CONTINUUM MODELS AND DISCRETE SYSTEMS

A two-point statistical parameter which naturally appears in variational bounds in the absorption problem for random media is studied. For random dispersions of nonoverlapping sphere an analytic formula for the parameter is first given through the radial distribution function for the spheres. Analyzing the asymptotic behaviour of the parameter, two kinds of formulae are derived: i) Simple relations between the values of the two-point correlation function and its derivatives at r = 0 with the values of radial distribution function and its derivatives at the “touching distance” r = 2a. ii) Relations between the moments of the two-point correlation on (0,∞) and the moments of the radial distribution function. As a simple application, the failure of the well-stirred approximation for sphere fractions higher than 1/8 is finally demonstrated.