Lattice Waves Research Articles

The nonlinear longitudinal lattice waves in a one-dimensional dusty chain with the plasma absorption effect

The nonlinear longitudinal dust lattice wave of a one-dimensional dust chain under the influence of the plasma absorption effect was investigated. A modified KdV-Burgers’ equation with the plasma absorption effect is derived under the continuum limit by the reductive perturbation method. Based on solutions of the Burgers’ equation, the effects of dynamic damping, absorption coefficient, characteristic length and shielding parameter on the shock structure are investigated. It is found that shock wave polarity is determined by hydrodynamical damping. Furthermore, as the electron-to-ion temperature ratio increases, shock amplitude increases correspondingly, but its width remains basically unchanged. Therefore, the shock structure of nonlinear longitudinal dust lattice wave with plasma absorption potential is different from the one under the conventional Debye–Hückel potential.

Charge-gradient instability of compressional dust lattice waves in electrorheological plasmas

It is shown that the longitudinal dust lattice mode in the one-dimensional string of microparticles oriented along the electric field (it highlights the major aspect of the electrorheological plasmas) can be subjected to a specific charge-gradient instability, associated with inhomogeneous dust charge distribution along the string due to the ion flow. This instability leads to the spontaneous excitation of compressional waves at elevated gas pressures with implications for the electrorheological plasmas studied in the Plasmakristall-4 facility in the ground based conditions and in microgravity on board the International Space Station. The obtained results can also be relevant for the stability analysis of the laboratory multilayer plasma crystals observed in the sheath of gas discharges.

Nonlinear transition waves in free-standing bistable chains

We propose an analytical framework to study the propagation of transition waves in one-dimensional free-standing lattices comprising concentrated masses and bistable springs. Starting from the discrete model, we derive the partial differential equation that describes the non-linear dynamic response of the system and obtain its exact closed-form solution. Such solution enables us to uncover the effect of the system’s parameters on the characteristics of the supported transition waves as well as to characterize the rarefaction front that precedes the pulse. As such, this work provides new opportunities to elucidate how transition waves propagate in systems in which the phase transition results in macroscopic volumetric changes.

Optical vector lattice breathers of a two-component Rabi-coupled Gross–Pitaevskii system with variable coefficients

A two-component Rabi-coupled Gross–Pitaevskii system with variable coefficients is under investigation. The system can be used to describe the optical vector pulse propagations in two complex electric fields in Bose–Einstein condensates. A rotation transformation and a similarity transformation are successively implemented to transform the system into the celebrated Manakov system. Via utilizing the vector breather solutions obtained of the Manakov system, and choosing several typical kinds of similarity transformation functions, novel vector lattice breathers are excited and observed. These breathers possess lattice background waves, and exhibit abundant patterns.

Stability of high-energy solitary waves in Fermi-Pasta-Ulam-Tsingou chains

The dynamical stability of solitary lattice waves in non-integrable FPUT chains is a long-standing open problem and has been solved so far only in a certain asymptotic regime, namely by Friesecke and Pego for the KdV limit, in which the waves propagate with near sonic speed, have large wave length, and carry low energy. In this paper we derive a similar result in a complementary asymptotic regime related to fast and strongly localized waves with high energy. In particular, we show that the spectrum of the linearized FPUT operator contains asymptotically no unstable eigenvalues except for the neutral ones that stem from the shift symmetry and the spatial discreteness. This ensures that high-energy waves are linearly stable in some orbital sense, and the corresponding nonlinear stability is granted by the general, non-asymptotic part of the seminal Friesecke-Pego result and the extension by Mizumachi. Our analytical work splits into two principal parts. First we refine two-scale techniques that relate high-energy waves to a nonlinear asymptotic shape ODE and provide accurate approximation formulas. In this way we establish the existence, local uniqueness, smooth parameter dependence, and exponential localization of fast lattice waves for a wide class of interaction potentials with algebraic singularity. Afterwards we study the crucial eigenvalue problem in exponentially weighted spaces, so that there is no unstable essential spectrum. Our key argument is that all proper eigenfunctions can asymptotically be linked to the unique bounded and normalized solution of the linearized shape ODE, and this finally enables us to disprove the existence of unstable eigenfunctions in the symplectic complement of the neutral ones.

