Layered Media Research Articles

Mathematical models for determining and analyzing thermal regimes in mining industry mechanism structures

Purpose. To develop linear and nonlinear mathematical models of heat conduction for isotropic heterogeneous media with internal heating. This will allow for an increased accuracy in determining temperature fields, which will subsequently impact the effectiveness of designing mechanisms, devices, and individual components of structures that have a layered structure and are subjected to heat stress. Methodology. For the development of linear and nonlinear mathematical models of the temperature field and the analysis of temperature regimes in layered media with internal thermal heating, the coefficient of thermal conductivity is described as a whole using asymmetric unit functions. This makes it possible to solve a differential equation with singular coefficients in both linear and nonlinear boundary value problems of heat conduction with appropriate boundary conditions. Findings. Quadratic equations are obtained to determine the analytical solutions of linear and nonlinear boundary problems of heat conduction for a layered plate with internal heat load. Originality. The scientific novelty lies in the given method of linearization of the nonlinear mathematical model of heat conduction and obtaining analytical solutions, in a closed form, of the corresponding linear and nonlinear boundary value problems for isotropic layered media subjected to internal heating. Practical value. The developed linear and nonlinear mathematical models for determining the temperature distribution in layered structures with internal heating make it possible to analyze heat exchange processes and ensure the thermal stability of such structures. This also makes it possible to increase the heat resistance of structures and protect them from overheating, which can lead to damage to individual components and elements of mechanisms, as well as to the entire structure as a whole. The resulting analytical solutions can be used to predict temperature fields in mine shafts, underground environments and mechanisms of mining equipment, in particular, in drilling and underground compressor stations, ventilation systems and other equipment, which improves work efficiency and reduces useful energy consumption.

Endothelial to mesenchymal transition is an active process in smokers and patients with early COPD contributing to pulmonary arterial pathology.

We have previously reported pulmonary arterial remodelling in smokers and patients with early COPD, which can be attributed to endothelial to mesenchymal transition (EndMT). In this study, we aimed to evaluate if EndMT is an active mechanism in smokers and COPD. Immunohistochemical staining for the EndMT biomarkers CD31, N-cadherin, vimentin and S100A4 was done on lung resection tissue from 49 subjects. These comprised 15 nonsmoker controls (NC), six normal lung function smokers (NLFS), nine patients with small airway disease (SAD), nine current smokers with mild-moderate COPD (COPD-CS) and 10 ex-smokers with COPD (COPD-ES). Pulmonary arteries were analysed using Image ProPlus software v7.0. We noted reduced junctional CD31+ endothelial cells (p<0.05) in the intimal layer of all smoking groups compared to NC. We also observed increased abundance of the mesenchymal markers N-cadherin (p<0.05) and vimentin (p<0.001) in all smoking groups and across all arterial sizes versus NC, except for N-cadherin in large arteries in COPD-CS. The abundance of S100A4 correlated with arterial thickness (small: r=0.29, p=0.05; medium: r=0.33, p=0.03; large: r=0.35, p=0.02). Vimentin in the small arterial wall negatively correlated with forced expiratory volume in 1 s/forced vital capacity (r= -0.35, p=0.02) and forced expiratory flow rate at 25-75% of forced vital capacity (r= -0.34, p=0.03), while increased cytoplasmic CD31 abundance in the intimal layer of medium and large arteries negatively correlated with predicted diffusing capacity of the lung for carbon monoxide (medium: r= -0.35, p=0.04; large: r= -0.39, p=0.03). This is the first study showing the acquisition of mesenchymal traits by pulmonary endothelial cells from NLFS, SAD and mild-moderate COPD patients through EndMT. This informs on the potential early origins of pulmonary hypertension in smokers and patients with early COPD.

