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In the first two papers of this series, we characterized the structure ofmaximally random jammed (MRJ) sphere packings across length scales by computinga variety of different correlation functions, spectral functions, holeprobabilities, and local density fluctuations. From the remarkable structuralfeatures of the MRJ packings, especially its disordered hyperuniformity,exceptional physical properties can be expected. Here, we employ thesestructural descriptors to estimate effective transport and electromagneticproperties via rigorous bounds, exact expansions, and accurate analyticalapproximation formulas. These property formulas include interfacial bounds aswell as universal scaling laws for the mean survival time and the fluidpermeability. We also estimate the principal relaxation time associated withBrownian motion among perfectly absorbing traps. For the propagation ofelectromagnetic waves in the long-wavelength limit, we show that a dispersionof dielectric MRJ spheres within a matrix of another dielectric material forms,to a very good approximation, a dissipationless disordered and isotropictwo-phase medium for any phase dielectric contrast ratio. We compare theeffective properties of the MRJ sphere packings to those of overlappingspheres, equilibrium hard-sphere packings, and lattices of hard spheres.Moreover, we generalize results to micro- and macroscopically anisotropicpackings of spheroids with tensorial effective properties. The analytic boundspredict the qualitative trend in the physical properties associated with thesestructures, which provides guidance to more time-consuming simulations andexperiments. They especially provide impetus for experiments to designmaterials with unique bulk properties resulting from hyperuniformity, includingstructural-color and color-sensing applications.

Characterization of Maximally Random Jammed Sphere Packings. III. Transport and Electromagnetic Properties via Correlation Functions