  We investigate the effective properties (conductivity, diffusivity and
elastic moduli) of model random composite media derived from Gaussian random
fields and overlapping hollow spheres. The morphologies generated in the models
exhibit low percolation thresholds and give a realistic representation of the
complex microstructure observed in many classes of composites. The statistical
correlation functions of the models are derived and used to evaluate rigorous
bounds on each property. Simulation of the effective conductivity is used to
demonstrate the applicability of the bounds. The key morphological features
which effect composite properties are discussed.
