Group Velocity Of Mode Research Articles

Tunable topological edge states and rainbow trapping in two dimensional magnetoelastic phononic crystal plates based on an external magnetostatic field

The elastic analogs of topological insulators (TIs) have attracted substantial research interest owing to their potential prospects in wave manipulation and low-loss transmission. However, most work in solid phononic crystal (PC) systems suffering from fixed-structure restrictions lack the active tunability of topological edge states, hindering their practical applications in dynamic situations. Here, we present a new design of tunable elastic TIs made up of smart magnetostrictive materials and perforated silicon plates. The topological phase transition is induced by altering the spatial intensity distribution of external magnetostatic field. Placing two topologically distinct magnetoelastic PC plates adjacent to each other, the pseudospin-Hall edge modes for plate-mode waves are obtained at the interface between them. Moreover, the reconfigurable propagation route and topological robustness of edge states are demonstrated by numerical simulations. Finally, the frequency and group velocity of edge modes can be continuously adjusted by an interfacial magnetic field. Utilizing such a contactless tunability, a reconfigurable topological rainbow is attained by reconstructing the gradient-descent interfacial magnetic field along the topological interface. The proposed system with magnetically tunable edge states can become a stepping-stone platform towards the designs of elastic wave devices with more applicability for dynamic conditions, such as waveguides, energy harvesters and buffers.

Wave mode computing method using the step-split Padé parabolic equation

Models based on a parabolic equation (PE) can accurately predict sound propagation problems in range-dependent ocean waveguides. Consequently, this method has developed rapidly in recent years. Compared with normal mode theory, PE focuses on numerical calculation, which is difficult to use in the mode domain analysis of sound propagation, such as the calculation of mode phase velocity and group velocity. To broaden the capability of PE models in analyzing the underwater sound field, a wave mode calculation method based on PE is proposed in this study. Step-split Padé PE recursive matrix equations are combined to obtain a propagation matrix. Then, the eigenvalue decomposition technique is applied to the matrix to extract sound mode eigenvalues and eigenfunctions. Numerical experiments on some typical waveguides are performed to test the accuracy and flexibility of the new method. Discussions on different orders of Padé approximant demonstrate angle limitations in PE and the missing root problem is also discussed to prove the advantage of the new method. The PE mode method can be expanded in the future to solve smooth wave modes in ocean waveguides, including fluctuating boundaries and sound speed profiles.

Experimental Method for Simultaneous Determination of the Lamb Wave A0 Modes Group and Phase Velocities.

Determining Lamb wave dispersion curves when measuring phase and group velocity values at a fixed frequency is now a common and relevant task. In most cases, in order to solve such a problem, it is necessary to know the exact properties of the material, particularly its thickness. In experimental methods, Lamb wave parameters are evaluated directly from the test materials. This paper proposes a new and simple experimental algorithm for A0 mode group and phase velocity determination based on signal filtering and zero-crossing estimating. The main idea is to capture the zero-crossing instances of the signals closest to the signal envelope peaks and use these time instances to determine the phase and group velocities. The reliability of the proposed method was evaluated using simulated and experimental signals propagating in an aluminum plate. Theoretical modeling has shown that the proposed method enables the calculation of the A0 mode group and phase velocities with a mean relative error of less than 0.7%. An accuracy of 0.8% was observed during the experimental measurements.

The holographic signal processing for the estimation of sound mode parameters in shallow water

The holographic method for estimation of the broadband sound field modes parameters by using a single receiver in shallow water is presented in the paper. The holographic method of signal processing is based on the two-dimensional Fourier transform (2D-FT) of the source moving in the shallow water waveguide. The sound field creates in waveguide a stable interference pattern (interferogram) in the frequency-time domain. The result of the 2D-FT of the interferogram is called the Fourier-hologram (hologram). It is shown in the paper that different sound field modes create different focal spots in the hologram domain. The filtering focal spots and applying the inverse 2D-FT to them allows restoring the field of the selected mode. In relation to the time-warping operator, the proposed method of signal processing provides a smaller error in the mode group velocity estimation. The results of the numerical simulation as well as the sound mode parameters estimation are presented and discussed in the paper. [Work supported by the RFBR (19-29-06075) and МК-6144.2021.4.]

