Environment-dependent continuous time random walk

doi:10.1088/1674-1056/20/4/040502

中国物理B ›› 2011, Vol. 20 ›› Issue (4): 40502-040502.doi: 10.1088/1674-1056/20/4/040502

Environment-dependent continuous time random walk

林方¹, 包景东²

(1)College of Physical Science and Technology, Sichuan University, Chengdu 610064, China; (2)Department of Physics, Beijing Normal University, Beijing 100875, China

收稿日期:2010-09-28 修回日期:2011-01-10 出版日期:2011-04-15 发布日期:2011-04-15
基金资助:
Project supported by the Scientific Research Foundation of Sichuan University for Young Teachers, China (Grant No. 2009SCU11120).

Environment-dependent continuous time random walk

Lin Fang(林方)^a)^† and Bao Jing-Dong(包景东)^b)

^a College of Physical Science and Technology, Sichuan University, Chengdu 610064, China; ^b Department of Physics, Beijing Normal University, Beijing 100875, China

Received:2010-09-28 Revised:2011-01-10 Online:2011-04-15 Published:2011-04-15
Supported by:
Project supported by the Scientific Research Foundation of Sichuan University for Young Teachers, China (Grant No. 2009SCU11120).

摘要/Abstract

摘要： A generalized continuous time random walk model which is dependent on environmental damping is proposed in which the two key parameters of the usual random walk theory: the jumping distance and the waiting time, are replaced by two new ones: the pulse velocity and the flight time. The anomalous diffusion of a free particle which is characterized by the asymptotical mean square displacement <x²(t)>～t^α is realized numerically and analysed theoretically, where the value of the power index α is in a region of 0 < α < 2. Particularly, the damping leads to a sub-diffusion when the impact velocities are drawn from a Gaussian density function and the super-diffusive effect is related to statistical extremes, which are called rare-though-dominant events.

关键词: continuous time random walk, environment-dependent, rare-though-dominate events, anomalous diffusion

Abstract: A generalized continuous time random walk model which is dependent on environmental damping is proposed in which the two key parameters of the usual random walk theory: the jumping distance and the waiting time, are replaced by two new ones: the pulse velocity and the flight time. The anomalous diffusion of a free particle which is characterized by the asymptotical mean square displacement $\langle x^2(t)\rangle\sim t^{\alpha}$ is realized numerically and analysed theoretically, where the value of the power index $\alpha$ is in a region of $0< \alpha <2$. Particularly, the damping leads to a sub-diffusion when the impact velocities are drawn from a Gaussian density function and the super-diffusive effect is related to statistical extremes, which are called rare-though-dominant events.

Key words: continuous time random walk, environment-dependent, rare-though-dominate events, anomalous diffusion

中图分类号: (Random walks and Levy flights)

05.40.Fb

05.20.Dd (Kinetic theory) 02.60.Cb (Numerical simulation; solution of equations)

林方, 包景东. Environment-dependent continuous time random walk[J]. 中国物理B, 2011, 20(4): 40502-040502.

Lin Fang(林方) and Bao Jing-Dong(包景东). Environment-dependent continuous time random walk[J]. Chin. Phys. B, 2011, 20(4): 40502-040502.

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Environment-dependent continuous time random walk

Environment-dependent continuous time random walk

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