Stratified Medium Research Articles

Study on electric field distribution of multi-layer dielectric under mixed voltage

The combination of field and circuit analysis method is used. Taking the multilayer flat dielectric structure as an example, the electric field distribution law of multilayer dielectric under mixing and polarity reversal voltage is studied by using the electromagnetic field theory. Then, according to the actual situation, two typical multilayer dielectric structures are selected, equivalent circuit model is established, and multilayer dielectric equivalent circuit experiment is carried out. At the same time, the equivalent circuit is simulated and analyzed by using the circuit simulation to further analyze the distribution law of electric field under various voltages. On this basis, the finite element simulation is used to simulate the double-layer plate dielectric structure model, which verifies the applicability of the finite element simulation method in the calculation of AC/DC hybrid electric field. Finally, the structural model of ±800kV converter outlet bushing is established, and the AC, DC, AC and DC superposition and polarity reversal voltage are loaded respectively. The electric field distribution in each medium of the complex insulation structure is calculated and analyzed accordingly. The results show that the finite element simulation method is simple and effective, and it is feasible to study the electric field distribution law and insulation structure optimization of the complex insulation structure under AC/DC mixed voltage. This paper studies E-field distribution law of multi-layer media under AC/DC mixed voltage, which has practical reference significance for the external insulation design of converter bushing, wall bushing and converter valve, and is of the great value for the actual DC power transmission and transformation project.

ELF-EM fields in the multi-layer spherical ‘Earth-ionosphere’ model based on WKB

Abstract With a high signal-to-noise ratio and a great depth of exploration, the wireless electromagnetic method (WEM) has wide applications in the exploration of deep mineral resources and oil and gas reservoirs. Extremely low-frequency electromagnetic (ELF) waves emitted from a horizontal antenna are used to achieve synchronous acquisition for different receivers of multi-coverage information in a global region. However, previous research based on a planar model ignored the curvature of the Earth. This work focuses on the electromagnetic fields (EM fields) in the model of a spherical ‘Earth ionosphere’ to extend the coverage of WEM. By transferring the EM fields from a vertical electric dipole (VED) as well as a vertical magnetic dipole (VMD) in the multi-layered medium of the Earth, we obtain the formulae for the EM fields emitted by a horizontal electric dipole (HED) by using a reciprocity theorem. The correctness of the proposed method is verified by comparing it with the approximate analytical formula and previous work. Based on the above results, we have studied the propagation and frequency characteristics of electromagnetic fields in a spherical waveguide consisting of the ionosphere and earth. The results show that the electromagnetic fields under the spherical model produce interference effects that are different from those of the planar model. The electromagnetic response of the layered Earth was then discussed, and its potential as an electromagnetic technique for exploring the deep Earth was demonstrated.

Design of shock wave attenuation effects on multi-impedance-matched laminated composites

To improve the protective performance of composite armor materials, three types of laminated composites with different arrangements were designed by the principle of impedance matching. The impedance combination schemes used in this work were high impedance→low impedance (type I), low impedance→high impedance (type II), and high and low impedance (type III). The microstructures and properties of the test samples prepared in a vacuum hot-pressing furnace were investigated by micro-indentation and dynamic impact experiments. According to the propagation theory of one-dimensional elastic waves in multilayered media, the propagation law of shock waves in the as-prepared laminated composites was examined. Micro-indentation test results revealed that the hardness of the Fe2Al5 intermetallic compound formed by the reaction of Al and 304 SS was the highest and ranged from 917.5 HV to 1026.3 HV. The type II layered composite had the highest compressive strength (1139 MPa) followed by the type I composite and the type III composite. The type III composite manifested the highest energy absorption efficiency (73%) followed by the type II layered composite and the type I composite.

Large-scale physically accurate modelling of real proton exchange membrane fuel cell with deep learning

Proton exchange membrane fuel cells, consuming hydrogen and oxygen to generate clean electricity and water, suffer acute liquid water challenges. Accurate liquid water modelling is inherently challenging due to the multi-phase, multi-component, reactive dynamics within multi-scale, multi-layered porous media. In addition, currently inadequate imaging and modelling capabilities are limiting simulations to small areas (<1 mm2) or simplified architectures. Herein, an advancement in water modelling is achieved using X-ray micro-computed tomography, deep learned super-resolution, multi-label segmentation, and direct multi-phase simulation. The resulting image is the most resolved domain (16 mm2 with 700 nm voxel resolution) and the largest direct multi-phase flow simulation of a fuel cell. This generalisable approach unveils multi-scale water clustering and transport mechanisms over large dry and flooded areas in the gas diffusion layer and flow fields, paving the way for next generation proton exchange membrane fuel cells with optimised structures and wettabilities.