Automatically Extracting Surface-Wave Group and Phase Velocity Dispersion Curves from Dispersion Spectrograms Using a Convolutional Neural Network

Abstract To image high-resolution crustal and upper-mantle structures, ambient noise tomography (ANT) has been widely used on local and regional dense seismic arrays. One of the key steps in ANT is to extract surface-wave group and phase velocity dispersion curves from cross-correlation functions of continuous ambient noise recordings. One traditional way is to manually pick the dispersion curves from dispersion spectrograms in the period-velocity domains, which is very labor intensive and time consuming. Another way is to automatically pick the dispersion curves using some predefined criteria, which are not reliable in many cases especially for phase velocity data. In this study, we propose a novel method named DisperPicker to automatically extract fundamental mode group and phase velocity dispersion curves using a convolutional neural network (CNN). The inputs to CNN include paired group and phase velocity dispersion spectrograms in the period-velocity domains, which are calculated from empirical surface-wave Green’s functions. In this way, group velocity dispersion curves can implicitly guide the extraction of phase velocity dispersion curves, which have large ambiguities to pick on the dispersion spectrograms. The labels or outputs of the network are the probability images converted from dispersion curves. The U-net architecture is adopted because it is powerful for image processing. We have assembled short-period surface-wave data from three different dense seismic arrays to train the network. The trained network is further tested and validated by two datasets close to Chao Lake, China. The tests show that DisperPicker has the generalization ability to efficiently and accurately extract dispersion curves of large datasets without new training.

Simultaneous modal phase and group velocity matching in microstructured optical fibers for second harmonic generation with ultrashort pulses.

Optical fibers provide a favorable medium for nonlinear optical processes owing to the small mode field size and concurrently high optical intensity combined with the extended interaction lengths. Second harmonic generation (SHG) is one of those processes that has been demonstrated in silica glass optical fibers. Since silica is centrosymmetric, generating SHG in an optical fiber requires poling of the glass. In addition and when one wants to use ultrashort pulses for SHG, achieving both phase and group velocity matching is crucial. Although fibers that feature either modal phase velocity or group velocity matching for SHG have been reported, the possibility of simultaneous modal phase and group velocity matching was never reported before. In this paper we address this challenge, and for the first time to our knowledge, we show that it is feasible to do so with silica microstructured optical fibers featuring at least one ring of air holes in the cladding and a heavily Germanium doped core (above 25 mol.%) by exploiting the LP01(ω) and LP02(2ω) modes at 1.06 µm pump and 0.53 µm second harmonic wavelengths. This finding can greatly impact applications requiring waveguide based SHG generation with ultrashort pulses, including microscopy, material characterization and nonlinear imaging.

Notable effect of magnetic order on the phonon transport in semi-hydrogenated graphene

Semi-hydrogenated graphene (SHG) is a ferromagnetic semiconductor with a large Curie temperature. Using this simple structure as a platform, we investigate how the coupling between magnetic order and lattice vibration affects the thermal transport by using first-principles calculations and the phonon Boltzmann transport equation. The results show that both paramagnetic and ferromagnetic phases are stable in SHG. The frequency features of the Raman-active phonon modes of the two phases clearly differ, which could serve as a fingerprint by which to identify the different magnetic orders. In addition, the coupling effect plays a critical role in the lattice thermal conductivity. At room temperature, SHG in its paramagnetic phase has a lattice thermal conductivity of about 24.5 W/mK, whereas, in its ferromagnetic phase, it is about 55.7 W/mK, almost twice as large as the paramagnetic case. An analysis of the phonon modes reveals that the enhanced thermal conductivity of ferromagnetic SHG is mainly due to the greater group velocity of the flexural acoustic mode and the attenuation of the anharmonicity of the transverse and longitudinal acoustic modes. These results reveal how magnetic order affects phonon transport in SHG and open the way for potential applications of magnetic monolayer materials as thermal switching devices.

