Wave Propagation Process Research Articles

Rapid-Transfer Matrix Method for Analysis of Electromagnetic Properties of Uniaxial/Biaxial Biaxially Anisotropic Media

The employment of uniaxial/biaxial bianisotropic materials in the field of optical device manufacturing is widespread due to the distinctive electromagnetic response characteristics exhibited by such materials. To effectively analyze the electromagnetic properties of uniaxial/biaxial bianisotropic materials, rapid-transfer matrix method (R-TMM) is proposed to investigate the propagation process of plane waves in the media. Starting from the Maxwell’s equations in the time domain, the homogeneous differential equation about the electric field is constructed by processing the matrix containing dielectric and magnetic conductivity, electric and magnetic loss, tellegen and chirality carrier parameters, and the complex matrix operation is applied to that equation to get the booker quartic equation, and then the formulae method are utilized to obtain the eigenvalues in the uniaxial/biaxial bianisotropic media. Subsequently, the tangential continuity of layered media at the interface is employed to establish a transfer matrix for single-layered media. In the case of multi-layered media, the transfer matrix of plane waves propagating in multi-layered uniaxial/biaxial bianisotropic media can be obtained by means of a continuous iteration process based on the transfer matrix of single-layered media. The formula for calculating the propagation coefficient of uniaxial/biaxial bianisotropic materials can be derived based on the different upward and downward waves in the reflection/transmission region. Finally, the reliability and efficiency of R-TMM is verified from two numerical experiments with the plane waves incident at different angles on a uniaxial/biaxial bianisotropic media. The first experiment is designed as a single-layered biaxial bianisotropic model with more general electromagnetic parameters, and the second experiment is designed as a double-layered uniaxial and biaxial bianisotropic model consisting of common optical materials, which are composed of two non-magnetic materials, lithium niobate (LiNbLO<sub>3</sub>) and cadmium sulfide (CdS). The experimental results demonstrate that, in comparison with the conventional conventional-transfer matrix method (C-TMM), the R-TMM reduces the computational memory and CPU time required for calculating the reflection and transmission coefficients of the uniaxial/ biaxial bianisotropic model by over 98%, while maintaining the accuracy of the reflection and transmission coefficients calculation. Therefore, R-TMM provides an efficient and dependable approach for the design of complex optical devices and the analysis for uniaxial/biaxial bianisotropic propagation characteristics.

ТРАНСПОРТНЫЕ РЕШЕНИЯ УРАВНЕНИЙ МАКСВЕЛЛА В БИКВАТЕРНИОННОМ ПРЕДСТАВЛЕНИИ ПРИ ДОСВЕТОВЫХ СКОРОСТЯХ

The most common movable radiation sources of electromagnetic waves among the operating ones located on the platforms of various vehicles. It is obvious that the speed of movement affects the processes of wave propagation in an environment with such electrical conductivity and magnetic permeability, as does the shape of the source itself and the nature of its operation. In this work are constructed and studied transport solutions of the biquaternion wave equation, which is a biquaternion generalization of Maxwell's equations. These equations describe the electromagnetic fields of emitters of electromagnetic (EM) waves and electro-gravimagnetic waves (EGM), moving in a fixed direction with a constant speed, which is less than the speed of propagation of waves in an electromagnetic medium (the speed of light). Fundamental and generalized transport solutions have constructed that describe the EM fields of moving objects in the entire range of speeds, from light to superluminal.The electromagnetic field generated by a moving point emitter on the Z-axis described by the biquaternion Green's function (bifunction) in a moving coordinate system constructed using the Fourier transform of generalized functions. The energy density and Poynting vector of this field were determined. Influence of movement speed researched on field characteristics

Analysis of wave-induced crack propagation through a coupling algorithm of the peridynamics and isogeometric analysis

Wave propagation analysis is important in the fields of defect detection, explosion protection, etc. Numerical methods derived from classical continuum mechanics (CCM) are widely applied in the analysis of wave propagation, but these methods cannot predict the cracks induced by wave propagation. Peridynamics (PD) theory is a nonlocal framework, which applies integral equations and remains valid in the presence of discontinuities such as cracks, so it can simulate fracture and damage. In this study, we develop a coupling model of isogeometric analysis (IGA) and bond-based PD theory to study the cracks induced by wave propagation in linear elastic solids. First, the wave propagation process based on bond-based PD theory is investigated to explore the wave dispersion phenomenon due to the spatial discretization of PD. Second, one-dimensional (1D) and two-dimensional (2D) IGA-PD numerical examples are tested to explore wave propagation in 1D and 2D structures, respectively. Third, the wave-induced fracture of the material and the law of crack propagation are investigated. Compared to the traditional CCM method and the pure PD method, the advantage of the proposed IGA-PD model is that it can simulate the material damage and crack propagation caused by wave propagation and improve the computational efficiency. The results show that the proposed coupling method can be successfully applied to simulate wave propagation and the damage and crack propagation it induces.

