Time-domain Wave Research Articles

Modeling Rayleigh wave in viscoelastic media with constant Q model using fractional time derivatives

The propagation of seismic waves within the near-surface weathering layers, characterized by their low-quality factors (Q), is often accompanied by strong attenuation and dispersion phenomena. Among these, the Rayleigh wave, with its sensitivity to dispersion, has proven to be a powerful tool for near-surface exploration. We propose a novel approach for simulating Rayleigh wave propagation in such low-Q media. Our method uses the time-domain fractional wave equation with memory effect, based on Kjartansson's constant-Q (CQ) model, for accurate characterization of the propagation process. To solve numerically the wave equation with the fractional derivatives, we employ a finite-difference method combined with the auxiliary differential equation-perfectly matched layer (ADE-PML) and the acoustic-elastic boundary approach (AEA). The algorithm's high computational accuracy is verified through comparison with the conventional integer-order wave equation based on the nearly constant-Q (NCQ) models in strong attenuation media. The research in this paper deepens our understanding of the propagation characteristics of Rayleigh waves in strongly weathering layers. This new method strongly supports those seismic imaging and inversion methods depending on seismic modeling, including the reverse time migration and the full waveform inversion of the internal structure of low-Q media.

Generalised eigenfunction expansion and singularity expansion methods for canonical time-domain wave scattering problems

The generalised eigenfunction expansion method (GEM) and the singularity expansion method (SEM) are applied to solve the canonical problem of wave scattering on an infinite stretched string in the time domain. The GEM, which is shown to be equivalent to d’Alembert’s formula when no scatterer is present, is also derived in the case of a point-mass scatterer coupled to a spring. The discrete GEM, which generalises the discrete Fourier transform, is shown to reduce to matrix multiplication. The SEM, which is derived from the Fourier transform and the residue theorem, is also applied to solve the problem of scattering by the mass–spring system. The GEM and SEM are also used to solve the problem of wave scattering by a mass positioned a fixed distance from an anchor point, which supports more complicated resonant behavior.

Effects of steady flow and side hull layouts on motions and added resistance of a trimaran sailing in waves

As a high-performance ship, the trimaran holds significant potential in military and civilian fields. This study proposes a novel numerical method based on the Rankine panel method for predicting the time domain motion and wave loads of trimarans navigating in waves. This approach incorporates a more accurate steady flow model for trimarans and meticulously derives the boundary value problem for the unsteady disturbance potential, while retaining the steady terms related to steady flow throughout the process. This approach ensures a comprehensive consideration of the impacts of speed effect and ship wave. The method was innovatively validated using the trimaran hull form, and its accuracy and reliability were confirmed through comparisons with experimental data. Then, the influence of steady flow on time domain motions and added resistance of trimarans was thoroughly investigated. Comparative analysis of different steady flow models demonstrates that the steady flow model for trimaran proposed provides high precision and advantages in predicting the time domain motions of high-speed trimarans in waves. Furthermore, a systematic investigation into the effects of ship speed and side hull layouts on trimaran's motion and added resistance in waves has been conducted, offering crucial technical support for trimarans' seakeeping optimal solution selection.

Nondestructive evaluation of microstructure and mechanical property of post-processing annealed selective laser melted 316L stainless steel by laser ultrasonics

By using the laser ultrasonics nondestructive technology, combined with the microstructure and mechanical property of post-processing annealed selective laser melted 316L stainless steel characterized by scanning electron microscopy (SEM), electron backscattering diffraction (EBSD), and mechanical property testing, selective laser melted 316L stainless steel after post-processing annealing was evaluated. The results show that the frequency domain attenuation coefficient of ultrasonic waves is positively correlated with the average grain size; the time domain attenuation coefficient of ultrasonic waves is negatively correlated with the low angle boundary content. The tensile strength has a good correlation with the time domain attenuation coefficient and wave speed, the correlation coefficients R2 are 0.95 and 0.89 respectively; the yield strength correlates with the time domain attenuation coefficient, the correlation coefficient R2 is 0.76; the elongation has a good correlation with the frequency domain attenuation coefficient and wave speed, the correlation coefficient R2 is 0.90 and 0.86 respectively.

