Electromagnetic wave propagation in polycrystalline materials: effective medium approach

Abstract

A theory for the propagation of electromagnetic waves in inhomogeneous solids made of anisotropic crystallites is developed in the framework of the effective medium approach. The macroscopic dielectric tensor can explicitly be expressed by characteristic integrals containing the radial distribution function and a single anisotropy parameter. The phase mismatch of the waves scattered from misoriented crystallites leads to absorption and refraction effects that are calculated using a self-consistent approach in the sense of the distorted-wave approximation. For higher frequencies resonance structures occur which can be interpreted as an interference effect between disturbed and undisturbed waves in the effective medium.     

Electromagnetic wave propagation in polycrystalline materials: effective medium approach

A theory for the propagation of electromagnetic waves in inhomogeneous solids made of anisotropic crystallites is developed in the framework of the effective medium approach. The macroscopic dielectric tensor can explicitly be expressed by characteristic integrals containing the radial distribution function and a single anisotropy parameter. The phase mismatch of the waves scattered from misoriented crystallites leads to absorption and refraction effects that are calculated using a self-consistent approach in the sense of the distorted-wave approximation. For higher frequencies resonance structures occur which can be interpreted as an interference effect between disturbed and undisturbed waves in the effective medium.     

Application of an effective medium theory for modeling ultrasound wave propagation in healing long bones

Quantitative ultrasound has recently drawn significant interest in the monitoring of the bone healing process. Several research groups have studied ultrasound propagation in healing bones numerically, assuming callus to be a homogeneous and isotropic medium, thus neglecting the multiple scattering phenomena that occur due to the porous nature of callus. In this study, we model ultrasound wave propagation in healing long bones using an iterative effective medium approximation (IEMA), which has been shown to be significantly accurate for highly concentrated elastic mixtures. First, the effectiveness of IEMA in bone characterization is examined: (a) by comparing the theoretical phase velocities with experimental measurements in cancellous bone mimicking phantoms, and (b) by simulating wave propagation in complex healing bone geometries by using IEMA. The original material properties of cortical bone and callus were derived using serial scanning acoustic microscopy (SAM) images from previous animal studies. Guided wave analysis is performed for different healing stages and the results clearly indicate that IEMA predictions could provide supplementary information for bone assessment during the healing process. This methodology could potentially be applied in numerical studies dealing with wave propagation in composite media such as healing or osteoporotic bones in order to reduce the simulation time and simplify the study of complicated geometries with a significant porous nature.     

On continuum mixture theories for shear wave propagation in trilaminated wave guides

Recently developed continuum mixture theories are extended to study the propagation of horizontally polarized shear waves in a trilaminated wave guide. A specific composite model is considered which resembles the case in which one of the materials acts as a bonding agent for the other two materials. Dispersion relations are derived and compared with exact predictions. Good correlation is shown for significant frequency ranges, especially for the lowest two modes.     

The influence of backward wave transmission on quantitative ultrasonic evaluation using Lamb wave propagation

In view of the various novel quantitative ultrasonic evaluation techniques developed using Lamb wave propagation, the influence of an important related phenomenon, backward transmission, is investigated in this paper. Using the discrete layer theory and a multiple integral transform method, the surface displacement and velocity responses of isotropic plates and cross-ply laminated composite plates due to the Lamb waves excited by parabolic- and piston-type transmitting transducers are evaluated. Analytical expressions for the surface displacement and velocity frequency response functions are developed. Based on this a large volume of calculations is carried out. Through examining the characteristics of the surface displacement and velocity frequency response functions and, especially, the different propagation modes' contributions to them, the influence of the backward wave transmission related to quantitative ultrasonic nondestructive evaluation applications is discussed and some important conclusions are drawn.     

