Lévy walks in nonhomogeneous environments

Area of Science:

• Physics
• Statistical Mechanics
• Complex Systems

Background:

• Lévy walk models describe anomalous diffusion.
• Understanding particle behavior in heterogeneous environments is crucial.

Purpose of the Study:

• To investigate Lévy walk processes with rests in nonhomogeneous trap distributions.
• To analyze the impact of trap heterogeneity on diffusion properties.

Main Methods:

• Derivation and asymptotic solution of the master equation for a position-dependent waiting time rate.
• Analysis of jumping time governed by an α-stable distribution.
• Monte Carlo simulations of individual trajectories.

Main Results:

• Time-dependent relative densities of resting and flying particles.
• Asymptotic stretched-exponential shape for particle distributions at large times.
• Transition from enhanced diffusion to subdiffusion due to heterogeneous traps.

Conclusions:

• Heterogeneous trap structures significantly alter diffusion dynamics.
• The Lévy walk model with rests provides insights into complex transport phenomena.
• Simulation results validate theoretical predictions for density distributions and mean squared displacements.