Microorganism billiards in closed plane curves

Abstract: Recent experiments have shown that many species of microorganisms leave a solid surface at a fixed angle determined by steric interactions and near-field hydrodynamics. This angle is completely independent of the incoming angle. For several collisions in a closed body this determines a unique type of billiard system, an aspecular billiard in which the outgoing angle is fixed for all collisions. We analyze such a system using numerical simulation of this billiard for varying tables and outgoing angles, and also utilize the theory of one-dimensional maps and wavefront dynamics. When applicable we cite results from and compare our system to similar billiard systems in the literature. We focus on examples from three broad classes: the ellipse, the Bunimovich billiards, and the Sinai billiards. The effect of a noisy outgoing angle is also discussed.