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

Palmero, F.; English, Lars Q.; Chen, Xuan-Lin; Li, Weilun; Cuevas–Maraver, Jesús; Kevrekidis, P. G.

doi:10.1103/physreve.99.032206

Cited by 30 publications

(13 citation statements)

References 37 publications

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“…For example, complex instabilities are known to emerge in driven elastic membranes 44 , but elastic composites with periodic heterogeneity have been shown to exhibit band gaps 45 , which our results suggest could be designed to mitigate these instabilities. Importantly, this approach can benefit from previous studies on creating and manipulating band gaps for different purposes, including the literature on topological edge states in both discrete systems [46][47][48] and continuous media 35,49 . The broader implications of this work for future studies include the modeling of heterogeneity in natural systems, such as in describing its coevolution with homogeneous states, and the mitigation of instabilities in experimental and man-made systems.…”

Section: Discussionmentioning

confidence: 99%

Heterogeneity-stabilized homogeneous states in driven media

et al. 2021

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Understanding the relationship between symmetry breaking, system properties, and instabilities has been a problem of longstanding scientific interest. Symmetry-breaking instabilities underlie the formation of important patterns in driven systems, but there are many instances in which such instabilities are undesirable. Using parametric resonance as a model process, here we show that a range of states that would be destabilized by symmetry-breaking instabilities can be preserved and stabilized by the introduction of suitable system asymmetry. Because symmetric states are spatially homogeneous and asymmetric systems are spatially heterogeneous, we refer to this effect as heterogeneity-stabilized homogeneity. We illustrate this effect theoretically using driven pendulum array models and demonstrate it experimentally using Faraday wave instabilities. Our results have potential implications for the mitigation of instabilities in engineered systems and the emergence of homogeneous states in natural systems with inherent heterogeneities.

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Section: Discussionmentioning

confidence: 99%

Heterogeneity-stabilized homogeneous states in driven media

et al. 2021

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“…There exist a number of physical systems where the existence of DBs has been proven experimentally, among them are macroscopic spring-mass chains and arrays of coupled pendula or magnets [6][7][8], granular crystals [9][10][11][12][13][14][15][16], micro-mechanical cantilever arrays [17][18][19], electrical lattices [20][21][22], nonlinear optical devices [23], Josephson junction arrays [24,25].…”

Section: Introductionmentioning

confidence: 99%

Effect of discrete breathers on the specific heat of a nonlinear chain

Singh,

Morkina,

Korznikova

et al. 2019

Preprint

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Defect-free crystal lattices can accommodate spatially localized, high amplitude atomic vibrations called either discrete breathers (DBs) or intrinsic localized modes (ILMs). This has been explored by a number of molecular dynamics studies and, in few cases, by the first-principles calculations. A number of experimental measurements of crystal vibrational spectra was performed aiming to prove the existence of DBs in thermal equilibrium at elevated temperature. However, the interpretation of these experimental results is still debated. Direct high-resolution imaging of DBs in crystals is hardly possible due to their nanometer size and short lifetime. An alternative way to substantiate the existence of DBs is to evaluate their impact on the measurable macroscopic properties of crystals and validate such prediction. One of such properties is specific heat. In fact, the measurements of heat capacity was done for alpha-uranium by Manley and co-workers in conditions where the presence of DBs was expected. In the present study, employing a one-dimensional nonlinear lattice with an on-site potential, we analyze the effect of DBs on its specific heat. In the most transparent way, this can be done by monitoring the chain temperature in a non-equilibrium process, at the emergence of modulational instability, with total energy of the chain being conserved. For the onsite potential of hard-type (soft-type) anharmonicity, the instability of q = π mode (q = 0 mode) results in the appearance of long-living DBs that gradually dissipate their energy and eventually the system approaches thermal equilibrium with spatially uniform and temporally constant temperature. The variation of specific heat at constant volume is evaluated during this relaxation process. It is concluded that DBs affect specific heat of the nonlinear chain and for the case of hard-type (softtype) anharmonicity they reduce (increase) the specific heat.

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“…In the present work, as a possible physical implementation approximately corresponding to this equation, we theoretically suggest and analyze a specially designed electric circuit network. Implementation of discrete nonlinear dynamic systems in the form of 1D and 2D electric networks has a long and rich history [50][51][52][53][54][55][56][57][58][59][60][61][62][63], including even experimental simulations of the integrable Toda chain [50][51][52][53]. Major attention has been devoted to modulationally unstable systems.…”

Section: Introductionmentioning

confidence: 99%

Discrete vortices on spatially nonuniform two-dimensional electric networks

Ruban

2019

Preprint

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Two-dimensional arrays of nonlinear electric oscillators are considered theoretically, where nearest neighbors are coupled by relatively small, constant, but non-equal capacitors. The dynamics is approximately reduced to a weakly dissipative defocusing discrete nonlinear Schrödinger equation with translationally non-invariant linear dispersive coefficients. Behavior of quantized discrete vortices in such systems is shown to depend strongly on the spatial profile of the inter-node coupling as well as on the ratio between time-increasing healing length and lattice spacing. In particular, vortex clusters can be stably trapped for a some initial period of time by a circular barrier in the coupling profile, but then, due to gradual dissipative broadening of vortex cores, they lose stability and suddenly start to move.

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

Cited by 30 publications

References 37 publications

Heterogeneity-stabilized homogeneous states in driven media

Heterogeneity-stabilized homogeneous states in driven media

Effect of discrete breathers on the specific heat of a nonlinear chain

Discrete vortices on spatially nonuniform two-dimensional electric networks

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