment and repulsion interactions between particles are necessary to form such patterns. We derive hydrodynamical equations with an introduction of the "small deviation" technique to describe the vortex phase. The method is applicable to other systems as well. Finally, we compare the theory with the results of both computer simulations and an experiment using Quincke rotors. A good agreement between the three is observed.
authors.affiliation: Department of Physics, Sharif University of Technology, P.O. Box 11155-9161, Tehran, Iran.
authors.forename: Hamid
authors.initials: H
authors.lastname: Seyed-Allaei
authors.affiliation: Department of Physics, Sharif University of Technology, P.O. Box 11155-9161, Tehran, Iran.
authors.forename: Mohammad Reza
authors.initials: MR
authors.lastname: Ejtehadi