Time-domain Wave Research Articles

Design and implementation of all optical OR and NOR gates based on PhC structure and nonlinear Kerr effect

Abstract In the present work, nonlinear ring resonator based on two-dimensional hexagonal photonic crystal structure is designed for all optical OR and NOR gates in the wavelength range of 1355–2053 nm. The OR and NOR gates are made up of four optical waveguides which are critically coupled to a nonlinear ring resonator. The electric field distribution and photonic band gap characteristic of the proposed gates are solved by Maxwell equations using finite difference time domain and plane wave expansion methods, respectively. Simulation results by finite difference time domain approach show the minimum contrast ratio of 12.04 and 11.81 dB for OR and NOR logic gates, respectively. Also, the minimum delay time is obtained 1 ps for OR and 1.5 ps for NOR logic gates.

Very low frequency waves as selective probe for Cysticercus tenuicollis, Hydatid cyst and Coenurus cerebralis bio-analysis using single cell-signal recording

Comparative electric behavior of Cysticercus tenuicollis, Hydatid cyst and Coenurus cerebralis at the Very Low Frequency (VLF) region has been studied in detail. This investigation could be significant, because of the economic and public health importance of these parasitic infections in domestic animals. In this report, a single cell signal recording technique has been adopted for comparison using a stainless steel (type: 316, diameter: ~ 300 µm, height: 2.00 cm) two identical electrode system, implanted on the surface of the tested cysts with inter electrode distance of 0.50 cm at a ~ 6.0 giga ohm (GΩ) sealed condition (based on the situation of the implanted electrode system). This process was achieved based on applying electrical interaction between the cysts and the VLF electrical signal. Relative to the measured time domain signal (Current–time diagram), the frequency domain (Current-frequency diagram) was estimated via applying a “Discrete Fast Fourier Transform” (DFFT) algorithm at a fixed time interval (5.0 min). Factors, having important influence on the sensitivity of the detection system including the type (waveform) of different alternating-current (AC) triggering stimulus signals (such as direct current, square wave, triangular, sin (t), etc.), the amplitude, as well as the frequency were optimized automatically through a written “Visual Basic 6” program by one-factor-at-a-time method. Direct applying this AC triggering VLF voltage to the cysts resulted in tracing an AC electrical current vs. time that considered as the time domain wave. However, this electrical current was decayed rapidly versus time during maximum 30.0 s time scale. Applying the DFFT algorithm to the measured time domain, resulted in accessing to the frequency domain at the selected frequency range between 2 and 5 kHz that was considered as the selected frequency for the selective differentiation of C. tenuicollis, Hydatid cyst and C. cerebralis. The related probable mechanism of this process may be attributed to the correlation between the triggering potential and the cyst’s electrical surface charge (Zeta potential) as the current source under similar conditions. The results of this study may help to introduce a new detection system for in vivo recognition of the cysts in future.

A space–time quasi-Trefftz DG method for the wave equation with piecewise-smooth coefficients

Trefftz methods are high-order Galerkin schemes in which all discrete functions are elementwise solution of the PDE to be approximated. They are viable only when the PDE is linear and its coefficients are piecewise-constant. We introduce a “quasi-Trefftz” discontinuous Galerkin (DG) method for the discretisation of the acoustic wave equation with piecewise-smooth material parameters: the discrete functions are elementwise approximate PDE solutions. We show that the new discretisation enjoys the same excellent approximation properties as the classical Trefftz one, and prove stability and high-order convergence of the DG scheme. We introduce polynomial basis functions for the new discrete spaces and describe a simple algorithm to compute them. The technique we propose is inspired by the generalised plane waves previously developed for time-harmonic problems with variable coefficients; it turns out that in the case of the time-domain wave equation under consideration the quasi-Trefftz approach allows for polynomial basis functions.