Semi‐Supervised Surface Wave Tomography With Wasserstein Cycle‐Consistent GAN: Method and Application to Southern California Plate Boundary Region

AbstractMachine learning algorithm has been applied to shear wave velocity (Vs) inversion in surface wave tomography, where a set of starting 1‐D Vs profiles and their corresponding synthetic dispersion curves are used in network training. Previous studies showed that the performance of such trained network is dependent on the diversity of the training data set, which limits its application to previously poorly understood regions. Here, we present an improved semi‐supervised algorithm‐based network that takes both model‐generated and observed surface wave dispersion data in the training process. The algorithm is termed Wasserstein cycle‐consistent generative adversarial networks (Wasserstein Cycle‐GAN [Wcycle‐GAN]). Different from conventional supervised approaches, the GAN architecture enables the inclusion of unlabeled data (the observed surface wave dispersion) in the training process that can complement the model‐generated data set. The cycle‐consistency and Wasserstein metric significantly improve the training stability of the proposed algorithm. We benchmark the Wcycle‐GAN method using 4,076 pairs of fundamental mode Rayleigh wave phase and group velocity dispersion curves derived in periods from 3 to 16 s in Southern California. The final 3‐D Vs model given by the best trained network shows large‐scale features consistent with the surface geology. The resulting Vs model has reasonable data misfits and provides sharper images of structures near faults in the top 15 km compared with those from conventional machine learning methods.

Study on bandgap and directional wave propagation of a two-dimensional lattice with a nested core

This paper proposes a two-dimensional lattice structure with a nested core. The bandgap distribution and the anisotropy of the phase velocity and group velocity were studied based on Bloch’s theorem and the finite element method. The effects of the eccentric ratio (e) and the rotation angle () of the dual-phase structure on the bandgap distribution were investigated, and the anisotropy was studied via phase velocity and group velocity. The structure of e = 0.3 displayed the maximum total bandgap width. As increased, the total bandgap widths of structures of different e all obviously increased and the low-frequency bandgap properties were improved. The phase velocity and group velocity of e = 0 displayed strong anisotropy, and the anisotropy was adjusted by tuning . Furthermore, the group velocity of the eighth mode displayed high-directional wave propagation. For practical applications, a single-phase structure was proposed and analyzed. Through additive manufacturing technology, the single-phase structure was prepared and tested by a low amplitude test setup. The experimental results displayed good agreement with the numerical results, which demonstrated high directional propagation. This finding may pave the way for practical applications of the proposed lattice metamaterial in terms of wave filtering.

Low-Frequency Bandgaps of the Lightweight Single-Phase Acoustic Metamaterials with Locally Resonant Archimedean Spirals.

In order to achieve the dual needs of single-phase vibration reduction and lightweight, a square honeycomb acoustic metamaterials with local resonant Archimedean spirals (SHAMLRAS) is proposed. The independent geometry parameters of SHAMLRAS structures are acquired by changing the spiral control equation. The mechanism of low-frequency bandgap generation and the directional attenuation mechanism of in-plane elastic waves are both explored through mode shapes, dispersion surfaces, and group velocities. Meanwhile, the effect of the spiral arrangement and the adjustment of the equation parameters on the width and position of the low-frequency bandgap are discussed separately. In addition, a rational period design of the SHAMLRAS plate structure is used to analyze the filtering performance with transmission loss experiments and numerical simulations. The results show that the design of acoustic metamaterials with multiple Archimedean spirals has good local resonance properties, and forms multiple low-frequency bandgaps below 500 Hz by reasonable parameter control. The spectrograms calculated from the excitation and response data of acceleration sensors are found to be in good agreement with the band structure. The work provides effective design ideas and a low-cost solution for low-frequency noise and vibration control in the aeronautic and astronautic industries.

Anisotropic thermal and electrical transport properties induced high thermoelectric performance in an Ir2Cl2O2 monolayer.

