Confined subdiffusion in three dimensions

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

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.

Keywords: confined subdiffusion three dimensions time-averaged mean squared displacement

Received: 19 March 2014
Revised: 20 May 2014
Accepted manuscript online:

PACS:	02.50.-r	(Probability theory, stochastic processes, and statistics)
	05.10.Gg	(Stochastic analysis methods)
	05.20.Dd	(Kinetic theory)

Fund: 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).

Corresponding Authors: He Yong
E-mail: liuxizhong123@163.com

Cite this article:

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

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