Nearly perfectly matched layer implementation for time domain spectral element modelling of wave propagation in 3D heterogeneous and anisotropic porous media

Numerical modelling of wave propagation in the heterogeneous and anisotropic porous media is important for seismic exploration. When modelling time-domain poroelastic waves in an unbounded region, the implementation of perfectly matched layer (PML) is a common technique to absorb the outgoing waves. The PML in terms of first-order equations has been well proposed. However, the first-order PML needs fundamental and nontrivial reconstructions when applied to the second-order systems in displacements, such as finite element method (FEM) and spectral element method (SEM). It is well known SEM is an efficient algorithm for simulating seismic waves for its high accuracy and geometrical flexibility. However, at present, few literature studies the implementation of PML into time-domain SEM for simulating waves in the 3D unbounded heterogeneous porous media. In this work, combining with auxiliary ordinary differential equations (ODEs), we first systematically extend nearly PML (NPML) into time-domain SEM in terms of the second-order poroelastic system. The scheme preserves the original form of wave equations, leading to a simple and flexible incorporation into the existing algorithm. It avoids the temporary convolution through solving a set of first-order ODEs in time domain, resulting in high computational efficiency. Furthermore, to solve the coupling poroelastic/acoustic/elastic waves, we employ domain decomposition technique to handle the different regions independently, and apply the corresponding boundary conditions at the region interfaces to guarantee the coupling. Numerical examples demonstrate the accuracy and stability of the proposed method by comparing the numerical results with the analytical solutions and other independent numerical solutions. Finally, we apply the algorithm to solve wave propagation in a large-scale model involved a fluid-filled borehole embedded in heterogeneous porous formations.

A linear approach to simulate a constant-Q model in time-domain ground-penetrating radar modeling using multiple Debye poles: Theory and application in karst carbonate rocks

Dispersion is an important effect contributing to attenuating ground-penetrating radar (GPR) signals and must be incorporated in wave propagation. The constant-[Formula: see text] model (quality factor [Formula: see text]) is valid in rocks for typical GPR frequency ranges. In time-domain wave modeling, to simulate a constant-[Formula: see text] medium, using multiple Debye poles, the number of poles and their parameters must be previously estimated to honor target values for [Formula: see text] and velocity in the demanded frequency band. For electromagnetic waves, this problem is usually formulated as a highly nonlinear optimization problem presenting several solutions, which is solved using global optimization methods. An efficient linear approach to estimate multiple Debye poles to simulate constant-[Formula: see text] media for GPR data is presented. The resulting inverse problem is easy to solve because the number of poles is relatively small. The approach allows for a novel rescaled solution that depends only on the frequency band and number of poles. Solutions satisfying specific target values for velocity and [Formula: see text] are obtained from the rescaled solution by multiplying this solution by a proportionality factor that depends only on the target values. Choosing the number of poles is done so that velocity [Formula: see text] and [Formula: see text] curves, as a function of frequency [Formula: see text], are approximately invariant in the specified frequency band. Using the criterion that [Formula: see text] and [Formula: see text] curves must present maximum percentage deviations from the respective target values smaller than 5%, we find that, for the 200 MHz antenna, whose useful frequency band is 50–800 MHz, only three poles are sufficient. The theory is validated by modeling dispersion effects using synthetic models. The importance of introducing dispersion effects is illustrated by presenting a trial-and-error modeling approach to approximately reproduce a 200 MHz radargram acquired in fractured and karstified carbonate rocks.

Seismic Response of Immersed Tunnel Subject to Oblique Incidence of SV Wave

In view of the near-field seismic action, considering that oblique incidence of seismic waves is more realistic than vertical incidence, the seismic response of the Hong Kong–Zhuhai–Macao immersed tunnel subjected to an obliquely incident SV wave is investigated. Using the finite element method and time-domain wave method, the seismic input is transformed into an equivalent node load with a viscous–spring artificial boundary, and a three-dimensional simulation technology for SV waves of oblique incidence is presented. A half-space numerical example is given to demonstrate the accuracy of the proposed simulation technology. Taking the stress field formed by the self-weight stress and hydrostatic pressure as the initial state of the dynamic response analysis, the static–dynamic coupling numerical simulation of the seismic response of a soil-immersed tunnel system is realized. The results show that the amplification in the vertical and longitudinal response of the tunnel, due to the oblique incidence, reaches maximum when the incident angle is close to the critical angle. Furthermore, the horizontal response and incident angle show the inverse relation and tend to be stable. In addition, the oblique incidence also causes asymmetric shearing in symmetric parts of the tunnel. The root of the shear key easily produces tensile cracks, while the end angle of the shear key is prone to stress concentration and local damage. Thus, the impact of oblique incidence should be considered in the seismic design, and attention should be paid to the optimization of the end angle of the shear key and the configuration of anti-crack reinforcement at the root of shear key to meet the seismic requirements.

