Understanding degeneracy of two-point correlation functions via Debye random media

It is well-known that the degeneracy of two-phase microstructures with the same volume fraction and two-point correlation function is generally infinite. To elucidate the degeneracy problem explicitly, we examine Debye random media (DRM), which are entirely defined by a purely exponentially decaying two-point correlation function. In this work, we consider three different classes of DRM. First, we generate the "most probable" class using the Yeong-Torquato construction algorithm. A second class of DRM is obtained by demonstrating that the corresponding two-point correlation functions are effectively realized by certain models of overlapping, polydisperse spheres. A third class is obtained by using the Yeong-Torquato algorithm to construct DRM that are constrained to have an unusual prescribed pore-size probability density function. We structurally discriminate these three classes of DRM from one another by comparing and contrasting their other statistical descriptors, percolation thresholds, as well as their diffusion and fluid transport properties. We find that these three classes of DRM are distinguished to varying degrees by the aforementioned descriptors and have visually distinct microstructures. We also discuss applications of our work to the design of materials with a spectrum of physical properties.