Numerical studies of one-way Lamb and SH mixing method in composite laminates with transverse-isotropic quadratic nonlinearity

Abstract The resonant behavior of one-way Lamb and SH (shear horizontal) mixing method in composite laminates with transverse-isotropic quadratic nonlinearity is investigated through numerical simulations in this paper. Different from previous studies, the composite constitutive model is combined from orthotropic elasticity and transverse-isotropic quadratic nonlinearity, which is implemented by ABAQUS/VUMAT subroutine. When two fundamental waves (S 0-mode Lamb waves and SH 0 waves) mix in composite laminates with quadratic nonlinearity, the resonant SH 0 waves can be generated with the resonance condition ω S 0 /ω SH 0 = 2 κ/(κ + 1). Meanwhile, the relationships between the acoustic nonlinear parameter (ANP) and damage degree, fundamental frequency, frequency deviation, propagation distance are also investigated. Moreover, the method of locating the damage region in composite laminates is proposed and verified by using the resonant wave time-domain signal.

An efficient ultrasonic wavenumber-domain plane wave imaging method towards the inspection of curved structures

Ultrasonic phased array testing is commonly employed for inspecting curved structures. Conventional plane wave imaging techniques, based on delay-and-sum in the time-domain, offer high image quality and inspection accuracy but suffer from low frame rates due to their high computational complexity. In this work, an efficient wavenumber-domain imaging method that combines non-stationary wavefield extrapolation and f-k migration is proposed for curved structure inspection. Special emission focal laws are designed to generate a sequence of steered plane waves through the curved interface. The raw data is then extrapolated to the top boundary of the region of interest, followed by f-k migration to reconstruct images with high time efficiency. Simulation and experimental evaluations demonstrate a time reduction by a factor of up to 32.24 compared to conventional time-domain plane wave image reconstruction with equivalent image quality, highlighting its potential for monitoring flaws in real-time.

A time-domain spectral finite element method for acoustoelasticity: Modeling the effect of mechanical loading on guided wave propagation

Ultrasonic testing techniques such as guided wave-based structural health monitoring aim to evaluate the integrity of a material with sensors and actuators that operate in situ, i.e. while the material is in use. Since ultrasonic wave propagation is sensitive to environmental conditions such as pre-deformation of the structure, the design and performance evaluation of monitoring systems in this context is a complicated task that requires quantitative data and the associated modeling effort. In our work, we propose a set of numerical tools to solve the problem of mechanical wave propagation in materials subjected to pre-deformation. This type of configuration is usually treated in the domain of acoustoelasticity. A relevant modeling approach is to consider two different problems: a quasi-static nonlinear problem for the large displacement field of the structure and a linearized time-domain wave propagation problem. After carefully reviewing the modeling ingredients to represent the configurations of interest, we propose an original combination of numerical tools that leads to a computationally efficient algorithm. More specifically, we use 3D shell elements for the quasi-static nonlinear problem and the time-domain spectral finite element method to numerically solve the wave propagation problem. Our approach can represent any type of material constitutive law, geometry or mechanical solicitation. We present realistic numerical results on 3D cases related to the monitoring of both isotropic and anisotropic materials, illustrating the genericity and efficiency of our method. We also validate our approach by comparing it to experimental data from the literature.

Risk prediction of pulse wave for hypertensive target organ damage based on frequency-domain feature map

The application of deep learning to the classification of pulse waves in Traditional Chinese Medicine (TCM) related to hypertensive target organ damage (TOD) is hindered by challenges such as low classification accuracy and inadequate generalization performance. To address these challenges, we introduce a lightweight transfer learning model named MobileNetV2SCP. This model transforms time-domain pulse waves into 36-dimensional frequency-domain waveform feature maps and establishes a dedicated pre-training network based on these maps to enhance the learning capability for small samples. To improve global feature correlation, we incorporate a novel fusion attention mechanism (SAS) into the inverted residual structure, along with the utilization of 3 × 3 convolutional layers and BatchNorm layers to mitigate model overfitting. The proposed model is evaluated using cross-validation results from 805 cases of pulse waves associated with hypertensive TOD. The assessment metrics, including Accuracy (92.74 %), F1-score (91.47 %), and Area Under Curve (AUC) (97.12 %), demonstrate superior classification accuracy and generalization performance compared to various state-of-the-art models. Furthermore, this study investigates the correlations between time-domain and frequency-domain features in pulse waves and their classification in hypertensive TOD. It analyzes key factors influencing pulse wave classification, providing valuable insights for the clinical diagnosis of TOD.

