Fractal model of the transition from ballistic to diffusive motion of a Brownian particle

被引：10
|
作者：
Gmachowski, Lech [1 ]
机构：
[1] Warsaw Univ Technol, Inst Chem, PL-09400 Plock, Poland
来源：
JOURNAL OF AEROSOL SCIENCE | 2013年 / 57卷
关键词：
Scale-dependent fractal dimension; Particle trajectory; Ballistic motion; Diffusive motion; Crossover behavior; DIMENSION; BEHAVIOR;
D O I：
10.1016/j.jaerosci.2012.11.006
中图分类号：
TQ [化学工业];
学科分类号：
0817 ;
摘要：
A formula is presented for calculation the particle mean square displacement normalized by the square of its mean free path as dependent on the time related to the momentum relaxation time. The obtained equation is a result of the fractal analysis of the particle trajectory being a sequence of linear segments. At very short times the motion is ballistic whereas for long times the particle starts to behave according to Einstein's theory. The slope of a log-log plot of time dependence of mean square displacement changes from two to one. The ballistic to diffusive transition is wider than that described by the Langevin equation and spans more than three decades of time. (C) 2012 Elsevier Ltd. All rights reserved.
引用
收藏
页码：194 / 198
页数：5
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