Confined subdiffusion in three dimensions

doi:10.1088/1674-1056/23/11/110206

›› 2014, Vol. 23 ›› Issue (11): 110206-110206.doi: 10.1088/1674-1056/23/11/110206

Confined subdiffusion in three dimensions

覃善林, 何勇

Hunan Key Laboratory for Super-microstructure and Ultrafast Process, Institute of Super Microstructure and Ultrafast Process in Advanced Materials, School of Physics and Electronics, Central South University, Changsha 410012, China

收稿日期:2014-03-19 修回日期:2014-05-20 出版日期:2014-11-15 发布日期:2014-11-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 21153002) and the Fundamental Research Funds for the Central Universities of China (Grant No. 2013zzts151).

Confined subdiffusion in three dimensions

Qin Shan-Lin (覃善林), He Yong (何勇)

Hunan Key Laboratory for Super-microstructure and Ultrafast Process, Institute of Super Microstructure and Ultrafast Process in Advanced Materials, School of Physics and Electronics, Central South University, Changsha 410012, China

Received:2014-03-19 Revised:2014-05-20 Online:2014-11-15 Published:2014-11-15
Contact: He Yong E-mail:liuxizhong123@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 21153002) and the Fundamental Research Funds for the Central Universities of China (Grant No. 2013zzts151).

摘要/Abstract

摘要： Three-dimensional (3D) Fick's diffusion equation and fractional diffusion equation are solved for different reflecting boundaries. We use the continuous time random walk model (CTRW) to investigate the time-averaged mean square displacement (MSD) of a 3D single particle trajectory. Theoretical results show that the ensemble average of the time-averaged MSD can be expressed analytically by a Mittag-Leffler function. Our new expression is in agreement with previous formulas in two limiting cases: <δ²> ～Δ in short lag time and <δ²>～Δ^1-α in long lag time. We also simulate the experimental data of mRNA diffusion in living E. coli using a 3D CTRW model under confined and crowded conditions. The simulation results are well consistent with experimental results. The calculations of power spectral density (PSD) further indicate the subdiffsive behavior of an individual trajectory.

关键词: confined subdiffusion, three dimensions, time-averaged mean squared displacement

Abstract: Three-dimensional (3D) Fick's diffusion equation and fractional diffusion equation are solved for different reflecting boundaries. We use the continuous time random walk model (CTRW) to investigate the time-averaged mean square displacement (MSD) of a 3D single particle trajectory. Theoretical results show that the ensemble average of the time-averaged MSD can be expressed analytically by a Mittag-Leffler function. Our new expression is in agreement with previous formulas in two limiting cases: <δ²> ～Δ in short lag time and <δ²>～Δ^1-α in long lag time. We also simulate the experimental data of mRNA diffusion in living E. coli using a 3D CTRW model under confined and crowded conditions. The simulation results are well consistent with experimental results. The calculations of power spectral density (PSD) further indicate the subdiffsive behavior of an individual trajectory.

Key words: confined subdiffusion, three dimensions, time-averaged mean squared displacement

中图分类号: (Probability theory, stochastic processes, and statistics)

02.50.-r

05.10.Gg (Stochastic analysis methods) 05.20.Dd (Kinetic theory)

覃善林, 何勇. Confined subdiffusion in three dimensions[J]. , 2014, 23(11): 110206-110206.

Qin Shan-Lin (覃善林), He Yong (何勇). Confined subdiffusion in three dimensions[J]. Chin. Phys. B, 2014, 23(11): 110206-110206.

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Confined subdiffusion in three dimensions

Confined subdiffusion in three dimensions

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