Theoretical prediction of the effective dynamic dielectric constant of disordered hyperuniform anisotropic composites beyond the long-wavelength regime [Invited

Torquato and Kim [Phys. Rev. X 11, 296 021002 (2021)10.1103/PhysRevX.11.021002] derived exact nonlocal strong-contrast expansions of the effective dynamic dielectric constant tensor ε e (k q ,ω) that treat general statistically anisoropic three-dimensional (3D) two-phase composite microstructures, which are valid well beyond the long-wavelength regime. Here, we demonstrate that truncating this general rapidly converging expansion at the two- and three-point levels is a powerful theoretical tool from which one can extract accurate approximations suited for various microstructural symmetries. Among other results, we show that such truncations yield closed-form formulas applicable to transverse polarization in layered media and transverse magnetic polarization in transversely isotropic media, respectively. We apply these formulas to estimate ε e (k q ,ω) for models of 3D disordered hyperuniform layered and transversely isotropic media: nonstealthy hyperuniform media and stealthy hyperuniform media. In particular, we show that stealthy hyperuniform layered and transversely isotropic media are perfectly transparent (trivially implying no Anderson localization, in principle) within finite wave number intervals through the third-order terms. For all models considered here, we validate that the second-order formulas, which depend on the spectral density, are already very accurate well beyond the long-wavelength regime by showing very good agreement with the finite-difference time-domain (FDTD) simulations. The high predictive power of the second-order formula is due to the fact that higher-order contributions are negligibly small, implying that it very accurately approximates multiple scattering through all orders. This implies that there can be no Anderson localization within the predicted perfect transparency interval in stealthy hyperuniform layered and transversely isotropic media in practice because the localization length (associated with only possibly negligibly small higher-order contributions) should be very large compared to any practically large sample size. Our predictive theory provides the foundation for the inverse design of novel effective wave characteristics of disordered and statistically anisotropic structures by engineering their spectral densities.

Calibration of absorbing boundary layers for geoacoustic wave modeling in pseudo-spectral time-domain methods

Abstract. This paper develops a calibration methodology of the artificial absorbing techniques typically used by Fourier pseudo-spectral time-domain (PSTD) methods for geoacoustic wave simulations. Specifically, we consider the damped wave equation (DWE) that results from adding a dissipation term to the original wave equation, the sponge boundary layer (SBL) that applies an exponentially decaying factor directly to the wavefields, and finally, a classical split formulation of the perfectly matched layer (PML). These three techniques belong to the same family of absorbing boundary layers (ABLs), where outgoing waves and edge reflections are progressively damped across a grid zone of NABL consecutive layers. The ABLs used are compatible with a pure Fourier formulation of PSTD. We first characterize the three ABLs with respect to multiple sets of NABL and their respective absorption parameters for homogeneous media. Next, we validate our findings in heterogeneous media of increasing complexity, starting with a layered medium and finishing with the SEG/EAGE 3D salt model. Finally, we algorithmically compare the three PSTD–ABL methods in terms of memory demands and computational cost. An interesting result is that PML, despite outperforming the absorption of the other two ABLs for a given NABL value, requires approximately double the computational time. The parameter configurations reported in this paper can be readily used for PSTD simulations in other test cases, and the ABL calibration methodology can be applied to other wave propagation schemes.

IMPROVEMENT OF THE NON-DESTRUCTIVE METHOD FOR DETERMINING THE MECHANICAL CHARACTERISTICS OF ELEMENTS OF MULTILAYER STRUCTURES ON THE EXAMPLE OF PAVEMENTS

