新型椭圆函数波导族的保角变换有限差分解法

保角变换一直是求解边值问题的重要方法，但以往在电磁场领域的应用多限于求解静态和准静态问题。利用保角变换及椭圆函数的理论和方法结合数值技术求解导波问题中的二维Ｈｅｌｍｈｏｌｔｚ方程。     

采用保角变换求解一类TEM模传输线的衰减常数

本文提出采用保角变换法求解一类TEM模传输线的衰减常数。通过适当的保角变换能够映射成(包括数值保角变换)正规圆同轴线或平板电容的情况均可采用这种方法。文中给出了解析结果和数值实例。     

椭圆带状线特性阻抗的准确解

本文借助于保角变换理论,导出了椭圆带状线特性阻抗的准确解,这为椭圆带状线的设计提供了理论数据。     

带有小椭圆度的圆波导移相器

引言圆波导中的H_(11)模通过加载圆波导移相器后,能形成圆极化波。理论上要计算这类问题是非常困难的,而计算加载方波导的相移变化是有法可循的。于是,我们很自然的想到能否将加载圆波导保角变换为加载方波导,使问题得到简化。本文通过保角变换介绍了加载圆波导的一种近似的相移计算方法。理论计算和实测结果比较符合,误差小于1.3°。保角变换在复杂截面输传线的特性阻抗计算中的作用是     

基于光学保角变换的电磁器件设计

保角变换是基于解析函数的一种非常重要的解析方法,利用保角变换可以将虚拟空间中复杂的边界曲线转化为物理空间中简单的边界曲线,从而求解二维平面场问题。文章主要综述并介绍保角变换在几何光学中的应用,通过控制光线传播来设计完美隐身衣、中继透镜、波导弯角和透镜天线等新型电磁器件。最后利用射线追踪仿真和全波仿真对设计加以证明。     

一种新型波导移相器的研制

借助相移-频率特性、保角变换和微扰理论,研制出了新型的宽带移相器。该移相器已用于卫星地面站,性能很好。实测数据与理论结果吻合。     

两种新型的圆极化器

根据微扰理论和保角变换理论,探讨了方波导对角微扰以及对角插入介质片后的相移特性,并研制了几种新型的波导圆极化器,理论与实测数据吻合较好。     

波导表面电极的电场分布

本文给出了波导表面平行电极的电场分布的两种理论计算方法,并给出了数值计算结果,最后比较了保角变换法和静电场近似法的优缺点。     

用Cassinian变换FDTD方法分析几种特殊截面波导传输特性

本文把保角变换应用于紧凑格式2D/FDTD算法,给出了保角变换FDTD算法差分公式,提出了焦点的处理方法.用Cassinian变换分别计算了椭圆波导、茧形波导的截止波长与色散曲线,以及屏蔽平行双线高阶模的截止波长.     

矩量法结合保角变换求解复杂二维边值问题

本文论述矩量法结合保角变换求解复杂二维边值问题。它通过保角变换使一种结构变成另一种新的结构,通过矩量法和“Collin原则”的结合,估计了耦合线的参数的数值上下界。文中还给出了某些紧耦合情况的应用实例。     

Numerical Stability and Numerical Dispersion of Compact Conformal Mapping 2D-FDTD Method Used for the Dispersion Analysis of Waveguides

In dispersion analysis of waveguides with particular cross-section by compact 2D-FDTD method, using conformal-boundary coordinates can obtain high computational accuracy. The transformation from conformal-boundary coordinates to rectangular coordinates can be done by conformal mapping technique in order to match Yee algorithm. In this paper, numerical stability and numerical dispersion equation of compact conformal mapping 2D-FDTD (CCM-2D-FDTD) method are derived. It is shown that the upper limit of Courant number for CCM-2D-FDTD is always smaller than 1/√2. As an example, the dispersion equation is used to examine the impact of number of cell for circular waveguide.     

