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arXiv · 2606.23628

Two-dimensional stealthy hyperuniform polycrystalline disk packings

Carlo Vanoni·Paul J. Steinhardt·Salvatore Torquato
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Abstract

Polycrystals consist of grains of local crystalline order separated by grain boundaries. Their structure is not hyperuniform, even though perfect crystals are, because polycrystals consist of randomly sized and oriented grains that generate appreciable long-wavelength density fluctuations. In this paper, we use a collective-coordinate optimization procedure to generate two-dimensional polycrystalline packings composed of identical disks arranged in a pattern that is ultradense, stealthy, and hyperuniform (hereafter named SHU). We compare them with polycrystalline disk packings obtained via a modified Lubachevsky--Stillinger rapid compression algorithm (hereafter named LS), a molecular dynamics protocol that serves as a standard reference model describing realistic, nonhyperuniform polycrystalline microstructures. We carry out an extensive comparison of polycrystalline SHU and LS packings that includes differences in two-point statistics, grain size, specific surface area, diffusion spreadability, and optical response as quantified by the imaginary part of the effective dynamic dielectric constant. We find that the polycrystalline SHU packings exhibit a distinctive grain-size distribution, a consequence of long-range correlations between different grains that is absent in the nonhyperuniform case. Within the nonlocal strong-contrast expansion, we confirm that polycrystalline SHU packings made of dielectric material are perfectly transparent to electromagnetic waves at small wave vectors, in contrast to LS packings. Moreover, polycrystalline SHU packings offer enhanced diffusion spreadability. Although polycrystalline SHU packings are not expected to form spontaneously in nature, they may be created for applications as metamaterials via nanolithography or 3D printing that take advantage of their distinctive optical and transport properties.

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Carlo Vanoni, Paul J. Steinhardt, Salvatore Torquato. 2026-06-22. Two-dimensional stealthy hyperuniform polycrystalline disk packings. https://arxiv.org/abs/2606.23628

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