Skip to main content
Journal cover image

Weak matching rules for quasicrystals

Publication ,  Journal Article
Socolar, JES
Published in: Communications in Mathematical Physics
May 1, 1990

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.

Duke Scholars

Altmetric Attention Stats
Dimensions Citation Stats

Published In

Communications in Mathematical Physics

DOI

EISSN

1432-0916

ISSN

0010-3616

Publication Date

May 1, 1990

Volume

129

Issue

3

Start / End Page

599 / 619

Related Subject Headings

  • Mathematical Physics
  • 5107 Particle and high energy physics
  • 4904 Pure mathematics
  • 4902 Mathematical physics
  • 0206 Quantum Physics
  • 0105 Mathematical Physics
  • 0101 Pure Mathematics
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Socolar, J. E. S. (1990). Weak matching rules for quasicrystals. Communications in Mathematical Physics, 129(3), 599–619. https://doi.org/10.1007/BF02097107
Socolar, J. E. S. “Weak matching rules for quasicrystals.” Communications in Mathematical Physics 129, no. 3 (May 1, 1990): 599–619. https://doi.org/10.1007/BF02097107.
Socolar JES. Weak matching rules for quasicrystals. Communications in Mathematical Physics. 1990 May 1;129(3):599–619.
Socolar, J. E. S. “Weak matching rules for quasicrystals.” Communications in Mathematical Physics, vol. 129, no. 3, May 1990, pp. 599–619. Scopus, doi:10.1007/BF02097107.
Socolar JES. Weak matching rules for quasicrystals. Communications in Mathematical Physics. 1990 May 1;129(3):599–619.
Journal cover image

Published In

Communications in Mathematical Physics

DOI

EISSN

1432-0916

ISSN

0010-3616

Publication Date

May 1, 1990

Volume

129

Issue

3

Start / End Page

599 / 619

Related Subject Headings

  • Mathematical Physics
  • 5107 Particle and high energy physics
  • 4904 Pure mathematics
  • 4902 Mathematical physics
  • 0206 Quantum Physics
  • 0105 Mathematical Physics
  • 0101 Pure Mathematics