Deriving the time-dependent dyadic Green’s functions in conductive anisotropic media

A homogeneous anisotropic conductive medium, characterized by symmetric positive definite permeability and conductivity tensors, is considered in the paper. In this anisotropic medium, the electric and magnetic dyadic Green’s functions are defined as electric and magnetic fields arising from impulsive current dipoles and satisfying the time-dependent Maxwell’s equations in quasi-static approximation. A new method of deriving these dyadic Green’s functions is suggested in the paper. This method consists of several steps: equations for electric and magnetic dyadic Green’s functions are written in terms of the Fourier images; explicit formulae for the Fourier images of dyadic Green’s functions are derived using the matrix transformations and solutions of some ordinary differential equations depending on the Fourier parameters; the inverse Fourier transform is applied numerically to obtained formulae to find dyadic Green’s functions values. Using suggested method images of electric and magnetic dyadic Green’s function components are obtained in such conductive anisotropic medium as the white matter of a human brain.     

Stable Boundary and Internal Data Reconstruction in Two-Dimensional Anisotropic Heat Conduction Cauchy Problems Using Relaxation Procedures for an Iterative MFS Algorithm

We investigate two algorithms involving the relaxation of either the given boundary temperatures (Dirichlet data) or the prescribed normal heat fluxes (Neumann data) on the over-specified boundary in the case of the iterative algorithm of Kozlov91 applied to Cauchy problems for two-dimensional steady-state anisotropic heat conduction (the Laplace-Beltrami equation). The two mixed, well-posed and direct problems corresponding to every iteration of the numerical procedure 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. The iterative MFS algorithms with relaxation are tested for over-, equally and under-determined Cauchy problems associated with the steady-state anisotropic heat conduction in various two-dimensional geometries to confirm the numerical convergence, stability, accuracy and computational efficiency of the method.     

The Effects of Chemical (isotropic) and Anisotropic Etching Processes on the Roughening of Nanocomposite Substrates

Simulation results of roughening of nanocomposite materials during both isotropic and anisotropic etching processes based on the level set method are presented. It is clearly shown that the presence of two phases with different etching rates affects the development of surface roughness and that some roughness characteristics obey simple scaling laws. In addition, certain scaling laws that describe the time dependence of the rms roughness w for various etching processes and different characteristics of the nanocomposite materials are determined.     

基于空间自适应Bayesian缩减的NSCT域图像去噪方法

提出了一种基于空间自适应Bayesian缩减的NSCT域图像去噪方法。该方法运用了广义高斯分布对NSCT域图像的子带系数进行建模,并通过构造各向异性的椭圆窗口来描述各个子带内系数的局部背景特性,从而建立了NSCT域空间自适应Bayesian缩减机制的图像去噪方法。通过图像去噪实验验证了所提出方法的有效性。同时,与4种具有平移不变性的Contourlet去噪方法做了对比,进一步证实了所提出方法的优良去噪性能。     

Elastic fields produced by a point source in solids of general anisotropy

Explicit expressions for three-dimensional elastostatic Green's functions in solids of general anisotropy are derived by means of an integral-representation technique and a subsequent application of the residue calculus. A direct calculation for the derivatives of the displacement Green's functions is quite complicated. However, relatively simple expressions can be obtained for the integration of the derivatives along a line or a surface. These integrals are in fact more useful, because, in most applications, not the derivatives, but their integrals along lines or surfaces are needed. Discussions regarding degenerate materials and details in evaluation of the residues at multiple poles are also given. The results presented in this paper are sufficient for the implementation of the boundary-element method for bodies of general anisotropic solids.     

各向异性介质波导结的研究

本文结合模式展开方法和矢量有限元方法，分析放置各向异性介质的N端口波导结，对几种Y型波导结进行数值计算，所得计算数据与有关文献中提供的实验数据吻合良好。     

基于偏微分方程的医学磁共振图像去噪

本文引入了基于偏微分方程的Perona-Malik模型,并结合了Catte的高斯扩散滤波器的概念,给出了一种针对医学磁共振图像去噪的方法及其实现。文中通过给出不同参数,对结果加以比较分析。把该方法应用于医学图像去噪,得到比较令人满意的结果。     

Effects of anisotropic scattering of radiation in laminar forced convection in a parallel-plate duct

Effects of anisotropic scattering to heat transfer in hydrodynamically-developed, thermally-developing steady laminar forced flow of a gray fluid between two infinite parallel plates are investigated for the case when the inlet temperature of the fluid is less than the wall temperature. An implicit finite difference scheme is applied to solve the energy equation, while the high order P_N method is used to solve the radiation part of this problem. The effects of the anisotropy, the conduction-to-radiation parameter, the optical thickness, the reflectivity of the plates and the inlet temperature on the local Nusselt number are studied.     

外加电场作用下光折变晶体的各向异性自衍射

对于晶体ｃ轴平行于入射面的实验配置，观察到了掺杂钾钠铌酸锶钡（ＫＮＳＢＮ）晶体在外加电场作用下的各向异性自衍射现象；同时给出了包含光栅波矢空间分布和空间电荷场二阶分量作用的各向异性自衍射的耦合波方程及其数值解，理论分析和实验结果都表明各向异性自衍射光来自于两束入射光的共同作用