Effectiveness of viscous damper on vibrations control of full -height lattice tower under wave and wind excitations in time-domain

Effectiveness of viscous damper on vibrations control of full -height lattice tower under wave and wind excitations in time-domain

Gravitational Wave-Signal Recognition Model Based on Fourier Transform and Convolutional Neural Network

The recent detection of gravitational waves is a remarkable milestone in the history of astrophysics. With the further development of gravitational wave detection technology, traditional filter-matching methods no longer meet the needs of signal recognition. Thus, it is imperative that we develop new methods. In this study, we apply a gravitational wave signal recognition model based on Fourier transformation and a convolutional neural network (CNN). The gravitational wave time-domain signal is transformed into a 2D frequency-domain signal graph for feature recognition using a CNN model. Experimental results reveal that the frequency-domain signal graph provides a better feature description of the gravitational wave signal than that provided by the time-domain signal. Our method takes advantage of the CNN's convolution computation to improve the accuracy of signal recognition. The impact of the training set size and image filtering on the performance of the developed model is also evaluated. Additionally, the Resnet101 model, developed on the Baidu EasyDL platform, is adopted as a comparative model. Our average recognition accuracy performs approximately 4% better than the Resnet101 model. Based on the excellent performance of convolutional neural network in the field of image recognition, this paper studies the characteristics of gravitational wave signals and obtains a more appropriate recognition model after training and tuning, in order to achieve the purpose of automatic recognition of whether the signal data contain real gravitational wave signals.

A Study of the Postprandial Plasma Glucose Waves and Fluctuations of 63 Fasting and 43 Non-Fasting Meals at Breakfast Using Time and Frequency Domains Plus Wave Along with Energy Theories of GH-Method: Math-Physical Medicine (No. 405)

This particular study investigates a few postprandial plasma glucose (PPG) characteristics, including glucose waves and wave fluctuations or glycemic variability (GV) of 106 breakfasts from 11/5/2020 to 2/22/2021, which include 63 fasting and 43 non-fasting meals. At first, the author utilizes wave theory to study PPG waves in time domain. He then applies signal processing techniques and Fast Fourier Transform program to convert these PPG waves into frequency domain. He can then estimate the relative energy levels associated with different glucoses of both fasting and non-fasting situations to understand the degree of organ impact related to these energies generated from or carried by glucoses in the blood system. In summary, from the time domain analysis, the non-fasting’s average PPG value is 15 mg/dL, which is 14% higher than the fasting’s average PPG; and the non-fasting’s peak PPG value is 21 mg/dL, which is 19% higher than the fasting’s peak PPG value. Even the PPG wave fluctuations (Max.-Min.) of the non-fasting is 12 mg/dL, which is 60% higher than the fasting. It is interesting to observe that the fasting glucose wave still has fluctuations even though it is much “calmer”. On the other hand, from the frequency domain analysis, there are two observations described below: 1. Relative energy associated with PPG wave reveals that non-fasting is 43% lower than fasting. This observation is counter to the author’s intuitive feeling; however, this phenomenon is due to the higher amplitude (Y-value) result of the frequency domain after the Fourier Transform operation from the time domain. In other words, this characteristic of glucose energy corresponding to different frequencies in frequency domain is different from the characteristic of glucose corresponding to various times in time domain. 2. The relative energy associated with PPG wave fluctuations reflects that non-fasting is 17% higher than fasting which is due to the difference of 12 mg/dL, which is 60% of PPG fluctuation (Max - Min) in time domain. Besides, the Fourier Transform operation did not change the PPG fluctuation’s characteristics in its frequency domain.

