Intrinsic Localized Modes Research Articles

QUANTUM QUASI-SOLITONS IN THE TWO-DIMENSIONAL FERROMAGNETIC LATTICE WITH AN EXTERNAL FIELD

Based on the quantum theory and a simplified version of the multiple-scale method, the nonlinear excitations in a two-dimensional ferromagnetic lattice with an external magnetic field are analytically investigated. The standard two-dimensional nonlinear Schrödinger equation is obtained. Results show that the quantum quasi-soliton can exist in the two-dimensional ferromagnetic lattice. In addition, when the group velocity is equal to zero, at the boundary of the Brillouin zone, the quantum quasi-soliton becomes the quantum intrinsic localized mode.

Modeling of self-localized vibrations and defect formation in solids

MD simulations of recoil processes, following the scattering of X-rays or neutrons are performed. At small energies (<10eV) the recoil can induce intrinsic localized modes and linear local modes associated with them. In ionic crystals the frequencies of these modes are located in the gaps of the phonon spectrum, being essentially dependent on long-range forces. In metals, as a result of the screening of atomic interactions by free electrons, their frequencies can be positioned above the phonon spectrum. The MD simulations of vibrations in Ni and Nb confirm this prediction. If the recoil energy exceeds tens of eV, the vacancies and interstitials can be formed. In fcc lattices a 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.

Switching dynamics and linear response spectra of a driven one-dimensional nonlinear lattice containing an intrinsic localized mode

An intrinsic localized mode (ILM) represents a localized vibrational excitation in a nonlinear lattice. Such a mode will stay in resonance as the driver frequency is changed adiabatically until a bifurcation point is reached, at which point the ILM switches and disappears. The dynamics behind switching in such a many body system is examined here through experimental measurements and numerical simulations. Linear response spectra of a driven micromechanical array containing an ILM were measured in the frequency region between two fundamentally different kinds of bifurcation points that separate the large amplitude ILM state from the two low amplitude vibrational states. Just as a natural frequency can be associated with a driven harmonic oscillator, a similar natural frequency has been found for a driven ILM via the beat frequency between it and a weak, tunable probe. This finding has been confirmed using numerical simulations. The behavior of this nonlinear natural frequency plays important but different roles as the two bifurcation points are approached. At the upper transition its frequency coalesces with the driver and the resulting bifurcation is very similar to the saddle-node bifurcation of a single driven Duffing oscillator, which is treated in an Appendix. The lower transition occurs when the four-wave mixing partner of the natural frequency of the ILM intersects the topmost extended band mode of the same symmetry. The properties of linear local modes associated with the driven ILM are also identified experimentally for the first time and numerically but play no role in these transitions.

The temperature dependence of the phononic band gap of NaI

The position and size of the energy gap in the phonon density of states of NaI single crystal have been investigated by inelastic neutron scattering in a wide range of temperatures from 10 to 700 K. The results reveal a pronounced temperature effect which effectively leads to closure of the phonon gap at temperatures in the range of 700–800 K. The results are discussed in the context of studies of possible intrinsic localized modes in the phonon gap of alkali halides.

Reduced systems for Intrinsic Localized Modes on an infinite oscillator array

We reduce the complex mechanics of an Intrinsic Localized Mode (ILM) on an infinite monodirectional nonlinear coupled oscillator array. By using Hamiltonian Mechanics, we derive two systems – a simple case when only the position of the ILM is allowed to vary, and the more complex case where both position and amplitude are allowed to change with time. We arrive at a systems of nonlinear equations of motion. For the position-only system, the dynamics are determined solely by the level sets of the Hamiltonian. The four-variable system has a richer structure. We also analyze the effect of a defect, or an impurity, on the motion of the ILM within our framework.

Bifurcation dynamics of a perturbed intrinsic localized mode in a driven micromechanical array

Bifurcation dynamics of a perturbed intrinsic localized mode in a driven micromechanical array

Breathers in periodic granular chains with multiple band gaps

We consider the localized nonlinear breathing modes that emerge in heterogeneous granular configurations of two materials with a periodicity of three and four beads. We examine as characteristic examples chains with one steel and two aluminum beads, as well as ones with one steel and three aluminum beads, although we briefly touch upon other configurations as well, illustrating their similar characteristics. We analyze the higher order gaps that emerge in such settings and explore the intrinsic localized modes that bifurcate from the edge of the upper bands. A generic surprising feature of such states is that they appear to be more robust than their counterparts bifurcating from the edges of the lower bands. Direct numerical simulations, using driving of the system at suitable frequencies through an actuator or taking advantage of the modulational instabilities of extended band edge states in the system, illustrate the spontaneous formation of localized modes within the corresponding nearest gaps. In these numerical experiments, we also account for the presence of dissipation and analyze its potential role.