Numerical simulation of ultrasonic wave propagation for the evaluation of dental implant biomechanical stability

Osseointegration of dental implants remains poorly understood. The objective of this numerical study is to understand the propagation phenomena of ultrasonic waves in prototypes cylindrically shaped implants and to investigate the sensitivity of their ultrasonic response to the surrounding bone biomechanical properties. The 10 MHz ultrasonic response of the implant was calculated using a finite difference numerical simulation tool and was compared to rf signals taken from a recent experimental study by Mathieu et al. [Ultrasound Med. Biol. 37, 262-270 (2011a)]. Reflection and mode conversion phenomena were analyzed to understand the origin of the different echoes and the importance of lateral wave propagation was evidenced. The sensitivity of the ultrasonic response of the implant to changes of (i) amount of bone in contact with the implant, (ii) cortical bone thickness, and (iii) surrounding bone material properties, was compared to the reproducibility of the measurements. The results show that, either a change of 1 mm of bone in contact with the implant, or 1.1 mm of cortical thickness or 12% of trabecular bone mass density should be detectable. This study paves the way for the investigation of the use of quantitative ultrasound techniques for the evaluation of bone-implant interface properties and implant stability.     

Structure functions for optical wave propagation in underwater medium

The features of the wave structure function (WSF) derived for spherical excitation in turbulent water are investigated. It is found that as the rate of the dissipation of turbulent kinetic energy ? decreases, WSF increases. The rate of dissipation of the mean-squared temperature X_T is observed to be proportional to the WSF value. Deviation from the source and the receiver axis reveals greater turbulence effect. Salinity driven turbulence gives greater WSF values compared to the temperature driven turbulence. As expected, WSF is found to increase as the propagation distance increases.     

Reverse wave propagation in a randomly-inhomogeneous medium

Conclusion Therefore, it has convincingly been demonstrated in this paper that the so-called RWF mirror that reverses the radiation wave front even when using a finite aperture will assure elimination of field fluctuations during propagation in media with large-scale scatterers. Both reproduction of the mean intensity distribution and suppression of the intensity fluctuations are assured here in two-pass schemes.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 51–63, November, 1985.     

Electromagnetic wave propagation in a medium with defects

The equations of the electromagnetic field in a solid with defects were obtained and an approximate wave solution was found by the Debye–Rytov method.     

An effective Lagrangian for dynamically broken gauge theories

Dynamical symmetry breaking in non-abelian gauge theories is studied by computing an effective potential for composite operators. We obtain consistent solutions of chiral and gauge symmetry breaking which are, in some cases, compatible with a short distance behavior. The effective theory determined is in agreement with the tumbling hypothesis.     

Recursive surface impedance matrix methods for ultrasonic wave propagation in piezoelectric multilayers

Two recursive surface impedance methods are described for acoustic wave propagation in multilayered piezoelectric structures. Both methods have the advantage of conceptual simplicity and flexibility brought about by the transfer matrix method. Moreover they do not have a priori computational limitations with respect to the total number of layers of the stratified structure nor with respect to the thickness of individual layers; nor is the computational stability limited by the frequency range. For both methods, numerical simulations were carried out in order to illustrate their performances and robustness when combined with suitable recursive numerical algorithms.     

色散介质电磁特性时域有限差分分析的Newmark方法

根据Debye模型、Drude模型和Lorentz模型3种常见色散介质模型频域极化率的特点,利用频域到时域的转换关系jω→?/?t,将极化矢量P与电场强度E的频域关系转换成时域内关于P的二阶微分方程,其对3种色散介质模型皆适用,具有统一的形式.然后采用相比于中心差分具有更高精度的Newmark两步算法(Newmark-β-γ法)求解该方程,进而得到E→P的递推公式,再结合本构关系得到D→E的时域递推式.实现了色散介质电磁场量的时域有限差分迭代计算.数值计算结果表明该方法是适用于3种色散介质模型的通用算法,并且相比于移位算子时域有限差分方法等以中心差分为基础的离散方案具有更高的计算精度.     

Elastic wave propagation in a randomly stratified solid medium

The mean-field method is used to analyse longitudinal and transverse (both SV- and SH-type) wave propagation in an unbounded randomly stratified solid medium. It is assumed that elastic moduli of the medium are constant while a density is a random function of the cartesian coordinate z. For a case of small density fluctuations, expressions are obtained for z-components of effective propagation vectors of P-, SV- and SH-waves for arbitrary relations between wavelengths and a correlation length of the random inhomogeneities. It is shown, that when the correlation length is small in comparison with the wavelengths, the mean-field attenuation coefficients are proportional to the frequency squared. In this case P- and SV-waves convert into each other. When the correlation length is large in comparison with the wavelengths, the mean-field attenuation coefficients are also proportional to the frequency squared, but in this case P- and SV-waves propagate independently.     

