Intrinsic Localized Modes Research Articles

Intrinsic Localized Modes in Antiferromagnetic Chains with Dzyaloshinsky-Moriya Interaction

In this paper, we present an analytical study on intrinsic localized spin-wave modes in antiferromagnetic chains with Dzyaloshinsky-Moriya interaction in semiclassical limit. By means of the method of multiple scales combined with a quasi-discreteness approximation, the nonlinear Schrodinger equation is derived for the conherent-state amplitude. It is found that a bright stationary intrinsic localized spin-wave mode can appear below the linear spin-wave spectrum. Besides, we show that the antiferromagnetic chain can produce a dark intrinsic localized spin-wave mode, namely, nonpropagating kink, which is a typical nonlinear resonant mode.

Intrinsic Localized Spin-Wave Modes in an Anisotropic Ferromagnet with Dzyaloshinsky—Moriya Interaction

The existence and properties of intrinsic localized spin-wave modes in a ferromagnetic XXZ spin chain with Dzyaloshinsky—Moriya interaction are investigated analytically in the semiclassical limit. The model Hamiltonian is quantized by introducing the Dyson—Maleev transformation and the coherent state representation is chosen as the basic representation of the system. By making use of the method of multiple scales combined with a quasidiscreteness approximation, the equation of motion for the coherent-state amplitude is reduced to the nonlinear Schrödinger equation. It is shown that a bright intrinsic localized spin-wave mode whose eigenfrequency lies below the bottom of the magnon frequency band can exist in the ferromagnetic system. We also show that the system can produce a dark intrinsic localized spin-wave mode, i.e., nonpropagating kink, whose eigenfrequency is below the upper of the magnon frequency band. In addition, we find that the introduction of the Dzyaloshinsky—Moriya interaction changes wave numbers in the Brillouin-zone corresponding to the appearance of intrinsic localized spin-wave modes.

Multiple high-temperature transitions driven by dynamical structures in NaI

Using inelastic neutron scattering, x-ray diffraction, and heat capacity measurements, the authors study intrinsic localized modes in NaI. Their results suggest that, as the temperature is varied, NaI undergoes several unconventional phase transitions that are due to anharmonicity of the lattice vibrations.

Analysis of intrinsic localised mode for a new energy harvesting cantilever array

Electromechanical model of an energy harvester that is comprised of 64 identical pairs of cantilever beams has been built in this work. Each pair consists of a short and a long cantilever with the same width and thickness. All the beams are bi-layer structures that include a piezoelectric layer and a substrate layer, which are coupled by the overhang part. The model is focused on analyzing the nonlinear dynamic behavior of the device, specifically when it is operated at intrinsic localized mode (ILM). The electrical charge generated on the surface of the piezoelectric layer has been derived using the beam theory and the piezoelectric equations. It has been found from numerical simulations that spatiotemporal chaos, in particular ILMs can arise during abrupt frequency changes of the external driving source, which could potentially be used to achieve high/concentrated energy output.

Quantum solitons in the Fermi–Pasta–Ulam model

In this paper, quantum solitons in the Fermi–Pasta–Ulam (FPU) model are investigated analytically. By using the canonical transform method and number-conserving approximation, we obtain the normal form of the phonon-conserving quantized Hamiltonian. In order to convert the quantized Hamiltonian into the coordinate space, we employ the inverse Fourier transform. With the help of the Hartree approximate and the semidiscrete multiple-scale method, the nonlinear Schrödinger (NLS) equation is derived. The results show that quantum solitons may exist in the FPU model. Moreover, it is found that moving quantum solitons become quantum intrinsic localized modes under certain condition. In addition, we obtain the energy level of quantum solitons, which indicates that the energy of such quantum solitons is quantized.

A numerical study on parametric resonance of intrinsic localized modes in coupled cantilever arrays

