Environment-dependent continuous time random walk

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

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.

Keywords: continuous time random walk environment-dependent rare-though-dominate events anomalous diffusion

Received: 28 September 2010
Revised: 10 January 2011
Accepted manuscript online:

PACS:	05.40.Fb	(Random walks and Levy flights)
	05.20.Dd	(Kinetic theory)
	02.60.Cb	(Numerical simulation; solution of equations)

Fund: Project supported by the Scientific Research Foundation of Sichuan University for Young Teachers, China (Grant No. 2009SCU11120).

Cite this article:

Lin Fang(林方) and Bao Jing-Dong(包景东) Environment-dependent continuous time random walk 2011 Chin. Phys. B 20 040502

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