In recent years, the energy crisis and global warming have been urgent problems that need to be solved. As is known, thermoelectric (TE) materials can transfer heat energy to electrical energy without air pollution. High-throughput calculations as a novel approach are adopted by screening promising TE materials. In this paper, we use first-principles calculations combined with the semiclassical Boltzmann transport theory to estimate the TE performance of monolayer Ir2Cl2O2 according to the prediction that Ir2Cl2O2 has potential as a good TE material via high-throughput calculations. The low thermal conductivities of 1.73 and 4.68 W mK-1 of Ir2Cl2O2 along the x- and y-axes are calculated, respectively, which exhibits the strong anisotropy caused by the difference in group velocities of low-frequency phonon modes. Then, the electronic transport properties are explored, and the figure of merit ZT is eventually obtained. The maximum ZT value reaches 2.85 (0.40) along the x-axis (y-axis) at 700 K, revealing that the TE properties of the Ir2Cl2O2 monolayer are highly anisotropic. This work reveals that the anisotropic layer Ir2Cl2O2 exhibits high TE performance, which confirms that it is feasible to screen excellent TE materials via high-throughput calculations.

Modulation instability of two TE modes in a thin left-handed film on a nonlinear right-handed substrate

The intramode wave beams in a thin left-handed film on a Kerr substrate are considered at a frequency near zero mode group velocity. Four coupled (1 + 1)-dimensional nonlinear Schrödinger equations, describing the interaction of forward and backward propagating beams with positive and negative group velocities, are derived. It is shown that self- and cross-phase modulation for four simultaneously propagating modes is possible only at strictly matched perturbations of their propagation constants, which is due to the contribution of spatial parametric mixing. The modulation instability of only two waveguide modes is analysed for different versions of their propagation. The specific features of modulation instability, related to the propagation of modes with negative group velocities, are investigated.

Fin whale localization and environmental inversion using modal arrivals of the 20-Hz pulse

Fin whale doublet calls, described as two 20-Hz pulses recorded at different interpulse intervals, have been attributed to the whale's calling behavior, however they could also result from acoustic mode propagation effects. Modes travel with their own frequency-dependent group velocities. The dispersion of these modes results in the sound being recorded as multiple arrivals on a receiver. Multiple modal arrivals of 20-Hz fin whale calls were recorded, with mode one arriving after mode two. The time delay between modal arrivals varied throughout the recording and is range dependent. The range dependency of this time delay was used to estimate the range of the whale from individual hydrophones by determining the modal group velocities that resulted in the observed delays. A pair of hydrophones was used to localize the whale for the duration of time when two modes were detected. The KRAKEN normal mode model was utilized in an inversion scheme to determine the compressional wave speed and depth-to-bedrock in the study area that supported the estimated modal group velocities. The inversion resulted in a depth-to-bedrock of 200 m and compressional wave speed of 1735 m/s, which were supported by measurements reported in literature for nearby regions. [Work supported by BOEM.]

Fast Electromagnetic Waves on Metamaterial’s Boundary: Modeling of Gain

The paper presents the results of the study of properties of fast surface electromagnetic waves that propagate along the flat interface between the active metamaterial and air (or vacuum). The case of homogeneous and isotropic metamaterial is considered. The dispersion properties, the wave spatial attenuation, the phase and group velocities, as well as the spatial distribution of the electromagnetic field of the eigen TE and TM modes of such a waveguide structure are studied in the frequency range where the metamaterial has a simultaneously negative permittivity and permeability. It is shown that fast surface electromagnetic waves can exist in this waveguide structure and their properties are studied. It is shown that the phase speed of TM mode is several times higher than the speed of light in vacuum, while the phase speed of TE mode is slightly higher than the speed of light in vacuum. The TM mode is a direct wave in which the phase and group velocities have the same direction. It is obtained that the group velocity of the TM mode varies from zero to the about half of speed of light in vacuum, and reaches a minimum at a certain value of wave frequency, which depends on the characteristics of the metamaterial. It is shown that the penetration depth of the TM mode into the metamaterial is much smaller than into the vacuum. The TE mode is a backward wave with opposite directed phase and group velocities. The absolute value of the group velocity of the TE mode is about six times less than the speed of light in vacuum. In contrast to the TM mode the penetration depth of the TE mode into the metamaterial is much greater than in vacuum. The obtained properties of the fast surface electromagnetic waves can be used for modeling and design of modern generation and amplification devices containing metamaterials.

