A geometric approach to self-propelled motion in isotropic and anisotropic environments

Abstract

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.

18 pages, 5 figures, published in EPJ-ST

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