Inhomogeneous Research Articles

Improving the shear resistance of ground technological quarry roads on loosely-bound subgrades

The study aims to solve the urgent problem of strengthening the subgrade of roads for heavy-duty vehicles. In the case of a limited road service life, it appears economically unfeasible to provide a strong cement-concrete subgrade. This case requires a solution maximizing the use of both local materials and production wastes, available in the work area. In order to perform calculations of stresses, arising at a great depth in the subgrade of the technological road under the influence of heavy-duty vehicle wheels, it is necessary to use appropriate mathematical models. In the present study, the calculations were carried out using a software application that implements the method of discrete elements. Using this method, stresses in highly inhomogeneous granular media can be calculated using the first[1]principle approach. The design of road structural layers suggests the use of geocontainers, made of used polypropylene big bags at the subgrade, which, due to their large size, have a greater shear resistance when filled with any soil mixture. The durability of the polypropylene fabric in the roadbed can reach several decades. The main task of the study was to calculate the protective layer of alternated crushed stone, clay soil, and polypropylene fabric. The thickness of layers was selected such that the tensile stresses during the passage of vehicles on the surface of a geocontainer remain within the strength limits of the container shell material.

Trajectory and Phase Shift Optimization for RIS-Equipped UAV in FSO Communications with Atmospheric and Pointing Error Loss

This paper proposes a new framework for reconfigurable intelligent surface (RIS)-equipped unmanned aerial vehicles (UAVs) in free-space optical (FSO) communication. To ensure practicality, we consider atmospheric loss caused by fog, which leads to an inhomogeneous medium for laser propagation. In addition, we incorporate the pointing error loss caused by the power fraction on the photodetector (PD) into the system and derive a closed-form expression for the elliptical beam footprint in the pointing error loss. We then propose a leading angle assisted particle swarm optimization (PSO) method to efficiently optimize the numerical results of pointing error loss. Furthermore, after obtaining these numerical results as a precondition, the UAV trajectory is optimized using the proximal policy optimization (PPO) method to achieve the maximum average capacity. Numerical simulations demonstrate that the proposed optimization method achieves greater efficiency and accuracy compared to the decode-and-forward (DF) relay and deep Q-learning (DQN) methods.

Mapping capabilities of geometric EM induction sounding in southern Yakutia permafrost

The purpose of the article is to consider the possibilities of the geophysical method in solving the problem of quantitative estimation of the strength of sedimentary rocks that form the basis of engineering structures at the Kyurgellakh station of the Amur-Yakutsk Railway located 572 km away from the town of Neryungri, which is an administrative center of southern Yakutia (Russia). The problem is solved using the method of geometric electromagnetic induction sounding and a new technique that explored the attenuation of the harmonic field induced by a vertical magnetic dipole in the inhomogeneous anisotropic geological medium at the frequencies of 1.125 and 0.281 MHz in the intermediate separation zone of 5–100 m. A comparative analysis has determined a good agreement in changes of geological and geophysical estimates of the average strength of laboratory water-saturated samples and sedimentary rock mass predicted in the same state at the comparable depth of 6–12 m. The measure of agreement when using the most adequate equation of the power function is high and equals 0.815 according to the normalized coefficient of multiple determination. This means that strength is the most important factor among the frozen ground characteristics affecting the electromagnetic field attenuation at the frequencies and spacing specified, contributing no less than 80 %. The tested geophysical method can thus correctly map the distribution boundaries of different strength sedimentary rocks. The crushed and fissured rocks with the strengths below 40–35 MPa are confined to the tectonic fractures of varying directions with a polygon-like structure. Geophysical data clearly delineate the structure at the depths of 12.3–27.5 m where predominate the rocks with high strengths (50–120 MPa). The geometric EM induction sounding is recommended to use at all stages of geotechnical investigations to map the development areas of southern Yakutia by rock strength classes.

Uniform decay rate estimates for the 2D wave equation posed in an inhomogeneous medium with exponential growth source term, locally distributed nonlinear dissipation, and dynamic Cauchy–Ventcel–type boundary conditions

AbstractWe study the wellposedness and stabilization for a Cauchy–Ventcel problem in an inhomogeneous medium with dynamic boundary conditions subject to a exponential growth source term and a nonlinear damping distributed around a neighborhood ω of the boundary according to the geometric control condition. We, in particular, generalize substantially the work due to Almeida et al. (Commun. Contemp. Math. 23 (2021), no. 03, 1950072), in what concerns an exponential growth for source term instead of a polynomial one. We give a proof based on the truncation of a equivalent problem and passage to the limit in order to obtain in one shot, the energy identity as well as the observability inequality, which are the essential ingredients to obtain uniform decay rates of the energy. We show that the energy of the equivalent problem goes uniformly to zero, for all initial data of finite energy taken in bounded sets of finite energy phase space. One advantage of our proof is that the decay rate is independent of the nonlinearity.

