Persistent-random-walk approach to anomalous transport of self-propelled particles

TL;DR

This paper models the movement of self-propelled particles as a persistent random walk, deriving exact expressions for displacement moments and analyzing the transition from anomalous to normal diffusion.

Contribution

It introduces an analytical framework for persistent random walks, revealing how step and turning angle distributions influence anomalous and normal diffusion behaviors.

Findings

Short-time anomalous diffusion observed

Crossover time depends on model parameters

Analytical expressions for skewness and kurtosis

Abstract

The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's displacement. It is shown that the interplay of step length and turning angle distributions and self-propulsion produces various signs of anomalous diffusion at short time scales and asymptotically a normal diffusion behavior with a broad range of diffusion coefficients. The crossover from the anomalous short time behavior to the asymptotic diffusion regime is studied and the parameter dependencies of the crossover time are discussed. Higher moments of the displacement distribution are calculated and analytical expressions for the time evolution of the skewness and the kurtosis of the distribution are presented.