DEEP LEARNING AND SUCCESSIVE ITERATIONS FOR AN INVERSE PROBLEM OF THE VARIABLE DENSITY RECONSTRUCTION BY THE BOUNDARY CONTROL METHOD

For the first time, two approaches, the deep learning and successive iterations, are proposed for use and implemented for enhancing the images reconstructed by the boundary control method. The construction of successive iterations is based on the reduction of a nonlinear inverse problem for a time-domain wave equation to a linear integral equation of the first kind. The computational effectiveness of the numerical techniques is demonstrated in the numerical experiments in two and three dimensions.

Design of ultra compact 4:2 encoder using two dimensional photonic crystals

In this paper all optical ultra compact 4:2 encoder is proposed and designed using two dimensional photonic crystals (PC). The proposed structure has silicon rods of refractive index 3.4 embedded in air host by creating line defects in hexagonal lattice platform. The analysis of the design is done for various experimental values of radius, lattice constant and pitch values using finite difference time domain (FDTD) and plane wave expansion (PWE) method of licensed OptiFDTD software tool. The structure is optimised to get maximum power confinement at the output of the two ports of the 4:2 encoder by inserting extra rods which interns acts like a resonator to couple the power to the two output waveguides. The structure is chosen in such a way that ( $$\frac{a}{\lambda }$$ ) will fall around 1550 nm wavelength only and is good for long distance transmission application as it is having low attenuation constant and high contrast ratio. Further, the proposed 4:2 encoder is operated at 1550 nm and it provides a high contrast ratio of 9.25 dB, propagation delay 33.1 fs and foot print of the structure is 119.34 $$\mu$$ m $$^2$$ . Hence it is highly advisable for photonic integrated circuits and optical signal processing.

Prediction of H-type Hypertension Based on Pulse Wave MFCC Features Using Mixed Attention Mechanism

PurposeH-type hypertension increases the risks of stroke and cardiovascular disease, posing a great threat to human health. Pulse diagnosis in traditional Chinese medicine (TCM) combined with deep learning can independently predict suspected H-type hypertension patients by analyzing their pulse physiological activities. However, the traditional time-domain feature extraction has a higher noise and baseline drift, affecting the classification accuracy. In this article, we propose an effective prediction on frequency-domain pulse wave features.MethodsFirst, we filter time-domain pulse waves via removal of high-frequency noises and baseline shift. Second, Hilbert–Huang Transform is explored to transform time-domain pulse wave into frequency-domain waveform characterized by Mel-frequency cepstral coefficients. Finally, an improved BiLSTM model, combined with mixed attention mechanism is built to be applied for prediction of H-type hypertension.ResultsWith 337 clinical cases from the Longhua Hospital affiliated to Shanghai University of TCM and Hospital of Integrated Traditional Chinese and Western Medicine, the threefold cross-validation results show that sensitivity, specificity, accuracy, F1-score and AUC reaches 93.48%, 95.27%, 97.48%, 90.77% and 0.9676, respectively. In addition, we calculate the feature importance both in time-domain and frequency-domain according to purity of nodes in Random Forest and study the correlation between features and classification.ConclusionThe proposed model achieves better generalization performance than the classical traditional ûmodels, and has a good reference value for TCM clinical auxiliary diagnosis.

Electromagnetic wave forward modeling of coal-gangue mixed model in top coal caving mining face

The automatic control of top coal caving is of great significance to realize intelligent coal mining. In the process of top coal caving, a coal-gangue mixed area containing coal, gangue, and air is formed at the tail beam of the hydraulic support, which has different electromagnetic parameters, different volumes, and different shapes. To explore the transmission characteristics of electromagnetic wave in coal-gangue mixed model and the influence of different gangue ratios on electromagnetic wave propagation, the coal-gangue mixed model is established based on the random medium theory. Some electromagnetic forward modeling is carried out with different coal-gangue granularities, electromagnetic parameters, and gangue ratios based on finite-difference time-domain (FDTD) and finite-integration time-domain (FITD) methods. The results show that different granularities of coal and gangue will affect the amplitude of electromagnetic wave time-domain waveform. Under the same particle size, the equivalent electromagnetic parameters in the coal-gangue mixed medium will be larger with higher gangue ratio. Furthermore, the difference of transmitted wave signals between different gangue ratios will be larger with higher electromagnetic parameters difference of the coal and gangue. For higher refractive index, the propagation velocity of electromagnetic wave in the medium and the transmitted wave amplitude will be smaller. In addition, the comparison results illustrate that the rules of electromagnetic wave propagation obtained by FDTD and FITD methods are basically the same, which verifies the correctness of the simulations in this paper. The simulation results can lay a theoretical foundation for identifying the coal-gangue mixed degree in the process of top coal caving.