Controlled evolution of spin waves in unconventional defective honeycomb antidot lattices

Abstract Efficacious control of spin wave dynamics is demonstrated in two-dimensional magnonic crystals in the form of defective honeycomb antidot lattices. The spin wave dynamics of this system is investigated using broadband ferromagnetic resonance spectrometer. A stark modification in magnonic spectra is achieved with the modulation in the lattice spacing and with the bias magnetic field strength and its orientation. A rich band of spin wave modes are obtained for the lattice with smallest periodicity, which finally converges to two modes in case of the largest one. The spin wave modes in all lattices possess a strong anisotropic behaviour with a six- and two-fold rotational symmetries as a function of the bias field orientation originating from the strong modulation of internal field distribution at different regions of such unorthodox system. The experimentally observed spin wave modes have been qualitatively well reproduced by micromagnetic simulations and the simulated mode profiles unravel the presence of diverse genres of extended and localized standing modes in these unusual magnonic crystals. These observations are significant for tunability and anisotropic propagation of spin waves leading towards the development of efficient magnonic devices competent with the future microwave communication systems.

Metastability of solitary waves in diatomic FPUT lattices$^\dagger$

It is known that long waves in spatially periodic polymer Fermi-Pasta-Ulam-Tsingou lattices are well-approximated for long, but not infinite, times by suitably scaled solutions of Korteweg-de Vries equations. It is also known that dimer FPUT lattices possess nanopteron solutions, i.e., traveling wave solutions which are the superposition of a KdV-like solitary wave and a very small amplitude ripple. Such solutions have infinite mechanical energy. In this article we investigate numerically what happens over very long time scales (longer than the time of validity for the KdV approximation) to solutions of diatomic FPUT which are initially suitably scaled (finite energy) KdV solitary waves. That is we omit the ripple. What we find is that the solitary wave continuously leaves behind a very small amplitude “oscillatory wake.” This periodic tail saps energy from the solitary wave at a very slow (numerically sub-exponential) rate. We take this as evidence that the diatomic FPUT “solitary wave” is in fact quasi-stationary or metastable.

Dispersive Traveling Wave Solution for Non-Linear Waves Dynamical Models

In waves dynamics, Generalized Kortewegde Vries (gKdV) equation and Sawada-Kotera equation (Ske) have been used to study nonlinear acoustic waves, an inharmonic lattice and Alfven waves in a collisionless plasma, and a lot of more important physical phenomena. In this paper, the simple equation method (SEM) is used to obtain new traveling wave solutions of gKdv and Ske. The physical properties of the obtained solutions are graphically illustrated using suitable parameters. The computational simplicity of the proposed method shows the robustness and efficiency of SEM.

Tunable in-plane topologically protected edge waves in continuum Kagome lattices

In this paper, we report the evidence of topologically protected edge waves (TPEWs) in continuum Kagome lattice. According to the bulk edge correspondence principle, such edge states are inherently linked with the topological characteristics of the material band structure and can, therefore, be predicted evaluating the associated topological invariant. Due to the non-trivial band structures shown in the context of quantum valley Hall effect, TPEWs are supported at the interface between two lattices characterized by different valley Chern numbers. The break of lattice symmetry is obtained here, in contrast with other similar works in continuum elastic structures, biasing in the stiffness properties of the unit cell, instead of manipulating mass at sublattice points. This opens new promising possibilities related to waveguide tunability and wave propagation control, exploiting the established techniques for stiffness modulation in elastic structures. A sensitivity analysis of robustness of the supported energy transport is provided, showing the amount of de-localized disorder the waveguide is immune to, and how performances are affected by perturbations in the nominal parameters of the lattice.

Strictly supersonic solitary waves in lattices with second-neighbor interactions

We consider a monatomic nonlinear mass–spring chain with first and second-neighbor interactions and show that there is a parameter range where solitary waves in this system are strictly supersonic. In these regimes standard quasicontinuum theories, targeting long-wave limits of lattice models, are not adequate since even weak strictly supersonic solitary waves are of envelope type and crucially involve a microscopic scale in addition to the mesoscopic scale of the envelope. To capture this effect in a continuum setting it is necessary to employ unconventional, higher-order quasicontinuum approximations carrying more than one length scale.

