Two-layer Medium Research Articles

Imaging a two-layered conductive medium by a modified factorization method

In this paper, we consider the inverse acoustic scattering problem of determining a two-layered inhomogeneous medium with a conductive transmission condition from far-field measurements. The well-posedness of the direct problem can be established by applying a variational method. For the inverse problem, we shall develop a modified factorization method for recovering the shape and location of the two-layered conductive medium. Finally, we provide some numerical experiments to demonstrate the practicability of the inversion algorithms.

An upscaling model for simulation of geothermal processes in stratified formations

In stratified porous media, non-uniform velocity between layers combined with thermal conduction across layers causes spreading of the thermal front: thermal Taylor dispersion. Conventional upscaling not accounting for this heterogeneity within simulation grid blocks underestimates thermal dispersion, leading to overestimation of thermal breakthrough time. We derive a model for effective longitudinal thermal diffusivity in the direction of flow, αeff, to represent the effective thermal dispersion in two-layer media. αeff, accounting for thermal Taylor dispersion, is much greater than the thermal diffusivity of the rock itself. We define a dimensionless number, NTC, a ratio of times for longitudinal convection to transverse conduction, as an indicator of transverse thermal equilibration of the system during cold- or hot-water injection. For NTC > 5, thermal dispersion in the two-layer system closely approximates a single layer with αeff. This suggests a two-layer medium satisfying NTC > 5 can be combined into a single layer with an effective longitudinal thermal diffusivity αeff. In application to a geothermal reservoir, one can apply the model to perform upscaling in stages, i.e. combining two layers satisfying the NTC criterion in each stage. The αeff model accounting for the fine-scale heterogeneity within simulation grid blocks would enhance the prediction accuracy of thermal breakthrough time and thus thermal lifetime.

Uniform Far-Field Asymptotics of the Two-Layered Green Function in Two Dimensions and Application to Wave Scattering in a Two-Layered Medium

Uniform Far-Field Asymptotics of the Two-Layered Green Function in Two Dimensions and Application to Wave Scattering in a Two-Layered Medium

Retrieval of sea ice thickness using FY-3E/GNOS-II data

Sea ice, a significant component in polar regions, plays a crucial role in climate change through its varying conditions. In Global Navigation Satellite System-Reflectometry (GNSS-R) studies, the observed surface reflectivity Γ serves as a tool to examine the physical characteristics of sea ice covers. This facilitates the large-scale estimation of first-year ice thickness using a two-layer sea ice-seawater medium model. However, it is important to note that when Sea Ice Thickness (SIT) becomes thicker, the accuracy of SIT retrieval via this two-layer model begins to decline. In this paper, we present a novel application of a spaceborne GNSS-R technique to retrieve SIT based on a three-layer model using the data from Fengyun-3E (FY-3E). Soil Moisture Ocean Salinity (SMOS) data are treated as the reference. The performance of the proposed three-layer model is evaluated against a previously established two-layer model for SIT retrieval. The analysis used the sea ice data from 2022 and 2023 with SITs less than 1.1 m. By comparing the retrieved SITs against reference values, the three-layer model achieved a Root Mean Square Error (RMSE) of 0.149 m and Correlation Coefficient (r) of 0.830, while the two-layer model reported the RMSE of 0.162 m and r value of 0.789. A scheme incorporating both models yielded superior results than either individual model, with the RMSE of 0.137 m and r reaching up to 0.852. This study is the first application of FY-3E for GNSS-R SIT retrieval, combining the advantages of a two-layer model and a three-layer model and extending the precision of GNSS-R retrieval for SIT to within 1.1 m. This provides a good reference for the future studies on GNSS-R SIT retrieval.

On the dynamics of aligned inertial particles settling in a quiescent, stratified two-layer medium

On the dynamics of aligned inertial particles settling in a quiescent, stratified two-layer medium

Stefan flow-inclusive mass transfer in a narrow cylindrical channel with a two-layer medium

The exploration and extraction of oil, coal, and gas reserves are closely tied to mass transfer phenomena within porous and fractured rock formations. Frequently, these processes involve the adsorption or desorption, dissolution, or evaporation of certain components on the surface of the pore channels. In these cases, Stefan hydrodynamic flows arise, and although they may be individually small, they can have a noticeable impact on mass transfer and flow structure considering particular length of the channel. The authors explore the issue of inert component diffusion from the surface of a capillary into a suspension flow. The analysis involves a two-layer flow, including a central two-phase (liquid and particles) component and a near-wall flow of the fluid carrier. A certain component from the channel’s surface permeates deep into the flow without interacting with the solid phase. In this research the authors solve a diffusion problem with boundary conditions that consider the presence of Stefan hydrodynamic flows. The calculations reveal that, depending on the magnitude of the Stefan flows and the length of the affected area, the porosity, and consequently, the viscosity of the two-phase flow zone can undergo significant variations.

