Effective Dielectric Response of Composites with Graded Material

The effective dielectric response of linear composites containing graded material is investigated under an applied electric field E₀. For the cylindrical inclusion with gradient dielectric function, ε_i(r)=b+cr, randomly embedded in a host with dielectric constant ε_m, we have obtained the exact solution of local electric potential of the composite media regions, which obeys a linear constitutive relation D=εE, using hypergeometric function. In dilute limit, we have derived the effective dielectric response of the linear composite media. Furthermore, for larger volume fraction, the formulas of effective dielectric response of the graded composite media are given.     

Study of the relationship between porous ratio and effective index in nanoporous film

In this paper, a theory model called 'composite media in parallel' is proposed to explain the connection between the porous ratio and effective index of the nanoporous film. This model comes from theory of composite media's effective dielectric constant in solid material field. From this model, a function relationship between the porous ratio and effective index of the nanoporous film is obtained. And the Finite Difference Time Domain (FDTD) method is used to construct the model of nanoporous film, simulate the propagation of lightwave in the film and calculate some effective indices according to different ratios of pore. Compared with Maxwell Garnett theory model and Bruggeman theory model, it is found that the function curve based on the composite media in parallel model is most consistent with the results simulated by FDTD method.     

Equivalent-inclusion approach and effective medium estimates for elastic moduli of two-dimensional suspensions of compound inclusions

An effective medium scheme is developed to estimate the elastic moduli of two-dimensional macroscopically isotropic suspensions of compound inclusions in a continuous matrix material. The two-phase (coated) compound inclusions are substituted by equivalent one-phase inclusions, using dilute solution results. Then, the available effective medium approximations and bounds are applied to the equivalent medium with homogeneous inclusions. Numerical fast Fourier transform simulations in some benchmark examples are compared favourably with the predictions of the scheme.     

Effective medium method of slightly compressible elastic media permeated with air-filled bubbles

An effective medium method is developed for the slightly compressible elastic media permeated with air-filled bubbles, according to the nonlinear oscillation of the bubble, which happens when compressional wave travels through the porous media. The effective Lame coefficients of the porous medium and the nonlinear elastic wave equation are deduced, based on the fact that the micro-unit of the effective medium should have the same stress and strain as the micro-unit of the porous media. The linearized properties obtained by this method are in good agreement with the results of Gaunaurd’s classic theory [Gaunaurd G.C. and überall H., J. Acoust. Soc. Am., 1978, 63: 1699–1711]. Furthermore, the nonlinear coefficient, which is an important property of the porous media, can also be acquired by this method. __________ Translated from Acta Acustica, 2006 (in Chinese) (in press)     

高浓度纤维增强材料介电特性计算方法

针对复合材料的微观结构非均匀和各向异性特点带来的数值方法计算慢、内存消耗大的问题,利用均匀化方法计算纤维增强复合材料的等效电磁参数.采用了纤维低体积添加比至高体积添加比的迭代方法,同时提出了一个描述材料微观结构的修正的特征长度,将现有的均匀化方法推广至非准静态(微波频段)条件下高纤维浓度情况.提出的修正的均匀化模型可直接用于反射系数、屏蔽效能等计算,其屏蔽效能与实际微观结构复合材料的数值仿真结果进行了对比,验证了提出的等效电磁参数计算公式的有效性和频率适用范围.     

Reflection and transmission coefficients of electromagnetic waves with different polarizations on a one-dimensional layer of an inhomogeneity of the medium

We have obtained strict formulas (without approximations) for the reflection and transmission coefficients of electromagnetic waves with an arbitrary polarization in an isotropic medium with a one-dimensional layer of an inhomogeneity of an arbitrary profile playing the role of a transition layer between two different homogeneous media. Since these formulas involve values that are found by numerically integrating the first-order ordinary differential equations, the result of this paper is a fast and convenient method for calculating the above coefficients. The calculated results for two particular cases are given. An analytical limiting passage from the obtained formulas to the particular case of a sharp interface between the media (i.e., to known Fresnel formulas) is presented.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 9, pp. 1075–1086, September, 1996.This work was supported by the Russian Foundation for Fundamental Research.     

