Patterns of traveling intrinsic localized modes in a driven electrical lattice

English, Lars Q.; Thakur, R. Basu; Stearrett, Ryan

doi:10.1103/physreve.77.066601

Cited by 44 publications

(39 citation statements)

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“…In this paper we present a detailed study of discrete breathers in an electric lattice in which ILMs have been experimentally observed [15][16][17]. We propose a theoretical model which allows us to systematically study their existence, stability and properties, and to compare our numerical findings with experimental results.…”

Section: Introductionmentioning

confidence: 99%

Discrete breathers in a nonlinear electric line: Modeling, computation, and experiment

et al. 2011

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We study experimentally and numerically the existence and stability properties of discrete breathers in a periodic nonlinear electric line. The electric line is composed of single cell nodes, containing a varactor diode and an inductor, coupled together in a periodic ring configuration through inductors and driven uniformly by a harmonic external voltage source. A simple model for each cell is proposed by using a nonlinear form for the varactor characteristics through the current and capacitance dependence on the voltage. For an electrical line composed of 32 elements, we find the regions, in driver voltage and frequency, where n-peaked breather solutions exist and characterize their stability. The results are compared to experimental measurements with good quantitative agreement. We also examine the spontaneous formation of n-peaked breathers through modulational instability of the homogeneous steady state. The competition between different discrete breathers seeded by the modulational instability eventually leads to stationary n-peaked solutions whose precise locations is seen to sensitively depend on the initial conditions.

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Section: Introductionmentioning

confidence: 99%

Discrete breathers in a nonlinear electric line: Modeling, computation, and experiment

et al. 2011

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“…(1) as [19,20]. Using the harmonic balance method to approximate a solution of the subharmonic response [21], such a solution assumes the form xðtÞ ¼ A 1 sinðT þ Þ þA 1=2 sinðT=2Þ þ B 1=2 cosðT=2Þ, where A 1 ¼ 1=ð1 À !…”

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confidence: 99%

Generation of Localized Modes in an Electrical Lattice Using Subharmonic Driving

et al. 2012

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We show experimentally and numerically that an intrinsic localized mode (ILM) can be stably produced (and experimentally observed) via subharmonic, spatially homogeneous driving in the context of a nonlinear electrical lattice. The precise nonlinear spatial response of the system has been seen to depend on the relative location in frequency between the driver frequency, ! d , and the bottom of the linear dispersion curve, ! 0 . If ! d =2 lies just below ! 0 , then a single ILM can be generated in a 32-node lattice, whereas, when ! d =2 lies within the dispersion band, a spatially extended waveform resembling a train of ILMs results. To our knowledge, and despite its apparently broad relevance, such an experimental observation of subharmonically driven ILMs has not been previously reported. DOI: 10.1103/PhysRevLett.108.084101 PACS numbers: 05.45.Yv, 63.20.Pw, 63.20.Ry It is well known that a damped nonlinear oscillator can respond at its intrinsic resonance frequency when it is driven at a multiple of that frequency. A direct example of such subharmonic driving is provided by the driven Van der Pol oscillator, where the ratio of response to driver frequency is exactly 1=3 [1,2]. Many other nonlinear oscillators exhibit similar subharmonic resonances (the Duffing oscillator being another extensively studied example). In fact, subharmonic response must be seen as a fairly generic property of nonlinear oscillators. Alternatively, a nonlinear oscillator with a parameter modulated at a particular frequency can also respond at a fraction of that frequency in what is called parametric excitation.What happens when such nonlinear oscillators are connected to one another in a regular lattice? In nonlinear lattices, an important generic phenomenon is the existence of self-trapped localized modes, known as intrinsic localized modes (ILMs) or discrete breathers. Such a mode represents an excitation which is (typically exponentially) spatially localized over a limited range of lattice nodes and decays to zero far from these, and it is temporally periodic. In this regard, it can be thought of as an analog of the solitons of continuous media. However, the discreteness of the lattice introduces interesting variations to the problem, including, for instance, the fact that ILMs may be dynamically stable in any dimension. Here, we blend these two broadly significant aspects of nonlinear systems by addressing the following question: can subharmonic or parametric excitations, which figure so prominently in isolated nonlinear oscillators, carry over to the lattice setting? That is, we examine whether ILMs can be generated and, especially, stabilized by subharmonic and/or parametric driving which is homogeneous in space. So far, this type of question seems to have been considered chiefly in the context of continuous media [10], or for parametric driving [11][12][13], and has been principally theoretical in nature. In this Letter, we demonstrate experimentally and corroborate through theoretical modeling and numerical computation, an...

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“…In 1D, Ref. [16] reported detailed measurement of ILM speed. It was found that the slowest a single ILM could move in a 1D lattice of 24 nodes was 15 nodes per millisecond (15 a/ms).…”

Section: Resultsmentioning

confidence: 99%

Energy localization and transport in two-dimensional electrical lattices

English¹,

Palmero²,

Stormes³

et al. 2014

IEICE Proceeding Series

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Abstract-Intrinsic localized modes (ILMs) have been generated and characterized in two-dimensional nonlinear electrical lattices which were driven by a spatially-uniform voltage signal. These ILMs were found to be either stationary or mobile, depending on the details of the lattice unit-cell, as had already been reported in one-dimensional lattices; however, the motion of these ILMs is qualitatively different in that it lacks a consistent direction. Furthermore, the hopping speed seems to be somewhat reduced in two dimensions due to an enhanced Peierls-Nabarro (PN)-barrier. We investigate both square and honeycomb lattices composed of 6 × 6 elements. These direct observations were further supported by numerical simulations based on realistic models of circuit components. The numerical study moreover allowed for an analysis of ILM dynamics and pattern formation for larger lattice sizes.

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Patterns of traveling intrinsic localized modes in a driven electrical lattice

Cited by 44 publications

References 15 publications

Discrete breathers in a nonlinear electric line: Modeling, computation, and experiment

Discrete breathers in a nonlinear electric line: Modeling, computation, and experiment

Generation of Localized Modes in an Electrical Lattice Using Subharmonic Driving

Energy localization and transport in two-dimensional electrical lattices

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