Asymptotic stepwise coupled modes for horizontally-variable acoustic media

The role of blocking dynamics and current on wave scattering due to finite floating elastic plate

P-wave reflection and transmission coefficients for non-welded interface play crucial roles in broad practical engineering productions, involving fracture properties prediction and seismic inversion. However, the existing reflection coefficient equations for non-welded interface in elasto-plastic media are seldom studied, although the elasto-plastic deformation is frequently encountered in the Earth’s subsurface due to artificial and tectonic activities. In this study, we proposed the accurate reflection and transmission coefficients equation for a non-welded interface embedded in an elasto-plastic deformed medium based on the elasto-plastic acoustoelastic and linear-slip theory. In detail, this paper uses elasto-plastic acoustoelastic theory to derive the reflection and transmission coefficients equation. The reflection and transmission coefficients matrix are solved using the linear-slip theory as the boundary condition. Moreover, we use the hardening parameter and plastic deformation to represent the plastic properties of the rock, which is a function of stress and plastic deformation. Through Numerical analysis, the deformation caused by static stress has significantly changed the amplitude and the slope of the reflection and transmission coefficients amplitude. As the stress increases, the rock’s velocity becomes higher, and all reflection and transmission coefficients (i.e., RPP, RPS, TPP, TPS) abruptly change at the critical angle. Furthermore, with the increase in plastic deformation, the critical angle of the incident P-wave and the hardening parameter becomes larger than the unstressed state. The non-welded interface exhibits a low-pass frequency filter for reflected SV-waves and a high-pass frequency filter for reflected P-waves and transmitted P and SV waves. In addition, we can observe that static vertical stress can weaken the anomalous reflections caused by non-welded formations, but the effect is insignificant. On the other hand, the effect of fracture normal compliance to reflection and transmission is detailly investigated. When N<2.5*10-10(MPa-1), The non-welded interface is close to the welded interface, while N>2.5*10-5(MPa-1), the non-welded interface is close to the solid-air interface.

The results of measurement and monitoring of reflection and transmission properties of cement-based specimens (blocks of mortar, concrete) during long time of their service lives, including hydration process, and different curing conditions at microwave frequencies (X-band) are presented. A simple and inexpensive measurement system that utilizes the nondestructive and contactless free space method is used. Dependencies of the reflection and transmission coefficients on water-to-cement ratio, preparing and curing conditions of the specimens are demonstrated. It is shown that the reflection coefficient is approximately stable after hydration process while the transmission coefficient changes during long time of the specimen's service life. The complex dielectric permittivity of the cement-based materials is calculated by a new method using only the amplitudes of the reflection and transmission coefficients. The expected applications of the results are discussed.

The variations of reflection and transmission coefficients, as well as of the fluorescence response of the arterial wall are studied as a function of temperature. In a first experiment, reflection coefficient, transmission coefficient, and temperature, are measured during laser irradiation of the tissue. The fluorescence spectrum is recorded in a second experiment, together with temperature, during heating of the arterial wall in a vapor bath. The temperature dependence of the optical parameters and of the fluorescence response are then deduced. For the reflection and transmission coefficients, a direct correlation of their variations with temperature is measured. Extrema are observed in the temperature region at about 50°C. A global decrease of the fluorescence intensity is characteristic of a temperature increase. These variations can be used as thermal markers, which in turn could give a criterion to control heat deposition in the tissue during laser anastomose.

Plane-wave reflection and transmission coefficients were calculated for a porous viscoelastic seabed with arbitrary pore-size distributions based on a previously developed theory [Yamamoto and Turgut, J. Acoust. Soc. Am. 83, 1744–1751 (1988)]. A sensitivity analysis indicated that, for a fixed permeability value, arbitrary pore-size distribution seems to broaden the frequency dependency of plane-wave reflection and transmission coefficients. Assuming a single pore-size Biot model, performance of global optimization inversion algorithms was investigated using the synthetic chirp signals reflected form a porous seabed with an arbitrary pore-size distribution. Inversion of porosity, shear modulus, and permeability was primarily attempted by assigning representative values to other Biot parameters which have secondary effects on the plane-wave reflection coefficient within their physical bounds. Perfect agreement was obtained between inverted and true values of porosity and shear modulus. However, estimated permeability values were always smaller than true permeabilty values due to the assumption of single pore size.

