Nonlinear dynamics of continuous-time random walks in inhomogeneous medium

Area of Science:

• Physics
• Statistical Mechanics
• Mathematical Modeling

Background:

• Continuous-time random walks (CTRWs) model particle motion with random waiting times.
• Standard CTRWs assume uniform waiting time distributions.
• Inhomogeneities in the medium can significantly alter particle transport dynamics.

Purpose of the Study:

• To investigate the diffusion limit of an inhomogeneous CTRW model.
• To analyze particle motion in a medium with a bounded trapping region and location-dependent waiting times.
• To determine how power-law waiting time distributions influence diffusive behavior.

Main Methods:

• Derivation of a diffusion limit for the inhomogeneous CTRW.
• Analysis of CTRW with power-law waiting times within a trapping region.
• Comparison of motion in the trapping region (anomalous diffusion) versus elsewhere (regular diffusion).

Main Results:

• The study derives a diffusion limit for the described inhomogeneous CTRW.
• It is shown that the particle's motion can exhibit nonlinear subdiffusion.
• Alternatively, standard diffusive motion is observed, contingent on the power-law distribution's index.

Conclusions:

• Location-dependent waiting times in CTRWs lead to complex transport phenomena.
• The presence of a bounded trapping region with power-law waiting times can induce subdiffusion.
• The resulting diffusive behavior is tunable via the power-law index, offering insights into anomalous transport in heterogeneous media.