Elastic wave propagation in a randomly stratified solid medium

Abstract

The mean-field method is used to analyse longitudinal and transverse (both SV- and SH-type) wave propagation in an unbounded randomly stratified solid medium. It is assumed that elastic moduli of the medium are constant while a density is a random function of the cartesian coordinate z. For a case of small density fluctuations, expressions are obtained for z-components of effective propagation vectors of P-, SV- and SH-waves for arbitrary relations between wavelengths and a correlation length of the random inhomogeneities. It is shown, that when the correlation length is small in comparison with the wavelengths, the mean-field attenuation coefficients are proportional to the frequency squared. In this case P- and SV-waves convert into each other. When the correlation length is large in comparison with the wavelengths, the mean-field attenuation coefficients are also proportional to the frequency squared, but in this case P- and SV-waves propagate independently.     

Assessment of flexural beam behaviour theories used for dynamics and wave propagation problems

In this work, different theories of beam flexural behaviour have been discussed and compared. This analysis includes various one-, two- and three-dimensional beam behaviour theories comprising the classical one-dimensional Bernoulli, Bernoulli–Rayleigh, Timoshenko and Reddy theories, as well as various higher order and/or higher-mode theories of beam flexural behaviour developed by the authors. The dispersion curves obtained by the use of Hamilton's principle and associated with each theory discussed in the paper have also been presented and analysed. The wide investigation programme carried out by the authors aimed at showing major differences and similarities between the beam theories and to discuss various numerical aspects of their application. Great attention has been paid on properties, limitations as well as difficulties associated with the use of particular theories of beam flexural behaviour. Based on a wide program on numerical calculations, the authors draw certain general conclusions that are valid not only in the field of wave propagation related problems, but also in the field of dynamics of engineering beam-like structures.     

A mixture theory for wave propagation in a laminated medium with debonding

In this paper wave propagation in the direction of the layering of a bi-laminated medium with the presence of imperfect bonding at the interfaces is investigated. The debonding mechanism is represented by a model which allows imperfect bonding both in the normal and tangential directions. A mixture theory is formulated in which every constituent has its own motion but is allowed to interact with the others. The resulting theory is applied to transient wave propagation in the laminated composite. It is shown that debonding in the tangential direction is significant in modifying the shape and amplitude of the propagating wave.     

Moment-screen method for wave propagation in a refractive medium with random scattering

Direct numerical solution of a parabolic equation (PE) for the second moment of the sound field in a refracting medium with random scattering is described. The method determines the mean-square sound pressure without requiring generation of random realizations of the propagation medium. The second-moment matrix is factored into components that are independently propagated with a conventional PE algorithm. A moment screen is periodically applied to attenuate the coherence of the wavefield, much as phase screens are often applied in the method of random realizations. An example involving upwind and downwind propagation in the near-ground atmosphere shows that the new direct method converges to an accurate solution faster than the method of random realizations and is particularly well suited to calculations at low frequencies.     

Monte Carlo simulation for millimeter wave propagation and scattering in rain medium

As the operating frequencies of communications systems more higher into the millimeter wave range, the effects of multiple scattering in precipitation media become more significant. This paper treats the problems of electromagnetic multiple scattering in rain medium by the Monte Carlo method. The em wave is regarded as a Markov chain of photon collisions in a medium in which it is scattered and absorbed. For the sake of simplicity, the polarization is not taken into account, the above mentioned problems are described by the scale integro-diffierential equation of transfer. When the plane wave through a random medium with particle size distribution, the technique of weighted average is used to characterize the radiation intensity, including average scattering, absorption coefficients and phase function. The Monte Carlo simulation algorithms are done for the rain attenuation and reflectance at millimeter wavelength region. Our computational results are in good agreement with experimental data of rain attenuation.