The probability distribution of a trapped Brownian particle in plane shear flows
Statistical Mechanics
2010-11-08 v3 Fluid Dynamics
Abstract
We investigate the statistical properties of an over-damped Brownian particle that is trapped by a harmonic potential and simultaneously exposed to a linear shear flow or to a plane Poiseuille flow. Its probability distribution is determined via the corresponding Smoluchowski equation, which is solved analytically for a linear shear flow. In the case of a plane Poiseuille flow, analytical approximations for the distribution are obtained by a perturbation analysis and they are substantiated by numerical results. There is a good agreement between the two approaches for a wide range of parameters.
Keywords
Cite
@article{arxiv.1008.2670,
title = {The probability distribution of a trapped Brownian particle in plane shear flows},
author = {Jochen Bammert and Walter Zimmermann},
journal= {arXiv preprint arXiv:1008.2670},
year = {2010}
}
Comments
5 pages, 4 figure