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Hyperuniformity, the suppression of density fluctuations at large length scales, is observed across a wide variety of domains, from cosmology to condensed matter and biological systems. Although the standard definition of hyperuniformity only utilizes information at the largest scales, hyperuniform configurations have distinctive local characteristics. However, the influence of global hyperuniformity on local structure has remained largely unexplored; establishing this connection can help uncover long-range interaction mechanisms and detect hyperuniform traits in finite-size systems. Here, we study the topological properties of hyperuniform point clouds by characterizing their persistent homology and the statistics of local graph neighborhoods. We find that varying the structure factor results in configurations with systematically different topological properties. Moreover, these topological properties are conserved for subsets of hyperuniform point clouds, establishing a connection between finite-sized systems and idealized reference arrangements. Comparing distributions of local topological neighborhoods reveals that the hyperuniform arrangements lie along a primarily one-dimensional manifold reflecting an order-to-disorder transition via hyperuniform configurations. The results presented here complement existing characterizations of hyperuniform phases of matter, and they show how local topological features can be used to detect hyperuniformity in size-limited simulations and experiments. Published by the American Physical Society2024
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This content will become publicly available on June 19, 2026
Existence of nonequilibrium glasses in the degenerate stealthy hyperuniform ground-state manifold
Nonequilibrium hard-sphere hyperuniform glasses (left panel) exist within the stealthy hyperuniform ground-state manifold. Accessible packing fractions for allχwithin the disordered regime (grey region in the left panel).
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- Award ID(s):
- 2133179
- PAR ID:
- 10657593
- Publisher / Repository:
- RSC Publishing
- Date Published:
- Journal Name:
- Soft Matter
- Volume:
- 21
- Issue:
- 24
- ISSN:
- 1744-683X
- Page Range / eLocation ID:
- 4898 to 4907
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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