用多极理论分析圆桩对称微波谐振腔

用多极理论计算具有复杂几何形状、圆柱对称微波腔的谐振频率,推导出用多极理论计算圆柱对称微波腔谐振频率的本征值方程。三个工程实例的计算结果表明,用多极理论计算圆柱对称微波腔谐振频率,不仅具有较高的计算精度,而且可以很方便地应用于复杂几何形状圆柱对称微波腔工程问题的设计与计算,多极理论是计算圆柱对称微波腔谐振频率的一种有效方法。     

用多极理论分析圆柱对称微波谐振腔

 用多极理论计算具有复杂几何形状、圆柱对称微波腔的谐振频率,推导出用多极理论计算圆柱对称微波腔谐振频率的本征值方程。三个工程实例的计算结果表明,用多极理论计算圆柱对称微波腔谐振频率,不仅具有较高的计算精度, 而且可以很方便地应用于复杂几何形状圆柱对称微波腔工程问题的设计与计算,多极理论是计算圆柱对称微波腔谐振频率的一种有效方法。     

Gelfand-Dickey算子分解,B?cklund-Darboux变换及对称

利用Gelfand-Dickey算子的分解导出了GKdV方程的n个B?cklund-Darboux(BD)变换及对应的对称的精确形式．这一结果推广了Lou等最近关于KdV,Kadomtsev-Petviashvilli(KP)等方程的BD变换同非局所对称性的结果．作为副产品同时给出Generalized-KdV方程的行列式形式解. 关键词：     

磁多极场场参数的理论计算与分析

根据磁多极场的对称性，首先导出了磁多极场磁场分量的泰勒级数展开式，定义了磁多极场的场参数，然后根据毕奥-萨伐尔定律，导出了马鞍型磁多极场线圈的场参数理论计算公式.对各个场参数数量级的大小进行了分析，找出了场参数的递推规律，给出了场参数高阶导数的计算方法，从而能够准确计算整个空间的磁场值.还从简单单根导线计算结果过渡到多根导线或具有某种连续分布的情况. 这对于磁二极场、磁四极场、磁六极场等的应用提供了可靠的理论依据. 关键词： 磁多极场 场参数 马鞍型线圈     

温度的相对论变换

同长度一样,热力学系统的内能增量和绝对温度也是洛仑兹收缩的,本文用相对论与势 方法导出了这些变换关系。     

电磁波相位不变性的推导

本文直接利用洛伦兹变换，导出电磁波四维波矢的变换关系，并以此为据导出电磁波的相位不变性。     

温度的相对论变换

同长度一样,热力学系统的内能增量和绝对温度也是洛仑兹收缩的．本文用相对论与热力学的方法导出了这些变换关系．     

孤子方程求解的投影矩阵法

本文全面论述了孤子方程求解的投影矩阵法。不仅导出孤子解间的变换关系(孤子变换),而且导出以前未明确得到的呼吸子解之间的变换关系(呼吸子变换),并一般地证明了孤子解的非奇异性。 关键词：     

用四端星形电阻网络到四端网状电阻网络的等效变换求田字形不对称电阻网络的等效电阻

本文简明推导了四端星形电阻网络到四端网状（全网）电阻网络的等效变换式,并应用它导出了田字形不对称电阻网络的等效电阻．     

低维非线性系统的一般多线性变量分离方法和局域激发模式

基于Bcklund变换的多线性变量分离方法(BT-MLVSA)是求解非线性系统的一种非常有效的方法. 一般多线性变量分离方法(GMLVSA)是该方法的推广. 实现GMLVSA主要有四种途径，一是先把场量按照多个任意函数(通常考虑两个函数的情形)展开得到关于多个函数的多线性方程，另一种途径是推广变量分离的假设，第三类是基于Darboux变换的多线性变量分离方法(DT-MLVSA)，第四类是导数相关泛函变量分离法. 利用第一类GMLVSA，可以得到(2+1)维mNNV系统和sine-Gordon系统的一般多线性变量分离解. 把第一类GMLVSA推广到二维非线性系统，这些系统是通过对称约化(2+1)维sine-Gordon.系统得到的. 也就是说，一般多线性变量分离可解性在对称约化下从高维系统到低维系统得到了保持. 这也提供了一条从高维非线性系统导出可GMLVSA求解的低维非线性系统的有效途径. 关键词： Bcklund变换 多线性变量分离 sine-Gordon系统 对称约化     

Approaches to the Monopole-Dynamic Dipole Vacuum Solution Concerning the Structure of Its Ernst Potential on the Symmetry Axis

The FHP (Fodor, Hoenselaers, Perjés) algorithm [1] allows to obtain the relativistic multipole moments of a vacuum stationary axisymmetric solution in terms of coefficients which appear in the expansion of its Ernst potential on the symmetry axis. First of all, we will use this result in order to determine, at a certain approximation degree, the Ernst potential on the symmetry axis of the metric whose only multipole moments are mass and angular momentum. By using Sibgatullin's method [2] we then analyse a series of exact solutions with the afore mentioned multipole characteristic; besides, we present an approximate solution whose Ernst potential is introduced as a power series of a dimensionless parameter. The calculation of its multipole moments allows us to understand the existing differences between both approximations to the proposed pure multipole solution.     

