Two-point probability function for distributions of oriented hard ellipsoids

The macroscopic properties of two-phase random heterogeneous media depend upon an infinite sequence of n-point functions S(i)n(x1,x2,...,xn) giving the joint probability of finding n points with positions x1,x2,...,xn all in phase i. This paper reports the first study and calculation of the two-point probability function S(i)2 for distributions of oriented, hard spheroids with eccentricity ε in a matrix. This is a useful model of statistically anisotropic two-phase media, enabling one to examine the special limiting cases of oriented disks (ε=0), spheres (ε=1), and oriented needles (ε=∞).