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

Based on the recognition of the huge change of the transport properties for diffusion particles in non-static media, we consider a Lévy walk model subjected to an external constant force in non-static media. Since the physical and comoving coordinates of non-static media are related by scale factor,...

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Bibliographic Details
Published in:Journal of statistical physics 2022, Vol.187 (1), p.9-9, Article 9
Main Authors: Zhou, Tian, Xu, Pengbo, Deng, Weihua
Format: Article
Language:English
Subjects:
Analysis
Asymptotic properties
Distribution (Probability theory)
Hermite polynomials
Kurtosis
Mathematical analysis
Mathematical and Computational Physics
Mathematical models
Media
Physical Chemistry
Physics
Physics and Astronomy
Probability density functions
Quantum Physics
Statistical analysis
Statistical Physics and Dynamical Systems
Theoretical
Transport properties
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Summary:Based on the recognition of the huge change of the transport properties for diffusion particles in non-static media, we consider a Lévy walk model subjected to an external constant force in non-static media. Since the physical and comoving coordinates of non-static media are related by scale factor, we equivalently transfer the process from physical coordinate into comoving coordinate and derive the master equation governing the probability density function of the position of the particles in comoving coordinate. Utilizing the Hermite orthogonal polynomial expansions, some statistical properties are obtained, including the asymptotic behaviors of the first two moments in both coordinates and kurtosis. For some representative types of non-static media and Lévy walks, the striking and interesting phenomena originating from the interplay between non-static media, external force, and intrinsic stochastic motion are observed. The stationary distribution are also analyzed for some cases through numerical simulations.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-022-02904-8