Green's Function for the Infinite Two-Dimensional Orthotropic Medium

The elastostatic Green's function (fundamental solution) for displacements of the two-dimensional infinite medium with orthotropic symmetry is derived in closed form in terms of elementary functions.     

The Green's Function for the Two-Dimensional Helmholtz Equation in Periodic Domains

Analytical techniques are described for transforming the Green's function for the two-dimensional Helmholtz equation in periodic domains from the slowly convergent representation as a series of images into forms more suitable for computation. In particular methods derived from Kummer's transformation are described, and integral representations, lattice sums and the use of Ewald's method are discussed. Green's functions suitable for problems in parallel-plate acoustic waveguides are also considered and numerical results comparing the accuracy of the various methods are presented.     

定向分布碳纤维复合材料介电性能研究

以碳纤维为填充物, 环氧树脂为基体, 制备了碳纤维/环氧树脂介电复合材料. 介绍了两种分布方式对复合材料介电性能的影响, 分别研究了两种分布方式的介电常数随碳纤维含量和长度的变化规律. 在2.6–8.2 GHz频率范围内, 轴向介电常数是径向介电常数的数倍; 实部和虚部都随着碳纤维含量的增加而增大; 碳纤维长度也对介电性能的各向异性影响显著. 双层微波传输带模型可以合理地解释这些规律.     

各向异性介质二维稳态热传导问题的分析解

本文利用双变量函数及其偏导数在闭区间上完整的双重付里叶级数表达式求得矩形区域中各向异性介质稳态热传导问题的分析解。文中例子给出各向异性介质内的温度场和热流密度的数字结果,并讨论介质的各向异性效应。     

Time-Domain Dyadic Green's Function for an Electric Source in a Conductive Plate

We have determined the quasi-static time-domain dyadic Green's function for an electric source in a conductive plate for use in electric field integral equations. Starting with a frequency-domain representation, we constructed the dyadic kernel from electric and magnetic scalar potentials defined with respect to a preferred direction normal to plate. The final time-domain expression has three parts: a free-space term, multiple image terms, and partial reflection terms. The free-space fundamental solution is expressed in terms of a three-dimensional Gaussian bell curve satisfying the diffusion equation. Similarly, the image terms are expressed in the same form with coordinates shifted so that each Gaussian curve centers on an image point. In order to carry out the inverse Laplace transform from the frequency domain to the time domain, we expand the partial reflection functions as asymptotic series before transforming them analytically. The resulting expression for dyadic Green's kernel can be evaluated efficiently and with well-controlled accuracy     

耗尽层的时域介电谱

从金属-半导体-绝缘体-金属（MSIM）层的非线性效应和慢极化效应分析了不能用正弦讯号的频域方法来研究其动态性质的原因．对于这种结构,用时域介电谱方法能更可靠地分出MOS结构的接触层和绝缘层中空间电荷运动的许多重要信息．     

An Alternating Iterative MFS Algorithm for the Cauchy Problem in Two-Dimensional Anisotropic Heat Conduction

In this paper, the alternating iterative algorithm originally proposed by Kozlov, Maz'ya and Fomin (1991) is numerically implemented for the Cauchy problem in anisotropic heat conduction using a meshless method. Every iteration of the numerical procedure consists of two mixed, well-posed and direct problems which are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method. For each direct problem considered, the optimal value of the regularization parameter is chosen according to the generalized cross-validation (GCV) criterion. An efficient regularizing stopping criterion which ceases the iterative procedure at the point where the accumulation of noise becomes dominant and the errors in predicting the exact solutions increase, is also presented. The iterative MFS algorithm is tested for Cauchy problems related to heat conduction in two-dimensional anisotropic solids to confirm the numerical convergence, stability and accuracy of the method.     