Numerical study of the development of premixed flame interface induced by shock wave: A parameterization study of inhomogeneity of medium and chemical reaction

The evolution of a perturbed flame interface induced by shock waves occurs frequently in natural phenomena and in engineering applications. In practice, spatial inhomogeneity can exist and have a significant impact on the interface development in the real world. On the other hand, the effect of the chemical reaction on the flame interface evolution is still not clear. Therefore, in the present study, the evolution of a novel configuration of interaction between a planar premixed flame interface and a straight incident shock wave in inhomogeneous medium is studied numerically by solving the two-dimensional, time-dependent, reactive, and compressible Navier–Stokes equations with a high-order numerical scheme. A series of numerical cases are designed such that the amplitude of density perturbation σ, representing the effect of medium inhomogeneity, and the activation energy Ea, representing the effect of chemical reaction, can be varied independently. The result shows a unique dual-spike structure of flame interface during the interaction in inhomogeneous medium, which is different from the conventional spike–bubble structure during the interaction in homogeneous medium. For the range of σ and Ea considered, when Ea is fixed, σ is found to appreciably affect the growth of mixing zone area on the flame interface. This is because larger σ leads to stronger vortices and subsequently results in a nonlinear growth rate in the area of mixing zone. In contrast, when σ is fixed, the impact of Ea on the growth of mixing zone area on the flame interface is mainly manifested as the local consumption of reactants and changes of the flame thickness. Similarly, a high reactivity (small Ea) results in a nonlinear growth rate of the mixing zone area. Finally, for the cases in the range in which the growth rate of mixing zone area is linear, an empirically mathematic model, involved in activation energy (Ea) and inhomogeneity (σ) as independent variables, is proposed to reasonably predict the growth rate of mixing zone area in the reactive and inhomogeneous medium.

Optical generation and detection of GHz longitudinal and transverse acoustic waves in solids assisted by two-dimensional metallic grating structure

Absorption of laser pulses with picosecond temporal width in a two-dimensional nano-scale metallic grating deposited on a transparent substrate launches both longitudinal and transverse acoustic waves in to the sample. The periodic metallic structure makes the generated acoustic waves propagate several different directions. The propagating acoustic waves are monitored optically by the delayed light pulses (probe light) as the transient reflectivity change which is known as the Brillouin oscillation. The probe light is also diffracted by the metallic grating, allowing the detection of the acoustic waves propagating in the multiple directions efficiently. The analysis of the Brillouin oscillation frequencies brings the longitudinal and transverse sound velocities and the optical refractive index simultaneously from a single measurement. We verify the above mentioned scheme using a sample with two-dimensional square lattice (period 380 nm) of aluminum square islands of lateral dimension 200 × 200 nm2 and thickness of 50 nm on a fused silica substrate of thickness 1 mm. From the obtained Brillouin oscillation frequencies in several tens GHz, the acoustic and optical properties of the substrate material are successfully retrieved. The technique would be applicable to investigate the acoustic and optical properties of more complicated systems, such as anisotropic and/or inhomogeneous medium.

Sound Pressure Field Reconstruction for Airborne Ultrasound Tactile Display Encountering Obstacles.

Airborne ultrasound tactile display (AUTD) is used to provide non-contact tactile sensations with specific foci sound fields through the optimization of transducer phases. However, most existing optimization approaches are not directly applicable in case of an inhomogeneous medium, such as in the presence of obstacles between the AUTD and objective sound field. Certain methods can perform optimizations by considering the sound-scattering surfaces of the obstacles to compute the transmission matrix, which requires several complex measurements. This study proposed two methods to reconstruct the sound field under an inhomogeneous medium, wherein the need to calculate the impact of the obstacles was eliminated. The two methods are Bayesian optimization and greedy algorithm with brute-force search. Further, the process of the foci field generation was assumed as a black box. The proposed methods require only the pressure intensity at the control point generated by the input phases, discarding the need for transmission matrix in the presence of obstacles. Moreover, these methods offer the advantage of optimization of the phases in the presence of obstacles. This study explains the working of proposed methods in different forms of foci fields encountering obstacles.

