Nonlinear excitations in magnetic lattices with long-range interactions

Molerón, Miguel; Chong, Christopher; Martínez, Alejandro J.; Porter, Mason A.; Kevrekidis, P. G.; Daraio, Chiara

doi:10.1088/1367-2630/ab0118

Cited by 24 publications

(14 citation statements)

References 55 publications

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“…The dashpot γ qm,n is a phenomenological term that we add to account for damping. Using such a term has yielded reasonable agreement with experiments in other, similar lattices [19,36,37]. The quantity F ext m,n is the external force that we apply to the magnet at (m, n).…”

Section: Methodssupporting

confidence: 69%

Nonlinear Localized Modes in Two-Dimensional Hexagonally-Packed Magnetic Lattices

Chong,

Wang,

Marechal

et al. 2020

Preprint

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We conduct an extensive study of nonlinear localized modes (NLMs), which are temporally periodic and spatially localized structures, in a two-dimensional array of repelling magnets. In our experiments, we arrange a lattice in a hexagonal configuration with a light-mass defect, and we harmonically drive the center of the chain with a tunable excitation frequency, amplitude, and angle. We use a damped, driven variant of a vector Fermi-Pasta-Ulam-Tsingou lattice to model our experimental setup. Despite the idealized nature of the model, we obtain good qualitative agreement between theory and experiments for a variety of dynamical behaviors. We find that the spatial decay is direction-dependent and that drive amplitudes along fundamental displacement axes lead to nonlinear resonant peaks in frequency continuations that are similar to those that occur in one-dimensional damped, driven lattices. However, driving along other directions leads to the creation of asymmetric NLMs that bifurcate from the main solution branch, which consists of symmetric NLMs. When we vary the drive amplitude, we observe such behavior both in our experiments and in our simulations. We also demonstrate that solutions that appear to be time-quasi-periodic bifurcate from the branch of symmetric time-periodic NLMs.

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Section: Methodssupporting

confidence: 69%

Nonlinear Localized Modes in Two-Dimensional Hexagonally-Packed Magnetic Lattices

Chong,

Wang,

Marechal

et al. 2020

Preprint

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“…For instance, waves cannot propagate freely through linear phononic crystals in the stop bands. But it was reported that different types of solitary waves, e.g., the KdV-like solitons [18][19][20], gap solitons [21][22][23], and gap breathers [24,25], can propagate in the stop bands through nonlinear phononic crystals. As is well known, a soliton is a solitary wave that can propagate stably with the dynamic behavior like a "particle."…”

Section: Introductionmentioning

confidence: 99%

Solitary waves in a granular chain of elastic spheres: Multiple solitary solutions and their stabilities

2019

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A granular chain of elastic spheres via Hertzian contact incorporates a classical nonlinear force model describing dynamical elastic solitary wave propagation. In this paper, the multiple solitary waves and their dynamic behaviors and stability in such a system are considered. An approximate KdV equation with the standard form is derived under the long-wavelength approximation and small deformation. The closed-form analytical single-and multiple-soliton solutions are obtained. The construction of the multiple-soliton solutions is analyzed by using the functional analysis. It is found that the multiple-soliton solution can be excited by the single-soliton solutions. This result is confirmed by the numerical analysis. Based on the soliton solutions of the KdV equation, the analytic solutions of multiple dark solitary waves are obtained from the original dynamic equation of the granular chain in the long-wavelength approximation. The stability of the single and multiple dark solitary wave solutions are numerically analyzed by using both split-step Fourier transform method and Runge-Kutta method. The results show that the single dark solitary wave solution is stable, and the multiple dark solitary waves are unstable.

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“…We note the existence of the second and the third harmonic of the excitation frequency in Figure 5B,C, due to the inherent nonlinearity in magnetic lattices. Such nonlinear response can be harnessed by increasing the amplitude of the excitation and introducing defects within the lattice (Boechler et al, 2011;Mehrem et al, 2017;Deng et al, 2018;Molerón et al, 2019;Chong et al, 2020;.…”

Section: Resultsmentioning

confidence: 99%

Demultiplexing Infrasound Phonons With Tunable Magnetic Lattices

Watkins

Bilal

2020

Front. Mater.

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Controlling infrasound signals is crucial to many processes ranging from predicting atmospheric events and seismic activities to sensing nuclear detonations. These waves can be manipulated through phononic crystals and acoustic metamaterials. However, at such ultra-low frequencies, the size (usually on the order of meters) and the mass (usually on the order of many kilograms) of these materials can hinder its potential applications in the infrasonic domain. Here, we utilize tunable lattices of repelling magnets to guide and sort infrasound waves into different channels based on their frequencies. We construct our lattices by confining meta-atoms (free-floating macroscopic disks with embedded magnets) within a magnetic boundary. By changing the confining boundary, we control the meta-atoms’ spacing and therefore the intensity of their coupling potentials and wave propagation characteristics. As a demonstration of principle, we present the first experimental realization of an infrasound phonon demultiplexer (i.e., guiding ultra-low frequency waves into different channels based on their frequencies). The realized platform can be utilized to manipulate ultra-low frequency waves, within a relatively small volume, while utilizing negligible mass. In addition, the self-assembly nature of the meta-atoms can be key in creating re-programmable materials with exceptional nonlinear properties.

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Nonlinear excitations in magnetic lattices with long-range interactions

Cited by 24 publications

References 55 publications

Nonlinear Localized Modes in Two-Dimensional Hexagonally-Packed Magnetic Lattices

Nonlinear Localized Modes in Two-Dimensional Hexagonally-Packed Magnetic Lattices

Solitary waves in a granular chain of elastic spheres: Multiple solitary solutions and their stabilities

Demultiplexing Infrasound Phonons With Tunable Magnetic Lattices

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