Sub-diffusive scaling with power-law trapping times

doi:10.1088/1674-1056/23/7/070514

中国物理B ›› 2014, Vol. 23 ›› Issue (7): 70514-070514.doi: 10.1088/1674-1056/23/7/070514

所属专题： TOPICAL REVIEW — Statistical Physics and Complex Systems

• TOPICAL REVIEW—Statistical Physics and Complex Systems • 上一篇下一篇

Sub-diffusive scaling with power-law trapping times

罗亮^a, 汤雷翰^{a b}

a Beijing Computational Science Research Center, Beijing 100084, China;
b Department of Physics and Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Hong Kong, China

收稿日期:2014-04-08 修回日期:2014-05-29 出版日期:2014-07-15 发布日期:2014-07-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11175013) and the Research Grants Council of the Hong Kong Special Administrative Region, China (Grant No. N HKBU 213/10).

Sub-diffusive scaling with power-law trapping times

Luo Liang (罗亮)^a, Tang Lei-Han (汤雷翰)^{a b}

a Beijing Computational Science Research Center, Beijing 100084, China;
b Department of Physics and Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Hong Kong, China

Received:2014-04-08 Revised:2014-05-29 Online:2014-07-15 Published:2014-07-15
Contact: Tang Lei-Han E-mail:lhtang@csrc.ac.cn
About author:05.40.-a; 05.40.Fb; 66.10.C-; 87.16.dp
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11175013) and the Research Grants Council of the Hong Kong Special Administrative Region, China (Grant No. N HKBU 213/10).

摘要/Abstract

摘要： Thermally driven diffusive motion of a particle underlies many physical and biological processes. In the presence of traps and obstacles, the spread of the particle is substantially impeded, leading to subdiffusive scaling at long times. The statistical mechanical treatment of diffusion in a disordered environment is often quite involved. In this short review, we present a simple and unified view of the many quantitative results on anomalous diffusion in the literature, including the scaling of the diffusion front and the mean first-passage time. Various analytic calculations and physical arguments are examined to highlight the role of dimensionality, energy landscape, and rare events in affecting the particle trajectory statistics. The general understanding that emerges will aid the interpretation of relevant experimental and simulation results.

关键词: anomalous diffusion, subdiffusive scaling, random walk in a disordered medium, glass transition

Abstract: Thermally driven diffusive motion of a particle underlies many physical and biological processes. In the presence of traps and obstacles, the spread of the particle is substantially impeded, leading to subdiffusive scaling at long times. The statistical mechanical treatment of diffusion in a disordered environment is often quite involved. In this short review, we present a simple and unified view of the many quantitative results on anomalous diffusion in the literature, including the scaling of the diffusion front and the mean first-passage time. Various analytic calculations and physical arguments are examined to highlight the role of dimensionality, energy landscape, and rare events in affecting the particle trajectory statistics. The general understanding that emerges will aid the interpretation of relevant experimental and simulation results.

Key words: anomalous diffusion, subdiffusive scaling, random walk in a disordered medium, glass transition

中图分类号: (Fluctuation phenomena, random processes, noise, and Brownian motion)

05.40.-a

05.40.Fb (Random walks and Levy flights) 66.10.C- (Diffusion and thermal diffusion) 87.16.dp (Transport, including channels, pores, and lateral diffusion)

罗亮, 汤雷翰. Sub-diffusive scaling with power-law trapping times[J]. 中国物理B, 2014, 23(7): 70514-070514.

Luo Liang (罗亮), Tang Lei-Han (汤雷翰). Sub-diffusive scaling with power-law trapping times[J]. Chin. Phys. B, 2014, 23(7): 70514-070514.

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Sub-diffusive scaling with power-law trapping times

Sub-diffusive scaling with power-law trapping times

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