Distribution function, 2 particle variant

The traditional apparatus of statistical physics employed to construct models of physico-chemical processes is the method of calculating the partition function [17,19,26]. The alternative method of correlation functions or distribution functions [75] is more flexible. It is now the main method in the theory of the condensed state both for solid and liquid phases [76,77]. This method has also found an application for lattice systems [78,79]. A new variant of the method of correlation functions - the cluster approach was treated in the book [80]. The cluster approach provides a procedure for the self-consistent calculation of the complete set of probabilities of particle configurations on a cluster being considered. This makes it possible to take account of the local inhomogeneities of a lattice in the equilibrium and non-equilibrium states of a system of interacting particles. In this section the kinetic equations for wide atomic-molecular processes within the gas-solid systems were constructed. 

As is well known, the considered microscopic Langevin equations, are equivalent to the reformulation of (2) as a Smoluchowski equation it is a variant of a Fokker-Planck equation [47]. It describes the temporal evolution of the distribution function F( r , f) of the particle positions... 

Log normal distribution (logarithmic normal distribution). A statistical probabiUty-density function, characterized by two parameters, that can sometimes provide a faithful representation of a polymer s molecular-weight distribution or the distribution of particle sizes in ground, brittle materials. It is a variant of the familiar normal or Gaussian distribution in which the logarithm of the measured quantity replaces the quantity itself. Its mathematical for is... 

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