Rototaxis: Localization of active motion under rotation

Abstract

The ability to navigate in complex, inhomogeneous environments is fundamental to survival at all length scales, giving rise to the rapid development of various subfields in biolocomotion such as the well established concept of chemotaxis. In this work, we extend this existing notion of taxis to rotating environments and introduce the idea of "rototaxis" to biolocomotion. In particular, we explore both overdamped and inertial dynamics of a model synthetic self-propelled particle in the presence of constant global rotation, focusing on the particle's ability to localize near a rotation center as a survival strategy. We find that, in the overdamped regime, a torque directing the swim orientation to the rotation origin enables the swimmer to remain on stable epicyclical-like trajectories. On the other hand, for underdamped motion with inertial effects, the intricate competition between self-propulsion and inertial forces, in conjunction with the rotation-induced torque, leads to complex dynamical behavior with nontrivial phase space of initial conditions which we reveal by numerical simulations. Our results are relevant for a wide range of setups, from vibrated granular matter on turntables to microorganisms or animals swimming near swirls or vortices.