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Issue 9, 2018
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Active ideal sedimentation: exact two-dimensional steady states

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Abstract

We consider an ideal gas of active Brownian particles that undergo self-propelled motion and both translational and rotational diffusion under the influence of gravity. We solve analytically the corresponding Smoluchowski equation in two space dimensions for steady states. The resulting one-body density is given as a series, where each term is a product of an orientation-dependent Mathieu function and a height-dependent exponential. A lower hard wall is implemented as a no-flux boundary condition. Numerical evaluation of the suitably truncated analytical solution shows the formation of two different spatial regimes upon increasing Peclet number. These regimes differ in their mean particle orientation and in their variation of the orientation-averaged density with height.

Graphical abstract: Active ideal sedimentation: exact two-dimensional steady states

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Article information


Submitted
22 Dec 2017
Accepted
29 Jan 2018
First published
07 Feb 2018

Soft Matter, 2018,14, 1614-1621
Article type
Paper

Active ideal sedimentation: exact two-dimensional steady states

S. Hermann and M. Schmidt, Soft Matter, 2018, 14, 1614
DOI: 10.1039/C7SM02515G

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