The article is devoted to solving the urgent problem of improving the method of nondestructive testing of the condition of non-rigid road clothes. In addition to the previously developed approach to determining the mechanical parameters of materials of structural layers of nonrigid road coverings based on solving the inverse coefficient problem of restoring operational elastic modules providing specified displacement fields, an approach was developed that allows determining the parameters of energy dissipation in the structure of multilayer road pavement based on the correction of dynamic hysteresis loops recorded in the field and calculated using mathematical model of dynamic VAT. The article presents the results of numerical simulation of dynamic hysteresis loops for two different variants of multilayer structures. The possibilities of correcting the shape of hysteresis loops and their area by varying the tangents of the energy loss angles in layers of a multilayer medium and the elastic modulus of a homogeneous half-space are shown. The complex correction of the elastic modulus values of the structural layers of road clothes and the calculated loops of dynamic hysteresis made it possible to fully take into account the processes of energy attenuation at a distance from the point of application of the load. During the correction, it was found that the values of the elastic modulus of the road layers and the tangents of the loss angles in them have a complex effect on the areas of dynamic hysteresis loops and the nature of energy attenuation at a distance from the point of application of the load. At the same time, the elastic modulus of the underlying half-space is not limited in thickness to the greatest extent on the area of dynamic hysteresis loops (which led to an increase in the elastic modulus of the underlying half-space from 120 and 150 MPa for road construction variants with a reinforced and non-reinforced base to 170 and 160 MPa, respectively), and a decrease in the dissipated energy at a distance from the point of application This is primarily due to the tangent of the angle of energy loss in the half-space. The obtained values of the tangents of the loss angles are obviously related to the patterns of energy dissipation at the boundaries of the contacting layers of the pavement, and also take into account all possible anomalies and delaminations in the calculated structures. Within the framework of this article, calculated hysteresis loops on the surface of the pavement were obtained for the first time, the deformation energy was calculated based on their areas, and the possibility of their comparison with those registered experimentally was proved.

Answers to questions about medial layer graphs of self-dual regular and chiral polytopes

Answers to questions about medial layer graphs of self-dual regular and chiral polytopes

Anisotropic medium sensing controlled by bound states in the continuum in polarization-independent metasurfaces.

Bound states in the continuum (BICs) with infinite quality factor (Q-factor) and significant field enhancement pave the way for realizing highly sensitive optical sensors with enhanced light-matter interactions on the nanoscale. However, current optical sensing methods are difficult to discriminate between isotropic and anisotropic media from resonance spectral lines, resulting in optical sensing methods still being limited to isotropic media. In this work, we demonstrate that BICs can be realized by modulating the period of structural units to convert BICs to QBICs without changing their space group symmetry, and propose a polarization-independent metasurfaces-based realization of highly sensitive refractive index sensors for isotropic and anisotropic media as well as discrimination. We propose a metasurface of tetrameric silicon nanoboxes with C4 symmetry as structural units to achieve the conversion of BICs to QBICs by modulating the period of structural units without changing the geometry of the structure. Two QBICs modes dominated by electric toroidal dipole and magnetic toroidal dipole are identified by multipolar decomposition and electromagnetic distribution calculations. Meanwhile, we realize the refractive index detection and resolution of isotropic and anisotropic media based on polarization-independent metasurfaces combined with isotropic and anisotropic media layers. Our work provides what we believe to be a new method for realizing the fast resolution and refractive index optical sensing of isotropic and anisotropic media, and offers new ideas for the design and application of polarization-independent metasurfaces.

Sub-10 fs unipolar pulses of a tailored waveshape from a multilevel resonant medium

We theoretically demonstrate the possibility to tune the temporal waveform of unipolar pulses of femtosecond duration emitted from a multilevel resonant medium. This is achieved through the control of the medium response by a properly adjusted sequence of half-cycle unipolar or quasi-unipolar driving pulses and the spatial density profile of resonant centers along the medium layer. We show the production of unipolar optical pulses of varying profiles, like rectangular or triangular ones, from an extended layer of a multilevel medium.

Mathematical Model of Freezing of Rocks Saturated With Salt Solution Taking Into Account the Influence of Osmosis

The paper presents a mathematical model of rocks freezing saturated with salt solution under impact of osmotic force. Osmosis is related to the salt concentration gradient, which is characteristic for solutions, and it is a powerful mechanism for the movement of solutions in poorly permeable porous media. A mathematical criterion for the formation of closed “pockets” with brines (cryopags) in frozen rocks has been obtained. This criterion is shown to be significantly depends on the osmosis coefficient. The model includes three layers of a porous medium saturated, respectively, with ice, ice and solution, and salt solution only. A special case was studied when there is only a second layer with a movable boundary, on which a phase transition from the second layer to the third one occurs. The investigated layer is saturated with a salt solution and ice in thermodynamic equilibrium. Other layers are replaced by boundary conditions. An approximate analytical solution of the problem is found in a self-similar formulation. The nature of the influence of osmotic force on the freezing process of rocks saturated with solution is shown. The characteristic patterns associated with the considered process are revealed. One of the features of the osmosis influence is the fact that it can cause the movement (migration) of the solution in the direction of increasing pressure, i.e. in the direction opposite to the driving force caused by the pressure gradient.

