In this paper, we study the physical properties of the hyperuniform maximally random jammed sphere packings.
M. A. Klatt and S. Torquato. Characterization of maximally random jammed sphere packings. III. Transport and Electromagnetic Properties Via Correlation Functions. Phys. Rev. E, 97:012118-1–17 (2018)
How do unique geometrical features of heterogeneous materials bring forth unique physical properties? Here, we study the link between the structure of sphere packings and a variety of physical properties using analytic approximations and rigorous bounds. In particular, we are interested in the most disordered among all mechanically stable packings of hard spheres (that are monodisperse and frictionless).
This maximally random jammed (MRJ) state exhibits an anomalous suppression of large-scale density fluctuations, known as hyperuniformity. Although the system is isotropic and locally disordered, it appears uniform on large scales. We compare the diffusion in the pore-space of the MRJ spheres to that of an equilibrium hard-sphere liquid or non-interacting spheres. Moreover, we study flow properties and effective conductivity; the latter also for anisotropic packings of spheroids. Therefore, we provide a comprehensive overview of rigorous bounds that connect these seemingly unrelated physical properties.
The most surprising result is found for electromagnetic waves that propagate through the MRJ sphere packings, where the wavelengths are much larger than the radii of the spheres. Usually disorder causes dissipation, but because of the unique property of hyperuniformity, the MRJ state forms, to a very good approximation, a dissipationless isotropic heterogeneous medium. This is demonstrated using an analytic strong-contrast expansion. It holds for any phase dielectric contrast ratio. The anomalous suppression of density fluctuations also suppresses the scattering of the electromagnetic waves.
This attribute could be useful for the design of photonic materials with novel structural color characteristics or color-sensing capabilities. Additive manufacturing fabrication techniques offer a simple production of samples for experiments with microwaves. So, our analytic results call for an experimental testing of these predicted qualitative trends in the physical properties associated with the MRJ structure.
Michael Andreas Klatt 
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