Eur. Phys. J. B (2012) 85: 281
https://doi.org/10.1140/epjb/e2012-30480-8

Regular Article

Time correlations and persistence probability of a Brownian particle in a shear flow

Max-Planck-Institut für Intelligente Systeme, Heisenberstr. 3, 70569 Stuttgart, Germany,
Institut für Theoretische und Angewandte Physik, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany

^a e-mail: chakraborty@is.mpg.de

Received: 16 June 2012
Received in final form: 25 June 2012
Published online: 13 August 2012

Abstract

In this article, results have been presented for the two-time correlation functions for a free and a harmonically confined Brownian particle in a simple shear flow. For a free Brownian particle, the motion along the direction of shear exhibit two distinct dynamics, with the mean-square-displacement being diffusive at short times while at late times scales as t³. In contrast the cross-correlation 〈 x(t)y(t) 〉 scales quadratically for all times. In the case of a harmonically trapped Brownian particle, the mean-square-displacement exhibits a plateau determined by the strength of the confinement and the shear. Further, the analysis is extended to a chain of Brownian particles interacting via a harmonic and a bending potential. Finally, the persistence probability is constructed from the two-time correlation functions.