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This study investigates anomalous diffusion in complex media with traps and memory effects. We found that system parameters determine whether diffusion is subdiffusive or enhanced, revealing distinct behaviors in bulk and near-surface regions.

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Area of Science:

  • Statistical Physics
  • Complex Systems
  • Nonlinear Dynamics

Background:

  • Stochastic motion in complex media is crucial for understanding various physical and biological processes.
  • Nonhomogeneous media with traps introduce complexities like long rests and memory effects, altering standard diffusion behavior.
  • Lévy stable statistics and subordination are advanced concepts for modeling anomalous diffusion.

Purpose of the Study:

  • To analyze diffusion properties in a nonhomogeneous medium featuring traps and memory effects.
  • To investigate how Lévy stable statistics and position-dependent memory influence particle motion.
  • To derive diffusion regimes and anomalous diffusion exponents under varying system parameters.

Main Methods:

  • Stochastic simulation of particle motion under Lévy stable statistics.
  • Modeling memory effects using position-dependent subordination.
  • Approximation by decoupling medium structure and memory, solved for power-law dependence.
  • Derivation of density distributions and moments for Gaussian statistics.
  • Analysis of Lévy flights with variable noise intensity near boundaries.

Main Results:

  • The system exhibits both subdiffusion and enhanced diffusion, dependent on geometry and memory parameters.
  • Two distinct diffusion regimes (bulk and near-surface) are identified for Lévy flights.
  • Anomalous diffusion exponents were derived as a function of system parameters.
  • Exact solutions were obtained for power-law position dependence of memory.

Conclusions:

  • The interplay of traps, nonhomogeneous media, and memory leads to complex anomalous diffusion behaviors.
  • The study provides a framework for understanding diffusion in systems with long-range correlations and heterogeneity.
  • Findings are relevant for diverse fields including biophysics, materials science, and finance.