Time-domain Wave Research Articles

Research on propagation law of one-dimensional stress wave in jointed rock mass under in-situ stress

The propagation law of stress wave in jointed rock mass under in-situ stress has important engineering significance on blasting excavation and protection engineering design of deep rock mass. Based on theoretical analysis, the propagation law of stress wave across multiple nonlinear deformation joints under the initial stress is studied. Firstly, the propagation equation of stress wave across multiple nonlinear joints considering the influence of initial stresses is established, through the discontinuous deformation method (DDM) and the recursive analysis method of stress wave in time domain. On this basis, parametric studies are conducted for the effects of stress wave propagation, such as initial stress, the amplitude of stress wave, the distance and the number of joints. The results show that the existence of initial stress will affect the propagation of stress wave, the geometric distribution of joints, such as spacing and number, can also cause the change of stress wave transmission coefficients, and the amplitude of incident wave varies can also lead to the change of stress wave propagation.

Time Domain Room Acoustic Solver with Fourth-Order Explicit FEM Using Modified Time Integration

This paper presents a proposal of a time domain room acoustic solver using novel fourth-order accurate explicit time domain finite element method (TD-FEM), with demonstration of its applicability for practical room acoustic problems. Although time domain wave acoustic methods have been extremely attractive in recent years as room acoustic design tools, a computationally efficient solver is demanded to reduce their overly large computational costs for practical applications. Earlier, the authors proposed an efficient room acoustic solver using explicit TD-FEM having fourth-order accuracy in both space and time using low-order discretization techniques. Nevertheless, this conventional method only achieves fourth-order accuracy in time when using only square or cubic elements. That achievement markedly impairs the benefits of FEM with geometrical flexibility. As described herein, that difficulty is solved by construction of a specially designed time-integration method for time discretization. The proposed method can use irregularly shaped elements while maintaining fourth-order accuracy in time without additional computational complexity compared to the conventional method. The dispersion and dissipation characteristics of the proposed method are examined respectively both theoretically and numerically. Moreover, the practicality of the method for solving room acoustic problems at kilohertz frequencies is presented via two numerical examples of acoustic simulations in a rectangular sound field including complex sound diffusers and in a complexly shaped concert hall.

Optical sensor based on two-dimensional photonic crystals for measuring glucose in urine

The design and simulation of two bio-optical sensors for the noninvasive measurement of glucose levels in urine of diabetic patients are presented. While the sensors are of the same shape and structure, their quality factors (QFs), sensitivities, and sizes are different. The structure developed is based on two-dimensional (2D)-hexagonal-latticed photonic crystals containing silicon rods immersed in urine. By creating line and point defects in the structure, two resonant modes are localized in the photonic bandgap (the photonic bandgap is a frequency range corresponding to mirror action for incident light of frequency within that range). Sensor 1 design was based on localized resonant mode 1, while sensor 2 uses localized resonant mode 2. The mechanism of these sensors relies on the change of the refractive index of urine as a result of the change in glucose concentration, which in turn causes shifts in resonant modes of the sensors. For tuning in the wavelength of 1.55 μm, the scaling method is utilized. The major difference between the proposed sensors and previously reported bio-optical sensors is the determination of glucose level based on the shift in resonant wavelengths. Previous works relied on the change of the amplitude of emerging waves for the same purpose. Consequently, the sensors presented here exhibit a higher QF and operate within the wavelength window of 1.55 μm. QF calculations and sensitivity simulations for sensor 1 yielded approximate values of 3800 and 500 nm/refractive index unit (RIU), respectively. For sensor 2, QF and sensitivity were 5540 and 500 nm / RIU, respectively. The sizes of sensor 1 and sensor 2 are 14.93 × 8.8 μm2 and 15.7 × 9.47 μm2, respectively. The 2D finite difference time domain and plane wave expansion methods were relied upon in the simulations.

Feasibility Study on the Audible Noise Measurement of Partial Discharge in Transformer Oil

Partial discharge fault detection based audible noise is a kind of new method. This paper set up a needle-plate discharge system, and investigates the feasibility of measuring the audible noise of partial discharge in transformer oil. A needle-plate discharge system is built, and audio noise of partial discharge inside and outside of transformer oil is measured by a microphone and a specially designed hydrophone. According to signal processing, it’s found that the characteristics of internal and external noise have good consistency on time domain wave, spectrum distribution, and time-frequency distribution, except that the former is much larger than the latter in amplitude. The experiment results show that it’s feasible to measure the noise of partial discharge in the transformer oil and have significant advantage in signal to noise ratio.

