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 moment of probability of displacement formula_2, is interpreted as mass diffusivity "D": Then the density of Brownian particles "ρ" at point "x" at time "t" satisfies the diffusion equation: Assuming that "N" particles start from the origin at the initial time "t"=0, the diffusion equation has the solution This expression (which is a normal distribution with the mean formula_12 and variance formula_13 usually called Brownian motion formula_14) allowed Einstein to calculate the moments directly. The first moment is seen to vanish, meaning that the Brownian particle is equally likely to move to the left as it is to move to