Solitary waves in bistable lattices with stiffness grading: Augmenting propagation control

In this study we introduce small perturbations in the forms of graded intersite stiffnesses and graded on-site potentials to a lattice composed of bistable unit cells under elastic interactions. Based on a known soliton solution in the $\ensuremath{\phi}$-4 model, we use a perturbation approach to approximate the effects of the perturbations on the propagation speeds of transition waves. Numerical validations follow on the exact discrete equations of motion, from which we observe eventual stoppage of transition waves in the periodic lattice under physical damping, unidirectional propagation of the waves in the direction of softening properties, and boomerang-like reflection of the waves in the stiffening direction. Finally, we present three-dimensional-printed experimental lattices, confirming the theoretical and numerical results. The observed behaviors imply the extreme controllability of solitary waves through slight engineering manipulations in material-level structures. We further find that both kink (rarefaction) and antikink (compression) waves are allowed at any site in the lattice, extending the functionality of the lattice in engineering applications such as energy harvesting.

Influence of quadratic Zeeman effect on spin waves in dipolar lattices

A lattice of particles with dipolar magnetic moments is considered under the presence of quadratic Zeeman effect. Two types of this effect are taken into account, the effect due to an external nonresonant magnetic field and the effect caused by an alternating quasiresonance electromagnetic field. The presence of the alternating-field quadratic Zeeman effect makes it possible to efficiently vary the sample characteristics. The main attention is payed to the study of spin waves whose properties depend on the quadratic Zeeman effect. By varying the quadratic Zeeman-effect parameter it is possible to either suppress or stabilize spin waves.

Effect of plasma absorption on dust lattice waves in hexagonal dust crystals

In the present paper, the effect of plasma absorption on lattice waves in 2D hexagonal dust crystals is investigated. The dispersion relations with the effect of plasma absorption are derived. It is found that the temperature effect (electron-to-ion temperature ratio τ) enhances the frequency of the dust lattice waves, while the spatial effect (dimensionless Debye shielding parameter weakens the frequency of the dust lattice waves. In addition, the system stabilities under the conditions of plasma absorption are studied. It is found that the temperature effect narrows the range of instability, while the spatial effect extends this range. And the range of instability is calculated, i.e. the system will always in the stable state regardless of the value of when τ > 3.5. However, the system will be unstable when τ = 1 and .

An energy-based stability criterion for solitary travelling waves in Hamiltonian lattices.

In this work, we revisit a criterion, originally proposed in Friesecke & Pego (Friesecke & Pego 2004 Nonlinearity17, 207-227. (doi:10.1088/0951715/17/1/013)), for the stability of solitary travelling waves in Hamiltonian, infinite-dimensional lattice dynamical systems. We discuss the implications of this criterion from the point of view of stability theory, both at the level of the spectral analysis of the advance-delay differential equations in the co-travelling frame, as well as at that of the Floquet problem arising when considering the travelling wave as a periodic orbit modulo shift. We establish the correspondence of these perspectives for the pertinent eigenvalue and Floquet multiplier and provide explicit expressions for their dependence on the velocity of the travelling wave in the vicinity of the critical point. Numerical results are used to corroborate the relevant predictions in two different models, where the stability may change twice. Some extensions, generalizations and future directions of this investigation are also discussed.This article is part of the theme issue 'Stability of nonlinear waves and patterns and related topics'.

Transport properties of disordered two‐dimensional complex plasma crystal

In this study, we numerically investigate the transport properties of a two‐dimensional (2D) complex plasma crystal using diffusion of coplanar dust lattice waves. In the limit where the Hamiltonian interactions can be decoupled from the non‐Hamiltonian effects, we identify two distinct types of wave transport: Anderson‐type delocalization and long‐distance excitation. We use a recently developed spectral approach to evaluate the contribution of the Anderson problem and compare it to the results of the simulation. The benefit of our approach to transport problems is twofold. First, we employ a highly tuneable macroscopic hexagonal crystal, which exhibits many‐body interactions and allows for the investigation of transport properties at the kinetic level. Second, the analysis of the transport problem in 2D is provided using an innovative spectral approach, which avoids the use of scaling and boundary conditions. The comparison between the analytically predicted and numerically observed wave dynamics allows for the study of important characteristics of this open system. In our simulations, we observe long‐distance lattice excitation, which occurs around lattice defects even when the initial perturbation does not spread from the centre to the exterior of the crystal. In the decoupled Hamiltonian regime, this many‐body effect can be attributed to the dust lattice interaction with the plasma environment.

