Nonlinear localized modes in two-dimensional electrical lattices

English, Lars Q.; Palmero, F.; Stormes, J.F.; Cuevas, J.; Carretero-González, R.; Kevrekidis, P. G.

doi:10.1103/physreve.88.022912

Cited by 52 publications

(39 citation statements)

References 44 publications

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“…Numerics are generally found to be in good quantitiative agreement with experimental results [12]. Now that numerical work has confirmed the experimental results and also, according to the bottom panels of Fig.…”

Section: Resultssupporting

confidence: 77%

See 1 more Smart Citation

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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Section: Resultssupporting

confidence: 77%

“…[12]). We characterize these breather states in parameter space, and we compare to numerical simulations and stability analysis.…”

Section: Introductionmentioning

confidence: 99%

Energy localization and transport in two-dimensional electrical lattices

English¹,

Palmero²,

Stormes³

et al. 2014

IEICE Proceeding Series

Self Cite

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“…Experimentally, moving discrete dissipative breathers have been observed in damped-driven electrical lattices, both one dimensional (1D) [16,17] as well as more recently two dimensional (2D) [18]. In the 1D lattice in Ref.…”

Section: Introductionmentioning

confidence: 99%

Strongly localized moving discrete dissipative breather-solitons in Kerr nonlinear media supported by intrinsic gain

2014

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We investigate the mobility of nonlinear localized modes in a generalized discrete Ginzburg-Landau-type model, describing a one-dimensional waveguide array in an active Kerr medium with intrinsic, saturable gain and damping. It is shown that exponentially localized, traveling discrete dissipative breather-solitons may exist as stable attractors supported only by intrinsic properties of the medium, i.e., in the absence of any external field or symmetry-breaking perturbations. Through an interplay by the gain and damping effects, the moving soliton may overcome the Peierls-Nabarro barrier, present in the corresponding conservative system, by self-induced time-periodic oscillations of its power (norm) and energy (Hamiltonian), yielding exponential decays to zero with different rates in the forward and backward directions. In certain parameter windows, bistability appears between fast modes with small oscillations and slower, large-oscillation modes. The velocities and the oscillation periods are typically related by lattice commensurability and exhibit period-doubling bifurcations to chaotically "walking" modes under parameter variations. If the model is augmented by intersite Kerr nonlinearity, thereby reducing the Peierls-Nabarro barrier of the conservative system, the existence regime for moving solitons increases considerably, and a richer scenario appears including Hopf bifurcations to incommensurately moving solutions and phase-locking intervals. Stable moving breathers also survive in the presence of weak disorder.

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“…Therefore, discrete breathers have attracted intense interest in many areas of physics as well as chemistry and biology over the past three decades, see, e.g., the most recent review articles [5][6][7]. Intriguingly, discrete breathers have been experimentally observed in a wide variety of different media such as atomic lattices 8,9 , alkali halides 10,11 , graphite 12 , charge-transfer solids 13 , Josephson junction arrays 14,15 , coupled antiferromagnetic layers [16][17][18][19] , layered high-T c superconductors 20 , micromechanical cantilever arrays [21][22][23] , torsionally coupled pendula 24 , granular crystals 25 , electrical lattices [26][27][28][29][30] , optical waveguides and photonic crystals [31][32][33][34][35] , Bose-Einstein condensation 36 , biopolymers 37,38 , and so on.…”

Section: Introductionmentioning

confidence: 99%

Energy thresholds of discrete breathers in thermal equilibrium and relaxation processes

Ling

et al. 2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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So far, only the energy thresholds of single discrete breathers in nonlinear Hamiltonian systems have been analytically obtained. In this work, the energy thresholds of discrete breathers in thermal equilibrium and the energy thresholds of long-lived discrete breathers which can remain after a long time relaxation are analytically estimated for nonlinear chains. These energy thresholds are size dependent. The energy thresholds of discrete breathers in thermal equilibrium are same as the previous analytical results for single discrete breathers. The energy thresholds of long-lived discrete breathers in relaxation processes are different from the previous results for single discrete breathers but agree well with the published numerical results known to us. Because real systems are either in thermal equilibrium or in relaxation processes, the obtained results could be important for experimental detection of discrete breathers. a) Electronic mail: meanyee@mail.ustc.edu.cn b) Electronic mail: zjding@ustc.edu.cn 1 Discrete breather is an intrinsic spatially localized nonlinear excitation which can be excited in any kind of discrete nonlinear systems. They can be excited both in thermal equilibrium and in relaxation processes. Once the long-lived discrete breathers are formed in the relaxation processes, the energy relaxations are very slow. The energy thresholds of discrete breathers in thermal equilibrium and relaxation processes can be only numerically estimated so far because of the strong interactions between breathers with other excitations, for instance, phonons. They are thus regarded as identical to the previous analytical energy thresholds of single discrete breathers in Hamiltonian systems. In this work, the energy thresholds of discrete breathers in thermal equilibrium and relaxation processes and thus of the slow energy relaxations are analytically estimated. The energy thresholds of discrete breathers in thermal equilibrium are same as the previous results for single discrete breathers. However, the energy thresholds of long-lived discrete breathers in relaxation processes are different from the previous results. Remarkably, they agree well with the published numerical results known to us. Real systems are either in thermal equilibrium or in relaxation processes. Therefore, the obtained energy thresholds, especially the size-dependence of them, are expected to be important for experimental detection of discrete breathers.

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Nonlinear localized modes in two-dimensional electrical lattices

Cited by 52 publications

References 44 publications

Energy localization and transport in two-dimensional electrical lattices

Energy localization and transport in two-dimensional electrical lattices

Strongly localized moving discrete dissipative breather-solitons in Kerr nonlinear media supported by intrinsic gain

Energy thresholds of discrete breathers in thermal equilibrium and relaxation processes

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