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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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Publication details

The article was received on 22 Dec 2017, accepted on 29 Jan 2018 and first published on 07 Feb 2018


Article type: Paper
DOI: 10.1039/C7SM02515G
Citation: Soft Matter, 2018,14, 1614-1621
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    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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