One-Dimensional Inverse Problem for Nonlinear Equations of Electrodynamics

For the system of nonlinear electrodynamics equations, we consider the problem of determining the medium conductivity coefficient multiplying the nonlinearity. It is assumed that the permittivity and permeability are constant and the conductivity depends only on one spatial variable, with this conductivity being zero on the half-line x . For a mode in which only two electromagnetic field components participate, the wave propagation process caused by the incidence of a plane wave with a constant amplitude from the domain x0 onto an inhomogeneity localized on the half-line x0 is considered. With a given conductivity coefficient, the conditions for the solvability of the direct problem and the properties of its solution are studied. To solve the inverse problem, the trace of the electrical component of the solution of the direct problem is specified on a finite segment of the axis x=0. A theorem on the local existence and uniqueness of the solution of the inverse problem is established, and a global estimate of the conditional stability of its solutions is found.

Seismogram Synthesis of Multi-Scale Layered Transversely Isotropic Saturated Half-Space Using a Revised Stiffness Matrix Method

Seismogram synthesis for a multi-scale transversely isotropic (TI) saturated layered half-space subjected to seismic dislocation source is studied by a revised stiffness matrix method in this paper. First, based on Biot’s theory of wave propagation in a fluid-saturated porous solid, the governing equations of motion in TI saturated medium are transformed by Fourier–Hankel integral transform. Next, the contribution of the seismic dislocation source can be imposed in the form of body forces. Then, the global stiffness matrix with well-conditioned properties is obtained by assembling each layer’s exact stiffness matrix, which can avoid accumulating errors in the matrix transmission. By extracting the divergence exponent terms of the stiffness matrix concerning thickness and wavenumber, the bottleneck of simulating the wave propagation process in multi-scale half-space, where the layer thickness and velocity vary sharply from the near-surface region to the crustal zone, could be overcome, and a fast and accurate seismogram synthesis could be achieved. The accuracy of the proposed method is verified by comparing the calculated results with those of published literature. Finally, the method is applied to the multi-scale system with realistic superficial fine layers. Numerical examples regarding thickness, TI properties and porosity are presented to illustrate the effects of superficial layers on ground motion. The numerical results show that the surface properties affect the wave propagation and energy distribution, leading to variable impacts on the surface response in different directions; this phenomenon is more pronounced in the case of high-frequency ground motions.

A mathematical model for simulating photoacoustic signal generation and propagation in biological tissues

Photoacoustic (PA) medical imaging is a crossbred technique relying on light-induced ultrasonic waves due to the PA effect phenomenon recorded primarily in 1880 by A. G. Bell. Numerical simulation, also known as in-silico, studies assist scientists in minimizing incorrect PA experiments in both in-vitro and in-vivo. Numerical modeling techniques help to achieve a fast simulation process in contrast to pure mathematics alone. However, if a suitable facilitated mathematical model can be established prior to applying numerical modeling, it will be of great interest to the whole numeric model. Numerous mathematical equations, theorems, and propositions have been proposed to model the whole PA signal generation and propagation process in biological media. However, most of them are complicated and difficult to be understood by researchers, especially beginners. That’s why this paper was introduced. Our paper aims to simplify the understanding of the generation and propagation process of biomedical PA waves. We have developed a facilitated mathematical model for the entire process. The introduced developed mathematical model is based on three steps: (1) pulsed laser stimulation, (2) light diffusion, and (3) PA stress wave generation and propagation. The developed mathematical model has been implemented utilizing COMSOL Multiphysics, which relies on the finite element method (FEM) numerical modeling principle. The in-silico time-dependent study's results confirmed that the proposed mathematical model is a simple, efficient, accurate, and quick starting point for researchers to simulate biomedical PA signals' generation and propagation process utilizing any suitable software such as COMSOL multiphysics.

