跨音速透平叶栅在迴转面上的速度图法设计

以往的速度图法设计,都限于平面流动,本文首先提出了相应于迥转流面的速度坐标的流函数方程和由速度面返回流面的积分方程,作为跨音透平叶栅亚音区部分的计算的基本方程。在超音区,我们从相应于迥转面的速度坐标流函数方程出发,导得了相应于迴转流面的压缩性函数,从而可以在迴转面上应用混合型方程的解析解。     

强流AVF型迴旋加速器中的空间电荷效应和束晕

详细推导了AVF型迴旋加速器中束团粒子在曲线坐标系中的动力学方程(考虑和不考虑空间电荷相互作用力两种情况).在假定动力学方程中各参数值的前提条件下,用Lunge-Kutta方法对考虑空间电荷时的动力学方程进行了数值计算.结果表明,束晕的形成和发展同样也是强流迴旋加速器中束流损失的一个主要原因.但束晕形成的机制不同于直线加速器的情况,它不是由共振和混沌引起,而是由于粒子的排斥运动和束团内粒子的涡流运动引起的.     

等离子体与外迴路有强耦合的平衡计算

本文考虑了快放电的特点,用积分方法解轴对称自由界面平衡方程。并与解迴路方程相结合,求出等离子体与外迴路有较强耦合情况下的平衡位形及位形随时间的演化。 关键词：     

Yang-Mills场方程的和乐泛函表述

从规范场理论的积分表述出发,我们把规范场的运动方程——无源的 Yang-Mills 方程改写为和乐泛函(即迴路位相因子)的泛函微分方程。由此进一步导出了二维时空规范理论中的无穷多个泛函微分方程形式的守恒定律.     

强碰撞下的漂移波稳定性

在碰撞存在时,考虑到在扰动电场作用下电子沿磁力线的宏观运动,用迴旋动力技术导出了强碰撞的积分本征方程。随后用LCN方法严格解析地证明了在平板剪切磁场的作用下,漂移波是绝对稳定的。 关键词：     

变截面铁氧体柱中电磁波传播的耦合波理论

在本文中,作者导出了一组普遍的耦合波方程,它描述了在部分填充以迴磁媒质的波导中电磁波的传播。利用这组方程,作者研究了纵向磁化铁氧体柱中的法拉第旋转(铁氧体柱的两端是截面变化的圆锥)。然后仍从耦合波的观点出发,研究了若干其他问题,如铁氧体柱对波的反射、柱的几何不规则性对法拉第旋转的影响。本文的分析说明,耦合波理论特别适用于复杂的包含有铁氧体的电磁场问题,这些问题如果用研究铁氧体时经常利用的正规方法来分析很难求得解决。     

高能俘获粒子对内扭曲模的稳定效应

用Greene,Johnson和Weimer的方法重新推导了各向异性托卡马克等离子体中的Grad-Shafranov平衡方程。从广义能量原理分析了各向异性高能粒子分量对托卡马克等离子体内扭曲模的稳定作用,并以能量慢化分布和压力随方位角变化基本呈方形的两种高能粒子分布为例仔细计算了此作用,找出了迴转点在强场一侧的高能俘获粒子对托卡马克等离子体内扭曲模的稳定窗口,并深入讨论了它与各物理参数的依赖关系。 关键词：     

圆域隧道结中的环形波解

用数值计算法研究圆域隧道结的问题。在充分大的k值、I′tot靠近I-V曲线的迴滞终点和适当的初值条件下,方程有自场φ_ρ的环形波解。经过若干次反射后,波形仍基本保持原来的形状。     

有限分枝分形上的自迴避迹行走

本文考虑在Sierpinski gasket及分支Koch曲线上的自迴避迹行走,运用实空间重整化群技术求出了相应的关联长度临界指数ν。结果表明,在Sierpinski gasket上,自迴避迹行走与自迴避行走属同一普适类;而在较高分枝度(R_max>3)的Koch曲线上,两者属不同普适类。 关键词：     

用电子迴旋共振加热抑制托卡马克中的撕裂模

利用电子迴旋共振加热的定域性,改善等离子体电流分布,从而改善撕裂模的稳定条件,只要电子迴旋共振加热的吸收区能覆盖住撕裂模的共振层,就有很好的稳定效应;而不一定要求电子迴旋共振面与撕裂模的共振面重合,在迴旋加热期间,撕裂模被有效地抑制住。 关键词：     

Identical motion in relativistic quantum and classical mechanics

The Klein-Gordon equation for the stationary state of a charged particle in a spherically symmetric scalar field is partitioned into a continuity equation and an equation similar to the Hamilton-Jacobi equation. There exists a class of potentials for which the Hamilton-Jacobi equation is exactly obtained and examples of these potentials are given. The partitionAnsatz is then applied to the Dirac equation, where an exact partition into a continuity equation and a Hamilton-Jacobi equation is obtained.     

