Two-layer Medium Research Articles

Investigation on THz EM Wave Scattering From Oil-Covered Sea Surface: Exploration for an Approach to Probe the Thickness of Oil Film

In this article, a theoretical study is carried out to seek an approach to remotely measure the thickness of the oil film. It is known that it is difficult to probe the oil thickness using a microwave radar due to the fact the dielectric constant of oil is very small compared with seawater for microwave frequencies. While in the range of terahertz (THz) electromagnetic (EM) wave frequency, the dielectric constants of oil and seawater are comparable, resulting in the THz EM fields scattered from the air–oil interface and those from the oil–water interface can produce constructive and destructive interference with the variation in the oil film thickness. Based on this principle, the sensitivity of the THz EM wave to the oil thickness is investigated in this work. First, the oil–seawater two-layer medium is equivalent to a single-layer medium by an equivalent dielectric constant model. Then, the THz EM scattering from the oil-covered sea surface is simulated using the first-order small slope approximation method (SSA-1) and the obtained equivalent dielectric constant. Meanwhile, the influences caused by the damping effect of the oil film, the reduction for friction velocity, and the change in equivalent permittivity on the normalized radar cross section (NRCS) are analyzed. The numerical results show that the NRCSs of THz frequencies are more sensitive to the change in oil thickness than that of microwave frequencies. This property makes the THz EM wave have the potential to probe the thickness of the oil film.

Service life of prestressed high-strength concrete pile in marine environment considering effects of concrete stratification and temperature

Prestressed high-strength concrete (PHC) piles have advantages of light weight and high load carrying capacity, which have been widely applied in coastal and offshore engineering. However, PHC piles serving in the coastal or offshore regions have already undergone severe durability problem. This paper presents a comprehensive method for predicting the service life of PHC piles in the marine environment, which reasonably takes the temperature effects and the concrete stratification caused by centrifugation of PHC piles into account. The pile service life is divided into the diffusion and corrosion periods. The service life of the diffusion period is predicted by solving the diffusion equation formulated for chloride ion diffusion in a two-layer ring medium, the results of which are compared with the data obtained from the elaborate experimental tests to examine the validity. The service life of the corrosion period is determined based on the ultimate corrosion expansion pressure produced by the accumulated corrosion products of steel bar. Various possible key factors, like protective cover thickness, initial chloride ion concentration, mortar layer thickness, etc., are considered to investigate how these parameters critically affect the pile service life. The results suggest that increasing mortar layer thickness can lead to a significant decrease of the service life in both diffusion and corrosion periods; and increasing protective cover thickness and sealing pile end are two effective ways to extend the service life of PHC piles.

Exponential convergence of Cartesian PML method for Maxwell’s equations in a two-layer medium

The perfectly matched layer (PML) method is extensively studied for scattering problems in homogeneous background media. However, rigorous studies on the PML method in layered media are very rare in the literature, particularly, for three-dimensional electromagnetic scattering problems. Cartesian PML method is favorable in numerical solutions since it is apt to deal with anisotropic scatterers and to construct finite element meshes. Its theories are more difficult than circular PML method due to anisotropic wave-absorbing materials. This paper presents a systematic study on the Cartesian PML method for three-dimensional electromagnetic scattering problem in a two-layer medium. We prove the well-posedness of the PML truncated problem and that the PML solution converges exponentially to the exact solution as either the material parameter or the thickness of PML increases. To the best of the authors’ knowledge, this is the first theoretical work on Cartesian PML method for Maxwell’s equations in layered media.

A logarithmic estimate for the inverse source scattering problem with attenuation in a two-layered medium

Abstract The paper aims a logarithmic stability estimate for the inverse source problem of the one-dimensional Helmholtz equation with attenuation factor in a two layer medium. We establish a stability by using multiple frequencies at the two end points of the domain which contains the compact support of the source functions.

Joint Inversion of DC Resistivity and Magnetic Data, Constrained by Cross Gradients, Compactness and Depth Weighting

In this paper we perform a 2-D joint inversion of DC resistivity and magnetic data, constrained by cross-gradients. Inspired by methods developed for potential fields, we introduce into both the separate and joint inversion algorithms also compactness and depth weighting functions, under the form of a model weighting-function. These constraints, usually not considered for DC resistivity inversion, reveal to be decisive for its joint inversion with magnetic data. A linear approximated forward problem of the resistivity is used for the joint inversion so that both the resistivity and magnetic problems are expressed as a linear integral equation under the form of a Fredholm integral of 1st kind. To examine the feasibility of the joint inversion algorithm, we first test the method with two synthetic cases: a thick dyke in a two-layered medium and a cavity located above a conductor. A third synthetic case involves a multisource model. The results are encouraging, revealing that the cross-gradient constraint is an effective tool to improve the separate inversions of DC resistivity and magnetic data. The joint inversion algorithm is also applied to data in the archeological area of the old Pompeii city, nearby Naples. Comparing the results of joint and separate inversions, we obtain a significant improvement in the interpretation of both kind of data in terms of buried walls of an ancient roman villa. In all the studied cases, the cross-gradient constraint appears to be a key-diagnostic tool to assess whether actual coherence is gained among DC resistivity and magnetic susceptibility models.