Fractional-order velocity-dilatation-rotation viscoelastic wave equation and numerical solution based on a constant-Q model

Viscoelastic wave equations based on the constant- Q (CQ) model can accurately describe the amplitude dissipation and phase distortion of waves in anelastic media. However, only three velocity or displacement components can be obtained directly by solving such equations. Starting from the time-domain second-order displacement viscoelastic wave equation, we derived the decoupled P- and S-wave displacement vector viscoelastic wave equation by using the polarization difference of P- and S-wave propagation in isotropic media. The equation can be transformed into the velocity-dilatation-rotation viscoelastic wave equation containing the first-order temporal derivative and fractional Laplacian operators, which can be solved directly by using the staggered-grid finite-difference and pseudospectral methods. We use the low-rank decomposition method to approximate the derived mixed space-wavenumber domain fractional Laplacian operators for modeling wave propagation in heterogeneous attenuating media. We also demonstrated the precision of our equation by comparing the numerical solutions with the analytical solutions. Furthermore, compared with the conventional velocity-stress viscoelastic wave equation, experimental results demonstrate that our equation can separate the pure P and S waves from the mixed wavefield during wavefield continuation. In addition, it can be separated into an equation containing predominantly an amplitude attenuation or a phase distortion term.

Split-based elevational localization of photoacoustic guidewire tip by 1D array probe using spatial impulse response.

Objective. Photoacoustic emitters on the tip of a therapeutic device have been intensively studied for echo-guided intervention purposes. In this study, a novel method for localizing the guidewire tip emitter in the elevation direction using a 1D array probe is proposed to resolve the issue of the tip potentially deviating from the ultrasound-imaged plane.Approach. Our method uses the 'interference split' that appears when the emitter is off-plane. Here, a point source from the emitter splits into two points in images. Based on the split, 'split-based elevation localization (SEL)' is introduced to estimate the absolute elevation position of the emitter. Additionally, 'Signed SEL' incorporates an asymmetric feature into the 1D probe to obtain the sign of the elevation localization. An attenuative coupler is attached to the half side of the probe to control the interference split. In SEL and Signed SEL, we propose a modeled split matching (MSM) algorithm to localize the tip position. MSM performs pattern matching of a measured split waveform with modeled split waveforms corresponding to all emitter positions in a region of interest. The modeled waveforms are precalculated using the spatial impulse response. The proposed method is numerically and experimentally validated.Main results. Numerical simulations for time-domain wave propagation clearly demonstrated the interference split phenomena. In the experimental validation with a vessel-mimicking phantom, the proposed methods successfully estimated the elevation positions,yb.SEL exhibited a root-mean-squared error (RMSE) of 2.0 mm for the range of 0 mm ≤yb≤ 30 mm, while Signed SEL estimated the absolute position with an RMSE of 2.4 mm and the sign with an accuracy of 80.8% for the range of -30 mm ≤yb≤ 30 mm.Significance.These results suggest that the proposed method could provide approximate tip positions and help sonographers track it by fanning the probe.

Theoretical modeling and dynamic analysis of designable grillages for repairing material surface defect

Designing structural grillages is an innovative solution to repair material surface defects. The grillages have advantages as lightweight and directionally enhanced, but their stability and stress concentration under dynamic loads may pose significant risks. Three analytical models of grillages above a semicircular defect are constructed. The analytical solution of the frequency-domain wave field around the semicircular defect under SH wave incidence is solved. The complex variable function method is introduced to simplify the wave field expression. The accuracy is verified by comparing it with classic examples. Applying the Modified Time-Frequency Transform to obtain the time-domain wave field. Based on the Multipoint Transient Input Method (MTIM), the transient surface displacement response of the grillage above the defect is derived, mainly discussing the superposition behavior of input waves in the grillage. MTIM is based on the analytical solution of local time-domain wave field and takes the time histories of the surface characteristic points as the wave input. It has been validated as an effective method for studying the dynamic response of structures. The numerical results show that grillage form, incident angle, and wave velocity ratio are important factors affecting the structural responses of grillage above the defect. This research aims to reveal the propagation characteristics of waves in grillages in filling material defects, providing theoretical guidance for the design and application of grillages in this field.