Semi-Infinite Anti-Plane Crack in a Piezoelectric Material

The problem of an impermeable semi-infinite crack in a piezoelectric material is considered. The electroelastic field due to a pair of concentrate forces and free charges applied at the crack surfaces is obtained by using the Mellin transform method, and the intensity factors of the quantities of concern and the mechanical strain energy release rate are given. The obtained results may be used as the fundamental solution, from which some general solutions can be calculated by superposition. The well-known solution for a purely elastic material will be recovered from the present solution if letting the coupling constant vanish.     

Time Domain Inverse Scattering of Buried Inhomogeneous Dielectric Cylinders

This paper presents the studies of time domain inverse scattering for a two-dimensional inhomogeneous dielectric cylinder buried in a half-space by the finite difference time domain (FDTD) method and evolutionary algorithms (EAs). For forward scattering, the FDTD method is employed to calculate the scattered E fields, while for the inverse scattering the evolutionary algorithms are utilized to determine the permittivity of the buried cylindrical scatterer with arbitrary cross section. The results obtained for different examples show that the dynamic differential evolution (DDE) algorithms outperform the non-uniform steady state genetic algorithm (NU-SSGA) variants in terms of finding best optima. The suitability and efficiency of applying these two methods for microwave imaging of 2-D inhomogeneous dielectric cylinders are examined. Moreover, when the measured scattered fields are contaminated with Gaussian noise, DDE is able to yield good reconstructed quality.     

利用格林函数求解三阶两点边值问题

本文讨论了利用格林函数方法对一类三阶常微分方程的两点边值问题进行数值求解。由三阶微分算子引出了格林函数,再根据边界条件构造了特定的格林函数,然后用数值例子加以说明。     

基于Green函数的两种STSF算法的比较

k-空间抽样格林函数法是目前基于Neumann边界条件空间声场变换技术格林函数的主要有限离散化算法。然而,该条件下的实空间积分格林函数法却很少应用在相关的课题研究中。所以对于该算法的重构特性以及这两种算法在空间声场变换中的优劣是人们一直普遍关注的问题。本文通过计算修正了该算法在Neumann边界条件下的计算参数,并通过数值仿真分析了实空间积分格林函数的相关特性,最后通过仿真计算给出了这两种方法在不同重构参数下的误差分析。这些分析结果可为进一步的工程实践提供参考。     

The Reflected Impedance of a Circular Coil in the Proximity of a Semi-Infinite Medium

Most analyses on a circular coil when used in the eddy current method for nondestructive testing are empirical. Theories based on simple models are often inadequate to account for some experimental observations when the spacing between the coil and the material became small. In the present paper this problem is formulated as a boundary value problem. Wave equations of the magnetic vector potential are solved. The change in the coil impedance, when placed above a semi-infinite medium, is obtained by means of the induced voltage method, which is shown to depend only on the ? component of the magnetic vector potential. This change in impedance is found to be dependent on a number of factors: the shape and size of the coil; the spacing between the coil and the metal; the thickness, conductivity, and composition of the material, etc. Numerical computations are discussed for a few selected materials in connection with experimental results obtained elsewhere. The comparison made lent support to the present analysis. Extension of this method to the case of a stratified media is included.     

Anisotropic Dielectric Properties of Carbon Fiber Reinforced Polymer Composites during Microwave Curing

Microwave cuing technology is a promising alternative to conventional autoclave curing technology in high efficient and energy saving processing of polymer composites. Dielectric properties of composites are key parameters related to the energy conversion efficiency during the microwave curing process. However, existing methods of dielectric measurement cannot be applied to the microwave curing process. This paper presented an offline test method to solve this problem. Firstly, a kinetics model of the polymer composites under microwave curing was established based on differential scanning calorimetry to describe the whole curing process. Then several specially designed samples of different feature cure degrees were prepared and used to reflect the dielectric properties of the composite during microwave curing. It was demonstrated to be a feasible plan for both test accuracy and efficiency through extensive experimental research. Based on this method, the anisotropic complex permittivity of a carbon fiber/epoxy composite during microwave curing was accurately determined. Statistical results indicated that both the dielectric constant and dielectric loss of the composite increased at the initial curing stage, peaked at the maximum reaction rate point and decreased finally during the microwave curing process. Corresponding mechanism has also been systematically investigated in this work.     