Результаты совместной интерпретации гравитационного и теплового полей Уральского региона

A method for solving conjugation problems for the Poisson equation is implemented, which makes it possible to interpret potential fields (gravitational and stationary thermal fields) based on unified grid algorithms. A numerical algorithm has been developed for recalculating the mantle component of the heat flow from the level of the earth’s surface to the “crust–mantle” boundary through a layered medium inhomogeneous in thermal conductivity. Paleoclimate corrections were introduced into the measured values of the temperature gradient and heat flux for the northern territories. In the axial part of the Ural geosyncline, it was possible to exclude the negative depression of the mantle component of the heat flow, obtained from the results of geothermal modeling; taking into account the Pleistocene-Holocene warming of the preceding interglacial paleoclimate cycle leads to positive values of the heat flow recalculated to the “crust–mantle” boundary. It is shown that the use of heat flow data can significantly increase the geological information content of gravity modeling.

Subcritical crack growth and arrest in the presence of a material interface

Reservoir systems often consist of layered rock formations that are naturally fractured. These can include both fractures that are confined within the main reservoir layer, and ones that penetrate adjacent confining layers or cut through into nearby reservoir strata. Layer-bound fractures have the effect of improving the overall permeability of a reservoir layer, however through-cutting fractures act as pathways for both fluid leakage and pressure communication between otherwise isolated formations. In this study, we investigate the subcritical propagation of a single crack from a stiff inner layer into more compliant and ductile outer layers. We model the crack growth numerically, by making use of recently formulated correction factors that account for the effect of mechanical boundaries on the crack tip energy release rate. Furthermore, we utilize a modified arc-length method to handle the stiff behaviour of the differential equations governing crack tip motion in a layered medium. Under different conditions, a fracture may be arrested permanently or temporarily at the layer boundary, propagate a short distance into the outer layer before arrest, or propagate critically in the outer layer forming a through-cutting fracture. We find that fractures are most likely to remain layer-bound in layers less than 5 m thick, a subcritical index below 10, and a low critical energy release rate relative to the confining layers. If the outer layer modulus is less than half that of the inner layer, the fracture is more likely to propagate a short distance into the confining layer before arrest. In the case of tectonic deformation characterized by steadily increasing far-field extensional strain, crack arrest at the layer boundary is likely to be only temporary, and the occurrence of layer-bound versus through-cutting fractures will be determined by the duration of said deformation together with the thickness and mechanical properties of the different layers.

Transmission probability of gas molecules through porous layers at Knudsen diffusion

Gas flow through layers of porous materials plays a crucial role in technical applications, geology, petrochemistry, and space sciences (e.g., fuel cells, catalysis, shale gas production, and outgassing of volatiles from comets). In many applications the Knudsen regime is predominant, where the pore size is small compared to the mean free path between intermolecular collisions. In this context common parameters to describe the gas percolation through layers of porous media are the probability of gas molecule transmission and the Knudsen diffusion coefficient of the medium. We show how probabilistic considerations on layer partitions lead to the analytical description of the permeability of a porous medium to gas flow as a function of layer thickness. The derivations are made on the preconditions that the molecule reflection at pore surfaces is diffuse and that the pore structure is homogenous on a scale much larger than the pore size. By applying a bi-hemispherical Maxwell distribution, relations between the layer transmission probability, the half-transmission thickness, and the Knudsen diffusion coefficient are obtained. For packings of spheres, expressions of these parameters in terms of porosity and grain size are derived and compared with former standard models. A verification of the derived equations is given by means of numerical simulations, also providing evidence that our analytical model for sphere packing is more accurate than the former classical models.

