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Memory-induced anomalous dynamics: Emergence of diffusion, subdiffusion, and superdiffusion from a single random walk

Niraj Kumar1, Upendra Harbola, Katja Lindenberg

  • 1Department of Chemistry and Biochemistry, BioCircuits Institute, University of California-San Diego, La Jolla, 92093-0340, USA.

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A novel random walk model demonstrates subdiffusive, diffusive, and superdiffusive behaviors by adjusting parameters. This analytically tractable, non-Markovian model offers insights into diverse movement patterns.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Complex Systems

Background:

  • Random walk models are fundamental in describing particle and system movement.
  • Understanding anomalous diffusion (subdiffusion, superdiffusion) is crucial in various scientific fields.
  • Existing models often capture only specific types of anomalous diffusion.

Purpose of the Study:

  • To introduce a unified random walk model capable of exhibiting subdiffusive, diffusive, and superdiffusive behaviors.
  • To provide a single, analytically tractable framework for studying diverse transport phenomena.
  • To explore the origins of different asymptotic behaviors within a single model.

Main Methods:

  • Development of a non-Markovian random walk model.
  • Incorporation of intermittent steps where the walker may not move.
  • Analysis of model behavior across different parameter regimes.

Main Results:

  • The model successfully reproduces subdiffusive, diffusive, and superdiffusive asymptotic behaviors.
  • Behavioral transitions are achieved solely by altering model parameters.
  • The model is analytically tractable, facilitating deeper theoretical analysis.

Conclusions:

  • A single, versatile random walk model can encompass all three major types of asymptotic transport.
  • The model's non-Markovian and intermittent features are key to its broad applicability.
  • This unified approach simplifies the study of anomalous diffusion and related phenomena.