ySchool of Engineering, The University of Shiga Prefecture2500 Hassaka-cho, Hikone, Shiga 522-8533, JapanzDepartment of Electrical Engineering, Kyoto UniversityKatsura, Nishikyo, Kyoto 615-8510, JapanEmail: kimura.m@e.usp.ac.jp, matsushita.y@e.usp.ac.jp, hikihara.takashi.2n@kyoto-u.ac.jpAbstract —In a coupled cantilever array modeled as acoupled ordinary di erential equation, symmetric and an-tisymmetric intrinsic localized modes (ILMs) exist. Thesymmetric ILM is stable while the other is unstable underthe regime in which the ratio in nonlinearities of inter-siteand on-site potentials is less than the critical value at whichthe stability change occurs. This paper shows that a sta-ble ILM loses its stability when the system is parametri-cally excited. If the amplitude of parametric excitation islarge enough, the destabilized ILM wanders in the wholesystem. The parameter region where the instability occursare numerically investigated and compared with that in theMathieu equation. The similarity of the shape of the re-gions strongly suggests that the instability is caused by theparametric resonance.1. IntroductionSpatially localized and temporary periodic vibrations of-ten appear in nonlinear coupled oscillators [1]. The energylocalized vibration in discrete media which is rst discov-ered by A. J. Sievers and S. Takeno [2] is called intrinsic lo-calized mode(ILM) or discrete breather(DB). Experimentalobservations of ILM have been reported for a variety ofphysical system in this decade as well as theoretical andnumerical studies. In particular of them, the observationin micro-mechanical cantilever array allow us to expectthe realization of applications using ILM in micro/nano-engineering [3], because it was also observed that ILM canmove without decaying its energy concentration and can bemanipulated by an extraneous stimulus [4].For the realization of such application, the controlscheme for the ILM should be established. The capture andrelease manipulation using the stability change is proposedas an alternative method to manipulate ILM in a micro-cantilever array [5]. For the manipulation method, it isutilized that a stable ILM begins to move after it loses itsstability. Therefore, the manipulation is a way to generatemoving ILM. In this paper, we propose another method togenerate moving ILM by parametric excitation of the ratioin nonlinearities. We rst investigate how moving ILMsbehave around a stable ILM. The motion of moving ILM isapproximated by a simple equation of pendulum. Then, be-haviors of moving ILM created by parametric excitation areshown. Finally, the region where a stable solution loses itsstability by parametric excitation is computed for an ILM,and is compared with that of the Mathieu equation.2. Coupled Cantilever ArrayCantilever array, which is often used as a coupled me-chanical resonator in nano/micro-engineering, is one ofnonlinear coupled oscillators in which ILM can be ob-served experimentally [3]. The motion of cantilevers canapproximately be described by ordinary di erential equa-tion [4–6],u¨

A study on feedback control of intrinsic localized modes in a micro-mechanical cantilever array

ySchool of Engineering, The University of Shiga Prefecture2500 Hassaka-cho, Hikone, Shiga 522-8533, JapanzDepartment of Electrical Engineering, Kyoto UniversityKatsura, Nishikyo, Kyoto 615-8510, JapanEmail: kimura.m@e.usp.ac.jp, matsushita.y@e.usp.ac.jp, hikihara.takashi.2n@kyoto-u.ac.jpAbstract —Intrinsic localized mode (ILM), which isalso called discrete breather (DB), is an energy localizedvibration in nonlinear coupled oscillators. It is well knownthat the ILM can move in the system without decay of itsenergy concentration. This paper shows that the positionof ILM can be controlled by proportional-derivative con-trol. To create a force to the ILM, linear on-site coe cientsare modulated linearly with respect to the lattice number.Namely, value of the linear on-site coe cients linearly in-crease/decrease as the lattice number increases. Magnitudeof the tilt is adjusted with PD control scheme. As a result ofnumerical simulations, a standing ILM is successfully con-trolled toward a reference position with keeping its energyconcentration.1. IntroductionSpatially localized and temporary periodic vibrations of-ten appear in nonlinear coupled oscillators [1]. The energylocalized vibration in discrete media which is rst discov-ered by A. J. Sievers and S. Takeno [2] is called intrinsic lo-calized mode(ILM) or discrete breather(DB). Experimentalobservations of ILM have been reported for a variety ofphysical system in this decade as well as theoretical andnumerical studies. In particular of them, the observationin micro-mechanical cantilever array allow us to expectthe realization of applications using ILM in micro/nano-engineering [3], because it was also observed that ILM canmove without decaying its energy concentration and can bemanipulated by an extraneous stimulus [4].For the realization of such application, the controlscheme for the ILM should be established. In our previ-ous research, it has been shown that a standing ILM losesits stability by parametric excitation [5]. This result impliesthat appropriately adjusting parameter can creates a force tostanding ILM, because the parametric resonance is usuallycaused by changing a potential shape. Therefore, if the pa-rameter of the system is changed appropriately based on thedistance from the reference position, the position of ILMcan be controlled by using an ordinary control method. Inthis paper, proportional-derivative control is applied to thecontrol of the position of ILM. First, an approximate equa-tion describing the motion of traveling ILM is derived. Sec-ond, behavior of moving ILM is shown when on-site linearcoe cients are gradually changed with respect to the lat-tice number. Finally, the proportional-derivative control ofILM is demonstrated and discussed.2. Coupled Cantilever Array and Standing ILMMicro-cantilever array is one of nonlinear coupled oscil-lators having ILM [3]. By focusing on the rst mode ofbeam vibrations, motions of each cantilever's tip are ap-proximately described by the following ordinary di eren-tial equation [4,6,7],¨u

Energy localization and transport in two-dimensional electrical lattices

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 mo- tion of these ILMs is qualitatively dierent in that it lacks a consistent direction. Furthermore, the hop- ping speed seems to be somewhat reduced in two di- mensions due to an enhanced Peierls-Nabarro (PN)- barrier. We investigate both square and honeycomb lattices composed of 6 6 elements. These direct ob- servations were further supported by numerical simu- lations based on realistic models of circuit components. The numerical study moreover allowed for an analysis of ILM dynamics and pattern formation for larger lat- tice sizes.

