Dynamical properties of particulate composites derived from ultradense stealthy hyperuniform sphere packings

Stealthy hyperuniform (SHU) many-particle systems in d-dimensional Euclidean space are distinguished by a structure factor that vanishes not only at zero wave number (as in "standard" hyperuniform systems) but also across an extended range of wave numbers near the origin. We generate disordered SHU packings of identical and "nonoverlapping" spheres in two and three dimensions using a modified collective-coordinate optimization algorithm that incorporates a soft-core repulsive potential between particles in addition to the standard stealthy pair potential. Compared to SHU packings without soft-core repulsions, these SHU packings are ultradense with packing fractions ranging from 0.67 to 0.86 for d=2 and 0.47 to 0.63 for d=3, spanning a broad spectrum of structures depending on the stealthiness parameter χ. We consider two-phase media composed of hard particles derived from ultradense SHU packings (phase 2) embedded in a matrix phase (phase 1) with varying stealthiness parameter χ and packing fractions ϕ. Our main objective is the estimation of the dynamical physical properties of such two-phase media, namely the effective dynamic dielectric constant and the time-dependent diffusion spreadability, which is directly related to nuclear magnetic relaxation in fluid-saturated porous media. We show through spreadability that two-phase media derived from ultradense SHU packings exhibit faster interphase diffusion due to the higher packing fractions achievable compared to SHU media obtained without soft-core repulsion. The imaginary part of the effective dynamic dielectric constant of SHU packings vanishes for a range of small wave numbers, implying perfect transparency for the corresponding wave vectors. While a larger packing fraction yields a smaller transparency interval, we show that it also displays a reduced height of the attenuation peak. We also obtain cross-property relations between transparency characteristics and long-time behavior of the spreadability for such two-phase media, showing that one leads to information about the other and vice versa. Our results demonstrate that disordered two-phase media derived from ultradense SHU packings exhibit advantageous transport and optical behaviors of both theoretical and experimental significance.