Planes approximation method for investigating the physical origins of deep, wide phononic bandgaps

The objective of this paper is to formulate a simple analytical model that describes Bragg and Mie scattering leading to the creation of bandgaps in phononic crystals (PnCs). The model is a homogenized, mean-field 1D model, dubbed the Planes Approximation Method (PAM). Bragg and Mie scattering are decoupled into independent 1D models and then recombined graphically to understand better and visualize bandgap creation. Due to the model's simplicity, it allows for rapid solutions compared to other computational methods. This paper argues that acoustic impedance mismatches yield bandgaps based on the formulation. PAM is demonstrated using a square lattice of microscale circular inclusions of tungsten with a lattice constant of 45 μm in a SiO2 matrix and then compared to results from finite difference time domain and plane wave expansion simulations.

Viscoacoustic wave equation for qP-wave in transversely isotropic media

The wave equation acts a pivotal part in seismic data processing. We derived two time-domain pure qP viscoacoustic wave equations suitable for attenuation anisotropic media, providing a choice for pure qP-wave forward modeling and inversion in attenuation anisotropic media. Our new qP-wave equation in vertical transversely isotropic (VTI) media are based on the dispersion relation for qP-wave in VTI media and obtained by the relaxation functions of the standard linear solid model and the Kjartansson's constant Q model respectively. Anelasticity including amplitude attenuation and phase dispersion can be dealt with by the proposed wave equation separately. With the coordinate transform, the corresponding two pure qP-wave viscoacoustic anisotropic wave equations for titled transversely isotropic media also are derived. Different from the common viscoacoustic anisotropic wave equation (a coupled second-order partial differential equations system), the new wave equations are simplified by decomposing the original pseudo-differential operator into a differential and a scalar opera- tors. For numerical calculation, the new wave equations can be solved more efficiently than the coupled wave equations. Meanwhile the new wave equations could simulate pure qP-wave steadily in attenuation anisotropic media without quasi-SV wave artifacts. Some synthetic examples, including attenuation Hess and Marmousi-2 models, demonstrate the feasibility of the derived pure qP-wave viscoacoustic wave equations in transversely isotropic media.

Kalman-filter-based time-domain plane wave superposition method for reconstructing an instantaneous sound field

A Kalman-filter-based time-domain plane wave superposition method (KF-TDPWSM) is proposed for reconstructing the instantaneous sound field generated by a source. In the KF-TDPWSM, a discrete state formulation is first acquired using the superposition formula of time-varying pressure on a hologram plane, which forms a multiple-input and multiple-output acoustical system. Then, an eigensystem realization algorithm is implemented to obtain the minimum realization of this system. The process and measurement equations of the KF-TDPWSM are established by combining the equation of the first-order smoothness condition with the minimum realization. Finally, the forward iteration calculation of the Kalman filter is used to estimate the state vector, including the pressure time–wavenumber spectra on a virtual source plane. The spectra estimated at all times are employed to calculate the time-varying pressure on a reconstruction plane. The KF-TDPWSM utilizes a forward iteration calculation and does not use the inverse calculation with the time-marching characteristic to improve the reconstruction stability of the instantaneous sound field. A numerical simulation is designed to investigate the reconstruction performance of the KF-TDPWSM. Simulation results confirm that the KF-TDPWSM effectively reconstructs the instantaneous sound field of a source in the time and space domains. The effects of certain parameters of the KF-TDPWSM are examined through simulations, and it is shown that its reconstruction accuracy is superior to that of the time-domain plane wave superposition method. An experiment is conducted to further validate the KF-TDPWSM.

