Effects of the Tempered Aging and the Corresponding Fokker–Planck Equation

Weihua Deng; Wanli Wang; Xinchun Tian; Yujiang Wu

doi:10.1007/s10955-016-1547-3

Effects of the Tempered Aging and the Corresponding Fokker–Planck Equation

Weihua Deng, Wanli Wang, Xinchun Tian, Yujiang Wu

Lanzhou University

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In the renewal processes, if the waiting time probability density function is a tempered power-law distribution, then the process displays a transition dynamics; and the transition time depends on the parameter λ of the exponential cutoff. In this paper, we discuss the aging effects of the renewal process with the tempered power-law waiting time distribution. By using the aging renewal theory, the p-th moment of the number of renewal events n_a(t_a, t) in the interval (t_a, t_a+ t) is obtained for both the weakly and strongly aged systems; and the corresponding surviving probabilities are also investigated. We then further analyze the tempered aging continuous time random walk and its Einstein relation, and the mean square displacement is attained. Moreover, the tempered aging diffusion equation is derived.

Original language	English
Pages (from-to)	377-398
Number of pages	22
Journal	Journal of Statistical Physics
Volume	164
Issue number	2
DOIs	https://doi.org/10.1007/s10955-016-1547-3
State	Published - 1 Jul 2016
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2016, Springer Science+Business Media New York.

Funding

The authors thank Eli Barkai for the discussions. This work was supported by the Fundamental Research Funds for the Central Universities under Grant No. lzujbky-2015-77, and the National Natural Science Foundation of China under Grant No. 11271173.

Funders	Funder number
National Natural Science Foundation of China	11271173
Fundamental Research Funds for the Central Universities	lzujbky-2015-77

Keywords

CTRW
Fokker–Planck equation
Renewal process
Tempered aging

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10.1007/s10955-016-1547-3

Cite this

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abstract = "In the renewal processes, if the waiting time probability density function is a tempered power-law distribution, then the process displays a transition dynamics; and the transition time depends on the parameter λ of the exponential cutoff. In this paper, we discuss the aging effects of the renewal process with the tempered power-law waiting time distribution. By using the aging renewal theory, the p-th moment of the number of renewal events na(ta, t) in the interval (ta, ta+ t) is obtained for both the weakly and strongly aged systems; and the corresponding surviving probabilities are also investigated. We then further analyze the tempered aging continuous time random walk and its Einstein relation, and the mean square displacement is attained. Moreover, the tempered aging diffusion equation is derived.",

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Effects of the Tempered Aging and the Corresponding Fokker–Planck Equation

Abstract

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Keywords

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