Numerical Simulation of the Plane Electromagnetic Wave Transient Propagation in Lossy Medium

In the field of geophysical exploration, it is of great value to study the transient propagation characteristics of electromagnetic waves in lossy medium. The equations of electric field and magnetic field are derived. The absorbing boundary conditions and numerical stability conditions are analyzed. The two-layer medium model is established to simulate the propagation characteristics of plane waves. The simulation results show that the transient analysis of electromagnetic wave propagation can reflect the time fluctuation characteristics of electromagnetic field in multilayer media, and provide the indication of the boundary position.

Modelling of dynamic processes in an elastic base with a heterogeneous coating

In this paper, we consider a mathematical model describing the dynamic properties of heterogeneous materials having a non-uniform layered structure in the form of a non-uniform elastic coating with a microstructure lying on an elastic base. The dispersion function for a two-layer composite medium is given, showing that the heterogeneous coating of an elastic half-space significantly changes the dynamics of the medium.

Effect of optical properties on radiative-conductive heat transfer in a system of two semitransparent layers

The paper offers a numerical simulation of the heat state for a two-layer semitransparent medium that imitates a hypothetical snow cover upon an opaque semi-infinite substrate; the layers of cover have different absorption and scattering coefficients. Computations were performed for key parameters typical of winter season. It was shown that, depending on the optical thickness of every layer and proportions of absorption to scattering in the incident radiation, we observe more intense heating of near-surface or deeper zones in the snow-ice medium. The radiation part of problem was solved using a modified average-flux method used to take into account the dependency of optical properties on the wavelength of incident radiation, scattering, and reflectance at the layers boundaries.

Chebyshev collocation spectral method for vector radiative transfer equation and its applications in two-layered media

The Chebyshev collocation spectral method (CCSM) is developed for solving the vector radiative transfer equation (VRTE) in participating media and then extended to polarized radiative transfer problems in two-layered media. The derivation of the CCSM discretization for the VRTE is presented and the numerical performance of the CCSM is investigated. The accuracy of the CCSM for solving the VRTE is first verified by comparing the CCSM solutions for the polarized radiative transfer in a plane-parallel medium with published results. Afterward, the CCSM is applied to polarized radiative transfer problems in inhomogeneous media, including two-layered media with different scattering characteristics and two-layered media with different refractive indices. Finally, taking both effects of different medium properties and reflective/refractive interface into account, we investigated the polarized radiative transfer in a realistic atmosphere-ocean system via the CCSM and discussed the distributions of the Stokes vector components. Results show that the CCSM is accurate and efficient for solving the VRTE and the distributions of Stokes vector for a realistic atmosphere-ocean system are presented in detail.

Методика прогноза напряженно-деформированного состояния крепи вертикального ствола на участке сопряжения с горизонтальной выработкой в соляных породах

The article proposes a method for predicting the stress-strain state of the vertical shaft lining in saliferous rocks at the drift landing section. The paper considers the development of geomechanical processes in the saliferous rock in the landing area, the support is viewed as a two-layer medium: the inner layer is concrete, the outer layer is compensation material. With this in view, the paper solves the problem of continuum mechanics in a spatial setting, taking into account the long-term deformation of salts and the compressibility of the compensation layer. Long-term deformation of saliferous rocks is described using the viscoplastic model of salt deformation into the numerical model, and the crushable foam model to simulate the deformation of the compensation layer. This approach considers all stages of the deformation of the compensation layer material and the development of long-term deformations of saliferous rocks, which makes it possible to increase the reliability of the forecast of the stress-strain state of the vertical shaft lining.

