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Dense, disordered packings of particles are useful models of low-temperatureamorphous phases of matter, biological systems, granular media, and colloidalsystems. The study of dense packings of nonspherical particles enables one toascertain how rotational degrees of freedom affect packing behavior. Here, westudy superballs, a large family of deformations of the sphere, defined inthree dimensions by $|x_1|^{2p}+|x_2|^{2p}+|x_3|^{2p}\leq1$, where $p>0$ is adeformation parameter indicating to what extent the shape deviates from asphere. As $p$ increases from the sphere point ($p=1$), the superball attainscubic symmetry, and attains octahedral symmetry when $p<1$. Previouscharacterization of superball packings has shown that they have a maximallyrandom jammed (MRJ) state, whose properties (e.g., packing fraction $\phi$)vary nonanalytically as $p$ diverges from unity. Here, we use an event-drivenmolecular dynamics algorithm to produce MRJ superball packings. We characterizetheir large-scale structure by examining the small-$Q$ behavior of theirstructure factors and spectral densities, which indicate these packings areeffectively hyperuniform. We show that the mean width $\bar{w}$ is a usefullength scale to make distances dimensionless in order to compare systematicallysuperballs of different shape. We also compute the complementary cumulativepore-size distribution $F(\delta)$ and find the pore sizes tend to decrease as$|1-p|$ increases. From $F(\delta)$, we estimate the fluid permeability, meansurvival time, and principal diffusion relaxation time of the packings.Additionally, we compute the diffusion spreadability and find the long-timepower-law scaling indicates these packings are hyperuniform. Our results can beused to help inform the design of granular materials with targeted densitiesand transport properties.

Characterization of Void Space, Large-Scale Structure, and Transport Properties of Maximally Random Jammed Packings of Superballs