Low-Regularity Local Well-Posedness for the Elastic Wave System

We present a mechanism to explicitly couple the finite-difference discretizations of 2D acoustic and isotropic elastic-wave systems that are separated by straight interfaces. Such coupled simulations allow for the application of the elastic model to geological regions that are of special interest for seismic exploration studies (e.g., the areas surrounding salt bodies), with the computationally more tractable acoustic model still being applied in the background regions. Specifically, the acoustic wave system is expressed in terms of velocity and pressure while the elastic wave system is expressed in terms of velocity and stress. Both systems are posed in first-order forms and are discretized on staggered grids. Special variants of the standard finite-difference operators, namely, operators that possess the summation-by-parts property, are used for the approximation of spatial derivatives. Penalty terms, which are also referred to as the simultaneous approximation terms, are designed to weakly impose the elastic-acoustic interface conditions in the finite-difference discretizations and couple the elastic and acoustic wave simulations together. With the presented mechanism, we are able to perform the coupled elastic-acoustic wave simulations stably and accurately. Moreover, it is shown that the energy-conserving property in the continuous systems can be preserved in the discretized systems with carefully designed penalty terms.

Elastic topological interface states induced by incident angle

The propagation of elastic waves in an electrically conducting solid permeated by a uniform, static magnetic field is discussed. In the case of plane wave motions, two systems of waves arise: simple uncoupled systems and a trimodal coupled system of waves. In the uncoupled case, in which polarizations are unaltered, two dispersive, complex phase velocities exist. For a weak impressed magnetic field, one of these velocities is close to the elastic wave velocity of the polarized wave in the absence of the field. The other wave, called an eddy current wave, although strongly attenuated, cannot be neglected in the solution of boundary value problems. When the theory of magnetoelastic interactions is applied to seismic motions in the conducting core of the earth, it is found that compressional waves are virtually unattenuated in the core for the pertinent values of frequency, conductivity, and magnetic intensity. It is concluded that magnetoelastic interactions are not a significant mechanism in the earth's core.

The transient deformation of an elastic half‐space under a line‐concentrated impulsive vector shear load applied momentarily is disclosed in this paper. While in an earlier work, the author gave an analytical–numerical method for the solution to this transient boundary‐value problem, here, the resultant response of the half‐space is presented and interpreted. In particular, a probe is set up for the kinematics of the source signature and wave fronts, both explicitly revealed in the strained half‐space by the solution method. The source signature is the imprint of the spatiotemporal configuration of the excitation source in the resultant response. Fourteen wave fronts exist behind the precursor shear wave S: four concentric cylindrical, eight plane, and two relativistic cylindrical initiated at propagating centres that are located on the stationary boundaries of the solution domain. A snapshot of the stressed half‐space reveals that none of the 14 wave fronts fully extend laterally. Instead, each is enclosed within point bounds. These wave arresting points and the two propagating centres of the relativistic waves constitute the source signature. The obtained 14 wave fronts are further combined into 11 disparate wave fronts that are grouped into four categories: an axis of symmetry wave—so named here by reason of being a wave front that is contiguous to the axis of symmetry, three body waves, five surface waves and two inhibitor waves—so named here by reason that beyond them the material motion dies out. Of the three body waves, the first is an unloading shear wave, the second is a diffracted wave and the third is a reflected longitudinal two‐branch wave. Of the two inhibitor waves, the first is a two‐joint relativistic wave, while the second is a two‐branch wave. The wave system, however, is not the same for all the dependent variables; a wave front that appears in the behaviour of one dependent variable may not exist in the behaviour of another. It is evident from this work that Saint–Venant's principle for wave propagation problems cannot be formulated. Therefore, the above results are valid for the particular proposed model for the momentary line‐concentrated shear load. The formulation of the source signature, the wave system, and their role in the half‐space transient deformation are presented here. Copyright © 2003 John Wiley & Sons, Ltd.

The parametric coupling between traveling electromagnetic and elastic waves in a ferrimagnet supplied by magnetic pumping is theoretically investigated. The pumping threshold is calculated for steady-state wave propagation in the presence of loss for plane electromagnetic and longitudinal elastic waves in an infinite ferrite medium. This threshold is compared to the threshold for second-order spin-wave instabilities and it is found that these spin wave processes should not prevent the magnetoelastic process from occurring. It is shown that this traveling wave system may be useful for amplifying electromagnetic or elastic waves.

We consider the following Cauchy problem for weakly coupled systems of semilinear damped elastic waves with a power source nonlinearity in three dimensions: urn:x-wiley:mma:media:mma5370:mma5370-math-0001 where with b2 > a2 > 0 and θ ∈ [0,1]. Our interests are some qualitative properties of solutions to the corresponding linear model with vanishing right‐hand side and the influence of the value of θ on the exponents p1,p2,p3 in to get results for the global (in time) existence of small data solutions.

We consider the Cauchy problem in R n for the system of elastic waves with structural damping. We derive (almost) optimal decay rates in time for the L 2-norm and the total energy which improves previous results for this system. To derive the estimates for elastic waves, we employ an improvement in a method in the Fourier space, which was developed in our previous works. Our estimates came from those for a generalized energy of α-order in the Fourier space.

