Multiple diffusive behaviors of the random walk in inhomogeneous environments

Area of Science:

• Physics
• Biophysics
• Physical Chemistry

Background:

• Anomalous diffusion is prevalent in complex, inhomogeneous environments like intracellular media.
• Understanding these behaviors is crucial for various biological and physical systems.

Purpose of the Study:

• To develop a unified theoretical framework for anomalous diffusion in inhomogeneous media.
• To model particle motion by coupling waiting times with local diffusion coefficients.

Main Methods:

• Development of a coupled continuous-time random walk (CTRW) model.
• Inclusion of power-law coupling between waiting time and local diffusion coefficient.
• Analysis using mean-squared displacement and probability density functions.

Main Results:

• The model successfully reproduces anomalous diffusion with exponents between 0 and 2.
• Both heavy-tailed and exponential waiting time densities were implemented.
• Brownian yet non-Gaussian diffusion was achieved within the framework.

Conclusions:

• The developed model provides a unified approach to understanding diverse anomalous diffusion behaviors.
• It offers a theoretical interpretation for random particle motion in complex environments.
• The model's validity is supported by its ability to reproduce experimental results from various systems.