STUDY OF THE CHARACTERISTICS OF VIBRORHEOLOGICAL MODELS OF BULK RAW MATERIALS IN THE WORKING AREA OF A VIBROCENTRIFUGAL MIXER

Determining the movement of loose media in vibrating equipment (in particular, vibratory volume processing, grinding, separation) is a rather complex task of dynamics, which has not been fully investigated to date. The reason for this is the cumbersomeness of the mathematical description of the dynamics of the fluid medium, simplifying hypotheses and assumptions, the linearity of the models, which do not always adequately reflect the real physics of the investigated vibrational process. In recent years, vibration mechanics and vibrorheology have played an important role in the emerging new direction of applied vibration theory - the theory of vibration processes and devices. This theory examines the regularities of the impact of vibrations in various mechanical systems. It also covers the theory of machines where vibration is used for useful purposes. Vibrorheology is a branch of mechanics that studies the change under the influence of vibration in the rheological properties of bodies in relation to slow forces, as well as the corresponding slow movements of bodies. In recent years, vibration mechanics and vibrorheology have gained significant importance in a new direction of applied vibration theory - the theory of vibration processes and devices. This branch investigates the patterns of creation and influence of vibrations in various mechanical systems; it also covers the theory of machines where vibrations are used for useful purposes. Using the models mentioned below, it was possible to describe the chaotic movement of a layer of loose medium under the influence of vibration. These movements have been well studied in liquid media and have also been successfully studied in loose media. This further confirms the possibility of modeling the slow movements of a loose medium using analogies related to the movements of a viscous liquid.

Broadband tunable terahertz metamaterial absorber having near-perfect absorbance modulation capability based on a patterned vanadium dioxide circular patch

A new tunable broadband terahertz metamaterial absorber has been designed based on patterned vanadium dioxide (VO2). The absorber consists of three simple layers, the top VO2 pattern layer, the middle media layer, and the bottom metal layer. Based on phase transition properties of VO2, the designed device has excellent absorption modulation capability, achieving the functional transition from broadband absorption to near-perfect reflection. When VO2 is in the metallic state, there are two absorption peaks observed at frequencies of 4.16 and 6.05 THz, exhibiting near-perfect absorption characteristics; the combination of these two absorption peaks gives rise to the broadband phenomenon and the absorption bandwidth, where the absorbance exceeds 90% and spans from 3.40 to 7.00 THz, with a corresponding relative absorption bandwidth of 69.23%. The impedance matching theory, near-field patterns, and surface current distributions are provided to analyze the causes of broadband absorption. Furthermore, the broadband absorption could be completely suppressed when VO2 presents the dielectric phase, and its absorbance could be dynamically adjusted from 100% to less than 0.70%, thereby achieving near-perfect reflection. Owing to its symmetrical structure, it exhibits excellent performance in different polarization directions and at large incidence angles. Our proposed absorber may have a wide range of promising applications and can be applied in a variety of fields such as communications, imaging, sensing, and security detection.

Models for Stabilization of Charged Particles with Surfactants in Nonpolar Media

Stabilization of charged particles in nonpolar media is one of the most complicated problems in modern colloid chemistry. The attribution to colloid chemistry is absolutely justified in this case: in nonpolar media, charged particles have, as a rule, a supramolecular nature. Low dielectric permittivity of a medium makes the existence of ions in the classical interpretation energetically disadvantageous. The key condition for the presence of charged particles in nonpolar media is their steric stabilization, which requires some revision of the classical concepts of the structure of the electrical double layer, primarily, its diffuse part. Detailed analyzing the structure of the electrical double layer in nonpolar media is of importance because of the high practical significance of electrokinetic phenomena in such systems. This review considers the main models for steric stabilization of charged particles with surfactants in dispersion media having dielectric permittivities lower than 5. The main attention is focused on not only the concentrations corresponding to the formation of reverse micelles, but also on the concentrations below the critical micelle concentration. In addition, nontypical examples of electrokinetic phenomena in organosols are considered.