Nonlinear generation of a zero group velocity mode in an elastic plate by non-collinear mixing

Zero Group Velocity (ZGV) modes are peculiar guided waves that can exist in elastic plates or cylinders, and have proved to be very sensitive tools in characterizing materials or thickness variations with sub-percent accuracy at space resolutions of about the plate thickness. In this article we show theoretically and experimentally how such a mode can be generated as the sum-frequency interaction of two high amplitude primary waves, and then serve as a local probe of material non-linearity. The solutions to the phase matching condition, i.e. condition for a constructive non-linear effect, are obtained numerically in the mark of classical, quadratic non-linearity. The coupling coefficients that measure the transfer rate of energy as a function of time from primary to secondary modes are derived. Experiments are conducted on an aluminum plate using piezo-electric transducers and a laser interferometer, and explore the interaction for incident symmetric and anti-symmetric fundamental Lamb modes. In an experiment operated without voltage amplifier we demonstrate that the resonant nature of these ZGV modes can be leveraged to accumulate energy from long excitations and produce detectable effects at extraordinarily low input power even in such weakly non-linear material.

Theoretical Issues with Rayleigh Surface Waves and Geoelectrical Method Used for the Inversion of Near Surface Geophysical Structure

We numerically simulate the field measurements of Rayleigh surface waves and electrical resistivity in which the target depth is set to be less than 50-m. The Rayleigh surface waves are simulated in terms of fundamental mode group and phase velocities. The seismic field data is assumed to be collected through a conventional shot-gather. The group velocities are found from the application of the multiple filter technique in a single-station fashion while for the phase velocities the slant stacking, or linear radon transform are applied in fashion of multichannel analysis of surface waves (MASW). The average seismic structure from the source to the receiver (or geophone) is represented by the group velocity curve while the average seismic structure underneath the geophone array is represented by the phase velocity curve. The single-station group velocity curves are transformed into local group velocity curves by setting a linear system through grid points. The shear-wave velocity cross section underneath the examined area is constructed by inverting these local group velocity curves. The electrical resistivity structure of the underground is similarly studied. The field compilation of the resistivity data is assumed to be completed by the application of the multiple electrode Pole-Pole array. The actual resistivity assemble underneath the analyzed area is inverted by considering the apparent (measured) resistivity values. Unique forms such as ore body, cavity, sinkhole, melt, salt, and fluid within the Earth may be examined by joint interpretation of electrical resistivities and seismic velocities. These formations may be better outlined by following their distinct signs such as high/low resistivities and high/low seismic velocities. Doi: 10.28991/HEF-2021-02-03-01 Full Text: PDF

Influence of seabed on very low frequency sound recorded during passage of merchant ships on the New England shelf.

An examination of the received spectrogram levels of about twenty merchant ship recordings on two vertical line arrays deployed on the New England continental shelf during the Seabed Characterization Experiment 2017 has identified an acoustic feature that can be attributed to the group velocities of modes 1 and 2 being equal at a frequency f=F. The observation of such a feature is a result of βnm(2πF)=∞, where βnm is the waveguide invariant for modes n and m. For the New England Mudpatch, the average value of F is about 24.5 Hz. An effective seabed model is inferred from a feature inversion method that has a deep sediment layer which lies between 190 m and 290 m beneath the seafloor with sound speeds on the order of 1810 m/s. This effective sediment model appears to be consistent with a previous seismic survey on the New England shelf that identified a deep low speed layer about 250 m beneath the water sediment interface.