An efficient and highly accurate singularity extraction method for the evaluation of transient potentials of stratified media

AbstractAn efficient and highly accurate method for extracting the singularity of scalar potential time‐domain Green's function (TDGF) of layered media is presented. The proposed method is based on the Taylor series expansion and is exploited in the finite‐difference (FD) technique. The presented method is accurate for the singularity behavior of the potential near the source. Also, the effect of singularity extraction box size on the calculation error of Green's functions is explained. Numerical results demonstrating the accuracy of the proposed singularity extraction method for calculating the TDGF of a PEC‐backed dielectric slab are presented. It is shown that the accuracy of the evaluated TDGF is improved by an order of magnitude using the proposed singularity extraction technique. Also, the effect of changing the spatial and temporal steps of the FD scheme on the calculation error is studied.

Mathematical modeling of seismic wave kinematics in complex media

A variational method of mathematical modeling of seismic wave kinematics has been developed at the Department of Seismometry and Geoacoustics of the Faculty of Geology of Lomonosov Moscow State University for studying the kinematics of seismic waves of different types in two-dimensional isotropic media (gradient and layered) is presented. The problem of determining the trajectories of seismic rays was solved by integrating using the Runge-Kutta method a system of differential equations with given initial conditions. The algorithm was studied in order to verify the accuracy and correctness of the solutions obtained, as well as its testing on a number of theoretical models of heterogeneous media. The developed ray tracing method was used to study the effect of the velocity gradient and the geometry of seismic boundaries on the kinematics of reflected waves in multilayer media. Based on the results of mathematical modeling of the kinematics of reflected waves, conclusions were drawn about the limits of applicability of simplified models of horizontally layered media, which often approximate complex inhomogeneous media.

Virtual double-slit differential dark-field chromatic line confocal imaging technology.

Chromatic line confocal imaging (LCI) can be used in high-speed 3D imaging of surface morphology, roughness, and multi-layered transparent media in industrial production, quality inspection, and other fields. However, even if they are compensated for or corrected accordingly, the resolution of the built measurement system differs from the theoretical design. In particular, to guarantee high-speed measurement characteristics of the LCI system, a mass center algorithm with poor accuracy is usually chosen for peak extraction, and with the improvement of the manufacturing level, the axial resolution of the measurement system also puts forward higher requirements. Therefore, in this Letter, we propose a virtual double-slit differential dark-field chromatic LCI (VDSDD-LCI) technology. Our approach can reconstruct the optical 3D profile with higher axial resolution and signal-to-noise ratio (SNR) by reducing the full width at half maximums (FWHMs) of the axial response curve without changing the components of the completed LCI system. The experiments on a coin and scrive board surface demonstrate the validity of the proposed method.

Scattering of a Plane Wave From a Wire Grid Parallel to the Interface Between Two Media

The problem of electromagnetic scattering by a grid of equidistant, mutually parallel, electrically thin wires located on a plane parallel to a flat interface between two dielectric media, one in which the grid is embedded, is solved under the formalism of dyadic Green’s functions. A number of variations of this problem have been dealt with in the literature, and also different analytical solutions have been used. In particular, the full analytical solution proposed here is put forward as an alternative to the long-standing, Hertz’s vector-based solution introduced by Wait. This formula is still the standard result for the case of thin wires that can be assumed to behave as current lines. However, Wait’s model has some limitations regarding its extension to the case of a stratified medium in front of the grid plane that are solved with the formalism proposed here. This new solution is tested against numerical simulations based on the finite element analysis or method (FEA or FEM) with a very high degree of agreement.

Shear wave velocity structure at the Fukushima forearc region based on H/V analysis of ambient noise recordings by ocean bottom seismometers

