Active swarms on a sphere

Rastko Sknepnek, Silke Henkes

Research output: Contribution to journalArticle

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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.
Original languageEnglish
Article numberarXiv:1407.8516v1
Number of pages5
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Publication statusPublished - 31 Jul 2014

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Swarm
Curvature
curvature
Hairy ball theorem
Motion
Vortex
vortices
Collective Motion
Endothelial Cells
incompatibility
Microtubules
Frustration
epithelium
frustration
Folding
Droplet
folding
bundles
balls
Bundle

Keywords

  • cond-mat.soft

Cite this

Active swarms on a sphere. / Sknepnek, Rastko; Henkes, Silke.

In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, 31.07.2014.

Research output: Contribution to journalArticle

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