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Witnessing the quasiperiodic-ordering transition of one-dimensional k-component Fibonacci sequences

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  • Tao, Yaqi

Abstract

How much disorder in sequences is a fundamental question in many fields of science. A quantity, ZL, is proposed to assess the degree of disorder (DOD) of one-dimensional k-component Fibonacci sequences, where k is an arbitrary integer and L is the sequence length. Hu et al. have proved that such sequences are quasiperiodic when k≤5, while still ordering when k>5 (Hu et al., 1993). It is numerically found that for each k, there is an inflection point in the function of ZL versus L at a certain Lk∗. On one side, ZL∝Lαk when L0 when k≥6. This result is consistent with what found by Hu et al.. Therefore, αk can be as a witness of the quasiperiodic-ordering transition in the studied sequences. On the other hand, ZL∝L2.0139 when L>Lk∗ for all k. Further, the larger the ZL, the more disordered the sequence is. For LLk∗, ZL is almost independent of k, i.e., the DOD is almost same for enough longer sequences. All these provide further understands of disorder properties in the interesting sequences.

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  • Tao, Yaqi, 2017. "Witnessing the quasiperiodic-ordering transition of one-dimensional k-component Fibonacci sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 40-44.
    • Handle: RePEc:eee:phsmap:v:473:y:2017:i:c:p:40-44
    DOI: 10.1016/j.physa.2017.01.020
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    1. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871, September.
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