Determination of the bone tissue mechanical properties by a numerical-digital method using CT data

Modeling of elements of inhomogeneous media is an actual direction in the study of composite materials and biomechanics objects. The need for research is determined by the insufficient development of methods for describing mechanical parameters, taking into account the anisotropy of materials. In this case, one of the directions is the use of digital prototyping and numerical modeling methods. In the field of biomechanics, the applicability of approaches to numerical modeling based on image data correlates with cases of clinical practice, which is due to the peculiarities of non-destructive testing methods and allows obtaining results that affect the quality of treatment. The paper considers a method for restoring effective mechanical properties of a material based on computational and field experiments. The simulation was based on the finite element method and assumed the use of data from a digital prototype obtained by computed tomography. The restoration of the calculated area was performed by filtering the initial grid relative to the proportion of the content of the material. The presented method makes it possible to restore the effective values of the elastic modulus and tangential modules based on the relationship established within the framework of the approach between the mechanical properties of the material and the loading parameters of the model sample. In the course of the work, the bone organs of pigs were modeled. Animal husbandry and experimental procedures were carried out in compliance with bioethical norms. Physical tests and numerical modeling were carried out under the conditions of bending action. Validation of the obtained distribution of values of the stress-strain state was performed according to the data of full-scale experiments. The presented solution showed a weak dependence of the results (less than 1 %) relative to the degree of discretization of the computational domain, which made it possible to perform calculations using fewer finite elements, avoiding the use of resource-intensive methods to restore the geometry of the sample. The results obtained in the framework of the work correspond to the literature data and determine the true values, the use of which in calculations makes it possible to assess the strength of the elements of an inhomogeneous structure under the action of external loads, taking into account the spatial distribution of the material.

Численное решение двумерной задачи определения скорости распространения сейсмических волн в неоднородных cредах с памятью

The numerical method for two-dimensional inverse dynamic seismic problem for a viscoelastic isotropic medium is presented. The system of differential equations of elasticity for isotropic medium of memory type is considered as a mathematical model. The unknown values are the displacement, the memory function of the medium (the kernel of the integral term) and the propagation velocity of elastic waves in a weakly horizontally inhomogeneous medium. Additional information for the inverse problem is the response displacement measured on the surface. The method is based on reducing the inverse problem to a system of Volterra-type integral equations and their sequential numerical implementation. The results of the study are analyzed and compared with the analytical solution. It is shown that the results are in satisfactory agreement.

Scattering and Attenuation in 5G Electromagnetic Propagation (5 GHz and 25 GHz) in the Presence of Rainfall: A Numerical Study

Rainfall has always been a concern for wireless communications systems. As 5G technology relies on high-frequency bands, it is fundamental to model and simulate the interaction of such radio waves with rainfall, as the deployment of large-scale infrastructure for 5G is highly expensive. This research presents a reformulation of the Maxwell equations for a bi-dimensional space in a transverse electric propagation mode, for a linear, inhomogeneous, and isotropic propagation medium with its magnetic and electric properties dependent on time. This reformulation was solved using the Finite Differences in Time Domain (FDTD) method with the Convolutional Perfectly Matched Layer (CPML) boundary condition. Two main frequency propagation scenarios were studied: 5 GHz (corresponding to Wi-Fi in the 802.11n standard as well as to the lowest bands of 5G) and 25 GHz (corresponding to 5G), within a 10m×3m rectangular domain in air and with rain. The rainfall was simulated using a parallel Ziggurat algorithm. According to the findings, while 5 GHz waves experience scattering processes, 25 GHz waves experience substantial dispersion and attenuation throughout the domain in low- to moderate-intensity rain.

Velocity model calibration for surface microseismic monitoring based on a 3D gently inclined layered equivalent model