Two-Dimensional Fourier Continuation and Applications

This paper presents a method (2D-FC) for construction of bi-periodic extensions of smooth non-periodic functions defined over general two-dimensional smooth domains. The approach can be directly generalized to domains of any given dimensionality, and even to non-smooth domains, but such generalizations are not considered here. The 2D-FC extensions are produced in a two-step procedure. In the first step the one-dimensional Continuation method is applied along a discrete set of outward boundary-normal directions to produce, along such directions, continuations that vanish outside a narrow interval beyond the boundary. Thus, the first step of the algorithm produces blending-to-zero along normals for the given function values. In the second step, the extended function values are evaluated on an underlying Cartesian grid by means of an efficient, high-order boundary-normal interpolation scheme. A Continuation expansion of the given function can then be obtained by a direct application of the two-dimensional FFT algorithm. Algorithms of arbitrarily high order of accuracy can be obtained by this method. The usefulness and performance of the proposed two-dimensional Continuation method are illustrated with applications to the Poisson equation and the time-domain wave equation within a bounded domain. As part of these examples the novel Fourier Forwarding solver is introduced which, propagating plane waves as they would in free space and relying on certain boundary corrections, can solve the time-domain wave equation and other hyperbolic partial differential equations within general domains at computing costs that grow sublinearly with the size of the spatial discretization.

An Adaptive High-Order Transient Algorithm to Solve Large-Scale Anisotropic Maxwell’s Equations

This article presents a stabilized nodal discontinuous Galerkin pseudospectral time-domain (DG-PSTD) algorithm for fully anisotropic electromagnetic waves. This solver permits arbitrary high-order basis functions and adaptive hexahedral elements, thus very efficient for large-scale wave propagation in complex media. Maxwell’s equations are reformulated in a unified hyperbolic form, where a localized anisotropic Riemann solver is derived to serve as a numerical flux to exchange information across adjacent elements in the DG-PSTD scheme. This local analysis method also helps impose the time-domain anisotropic plane wave incidence in the total/scattering field framework. Numerical validations and applications demonstrate the efficiency, accuracy, and capability of this new high-order solver for 3-D large-scale generally anisotropic electromagnetic media.

Active terahertz modulator based on optically controlled organometal halide perovskite MAPbI2Br.

In this paper, an active terahertz modulator based on optically controlled organometal halide perovskite MAPbI2Br is proposed. The terahertz wave time-domain transmission of the MAPbI2Br/Al2O3 sample was measured by a terahertz time-domain spectrometer. Experimental results indicate that the MAPbI2Br/Al2O3 sample showed an obvious optical-power-dependent modulation effect on transmission of the terahertz wave; the maximum modulation depth of the modulator can reach 59.99% at 0.3 THz when the external pump optical power is up to 1500 mW.

Numerical Simulation of Elastic Wave Field in Viscoelastic Two-Phasic Porous Materials Based on Constant Q Fractional-Order BISQ Model.

The fractional-order differential operator describes history dependence and global correlation. In this paper, we use this trait to describe the viscoelastic characteristics of the solid skeleton of a viscoelastic two-phasic porous material. Combining Kjartansson constant Q fractional order theory with the BISQ theory, a new BISQ model is proposed to simulate elastic wave propagation in a viscoelastic two-phasic porous material. The corresponding time-domain wave propagation equations are derived, and then the elastic waves are numerically simulated in different cases. The integer-order derivatives are discretised using higher-order staggered-grid finite differences, and the fractional-order time derivatives are discretised using short-time memory central differences. Numerical simulations and analysis of the wave field characterisation in different phase boundaries, different quality factor groups, and multilayered materials containing buried bodies are carried out. The simulation results show that it is feasible to combine the constant Q fractional-order derivative theory with the BISQ theory to simulate elastic waves in viscoelastic two-phasic porous materials. The combination can better describe the viscoelastic characteristics of the viscoelastic two-phasic porous materials, which is of great significance for further understanding the propagation mechanism of elastic waves in viscoelastic two-phasic porous materials and viscoelastic two-phasic porous materials containing buried bodies. This paper provides a theoretical forward simulation for fine inversion and reconstruction of layer information and buried body structure in viscoelastic two-phasic porous materials.