Active swarms on a sphere

Abstract

Here we show that coupling to curvature has profound effects on collective motion in active systems, leading to patterns not observed in flat space. Biological examples of such active motion in curved environments are numerous: curvature and tissue folding are crucial during gastrulation, epithelial and endothelial cells move on constantly growing, curved crypts and vili in the gut, and the mammalian corneal epithelium grows in a steady-state vortex pattern. On the physics side, droplets coated with actively driven microtubule bundles show active nematic patterns. We study a model of self-propelled particles with polar alignment on a sphere. Hallmarks of these motion patterns are a polar vortex and a circulating band arising due to the incompatibility between spherical topology and uniform motion - a consequence of the hairy ball theorem. We present analytical results showing that frustration due to curvature leads to stable elastic distortions storing energy in the band.

5 pages, 4 figures plus Supporting Information

References in corpus (7)

• Novel type of phase transition in a system of self-driven particles
• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• Spontaneous motion in hierarchically assembled active matter
• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• Collective motion of self-propelled particles interacting without cohesion
• Topology and Dynamics of Active Nematic Vesicles
• Phase transition in the collective migration of tissue cells: experiment and model