title: 111 years of Brownian motion.
abstract: We consider the Brownian motion of a particle and present a tutorial review over the last 111 years since Einstein's paper in 1905. We describe Einstein's model, Langevin's model and the hydrodynamic models, with increasing sophistication on the hydrodynamic interactions between the particle and the fluid. In recent years, the effects of interfaces on the nearby Brownian motion have been the focus of several investigations. We summarize various results and discuss some of the controversies associated with new findings about the changes in Brownian motion induced by the interface.
authors.affiliation: Division of Applied Mathematics, Brown University, Providence, RI 02912, USA. xin_bian@brown.edu changhokim@lbl.gov george_karniadakis@brown.edu.
authors.forename: Xin
authors.initials: X
authors.lastname: Bian
authors.forename: Changho
authors.initials: C
authors.lastname: Kim
authors.forename: George Em
authors.initials: GE
authors.lastname: Karniadakis