Approximate ILM dynamics in DNA models

We investigate the existence of Intrinsic Localized Modes (ILMs) in nonlinear one-dimensional KleinGordon chains. We use the Lagrangian averaging approach parameterizing ILM by several slow-varying variables, and apply the averaging directly in the action principle. Our preliminary studies yield results for ILM dynamics in accordance with those obtained by other methods.

Intrinsic localized modes observed as a precursor to polar nanoregion formation in a relaxor ferroelectric

Intrinsic localized modes observed as a precursor to polar nanoregion formation in a relaxor ferroelectric

Theory and molecular dynamics simulations of intrinsic localized modes and defect formation in solids

Molecular dynamics (MD) simulations of recoil processes following the scattering of x-rays or neutrons have been performed in ionic crystals and metals. At small energies (< 10 eV) the recoil can induce intrinsic localized modes (ILMs) and linear local modes associated with these modes. As a rule, the frequencies of such modes are located in the gaps of the phonon spectrum. However, in metallic Ni, Nb and Fe, due to the renormalization of atomic interactions by free electrons, the frequencies mentioned are found to be positioned above the phonon spectrum. It has been shown that these ILMs are highly mobile and can efficiently transfer a concentrated vibrational energy over large distances along crystallographic directions. If the recoil energy exceeds tens of eVs, vacancies and interstitials can be formed, which are strongly dependent on the direction of the recoil momentum. In NaCl-type lattices the recoil in (110) direction can produce a vacancy and a crowdion, while in the case of a recoil in (100) and in (111) directions a bi-vacancy and a crowdion can be formed.

Intrinsic localized modes of a classical discrete anisotropic Heisenberg ferromagnetic spin chain

We report several exact intrinsic localized mode solutions of the classical spin evolution equation of a one-dimensional anisotropic Heisenberg ferromagnetic spin chain in terms of Jacobian elliptic functions. These include one, two and three spin excitations. All these solutions have smooth anticontinuum limits. Their linear stability and semiclassical quantization are also discussed briefly.

Lattice dynamics of NaI studied by inelastic neutron scattering: Absence of thermally induced discrete breathers

The paper presents an inelastic neutron scattering study of lattice dynamics of the NaI alkali halide crystal, aimed to check the previously reported signatures of intrinsic localized modes, so-called discrete breathers. It is shown that three unusual spectral features, previously interpreted as an evidence for thermally induced discrete breathers (an anomalous spectral band in the phononic gap, longitudinal acoustic ${\ensuremath{\Lambda}}_{1}$ phonon branch overbending, and fragmentation of the $X$-point transverse optic mode response) are all absent in the independent experiments reported here.

Intrinsic Localized Modes of Harmonic Oscillations in Pendulum Arrays Subjected to Horizontal Excitation

The behavior of intrinsic localized modes (ILMs) is investigated for an array with N pendula which are connected with each other by weak, linear springs when the array is subjected to horizontal, sinusoidal excitation. In the theoretical analysis, van der Pol's method is employed to determine the expressions for the frequency response curves for fundamental harmonic oscillations. In the numerical calculations, the frequency response curves are presented for N = 2 and 3 and compared with the results of the numerical simulations. Patterns of oscillations are classified according to the stable steady-state solutions of the response curves, and the patterns in which ILMs appear are discussed in detail. The influence of the connecting springs of the pendula on the appearance of ILMs is examined. Increasing the values of the connecting spring constants may affect the excitation frequency range of ILMs and cause Hopf bifurcation to occur, followed by amplitude modulated motions (AMMs) including chaotic vibrations. The influence of the imperfections of the pendula on the system response is also investigated. Bifurcation sets are calculated to examine the influence of the system parameters on the excitation frequency range of ILMs and determine the threshold value for the connecting spring constant above which ILMs do not appear. Experiments were conducted for N = 2, and the data were compared with the theoretical results in order to confirm the validity of the theoretical analysis.

On the role of disorder in catalysis driven by discrete breathers

A new mechanism of catalysis is discussed, which is based on the rate-promoting effect of large-amplitude anharmonic lattice vibrations, a.k.a. intrinsic localized modes or ‘discrete breathers’ (DBs), which can excite atoms at specific ‘active sites’ rather strongly, giving them energy far exceeding the energy of thermal vibrations for hundreds of oscillation periods. The DB-induced modulation of activation energies (free energy barriers between reactants and products) results in a drastic amplification of the reaction rates, which can be described by a simple analytical expression in the adiabatic limit. The striking site selectiveness of DB excitation dynamics in the presence of spatial (quenched) disorder makes these nonlinear vibrations viable candidates to play the role of ‘active modes’ in the catalytic process in various physical, chemical and biological systems.

