| Original Articles |
|
|
|
|
Some Invariants of the Silk Quasi-lattices |
| LUAN Chang-Fu |
| Department of Mathematics, South China University of Technology, Guangzhou 510640 |
|
| Cite this article: |
|
LUAN Chang-Fu 2003 Chin. Phys. Lett. 20 267-268 |
|
|
|
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
|
|
|
|
|
|
|
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