Surface Plasmon-polariton Study of the Optical Dielectric Function of Copper

Abstract

The optical dielectric function of copper is measured by excitation of surface plasmon-polaritons on a copper-covered silica grating for a range of wavelengths in the visible region of the spectrum. By exciting the surface plasmon-polariton at the grating/copper interface, the copper is protected from oxidation and contamination. Comparison of angle-dependent reflectivities to grating modelling theory gives both the real and imaginary parts of the dielectric function of the copper. The results compare very favourably with those obtained by other workers using more conventional methods for samples held in a vacuum.     

Domain Walls Due to Anisotropic Diffusion in 3.8% 3He-4He Solutions

Nonlinear anisotropic spin diffusion is considered in ³He-⁴He solutions at the ³He concentration 3.8% where spin-rotation effects are absent. For large anisotropy D _∥ D _⊥ it is shown that a long-lived domain wall solution exists in which transverse magnetization is confined in a tube between two reservoirs of up and down spins, as in a longitudinal spin diffusion experiment. This is possible when D _∥ D _⊥ because diffusion of the transverse magnetization away from the domain wall is balanced by longitudinal diffusion toward the wall. Furthermore, the spin current between the up- and down-spin reservoirs is reduced because the spins must diffuse through the domain wall via transverse diffusion. The decay rate of the wall due to small external and demagnetizing field gradients is also calculated.     

Green's Function Method for the Radiative Transfer Problem. I. Homogeneous non-Lambertian Surface

An application of the Green's function method to the one-dimensional radiative transfer problem with a non-Lambertian surface is described. This method separates atmospheric radiative transport from the lower boundary condition and allows expressing a solution analytically for an arbitrary surface reflectance. In the physical sense, the Green's function represents bidirectional atmospheric transmission for the unitary radiance source located at the bottom of the atmosphere. The boundary-value problem for the Green's function is adjoint to the problem for atmospheric path radiance, and therefore it can be solved by use of existing numerical methods by reversal of the direction of light propagation. From an analysis of an exact operator solution and extensive numerical study, we found two accelerating parameterizations for computing the surface-reflected radiance. The first one is a maximum-eigenvalue method that is comparable in accuracy with rigorous radiative transfer codes in calculations with realistic land-cover types. It requires a total of the first three orders of the surface-reflected radiance. The second one is based on the Lambertian approximation of multiple reflections. Designed for operational applications, it is much faster: Already the first-order reflected radiance ensures an average accuracy of better than 1%.     

3-D Nonequilibrium Green's Function Simulation of Nonperturbative Scattering From Discrete Dopants in the Source and Drain of a Silicon Nanowire Transistor

As these As transistors are scaled to nanometer dimensions, the discreteness of the dopants becomes increasingly important. Transistors of 3 times 3 nm² cross section contain, on average, approximately one dopant atom per nanometer of length, making any self-averaging impossible. The individual random dopants act as localized scatterers whose distribution, and therefore, impact on the electron transport, varies from device to device. This is complemented by electrostatic variation in the potential that controls the threshold voltage and the dominant current paths. The current density is greatly influenced by resonances associated with the attractive potential of the donors and screening effects. In this paper, for the first time, a full 3-D nonequilibrium Green's function (NEGF) simulation in the effective mass approximation has been used to study the influence of individual discrete donors in the source/drain on the I-V characteristics of a narrow n-channel Si nanowire transistor. We have compared devices with microscopically different configuration of dopants. The simulated variations in the I-V curves are analyzed with reference to the behavior of the transmission coefficients. We have highlighted the importance of resonance states when solving the NEGF and Poisson equations self-consistently.