Recurrent relations for correlation functions

Abstract

We have considered the basic problem of the mathematical description of the viscous motion of a metallic melt, accompanied by the overcoming of internal friction caused by the motion of the melt particles and the overcoming of the forces of their interaction. The novelty of the research is that the correlation functions of viscosity are justified from the point of view of the quantum-statistical method. The correlation between correlation functions and the radial distribution functions is established. Based on the cluster theory of melt flow, a relationship is established between the viscosity and the interatomic potential. The relationships found allow
us to determine the mean values of any physical parameters, and also to represent the potential energy of the system as a sum of the energies of the pair interaction of the particles. Two-particle radial distribution functions are sufficient to determine the average values of physical parameters, in particular, the transfer coefficients of molten metals. Three or more orders of correlation functions can be taken into account by recurrence formulas.