Electronic Resource
Springer
Communications in mathematical physics
129 (1990), S. 599-619
ISSN:
1432-0916
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract 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 forN-fold symmetric tilings, whereN 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 forN-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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02097107
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