https://doi.org/10.1140/epjst/e2015-02465-0
Regular Article
A geometric approach to self-propelled motion in isotropic & anisotropic environments
1 Physikalisch-Technische Bundesanstalt, Abbestr. 2-12, 10587 Berlin, Germany
2 Laboratoire J.A. Dieudonné, Université de Nice Sophia Antipolis, UMR 7351 CNRS, Parc Valrose, 06108 Nice Cedex 02, France
a e-mail: grossmann@physik.hu-berlin.de
Received: 10 April 2015
Revised: 18 May 2015
Published online: 24 July 2015
We propose a geometric perspective to describe the motion of self-propelled particles moving at constant speed in d dimensions. We exploit the fact that the vector that conveys the direction of motion of the particle performs a random walk on a (d − 1)-dimensional manifold. We show that the particle performs isotropic diffusion in d-dimensions if the manifold corresponds to a hypersphere. In contrast, we find that the self-propelled particle exhibits anisotropic diffusion if this manifold corresponds to a deformed hypersphere (e.g. an ellipsoid). This simple approach provides an unified framework to deal with isotropic as well as anisotropic diffusion of particles moving at constant speed in any dimension.
© EDP Sciences, Springer-Verlag, 2015
