Confined subdiffusion in three dimensions  

作　　者：覃善林 何勇 

机构地区：[1]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

出　　处：《Chinese Physics B》2014年第11期145-151,共7页中国物理B（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.21153002);the Fundamental Research Funds for the Central Universities of China(Grant No.2013zzts151)

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 dis- placement （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 formu- las in two limiting cases： （^-δ2） ~ △1 in short lag time and （^-δ2} ~ △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.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 dis- placement （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 formu- las in two limiting cases： （^-δ2） ~ △1 in short lag time and （^-δ2} ~ △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 

分 类 号：O241.8[理学—计算数学]