Flattening maps for the visualization of multibranched vessels

In this paper, we present two novel algorithms which produce flattened visualizations of branched physiological surfaces, such as vessels. The first approach is a conformal mapping algorithm based on the minimization of two Dirichlet functionals. From a triangulated representation of vessel surfaces, we show how the algorithm can be implemented using a finite element technique. The second method is an algorithm which adjusts the conformal mapping to produce a flattened representation of the original surface while preserving areas. This approach employs the theory of optimal mass transport. Furthermore, a new way of extracting center lines for vessel fly-throughs is provided.     

平面镜像法与有源保角变换

本文把镜像法与复保角变换有机地结合起来。指出对于实际中的一大类问题,只须采用平面镜像做基本模型,而对复杂形状作有源保角变换,就可以归结为平面镜像。特别有兴趣的是变换后的求解区域可以允许存在原问题∞处的镜像电荷,从而突破了一般镜像法的一个准则。     

A method of face recognition using 3D facial surfaces

Face recognition is one of the most rapidly developing areas of image processing and computer vision. In this work, a new method for face recognition and identification using 3D facial surfaces is proposed. The method is invariant to facial expression and pose variations in the scene. The method uses 3D shape data without color or texture information. The method is based on conformal mapping of original facial surfaces onto a Riemannian manifold, followed by comparison of conformal and isometric invariants computed in this manifold. Computer results are presented using known 3D face databases that contain significant amount of expression and pose variations.     

计算复杂形状波导截止频率的高效方法

提出一种使用保角变换结合矩量法,计算复杂形状波导截止频率的新方法,该方法采用解析法或数值法,把复杂截面的波导变换为圆形区域,再采用矩量法求解波导的截止频率。实验结果验证了该方法的有效性。     

保角映射方法在四孔垂直型霍尔器件性能预测中的应用

不同于传统的结构上对称的五孔结构，新型的四孔和六孔垂直型霍尔器件更具有电流上的对称性，因此可以更好地采用旋转电流技术来消除器件的初始失调。本文利用保角映射方法实现了对四孔垂直型霍尔器件性能的预测。并改进了该方法，在其中加入了对结场效应的计算，使得计算结果更加精确。最后对计算和仿真结果进行了分析对比，其中电流灵敏度的误差小于5%，电压灵敏度的误差约为13%。充分证明了保角映射方法可以应用于对垂直型霍尔器件的性能预测。     

A comment on "Modeling of MOS transistors with nonrectangular gate geometries"

In the above mentioned paper, MOS transistors are investigated using the well-known Sah model. It was proved that for a given sheet conductivity law, conformal mapping techniques can be used to treat the nonlinear potential equation. It will be demonstrated that, by introducing an auxiliary potential function, the problem is reduced to the Laplace' equation, for which conformal mapping techniques are obvious. The method is also extended to arbitrary sheet conductivities.     

Genus zero surface conformal mapping and its application to brain surface mapping

We developed a general method for global conformal parameterizations based on the structure of the cohomology group of holomorphic one-forms for surfaces with or without boundaries (Gu and Yau, 2002), (Gu and Yau, 2003). For genus zero surfaces, our algorithm can find a unique mapping between any two genus zero manifolds by minimizing the harmonic energy of the map. In this paper, we apply the algorithm to the cortical surface matching problem. We use a mesh structure to represent the brain surface. Further constraints are added to ensure that the conformal map is unique. Empirical tests on magnetic resonance imaging (MRI) data show that the mappings preserve angular relationships, are stable in MRIs acquired at different times, and are robust to differences in data triangulation, and resolution. Compared with other brain surface conformal mapping algorithms, our algorithm is more stable and has good extensibility.     

Analyzing Semicircular Groove Guide with the Conformal Mapping Technique

Semicircular groove guide is a kind of waveguide for millimeter waves. In this paper, a conformal mapping technique is used to analyze it. Several semicircular groove guides are calculated with the method. It is shown that their cutoff wavelength calculated by the method are very close to those calculated by the transverse resonance method.