BROWNIAN PARTICLES IN SHEAR-FLOW AND HARMONIC POTENTIALS - A STUDY OF LONG-TIME TAILS
BROWNIAN PARTICLES IN SHEAR-FLOW AND HARMONIC POTENTIALS - A STUDY OF LONG-TIME TAILS
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DOI：
10.1103/physreva.46.1942
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发表时间：
1992-08-15
影响因子：
2.9
通讯作者：
SCHRAM, PPJM
中科院分区：
文献类型：
--
作者：
CLERCX, HJH;SCHRAM, PPJM
本文给出了布朗粒子在调和势中的均方位移和布朗粒子在剪切流中的均方位移的研究结果。我们着重研究了均方位移的长时间行为。与以前的结果相比，提出了其他人谁研究了这些问题的Stokes极限，我们研究了这个问题，使用时间相关的线性化不可压缩的Navier-Stokes方程来描述流体运动。然后，我们看到，均方位移的强烈影响，在流体中的回流效应，导致，除其他外，在相关函数的长时间尾巴。我们比较了我们的结果与斯托克斯极限计算的结果，它们之间存在重要的差异。主要的区别是相关函数的长时间尾巴，与它们相关的，更大的时间尺度，应该被认为是获得扩散行为的情况下的布朗粒子在谐波势或获得立方制度的布朗粒子在剪切流的均方位移。此外，我们还研究了简谐势中布朗粒子的速度自相关函数。在过阻尼的情况下，我们已经示出了τ-7/2长时间尾部，而不是可以在斯托克斯极限中获得的指数尾部。两个尾巴的符号也不一样。
In this paper we present the results of a study of the mean-square displacement of a Brownian particle in a harmonic potential and of a Brownian particle in shear flow. We have focused on the long-time behavior of the mean-square displacement. In contrast with earlier results, presented by others who studied the Stokes limit of these problems, we have studied this problem using the time-dependent linearized incompressible Navier-Stokes equations to describe the fluid motion. Then we see that the mean-square displacement is strongly influenced by backflow effects in the fluid, resulting, among other things, in long-time tails of correlation functions. We have compared our results with those calculated in the Stokes limit; important differences exist between them. The main differences are the long-time tails in correlation functions and, related with them, the larger time scales that should be considered to obtain diffusive behavior in the case of a Brownian particle in a harmonic potential or to obtain the cubic regime in the mean-square displacement of a Brownian particle in shear flow. Furthermore, we have studied the velocity autocorrelation function of a Brownian particle in a harmonic potential. In the over-damped case we have shown a tau--7/2 long-time tail instead of the exponential tail that can be obtained in the Stokes limit. Also the sign of both tails differ.