Langevin picture of anomalous diffusion processes in expanding medium

TL;DR

This paper develops a Langevin equation framework to analyze anomalous diffusion in expanding media, revealing how different expansion rates and intrinsic particle behaviors influence diffusion phenomena through theoretical and simulation studies.

Contribution

It introduces a Langevin picture for anomalous diffusion in expanding media, extending beyond previous CTRW models to include diverse diffusion processes and physical observables.

Findings

Different expansion rates cause distinct diffusion behaviors.

Intrinsic particle diffusion properties significantly affect outcomes.

Theoretical and simulation results provide comprehensive insights.

Abstract

Expanding medium is very common in many different fields, such as biology and cosmology. It brings a nonnegligible influence on particle's diffusion, which is quite different from the effect of an external force field. The dynamic mechanism of particle's motion in expanding medium has only been investigated in the framework of continuous-time random walk. To focus on more diffusion processes and physical observables, we build the Langevin picture of anomalous diffusion in expanding medium, and conduct detailed analyses in the framework of Langevin equation. With the help of a subordinator, both subdiffusion process and superdiffusion process in expanding medium are discussed. We find that the expanding medium with different changing rate (exponential form and power-law form) leads to quite different diffusion phenomena. The particle's intrinsic diffusion behavior also plays an important role. Our detailed theoretical analyses and simulations present a panoramic view of investigating anomalous diffusion in expanding medium under the framework of Langevin equation.