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
Brownian motion left then after "N" collisions the particle's velocity will have changed by Δ"V"(2"N" − "N"). The multiplicity is then simply given by: and the total number of possible states is given by 2. Therefore, the probability of the particle being hit from the right "N" times is: As a result of its simplicity, Smoluchowski's 1D model can only qualitatively describe Brownian motion. For a realistic particle undergoing Brownian motion in a fluid many of the assumptions cannot be made. For example, the assumption that on average occurs an equal number of collisions from the right as from the left falls