During the past decades, phononic crystals and elastic wave metamaterials as the artificial periodic structures have received considerable attention. Due to their distinguishing properties, these structures can be used for the wave energy manipulation, e.g., band gaps, elastic wave cloaking and topological state, etc. A well-known characteristic is the band gap which means that the elastic wave cannot propagate in some certain frequency regions. Based on this property, many engineering applications can be achieved, e.g., filtering and wave isolation, etc. The investigations mentioned above are mainly focused on the linear elastic problems which cannot present the nonlinear wave properties. However, the nonlinearity appearing in the materials and structures can bring new and interesting wave phenomena. One of the nonlinear characteristics is the generation of the higher order harmonics. It can be applied to the nonlinear nondestructive testing. Recently, increasing attention has been focused on the nonlinear wave motion, which can result in the nonlinear band gap and acoustic diode. The new concept named as the acoustic diode has been presented by the combination of the band gap and material nonlinearity, which permits the wave propagation in only one direction. It can be achieved when the fundamental wave sits in the stop band but the second harmonic belongs to the pass band. However, the acoustic wave has one direction displacement component and usually propagates in the air or liquid. Thus we wonder whether the nonreciprocal phenomenon of the elastic wave can be achieved in the solid materials. The problem will become more interesting and necessary because of the coupling displacements with the vector characteristic in solids. In our previous work, we have discussed the nonreciprocal transmission for the incident SH and in-plane elastic waves in a nonlinear elastic wave metamaterial. The interface in the consecutive layers is always assumed as perfect, which means that the displacement and stress components are continuous across the interface. But perfect interfaces may become imperfect in practice during the manufacture, which indicates that the interfacial property on the band gaps is obvious. Then the imperfect interface can offer a new opportunity to tune the nonreciprocal transmission of the elastic wave which depends on the band gap property. In this work, the nonreciprocal transmission for the SH wave in a layered nonlinear elastic wave metamaterial with the imperfect interfaces is investigated. The combination of the structural asymmetry and material nonlinearity breaks the inherent reciprocity of the classic wave system. The second harmonic can be generated by the interaction between the incident SH wave and material nonlinearity. Based on the Bloch’s law and stiffness matrix method, the band gaps and transmission coefficients of both the fundamental and second harmonic waves are obtained. The effects of the interfacial properties on the nonlinear phononic crystal and elastic wave metamaterial are discussed. We find that comparing with the perfect interface system, the central frequency of the nonreciprocal regions shifts towards the low frequency region by the effects of imperfect interfaces. This present work is expected to be helpful to design the practical devices with the tuning nonreciprocal transmission of the elastic wave.

Reconfigurable directional selective tunneling of p-type phonons in polarized elastic wave systems

One of the hallmark of topological insulators is having conductivity properties that are unaffected by the possible presence of defects. In this work, by going beyond backscattering immunity and topological invisibility across defects or disorder is obtained. Using a combination of chiral and mirror symmetry, the transmission coefficient is guaranteed to be unity. Importantly, but no phase shift is induced making the defect completely invisible. Many lattices possess the chiral‐mirror symmetry, and the principle is chosen to be demonstrated on an hexagonal lattice model with Kekulé distortion displaying topological edge waves, and analytically and numerically is shown that the transmission across symmetry preserving defects is unity. Then this lattice in an acoustic system is realized, and the invisibility is confirmed with numerical experiments. It is foreseen that the versatility of the model will trigger new experiments to observe topological invisibility in various wave systems, such as photonics, cold atoms or elastic waves.

Bound states in the continuum (BICs) are perfectly confined resonances within the radiation continuum. The novel characteristics of single BICs have been studied in great detail in various wave systems, including electromagnetic waves, acoustic waves, water waves, and elastic waves in solids. In practice, the performance of BICs is limited by the finite size of the structure, while the combination of multiple BICs can further improve the localization of resonances. In this study, we experimentally demonstrate the combination of Fabry-Perot and symmetry-protected BICs at near infrared wavelengths by employing a compound photonic crystal system composed of a photonic crystal slab and a distributed Bragg reflector, resulting in an enhanced high quality factor.

Chapter 5 - Transformation Optics

Bound states in the continuum (BICs) are waves that remain localized even though they coexist with a continuous spectrum of radiating waves that can carry energy away. Their very existence defies conventional wisdom. Although BICs were first proposed in quantum mechanics, they are a general wave phenomenon and have since been identified in electromagnetic waves, acoustic waves in air, water waves and elastic waves in solids. These states have been studied in a wide range of material systems, such as piezoelectric materials, dielectric photonic crystals, optical waveguides and fibres, quantum dots, graphene and topological insulators. In this Review, we describe recent developments in this field with an emphasis on the physical mechanisms that lead to BICs across seemingly very different materials and types of waves. We also discuss experimental realizations, existing applications and directions for future work. The fascinating wave phenomenon of ‘bound states in the continuum’ spans different material and wave systems, including electron, electromagnetic and mechanical waves. In this Review, we focus on the common physical mechanisms underlying these bound states, whilst also discussing recent experimental realizations, current applications and future opportunities for research.

Transient vibrational power flows in slender random structures: Theoretical modeling and numerical simulations

Whispering-gallery-mode (WGM) cavity is important for exploring physics of strong light-matter interaction. Yet it suffers from the notorious radiation loss universally due to the light tunneling effect through the curved boundary. In this work, we propose and demonstrate an optical black hole (OBH) cavity based on transformation optics. The radiation loss of all WGMs in the ideal OBH cavity is completely inhibited by an infinite wide potential barrier. Besides, the WGM field in the OBH cladding is revealed to follow 1/r^alpha decay rule based on conformal mapping, which is fundamentally different from the conventional Hankel-function distributions in a homogeneous cavity. Experimentally, a truncated OBH cavity is achieved based on the effective medium theory, and both the Q-factor enhancement and tightly confined WGM fields are measured in the microwave spectra which agree well with the theoretical results. The circular OBH cavity is further applied to the arbitrary-shaped cavities including single-core and multi-core structures with high-Q factor via the conformal mapping. The OBH cavity design strategy can be generalized to resonant modes of various wave systems, such as acoustic and elastic waves, and finds applications in energy harvesting and optoelectronics.