SUMMARYThis study presents the shear wave velocity (VS) structures of sedimentary sequences and a section of the upper crustal layer in the Fukushima forearc region of the Japan Trench subduction zone, which were obtained by analysing the horizontal-to-vertical (H/V) spectral ratios of ambient vibration records. The H/V curves were derived using 31 d of continuous seismic data from 3 broad-band and 16 short-period ocean bottom seismometer (OBS) stations. Using the broad-band data, H/V ratios from 0.01 to 10 Hz were derived, but the ratios below 0.1 Hz frequencies were unusually large and temporally unstable. Characterization of seismic noise energy from ∼1 yr of seismic data of three broad-band OBSs revealed variable and elevated energy conditions below 0.1 Hz due to typical long-period oceanic noise; we link these observations with the unstable H/V ratios below this frequency. Therefore, H/V analysis was performed in the frequency range of 0.1–10 Hz for both broad-band and short-period OBSs to obtain subsurface VS profiles. For the forward calculation of the H/V ratios in the inversion process, we used the recently developed ‘hvgeneralized’ method, which is based on the diffuse field assumption, and accounts for the water layer on top of stratified media. Moreover, available prior geological and geophysical information was utilized during the inversion of the H/V curves. We found that subsurface VS ranged from approximately 30 m s−1 at the seabed to approximately 4900 m s−1 at 7000 m below the sea floor (mbsf). Starting with the best model candidate at each OBS location, the effect of the water layer on the H/V curve in the deep ocean was investigated by comparing synthetic H/V curves with and without the water layer. The synthetic H/V analysis revealed that the water layer had a significant effect on H/V amplitudes at higher frequencies (&amp;gt;1 Hz), whereas comparatively little effect was observed at lower frequencies (&amp;lt;1 Hz). This study provides an empirical basis for H/V analysis using OBS data to determine VS down to several kilometres of sedimentary sequences to the upper crust with high-resolution.

Conversion of underwater concrete images to air in detection of hydraulic structures

Taking underwater concrete images with an optical camera is an important measure for underwater defect detection. However, the underwater low-light environment and light refraction on the surface of different media result in poor image quality. In order to make the collected underwater images effectively reflect the real situation of underwater concrete defects, we propose an image conversion algorithm combining underwater image color enhancement and refraction distortion correction, which can convert underwater images into aerial equivalent images. In this paper, two conversion models of underwater image to air conversion are proposed, one of which models the refractive distortion of the underwater multilayered media through the ray projection method to correct the refractive distortion of underwater images and image field of view (FOV) conversion. The other is that by analyzing the problem of low image-imaging quality and loss of edge information due to the uneven illumination environment underwater, we process the dark channel priority adaptive enhancement algorithm to improve underwater image quality. The experimental results from real scenes show that the imaging quality of underwater images is improved by converting underwater images to air. The pixel error of images converted into the air is ⩽1 pixel, and the FOV error of images is ⩽8.5%. The high-precision underwater image conversion provides strong support for subsequent underwater measurement.

Experimental modelling of hydraulic parameters for fluid flow in stratified porous media

From works in in-situ seepage through dams and laboratory experiments using Layered Heterogeneous Porous Media (LHPM), it has been noted that a refraction-like phenomenon, such as that experienced in light, affects fluids’ flowlines when crossing the contact interface of layers characterised by different porosity viz-a-viz permeability. This concept has many applications in fluid dynamics, such as the dispersion process in stratified media. Currently, no study exists that models and analyses the relationship between the porosities of two layers in contact and the resulting flowline refraction using validated LHPM data. Hence, this work aims to establish a relationship between the porosity ratio Φr of stratified media made up of two layers and the refraction angle θmax of the maximum volume flux qmax. Volume flux data from the flow of a single-phase fluid through five LHPMs with Φr ranging from 0.8325 to 0.9524 were used in the modelling. The flow was oriented from the lower to the higher porosity vis-à-vis permeability layer. It was found that θmax which is also the refraction angle of the peak solute plume flux, refracts away from the normal as Φr reduces. This indicates an increase in the dilution rate vis-à-vis spread of plumes with the reduction in homogeneity between the two layers. Also, θmax does not correlate with the stratification inclination α, but the qmax which is also the peak solute plume flux correlates with α. Furthermore, an efficient model, which is the best-unbiased estimator, with R2=0.99 was derived. Findings from this work can help better understand solute plume dispersion and the general fluid flow dynamics in stratified media such as capillary barrier effect covers for pollution control and hydrocarbon reservoirs.

Migration and redistribution of LNAPL in inclined stratified soil media

Leakage of light non-aqueous phase liquid (LNAPL) into soil can cause serious environmental issues. In this study, a two-dimensional device with adjustable dip angles was designed to investigate the migration and redistribution of LNAPL in natural inclined stratified soil media by the light transmission visualization (LTV) technology. The captured experimental images were processed to obtain the diesel distribution based on gray value which could represent the LNAPL saturation distribution. LNAPL may not be able to penetrate through the fine-coarse interface due to the capillary barrier effects. In this case, the vertical and horizontal migration distances (V and H), contaminated area (S), as well as deviation angle (γ) of centroid increased with the dip angle. Increasing the leakage amount to more than 30 mL would result in LNAPL breakthrough at the 10°-inclined interface, leading to much larger V, H, S, and γ than those at 10 mL, while 20-mL LNAPL failed to break through. In the latter case, a lower leakage rate than 10 mL/min would cause larger H and γ but similar V or S in the long term. This study could enrich the understanding of LNAPL contamination in vadose zone, providing reference for the prediction and treatment in realistic inclined contaminated sites.

