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Fractional Brownian motion with fluctuating diffusivities.

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This study introduces a generalized diffusion model for anomalous diffusion, accounting for environmental and tracer heterogeneities. The new framework provides analytical solutions for complex diffusion systems, validated by simulations.

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Area of Science:

  • Physics
  • Physical Chemistry
  • Statistical Mechanics

Background:

  • Fractional Brownian motion (fBm) successfully models anomalous diffusion with temporal correlations.
  • Existing models fall short when incorporating heterogeneities in tracers or the environment.
  • A generalized diffusion framework is needed for complex, heterogeneous systems.

Purpose of the Study:

  • To develop a modified Lévy's representation of fBm for stochastic diffusion coefficients.
  • To derive analytical expressions for key diffusion metrics in heterogeneous systems.
  • To validate the new framework using numerical simulations in two-state systems.

Main Methods:

  • Modification of Lévy's representation for fractional Brownian motion.
  • Derivation of analytical expressions for autocovariance function and mean squared displacements (MSD).
  • Validation through numerical simulations of two-state systems and comparison with analytical results.

Main Results:

  • Analytical expressions for autocovariance and ensemble/time-averaged MSD were successfully derived.
  • The developed framework accurately models anomalous diffusion in heterogeneous systems.
  • Simulations confirmed the efficacy of the analytical asymptotic expressions in two-state systems.

Conclusions:

  • The proposed generalized diffusion model effectively incorporates stochastic diffusion coefficients and heterogeneities.
  • The analytical solutions provide valuable insights into complex diffusion dynamics.
  • This framework offers a more comprehensive approach to modeling anomalous diffusion in diverse scientific fields.