Vertical diffusion of bubbles injected beneath a flat-bottomed ship for frictional drag reduction

There has been concern about the short effective distance of frictional drag reduction achieved by air lubrication, but recent model ship experiments have shown over 30 m longer than our expectation. Also, the reduction ratio can be improved through the artificial generation of void waves appearing beneath the hull. These topics relate to the spatiotemporal bubble distribution and an understanding of them requires clarification of the distribution. In this study, optical probes were used to measure the distributions of bubble states beneath a 20-m long flat-bottomed ship towed with 6–8 m/s. The measurements explained the long effective distance of drag reduction and the process of void wave generation and development. The drag reduction ratio was about 7–25% and mainly depended on the void fraction within 10 mm of the hull. The vertical distribution of the void fraction remained unchanged over long downstream distances. The development of void waves was affected by the streamwise velocity difference between bubble clusters near the hull. The velocity was determined by the number density of the bubbles, decreasing to the half of ship speed until reaching a certain number density, 100 per meter in our experiments, and then becoming constant at higher density.

Modeling of autowave processes in active media with inhomogeneous properties

This paper shows the results of computer modeling of the processes of excitation and propagation of autowaves in distributed active media with inhomogeneous properties. The study of autowaves by the cellular automata method is based on the Wiener–Rosenbluth model, according to which each element of the active environment can be in one of three states: rest, excitation and refractoriness. The software module "AutoWaveModel" has been developed in C++ using the Qt library and OpenGL technology for modeling dynamic processes of excitation of spiral waves and pacemakers. The heterogeneity of the properties of the active environment in the model under consideration is set, in particular, by introducing into the field (volume) of modeling a certain number of inactive elements distributed according to a random law. It is established that the decay of autowaves occurs when about 30-60% of inactive elements are introduced from their total number in the model, moreover, the wave propagation process becomes more stable with an increase in the decay coefficient of the activator of all elements. As one of the factors creating heterogeneity of the active distributed environment, the change in the decay coefficient of the activator in its volume is also considered. In this case, each cell of the model is assigned a random value of the specified coefficient, lying in a given interval from the minimum to the maximum value. With a significant difference in the values of the activator decay coefficient in near areas of the active environment and a sufficiently high excitation threshold, the wave front is curved due to its acceleration or deceleration. In this case, the destruction of the wave is also observed, which is unable to overcome the area with a reduced decay coefficient of the activator.

Status of X-ray Acoustooptics at the Institute of Microelectronics Technology Russian Academy of Sciences

The electrical measurement method, scanning electron microscopy method and high-resolution X-ray diffraction method have been used to investigate the process of the surface acoustic wave (SAW) propagation in a LiNbO3 ferroelectric crystal. Measurement of the amplitude-frequency response provides information on the losses in the acoustoelectronic device during the process of the SAW propagation. The scanning electron microscopy method permits to visualize the SAW on the surface of piezoelectric crystals in the real-time mode and to observe diffraction phenomena in acoustic beam. The X-ray diffraction method is sensitive to the crystal lattice distortions by surface acoustic wave and allows determining the SAW amplitudes.

ABOUT THE BOUNDARY CONDITION APPROXIMATION IN THE HIGHER-ORDER GRID-CHARACTERISTIC SCHEMES

In this paper, we consider the problem of constructing a numerical solution to the system of equations of an acoustic medium in a fixed domain with a boundary. Physically, it corresponds to the process of the seismic wave propagation in geological media during the procedure of the seismic exploration of hydrocarbon deposits. The system of partial differential equations under consideration is hyperbolic. To construct its numerical solution, a grid-characteristic method is used on an extended spatial stencil. This approach makes it possible to construct a higher-order approximation scheme at the internal points of the computational domain. However, it requires a careful construction of the numerical solution near the boundaries. In this paper, the approach that preserves the increased approximation order up to the boundary is proposed. The verification numerical simulations were carried out.

Full-field dynamic response of low-velocity impact on an elastic plate using 3D digital image correlation

Measurement of the impact process is challenging due to its short duration and high frequency response. Due to the very small strain in low-velocity impacts, the requirements for the temporal and spatial resolution of test methods are extremely high. Traditionally, strain gauges or lasers are commonly used to measure the dynamic response of a single point, or quasi-static loading is used to achieve full-field response. To finely describe the transient full-field deformation process of low-velocity impacts, a high-speed imaging system combined with 3D digital image correlation (DIC) technique is set up to investigate the instantaneous responses of impact on a polyvinyl chloride (PVC) plate at the ms and με level. The full-field deformation of the contact surface and the whole process of elastic wave propagation are measured. The measurement by DIC closely matches the measurement by strain gauges and agrees well with the numerical simulation results. The measurement reveals that the “multi-micro-impacts” phenomenon may happen during a complete impact process due to the complex strain wave propagation. This work provides a benchmark case for low-velocity impact full-field testing, and the results show that 3D DIC can accurately evaluate dynamic behaviors of low-velocity impact between flexible bodies and can accurately describe the spatiotemporal propagation characteristics of strain waves.