Photonic Crystal and its Application as a Biosensor for the Early Detection of Cancerous Cells

The motivation for this paper is the strikingly sad statistics, obtained from various research bodies globally, regarding the effect of cancers on the global populace and the impact of current methods put in place for the early diagnosis of cancer. This paper is novel for many reasons. Primarily, it presents the use of an optical biosensor based on photonic crystal for cancer cell detection. This biosensor was recently developed as an ultra-compact biochemical sensor based on a 2D photonic crystal cavity known for altering its spectrum in proportion to minute changes in refractive index. Secondarily, The Finite Difference Time Domain (FDTD) and Plane Wave Expansion (PWE) techniques were applied to analyze the possibility of using photonic crystals as biosensors for the detection of cancer cells. The obtained resonant wavelength from the analysis of simulated results was 1.54964 µm and transmitted power obtained from the analysis was 51.9%. For the cancerous cell sample, The PC 12 Cell, the obtained resonant wavelength from analysis of the simulated results was 1.54964 µm and the transmitted power obtained from the analysis was 55.6%.

Seismic response of soil slope reinforced by compression anchor and frame beam based on shaking table test

Compression anchor is a good anchorage structure in the slope and landslide project. Compared with tension anchor, it is a relatively new retaining structure, and the studies on compression anchor under seismic loadings are very limited. To investigate the seismic behavior of compression anchor under earthquake and get it to work much better in an earthquake-prone area, based on the shaking table test, a soil model slope reinforced with compression anchor and frame beam was carried out. In the test, the smooth steel bar and Q235 steel plate ring were used to simulate the anchor tendon and bearing plate of the compression anchor. The testing results indicate that the anchoring slope shows an obvious amplification effect on input seismic waves in both time domain and frequency domain, and the amplification effect of the acceleration response increases along the slope height. The axial force of the compression anchor is relatively uniform along the length of the anchor. As for different anchors in the same column, at 0.05~0.2 g, the axial forces of all anchors show tiny values, and the axial force of the bottom anchor is slightly greater than that of other anchors. The axial force of the bottom anchor is about 2.1~2.8 times that of the other anchors. At 0.3~0.6 g, the axial forces of the upper two anchors and the bottom anchor increase rapidly, while the axial forces of the other two middle anchors increase a little. The axial force ratio of the five rows of anchors from the bottom to the top at 0.3 g, 0.4 g, and 0.6 g is 4.2:1:1:2.1:2.9, 4.2:1:0.9:3.1:3.4, and 3.6:1:0.8:3.2:3.8, respectively. As for different beams, at 0.05~0.2 g, the bending moments of all beams show tiny values, and the bending moment of the bottom beam is slightly greater than that of other four beams. At 0.3~0.6 g, the bending moment of the top beam plays a more and more vital role, while the bending moment of the other four beams shows little variation.

Optimization of an All-Optical Photonic Crystal NOT Logic Gate Using Switch Based on Nonlinear Kerr Effect and Ring Resonator

In this paper, the use of the Kerr effect in a two-dimensional square lattice of In0.82Ga0.18As0.40P0.60 rods in photonic crystal proposes an ultra-compact all-optical NOT logic gate. The main device operation is based on the concept of all the optical switches. In our work, the novelty lies in the design of a new simple nonlinear ring based on the combination of silicon nano-crystal "Si–Nc/In0.82Ga0.18As0.40P0.60" materials that can be used. The contrast ratio and delay time for the proposed NOT logic gate are respectively 25.52 dB and 0.66 ps. The structure size is equal to 168 μm2. Designed logic gates are characterized by low energy consumption, high-speed response, compactness and easy integration. All simulations are based on Non-Linear-Finite Difference Time Domain (NL-FDTD) and Plane Wave Expansion (PWE) numerical methods.

Computational modelling and experimental tank testing of the multi float WaveSub under regular wave forcing

A submerged wave device generates energy from the relative motion of floating bodies. In WaveSub, three floats are joined to a reactor; each connected to a spring and generator. Electricity generated damps the orbital movements of the floats. The forces are non-linear and each float interacts with the others. Tuning to the wave climate is achieved by changing the line lengths, so there is a need to understand the performance trade-offs for a large number of configurations. This requires an efficient, large displacement, multidirectional, multi-body numerical scheme. Results from a 1/25 scale wave basin experiment are described. Here, we show that a time domain linear potential flow formulation (Nemoh, WEC-Sim) can match the tank testing provided that suitably tuned drag coefficients are employed. Inviscid linear potential models can match some wave device experiments; however, additional viscous terms generally provide better accuracy. Scale experiments are also prone to mechanical friction, and we estimate friction terms to improve the correlation further. The resulting error in mean power between numerical and physical models is approximately 10%. Predicted device movement shows a good match. Overall, drag terms in time domain wave energy modelling will improve simulation accuracy in wave renewable energy device design.

