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Lévy walks in nonhomogeneous environments.

A Kamińska1, T Srokowski1

  • 1Institute of Nuclear Physics, Polish Academy of Sciences, PL 31-342 Kraków, Poland.

Physical Review. E
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Summary
This summary is machine-generated.

This study explores Lévy walk with rests, finding that nonhomogeneous trap distributions can shift enhanced diffusion to subdiffusion. Particle densities exhibit time-dependent, stretched-exponential behavior at long times.

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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.