Variations in crustal and lithospheric structure across the Eastern Indian Shield from passive seismic source imaging: Implications to changes in the tectonic regimes and crustal accretion through the Precambrian

Changes in the dominant tectonic regimes and the modes of formation and maturation of the continental crust during the Precambrian are a subject of active debate. Here, we discuss these issues in terms of new information on the crustal and lithospheric architecture of the different terranes in the Eastern part of the Indian Shield (EIS). We present well-constrained estimates of the crustal and lithospheric thickness characterizing different terranes of the EIS through the joint inversion of P-receiver functions (PRF) and fundamental mode group velocity dispersion data of Rayleigh waves (10–100 s). The lithospheric thicknesses are also computed independently using the S-receiver function (SRF) modeling. The study involved 2167 PRFs and 100 SRFs from 15 broadband stations. Our modeling detects a marked crustal (~4–8 km) and lithospheric (~15–20 km) thinning beneath the Singhbhum-Odisha-Craton (SOC), spatially correlating with the central part of the craton comprising the gneissic terrain contrasted by a crustal thickening (~2–6 km) beneath the horseshoe-shaped Iron Ore Group. We propose that such a crustal configuration beneath the Paleoarchean craton may suggest the dominance of vertical tectonic processes such as thickening of an oceanic mafic plateau and recurrent melting producing the TTGs and the Singbhum Granite suite. Infra-crustal reworking involving Rayleigh-Taylor instabilities and gravitational processes could explain the crustal architecture of the SOC much similar to a few other Paleoarchean cratons such as Pilbara (Australia), Barberton and Kappvaal (South Africa). Our modeling has also revealed a relatively smaller degree of crustal (2–4 km) and lithospheric thinning (4–10 km) beneath the Eastern Ghat Mobile Belt, south of the SOC. We observe a relatively thicker crust (~42 km) characterized by a flat Moho over a large area (~40,000 sq. km) encompassing the Chota Nagpur Granite Gneiss Terrane (CGGT). Such thickening is consistent with the convergence and collision tectonics involving the SOC and CGGT. However, we note a 15–20 km lithospheric thinning associated with the CGGT. Such thinning may mainly relate to Phanerozoic rifting along the Damodar graben and Rajmahal magmatism. Broadly, our model of the crustal and lithospheric architecture of the EIS reflects the imprints of northward subduction of SOC beneath the CGGT.

Correlation of deep seabed structure with waveguide invariant β in ±∞ regime

An examination of the received spectrogram levels of merchant ship recordings has identified an important acoustic feature at the very-low frequencies (VLF). The data were recorded on vertical line arrays deployed in the New England Mudpatch during the Seabed Characterization Experiment 2017 in about 75 m of water. The VLF feature occurs when the group velocities of modes 1 and 2 are equal at a frequency f = F. The average value of F from about twenty ship signatures observed in the Mudpatch is about 24.5 Hz. Generally, the observation of this VLF feature is a result of βmn( F) = infinity where βmn is the waveguide invariant for modes n and m. The sign of the waveguide invariant is determined by the sign of the difference between the phase speeds at F. Also, we predict what F would be in two areas south of the Mudpatch, including a second smaller Mudpatch in about 125 m of water and an area near the slope in about 250 m of water where the sediment is reported to be sand over multiple layers of softer sediments. Finally, F is predicted on the Atlantis II seamount with a limestone seabed in about 1650 m of water.

A quick method to construct 3-D velocity contour map for assessing anomalies in concrete

In this study, a quick way to assess the location of anomalies in concrete is presented. The test of one test line is done with one tap of the steel ball and the receiver far from the signal source. The spectrogram of the recorded waveform is obtained by Short-Time Fourier transform (STFT) and reassigned method. Then the dispersion curve of A0 modal group velocity is extracted from the spectrogram. This research proposes a fast and systematic procedure, which starts from setting the layout of the test line to constructing the 3-D map of the A0 modal group velocity. Observing the dispersion curve with test line passing only single defect, the loss of wave speed usually begins at wavelengths approximately 2 times the defect depth. For delaminated crack, the larger and shallower the defect, the more reduction of the wave velocity is found under the described wavelength. Since the grid lines may pass through multiple defects, the low-velocity area in the 3-D velocity image may indicate possible defects in its vicinity instead of precise depth and location. Because the current method reduces the consumption of manpower and time, resources can be placed on potential defect areas to conduct detailed investigations with conventional C-scan methods.