The nature of acoustic contrast, i.e. the connection of the amplitude and phase of the output signal of the acoustic microscope with the local values of the acoustic parameters of the sample (density, elasticity, viscosity) is a central problem of acoustic microscopy. Two approaches have become established to the analysis of formation of the output signal of the microscope. In one of these approaches (C. Quate, 1978; A. Atalar, 1979; H. Wikramasinghe, 1979) the converging beam is regarded as an ensemble of plane waves and its interaction with the sample is described by the methods of Fourier optics. The output signal is expressed in an integral manner through the coefficient of reflection at the immersion liquid-sample interface (reflection mode) or through the coefficient of transmission through the sample (transmission mode). The coefficients of reflection and transmission carry the basic information concerning the acoustic properties of the sample. Such an approach provides a possibility of constructing a strict quantitative theory of output signal formation for objects with plane boundaries. Mathematical difficulties confine the applicability of this approach, in the main, to numerical calculations. The ray approach (R. Wilson and R. Weglein, 1984; W. Parmon and G. Bertoni, 1979), based on geometrical optics, appears to be descriptive. Within the framework of this approach the focused beam as an ensemble of rays interacting with the object. The incident rays are reflected and refracted on the object boundaries in the usual manner some of the rays, falling on the interface at definite angles, excite side waves in the sample; outflowing surface waves or waveguide modes (of Sezawa or Lamb type), etc. Propagating along the surface of the sample, such waves are re-radiated again in-to the immersion liquid and participate in the formation of the output signal of the microscope.

SUMMARY The reflection and transmission of elastic waves are of great significance for predicting reservoir physical properties, interpreting seismic data and detecting crustal structures. Most studies only consider the initial vertical stress state when studying the reflection and transmission of elastic waves at imperfectly bonded interfaces, but few studies consider the influence of initial stress on boundary conditions. Moreover, the effect of initial stress on the energy distribution of elastic waves at imperfectly bonded interfaces has rarely been investigated. We propose a unified method to calculate the energy reflection and transmission coefficients for different incident waves at welded or imperfectly bonded interfaces in stressed media. The effects of initial stress on the equation of motion, the elastic properties of the medium and the boundary conditions at the interface are considered. The elastic properties of rocks under initial stress are described by acoustoelasticity theory. In addition, we define a new stress tensor to modify the linear-slip model for describing boundary conditions at the imperfectly bonded interface in the presence of initial stress. Numerical results show that the energy reflection and transmission coefficients at the non-welded interface in stressed media depend on the elastic properties of the incident and transmitted media, the initial stress, the type and magnitude of the interfacial compliance and the frequency and propagation direction of the incident wave. The initial vertical and horizontal stresses dominate the reflection and transmission coefficients at small and large angles, respectively. The discontinuity in displacement across the imperfectly bonded boundary results in the frequency dependence of the reflection and transmission coefficients. Imperfect bonding enhances P-wave and SV-wave energy reflection and weakens P-wave energy transmission. However, imperfect bonding can enhance the energy transmission of the SV wave for the imperfectly bonded interface with high contrast between tangential and normal compliance and a resonance peak appears at a specific frequency. We also notice that imperfectly bonded interfaces with interfacial compliance less than $1.0 \times {10}^{ - 11}$ m Pa−1 can be regarded as welded interfaces in the seismic frequency band (lower than 100 Hz). In addition, the initial stress greatly influences the reflection coefficients at high frequencies and the transmission coefficients at low frequencies. The initial vertical stress can reduce the energy transmission of SV waves at imperfectly bonded interfaces. In contrast, the initial horizontal stress can significantly increase the energy transmission of low-frequency SV waves and may lead to the disappearance of the resonant peak in the transmission coefficients.

