Active Brownian motion with orientation-dependent motility: theory and experiments

Combining experiments on active colloids, whose propulsion velocity can be controlled via a feedback loop, and theory of active Brownian motion, we explore the dynamics of an overdamped active particle with a motility that depends explicitly on the particle orientation. In this case, the active particle moves faster when oriented along one direction and slower when oriented along another, leading to an anisotropic translational dynamics which is coupled to the particle's rotational diffusion. We propose a basic model of active Brownian motion for orientation-dependent motility. Based on this model, we obtain analytic results for the mean trajectories, averaged over the Brownian noise for various initial configurations, and for the mean-square displacements including their non-Gaussian behavior. The theoretical results are found to be in good agreement with the experimental data. An orientation-dependent motility is found to induce a significant anisotropy in the particle displacement, mean-square displace...