Brownian motion on the discontinuous structure of matter". The direction of the force of atomic bombardment is constantly changing, and at different times the particle is hit more on one side than another, leading to the seemingly random nature of the motion. The many-body interactions that yield the Brownian pattern cannot be solved by a model accounting for every involved molecule. In consequence only probabilistic models applied to molecular populations can be employed to describe it. Two such models of the statistical mechanics, due to Einstein and Smoluchowski are presented below. Another, pure probabilistic class of models is the class of the
Reflected Brownian motion Reflected Brownian motion In probability theory, reflected Brownian motion (or regulated Brownian motion, both with the acronym RBM) is a Wiener process in a space with reflecting boundaries. RBMs have been shown to describe queueing models experiencing heavy traffic as first proposed by Kingman and proven by Iglehart and Whitt. A "d"–dimensional reflected Brownian motion "Z" is a stochastic process on formula_1 uniquely defined by where "X"("t") is an unconstrained Brownian motion and with "Y"("t") a "d"–dimensional vector where The reflection matrix describes boundary behaviour. In the interior of formula_4 the process behaves like a Wiener process, on the boundary