Effect of Three Types of Gravity Modulation on Rivlin Ericksen Nanofluid Saturated in Porous Medium with Internal Heating

In this paper, authors have studied the Rivlin-Ericksen elastico-viscous nanofluid thermal instability with internal heating under three types of gravity modulation in a horizontal layer of porous medium using both linear and nonlinear ways. Linear stability analysis is done using normal mode approach, whereas nonlinear stability analysis is done using truncated Fourier series method. The results demonstrate that the internal heating, modified diffusivity ratio, and concentration Rayleigh number advance the initiation of convective motion in the system. On the other hand, Darcy number stabilize the system. To understand the behaviour of mass/heat transfer in the system two different approaches viz Mathematica NDSolve and Runge-Kutta-Fehlberg method (RKF-45) are used, and it is found that the rate of heat/mass transfer is exactly the same in both cases. In comparison to other gravity modulation profiles, day-night gravity modulation profile accelerates mass/heat transfer more quickly than the other two types of gravity modulation profiles. Steady state graph has demonstrated, convection occurs earlier when internal heating and amplitude values are increased. Moreover, it is also observed that heat/mass transport is very much affected by the variation of kinematic viscoelasticity parameter.

Laser Vibrometry of Shear Waves in a Layer of a Gel-Like Medium

Laser Vibrometry of Shear Waves in a Layer of a Gel-Like Medium

Обследование скрытых участков стальных труб малого диаметра с применением ультразвуковой дефектоскопии

According to the current regulatory documents, as the established service life of gas pipelines for various purposes expires, they must be inspected in order to assess the current technical condition, make a decision on the residual life and the possibility of further operation at hazardous production facilities, as well as other buildings and structures. The possibility is considered related to using ultrasonic testing for detecting damage of corrosion origin in the sections of such pipelines hidden from the direct observation in interfloor ceilings and passages through the walls of buildings at the facilities in various branches of industries, as well as in gas distribution and gas consumption systems, and water pipelines. In addition, the possibility of identifying layered deposits of various origins in the cavity of small-diameter steel pipes is considered. At energy facilities, as well as in water supply pipelines, such deposits can lead to a significant reduction in the flow area of the pipeline, up to its complete blocking. Deposits inside the pipelines form an anisotropic layered medium, and the passage of ultrasonic waves through it has a number of features that prevent the use of traditional ultrasonic echo testing. For small-diameter pipes, the criterion is given under which it is possible to perform «remote» (waveguide) ultrasonic testing of the hidden sections of pipes at a distance of up to 600 mm. It is illustrated how, from such a distance, it is possible to detect corrosion deposits in pipes by ultrasonic testing methods using phased array antennas. At the same time, it is possible to assess the thickness («power») of layered deposits and their structure even when the passage section of the pipeline is filled with such deposits up to 100 %. Use of the methods presented in the article allows to increase the accuracy of calculating the residual life of the pipeline and reduce the uncertainty in setting safety factors in such calculations.

A Rapid Forward for Grounded Long Wire Source Transient Electromagnetic Method

Aiming at enhancing the forward and inversion efficiency of grounded long wire source TEM (Transient ElectroMagnetic method), a new rapid layered medium forward method is proposed in the paper. This forward method is based on two points, one is to approximate the vertical magnetic component in frequency domain of a grounded long wire source by the response of several circular loops, and the other is to introduce the technique of "flow through" into the digital filtering calculation of sinusoidal transformation. The result of model tests shows that the calculation efficiency of proposed method is improved greatly (dozens of times) compared with that of the conventional method.

Reflective properties of active layered media at second optical harmonic generation

We studied the reflective properties of an active periodic medium with quadratic nonlinearity using numerical modeling based on the description of the generation of the second optical harmonic in the quasi-optical approximation. The model under consideration appears to be a system of four coupled equations for slowly varying amplitudes of forward and backward waves. Based on numerical simulation, the influence of the asymmetric Bragg coupling of counterpropagating waves at the fundamental frequency on the absorbing/generating and reflecting properties of the active medium is analyzed.