Abstract Shale gas has become a major source of natural gas production and has received worldwide attention. Hydraulic fracturing is widely performed to stimulate oil and gas wells with considerable success. Given high-precision microseismic (MS) event locations, we can predict the development trend and region of fracturing and evaluate the stimulation effect, thereby providing technical guidance for subsequent exploitation. An accurate velocity model is essential for MS event positioning. However, simple velocity models, such as the uniform or vertical transverse isotropy (VTI) velocity model, are generally applied to calibrate the velocity model. Despite calibration, the VTI model may still face challenges in obtaining accurate MS event locations. Based on the structural characteristics of shale, we propose a novel local velocity model calibration algorithm for surface MS monitoring. To calibrate the velocity model, the actual strata interfaces are replaced with 3D gently inclined planes. We use very fast simulated annealing to concurrently tune the velocity, depth, and angle parameters of the model. Through the assessment of both the stacked amplitude at the position of the perforation shot and the relocation error of the perforation shot, we determine the ideal velocity model. To evaluate the effectiveness of our approach, we conduct experiments on both a synthetic model and a field dataset, and statistically analyze the location error. The results show that the proposed method obviously reduces the perforation shot relocation error and is well-suited for calibrating velocity models that are close to slightly inhomogeneous layered media.

Nonlinear forced response of doubly-curved laminated panels composed of cnt patterned layers within first order shear deformation theory

In this study, the solution of the nonlinear forced vibration (NFV) problem of double curvature panels consisting of inhomogeneous (INH) nanocomposite (NC) layers is discussed within first order shear deformation theory (FSDT), taking into account the viscous damping effect. First, the mechanical properties of laminated double curvature panels composed of carbon nanotube patterned layers are modeled mathematically. Then, based on FSDT with a von Kármán-type nonlinearity derived the nonlinear basic relationships and partial differential equations (PDEs). The expression for the NFV frequency of multilayer panels made of inhomogeneous nanocomposite layers (INHNCLs) is obtained within FSDT, using the multi-scale method to the nonlinear PDEs for the first time. Finally, the influences of the external excitation, nonlinearity, transverse shear strains, number and arrangement of layers and CNT-models on the forced vibration frequencies are studied in detail.

Vectorial EM Propagation Governed by the 3D Stochastic Maxwell Vector Wave Equation in Stratified Layers

The modeling and processing of vectorial electromagnetic (EM) waves in inhomogeneous media are important problems in physics and engineering, and new methods need to be developed to incorporate novel vector sensor technology. Vectorial phenomena of EM waves in stratified atmospheric layers can be incorporated into governing equations by retaining the gradient of the refractive index when deriving the Maxwell Vector Wave Equation (MVWE) from Maxwell’s equations. The MVWE, as opposed to the scalar wave, Helmholtz, and paraxial equations, couples the EM field components in inhomogeneous media and thus captures important physics phenomena such as depolarization. Here, recent developments are reviewed on using sensor time series data to reconstruct electromagnetic waves that propagate through stratified media. In modern applications, often many sensors can be deployed simultaneously to observe electromagnetic waves. These networks of sensors can be used to improve the quality of the reconstructed EM wave fields and cross-validate the observed sensor time series. Lastly, the effects of noisy current densities on sensor time series are considered. Generally, as the sensor observes for longer periods of time, the variance of estimates of the wave field obtained from sensor time series data increases. As a result, longer sensor observation times do not always result in better estimates of the EM wave fields, and an optimal observation time can be obtained.

An adaptive finite-difference method for seismic traveltime modeling based on 3D eikonal equation

3D eikonal equation is a partial differential equation for the calculation of first-arrival traveltimes and has been widely applied in many scopes such as ray tracing, source localization, reflection migration, seismic monitoring and tomographic imaging. In recent years, many advanced methods have been developed to solve the 3D eikonal equation in heterogeneous media. However, there are still challenges for the stable and accurate calculation of first-arrival traveltimes in 3D strongly inhomogeneous media. In this paper, we propose an adaptive finite-difference (AFD) method to numerically solve the 3D eikonal equation. The novel method makes full use of the advantages of different local operators characterizing different seismic wave types to calculate factors and traveltimes, and then the most accurate factor and traveltime are adaptively selected for the convergent updating based on the Fermat principle. Combined with global fast sweeping describing seismic waves propagating along eight directions in 3D media, our novel method can achieve the robust calculation of first-arrival traveltimes with high precision at grid points either near source point or far away from source point even in a velocity model with large and sharp contrasts. Several numerical examples show the good performance of the AFD method, which will be beneficial to many scientific applications.

Toward the theory of semi-linear Beltrami equations

We study the semi-linear Beltrami equation $\omega_{\bar{z}}-\mu(z) \omega_z=\sigma(z)q(\omega(z))$ and show that it is closely related to the corresponding semi-linear equation of the form ${\rm div} A(z)\nabla\,U(z)=G(z) Q(U(z)).$ Applying the theory of completely continuous operators by Ahlfors-Bers and Leray-Schauder, we prove existence of regular solutions both to the semi-linear Beltrami equation and to the given above semi-linear equation in the divergent form, see Theorems 1.1 and 5.2. We also derive their representation through solutions of the semi-linear Vekua type equations and generalized analytic functions with sources. Finally, we apply Theorem 5.2 for several model equations describing physical phenomena in anisotropic and inhomogeneous media.