Thermally populated intrinsic localized modes in pure alkali halide crystals

The possibility of thermal excitation of intrinsic localized modes (ILMs) arising from anharmonicity in ionic perfect crystals is studied numerically for realistic model systems in one and three dimensions. Implications are discussed for an interesting high-temperature feature seen in earlier inelastic neutron scattering experiments on single crystal NaI. The general conclusion is that ILM formation energies are far too large for thermal excitation of ILMs to account for the observed feature in a pure crystal.

INTRINSIC LOCALIZED MODES IN QUANTUM FERROMAGNETIC ISING–HEISENBERG CHAINS WITH SINGLE-ION UNIAXIAL ANISOTROPY

Based on the coherent-state method combined with the Dyson–Maleev representation of spin operators, the existence and properties of intrinsic localized spin-wave modes in quantum ferromagnetic Ising–Heisenberg chains with single-ion uniaxial anisotropy are investigated analytically in the semiclassical limit. With the help of the multiple-scale method combined with semidiscrete approximation, the equation of motion for the coherent-state amplitude is reduced to the nonlinear Schrödinger equation. It is found that, at the center of the Brillouin zone, a bright type intrinsic localized spin-wave mode can exist below the bottom of the linear spin-wave spectrum. Besides, we show that, at the boundary of the Brillouin zone, a dark type intrinsic localized spin-wave mode appears above the top of the linear spin-wave spectrum, which is different from the resonant nonpropagating kink mode.

Nonlinear localized modes in two-dimensional electrical lattices

We report the observation of spontaneous localization of energy in two spatial dimensions in the context of nonlinear electrical lattices. Both stationary and moving self-localized modes were generated experimentally and theoretically in a family of two-dimensional square as well as honeycomb lattices composed of 6 × 6 elements. Specifically, we find regions in driver voltage and frequency where stationary discrete breathers, also known as intrinsic localized modes (ILMs), exist and are stable due to the interplay of damping and spatially homogeneous driving. By introducing additional capacitors into the unit cell, these lattices can controllably induce mobile discrete breathers. When more than one such ILMs are experimentally generated in the lattice, the interplay of nonlinearity, discreteness, and wave interactions generates a complex dynamics wherein the ILMs attempt to maintain a minimum distance between one another. Numerical simulations show good agreement with experimental results and confirm that these phenomena qualitatively carry over to larger lattice sizes.

Intrinsic localized modes in a nonlinear electrical lattice with saturable nonlinearity

This experimental study of driven intrinsic localized modes (ILMs) in an electronic circuit lattice with saturable nonlinearity follows the theoretical work of Hadžievski and coworkers. They proposed that a saturable nonlinearity could introduce transition points where localized excitations in nonintegrable lattices would move freely. In our experiments MOS capacitors provide the saturable nonlinearity in an electric lattice. Because of the soft nonlinearity driver locked, auto-resonance stationary ILMs are observed below the bottom of a linear frequency band of the lattice. With decreasing driver frequency the width of the ILM changes in a stepwise manner as does the softening of the barrier between site-centered and bond-centered ILM locations in agreement with theoretical expectations. However, the steps show hysteresis between up and down frequency scans and such hysteresis inhibits the free motion of ILMs.

Intrinsic Localized Modes of Harmonic Oscillations in Nonlinear Oscillator Arrays

Intrinsic localized modes (ILMs) are investigated in an array with N Duffing oscillators that are weakly coupled with each other when each oscillator is subjected to sinusoidal excitation. The purpose of this study is to investigate the behavior of ILMs in nonlinear multi-degree-of-freedom (MDOF) systems. In the theoretical analysis, van der Pol's method is employed to determine the expressions for the frequency response curves for fundamental harmonic oscillations. In the numerical calculations, the frequency response curves are shown for N = 2 and 3 and compared with the results of the numerical simulations. Basins of attraction are shown for a two-oscillator array with hard-type nonlinearities to examine the possibility of appearance of ILMs when an oscillator is disturbed. The influences of the connecting springs for both hard- and soft-type nonlinearities on the appearance of the ILMs are examined. Increasing the values of the connecting spring constants may cause Hopf bifurcation followed by amplitude modulated motion (AMM) including chaotic vibrations. The influence of the imperfection of an oscillator is also investigated. Bifurcation sets are calculated to show the influence of the system parameters on the excitation frequency range of ILMs. Furthermore, time histories are shown for the case of N = 10, and many patterns of ILMs may appear depending on the initial conditions.