Stability of a lined rock cavern for compressed air energy storage containing a weak interlayer during blasting in the adjacent cavern: model tests and numerical simulation

To evaluate the stability of a lined rock cavern (LRC) for compressed air energy storage (CAES) containing a weak interlayer during blasting in the adjacent cavern, a newly excavated tunnel-type LRC was taken as the research object. By combining similar model tests and numerical simulation, the dynamic responses and deformation characteristics of the LRC for CAES under joint action of factors including the gas storage pressure, weak interlayer, and blast load were studied. The influences of the thickness, dip angle, and location of the weak interlayer on deformation of the LRC were discussed. The results show that as the gas storage pressure increases, the rate of change in strains in regions of the LRC near the weak interlayer is accelerated, and the gas storage pressure more significantly influences the sealing layer and lining than the surrounding rocks. The presence of the weak interlayer causes stress concentration in the LRC and increases the circumferential strain and residual strain of the LRC. Under the blast load, the right-side wall of the LRC shows the poorest stability, and the presence of the weak interlayer results in the energy loss in the propagation process of stress waves and an increment of peak strain in regions of the LRC around the interlayer. When the weak interlayer is separated from the LRC, as the thickness of the weak interlayer increases, the confinement of surrounding rocks at the interlayer on the LRC reduces and the circumferential strain increases. As the dip angle of the interlayer increases, the peak strain in the right upper side of the LRC grows significantly. As the distance from the weak interlayer to the LRC boundary increases, the circumferential strain in regions of the LRC near the interlayer decreases significantly. If the distance is less than 0.2r, the increment of the distance significantly affects the peak strain.

Studying the Effects of Wave Dissipation Structure and Multiple Size Diffusion Chambers on Explosion Shock Wave Propagation

Explosion chambers are crucial to the technology used to prevent coal mine gas explosions. Investigating the shock wave propagation law at various coal mine tunnel cross-sections helps ensure mine safety. A self-built, highly explosive experimental setup was used to conduct empirical research on straight tubes, eight sizes of single-stage explosion chambers, and multi-stage tandem explosion chambers. Ansys Fluent numerical simulation software constructed five different tandem explosion chamber models. The wave dissipation efficiency of various types of explosion chambers was calculated, the propagation law and process of shock waves across multiple explosion chambers were examined, and the best size and type of explosion chambers were summarized to increase the wave dissipation efficiency of single-stage explosion chambers. Gun silencers inspired these models. The findings indicate that the three-stage tandem explosion chamber is the best diffusion tandem combination form, the 60° silencer-type explosion chamber is the best single-stage explosion chamber modification program, and the 500 mm × 500 mm × 200 mm explosion chamber is the best single-stage explosion chamber.

A study of issues of impact dynamics based on the SPH method

Based on the SPH method, this paper investigates a number of key issues in shock dynamics, including the nonlinear phenomenon and its influencing factors in the propagation process of shock waves, and the process and mechanism of the interaction between shock waves and the surface of an object. Through the design of the experiments and the analysis of the results, the main conclusions and contributions of this study are drawn. At the same time, deficiencies and directions for further improvement are also pointed out, and prospects and suggestions for future research on impact dynamics are presented. This study is of great significance in promoting the research of impact dynamics.

A study of issues of impact dynamics based on the SPH method

Based on the SPH method, this paper investigates a number of key issues in shock dynamics, including the nonlinear phenomenon and its influencing factors in the propagation process of shock waves, and the process and mechanism of the interaction between shock waves and the surface of an object. Through the design of the experiments and the analysis of the results, the main conclusions and contributions of this study are drawn. At the same time, deficiencies and directions for further improvement are also pointed out, and prospects and suggestions for future research on impact dynamics are presented. This study is of great significance in promoting the research of impact dynamics.

Local propagation of visual stimuli in focus of attention

Fast reactions to changes in the surrounding visual environment require efficient attention mechanisms to reallocate computational resources to the most relevant locations in the visual field. In this paper, we present a biologically-plausible computational model of focus of attention that exhibits spatiotemporal locality and that is very well-suited for parallel and distributed implementations. Attention emerges as a wave propagation process originated by visual stimuli corresponding to details and motion information. The resulting field obeys the principle of “inhibition of return” so as not to get stuck in potential holes. The proposed model is obtained as a hyperbolic regularization of the Poisson equation to which it reduces in the limit of high speed of propagation. According to the MultiMatch algorithm for scanpaths comparison, the proposed model achieves very competitive results when considering dynamical input stimuli.