Phonon-interference resonance effects by nanoparticles embedded in a matrix

We report an unambiguous phonon resonance effect originating from germanium nanoparticles embedded in silicon matrix. Our approach features the combination of phonon wave-packet method with atomistic dynamics and finite element method rooted in continuum theory. We find that multimodal phonon resonance, caused by destructive interference of coherent lattice waves propagating through and around the nanoparticle, gives rise to sharp and significant transmittance dips, blocking the lower-end frequency range of phonon transport that is hardly diminished by other nanostructures. The resonance is sensitive to the phonon coherent length, where the finiteness of the wave packet width weakens the transmittance dip even when coherent length is longer than the particle diameter. Further strengthening of transmittance dips are possible by arraying multiple nanoparticles that gives rise to the collective vibrational mode. Finally, it is demonstrated that these resonance effects can significantly reduce thermal conductance in the lower-end frequency range.

Dust lattice waves in Debye binary dust chain

The dust lattice waves in a one-dimensional Debye binary dust chain consisting of two distinct dust particle species with different charges and masses are investigated. It is found that there are two branches for both longitudinal and transverse modes, namely the optical mode of high frequency and the acoustic mode of low frequency, which will be merged into one ordinary longitudinal (transverse) mode of single dust chain. The influence of the parameters, i.e., the dimensionless lattice parameter α, the mass ratio σ, and the charge ratio ε of the two particles, on the dispersion relation of longitudinal and transverse waves is discussed. Furthermore, the branching and the merging of longitudinal and transverse waves are discussed in detail.

A review of computational phononics: the bulk, interfaces, and surfaces

Broad-based interest in microscale heat transport in novel materials, engineered phononic materials, metamaterials, and their relevant systems has created significant demand for computational approaches to aid in investigation and design of materials that support phonons. This review describes the significant improvements that have been made and new needs that have emerged for capabilities associated with the computability of phonons. The technical scope encompasses issues, especially relevant to bulk, interface, and surface effects. Traditional approaches such as molecular dynamics, lattice dynamics, and Boltzmann transport equation continue to advance the field but are frequently extended to the limits of their physical or numerical validity. New materials beyond traditional group-IV, III–V, and II–VI semiconductors, phenomena that critically depend on scattering, such as in low-dimensional nanostructures, materials with interior surfaces and defects, and in high-temperature environments, continue to push these limits. The basis for the traditional calculation methods shares their origins with the earliest theories for thermal transport, acoustic waves in solids, spectroscopy and dynamical crystal lattices. These will remain in wide use in the future. But computing methods and the accompanying advances in microprocessor technologies have enabled growth of phonon computing models and methods in sophistication, accuracy, fidelity and complexity that will lead to fundamental impacts beyond the classic types of problems for which they were developed. With their increasingly integrated use for design and research, the myriad developments that presently exist must be understood for their suitability for certain applications and their ability to aid in the pursuit of new technologies.

Solitary waves in FPU lattices with alternating bond potentials

We consider an infinite chain of alternating stiffer and softer bonds with constant ratio of elastic moduli. Using multiple scale analysis in the limit of high mismatch between the moduli, we derive the asymptotic orthogonality condition for the ratio of the moduli at which the system supports genuine solitary waves. We show that under some generic conditions, there exists an infinite sequence of such ratios accumulating to zero. This result is illustrated by an exact calculation for a Toda lattice with alternating bonds and corroborated by numerical simulations.

Nonlocal magnon-polaron transport in yttrium iron garnet

The spin Seebeck effect (SSE) is observed in magnetic insulator|heavy metal bilayers as an inverse spin Hall effect voltage under a temperature gradient. The SSE can be detected nonlocally as well, viz. in terms of the voltage in a second metallic contact (detector) on the magnetic film, spatially separated from the first contact that is used to apply the temperature bias (injector). Magnon-polarons are hybridized lattice and spin waves in magnetic materials, generated by the magnetoelastic interaction. Kikkawa et al. [Phys. Rev. Lett. \textbf{117}, 207203 (2016)] interpreted a resonant enhancement of the local SSE in yttrium iron garnet (YIG) as a function of the magnetic field in terms of magnon-polaron formation. Here we report the observation of magnon-polarons in \emph{nonlocal} magnon spin injection/detection devices for various injector-detector spacings and sample temperatures. Unexpectedly, we find that the magnon-polaron resonances can suppress rather than enhance the nonlocal SSE. Using finite element modelling we explain our observations as a competition between the SSE and spin diffusion in YIG. These results give unprecedented insights into the magnon-phonon interaction in a key magnetic material.