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Related Experiment Videos

Lévy flight with absorption: A model for diffusing diffusivity with long tails.

Rohit Jain1, K L Sebastian1

  • 1Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560012, India.

Physical Review. E
|April 19, 2017
PubMed
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Particle diffusion in a changing environment shows Fickian behavior at short times but transitions to anomalous diffusion at long times. This study models diffusivity as a Lévy flight process, revealing a non-Gaussian displacement distribution over time.

Area of Science:

  • Statistical Mechanics
  • Physical Chemistry
  • Complex Systems

Background:

  • Particle diffusion in dynamic environments is crucial in various scientific fields.
  • Previous models like "diffusing diffusivity" showed non-Gaussian displacement distributions.
  • Understanding time-dependent diffusivity is key to explaining particle transport.

Purpose of the Study:

  • To investigate particle diffusion where diffusivity is a stochastic function of time, modeled as a Lévy flight process.
  • To analyze the transition from Fickian to anomalous diffusion based on diffusivity distribution.
  • To characterize the particle displacement probability distribution under these conditions.

Main Methods:

  • Modeling particle diffusivity as a Lévy flight process with a power-law tailed distribution (πe(D)∼D^{-1-α}).

Related Experiment Videos

  • Analyzing the mean square displacement and width of the displacement distribution over time.
  • Determining the functional form of the particle displacement probability distribution.

    • Main Results:

    • Short-time diffusion is Fickian, with displacement width proportional to √T.
    • Long-time diffusion exhibits anomalous behavior, with width proportional to T^{1/2α}.
    • The particle displacement distribution is a symmetric stable distribution with stability index 2α, maintaining its shape over time.

    Conclusions:

    • The Lévy flight model for diffusivity captures a transition from Fickian to anomalous diffusion.
    • The resulting non-Gaussian displacement distribution has implications for understanding transport in complex media.
    • This framework provides a new perspective on stochastic processes in disordered systems.