The tunneling effect is a phenomenon of the behavior of particles with small energy having a probability to penetrate the barrier potential. The transmission coefficient is the ratio of breakthrough particles to incoming particles. The reflection coefficient is the ratio of reflected particles to incoming particles. The tunneling effect is analyzed using the Schrodinger equation with the matrix propagation method. The purpose of this study is to analyze the relationship between the distance barriers with the transmission coefficient and the reflection coefficient. The barriers used are GaAs and GaAs with potential energy of 1,424 eV with a bandgap of 0.565 nm. The researcher used 1 eV with a distance between barriers 0.25-2 nm with a change in the distance between barriers is 0.25 nm. Changes in the distance between barriers GaAs and GaAs affect the value of the transmission coefficient and the reflection coefficient. Changes in the distance between the barrier produce a transmission coefficient and a reflection coefficient that is periodic because the distance between the barriers has the form of complex exponential functions. This research application is used to design and develop new structures in improving the quality of semiconductor devices such as diodes, transistors, and IC.

The microwave magnetoresistance of CoFe/Cu/CoFe/FeMn spin valves and CoFe/Cu/CoFe three-layer nanostructures with high magnetoresistance has been studied. The transmission and reflection coefficients were measured at the frequency range from 26 to 38 GHz in magnetic fields up to 12 kOe. It is shown that the dependences of the transmission coefficient of spin valves are not symmetric with respect to the H = 0 axis, as well as the dependences of magnetoresistance. It is established that the relative changes in the microwave transmission coefficient are 1.5–2 times higher than the relative magnetoresistance measured at direct current. Changes in the reflection coefficient have a smaller value and the opposite sign with respect to changes in the transmission coefficient.

This paper presents the theoretical development of the covariance between reflection and transmission coefficients caused by system loads in electric grids. This result allows the calculation of the expected value and covariance of the channel response; these parameters can be used as design criteria in telecommunication networks over power lines in in-home environments. Additionally, the product of these variables is encountered commonly in the channel transfer function, whereby it can be determined if the calculation of these parameters can be simplified when this product is on a given path. For this purpose, the random behavior of the channel response caused by human activity is represented by a multipath model with a stochastic addition, where the reflection coefficient is treated as a random complex variable, providing more information compared to the real field.

Diffraction of water waves by a small cylindrical elevation of the bottom of a laterally unbounded ocean covered by an ice sheet is investigated by the perturbation analysis. The ice sheet is modelled as a thin elastic plate. The reflection and transmission coefficients are evaluated up to the first order in terms of integrals involving the shape function representing the bottom elevation. Three particular forms of the shape function are considered for which explicit expressions for these coefficients are obtained. For the particular case of a patch of sinusoidal undulations at the bottom, the reflection coefficient up to first order is found to be an oscillatory function of the ratio of the wavelength of the bottom undulations and that of the incident wave train. When this ratio approaches 0.5, the reflection coefficient becomes a multiple of the number of undulations and high reflection of the incident wave energy occurs if this number is large. Reflection coefficient is depicted graphically to visualize the effect of the presence of ice-cover and the number of undulations.

The transmission and reflection coefficients of electromagnetic waves propagating through the finite periodically layered chiral structure are defined both theoretically (using the propagation matrix method) and experimentally. The coefficients of the propagation matrix of the periodically layered chiral medium are obtained. The boundaries of the forbidden bands for a periodic medium, whose unit cell consists of two different chiral layers were determined. It is shown that the boundaries of the forbidden bands do not depend on the chirality parameter of the layers. It is found that for certain values of the layers thicknesses, the forbidden band widths tend to zero and that the proposed method for calculation of the reflection and transmission coefficients can be used to determine the effective constitutive parameters of artificial chiral metamaterials. The transmission and reflection coefficients of plane electromagnetic waves propagated through the finite periodically layered chiral structure were determined experimentally for 20-40 GHz range. A good agreement between the experimental results and theoretical studies of the forbidden band spectrum for the structure under research has been shown.

