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Some Invariants of the Silk Quasi-lattices |
LUAN Chang-Fu |
Department of Mathematics, South China University of Technology, Guangzhou 510640 |
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Cite this article: |
LUAN Chang-Fu 2003 Chin. Phys. Lett. 20 267-268 |
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Abstract Based on the spectral structure of a class of one-dimensional three-tile quasiperiodic lattice models that are established in 1990 for which the (concurrent) substitution rules are S → M, M → L, and L → LS, with S, M, and L representing the short, medium, and long tiles of atomic spacings, respectively, we suggest that S is E (egg), M is SI (silkworm) and L is M (moth), for easily understanding. By the use of the number theory, we have rigorously proven the existence of the limit θ = limn → ∞ Sn-1/Sn ≈ 0.68232789 ..., where Sn is the number of elements contained in the n-th silk sequence. Some relations among the sequences En, SIn, and Mn are found, where the subscript n means the n-th generation.
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Keywords:
64.60.Ak
71.25.Mg
02.10.+w
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Published: 01 February 2003
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