Multifrequency and edge breathers in the discrete sine-Gordon system via subharmonic driving: Theory, computation and experiment

Palmero, F.; Han, Jie; English, Lars Q.; Alexander, Tristram J.; Kevrekidis, P. G.

doi:10.1016/j.physleta.2015.10.061

Cited by 13 publications

(5 citation statements)

References 32 publications

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“…This finding, i.e. the wider range of stabilization of the EB relative to the BB, has been also experimentally observed in a chain of coupled pendula [26].…”

Section: A Driving Near the Lowest Frequency Modesupporting

confidence: 77%

Nonlinear edge modes in a honeycomb electrical lattice near the Dirac points

Palmero,

English,

Cuevas-Maraver

et al. 2020

Preprint

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We examine -both experimentally and numerically -a two-dimensional nonlinear driven electrical lattice with honeycomb structure. Drives are considered over a range of frequencies both outside (below and above) and inside the band of linear modes. We identify a number of discrete breathers both existing in the bulk and also (predominantly) ones arising at the domain boundaries, localized either along the arm-chair or along the zig-zag edges. The types of edge-localized breathers observed and computed emerge in distinct frequency bands near the Dirac-point frequency of the dispersion surface while driving the lattice subharmonically (in a spatially homogeneous manner). These observations/computations can represent a starting point towards the exploration of the interplay of nonlinearity and topology in an experimentally tractable system such as the honeycomb electrical lattice.

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“…This finding, i.e. the wider range of stabilization of the EB relative to the BB, has been also experimentally observed in a chain of coupled pendula [26].…”

Section: A Driving Near the Lowest Frequency Modesupporting

confidence: 77%

Nonlinear edge modes in a honeycomb electrical lattice near the Dirac points

Palmero,

English,

Cuevas-Maraver

et al. 2020

Preprint

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“…In mechanical lattices, the study of nonlinear waves dates back to the classical 1D Fermi-Pasta-Ulam-Tsingou (FPUT) lattice [20], with its 2D extension still being analyzed quite recently [21,22]. Coupled pendula have been extensively studied in terms of synchronization and destabilization [23], while coherent structures therein such as breathers continue to capture considerable interest [24][25][26]. Nonlinear elastic metamaterials known as granular crystals have attracted much recent attention [27], with topological effects already demonstrated [28].…”

mentioning

confidence: 99%

Edge solitons in a nonlinear mechanical topological insulator

Snee

2019

Extreme Mechanics Letters

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We report localized and unidirectional nonlinear traveling edge waves discovered theoretically and numerically in a 2D mechanical (phononic) topological insulator. The lattice consists of a collection of pendula with weak Duffing nonlinearity connected by linear springs. We show that the classical 1D nonlinear Schrödinger equation governs the envelope of 2D edge modes, and study the propagation of traveling waves and rogue waves in 1D as edge solitons in 2D. As a result of topological protection, these edge solitons persist over long time intervals and through irregular boundaries.Topological insulators (TIs) are a unique state of matter with behavior that has significant ramifications in the fields of both condensed matter physics and optics. The importance of TIs has been established in the condensed matter community for almost a decade, with extensive literature on both one-dimensional and multidimensional systems [1][2][3]. The one stand out property of TIs which holds the ongoing interest in the topic is that a clear dichotomy exists between the edge (surface) and the bulk of the material as electrons are conducted only on the edge whilst the bulk is insulating. The existence of such edge states at the interface between two bulk materials with different topological invariants is guaranteed by the principle of bulk-edge correspondence [4,5]. More recently, the theoretical framework underlying quantum TIs has been generalized to photonic systems governed by classical electromagnetic fields [6][7][8]. In analogy to electrons in traditional TIs, electromagnetic waves in photonic TIs propagate along the edge with very little backscattering, even in the presence of disorders such as missing site(s) on the edge of a photonic lattice [9][10][11].The emerging field of topological mechanics utilizes such topological principles to reveal new collective excitations in classical mechanical (phononic) systems [12,13]. These topological acoustic metamaterials can be classified into two families depending on whether the topological edge modes appear at zero frequency or high frequencies. In the zero frequency case, these edge modes are identified as floppy modes and self-stress states in Maxwell frames [14]. Here we focus on the high frequency case, where topologically protected transport via phonons is enabled. Seminal work in this direction includes analogues of the quantum Hall effect using a lattice of hanging gyroscopes [15], and the quantum spin Hall effect (QSHE) using a lattice of coupled pendula [16] and bi-layered lattices of disks and springs [17].Over the last century, the theory of nonlinear waves in continuous systems has formed a cornerstone of nonlinear science [18]. A fundamental result is that in such systems, dispersion can balance with nonlinearity to produce robust localized nonlinear traveling waves known as solitons. The theory of nonlinear waves in discrete systems has flourished more recently, especially in the context of nonlinear optics and Bose-Einstein condensates [19]. In mechanical lattices, t...

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“…Since then, there has been a wide variety of systems in which experimental observations of structures have been reported that are exponentially localized in space and periodic in time. Among them, one can note arrays of Josephson junctions [4,5], mechanical [6,7] and magnetic pendula [8], microcantilevers [9], electrical chains [10,11], granular crystals, [12,13], ionic crystals such as PtCl [14] and antiferromagnets [15]. Moreover, these types of structures have been offered as plausible explantions of experimental findings in settings such as the DNA denaturation [16], α-uranium [17] or NaI [18]; see also the relevant review of [19].…”

Section: Introductionmentioning

confidence: 99%

Experimental and numerical observation of dark and bright breathers in the band gap of a diatomic electrical lattice

et al. 2019

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We observe dark and bright intrinsic localized modes (ILMs) or discrete breathers (DB) experimentally and numerically in a diatomic-like electrical lattice. The generation of dark ILMs by driving a dissipative lattice with spatially-homogenous amplitude is, to our knowledge, unprecedented. In addition, the experimental manifestation of bright breathers within the bandgap is also novel in this system. In experimental measurements the dark modes appear just below the bottom of the top branch in frequency. As the frequency is then lowered further into the band-gap, the dark DBs persist, until the nonlinear localization pattern reverses and bright DBs appear on top of the finite background. Deep into the bandgap, only a single bright structure survives in a lattice of 32 nodes. The vicinity of the bottom band also features bright and dark self-localized excitations. These results pave the way for a more systematic study of dark breathers and their bifurcations in diatomic-like chains.

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Multifrequency and edge breathers in the discrete sine-Gordon system via subharmonic driving: Theory, computation and experiment

Cited by 13 publications

References 32 publications

Nonlinear edge modes in a honeycomb electrical lattice near the Dirac points

Nonlinear edge modes in a honeycomb electrical lattice near the Dirac points

Edge solitons in a nonlinear mechanical topological insulator

Experimental and numerical observation of dark and bright breathers in the band gap of a diatomic electrical lattice

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