Intrinsic localized modes in coupled DNLS equations from the anti-continuum limit

In the present work, we generalize earlier considerations for intrinsic localized modes consisting of a few excited sites, as developed in the one-component discrete nonlinear Schrödinger equation model, to the case of two-component systems. We consider all the different combinations of “up” (zero phase) and “down” (π phase) site excitations and are able to compute not only the corresponding existence curves, but also the eigenvalue dependence of the small eigenvalues potentially responsible for instabilities, as a function of the nonlinear parameters of the model representing the self/cross phase modulation in optics and the scattering length ratios in the case of matter waves in optical lattices. We corroborate these analytical predictions by means of direct numerical computations. We infer that all the modes which bear two adjacent nodes with the same phase are unstable in the two component case and the only solutions that may be linear stable are ones where each set of adjacent nodes, in each component is out of phase.

Intrinsic localized modes in two-dimensional vibrations of crystalline pillars and their application for sensing

We present a complete analysis on the possibility of exciting and observing the intrinsic localized modes (ILMs) in a crystalline linear array of nano pillars. We discuss the nano-fabrication techniques for these arrays and visualization procedures to observe the real-time dynamics. As a consequence, we extend previous models to the study of two dimensional vibrations to be consistent with these restrictions. For these pillars, the elastic properties and hence the dynamics depend on the pillar's shape and the orientation of the crystal axes. We show that ILMs do form in the system, but their stability, defect pinning, and reaction to friction strongly depend on the crystals properties, with the optimal dynamics only achieved in a rather small region of the parameter space. We also demonstrate fabrication techniques for these pillars and discuss the applications of these pillar arrays to sensing.

Modification of reaction rates under irradiation of crystalline solids: Contribution from intrinsic localized modes

Recent experimental and molecular dynamics results give evidence for the existence of the discrete solitons (DS’s), a.k.a. intrinsic localized modes (ILM’s), discrete breathers (DB’s) and quodons, which are stable, highly localized lattice excitations that can transfer energy along close-packed crystal directions. The DS interaction with crystal defects results in the amplification of the reaction rates, such as atom ejection and diffusion. In this paper, recent results on the DS detecting in three-dimensional crystal structures by means of molecular dynamics are discussed, and a new method of the rate theory modification in solids under irradiation is presented.

Ferroelectric-thermoelectricity and Mott transition of ferroelectric oxides with high electronic conductivity

This paper reviews ferroelectric oxides in the unusual condition where the concentration of electronic carriers is close to a metal–insulator transition; in certain structures and compositions these materials have properties of interest for oxide based thermoelectric applications. In relaxor ferroelectrics, nanopolar regions associated with intrinsic localized phonon modes provide glass-like phonon characteristics due to the large levels of phonon scattering. The (Sr1−xBax)Nb2O6−δ relaxor ferroelectric single crystals have a high thermoelectric power factor, S2σ ∼ 40 μW/cm K2 at 277 °C along the c-axis, which is competitive with the best thermoelectrics. In the heavily reduced, nonstoichiometric n-type perovskite BaTiO3−δ and tungsten bronze (Sr1−xBax)Nb2O6−δ, it is shown that metallic-like conductivity occurs in the paraelectric phase and the onset of ferroelectricity stabilizes semiconducting character. Both the phase transition temperature dependence on the carrier concentration and evidence for polarization coupling to the conductivity mechanism will be discussed.

Generation of Localized Modes in an Electrical Lattice Using Subharmonic Driving

We show experimentally and numerically that an intrinsic localized mode (ILM) can be stably produced (and experimentally observed) via subharmonic, spatially homogeneous driving in the context of a nonlinear electrical lattice. The precise nonlinear spatial response of the system has been seen to depend on the relative location in frequency between the driver frequency, ω(d), and the bottom of the linear dispersion curve, ω(0). If ω(d)/2 lies just below ω(0), then a single ILM can be generated in a 32-node lattice, whereas, when ω(d)/2 lies within the dispersion band, a spatially extended waveform resembling a train of ILMs results. To our knowledge, and despite its apparently broad relevance, such an experimental observation of subharmonically driven ILMs has not been previously reported.

