Energy transmission in nonlinear chains of harmonic oscillators with long-range interactions
In this work, the phenomenon of supratransmission in nonlinear sine-Gordon chains with global interactions will be predicted analytically for the first time in the literature. The model considered is an extension of the classical sine-Gordon chain which describes the dynamics of pendula attached thr...
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| Format: | Article |
| Language: | English |
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Elsevier
2020-09-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379720316776 |
| _version_ | 1819109752710365184 |
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| author | J.E. Macías-Díaz A.B. Togueu Motcheyo |
| author_facet | J.E. Macías-Díaz A.B. Togueu Motcheyo |
| author_sort | J.E. Macías-Díaz |
| collection | DOAJ |
| description | In this work, the phenomenon of supratransmission in nonlinear sine-Gordon chains with global interactions will be predicted analytically for the first time in the literature. The model considered is an extension of the classical sine-Gordon chain which describes the dynamics of pendula attached through strings. Using a relatively simple analytical theory, we derive the threshold that triggers the supratransmission process for relatively high degrees of interaction. The threshold for the classical model is a particular case of our predictions when the degree of interaction tends to infinity. We confirm numerically the validity of our results using a systematic computational approach. We obtain numerically bifurcation diagrams for the supratransmission threshold and compare them with the theoretical predictions, obtaining a good agreement. |
| first_indexed | 2024-12-22T03:30:49Z |
| format | Article |
| id | doaj.art-7cd233f077304b2aa01dca5641b73a04 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-12-22T03:30:49Z |
| publishDate | 2020-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-7cd233f077304b2aa01dca5641b73a042022-12-21T18:40:31ZengElsevierResults in Physics2211-37972020-09-0118103210Energy transmission in nonlinear chains of harmonic oscillators with long-range interactionsJ.E. Macías-Díaz0A.B. Togueu Motcheyo1Departamento de Matemáticas y Física, Universidad Autónoma de Aguascalientes, Avenida Universidad 940, Ciudad Universitaria, Aguascalientes, Ags. 20131, Mexico; Corresponding author.Applied Biotechnology and Engineering Laboratory, Department of Mechanical Engineering, Higher Technical Teacher’s Training College (ENSET) Ebolowa, University of Yaounde I, P.O. Box 886, Ebolowa, CameroonIn this work, the phenomenon of supratransmission in nonlinear sine-Gordon chains with global interactions will be predicted analytically for the first time in the literature. The model considered is an extension of the classical sine-Gordon chain which describes the dynamics of pendula attached through strings. Using a relatively simple analytical theory, we derive the threshold that triggers the supratransmission process for relatively high degrees of interaction. The threshold for the classical model is a particular case of our predictions when the degree of interaction tends to infinity. We confirm numerically the validity of our results using a systematic computational approach. We obtain numerically bifurcation diagrams for the supratransmission threshold and compare them with the theoretical predictions, obtaining a good agreement.http://www.sciencedirect.com/science/article/pii/S2211379720316776Globally interacting chainsHarmonic oscillatorsNonlinear supratransmission |
| spellingShingle | J.E. Macías-Díaz A.B. Togueu Motcheyo Energy transmission in nonlinear chains of harmonic oscillators with long-range interactions Results in Physics Globally interacting chains Harmonic oscillators Nonlinear supratransmission |
| title | Energy transmission in nonlinear chains of harmonic oscillators with long-range interactions |
| title_full | Energy transmission in nonlinear chains of harmonic oscillators with long-range interactions |
| title_fullStr | Energy transmission in nonlinear chains of harmonic oscillators with long-range interactions |
| title_full_unstemmed | Energy transmission in nonlinear chains of harmonic oscillators with long-range interactions |
| title_short | Energy transmission in nonlinear chains of harmonic oscillators with long-range interactions |
| title_sort | energy transmission in nonlinear chains of harmonic oscillators with long range interactions |
| topic | Globally interacting chains Harmonic oscillators Nonlinear supratransmission |
| url | http://www.sciencedirect.com/science/article/pii/S2211379720316776 |
| work_keys_str_mv | AT jemaciasdiaz energytransmissioninnonlinearchainsofharmonicoscillatorswithlongrangeinteractions AT abtogueumotcheyo energytransmissioninnonlinearchainsofharmonicoscillatorswithlongrangeinteractions |