Stability Of Discrete Breathers Research Articles

Structure and stability of discrete breather in zigzag and armchair carbon nanotubes

Structure and stability of discrete breather in zigzag and armchair carbon nanotubes

High-order nonlinear excitations in the Joyeux-Buyukdagli model of DNA.

By means of the semidiscrete multiple-scale method, we study the existence and properties of high-order envelope solitons and discrete breathers in a homogeneous DNA chain model that is based on pairing enthalpies and site-dependent finite stacking. We obtain the analytical solutions for an envelope soliton, and find that at the Brillouin zone center, discrete breather solutions can appear below the bottom of the phonon band. The behavior of two solitons in collisions and the stability of discrete breathers are confirmed by numerical simulations of the exact equations of the system.

Dynamics and stability of a discrete breather in a harmonically excited chain with vibro-impact on-site potential

We investigate the existence and stability of discrete breathers in a chain of masses connected by linear springs and subjected to vibro-impact on-site potentials. The latter are comprised of harmonic springs and rigid constraints limiting the possible motion of the masses. Local dissipation is introduced through a non-unit restitution coefficient characterizing the impacts. The system is excited by uniform time-periodic forcing. The present work is aimed to study the existence and stability of similar breathers in the space of parameters, if additional harmonic potentials are introduced. Existence–stability patterns of the breathers in the parameter space and possible bifurcation scenarios are investigated analytically and numerically. In particular, it is shown that the addition of a harmonic on-site potential can substantially extend the stability domain, at least close to the anti-continuum limit. This result can be treated as an increase in the robustness of the breather from the perspective of possible practical applications.

Stability of discrete breathers in nonlinear Klein-Gordon type lattices

Stability of discrete breathers in nonlinear Klein-Gordon type lattices

Existence and stability of discrete breathers in Fermi-Pasta-Ulam lattices

Existence and stability of discrete breathers in Fermi-Pasta-Ulam lattices

Stability of discrete breathers in diatomic nonlinear oscillator chains

Stability of discrete breathers in diatomic nonlinear oscillator chains

Existence and stability of discrete breathers in diatomic Fermi–Pasta–Ulam type lattices

We consider discrete breathers in one-dimensional diatomic Fermi–Pasta–Ulam type lattices. A discrete breather in the limit of zero mass ratio, i.e. the anti-continuous limit, consists of a finite number of in-phase or anti-phase excited light particles, separated by particles at rest. The existence of discrete breathers is proved for small mass ratio by continuation from the anti-continuous limit. We prove that the discrete breathers are all unstable near the anti-continuous limit, except for those continued from solutions consisting of alternating anti-phase excited particles.

Intrinsic energy localization through discrete gap breathers in one-dimensional diatomic granular crystals

We present a systematic study of the existence and stability of discrete breathers that are spatially localized in the bulk of a one-dimensional chain of compressed elastic beads that interact via Hertzian contact. The chain is diatomic, consisting of a periodic arrangement of heavy and light spherical particles. We examine two families of discrete gap breathers: (1) an unstable discrete gap breather that is centered on a heavy particle and characterized by a symmetric spatial energy profile and (2) a potentially stable discrete gap breather that is centered on a light particle and is characterized by an asymmetric spatial energy profile. We investigate their existence, structure, and stability throughout the band gap of the linear spectrum and classify them into four regimes: a regime near the lower optical band edge of the linear spectrum, a moderately discrete regime, a strongly discrete regime that lies deep within the band gap of the linearized version of the system, and a regime near the upper acoustic band edge. We contrast discrete breathers in anharmonic Fermi-Pasta-Ulam (FPU)-type diatomic chains with those in diatomic granular crystals, which have a tensionless interaction potential between adjacent particles, and note that the asymmetric nature of the tensionless interaction potential can lead to hybrid bulk-surface localized solutions.

Breathers in one-dimensional binary metamaterial models

The existence and stability of discrete breathers is studied theoretically for a model magnetic metamaterial composed of a periodic binary array of split-ring resonators with resonance frequency mismatch. It is demonstrated that breathers can be excited spontaneously by frequency chirping of the driving field, a method that is well suited for experiments.