Two-dimensional finite-difference time-domain formulation for sound propagation in a temperature-dependent elastomer-fluid medium.

This study focuses on the two-dimensional (2-D) finite-difference time-domain (FDTD) formulations to investigate the acoustic wave propagation in elastomers contained in a fluid region under different thermal conditions. The developed FDTD formulation is based on a direct solution of the time-domain wave equation and the Havriliak-Negami (H-N) dynamic mechanical response of the elastomers. The H-N representation, including double fractional derivative operators, can be accurately transferred from the frequency-domain to the time-domain by using Riemann-Liouville theory and the Grunwald-Letnikov operator for fractional derivative approximations. Since the Williams-Landel-Ferry shift function is related to the relaxation time for different thermal conditions, the proposed scheme represents a simple and accurate prediction of acoustic wave propagation for varying thermal conditions. The pulse-wave propagation in a viscous fluid field is simulated by investigating the Navier-Stokes equations. The acoustic properties of different elastomers in a variety of temperatures are obtained by means of the proposed FDTD formulation and validated by a good agreement with the experimental data over a wide frequency range. Additionally, the 2-D examples relevant to wave propagation in different elastomers contained in a fluid field are implemented. The proposed FDTD formulation can be used to predict 2-D acoustic wave propagation in different thermal conditions accurately.

Dynamic Response of Rock Slopes under Obliquely Incident Seismic Waves

In this study, the seismic input model of slope is proposed to investigate the dynamic response of the rock slope under obliquely incident seismic wave on the basis of the time‐domain wave analysis method. The model includes viscoelastic boundary considering the infinite foundation radiation damping and the seismic obliquely incident method. The semi‐infinite space numerical example is simulated to verify the validity and accuracy of the model. Based on the established model, the effects of the variation of the seismic wave incident angles and slope angles on the dynamic response of a rock slope are analyzed. The results demonstrate that the changes of the incident angle and the slope angle have no discernible effect on the dynamic response of the rock slope when the P wave is obliquely incident. As the SV wave is obliquely incident, the peak ground acceleration amplification coefficient along the slope surface gradually increases with the increase of the incident angle; when the slope angle gradually increases, the peak ground acceleration amplification coefficient along the slope surface will also gradually increase at the upper part of the slope. The research results can provide some basis for the pseudostatic method to determine the seismic action coefficient.

Design of a highly sensitive photonic crystal refractive index sensor incorporating ring-shaped GaAs cavity

Two highly sensitive optical sensor topologies are proposed and simulated in this paper. The proposed structures are optimized to provide better performance characteristics such as sensitivity, detection limit, and quality factor. They are based on two-dimensional photonic crystals consisting of rectangular arrays of GaAs rods in SiO 2 substrates. Such lattices have bandgaps for transverse magnetic modes. Two-dimensional finite difference time domain and plane wave expansion methods are used for the simulation and analysis of the refractive index sensors and particle swarm optimization method is used to optimize the structural parameters. The designed structures show a high sensitivity to refractive index variations. They are able to detect refractive indices from 1.33 to 1.5. An excellent figure of merit equal to 737 RIU −1 is observed for the proposed structure and a significant improvement is observed compared to the structures reported in the literature.

Quantitative Detection of Interfacial Air Gap in Insulation Equipment Based on Terahertz Wave Contrast Method

The nondestructive testing of internal defects in power grid equipment has always been a spotlight of research. Since terahertz wave has good application in the nondestructive detection fields, we apply terahertz wave to detect the interfacial air gap of insulation equipment. At present, terahertz wave is difficult to measure the thickness of the internal air gap. Hence, this paper presents a method for quantitative measurement of internal air gap based on the waveform database. In addition, the propagation characteristics of the terahertz wave in medium are analyzed. Furthermore, based on the value of $n(\omega)$ and $\kappa (\omega)$ , the calculation formula of the transmission and reflection coefficients is simplified. After obtaining the reflected wave of the single outer layer material, we quantitatively calculate the time-domain reflection wave of interface. According to the principle of terahertz detection based on photoconductive antenna, the detection of multiple reflection waves is analyzed. To verify the superposition characteristics of multiple waves, the terahertz reflection waves of samples with interfacial air gap are tested. By comparing the measured waves and the artificially calculated waves, we prove that the superposition of the waveform is approximately linear. Based on the good coincidence between artificially generated waveform and measured waveform, we propose a method of quantitatively diagnosing the interface air-gap defect. Indeed, the deviation between the test results and the actual air-gap size is small.