A generalized time-domain velocity-stress seismic wave equation for composite viscoelastic media with a topographic relief and an irregular seabed

A generalized time-domain velocity-stress seismic wave equation for composite viscoelastic media with a topographic relief and an irregular seabed

Frequency encoded tristate Pauli X-gate using SOA assisted photonic band gap crystal

The quantum optical tristate Pauli-X gate can broadly be used due to its very fast speed of operation up to THz order, very fast information processing rate, and a wide domain of application. This Pauli X-gate is also important as it can undergo inversion operation. In this proposed scheme, the quantum tristate Pauli-X logic gate has been constructed by a closely packed square lattice of 2D air photonic band gap crystal (PhCs) composed of GaAsInP-dopped rods. The photonic band gap crystal-based tristate Pauli-X gate is performed also as an all-optical reversible quantum logic gate which has the character of low-powered output, very fast speed and a densely packed design structure. This photonic crystal-based structure is also verified by simulation experiment that this proposed scheme performs as the path of two input signals are cross-exchanged to one another at the output, retaining the path of the other input signal same. In this paper, the frequency encoding technique is used in all the designs to establish the logic of all-optical tristate Pauli X-gate towards the need of obtaining a three-input-three-output inversion system. The frequency encoding technique and the photonic crystal-based three Semiconductor Optical Amplifiers (pc-SOAs) are used here in all the schemes to establish the logic of the tristate Pauli-X gate scheme. Tristate Pauli-X gates have been designed and analyzed by Finite-Difference Time-Domain (FDTD) and Plane Wave Expansion (PWE) techniques. The Plane Wave Expansion (PWE) technique is used here in each system for determining the frequency range of band gap structure of transverse electric (TE) mode in the units of μm-1. All of these devices perform within the frequency range 0.629818≤ω2πc≤0.888037 and 1.17551≤ω2πc ≤ 1.34921 μm-1. The wafer dimension of each photonic band gap crystal-based device is 19.20 μm (length) × 16.20 μm (width) providing a very fast response time and very fast information handling (bit rate) capacity, which is found good for these THz Photonic crystal devices. Simulation results show that the proposed gate provides a response period of 0.291 ps and a bit rate of 3.44 Tbps, operating with a low input power of 3.45 mW. The reversible gate exhibits a response period of 0.289 ps and a bit rate of 3.46 Tbps, operating also with a low input power of 2.70 mW. Additionally, the alternative Pauli-X gate demonstrates a response time of 0.291 ps and a bit rate of 3.44 Tbps, operating with a low input power of 2.83 mW.

Practical Aspects of Physics-Informed Neural Networks Applied to Solve Frequency-Domain Acoustic Wave Forward Problem

Abstract Physics-informed neural networks (PINNs) have been used by researchers to solve partial differential equation (PDE)-constrained problems. We evaluate PINNs to solve for frequency-domain acoustic wavefields. PINNs can solely use PDEs to define the loss function for optimization without the need for labels. Partial derivatives of PDEs are calculated by mesh-free automatic differentiations. Thus, PINNs are free of numerical dispersion artifacts. It has been applied to the scattered acoustic wave equation, which relied on boundary conditions (BCs) provided by the background analytical wavefield. For a more direct implementation, we solve the nonscattered acoustic wave equation, avoiding limitations related to relying on the background homogeneous medium for BCs. Experiments support our following insights. Although solving time-domain wave equations using PINNs does not require absorbing boundary conditions (ABCs), ABCs are required to ensure a unique solution for PINNs that solve frequency-domain wave equations, because the single-frequency wavefield is not localized and contains wavefield information over the full domain. However, it is not trivial to include the ABC in the PINN implementation, so we develop an adaptive amplitude-scaled and phase-shifted sine activation function, which performs better than the previous implementations. Because there are only two outputs for the fully connected neural network (FCNN), we validate a linearly shrinking FCNN that can achieve a comparable and even better accuracy with a cheaper computational cost. However, there is a spectral bias problem, that is, PINNs learn low-frequency wavefields far more easily than higher frequencies, and the accuracy of higher frequency wavefields is often poor. Because the shapes of multifrequency wavefields are similar, we initialize the FCNN for higher frequency wavefields by that of the lower frequencies, partly mitigating the spectral bias problem. We further incorporate multiscale positional encoding to alleviate the spectral bias problem. We share our codes, data, and results via a public repository.

