Microorganism billiards in closed plane curves

TL;DR

This paper investigates microorganism billiards in closed curves, modeling their fixed-angle interactions with surfaces, analyzing their dynamics through simulations and mathematical tools, and exploring effects of noise across different billiard shapes.

Contribution

It introduces a novel billiard model based on microorganism surface interactions, combining numerical simulations and wavefront theory to analyze dynamics in various geometries.

Findings

Fixed outgoing angle leads to unique billiard dynamics.

Different table geometries exhibit distinct stability properties.

Noise impacts the long-term behavior of microorganism billiards.

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.