Numerical Analysis of the Ultimate Bearing Capacity of Strip Footing Constructed on Sand-over-Clay Sediment

This paper analyzes the bearing capacity of two-layered soil medium using finite element (FE) software ABAQUS/CAE 2023. Although geotechnical engineers design foundations for layered soil, majorly current geotechnical studies emphasize single homogenous soil. So, this research has significant novelty as it focuses on layered soil and adds to the current literature. A nonlinear FE model was prepared and analyzed to determine the ultimate bearing capacity of two-layered soil (sandy soil over clayey soil). The Drucker–Prager and Mohr–Coulomb models were used to represent sandy soil and clayey soil layers, respectively. Strip footing material properties were considered isotropic and linearly elastic. This study performed parametric studies to understand the effects of thickness, unit weight, and the modulus of the elasticity of sandy soil on the ultimate soil bearing capacity. Additionally, it also analyzed the effect of the cohesive strength of clayey soil on layered soil bearing capacity. Results showed that an increase in sandy soil layer thickness strengthens the layered soil, and thus, improves the bearing capacity of soil. Increasing the sandy soil layer thickness over footing width (h1/B) ratio from 0.15 to 2.0 improved the ultimate bearing capacities with elastic settlements of 350 mm and 250 mm by 145.62% and 101.66%, respectively. Additionally, for a thicker sandy soil layer, an increase in the unit weight and modulus of the elasticity of sandy soil led to higher ultimate bearing capacity. Furthermore, it was concluded that an increase in clayey soil’s cohesive strength from 20 kPa to 30 kPa resulted in a 24.31% and 3.47% increase in soil bearing capacity for h1/B = 0.15 and h1/B = 2.0, respectively. So, the effect of cohesion is prevalent in the case of a thicker clayey soil layer.

Numerical Analysis of Unsteady Vibrations of a Plate Resting on an Elastic Isotropic Half-Space

The paper is devoted to the numerical solution of the problem of vibrations of an infinite elastic plate resting on an elastic isotropic half-space using the analytical method based on the ray method with its numerical realization via the Maplesoft package. Unsteady oscillations are caused by the action of instantaneous loads on the plate, resulting in the appearance of two plane wave surfaces of strong discontinuity in the elastic half-space, behind the fronts of which, up to the contact boundary, the solution is constructed using ray series. The unknown functions entering the coefficients of the ray series and the equation of plate motion are determined from the boundary conditions of the contact interaction between the plate and the half-space. Previously, the approximate solution of this problem was obtained analytically without using mathematical packages, and the dynamic deflection of the plate involving only the first three terms of the ray series was written down. In this work, a two-layer medium with different properties was investigated using an algorithm developed to solve contact dynamic problems related to the occurrence and propagation of strong and weak discontinuity surfaces.

Mine seismic source location via forward modeling of spherical waves in a multilayered horizontal or inclined medium

Seismic source location is a classic inverse problem in seismology. In mathematical physics, inverse problems have multiple natural solutions. The objective of this study was to develop a generic theory and method of seeking the true solution from multiple solutions for the location of a coal mine seismic source in an idealized velocity structure model of a coal mine with a small scale and complex geological environment. Starting from the simplest velocity structure model, the complexity of the model gradually increased, until it approached the real velocity structure model, i.e., the multilayered horizontal and inclined velocity structure model, in order to find a generic method for solving the multi-solution inverse problem of coal mine seismic source location. Specifically, the wavefront distribution equation in a two-layer horizontal medium was derived and then expanded to any multi-layer horizontal medium. Based on this equation, a positive definite nonlinear equation system was established from the perspective of any observation system. The equation system contained four unknown variables of the spatiotemporal position of the seismic source. To determine the spatiotemporal parameters of the seismic source, nonlinear equations for four stations were required. To solve the nonlinear equation system, an initial iteration value was determined. In order to reduce the difficulty of determining the initial iteration value, the variable substitution method was used to reduce the number of location parameters. By rotating the original geodetic coordinate system of the station to be parallel and orthogonal to the medium interface, the wavefront method was extended to inclined medium. In conclusion, in this study, the problem of coal mine seismic source location in a multi-layer horizontal or inclined medium was effectively solved. The method proposed in this study provides a reference for solving the true solution from multiple solutions for the location of a coal mine seismic source in small-scale coal mines with complex geological environments.