Mask correction method for surface plasmon lithography.

Surface plasmon lithography (SPL) has emerged as an innovative approach to nano-fabrication, offering an alternative to traditional patterning methods. To enhance its pattern fidelity in manufacturing, it is essential to incorporate mask correction to reduce critical dimension (CD) errors between the intended target features and the photoresist image. Traditionally, the aerial image of SPL has been modeled and simulated using methods such as finite difference time domain (FDTD) or rigorous coupled wave analysis (RCWA). These models have allowed us to obtain aerial images of the mask patterns. However, relying solely on the aerial image proves insufficient for meeting the rigorous manufacturing standards for mask correction. In our research, we propose a comprehensive model that combines the optical model, employing the FDTD method, and the resist model, tailored to the specific surface plasmon lithography process. Test patterns were meticulously designed with a target CD of 130nm, and the model was applied to simulate these test patterns, producing the after-development image (ADI) under predefined process conditions. Following a thorough analysis and data processing of the test patterns and ADI data, we established rule tables for the correction of both 1D line patterns and line end patterns. The simulation results unequivocally demonstrate the improved CD error performance achieved by the post-corrected patterns.

Recovering both the wave speed and the source function in a time-domain wave equation by injecting contrasting droplets

Recovering both the wave speed and the source function in a time-domain wave equation by injecting contrasting droplets

Coefficient inverse problem for anisotropic time-domain wave equation

In this paper, we investigate an inverse problem of determining coefficient via partial boundary data in anisotropic media. More precisely, we study a scheme for asymptotic reconstruction on coefficient inverse problem for anisotropic time-domain wave equation by a geometric control method. As an initial attempt, it seems natural to treat the case of two dimensional Euclidean space in analogy with many other well-known inverse boundary problems.

Single-Ended Protection of VSC-HVdc Outgoing Line Based on Backward Traveling Wave Time-Domain Weighted Optimization

Single-Ended Protection of VSC-HVdc Outgoing Line Based on Backward Traveling Wave Time-Domain Weighted Optimization

Time-domain acoustic wave propagations in multi-fluids using a weak-form meshfree method

In this work, we focus on the derivation of the weak-form for meshfree methods in analyzing the time-domain acoustic wave propagation in multi-fluids. Due to the employment of meshfree shape functions not restricted to a local background cell, the continuity condition for acoustic particle velocity cannot be spontaneously satisfied, leading to inaccurate simulations of acoustic wave upon the interface. Thus, the penalty function method is utilized here in the weak-form for meshfree methods in order to cure this discontinuity issue without introducing any addition degrees of freedom. By conducting a number of numerical analyses, the numerical results obtained from a radial point interpolation meshfree method are in accord with the analytical solutions and the numerical results of bilinear and quadratic finite elements, validating the effectiveness of the weak-form derived for meshfree methods. Moreover, the numerical accuracy of the used meshfree method can surpass those of bilinear and quadratic finite elements when the same sets of nodes are employed, especially for relatively high frequencies.

Ultra compact, high contrast ratio all optical NOR gate using two dimensional photonic crystals

An all-optical NOR gate is implemented using a two-dimensional photonic crystal waveguide. The paper provides a structure of an all-optical NOR gate constructed by introducing a line and point defect. The proposed NOR gate uses a hexagonal lattice structure with E shaped waveguide. The contrast ratio, response time and bit rate of three input NOR gate are 29.59 dB, 0.8 ps and 1.19 Tbps, respectively. The proposed gate is constructed with the operating wavelength of 1550 nm. The structure has been simulated and analyzed using Finite Difference Time Domain (FDTD) and Plane Wave Expansion (PWE) methods. It offers high contrast ratio, better response time with ultra-compact size. Hence it is suitable for high speed optical integrated circuits and switching devices.