Photonic crystal and split ring resonator (SRR) metamaterial waveguides with Kerr nonlinear dielectric impurities are studied. The transmission coefficients for two guided modes of different frequencies scattering from the Kerr impurities are computed. The systems are shown to exhibit multiple transmission coefficient solutions arising from the Kerr nonlinearity. Multiple transmission coefficients occur when different input intensities into a waveguide result in the same transmitted output intensities past its nonlinear impurities. (In the case of a single incident guided mode the multiplicity of transmission coefficients is known as optical bistability.) The analytical conditions under which the transmission coefficients are single and multiple valued are determined, and specific examples of both single and multiple valued transmission coefficient scattering are presented. Both photonic crystal and split ring resonator systems are studied as the Kerr nonlinearity enters the photonic crystal and SRR systems in different ways. This allows for an interesting comparison of the differences in behaviors of these two types of system which are described by distinctly different mathematical structures. Both the photonic crystal and SRR models used in the calculations are based on a difference equation approach to the system dynamics. The difference equation approach has been extensively employed in previous papers to model the basic properties of these systems. The paper is a continuation of work on the optical bistability of single guided modes interacting with Kerr impurities in photonic crystals originally considered by McGurn [Chaos 13, 754 (2003)] and work on the resonant scattering from Kerr impurities in photonic crystal waveguides considered by McGurn [J. Phys.: Condens. Matter 16, S5243 (2004)]. It generalizes this work making the extension to the more complex interaction of two guided modes at different frequencies. It extends the two guided mode treatment by McGurn [Organ. Electron. 8, 227 (2007)] which was limited to a special case of one of the photonic crystal systems considered here.

The global incidence of cancer-related diseases and mortality continues to rise, making early and accurate diagnosis crucial for effective treatment. A key step in cancer treatment is the identification and removal of tumorous tissue, which is subsequently analyzed through pathological examinations. However, traditional pathology reports can take several weeks or even months to be processed. To expedite diagnosis, this study employs microwave measurement techniques to distinguish between healthy and cancerous colon tissue samples. The free-space measurement method is selected due to its suitability for evaluating sensitive pathological tissues. Measurements are conducted across 201 points within the 18-26 GHz frequency range, capturing the scattering parameters of various tissue types. Based on these measurements, four distinct datasets are created, incorporating features such as reflection coefficients, transmission coefficients, and frequency values. Three widely used classification algorithms-k-nearest neighbors (KNNs), artificial neural networks (ANNs), and Support Vector Machines (SVMs)-are evaluated for their performance on these datasets. The highest classification accuracy is achieved using the KNN algorithm on the dataset containing both reflection and transmission coefficients, along with measurement frequency. Bioelectromagnetics. 00:00-00, 2025. © 2025 © 2025 Bioelectromagnetics Society.

Flexural gravity wave scattering by two semi-infinite non-identical ice sheets, which are separated by a clean water surface, is investigated in the presence of a step bottom topography. The problem is investigated in the cases of (i) intermediate water depth and (ii) shallow water. The effect of two edge conditions, (i) simply supported edge and (ii) free edge, on wave scattering is also analyzed. Employing linear velocity potential theory, the problem is studied in the frequency domain. The physical phenomenon is modeled as a boundary value problem having the Laplace equation as the governing equation, and it is solved using the eigenfunction expansion method. Considering the bottom topography and upper boundary, the fluid domain is divided into three regions, and in each region, velocity potential is expressed in terms of infinite Fourier series. Velocity and pressure are matched at the intermediate surface of two regions, and a system of algebraic equations with unknown coefficients is obtained. The complete solution of the present problem is recognized by solving the system of equations numerically. The energy relation is derived using Green's theorem. The reflection and transmission coefficients are computed and compared with the energy relation to check the accuracy of the present method. For different parameters (depth ratio, clean waterway, and different ice properties), reflection coefficient and transmission coefficient are computed and presented as a function of angular frequency. The value of the reflection coefficient ranges from zero to unity, whereas at certain frequencies, the transmission coefficient attends value more than unity.