Hyperuniformity and anti-hyperuniformity in one-dimensional substitution tilings

Oǧuz, E.C.; Socolar, J.E.S.; Steinhardt, P.J.; Torquato, S.

doi:10.1107/S2053273318015528

Acta Crystallographica Section A
Acta Crystallographica
Section A FOUNDATIONS AND ADVANCES

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Figure 8
Top: periodic sublattices of the limit-periodic point set generated by equation (54)

. Each point is plotted at a height n corresponding to the subset that contains it. Points of the same color form a periodic pattern with period 3ⁿ. Second: deviation of [|A(k_n)|]

from 1/3ⁿ. Third: the integrated structure factor for the limit-periodic tiling with $[\lambda_2 = 0]$ , computed from subsets with $[n\le 8]$ . The straight red (dashed) line of slope 5 is a guide to the eye for observing the concavity of the curve. Bottom: plot of the number variance for the limit-periodic tiling with $[\lambda_2 = 0]$ .

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ISSN: 2053-2733

Volume 75| Part 1| January 2019| Pages 3-13

https://doi.org/10.1107/S2053273318015528

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