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.

Full Text

Duke Authors

Cited Authors

  • O─čuz, EC; Socolar, JES; Steinhardt, PJ; Torquato, S

Published Date

  • January 2019

Published In

Volume / Issue

  • 75 / Pt 1

Start / End Page

  • 3 - 13

PubMed ID

  • 30575579

Pubmed Central ID

  • PMC6302933

Electronic International Standard Serial Number (EISSN)

  • 2053-2733

International Standard Serial Number (ISSN)

  • 2053-2733

Digital Object Identifier (DOI)

  • 10.1107/s2053273318015528


  • eng