Microstructure functions for random media with impenetrable particles.
We introduce a model consisting of nonaligned and impenetrable particles. This model is obtained by placing particles of random orientation within "security spheres," typically chosen to be spheres in thermal equilibrium. The particles in general are allowed to be nonspherical. We obtain an analytical expression for the function S(n), the probability that n points simultaneously lie outside of the particle phase. This characterization of the microstructure appears in certain rigorous bounds on the effective properties of random materials. We also evaluate S2 for various specific examples of this model, including nonaligned impenetrable ellipsoids.
Quintanilla
J
J
Department of Mathematics, University of North Texas, Denton, Texas 76203, USA. johnq@unt.edu