Extended angular-spectrum modeling (EASM) of light energy transport in scattering media.

The exact modeling of light transport in scattering media is critical in biological imaging, free-space communication, and phosphor-converted lighting. Angular spectrum is proved to be a fast and effective approach to reconstructing the wavefront dynamics during the propagation in scattering media, however, finding it difficult in acquiring the wavefront and energy change simultaneously. Besides, conventional methods for energy tracing, such as the Monte Carlo method, are inefficient in speed and hard to simulate the wavefront change. Here, we propose an extended angular-spectrum modeling (EASM) approach using tenuous scattering approximate solutions to obtain a time-efficient and accurate method for reconstruction of energy and wavefront dynamics in various scattering media. The generality of our method is numerically simulated and experimentally verified with a set of scattering media with different properties. EASM has a time advantage under the guarantee of calculation accuracy, especially when calculating several thickness changes after the calculation model is established. Furthermore, multi-layered media can also be simulated by EASM with a good precision. The results suggest that EASM performs certain computations more efficiently than the conventional method and thus provides an effective and flexible calculation tool for scattering media.

The viscoacoustic Green's function for the Helmholtz equation in a velocity gradient interface model

SUMMARY In viscoacoustically stratified media where the density is constant, 3-D wave propagation in the frequency–radial wavenumber domain is governed by the Helmholtz equation. In the case that the model is a velocity gradient interface where the squared velocity in depth is represented by a smooth Heaviside function of the Fermi–Dirac distribution type, the Helmholtz equation for a point source at arbitrary location is shown to have analytical solution for the Green's function. The velocity depth profile, which is a modification of the Epstein profile which has been thoroughly studied in different branches of physics, is described by four parameters: the velocities at minus and plus infinity, the reference depth of the gradient interface, and its smoothness. The Helmholtz equation is first solved in a model where the point source is absent. The solution to the source-free equation has four unknown constants that must be determined. The radiation conditions at minus and plus infinity and two conditions on the Green's function at the source depth allow the constants to be found. The Green's function solution can be represented in two mathematically equivalent algebraic forms involving ordinary hypergeometric functions. The first form allows a numerically stable implementation over all wavenumber components. The second form allows a physical, intuitive interpretation and is expressed mathematically as the sum of two terms. Each of the terms contains the product of constant-velocity reference phase shift functions and hypergeometric functions which take the role to adjust the amplitude and phase shift calculated by the reference phase shift functions to account for the depth varying velocity profile. Inverse Fourier transforms take the Green's function from the frequency–wavenumber domain to the frequency–space domain or time–space domain. The Green's function solution is valid for any sharpness of the interface. Selected numerical results are presented for the 1-D and 2-D Helmholtz equation to demonstrate the influence of the velocity gradient zone on the wavefield. The 1-D solution in an acoustic model is compared in time domain to the classical finite-difference wave propagation solution. For the purpose of interpretation of seismograms, we model for comparison the wavefield response in a model of two half-spaces in welded contact. For brevity, the latter model is referenced as the HS model.

Turbulent heating in a stratified medium

ABSTRACT There is considerable evidence for widespread subsonic turbulence in galaxy clusters, most notably from Hitomi. Turbulence is often invoked to offset radiative losses in cluster cores, both by direct dissipation and by enabling turbulent heat diffusion. However, in a stratified medium, buoyancy forces oppose radial motions, making turbulence anisotropic. This can be quantified via the Froude number Fr, which decreases inward in clusters as stratification increases. We exploit analogies with MHD turbulence to show that wave–turbulence interactions increase cascade times and reduce dissipation rates ϵ ∝ Fr. Equivalently, for a given energy injection/dissipation rate ϵ, turbulent velocities u must be higher compared to Kolmogorov scalings. High-resolution hydrodynamic simulations show excellent agreement with the ϵ ∝ Fr scaling, which sets in for Fr ≲ 0.1. We also compare previously predicted scalings for the turbulent diffusion coefficient D ∝ Fr2 and find excellent agreement, for Fr ≲ 1. However, we find a different normalization, corresponding to stronger diffusive suppression by more than an order of magnitude. Our results imply that turbulent diffusion is more heavily suppressed by stratification, over a much wider radial range, than turbulent dissipation. Thus, the latter potentially dominates. Furthermore, this shift implies significantly higher turbulent velocities required to offset cooling, compared to previous models. These results are potentially relevant to turbulent metal diffusion in the galaxy groups and clusters (which is likewise suppressed), and to planetary atmospheres.