A multiparameter mathematical model for the problem of nonlinear filtration of fluids in two-layer media

In the realm of fluid dynamics and porous media, the nonlinear filtration of fluids in two-layer media presents a complex and intriguing challenge that demands a comprehensive mathematical framework for accurate representation and analysis. This paper introduces a multiparameter mathematical model designed to elucidate the intricacies of fluid filtration in heterogeneous environments, specifically focusing on two-layer media. The authors research the construction of a multiparameter mathematical model and numerical solution of nonlinear problems of the theory of filtration of unstructured and structured fluids in hydrodynamically connected multilayer formations with different characteristics. The developed models and solution algorithms were tested on hypothetical data.

Statistics of maximum photon penetration depth in a two-layer diffusive medium.

We present numerical results for the probability density function f(z) and for the mean value of photon maximum penetration depth ‹zmax› in a two-layer diffusive medium. Both time domain and continuous wave regime are considered with several combinations of the optical properties (absorption coefficient, reduced scattering coefficient) of the two layers, and with different geometrical configurations (source detector distance, thickness of the upper layer). Practical considerations on the design of time domain and continuous wave systems are derived. The methods and the results are of interest for many research fields such as biomedical optics and advanced microscopy.

Experimental investigation of the mutual influence of micro- and macroscale processes on the displacement of viscous oil by water in a two-layer porous medium

This paper presents the results of an experimental and theoretical study of the immissible displacement of high-viscosity model oil from the two-layer porous medium with different layers permeability. The experiments were performed using cylindrical model of the porous medium having the ratio of transverse size to length D/L equals to 0.05 and ratio of layers permeability equals to 0.46 during forced imbibition and drainage. It is shown that the alignment of a displacement front in the layers is caused by macroscale capillarity-driven flow arising from the curvature of the front. The conditions for stabilized motion of the displacement front for this case are determined using the analytical model and proved using experimental data on the recovery of displaced fluid. Microscale processes in pore level caused by the influence of the capillary forces are taken into account throw the relative phase permeability and capillary pressure curves.

Electromagnetic wave scattering by an elastic body in a two-layered medium

Electromagnetic wave scattering by an elastic body in a two-layered medium

Stability for the inverse source problem in a two-layered medium separated by rough interface

Stability for the inverse source problem in a two-layered medium separated by rough interface

Effect of the Cross-Section of a Porous Burner on the Combustion Stability Limit of Premixed Oxy-Methane Flames.

This study presents the idea of using a porous media burner to improve the oxy-methane combustion reaction rate and broaden the stability limit. Numerical studies on the premixed combustion of CH4/O2/CO2 in a two-layer porous medium burner using a two-dimensional symmetrical volume-average model with the skeleton mechanism based on OpenFOAM. The combustion characteristics of burners with variable cross-sectional (VC) and straight cylindrical (SC) structures were compared, including stable range, temperature field, thermal cycle efficiency, and CO emissions. It is confirmed that the cross-sectional structure is effective for broadening the stable range, and the broadening rate is more than 4 times. As more heat is lost from the outlet due to the increased cross-section, the solid-phase temperature of VC is lower than that of SC. As a result, the flame temperature of VC will be about 200 K lower than that of SC under the condition of insulated walls. It also leads to a reduction of about 2% in thermal cycle efficiency compared with SC. Meanwhile, it is shown that the VC structure slightly increases CO emissions at low thermal power but is smaller than that of SC at high power. When the wall heat loss of the burner is considered, the VC structure is still effective for improving the stable range. In addition, the VC structure slightly affects flame tilt and temperature uniformity at the burner outlet when the thermal power is large. It is confirmed that the VC structure is effective for increasing the power adjustment range and reducing pollutant emissions at high power.

Experimental Assessment of the Impact of Sonication Parameters on Necrotic Lesions Induced in Tissues by HIFU Ablative Device for Preclinical Studies

We have designed and built ultrasound imaging-guided HIFU ablative device for preclinical studies on small animals. Before this device is used to treat animals, ex vivo tissue studies were necessary to determine the location and extent of necrotic lesions created inside tissue samples by HIFU beams depending on their acoustic properties. This will allow to plan the beam movement trajectory and the distance and time intervals between exposures leading to necrosis covering the entire treated volume without damaging the surrounding tissues. This is crucial for therapy safety. The objective of this study was to assess the impact of sonication parameters on the size of necrotic lesions formed by HIFU beams generated by 64-mm bowl-shaped transducer used, operating at 1.08 MHz or 3.21 MHz. Multiple necrotic lesions were created in pork loin samples at 12.6-mm depth below tissue surface during 3-s exposure to HIFU beams with fixed duty-cycle and varied pulse-duration or fixed pulse-duration and varied duty-cycle, propagated in two-layer media: water-tissue. After exposures, the necrotic lesions were visualized using magnetic resonance imaging and optical imaging (photos) after sectioning the samples. Quantitative analysis of the obtained results allowed to select the optimal sonication and beam movement parameters to support planning of effective therapy.

