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

⟨ x^{2} (t) ⟩ \sim 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.

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

[1]	Montroll E W and Weiss G H 1965 J. Math. Phys. 6 167
[2]	Scher H and Montroll E W 1975 Phys. Rev. B 12 2455
[3]	Metzler R and Klafter J 2000 Phys. Rep. 339 1
[4]	Shlesinger M F, West B J and Klafter J 1987 Phys. Rev. Lett. 58 1100
[5]	Barkai E 2002 Chem. Phys. 284 13
[6]	Barkai E, Metzler R and Klafter J 2000 Phys. Rev. E 61 132
[7]	Lenzi E K, Anteneodo C and Borland L 2001 Phys. Rev. E 63 051109
[8]	Barkai E 2003 Phys. Rev. E 68 055104
[9]	Heinsalu E, Patriarca M, Goychuk I, Schmid G and Hänngi P 2006 Phys. Rev. E 73 046133
[10]	Heinsalu E, Patriarca M, Goychuk I and Hänggi P 2007 J. Phys.: Condens. Matter 19 065114
[11]	Barkai E and Silbey R J 2000 J. Phys. Chem. B 104 3866
[12]	Friedrich R, Jenko F, Baule A and Eule S 2006 Phys. Rev. Lett. 96 230601
[13]	Solomon T H, Weeks E R and Swinney H L 1993 Phys. Rev. Lett. 71 3975
[14]	Kozubowski T J and Rachev S T 1999 J. Comput. Anal. Appl. 1 177
[15]	Chechkin A V and Gonchar V Yu 2000 Physica A 277 312
[16]	Bao J D, Wang H Y, Jia Y and Zhuo Y Z 2005 Phys. Rev. E 72 051105
[17]	Bao J D 2009 The Stochastic Simulation Methods in Calssical and Quantum Dissipation Systems (Beijing: Science Press) (in Chinese)
[18]	Jespersen S, Metzler R and Fogedby H C 1999 Phys. Rev. E 59 2736
[19]	Fogedby H C 1994 Phys. Rev. Lett. 73 2517
[20]	Sokolov I M, Heinsalu E, Hänggi P and Goychuk I 2009 Europhys. Lett. 86 30009
[21]	Bouchaud J P and Georges A 1990 Phys. Rep. 195 127
[22]	Bao J D and Zhuo Y Z 2003 Phys. Rev. Lett. 91 138104
[23]	Weiss U 1999 Quantum Dissipative Systems 2nd edn. (Singapore: World Scientific)

[1]	Anomalous diffusion in branched elliptical structure Kheder Suleiman, Xuelan Zhang(张雪岚), Erhui Wang(王二辉),Shengna Liu(刘圣娜), and Liancun Zheng(郑连存). Chin. Phys. B, 2023, 32(1): 010202.
[2]	Diffusion dynamics in branched spherical structure Kheder Suleiman, Xue-Lan Zhang(张雪岚), Sheng-Na Liu(刘圣娜), and Lian-Cun Zheng(郑连存). Chin. Phys. B, 2022, 31(11): 110202.
[3]	Ergodicity recovery of random walk in heterogeneous disordered media Liang Luo(罗亮), Ming Yi(易鸣). Chin. Phys. B, 2020, 29(5): 050503.
[4]	Uphill anomalous transport in a deterministic system with speed-dependent friction coefficient Wei Guo(郭伟), Lu-Chun Du(杜鲁春), Zhen-Zhen Liu(刘真真), Hai Yang(杨海), Dong-Cheng Mei(梅冬成). Chin. Phys. B, 2017, 26(1): 010502.
[5]	Computational analysis of the roles of biochemical reactions in anomalous diffusion dynamics Naruemon Rueangkham, Charin Modchang. Chin. Phys. B, 2016, 25(4): 048201.
[6]	Anomalous transport in fluid field with random waiting time depending on the preceding jump length Hong Zhang(张红), Guo-Hua Li(李国华). Chin. Phys. B, 2016, 25(11): 110504.
[7]	Pattern formation in superdiffusion Oregonator model Fan Feng(冯帆), Jia Yan(闫佳), Fu-Cheng Liu(刘富成), Ya-Feng He(贺亚峰). Chin. Phys. B, 2016, 25(10): 104702.
[8]	Sub-diffusive scaling with power-law trapping times Luo Liang (罗亮), Tang Lei-Han (汤雷翰). Chin. Phys. B, 2014, 23(7): 070514.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Environment-dependent continuous time random walk

Cite this article:

Online attention