Orthogonal run-and-tumble walks

TL;DR

This paper analyzes planar orthogonal run-and-tumble walks, deriving probability distributions and diffusion properties for symmetric cases, and explores how different motion classes affect effective diffusivity.

Contribution

It provides general expressions for probability distributions, mean square displacement, and diffusion constants for orthogonal run-and-tumble walks, including specific cases like cyclic motion.

Findings

Enhanced diffusivity in cyclic and backward motion cases.

Analytic expressions for probability distributions in certain motion classes.

Reduced diffusivity compared to standard active motion in some scenarios.

Abstract

Planar run-and-tumble walks with orthogonal directions of motion are considered. After formulating the problem with generic transition probabilities among the orientational states, we focus on the symmetric case, giving general expressions of the probability distribution function (in the Laplace-Fourier domain), the mean square displacement and the effective diffusion constant in terms of transition rate parameters. As case studies we treat and discuss two classes of motion, alternate/forward and isotropic/backward, obtaining, when possible, analytic expressions of probability distribution functions in the space-time domain. We discuss at the end also the case of cyclic motion. Reduced (enhanced) effective diffusivity, with respect to the standard 2D active motion, is observed in the cyclic and backward (forward) cases.