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Diffusion is a type of passive transport. In passive transport, a substance tends to move from an area of high concentration to an area of low concentration until the concentration is equal across the space. For example, take the diffusion of substances through the air. When someone opens a perfume bottle in a room filled with people, the perfume is at its highest concentration in the bottle and is at its lowest at the edges of the room. The perfume vapor will diffuse, or spread away, from the...
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Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes.

Andrey G Cherstvy1, Ralf Metzler1

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This study explores particle diffusion in disordered media, examining how fluctuating local diffusivity affects movement. Simulations and analytical methods reveal insights into normal and anomalous diffusion, including sub- and superdiffusive behaviors.

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Area of Science:

  • Physics
  • Physical Chemistry
  • Materials Science

Background:

  • Particle diffusion in disordered media is crucial for understanding transport phenomena.
  • Local diffusivity fluctuations and deterministic trends significantly impact diffusion dynamics.

Purpose of the Study:

  • To investigate particle diffusion in a model disordered medium with time-varying local diffusivity.
  • To compare simulation results with analytical predictions for various diffusion regimes.
  • To analyze the influence of inertial effects on particle motion.

Main Methods:

  • Computer simulations of the stochastic Langevin equation.
  • Analytical calculations for ensemble and time-averaged mean squared displacements.
  • Exploration of normal, subdiffusive, and superdiffusive regimes.

Main Results:

  • The study successfully models particle diffusion with fluctuating and trending local diffusivity.
  • Agreements and discrepancies between simulations and analytical results were identified across different regimes.
  • Inertial effects were found to modify particle motion, particularly in superdiffusive scenarios.

Conclusions:

  • The model provides a framework for understanding diffusion in complex, disordered environments.
  • Both normal Brownian motion and anomalous diffusion behaviors were observed and characterized.
  • The findings contribute to the broader understanding of transport processes in heterogeneous media.