Anomalous particle diffusion influenced by angular heterogeneity

TL;DR

This paper introduces a generalized persistent random walk model to analyze how angular heterogeneity affects anomalous particle diffusion, revealing different diffusion behaviors including Gaussian, non-Gaussian, and superdiffusion.

Contribution

The paper presents a novel GPRW model that incorporates angular heterogeneity and past conditions, advancing understanding of complex diffusion processes in heterogeneous environments.

Findings

Particles show Gaussian diffusion with directional drift in memoryless systems.

Full distribution diverges from Gaussian when speed influences direction persistence.

Superdiffusion occurs when historical distance influences direction persistence.

Abstract

A generalized persistent random walk (GPRW) model to study anomalous particle diffusion influenced by angular heterogeneity is presented. Consider the motion of a particle is composed of many consecutive straight line segments. At the end of each straight motion, the particle can switch to a new moving direction. Angular heterogeneity occurs when the probability of choosing a moving direction is non-uniformly distributed and influenced by surrounding environment and by the particle past conditions. Based on the model, we show that particles perform Gaussian Fickian diffusion with directional drifting in a memoryless system with spatial dependent angular heterogeneity. When the probability of maintaining the current moving direction is correlated with the particle speed, these particles perform Fickian diffusion, but their full distribution diverges from Gaussian. When the probability of maintaining te current moving direction is correlated with the historical moving distance, particles perform superdiffusion. The GPRW framework presented can be applied to study protein diffusion, cell migration and solute transport in complex heterogeneous environments.