Simple and accurate model of diffuse reflectance for two-layer medium mimics brain tissues based on diffusion approximation

Simple and accurate model of diffuse reflectance for two-layer medium mimics brain tissues based on diffusion approximation

Analytical solution for the single scattered radiance of two-layered turbid media in the spatial frequency domain, Part 1: Scalar radiative transfer equation

In this paper analytical solutions to the radiative transport equation are derived for the angular resolved single scattered radiance in a semi-infinite turbid medium having depth dependent optical properties. Explicit formulas are given for a two-layered turbid medium. A difference in the refractive index between the surrounding non-scattering medium and the two-layered medium is considered. The result displays a linear relationship between the phase functions of both layers and the radiance. In order to verify the results, the Monte Carlo method is used to compare calculations for varying configurations of the medium and phase functions. For all cases, the analytical solution and the Monte Carlo simulations show excellent agreement with one another.

A diffuse interface–lattice Boltzmann model for conjugate heat transfer with imperfect interface

A diffuse interface-lattice Boltzmann model is proposed for modeling conjugate heat transfer problems with imperfect interfaces. According to the continuity condition of heat flux and jump condition of temperature across the imperfect interface, a unified sharp interface equation of the temperature field with a singular source term in the composite media domain is established. Then a diffuse interface equation is obtained by making a smoothed approximation of the unified sharp interface equation. The novel diffuse interface equation is restructured into a second-order heat diffusion equation with an anisotropic diffusion coefficient tensor. To numerically solve the second-order anisotropic diffusion equation, a multiple-relaxation-time (MRT) lattice Boltzmann (LB) scheme is employed. Several numerical simulations of benchmark test examples with analytical solutions are carried out to demonstrate the accuracy of the present model, including the steady-state heat diffusion in a two-layer medium with a flat interface, steady heat diffusion in a square domain with a curved interface and unsteady-state temperature diffusion with two-layer media. The numerical results show that the phenomenon of temperature jump across the imperfect interface can be successfully and correctly captured. Moreover, as an example of practical application, the new proposed diffuse interface model is utilized to predict the effective thermal conductivity of porous media with thermal contact resistance at pore scale. The variation law of the effective thermal conductivity is obtained for each parameter by studying the effects of thermal conductivity ratios of the dual-component material, the shape and volume fraction of blocks in the material, the interfacial thermal conductance coefficient, and the number of blocks on the effective thermal conductivity. Both uniform and random pore structures are considered. The previous theoretical equations strongly support the validity of the present model.

PROPAGATION OF MECHANIC WAVE IN TWO-DIMENSION STRATIFIED MEDIUM

The principle of emergence encourages us to look for new properties in future materials as a result of structuring of constituent elements, and mostly we are talking about non-obvious structuring. For example, understanding and simulating isotropy is on the way to robustness against internal vibrations. Structurality itself is a characteristic feature of the world around a person (protein molecules, crystal lattices, etc.). However, the variety of natural structures is so numerous that directly studying them to identify new properties appears to be quite a difficult task. Therefore, to a certain extent, the principle of emergence supposedly contrasts the need to copy or imitate natural structures with the ability to carry out inventions. Just as a wide variety of patterns are formed in an optical kaleidoscope thanks to 2 or 3 optical elements, the principle of emergence gives reason to expect that as a result of structuring only a few components of the future environment, new properties can be obtained. The development of technology, in particular, 3D printing, opens up opportunities to look at the methodology of structuring the environment in a new way. If, in addition, this process is relatively economic, then empirically, by carrying out structuring, it is possible to obtain experimental laboratory samples. Today they are talking about the possibility of achieving such effects as lensing of mechanical waves precisely thanks to emergent properties. The corresponding devices promise to find application, for example, in ultrasound diagnostics in medicine (Assoc. Prof. J. Memoli, University of Sussex, UK). The paper considers the problem of the propagation of mechanical waves in a folding periodic two-layer medium - a flat model. For such a medium, a wave equation is written and solved by the method of separation of variables. Such an equation turns out to be a linear differential equation with periodic piecewise-stable coefficients. From the basic theory of differential equations with periodic coefficients (Floquet theory), the method of transfer matrices (a method for calculating the passage of waves through multilayer media) is well known, which makes it possible to obtain a composite condition for the solvability of the wave equation. The work develops an approach to obtaining solvability conditions (constructing a dispersion equation) along with the classical method of transfer matrices. The proposed approach is in a certain sense equivalent to the transfer matrix method, however, it has some remarkable differences, in particular, it provides a rigorous mathematical basis for the transition to media with a finite number of layers.