Chin. Phys. Lett.  2003, Vol. 20 Issue (2): 267-268    DOI:
Original Articles |
Some Invariants of the Silk Quasi-lattices
LUAN Chang-Fu
Department of Mathematics, South China University of Technology, Guangzhou 510640
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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.

Keywords: 64.60.Ak      71.25.Mg      02.10.+w     
Published: 01 February 2003
PACS:  64.60.Ak  
  71.25.Mg  
  02.10.+w  
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https://cpl.iphy.ac.cn/       OR      https://cpl.iphy.ac.cn/Y2003/V20/I2/0267
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