A property ofm-tuplings morse sequence

Niu, Min; Zhou, Wen

doi:10.1007/bf02836646

Cited by 7 publications

(2 citation statements)

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“…For the tight-binding quantum model, the aperiodic properties of the generalized Thue-Morse systems have been studied in great detail by [47][48][49][50][51][52][53][54][55][56][57][58]60,62,71]. Additionally, in classical dual and direct transmission lines the Thue-Morse and the m−tupling distribution of capacitances and inductances have been studied by [83][84][85].…”

Section: Generalized Thue-morse Sequencementioning

confidence: 99%

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Localization Properties of Non-Periodic Electrical Transmission Lines

Lazo

2019

Symmetry

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The properties of localization of the I ω electric current function in non-periodic electrical transmission lines have been intensively studied in the last decade. The electric components have been distributed in several forms: (a) aperiodic, including self-similar sequences (Fibonacci and m-tuplingtupling Thue–Morse), (b) incommensurate sequences (Aubry–André and Soukoulis–Economou), and (c) long-range correlated sequences (binary discrete and continuous). The localization properties of the transmission lines were measured using typical diagnostic tools of quantum mechanics like normalized localization length, transmission coefficient, average overlap amplitude, etc. As a result, it has been shown that the localization properties of the classic electric transmission lines are similar to the one-dimensional tight-binding quantum model, but also features some differences. Hence, it is worthwhile to continue investigating disordered transmission lines. To explore new localization behaviors, we are now studying two different problems, namely the model of interacting hanging cells (consisting of a finite number of dual or direct cells hanging in random positions in the transmission line), and the parity-time symmetry problem ( PT -symmetry), where resistances R n are distributed according to gain-loss sequence ( R 2 n = + R , R 2 n − 1 = − R ). This review presents some of the most important results on the localization behavior of the I ω electric current function, in dual, direct, and mixed classic transmission lines, when the electrical components are distributed non-periodically.

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Section: Generalized Thue-morse Sequencementioning

confidence: 99%

“…From the long-range correlated sequence {x n (α > 0.5)} , we can generate the asymmetric ternary sequence {v n (b 1 , b 2 )} formed with three letters, A, B and C, (62) with b 2 ≥ b 1 . The symmetric ternary map is obtained when b 2 = −b 1 = b.…”

Section: Discrete Sequencesmentioning

confidence: 99%