Slow light enhanced bio sensing properties of silicon sensors

In this paper, we investigated slow light to increase sensitivity and quality factor of our recently designed bio-sensors. A finite difference time domain and Plane Wave Expansion methods are employed to figure out sensors’ performances. We proposed slow light based photonic crystal structures with elliptical cells and we obtained higher sensitivity and quality factor as previously reported. For the first proposed sensor, the results showed that quality factor increased from 570 to 723 and a detection limit below 10−3. For the second sensor, the sensitivity increased from 550 to 650 nm/RIU and the detection limit is around 10−3. These two proposed structures would offer great potential for novel compact biosensors in medical application.

Bayesian transdimensional seismic full-waveform inversion with a dipping layer parameterization

Seismic full-waveform inversion (FWI) has become a popular tool for estimating subsurface models using the amplitude and phase of seismograms. Unlike the conventional gradient-based approach, Bayesian inference using Markov chain Monte Carlo (MCMC) sampling can remove dependence on starting models and can quantify uncertainty. We have developed a Bayesian transdimensional (trans-d) MCMC seismic FWI method for estimating dipping-layer velocity models, in which the number of layers is unknown. A time-domain staggered-grid finite-difference wave equation solver is used for forward modeling. The FWI and MCMC methods are known to be computationally expensive. Two strategies are used to get practical computational performance. A layer-stripping strategy is used to accelerate sampler convergence, and a parsimonious dipping layer parameterization is used so that the MCMC algorithm can search broadly with fewer iterations. The parameters for each layer are velocity, thickness, and lower interface dip angle. We find that this parameterization has sufficient flexibility to invert for narrow 2D velocity models using small offset data. Model stitching is then used to bring several such inversions together to create larger 2D models. In turn, these can be used as starting models for gradient-based adjoint FWI to image complicated geologic settings. Two synthetic 2D numerical examples, including the Marmousi model, are considered, using seismic data dominated by reflections. Creation of good starting models traditionally requires significant human effort. We determine how much of that effort can be substituted with computation.

Contained Laboratory Earthquakes Ranging From Slow to Fast

AbstractLoading a 3‐m granite slab containing a saw‐cut simulated fault, we generated slip events that spontaneously nucleate, propagate, and arrest before reaching the ends of the sample. This work shows that slow (0.07 mm/s slip speeds) and fast (100 mm/s) contained slip events can occur on the same fault patch. We also present the systematic changes in radiated seismic waves both in time and frequency domain. The slow earthquakes are 100 ms in duration and radiate tremor‐like signals superposed onto a low‐frequency component of their ground motion. They are often preceded by slow slip (creep) and their seismic radiation has an ω−1 spectral shape, similar to slow earthquakes observed in nature. The fastest events have slip velocity, stress drop, and apparent stress (0.2 m/s, 0.4 MPa, and 1.2 kPa, respectively) similar to those of typical M −2.5 earthquakes, with a single distinct corner frequency and ω−2 spectral falloff at high frequencies, well fit by the Brune earthquake source model. The gap between slow and fast is filled with intermediate events with source spectra depleted near the corner frequency. This work shows that a fault patch of length p with conditions favorable to rupture can radiate in vastly different ways, based on small changes in where h* is a critical nucleation length scale. Such a mechanism can help explain atypical scaling observed for low‐frequency earthquakes that compose tectonic tremor.

Reflective metamaterial polarizer enabled by solid-immersion Lloyd's mirror interference lithography

Metamaterials with induced form birefringence arising from orderly arrangements of subwavelength structures can realize effective refractive indices that do not exist in nature. Using lithographically-defined thin film or multilayered metasurfaces, such form birefringence can be used for polarization and phase control in thin-film elements. In this work, the authors experimentally demonstrate a highly birefringent omnidirectional broadband reflective metamaterial polarizer (RMP), fabricated using a solid-immersion Lloyd's mirror interference lithography (SILMIL) technique. This technique can create 55 nm half-pitch gratings, up to 200 nm tall, using single 405 nm exposures. Angle-resolved reflection spectra of SILMIL-fabricated subwavelength dual-silver grating RMPs exhibit excellent omnidirectionality over a broad spectral bandwidth in the optical range. The behavior and mechanism of the double-layer RMP has been analyzed with finite-difference time domain and rigorous coupled wave analysis simulations, showing coupling between excited surface plasmon polaritons and multiple Fabry–Perot resonances. Furthermore, the authors propose via simulation that by switching from a dielectric resonator to a metallic resonator, the SILMIL technique can be used to fabricate dual-layer thin-film metamaterials that have the capability of phase retardation control, providing a new scheme for reflective thin-film waveplates.

