Integral-equation approaches in liquid state theory in higher dimensions

Abstract

In this thesis we will discuss the numerical solution of techniques, that allow the calculation of thermodynamic properties and the specific numerical structure of integral equations, describing simple fluids. The calculation is performed by a program, written in FORTRAN. It uses different specific numerical algorithms to solve the Ornstein-Zernike integral equation in combination with a closure relation. The solution leads to the correlation functions, as well as to the pair distribution functions for more component systems. \\ As solutions of the OZ-equations are sometimes required in higher dimensions as well, the code was generalised from the original three-dimensional case to higher (odd) dimensions. To verify the adaptations, the numerical solutions for the special case of a hard-sphere potential in different dimensions were compared to the corresponding analytic hard-sphere solutions, available for the Percus-Yevic closure relation. The program was then applied to a binary, symmetric mixture, where the cross interaction was assumed to be soft. This case is of relevance in investigations of glassy systems.