Magnetoinductive breathers in metamaterials

The existence and stability of discrete breathers (DBs) in one- and two-dimensional magnetic metamaterials (MMs), which consist of periodic arrangements (arrays) of split-ring resonators (SRRs), are investigated numerically. We consider different configurations of the SRR arrays, which are related to the relative orientation of the SRRs in the MM, in both one and two spatial dimensions. In the latter case we also consider anisotropic MMs. Using standard numerical methods we construct several types of linearly stable breather excitation in both Hamiltonian and dissipative MMs (dissipative breathers). The study of stability in both cases is performed using standard Floquet analysis. In both cases we find that the increase of dimensionality from one to two spatial dimensions does not destroy the DBs, which may also exist in the case of moderate anisotropy (in two dimensions). In dissipative MMs, the dynamics is governed by a power balance between the mainly Ohmic dissipation and driving by an alternating magnetic field. In that case it is demonstrated that DB excitation locally alters the magnetic response of MMs from paramagnetic to diamagnetic. Moreover, when the frequency of the applied field approaches the SRR resonance frequency, the magnetic response of the MM in the region of the DB excitation may even become negative (extremely diamagnetic).

Discrete breathers in two-dimensional anisotropic nonlinear Schrödinger lattices

We study the structure and stability of discrete breathers (both pinned and mobile) in two-dimensional nonlinear anisotropic Schrödinger lattices. Starting from a set of identical one-dimensional systems we develop the continuation of the localized pulses from the weakly coupled regime (strongly anisotropic) to the homogeneous one (isotropic). Mobile discrete breathers are seen to be a superposition of a localized mobile core and an extended background of two-dimensional nonlinear plane waves. This structure is in agreement with previous results on one-dimensional breather mobility. The study of the stability of both pinned and mobile solutions is performed using standard Floquet analysis. Regimes of quasi-collapse are found for both types of solutions, while another kind of instability (responsible for the discrete breather fission) is found for mobile solutions. The development of such instabilities is studied, examining typical trajectories on the unstable nonlinear manifold.

Existence and Stability of Localized Oscillations in 1-Dimensional Lattices With Soft-Spring and Hard-Spring Potentials

In this paper, we use the method of homoclinic orbits to study the existence and stability of discrete breathers, i.e., spatially localized and time-periodic oscillations of a class of one-dimensional (1D) nonlinear lattices. The localization can be at one or several sites and the 1D lattices we investigate here have linear interaction between nearest neighbors and a quartic on-site potential Vu=12Ku2±14u4, where the (+) sign corresponds to “hard spring” and (−) to “soft spring” interactions. These localized oscillations—when they are stable under small perturbations—are very important for physical systems because they seriously affect the energy transport properties of the lattice. Discrete breathers have recently been created and observed in many experiments, as, e.g., in the Josephson junction arrays, optical waveguides, and low-dimensional surfaces. After showing how to construct them, we use Floquet theory to analyze their linear (local) stability, along certain curves in parameter space (α,ω), where α is the coupling constant and ω the frequency of the breather. We then apply the Smaller Alignment Index method (SALI) to investigate more globally their stability properties in phase space. Comparing our results for the ± cases of Vu, we find that the regions of existence and stability of breathers of the “hard spring” lattice are considerably larger than those of the “soft spring” system. This is mainly due to the fact that the conditions for resonances between breathers and linear modes are much less restrictive in the former than the latter case. Furthermore, the bifurcation properties are quite different in the two cases: For example, the phenomenon of complex instability, observed only for the “soft spring” system, destabilizes breathers without giving rise to new ones, while the system with “hard springs” exhibits curves in parameter space along which the number of monodromy matrix eigenvalues on the unit circle is constant and hence breather solutions preserve their stability character.

Existence and stability of discrete gap breathers in a diatomic beta Fermi-Pasta-Ulam chain.

We study the existence and stability of discrete breathers in a chain consisting of alternating light and heavy particles, with nearest-neighbor coupling containing quartic soft or hard anharmonicity. This study is focused on breathers with frequency in the gap that separates the acoustic and optical bands of the phonon spectrum. Simple analytical and physical results obtained through explicit solutions of algebraic equations demonstrate the possibility of the existence of gap breathers with both types of symmetry, i.e., symmetric and antisymmetric. The specific pattern depends on the type of anharmonicity present, i.e., soft or hard, and whether the center of the breather is on a light or a heavy particle. These analytical results are verified systematically through the use of a numerically exact procedure from the anticontinuous limit.