Corrections to the classical continuity boundary conditions at the interface of a composite medium

Using the multiple-scales homogenization method, we derive generalized sheet transition conditions (GSTCs) for electromagnetic fields at the interface between two media, one of which is free-space and the other a certain type of composite material. The parameters in these new boundary conditions are interpreted as effective electric and magnetic surface susceptibilities, which themselves are related to the geometry of the scatterers that constitute the composite. We show that the effective tangential E and H fields are not continuous across the interface except in the limit when the lattice constant (the spacing between the scatterers—atoms, molecules or inclusions in the case of a composite material) of the composite medium is very small compared to a wavelength. We derive first-order corrections to the classical continuity conditions. For naturally occurring materials whose lattice constants are on an atomic scale, these effects are shown to be negligible for waves at optical frequencies or lower. However, once the lattice constant becomes a significant fraction of a wavelength (which is the case for many artificial dielectrics and metamaterials), the corrections can be important. In previous work we have alluded to the fact that such a GSTC is needed to correctly account for the surface effects when extracting the effective material properties of a metamaterial. The results of this current paper justify the assumptions made in that previous work. In general, these GSTCs will result in corrections to the classical Fresnel reflection and transmission coefficients (which are themselves merely zeroth-order approximations to the actual reflection and transmission coefficients), and in a separate publication we will use these GSTCs to address this issue.     

柱等离子体中广义磁流体方程组的简化形式与本征模解

本文从含有广义欧姆定律的磁流体力学方程组出发,仅作符合加热托卡马克等离子体具体实验条件的近似,把广义磁流体方程组简化成4元一阶微分方程组。对均匀密度等离子体柱情况求出解析色散关系(本征模解),并证明Appert理论是本文的极限情况。 关键词：     

磁性颗粒膜法拉第转角的研究

在外磁场作用下,复合介质的法拉第磁光效应依赖于颗粒膜电介质张量。而复合介质的电介质张量的计算相当复杂。运用了有效介质近似理论,利用非均匀复合介质的有效电场等于单个颗粒中局域场的平均值的自恰条件,由电介质张量εe方程及自洽条件导出了计算磁性颗粒膜系统磁光法拉第转角的解析公式。并应用导出的关系,以Cu金属颗粒为例,讨论了颗粒膜中金属颗粒含量及对应的基质、离子浓度、颗粒形状对法拉第转角的影响,结果表明,利用有效介质近似理论计算的结果与实验结果一致。     

导电平板上任意缝隙填充各向异性介质时TM波散射和传输特性分析

简单介绍了用于分析任意口径问题的通用频域方法——广义网络原理,并利用边界积分法和广义网络原理分析导电平板上任意缝隙填充各向异性介质时TM波的散射及传输特性.由于缝隙填充各向异性介质的情形尚未见公开文献报道,作为验证,将本方法退化计算各向同性介质填充时缝隙的散射和传输特性,并与文献结果进行比较.最后,给出了缝隙填充各向异性介质时的算例.     

On the theory of X-ray coherent reflection from a rough surface

A solution of the problem of X-ray specular reflection from a statistically rough surface is presented. It is based on using the Green function formalism. The Kirchhoff formula is used to describe the transmission of the wave field through a rough interface. Generally, microscopically exact expressions for the coefficients of transmission through a rough surface and reflection from it are obtained by taking multiple scattering effects into account. Averaging of the obtained expressions over possible realizations of random roughness of the interface between media allows to obtain rigorous expressions for specular reflection and transmission coefficients. The behavior of exact solutions in the limiting case of infinite correlation lengths is studied. It is shown that, in this case, the obtained solution corresponds to the Debye-Waller normalization. Expressions for the reflection and transmission coefficients making it possible to carry out numerical calculations are obtained in the Bourret approximation of multiple-scattering theory.     

New assembly route for three-dimensional metamaterials obtained through effective medium theory

In this study,we illustrate the effective medium theories in the designs of three-dimensional composite metamaterials of both negative permittivity and negative permeability.The proposed metamaterial consists of random coated spheres with sizes smaller compared to the wavelength embedded in a dielectric host.Simple design rules and formulas following the effective medium models are numerically and analytically presented.We demonstrate that the revised Maxwell-Garnett effective medium theory enables us to design three-dimensional composite metamaterials through the assembly of coated spheres which are random and much smaller than the wavelength of the light.The proposed approach allows for the precise control of the permittivity and the permeability and guides a facile,flexible,and versatile way for the fabrication of composite metamaterials.     

On the criterion for effectiveness of wave linear transformation in a smoothly inhomogeneous medium and of nonadiabatic transitions during atomic collisions

A universal criterion for effectiveness of linear transformation of waves with locally close characteristic exponents in smoothly inhomogeneous media is obtained. The same criterion is applicable for estimating the effectiveness of nonadiabatic transitions in slow atomic collisions. The formalism developed for an analysis of the linear interaction of waves is based of the WKB asymptotic form of the solution of a scalar nth order ordinary differential equation. The obtained criterion can be applied in any practical problem for drawing a conclusion about the effectiveness of the linear interaction of modes if only the characteristic equation of waves in a homogeneous medium and the coefficients of the initial differential equation are known. In this case, the solution of the problem is reduced to elementary arithmetic calculations.     

