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Lévy Walk Dynamics in an External Constant Force Field in Non-Static Media.

Tian Zhou1, Pengbo Xu2, Weihua Deng1

  • 1Gansu Key Laboratory of Applied Mathematics and Complex Systems, School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000 People's Republic of China.

Journal of Statistical Physics
|March 7, 2022
PubMed
Summary

This study models Lévy walk diffusion in non-static media under an external force. We observed unique phenomena arising from the interaction between media dynamics, force, and particle motion.

Keywords:
Constant forceHermite orthogonal polynomialLévy walkNon-static mediaScale factor

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Area of Science:

  • Statistical Physics
  • Non-equilibrium Systems
  • Complex Systems

Background:

  • Transport properties of diffusion particles significantly change in non-static media.
  • Lévy walk models are crucial for describing anomalous diffusion.
  • Understanding particle behavior under external forces in dynamic environments is essential.

Purpose of the Study:

  • To investigate a Lévy walk model subjected to an external constant force in non-static media.
  • To derive and analyze the master equation governing particle probability density in comoving coordinates.
  • To explore statistical properties and emergent phenomena in this complex system.

Main Methods:

  • Transformation of the physical coordinate system to a comoving coordinate system using a scale factor.
  • Derivation of the master equation for the probability density function.
  • Application of Hermite orthogonal polynomial expansions to obtain statistical properties.

Main Results:

  • Asymptotic behaviors of the first two moments and kurtosis were derived in both physical and comoving coordinates.
  • Striking phenomena were observed due to the interplay of non-static media, external force, and stochastic motion.
  • Stationary distributions were analyzed for specific cases via numerical simulations.

Conclusions:

  • The study provides a theoretical framework for understanding diffusion in dynamic, forced environments.
  • The interplay between media dynamics, external forces, and intrinsic stochasticity leads to complex behaviors.
  • Results offer insights into non-equilibrium statistical mechanics and transport phenomena.