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1994•Journal of Physics A Mathematical and GeneralOpen access

Fibonacci chain as a periodic chain with discommensurations

Zhoufutu Wen, Τ. Janssen, F. M. Dekking

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Abstract

The quasiperiodic Fibbonacci chain can be obtained by finite displacements from a periodic chain if one introduces ordered defects that are similar to discommensurations in incommensurate crystal phases. It is shown that the chain with discommensurations can also be constructed by means of a substitution rule having the Pisot property. In superspace the defect structure is a superstructure for the two-dimensional array that corresponds to the Fibonacci chain.

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The quasiperiodic Fibbonacci chain can be obtained by finite displacements from a periodic chain if one introduces ordered defects that are similar to discommensurations in incommensurate crystal phases. It is shown that the chain with discommensurations can also be constructed by means of a substitution rule having the Pisot property. In superspace the defect structure is a superstructure for the two-dimensional array that corresponds to the Fibonacci chain.

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Available abstract

The quasiperiodic Fibbonacci chain can be obtained by finite displacements from a periodic chain if one introduces ordered defects that are similar to discommensurations in incommensurate crystal phases. It is shown that the chain with discommensurations can also be constructed by means of a substitution rule having the Pisot property. In superspace the defect structure is a superstructure for the two-dimensional array that corresponds to the Fibonacci chain.

Key concepts: Fibonacci number, Quasiperiodic function, Chain (unit), Superspace, Superstructure, Physics, Superlattice, Crystallography

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