Mobile Intrinsic Localized Modes of a Spatially Periodic and Articulated Structure

The intrinsic localized mode (ILM) in a spatially periodic and articulated structure is examined in detail numerically. The structure is composed of identical, uniform and rigid members connected with neighboring ones at junctions through couplers giving nonlinear restoring moments. The system, with both free ends, constitutes a constrained Hamiltonian system subject to holonomic constraints by continuity of displacements at junctions. The formulation of flexural motions of the system has been already given in the previous paper [Y. Watanabe, K. Hamada, and N. Sugimoto: Wave Motion 45 (2007) 100], where the existence and properties of the stationary ILMs were examined in detail. In this paper, it is revealed by calculations under asymmetrical initial conditions with respect to the center of the structure, that there are two types of mobile ILMs: one is a trapped type at either end of the structure and the other is a propagating type at a constant speed, but subject to reflections at both ends. It is the former that shows the general behavior of the ILMs in the structure and the stationary type of ILM found in the previous paper should be regarded as a special case.

Experimental manipulation of intrinsic localized modes in macro-mechanical system

A macro-mechanical cantilever array is proposed for experimental investigation of intrinsic localized modes (ILMs). The array is designed to have tunable on-site potentials that can be adjusted individually. Thus, it is easy to realize an array, in which an ILM can be excited. In addition, impurities can be induced in and removed from the array. Several ILMs were successfully generated by an external sinusoidal excitation, and the generated ILMs were manipulated by adding an impurity to the cantilever array. The manipulation mechanism is discussed numerically on the basis of the structure of phase space. Coexisting ILMs, unstable manifolds, and the domains of attraction of a stable ILM are shown for an ILM manipulated by adding an impurity.

Numerical Study on Unstable Perturbation of Intrinsic Localized Modes in Graphene

A nonlinear vibration mode, referred to as the intrinsic localized mode (ILM), in graphene is investigated based on precise numerical solutions obtained by the iteration method coupled with molecular dynamics simulations. We obtain ILMs for which the frequency is greater than the maximum frequency of the phonon bands of graphene. The amplitude and structure of ILMs indicate that these ILMs are simply vibration modes due to the nonlinearity of the system. Moreover stability analysis of ILMs in graphene is performed numerically by solving the eigenvalue problem of the monodromy matrix based on Floquet theory for periodic solutions. In all cases, the ILM was found to have unstable perturbation modes. The growth rate of the unstable perturbation modes exhibits complex change behavior as the period of ILMs changes. The structure and growth rate of the unstable perturbation modes can be classified into two types. The most unstable perturbation mode is also localized and provides cooperative motions of neighbor atoms of the ILM.

A Study on Intrinsic Localized Modes in a Macro-mechanical Cantilever Array with Tunable on-site Nonlinearity

A macro-mechanical cantilever array with tunable on-site nonlinearity is proposed for experimental study on dynamics of intrinsic localized mode (ILM). In this paper, the cantilever array is first introduced and the equation of motion is derived. An experimentally excited ILM is shown and compared with the corresponding ILM obtained numerically. In addition, an unstable ILM is also shown with its waveform and Floquet multipliers.

Intrinsic localized mode as in-plane vibration in two-dimensional Fermi-Pasta-Ulam lattices

Intrinsic localized modes (ILMs) in two dimensional Fermi-Pasta-Ulam lattices are investigated. We consider in-plane vibrations of particles which have two degrees of freedom. We find two types of ILMs, quasi-one dimensional ILM and two dimensional ILM. Effect of interaction of second nearest neighbor lattices on stricture is also discussed.

Analysis of ILM Logic Operations via van der Pol Phase Planes

Logic operations that have previously been numerically demonstrated using intrinsic localized modes (ILMs) in a driven nonlinear 1-D lattice are analyzed using van der Pol phase planes. The time dependent application of a vibrational impurity mode either can produce or destroy an ILM. The appearance or absence of the resulting ILM can be understood via trajectories in the phase plane controlled by the evolving attractors associated with the time dependent impurity mode. Switching between the two possible branches depends on the phase of the amplitude modulation when the impurity mode is removed.

Discrete breathers in a nutshell

I give a nutshell introduction to the exciting field of discrete breathers / intrinsic localized modes. I focus on how to obtain these states, how they are localized in space, and how they may interact with extended plane wave states. This work is dedicated to Shozo Takeno, one of the early pioneers in the field.

Shozo Takeno and intrinsic localized modes

Research into defect lattice dynamics played an important roll in the development of our work on the local mode properties of anharmonic lattices. Using a historical perspective I show that the different theoretical and experimental studies of the impurity-induced absorption associated with the low frequency resonances in alkali halide crystals provided the kernel for our breakout into a new area.