三种柱面形静电场问题的探讨

运用复变函数、保角变换等理论，把分离圆柱面形、偏心圆柱面形和偏轴椭圆柱面形变换成横截面为平行板，并计算出它们的电容、电势和电场强度等静电场问题．     

平行板-圆柱平板线中的TEM波及其特性阻抗

用保角变换法得出平行板-圆柱平板线TEM波分布的近似解析解.首先通过保角变换将平行板-圆柱平板线的横截面变换为圆同轴线的横截面,求出由静态场在此边界条件下电场的解,再乘以波动因子得到TEM波的电场解,然后根据由麦克斯韦方程所联系的电场与磁场的关系,得到磁场的分布,从而给出平行圆同轴线中TEM波的分布规律,最后由变换函数关系得到平行板-圆柱平板线TEM波的分布规律.通过数学软件MATLAB绘制出TEM波在其横截面上的结构图,并计算出其特性阻抗.研究结论对于计算该传输线的衰减常数、了解其功率容量、考虑功率耦合及设计有关的有源器件均有一定的参考价值.     

两平行相交带电圆柱导体的空间电场

用镜象法求解由两平行相交带电圆柱导体所组成的柱形导体边界静电场边值问题,通过简单的数学分析,获得两类平行相交带电圆柱导体问题的空间电场分布．     

同轴谐振腔高阶横磁模式参数的研究

理论计算和分析了微波圆柱同轴谐振腔高阶横磁(TM)模式的系列关联参数.研究发现：与圆柱腔相比, 同轴谐振腔的TM_n10模式有较大的模式间隔，即工作模式能够远离非工作模式的干扰，这有利于保持器件稳定的频率和功率；在保持腔长不变、腔横截面外半径取特定值时，腔内电场峰值位置的轴向特性阻抗随内径的变化存在极大值；在高频段可以采用任意大横截面的腔体结构和任意阶的模式.计算结果与仿真结果相一致. 关键词： 高阶横磁模式 圆柱同轴谐振腔 特性阻抗 多注速调管     

点电荷和介质球系统的镜像电荷分布

用镜像法处理介质中的静电问题,一般书刊上只论及到两种情形:一是两均匀电介质交界面为一无限大平面,在其中一种介质中有一点电荷;二是无限长均匀电介质圆柱置于另一均匀介质之中,在圆柱内或圆柱外有一与其轴线平行的无限长线电荷.在这两种情形中,电势都可以用简单的镜像系表示     

平行板-偏心圆柱耦合传输线的特性阻抗

提出用保角变换边界元组合法计算平行板-偏心圆柱耦合传输线的特性阻抗。通过对三种基本偏心结构的计算,获得平行板-偏心圆柱耦合传输线的特性阻抗数据。这些数据不仅可为平行板-偏心圆柱耦合传输线的准确设计提供理论依据,而且可为同轴传输线的加工制作精度提供理论参考。     

两平行接地大导体板间带电圆柱体的电场及系统的电容

利用保角变换,给出两平行接地大导体板间带电圆柱体电场的分布规律,绘制其横截面上的电场线与等势线图,并计算该导体系统单位长度的电容.     

微粗糙圆柱的各向异性散斑特性研究

分析了高斯光束照射微粗糙圆柱在菲涅尔衍射区形成的散斑图像统计特性,给出了强度起伏自相关函数与表面曲率及粗糙程度等参数之间的关系.根据强度起伏自相关函数的离散化定义,实验并计算了圆柱轴向与径向结构有差异情况下的散斑强度起伏相关函数.结果表明,对于C1和C2圆柱沿垂直于圆柱轴向的散斑尺寸变长,强度起伏自相关函数沿平行和垂直于圆柱轴两个方向的波动相差较大;对于C3和C4圆柱两个方向上的散射特性基本相同;测量C1和C3的结果表明,散斑尺寸和形状依赖于圆柱表面的皱褶和圆柱表面曲率两个因素.研究结果对于如柱型管道、轴承等方面的机械制造的质量控制有重要的应用价值.     

巧算常见均质旋转体对母线的转动惯量

运用惯量张量法及平行轴定理，较方便地计算常见均质旋转体(圆锥、圆台)对母线的转动惯量，而均质圆柱对母线的转动惯量可以作为一特例给出．     

一种自聚焦透镜的成像解

自聚焦锥透镜与圆柱透镜相比较，有其特殊之处。柱透镜在近轴平行光入射时，光线的振幅、相位、周期保持不变，而锥透镜的三者均发生变化，而且求解锥透镜的光线方程也比圆柱透镜复杂得多。本文推导了一个锥透镜的光线方程。可据此设计经过锥透镜后的光源大小，这在微系统照明中非常有用。     

海面与其上方双矩形截面柱复合散射的混合算法研究

采用Pierson-Moscowitz(PM)海谱和Monte Carlo方法模拟实际的粗糙海面, 基于矩量法和基尔霍夫近似的混合算法研究了海面与其上方双矩形截面导体柱的复合电磁散射特性, 得出了复合散射系数的角分布曲线, 计算了复合散射系数随海面参数、矩形截面柱参数以及入射波参数的变化情况, 并做了详细分析与讨论, 得到了PM谱海面与其上方双矩形截面柱复合散射特性. 结果表明, 与单纯的矩量法相比较, 采用基于矩量法和基尔霍夫近似的混合算法, 既可获得较高的准确性, 同时又可减少计算时间和内存占用量, 而且粗糙面尺度越大该优势越明显.     

