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非静态介质中外部恒力场中的 Lévy 行走动力学。

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

作者信息

Zhou Tian, Xu Pengbo, Deng Weihua

机构信息

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

School of Mathematical Sciences, Peking University, Beijing, 100871 People's Republic of China.

出版信息

J Stat Phys. 2022;187(1):9. doi: 10.1007/s10955-022-02904-8. Epub 2022 Feb 28.

DOI:10.1007/s10955-022-02904-8
PMID:35250092
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC8883250/
Abstract

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.

摘要

基于对非静态介质中扩散粒子输运性质巨大变化的认识，我们考虑在非静态介质中受外部恒定力作用的 Lévy 行走模型。由于非静态介质的物理坐标和共动坐标通过尺度因子相关联，我们将该过程等效地从物理坐标转换到共动坐标，并推导了控制共动坐标中粒子位置概率密度函数的主方程。利用埃尔米特正交多项式展开，得到了一些统计性质，包括两个坐标中前两阶矩的渐近行为和峰度。对于一些具有代表性的非静态介质类型和 Lévy 行走，观察到了源于非静态介质、外力和内在随机运动之间相互作用的显著而有趣的现象。还通过数值模拟分析了某些情况下的平稳分布。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6290/8883250/5ef48f2ef0eb/10955_2022_2904_Fig14_HTML.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6290/8883250/c05e445fb9c3/10955_2022_2904_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6290/8883250/de41b4f00573/10955_2022_2904_Fig5_HTML.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6290/8883250/25294cc8e8b5/10955_2022_2904_Fig7_HTML.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6290/8883250/5ef48f2ef0eb/10955_2022_2904_Fig14_HTML.jpg

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本文引用的文献

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Phys Rev E. 2021 Mar;103(3-1):032151. doi: 10.1103/PhysRevE.103.032151.
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