Hyperuniformity and anti-hyperuniformity in one-dimensional substitution tilings.
Journal Article (Journal Article)
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.
- Oğuz, EC; Socolar, JES; Steinhardt, PJ; Torquato, S
- January 2019
Volume / Issue
- 75 / Pt 1
Start / End Page
- 3 - 13
Pubmed Central ID
Electronic International Standard Serial Number (EISSN)
International Standard Serial Number (ISSN)
Digital Object Identifier (DOI)