An accurately fast algorithm of calculating reflection/transmission coefficients

For the boundary between transversely isotropic media with a vertical axis of symmetry (VTI media), the interface between a liquid and a VTI medium, and the free-surface of an elastic half-space of a VTI medium, an accurately fast algorithm was presented for calculating reflection/transmission (R/T) coefficients. Specially, the case of post-critical angle incidence was considered. Although we only performed the numerical calculation for the models of the VTI media, the calculated results can be extended to the models of transversely isotropic media with a horizontal axis of rotation symmetry (HTI media). Compared to previous work, this algorithm can be used not only for the calculation of R/T coefficients of the boundary between ellipsoidally anisotropic media, but also for that between generally anisotropic media, and the speed and accuracy of this algorithm are faster and higher. According to the anisotropic parameters of some rocks given by the published literature, we performed the calculation of R/T coefficients by using this algorithm and analyzed the effect of the rock anisotropy on R/T coefficients. We used Snell’s law and the energy balance principle to perform verification for the calculated results. Supported by the Natural Science Foundation of Shaanxi Province, China (Grant No. 2007D15)     

复相介质及界面结构温度场跨尺度计算

本文针对复相介质及界面结构的跨层次热问题,提出了计算界面结构导热系数的分子动力学方法,复相介质宏观有效导热系数和温度函数的均匀化与多尺度渐近展开方法以及界面结构局域温度场的量子修正。建立了微观与宏观相关联的跨尺度计算模式,初步实现了从量子力学到连续模型的跨越。     

Temperature profiles in a two-component heterogeneous system heated with a cw laser

A formalism has been developed to calculate the steady-state temperature profiles induced by a cw laser in a composite system comprising a thick medium covered with a film of another medium. The analysis is carried out assuming that thermal and optical properties of the media are temperature-independent. A concept of the effective thermal conductivity for the system is introduced in terms of the maximum temperature rise. Temperature-distributions are numerically computed in typical cases for a circular Gaussian beam to illustrate dependence on film thickness, thermal conductivities and absorption coefficients of the media and size of the laser beam.     

A generic approach to boundary reflection in periodic media

Waves in periodic media, whose propagation is governed by nearest neighbour interaction, are investigated. The reflection and transmission coefficients are derived for a plane wave incident from medium 1 upon medium 2, without invoking common approximations. The derivation is valid for a class of waves including magneto- and electro-inductive waves, waves on short loaded dipoles, nanoparticles, coupled waveguides and acoustic waves in monatomic media. For this last case hitherto unknown microscopic reflection and transmission coefficients are derived and shown to reduce in the continuous limit to the well-known expressions in terms of acoustic impedances.     

Theoretical study of combined radiative conductive and convective heat transfer in semi-transparent porous medium in a spherical enclosure

A new method for the solution of the radiative transfer equation in spherical media based on a modified discrete ordinates method is extended to study radiative, conductive and convective heat transfer in a semi-transparent scattering porous medium. The set of differential equations is solved using the fourth-order Runge-Kutta method. Various results are obtained for the case of combined radiative and conductive heat transfer, as well as for the interaction of those modes with convection. The effects of some radiative properties of the medium on the heat transfer rate are examined.     

基于阻抗模拟的等效电磁参数研究

为能够较好的计算混合介质等效复介电常数和复磁导率, 提出了一种基于等效电路理论的阻抗模拟方法.导出了材料的电磁参数与材料容抗、感抗之间的对应关系, 并建立了能够较完整、精确地刻画实际复合材料的模型.通过求解混合介质的等效阻抗, 进一步反演其等效电磁参数.将计算结果与经典理论公式以及基于有限差分的数值方法进行了比较, 结果都符合得很好, 说明该方法可以用于计算材料的等效电磁参数.另外, 引入薄膜层结构来刻画表面效应等因素, 使得计算结果更加符合实验结果, 弥补了经典公式在这方面的不足, 同时也体现了该方法在刻画实际模型时所具有的优势. 关键词： 等效电磁参数 阻抗模拟 等效电路 混合介质     

On relativistic kinetic gas theory: XVI. The temperature dependence of the transport coefficients for a simple gas of hard spheres

Analytical and numerical results are obtained for the first three approximations to the transport coefficients of a simple gas consisting of massive particles with constant differential cross section. The complete temperature regime is studied, while special attention is paid to both the weakly-relativistic and the ultra-relativistic limiting cases. The behaviour of the successive approximations indicates that the series for the transport coefficients converge in a satisfactory way over the whole temperature range.