Dynamic responses of layered poroelastic ground under moving traffic loads considering effects of pavement roughness

This study aims to investigate the dynamic responses of layered poroelastic ground underlying rough pavement subjected to traffic loads. Particular attention has been given to the roles of the pavement roughness idealized as sinusoidal waves. The vehicle is simplified as a multi-rigid-body vibration system and the pavement roughness results in dynamic traffic loads in addition to the static component due to the vehicle weight. The pavement layer is modelled as a thin Kirchhoff plate, while the underlying base and the subgrade are treated as saturated two-layered poroelastic medium obeying Biot's dynamics theory. Frequency-wavenumber domain responses of the vehicle-pavement-underlying ground are solved by Fourier integral transform, transfer matrix method and considering stress and displacement compatibility conditions at the pavement-ground interface. The corresponding time-domain solution is numerically obtained from the inverse Fourier transform. Based on this semi-analytical solution, the influences of surface roughness, vehicle velocities and mechanical properties of pavement and base materials are discussed to provide practical guideline for the design of rough pavement system.

Unique determination of inverse electromagnetic scattering by a two-layered cavity

This paper is concerned with the inverse electromagnetic scattering by a two-layered medium in the non-magnetic case. We prove that both the electric permittivity and the conductivity can be uniquely recovered in an unknown annular domain by the internal wave-field measurements at one fixed frequency, if and are both assumed to be constant. Furthermore, we prove that the unknown annular domain can be also uniquely recovered using the same measurements. The method proposed in this paper essentially depends on the uniform a priori estimate for the scattered magnetic field in the sense when the incident fields are induced by a sequence of deformed electric dipoles. Another important ingredient for our method is to reconstruct well-defined PDE systems in a sufficiently small domain by using the solutions to the electromagnetic scattering problem in the two-layered cavity.

Frequency of Formation of Vapor Bubbles in a Two-Layer Medium of Magnetic and Nonmagnetic Liquid

A method for measuring the frequency of formation of vapor bubbles formation during the boiling of opaque liquids using a two-layer system (with opaque and transparent media) is proposed and implemented. An experimental device has been developed, and experiments have been carried out to determine the frequency of formation of vapor bubbles during the boiling of opaque liquids. The frequency of the formation of the vapor bubbles is measured in the boiling of a two-layer medium of magnetic and nonmagnetic liquids on a horizontal surface with a point heat source in a uniform external magnetic field. It has been found that with an increase in a uniform constant magnetic field, the frequency of the formation of vapor bubbles in the boiling of a two-layer medium of magnetic and nonmagnetic liquids on an unlimited horizontal plate decreases, whereas the temperature of the heat-releasing surface, at which the vaporization process begins, increases for the samples of magnetic liquids with a high magnetic phase content.

Inverse obstacle scattering for Maxwell’s equations in an unbounded structure

This paper is concerned with the electromagnetic scattering of a point source by a perfectly electrically conducting obstacle which is embedded in a two-layered lossy medium separated by an unbounded rough surface. Given a dipole point source, the direct problem is to determine the electromagnetic wave field for the given obstacle and unbounded rough surface; the inverse problem is to reconstruct simultaneously the obstacle and unbounded rough surface from the reflected and transmitted fields measured on a plane surface which is above and below the unknown objects, respectively. For the direct problem, its well-posedness is established and a new boundary integral equation is proposed. The analysis is based on the exponential decay of the dyadic Green function for Maxwell’s equations in a lossy medium. For the inverse problem, the global uniqueness is proved and a local stability is discussed. A crucial step in the proof of the stability is to obtain the existence and characterization of the domain derivative of the electric field with respect to the shape of the obstacle and unbounded rough surface.

On the propagation of nonlinear SH waves in a two-layered compressible elastic medium

We examine nonlinear shear horizontal (SH) waves in a two-layered medium of uniform thickness. Materials in both layers having different material properties are assumed to be nonlinear elastic, homogeneous, compressible and isotropic. Furthermore, $$c_1<c_2$$ is chosen where $$c_1$$ and $$c_2$$ are the linear shear wave velocities of the top and bottom layers, respectively. The propagation of SH waves in a two-layered medium exists only if either of the inequalities $$c_1<c< c_2$$ and $$c_1<c_2< c$$ is satisfied where c refers to the phase velocity of waves. The dispersion relations of linear SH waves corresponding to these phase inequalities are obtained. Then, the self-modulation of nonlinear SH waves is investigated by using an asymptotic perturbation method for each case. By balancing dispersion and weak nonlinearity, it is shown that the self-modulation of the first-order slowly varying amplitude of nonlinear SH waves is characterized asymptotically by nonlinear Shrodinger (NLS) equation. The form of NLS equations corresponding to each phase inequality is identical except their coefficients. Then, the effects of nonlinearity of the materials in layers on the linear stability of the solution of NLS equation and on the existence of solitary wave solutions are studied by employing several fictive material parameter models.

