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Marcin Magdziarz1, Aleksander Weron

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Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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This study confirms that fractional Fokker-Planck dynamics can exhibit competition between subdiffusion and Lévy flights. Monte Carlo simulations visualize this competition in anomalous diffusion processes.

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Area of Science:

  • Physics
  • Complex Systems
  • Statistical Mechanics

Background:

  • Anomalous diffusion describes particle transport deviating from Brownian motion.
  • Fractional Fokker-Planck equations model complex diffusion dynamics.
  • Metzler and Klafter posed a question regarding competing diffusion mechanisms.

Purpose of the Study:

  • To investigate the competition between subdiffusion and Lévy flights.
  • To validate findings within the fractional Fokker-Planck dynamics framework.
  • To demonstrate this competition using computational methods.

Main Methods:

  • Utilizing Monte Carlo simulations.
  • Employing a stochastic representation for fractional Fokker-Planck dynamics.
  • Analyzing both individual particle trajectories (realizations) and overall probability distributions.

Main Results:

  • Positive confirmation of competing subdiffusion and Lévy flight behaviors.
  • Demonstration of this competition across different analysis levels.
  • Successful simulation of anomalous diffusion processes.

Conclusions:

  • Fractional Fokker-Planck dynamics inherently support competing subdiffusion and Lévy flight mechanisms.
  • Monte Carlo simulations provide a viable method for observing these competing dynamics.
  • The study answers a key question in the field of anomalous diffusion research.