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|Abstract:||This work considers the scaling properties characterizing the hyperuniformity (or anti-hyperuniformity) of long-wavelength fluctuations in a broad class of one-dimensional substitution tilings. A simple argument is presented which predicts the exponent α governing the scaling of Fourier intensities at small wavenumbers, tilings with α > 0 being hyperuniform, and numerical computations confirm that the predictions are accurate for quasiperiodic tilings, tilings with singular continuous spectra and limit-periodic tilings. Quasiperiodic or singular continuous cases can be constructed with α arbitrarily close to any given value between -1 and 3. Limit-periodic tilings can be constructed with α between -1 and 1 or with Fourier intensities that approach zero faster than any power law.|
|Citation:||Oğuz, Erdal C., Socolar, Joshua E.S., Steinhardt, Paul J., Torquato, Salvatore. (2019). Hyperuniformity and anti-hyperuniformity in one-dimensional substitution tilings.. Acta crystallographica. Section A, Foundations and advances, 75 (Pt 1), 3 - 13. doi:10.1107/S2053273318015528|
|Pages:||1 - 13|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||Acta crystallographica. Section A, Foundations and advances|
|Version:||Final published version. This is an open access article.|
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