天线理论中的第二类积分方程

本文提出一个决定柱状天线电流分布的新的积分方程,这是一个一维的Fredholm第二类积分方程。它不同于天线理论中惯用的Hallen积分方程。本文着重分析了在天线为无穷长时,由两个方程所解得的电流和磁场,说明第二类积分方程比Hallen方程更适于描述天线的实际情况。还初步进行了有限长度天线的数值计算,结果表明用第二类积分方程进行天线的数值计算是可行的。     

ANALYTICAL SOLUTION OF THE 2n-DIMENSIONAL FOKKER-PLANCK EQUATION WITH HARMONIC OSCILLATOR POTENTIAL

An analytical solution is obtained for the 2n-dimensiona Fokker-Planck equation (F-P equation for short) with the harmonic oscillator potential. A few steps are involved in the derivation. First,the Lagrangian subsidiary equation is solved; then with its integral constants as new variables of the F-P equation, the diffusion equation is obtained and solved; at last, expressed in the original phase space, the solution of the F-P equation .is finally obtained. The analysis for the solution is made. The solution is a Gaussian type function and a δ-function of time. If a particle moves in a well in ali directions, then as t→∞, the distribution function can reach a stationary nonzero distribution-Maxuwell-Boltzmann type distribution (M-B distribution for short).As an example, the 2-dimensional F-P equation is solved and discussed in detail.     

The Einstein-Dirac Equation in Robertson-Walker Space-Time Does Not Admit Standard Solutions

The Einstein-Dirac equation is considered in the Robertson-Walker space-time. Solutions of the equation are looked for in the class of standard solutions of the Dirac equation. It is shown that the Einstein-Dirac equation does not have standard solutions for both massive and massless Dirac field. Also superpositions of massive standard solutions are not solutions of the Einstein-Dirac equation. The result, that is briefly commented, is coherent and complementary to other existing results.     

Wave propagation in a random medium: The solution of the m-nth moment equation with different wavenumbers

The moment equation with different wavenumbers and different transverse coordinates for wave propagation in a random medium is a linear differential equation. It often appears in the study of problems related to wave propagation in a random medium. The differential equation can be converted into an integral equation by using Green's functions and the integral equation can be solved by iteration. The moment equation is solved by the method of successive scatters, too. The solution of the moment equation is a Dyson expansion. The physical implication of the successive solution of the moment equation with different wavenumbers is explained.     

Off-Shell Relativistic Quantum Mechanics and Formulation of Dirac's Equation Using Characteristic Matrices

It is argued that the Klein-Gordon equation isan equation for characteristic functions, i.e.,Fourier-transformed Wigner functions, not for wavefunctions. This statement is derived starting from theoff-shell formulation of relativistic quantum mechanicsby expressing the condition that the mass of theparticle is exactly known. A particular class ofsolutions of the Klein–Gordon equation is formedby the integrable superpositions of pure momentum states. Adirect sum of four copies of the associatedGelfand–Naimark–Segal representation isconsidered. Then one can derive from the Klein-Gordonequation an equation for spinor wave functions. Solutions of the latterequation are in one-to-one correspondence to thesolutions of the Fourier-transformed Dirac equation.Finally, the equation is reformulated as an equation for characteristic matrices.     

输油管道油流静电带电数值计算

对输油管道内油品流动带电问题的数值计算进行了研究.紊流条件下的电荷输运方程是一个对流占优的对流扩散反应方程,采用算子分裂法,将该方程分解为纯对流方程、纯扩散方程和纯反应方程,分别采用特征线法和差分法求解.算例证明,该方法能准确描述管道内电荷分布,因而提供了一种获取冲流电流的可靠方法.     

A new hierarchy system on the basis of a “Master” Boltzmann equation for microscopic density

It is shown that Boltzmann's equation written in terms of microscopic density (namely the unaveraged Boltzmann function) has a wider range of validity as well as finer resolvability for fluctuations than the conventional Boltzmann equation governing Boltzmann's function. In fact the new Boltzmann equation for ideal gases has implications as a microscopically exact continuity equation like Klimontovich's equation for plasmas, and can be derived without invoking any statistical concepts, e.g., distribution functions, or molecular chaos. The Boltzmann equation in the older formalism is obtained by averaging this equation only under a restricted condition of the molecular chaos. The new Boltzmann equation is seen to contain information comparable with Liouville's equation, and serves as a master kinetic equation. A new hierarchy system is formulated in a certain parallelism to the BBGKY hierarchy. They are shown to yield an identical one-particle equation. The difference between the two hierarchy systems first appears in the two-particle equation. The difference is twofold. First, the present formalism includes thermal fluctuations that are missing in the BBGKY formalism. Second, the former allows us to formulate multi-time correlations as well, whereas the latter is restricted to simultaneous correlation. These two features are favorably utilized in deriving the Landau-Lifshitz fluctuation law in a most straightforward manner. Also, equations describing the nonequilibrium interaction between thermal and fluid-dynamical fluctuations are derived.