A high-order multiscale finite-element method for time-domain elastic wave modeling in strongly heterogeneous media

Efficient and accurate numerical methods for elastic wave modeling in complex media have many important applications. However, it is fairly challenging to model elastic wave propagation in strongly heterogeneous media with high computational efficiency and high-order accuracy simultaneously. We develop a novel high-order multiscale finite-element method to model elastic wave propagation in strongly heterogeneous media in the time domain. The most important feature of our method is a generalization of standard multiscale finite element method by using high-order multiscale finite-element basis functions to capture the fine-scale heterogeneities on the coarse mesh, in contrast to conventional finite-element basis functions that are merely determined by the order of polynomials. These multiscale basis functions leads to a system matrix with significantly reduced dimension, thus enable us to solve the elastic wave equation on the coarse mesh with high-order accuracy and very low computational time cost. We use 2D and 3D numerical examples to demonstrate the superior efficiency and accuracy of our new modeling method compared with the conventional spectral-element method.

Viscoacoustic least-squares reverse time migration using a time-domain complex-valued wave equation

With limited recording apertures, finite-frequency source functions, and irregular subsurface illuminations, traditional imaging methods have been insufficient to produce satisfactory reflectivity images with high resolution and amplitude fidelity. This is because most traditional imaging approaches are commonly formulated as the adjoint instead of the inverse operator with respect to the forward-modeling operator. In addition, intrinsic attenuation introduces amplitude loss and phase dispersion during wave propagation. Without considering these effects, migrated images might be kinematically and dynamically incorrect. We have developed a viscoacoustic least-squares reverse time migration (LSRTM) method based on a time-domain complex-valued wave equation. According to the Born approximation, we first linearized the viscoacoustic wave equation and derived a demigration operator. Then, using the complex-valued Lagrange multiplier method, we derived the adjoint viscoacoustic wave equation and corresponding sensitivity kernel. With the forward and adjoint operators, a linear inverse problem is formulated to estimate the subsurface reflectivity model. A total-variation regularization scheme is introduced to enhance the robustness of our viscoacoustic LSRTM, and a diagonal Hessian is used as the preconditioner to accelerate the convergence. Three synthetic examples are used to demonstrate that our approach enables us to compensate attenuation effects, improve imaging resolution, and enhance amplitude fidelity in comparison with the adjoint imaging method.

A simple implementation of PML for second-order elastic wave equations

When modeling time-domain elastic wave propagation in an unbound space, the standard perfectly matched layer (PML) is straightforward for the first-order partial differential equations (PDEs); by contrast, the PML requires tremendous re-constructions of the governing equations in the second-order PDE form, which is however preferable, because of much less memory and time consumption. Therefore, it is imperative to explore a simple implementation of PML for the second-order system. In this work, we first systematically extend the first-order Nearly PML (NPML) technique into second-order systems, implemented by the spectral element and finite difference time-domain algorithms. It merits the following advantages: the simplicity in implementation, by keeping the second-order PDE-based governing equations exactly the same; the efficiency in computation, by introducing a set of auxiliary ordinary differential equations (ODEs). Mathematically, this PML technique effectively hybridizes the second-order PDEs and first-order ODEs, and locally attenuates outgoing waves, thus efficiently avoid either spatial or temporal global convolutions. Numerical experiments demonstrate that the NPML for the second-order PDE has an excellent absorbing performance for elastic, anelastic and anisotropic media in terms of the absorption accuracy, implementation complexity, and computation efficiency.

Explicit time integration with lumped mass matrix for enriched finite elements solution of time domain wave problems

We present a partition of unity finite element method for wave propagation problems in the time domain using an explicit time integration scheme. Plane wave enrichment functions are introduced at the finite elements nodes which allows for a coarse mesh at low order polynomial shape functions even at high wavenumbers. The initial condition is formulated as a Galerkin approximation in the enriched function space. We also show the possibility of lumping the mass matrix which is approximated as a block diagonal system. The proposed method, with and without lumping, is validated using three test cases and compared to an implicit time integration approach. The stability of the proposed approach against different factors such as the choice of wavenumber for the enrichment functions, the spatial discretization, the distortions in mesh elements or the timestep size, is tested in the numerical studies. The method performance is measured for the solution accuracy and the CPU processing times. The results show significant advantages for the proposed lumping approach which outperforms other considered approaches in terms of stability. Furthermore, the resulting block diagonal system only requires a fraction of the CPU time needed to solve the full system associated with the non-lumped approaches.