title: Active swarms on a sphere.
abstract: We show that coupling to curvature nontrivially affects collective motion in active systems, leading to motion patterns not observed in flat space. Using numerical simulations, we study a model of self-propelled particles with polar alignment and soft repulsion confined to move on the surface of a sphere. We observe a variety of motion patterns with the main hallmarks being polar vortex and circulating band states arising due to the incompatibility between spherical topology and uniform motion-a consequence of the "hairy ball" theorem. We provide a detailed analysis of density, velocity, pressure, and stress profiles in the circulating band state. In addition, we present analytical results for a simplified model of collective motion on the sphere showing that frustration due to curvature leads to stable elastic distortions storing energy in the band.
authors.affiliation: Division of Physics and Division of Computational Biology, University of Dundee, Dundee DD1 5EH, United Kingdom.
authors.forename: Rastko
authors.initials: R
authors.lastname: Sknepnek
authors.affiliation: Institute of Complex Systems and Mathemathical Biology, Department of Physics, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom.
authors.forename: Silke
authors.initials: S
authors.lastname: Henkes
mesh_terms: D003198:Computer Simulation; D008962:Models, Theoretical; D009038:Motion; D011312:Pressure; D013499:Surface Properties