Spiral diffusion of rotating self-propellers with stochastic perturbation

TL;DR

This paper presents a theory describing the spiral motion of mean trajectories of rotating self-propellers with stochastic perturbations, supported by experimental evidence from microscopic motors, and highlights its potential for parameter estimation.

Contribution

It introduces a theoretical model for spiral diffusion of rotating self-propellers under stochastic influences, validated by experiments with microscopic motors, and suggests a new method for parameter determination.

Findings

Mean trajectory exhibits spiral motion depending on propulsion and diffusion parameters.

Experimental validation with tadpole-like and Janus sphere motors confirms the theory.

Sensitivity analysis indicates potential for parameter estimation.

Abstract

Translationally diffusive behavior arising from the combination of orientational diffusion and powered motion at microscopic scales is a known phenomenon, but the peculiarities of the evolution of expected position conditioned on initial position and orientation have been neglected. A theory is given of the spiral motion of the mean trajectory depending upon propulsion speed, angular velocity, orientational diffusion and rate of random chirality reversal. We demonstrate the experimental accessibility of this effect using both tadpole-like and Janus sphere dimer rotating motors. Sensitivity of the mean trajectory to the kinematic parameters suggest that it may be a useful way to determine those parameters.