Lattice Boltzmann method for radiative transfer in two-layered slab with graded-index and Fresnel reflecting surfaces

Analysis of transport of radiative transfer in an inhomogeneous two-layered slab with graded refractive indices and bounded by Fresnel's reflecting walls is carried out using the lattice Boltzmann method. The radiative intensity in each layer is found as a superposition of two radiative waves, which undergo multiple reflections and refractions at the boundaries and interface. The accuracy and efficiency of the methodology is first tested for steady-state problems with constant or variable refractive indices and for time-resolved reflectance and transmittance in a single layer with graded-index. The effect of the governing parameters is examined and the results show that these parameters significantly influence radiative transfer. Especially, the curvature of the incoming beam due to refractive index variation changes when considering the increasing or decreasing variation of the refractive index. The smaller refractive index gap at the interface induces smaller reflection and radiative intensity discontinuity at the interface, while increasing the scattering albedo has no significant effect on the transmittance signal but corresponds to increasing the reflectance signal which takes more time to show the steady state profile. Moreover, the developed LBM is an efficient, powerful, and accurate solver for radiative transport in inhomogeneous layered media with graded-index.

Evaluation of low magnetic field magnetocapacitance effect in Ni–NiO inhomogeneous medium

Evaluation of low magnetic field magnetocapacitance effect in Ni–NiO inhomogeneous medium

Controlling the thermal and electric fields in isotropic and anisotropic media

In this study, we theoretically propose cloaking and concentration devices allowing simultaneous control of electric and thermal fields in spherically inhomogeneous layered medium with isotropic and anisotropic layers. The above combination of layers (isotropic and anisotropic ones) is obtained by the transformation coordinate approach applied to a spherically inhomogeneous layered medium which contains isotropic and anisotropic layers. It is shown that in steady-state conditions, both thermal and electric fields can pass smoothly around the targeted area while preventing any disturbance in the surrounding medium. The constitutive parameters of both fields have been determined analytically. In this work, we have combined two different methodologies to achieve cloaking in ideal state and in homogenized structure for cylindrical and spherical cases. Numerical validation of the obtained solutions using COMSOL software is performed in this study.

Hyperbolic Conduction and Radiation Heat Transfer in Axisymmetric Cylinders with Variable Properties

This work investigates the combined mode of hyperbolic heat conduction and radiation transfer in a one-dimensional axisymmetric cylinder filled with absorbing, emitting, and scattering media. The volumetric radiation is investigated thanks to the semianalytic solution of the matrix formulation of the spherical harmonics equations PN. The governing hyperbolic energy equation is solved using the finite volume method (FVM) with Roe’s correction of interface fluxes in order to enhance the performances of the method, and the lattice Boltzmann method (LBM) has been designed for comparisons. The effects of the parameters such as constant and spatial-dependent scattering albedos, temperature-dependent thermal conductivity, heat-generated sources, extinction, and the conduction–radiation parameter on both the temperature and heat flux distributions for steady and transient states within the medium are examined. The results of the present work are in excellent agreement with those available in the literature. The PN−FVM results are also compared to those obtained with the PN−LBM combination, and excellent agreement is obtained. These results show that the mentioned parameters have a significant effect on both the temperature profiles and the hyperbolic sharp wave front. This study also shows that the proposed layered approach is an efficient, fast, and accurate solution method for radiative analysis in inhomogeneous media, whereas the Roe’s correction of interface fluxes in the FVM is suitable to accommodate a thermal wave front in non-Fourier analysis.

Uniqueness of refractive indices and transmission coefficients by an inhomogeneous medium in acoustic scattering

Abstract We are concerned with the inverse scattering problem of recovering the refractive indices and transmission coefficients by the corresponding acoustic far-field measurement encoded into the scattering amplitude. Our first uniqueness result is to determine a constant refractive index by the fixed incident direction scattering amplitude, the proof of which is mainly based on the discreteness of the corresponding interior transmission eigenvalues. Then motivated by the previous work (Xiang & Yan 2021), the second uniqueness result is established to recover a piecewise constant refractive index from the far-field pattern at a fixed frequency.