Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators

Duanmu, M.; Whitaker, N.; Kevrekidis, P. G.; Vainchtein, Anna; Rubin, Jonathan E.

doi:10.1016/j.physd.2016.02.001

Cited by 10 publications

(6 citation statements)

References 27 publications

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“…The existence of this dip can be justified in the limit of small coupling (see section VI and Appendix B). Interestingly, similar profiles were obtained for traveling fronts in a chain of bistable oscillators [24]. To investigate the influence of inertia on propagation, we show in Fig.…”

Section: Traveling Wavessupporting

confidence: 66%

Traveling waves in a spring-block chain sliding down a slope

2017

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Traveling waves are studied in a spring slider-block model. We explicitly construct front waves (kinks) for a piecewise-linear spinodal friction force. Pulse waves are obtained as the matching of two traveling fronts with identical speeds. Explicit formulas are obtained for the wavespeed and the wave form in the anticontinuum limit. The link with localized waves in a Burridge-Knopoff model of an earthquake fault is briefly discussed.

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Section: Traveling Wavessupporting

confidence: 66%

Traveling waves in a spring-block chain sliding down a slope

2017

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“…This viewpoint was explored for traveling breathers in [69]. In our view, pursuing both of these approaches (discrete versus continuum), comparing their spectra (see also the recent work of [49]), and appreciating their similarities and differences is a crucial open area in the mathematical analysis of traveling waves in discrete Hamiltonian systems.…”

Section: -3mentioning

confidence: 99%

“…( 17), which one can achieve by discretizing Eq. ( 17) in the variable ξ and employing Newton iterations to approximate the solution [49,193,197]. Upon this discretization, Eq.…”

Section: Compactons and Chaos In Strongly Nonlinear …mentioning

confidence: 99%

Nonlinear coherent structures in granular crystals

Chong

Porter

Kevrekidis

et al. 2017

J. Phys.: Condens. Matter

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The study of granular crystals, metamaterials that consist of closely packed arrays of particles that interact elastically, is a vibrant area of research that combines ideas from disciplines such as materials science, nonlinear dynamics, and condensed-matter physics. Granular crystals, a type of nonlinear metamaterial, exploit geometrical nonlinearities in their constitutive microstructure to produce properties (such as tunability and energy localization) that are not conventional to engineering materials and linear devices. In this topical review, we focus on recent experimental, computational, and theoretical results on nonlinear coherent structures in granular crystals. Such structures -which include traveling solitary waves, dispersive shock waves, and discrete breathers -have fascinating dynamics, including a diversity of both transient features and robust, long-lived patterns that emerge from broad classes of initial data. In our review, we primarily discuss phenomena in one-dimensional crystals, as most research has focused on such scenarios, but we also present some extensions to two-dimensional settings. Throughout the review, we highlight open problems and discuss a variety of potential engineering applications that arise from the rich dynamic response of granular crystals.

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“…1 On the other hand, scalable mechanical actuation can be realized by traveling waves that are spontaneously developed in linearly connected electromechanical oscillators. 2 Their properties have been investigated in a variety of oscillator networks, including a chain of selfsustained oscillators described by the Ginzburg-Landau equation, 3,4 unidirectionally coupled parametric oscillators, 5 bistable self-sustained oscillators with inductive coupling, 6 bistable Duffing oscillators with unidirectional coupling, 7,8 nonlinearly coupled oscillators, 9,10 and excitable oscillators such as the FitzHugh-Nagumo oscillators. [11][12][13][14][15] In addition, pulsed wave tends to rotate in an oscillator lattice loop.…”

Section: Introductionmentioning

confidence: 99%

Mutual synchronization of rotary pulses in coupled tunnel‐diode oscillator lattice loops

Narahara

2022

Circuit Theory & Apps

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Coupled tunnel-diode oscillator lattice loops are investigated to characterize the mutual synchronization of nonlinear rotary pulses. In a properly biased lattice loop, a pulsed phase wave autonomously rotates. When two loops are coupled, these pulses are supposed to be mutually synchronized to start rotating with a fixed phase difference. To quantify the synchronization properties of both the in-phase and out-of-phase rotary pulses, two five-cell loops that are point-coupled by a capacitor are studied using bifurcation analyses with respect to the bias voltage and coupling capacitance. In-phase pulses are allowed irrespective of the coupling capacitance, whereas relatively small coupling is favorable for out-of-phase pulses. Moreover, a solution exists whose phase difference continuously varies with the bias voltage, which bifurcates from the out-of-phase pulses through pitchfork bifurcation. This study presents the result from the bifurcation analyses. For validation of the rotary pulse in the coupled loops, we measured a breadboarded test circuit in both the frequency and time domains. The in-phase, out-of-phase, and symmetry-broken rotary pulses were detected successfully.

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Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators

Cited by 10 publications

References 27 publications

Traveling waves in a spring-block chain sliding down a slope

Traveling waves in a spring-block chain sliding down a slope

Nonlinear coherent structures in granular crystals

Mutual synchronization of rotary pulses in coupled tunnel‐diode oscillator lattice loops

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