Confinement of columnar diblock copolymers: Simulations, theory and applications

The inherent nanoscale morphologies of self-organizing diblock copolymer melts are now being investigated for a variety of technological applications. To obtain global, well-oriented, regular patterns requires suitably confining and aligning the melt between two flat plates. Here we consider such confinement for an asymmetrical diblock melt, which forms columns of the minority phase in a matrix of the majority phase. We investigate this system with a combination of numerical simulations and strong segregation theory and make suggestions as to when perpendicular orientation should prevail over parallel orientation of the columns. Received 22 May 2001 and Received in final form 14 February 2002     

Percolation in Media with Columnar Disorder

We study a generalization of site percolation on a simple cubic lattice, where not only single sites are removed randomly, but also entire parallel columns of sites. We show that typical clusters near the percolation transition are very anisotropic, with different scaling exponents for the sizes parallel and perpendicular to the columns. Below the critical point there is a Griffiths phase where cluster size distributions and spanning probabilities in the direction parallel to the columns have power-law tails with continuously varying non-universal powers. This region is very similar to the Griffiths phase in subcritical directed percolation with frozen disorder in the preferred direction, and the proof follows essentially the same arguments as in that case. But in contrast to directed percolation in disordered media, the number of active (“growth”) sites in a growing cluster at criticality shows a power law, while the probability of a cluster to continue to grow shows logarithmic behavior.     

异核多脉冲实验的相位循环设计方法

本文介绍了异核多脉冲实验相位循环的设计方法.先分别设计两个不同核的相位循环编码行列,然后根据正交检测相位要求把两个列数相等的行列以并联方式结合起来,就可得异核多脉冲实验的相位循环.     

Multi-scattering of electromagnetic waves by nanoshell aggregates

A general analytical expression is derived for calculating the total scattering cross-section of an aggregate of nanoparticles. The approach is based on the far zone approximation and repeated use of recursive relations for Bessel functions and Legendre polynomials. In comparison with the existing formula for total scattering cross-section, the expression converges faster and makes it easier to analyze the terms that characterize the interactive coupling between nanoparticles during multiple scattering of electromagnetic waves. The expressions are valid for particle aggregates in which no two particles are in direct contact. Calculated results compare well with measurements for a nanoshell dimer. For a linear chain of particles with the chain axis parallel to the polarization direction of the electric field, analysis shows that the red-shift of resonance peaks results primarily from electrons in metal shells of two adjacent particles oscillating out-of-phase to cancel each other’s radiation effects. Multi-scattering in aggregates with more complex arrangements may be explained by combining the effects of linear particle chains.     

Design of Multichannel Optical Splitter without Bends

The theory of a planar geometry splitter involving only parallel waveguide channels of rectangular cross-section is presented. The strictly parallel geometry allows for a semi-analytical analysis that makes possible the design of a splitter, which can divide an optical signal into uncoupled outputs carrying designated fractions of the input power. The theoretical intrinsic losses in the proposed splitter is shown to be minimal, and device design parameters are provided.     

On the influence of anisotropy on the magnetic small-angle neutron scattering of superparamagnetic particles

This paper presents a calculation of the magnetic small-angle neutron scattering cross-section resulting from a dilute ensemble of superparamagnetic particles exhibiting uniaxial magnetic anisotropy. We focus on the two experimentally relevant scattering geometries in which the incident neutron beam is perpendicular or parallel to an applied magnetic field, and we discuss several orientations of the anisotropy axes with respect to the field. Magnetic anisotropy has no influence on the magnetic small-angle neutron scattering when the particles are mobile, as is the case e.g. in ferrofluids, but, when the particles are embedded in a rigid non-magnetic matrix and the orientations of the anisotropy axes are fixed, significant deviations compared to the case of negligible anisotropy are expected. For the particluar situation in which the anisotropy axes are parallel to the applied field, closed-form expressions suggest that an effective anisotropy energy or anisotropy-energy distribution can be determined from experimental scattering data. Received 8 November 2001     

Structural waveguide behaviour of a beam–plate system

Structures which have a constant cross-section normal to a longitudinal axis can be considered as waveguides in which vibration can propagate in the form of various waves in the longitudinal direction. The dynamic behaviour of such systems can be found by using a Fourier transform approach in terms of wavenumbers in the longitudinal direction. Analytical solutions are available for simple, infinitely long waveguides, whereas for more complex waveguides numerical approaches have been developed using finite element techniques to describe the cross-section. In the present paper an analytical Fourier transform approach is used to find the dynamic behaviour of a system consisting of two parallel beams coupled by a plate, when a point force is applied to one of the beams. Multiple waves occur in the longitudinal direction, the number of waves depending on the number of modes of the equivalent cross-section. However, the motion of the driven beam is shown to be dominated by the contribution from only one or two waves at each frequency, these having wavenumbers closest to that of the uncoupled beam. The motion of the plate is also shown to be dominated by these wavenumbers for excitation on the beam. Experimental results are obtained on beam–plate–beam systems with identical and non-identical beams, which show good agreement with the predictions. In particular, these confirm that the plate response is dominated by waves with wavenumbers in the beam direction that follow those of the excited beam.