Dynamics of sedimenting active Brownian particles

  • Jérémy Vachier
  • Marco G. MazzaEmail author
Open Access
Regular Article


We investigate the stochastic dynamics of one sedimenting active Brownian particle in three dimensions under the influence of gravity and passive fluctuations in the translational and rotational motion. We present an analytical solution of the Fokker-Planck equation for the stochastic process which allows us to describe the dynamics of one active Brownian particle in three dimensions. We address the time evolution of the density, the polarization, and the steady-state solution. We also perform Brownian dynamics simulations and study the effect of the activity of the particles on their collective motion. These results qualitatively agree with our model. Finally, we compare our results with experiments (J. Palacci et al., Phys. Rev. Lett. 105, 088304 (2010)) and find very good agreement.

Graphical abstract


Flowing matter: Nonlinear Physics and Mesoscale Modeling 



Open Access funding provided by Max Planck Society.


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© The Author(s) 2019

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  1. 1.Max Planck Institute for Dynamics and Self-OrganizationGöttingenGermany
  2. 2.Interdisciplinary Centre for Mathematical Modelling and Department of Mathematical SciencesLoughborough UniversityLoughborough, LeicestershireUK

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