Weak matching rules for quasicrystals

Journal Article (Journal Article)

Weak matching rules for a quasicrystalline tiling are local rules that ensure that fluctuations in "perp-space" are uniformly bounded. It is shown here that weak matching rules exist for N-fold symmetric tilings, where N is any integer not divisible by four. The result suggests that, contrary to previous indications, quasicrystalline ground states are not confined to those symmetries for which the incommensurate ratios of wavevectors are quadratic irrationals. An explicit method of constructing weak matching rules for N-fold symmetric tilings in two dimensions is presented. It is shown that the generalization of the construction yields weak matching rules in the case of icosahedral symmetry as well. © 1990 Springer-Verlag.

Full Text

Duke Authors

Cited Authors

  • Socolar, JES

Published Date

  • May 1, 1990

Published In

Volume / Issue

  • 129 / 3

Start / End Page

  • 599 - 619

Electronic International Standard Serial Number (EISSN)

  • 1432-0916

International Standard Serial Number (ISSN)

  • 0010-3616

Digital Object Identifier (DOI)

  • 10.1007/BF02097107

Citation Source

  • Scopus