Discrete element analysis of geogrid–aggregate interface shear behavior under cyclic normal loading

The stability of a geogrid-stabilized structure affected by cyclic normal loading (CNL) is significant but has not been fully revealed. Using the discrete element method (DEM), the effect of CNL on the microscale mechanical responses (i.e., stress states, contact evolution, fabric deformation) of the geogrid–aggregate interface direct shear test is first investigated. The complex shear behaviors at the interface with normal cyclic excitation at different frequencies and amplitudes are simulated. The DEM model is able to capture the macroscopic dynamic shear laws at the geogrid–aggregate interface in a similar way to those tested experimentally. The detailed behavior of the aggregate interacting with the geogrid under CNL is investigated. Compared with the simulation under static normal loading (SNL), CNL makes the stabilized layer more prone to failure, which could be quantitively evaluated by analyzing the local shear strain and the interparticle interlocking level. Microscale studies on the load wave propagation process and the confinement zone indicate that the present method can provide an applicable tool for dynamic service assessment and reliable forecasting of the undesirable effect of CNL on a mechanically stabilized layer.

Attenuation effect of a preset bubble on hydrodynamic ram induced by fragments impacting fluid-filled tank

When the fluid-filled structure is impacted by a high-velocity penetrator, the hydrodynamic ram (HRAM) will appear and may induce catastrophic damage. Based on the damage mechanism of HRAM, a countermeasure through presetting a bubble inside the fluid-filled tank is proposed to attenuate the HRAM loads and thus alleviate the vulnerability of the tank structure under the impact of high-velocity projectile. Experimental tests are performed to compare the tank’s damage considering the effect of bubble by the charge-driven preset fragments. The experimental results show that the peak pressure and impulse of the initial impact wave acting on the tank rear plate are reduced by 78% and 88%, respectively, and the cavitation collapsing pressure acting on the rear plate almost disappeared. Meanwhile, the maximum deformation of the front plate is reduced by about 15%. In addition, numerical simulation is employed to reproduce the experimental process. By comparing the structural dynamic response and the shock wave propagation process, the attenuation mechanism of the preset bubble on HRAM is revealed. Furthermore, the influence of the bubble position and size on the attenuation effect is investigated. Numerical results show that a smaller distance between the bubble and the front plate, and a larger bubble size lead to a better attenuation effect.

A simplified approach for efficiently simulating submarine slump generated tsunamis

A simplified approach was proposed to efficiently simulate the tsunamis generated by a submarine slump. The landslide tsunami generation process was simulated using a long-wave model, simplifying the wave generation problem as a slump traveling down a plane slope with a prescribed trajectory. As a result, the landslide tsunami generation process was parameterized by 11 input parameters. The wave profile at the end of the wave generation process can then be specified as the initial conditions in any numerical tsunami propagation model to study the subsequent tsunami propagation. To demonstrate the capability of this new landslide tsunami generation approach, we used it in combination with an existing Boussinesq wave solver to simulate the 1998 Papua New Guinea landslide tsunami. The results based on the newly calculated physics-based wave profile compare reasonably well with field measurements and the results based on an existing tuning-based wave profile. Sensitivity tests were performed to examine the sensitivity of the runup results to each of the 11 input parameters. Six sets of 100-case Monte Carlo experiments were conducted to investigate the propagation of uncertainty from the input parameters to the runup results. Runup uncertainty was found to be approximately 1.5 times the parameter uncertainty, highlighting the uncertain nature of landslide tsunamis.

Experimental and numerical investigations on the stress waves propagation in strain-hardening fiber-reinforced cementitious composites: Stochastic analysis using polynomial chaos expansions

The propagation of stress waves can result in spalling fractures in materials, which poses a threat to the safety of engineering structures. Hence, in-depth studies are necessary to mitigate such risks. Ultra-high toughness cementitious composites (UHTCC) with significant tensile strain-hardening properties are advanced engineering materials with great potential for impact engineering. The study used a combination of experimental and numerical methods to analyse the propagation and attenuation behaviour of stress waves in the UHTCC. The numerical model was developed using the Smooth Particle Galerkin (SPG) method and the Karagozian & Case concrete/cementitious (KCC) material constitutive model. Additionally, a quantitative global sensitivity analysis (GSA) using a polynomial chaos expansion (PCE) surrogate model and Sobol's method was conducted to analyse the stochastic input parameters of the numerical model. Results show that compressive stress waves undergo significant attenuation during propagation in UHTCC, and the developed numerical model accurately simulated the stress wave propagation process Furthermore, the PCE-Sobol GSA revealed that the selected stress wave propagation responses are most sensitive to the tensile strength of UHTCC. This study is expected to deepen the understanding of the propagation behaviour of stress waves in UHTCC and pave the way for promising applications of UHTCC in impact engineering.