Three‐dimensional frequency‐domain optical anisotropy imaging of biological tissues with near‐infrared light

Near-infrared optical imaging aims to reconstruct the absorption and scattering coefficients in order to detect tumors at early stage. However, the reconstructions have only been limited to and due to theoretical and computational limitations. The authors propose an efficient method of the reconstruction, in three-dimensional geometries, of the anisotropy factor g of the Henyey-Greenstein phase function as a new optical imaging biomarker. The light propagation in biological tissues is accurately modeled by the radiative transfer equation (RTE) in the frequency-domain. The reconstruction algorithm is based on a gradient-based updating scheme. The adjoint method is used to efficiently compute the gradient of the objective function which represents the discrepancy between simulated and measured boundary data. A parallel implementation is carried out to reduce the computational time. We show that by illuminating only one surface of a tissue-like phantom, the algorithm is able to accurately reconstruct optical values and different shapes (spherical and cylindrical) that characterize small tumor-like inclusions. Numerical simulations show the robustness of the algorithm to reconstruct the anisotropy factor with different contrast levels, inclusion depths, initial guesses, heterogeneous background, noise levels, and two-layered medium. The crosstalk problem when reconstructing simultaneously and g has been reported and achieved with a reasonable quality. The proposed RTE-based reconstruction algorithm is robust to spatially retrieve and localize small tumoral inclusions. Heterogeneities in g-factor have been accurately reconstructed which makes the new algorithm a candidate of choice to image this factor as new intrinsic contrast biomarker for optical imaging.

Acoustic source localization in heterogeneous media

Acoustic source localization (ASL) or predicting the location of the acoustic source in a structure by analyzing the recorded signals at the receivers is of considerable interest for various applications. Recent research advances on this topic have been limited to homogeneous media. This paper presents a solution for acoustic source localization in a heterogeneous medium without knowing the properties of different materials constituting the heterogeneous structure.In this paper new developments for acoustic source localization in an anisotropic plate is first reviewed briefly. Then an ASL technique is presented for localizing acoustic source in heterogeneous layered structures when the layer properties are not known. The proposed technique is verified experimentally and numerically. The experimental results were generated with a specimen having one interface while numerical results were generated for both two-layered medium with one interface and three-layered medium with two interfaces.

Surface Magnetoacoustic Waves in Magnetostrictive Media

It is known that in absence of external magnetic field it is always possible to excite a surface Love wave in a two-layered medium, whose speed is less than the speed of transverse bulk waves in the substrate and greater than the speed of these bulk waves in the layer. This paper is devoted to the issues of existence and propagation of surface magnetoacoustic waves in layered magnetostrictive half-spaces. It is shown that besides the noted pure elastic waves, the new type of surface magnetoacoustic wave exists, which existence is exclusively conditioned by magnetostrictive properties of medium. It is established that the speed of this new wave can be less than the speed of transverse bulk waves in the layer. It is also established that the new wave propagates with dispersion.

The Frequency of Vapor Bubbles Formation in a Two-Layer Medium of Magnetic-Non-Magnetic Liquids

The Frequency of Vapor Bubbles Formation in a Two-Layer Medium of Magnetic-Non-Magnetic Liquids

Измерение степени полимеризации полимерных материалов изоляционной системы высоковольтного оборудования

The use of polymeric materials polymerization degree (PD) as a parameter from which the state of power equipment insulation system as a whole is estimated imparts much importance and significance to the PD measurement problem. The possibility of using the PD value as a parameter for estimating the state of power equipment items that have been in operation for a long time also attracts the attention of specialists. In this regard, practical methods for measuring the spectrum of dielectric absorption currents, which make it possible to monitor the polymeric material polarization degree, are of special interest. These methods are based on the theoretical concepts about the motion of a charged particle as a Stokes body in dielectric medium with specific viscosity ƞsp under the effect of a constantly applied electric field. To this end, the conductivity of a specially formed two-layer dielectric medium is monitored in the method being analyzed. One of these layers is a sample of the material being monitored, and the second one, which is in close contact with the first one, is a material the viscosity of which is known or can be easily measured using accessible methods, as in the case of a liquid dielectric. The proposed method for determining the PD of organic dielectric materials by measuring the spectrum of dielectric absorption currents is essentially a dielectric medium viscosity monitoring technique. It is exactly this parameter that governs the charged particle motion pattern in a dielectric and, hence, the characteristic features of the spectrum of dielectric absorption currents in the insulation gap being monitored. Owing to the clear physical principles laid down in the proposed method for estimating the polymerization degree, commercial availability of the equipment for its implementation, the availability of user-friendly software, and the simplicity of interpretation and analysis of the obtained results, the new method significantly extends the existing tools for assessing the insulation system state and determining the remained lifetime of operating power equipment.