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Active matter on Riemannian manifolds

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Abstract

We formulate the dynamics of overdamped Brownian active particles (swimmers) moving on any Riemannian 2-manifold. To characterize such dynamics at short times, an analytical expression for the variance of swimmers diffusing on any Riemmanian 2-manifold is derived. To show the generality of the present work, we apply the latter dynamics to swimmers moving on the surface of a spheroid and a torus, and offer analytical expressions for both their long-time variances and steady angular marginal probability density functions. Finally, Brownian dynamics simulations are used to validate our theoretical findings.

Graphical abstract: Active matter on Riemannian manifolds

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Publication details

The article was received on 19 May 2018, accepted on 08 Nov 2018 and first published on 15 Nov 2018


Article type: Paper
DOI: 10.1039/C8SM01034J
Citation: Soft Matter, 2018, Advance Article
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    Active matter on Riemannian manifolds

    L. Apaza and M. Sandoval, Soft Matter, 2018, Advance Article , DOI: 10.1039/C8SM01034J

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