Topological sound and flocking on curved surfaces

Suraj Shankar, Mark J. Bowick, M. Cristina Marchetti

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23 Scopus citations

Abstract

Active systems on curved geometries are ubiquitous in the living world. In the presence of curvature, orientationally ordered polar flocks are forced to be inhomogeneous, often requiring the presence of topological defects even in the steady state because of the constraints imposed by the topology of the underlying surface. In the presence of spontaneous flow, the system additionally supports long-wavelength propagating sound modes that get gapped by the curvature of the underlying substrate. We analytically compute the steady-state profile of an active polar flock on a two-sphere and a catenoid, and show that curvature and active flow together result in symmetry-protected topological modes that get localized to special geodesics on the surface (the equator or the neck, respectively). These modes are the analogue of edge states in electronic quantum Hall systems and provide unidirectional channels for information transport in the flock, robust against disorder and backscattering.

Original languageEnglish (US)
Article number031039
JournalPhysical Review X
Volume7
Issue number3
DOIs
StatePublished - Sep 7 2017

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ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Shankar, S., Bowick, M. J., & Marchetti, M. C. (2017). Topological sound and flocking on curved surfaces. Physical Review X, 7(3), [031039]. https://doi.org/10.1103/PhysRevX.7.031039