Hierarchically Coupled Ornstein–Uhlenbeck Processes for Transient Anomalous Diffusion

Author:

Wang Jingyang1,Voulgarakis Nikolaos K.1ORCID

Affiliation:

1. Department of Mathematics and Statistics, Washington State University, Pullman, WA 99164, USA

Abstract

The nonlinear dependence of the mean-squared displacement (MSD) on time is a common characteristic of particle transport in complex environments. Frequently, this anomalous behavior only occurs transiently before the particle reaches a terminal Fickian diffusion. This study shows that a system of hierarchically coupled Ornstein–Uhlenbeck equations is able to describe both transient subdiffusion and transient superdiffusion dynamics, as well as their sequential combinations. To validate the model, five distinct experimental, molecular dynamics simulation, and theoretical studies are successfully described by the model. The comparison includes the transport of particles in random optical fields, supercooled liquids, bedrock, soft colloidal suspensions, and phonons in solids. The model’s broad applicability makes it a convenient tool for interpreting the MSD profiles of particles exhibiting transient anomalous diffusion.

Funder

National Science Foundation

Publisher

MDPI AG

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