Two-dimensional amorphous silica exhibits a novel state of matter, disordered hyperuniformity, and enhanced electronic transport.

A hyperuniform random heterogeneous material is one in which the local volume fraction fluctuations in an observation window decay faster than the reciprocal window volume as the window size increases. Recent studies show that this class of materials are endowed with superior physical properties such as large isotropic photonic band gaps and optimal transport properties. Here we employ a stochastic optimization procedure to systematically generate realizations of hyperuniform heterogeneous materials with controllable short-range order, which is partially quantified using the two-point correlation function $S_2\left(r\right)$ associated with the phase of interest. Specifically, our procedure generalizes the widely used Yeong-Torquato reconstruction procedure by including an additional constraint for hyperuniformity, i.e., the volume integral of the autocovariance function $\chi \left(r\right)=S_2\left(r\right)-{\varphi }^2$ over the whole space is zero. In addition, we only require the reconstructed $S_2$ to match the target function up to a certain cutoff distance $\gamma$, in order to give the system sufficient degrees of freedom to satisfy the hyperuniform condition. By systematically increasing the $\gamma$ value for a given $S_2$, one can produce a spectrum of hyperuniform heterogeneous materials with varying degrees of partial short-range order compatible with the specified $S_2$. The mechanical performance including both elastic and brittle fracture behaviors of the generated hyperuniform materials is analyzed using a volume-compensated lattice-particle method. For the purpose of comparison, the corresponding nonhyperuniform materials with the same short-range order (i.e., with $S_2$ constrained up to the same $\gamma$ value) are also constructed and their mechanical performance is analyzed. Here we consider two specific $S_2$ including the positive exponential decay function and the correlation function associated with an equilibrium hard-sphere system. For the constructed systems associated with these two specific functions, we find that although the hyperuniform materials are softer than their nonhyperuniform counterparts, the former generally possess a significantly higher brittle fracture strength than the latter. This superior mechanical behavior is attributed to the lower degree of stress concentration in the material resulting from the hyperuniform microstructure, which is crucial to crack initiation and propagation.

The geometrical and topological configurations of particles have great influences on their surrounding pore tortuosity and the permeability of granular‐porous media. In this work, we develop a relaxation iteration scheme to create random dense packings of different anisotropic‐shaped spheroidal particles with monodispersity and polydispersity in sizes, which manifest the effects of particle shape, fineness, and size distribution on the random packing fraction of particles. Subsequently, we propose a direction‐guided rapidly exploring random tree (DGRRT) algorithm to probe the geometrical tortuosity of complex pore space interstitial to spheroidal particles. A non‐linear pore tortuosity prediction model that relies on the specific surface area and packing fraction of particles, is developed to suit for polydisperse and monodisperse spheroidal particle systems. We further investigate the permeability of granular‐porous media through the lattice Boltzmann method (LBM) of fluid flow. These proposed methods can accurately predict the tortuosity and permeability by comparing against available experimental, theoretical, and numerical results reported in literature. Moreover, the effects of particle packing fraction (i.e., porosity), shape, fineness, and size distribution on the pore tortuosity and permeability of granular‐porous media are evaluated. The results reveal that these microstructural configurations have important influences on the permeability and tortuosity. Our results give an intrinsic interplay between the geometrical tortuosity and permeability of monodisperse and polydisperse particle systems, which have implications for a broad range of scientific disciplines, including the properties of rocks, sandstones and soils, and the design of ultra‐high performance concrete.

Continuum percolation of randomly orientated congruent overlapping spherocylinders (composed of cylinder of height $H$ with semispheres of diameter $D$ at the ends) with aspect ratio $\alpha =H/D$ in $[0,\infty )$ is studied. The percolation threshold ${\varphi }_c$, percolation transition width Δ, and correlation-length critical exponent $\nu$ for spherocylinders with $\alpha$ in [0, 200] are determined with a high degree of accuracy via extensive finite-size scaling analysis. A generalized excluded-volume approximation for percolation threshold with an exponent explicitly depending on both aspect ratio and excluded volume for arbitrary $\alpha$ values in $[0,\infty )$ is proposed and shown to yield accurate predictions of ${\varphi }_c$ for an extremely wide range of $\alpha$ in [0, 2000] based on available numerical and experimental data. We find ${\varphi }_c$ is a universal monotonic decreasing function of $\alpha$ and is independent of the effective particle size. Our study has implications in percolation theory for nonspherical particles and composite material design.

The leaf vein network is a hierarchical vascular system that transports water and nutrients to the leaf cells. The thick primary veins form a branched network, while the secondary veins can develop closed loops forming a well-defined cellular structure. Through extensive analysis of a variety of distinct leaf species, we discover that the apparently disordered cellular structures of the secondary vein networks exhibit a universal hyperuniform organization and possess a hidden order on large scales. Disorder hyperuniform systems lack conventional long-range order, yet they completely suppress normalized infinite-wavelength density fluctuations like crystals. Specifically, we find that the distributions of the geometric centers associated with the vein network loops possess a vanishing static structure factor in the limit that the wave number $k$ goes to 0, i.e., $S(k)\sim k^{\alpha }$, where $\alpha \approx 0.64\pm 0.021$, providing an example of class III hyperuniformity in biology. This hyperuniform organization leads to superior efficiency of diffusive transport, as evidenced by the much faster convergence of the time-dependent spreadability $\mathcal{S}(t)$ to its longtime asymptotic limit, compared to that of other uncorrelated or correlated disordered but nonhyperuniform organizations. Our results also have implications for the discovery and design of novel disordered network materials with optimal transport properties.