电磁多极场的分析和计算

多极系统是由几个对称地放置在方位角方向上、并具有一定电(磁)位的电(磁)极所组成的系统。它们所产生的非旋转对称场称为多极场。多极场是一种广泛类型的电磁场。例如包括了各种偏转场,四极、六极、八极透镜场等。它们在电子束器件、电子光学仪器和高能加速器中得到广泛应用。本文采用傅里叶展开法将求解空间(三维)的电磁多极场问题化为求解一系列的二维谐波电(磁)位的问题。这些谐波电(磁)位满足一定的二阶偏微分方程,在一定的边界条件下,可以采用逐次张弛方法进行求解。然后将谐波电(磁)位迭加,便得到所要求的多极场的电(磁)位分布。编制了计算电磁多极场的通用程序。对于几种典型的多极场模型(单个和二单元的四极透镜,以及圆柱环形偏转线圈等)进行了计算与检验。计算实践表明,这种傅里叶展开法适用于计算电子束器件和各种电子光学仪器中的多极场,并可算出其边缘效应(弥散场),因此具有一定的意义。 关键词：     

Baryon octupole moments<Superscript>⋆</Superscript>

We report on a calculation of higher electromagnetic multipole moments of baryons in a non-covariant quark model approach. The employed method is based on the underlying spin-flavor symmetry of the strong interaction and its breaking. We present results on magnetic octupole moments of decuplet baryons and discuss their implications.     

Zur Aufspaltung von Kristalltermen vermöge der Wechselwirkung äquivalenter Gitterteilchen

The interaction between equivalent ions in a crystal is expanded in a series of coupled multipole transitions between the states of the ions. The possible multipole transitions are selected grouptheoretically with regard to the symmetry of the crystalline field. Thus the splitting ofBethe's crystal levels is calculated.     

The theory of conductivity of ternary composite films with a two-sublattice structure

A general method is suggested for solving problems on the conductivity and other effective characteristics of two-dimensional ternary two-sublattice models with inclusions of arbitrary shape. The complex potential outside of the inclusions is expressed in terms of the Weierstrass zeta function and its derivatives. The electric field induced on a separate inclusion is described using the matrix of multipole polarizabilities, for which the symmetry relation is found. The suggested approach enables one to find exact virial expansions for the basic electrophysical characteristics of such systems.     

Cc,Cs, and parasitic correction in quadrupole probe-forming lenses

Approximate expressions are derived for the second and third order aberrations of a quadrupole doublet, allowing for aberrations intrinsic to fields of perfect symmetry, for parasitic aberrations of imperfect symmetry, and for compensating multipole lenses. Five third-order coefficients are found, and expressed in terms of four octopole strengths and the first-order parameters of the doublet as determined by its dimensions. For compensation of third-order aberrations of achromatic quadrupole/octopole lenses, either skew octopole lenses are required externally, or lenses with more than 8 poles are required coincident with the quadrupoles. If an octopole lens is added between the quadrupoles of the achromatic doublet, the spherical aberration of a condenser lens may be compensated. Such a Cs and Cc compensated quadrupole doublet is suitable for use as a probe-forming lens in focused ion beam systems and ion microscopes.     

The two-body multipole problem of electrodynamics

A 2-body system composed of two objects having arbitrary distributions of charge and current is discussed. An expression for the velocity dependent potential between these two objects has been obtained in the non-relativistic approximation. This potential consists of two parts viz. a velocity independent scalar potential Φ_eff and another part which is linearly dependent on the relative velocity between the objects. The second part naturally suggests a vector potential A_eff. The potentials have been expanded into multipole terms. It has been found that Φ_eff is a sum of two components viz. Φ_EE and Φ_MM such that each multipole term in Φ_EE represents an interaction between the electric multipoles of the two systems, each term in Φ_MM represents an interaction between their magnetic multipoles whereas each term in A_eff represents an interaction between an electric multipole of one and a magnetic multipole of the other. The results have been applied to the interaction between an electric dipole and a magnetic dipole. The symmetry among the multipole terms in A_eff suggests vanishing vector potential between two identical objects. A corollary of this appears to be absence of spin orbit interaction between two identical particles in the same spin state.     

Monopole-quadrupole static axisymmetric solutions of Einstein field equations

An infinite family of exact solutions of the Einstein vacuum equations for the static case with axial symmetry is presented in an explicit form. Each solution of this family contains two arbitrary parametersM andQ that represent the mass and quadrupole moment of the source. In addition, each solution can be interpreted physically as the pure relativistic quadrupole correction to the Schwarzschild solution at a given multipole order.     

The quadrupole–quadrupole polarizability of a non-magnetic molecule

The quadrupole–quadrupole polarizability of a molecule introduced by Buckingham is not a unique molecular property, in the sense that it depends on an arbitrary choice of the origin of the molecular coordinates. To obtain a physically acceptable form of this property for a non-magnetic molecule, a linear combination is taken of molecular polarizabilities of the relevant multipole order (electric octopole-magnetic quadrupole). By requiring this combination to possess the desired space–time and symmetry properties, as well as origin independence, an acceptable quadrupole–quadrupole polarizability is obtained. Expressions are presented for the components of this polarizability for molecules of certain symmetries.