An efficient parametrized optical infrared thermography 3D finite element framework for computer vision applications

Matching infrared thermography (IRT) with deep learning-based computer vision has recently gained a lot of interest for automated defect assessment in materials. One of the remaining bottlenecks concerns the necessity of a large and diverse experimental and/or virtual training dataset in order to achieve a sufficiently generalizable computer vision algorithm. This paper presents a parametrized 3D finite element (FE) framework, implemented in Fortran90, for efficiently simulating optical infrared thermographic inspection of multi-layer anisotropic media and establishing large-scale virtual dataset with sufficient diversity. The interface element is introduced for the modelling of an imperfect thermal contact, allowing to simulate a variety of defect types. The flexibility of the interface element makes it possible to simulate delaminations with different thickness using the same discretized model. Validation is done for two benchmark cases which are representative for a fiber reinforced polymer laminate with delamination-like defects. In order to achieve true-to-nature thermographic simulation data, non-uniform heating conditions are adopted from experiment, and a stochastic morphology generator is introduced for modelling realistic irregular defect geometries. To demonstrate the added value of a large, diverse and true-to-nature virtual database for computer vision applications, a Faster-RCNN model was trained on a generated virtual dataset for the detection of delamination-like defects in fiber reinforced polymer laminates. Application of the trained Faster-RCNN on experimental thermographic data yields excellent inference results, illustrating the high generalization ability of the virtually trained object detector.

Stability of inverse random source scattering problems in a multi-layered medium

In this paper, stability results on the inverse random source scattering problems are shown for the one-dimensional Helmholtz equation in a multi-layered medium, where the source function is driven by a spatial Brownian motion. The statistical properties of the random source including expectation and variance are reconstructed from physically realizable measurements. By using multi-frequency data, the increasing stability for the inverse random source scattering problems can be achieved. More precisely, the stability estimate consists of a Lipschitz stability term and a logarithmically unstable term, and the latter logarithmic term decreases as the upper bound of the frequency grows, which makes the problem have an almost Lipschitz stability. The numerical results demonstrate that the better stability can be obtained by using more frequencies and realizations.

Stability of a one-dimensional inverse source scattering problem in a multi-layered medium

In this paper, a stability result on an inverse source scattering problem is shown for Helmholtz equation in a multi-layered medium. The stability estimate consists of a Lipschitz stability term for low frequencies and a logarithmically unstable term for high frequencies, based on the Green's function of the problem. Moreover, the logarithmic term decreases as the frequency grows, which indicates the stability is almost Lipschitz. This result demonstrates that increasing stability for inverse source scattering problems can be achieved by utilizing multi-frequency measurement data.

Nonconservative Cascades in a Shell Model of Turbulence

Developed turbulent flows in which the intervention of external forces is fundamentally important at scales where the inertial range should exist are quite common. Then the cascade processes are not conservative any more and, therefore, it is necessary to adequately describe the external forces acting in the whole range of scales. If the work of these forces has a power law scaling, then one can assume that the integral of motion changes and the preserving value becomes a quadratic quantity, which includes the dependence on the scale. We develop this idea within the framework of shell models of turbulence. We show that, in terms of nonconservative cascades, one can describe various situations, including (as a particular case) the Obukhov – Bolgiano scaling proposed for turbulence in a stratified medium and for helical turbulence with a helicity injection distributed along the spectrum.

Anomalous response of a stratified medium to volume heat release

A linear stationary problem of the response of a semi-bounded stably stratified fluid/gaseous medium to volumetric spatially inhomogeneous heat release in the Boussinesq approximation is theoretically investigated. The most important similarity parameters are the analogue of the Rayleigh number and the aspect ratio of the source of buoyancy. For a perturbation in the form of a single horizontal harmonic, an analytical solution has been found that makes it possible to analyze a number of significant regularities. The nontrivial possibility of an intense hydrothermodynamic response to a weak heat release at a certain ratio of the mentioned parameters is found. Keywords: stratified medium, volume heat release, convection, density flows, analytical solution, intense response, instability.