旋转带电圆柱体的静磁场

利用1/︱r-r︱的柱函数展开式及特殊函数的性质,计算出了旋转有限长带电圆柱体的空间磁场分布,并对结果进行了讨论.     

轴对称磁场的数值问题

用现行的一次有限元解轴对称磁场时，在单元中心得到的磁感应强度会随径向格点作非物理的激烈振荡。我们分析了产生这种振荡的原因及其特性，并与网格的不均匀性引起的振荡作了比较。     

Tesla变压器耦合系数的静磁场解法

 为研究Tesla变压器耦合系数与各参量的关系,采用静磁场分析方法,从柱坐标系磁场Laplace方程出发,推导出磁场级数表达式的系数矩阵方程组,计算出磁芯磁场的轴向分布和间隙磁场的轴向、径向分布。引入了一种平均耦合系数概念——次级绕组每匝线圈具有独立的耦合系数,用全部单匝耦合系数的平均值作为Tesla变压器的耦合系数。重点研究了平均耦合系数与磁芯纵横比、半径比、初级绕组-磁芯长度比、磁芯材料磁导率的相对变化关系。结果表明:增大纵横比、减小半径比是提高Tesla变压器耦合系数的有效方法;增大磁芯材料的磁导率可提高耦合系数,但效果随磁导率增大而降低;初级绕组长度与磁芯长度之比约为0.7时,耦合系数达到最大值。     

Tesla变压器耦合系数的静磁场解法

为研究Tesla变压器耦合系数与各参量的关系,采用静磁场分析方法,从柱坐标系磁场Laplace方程出发,推导出磁场级数表达式的系数矩阵方程组,计算出磁芯磁场的轴向分布和间隙磁场的轴向、径向分布。引入了一种平均耦合系数概念——次级绕组每匝线圈具有独立的耦合系数,用全部单匝耦合系数的平均值作为Tesla变压器的耦合系数。重点研究了平均耦合系数与磁芯纵横比、半径比、初级绕组-磁芯长度比、磁芯材料磁导率的相对变化关系。结果表明:增大纵横比、减小半径比是提高Tesla变压器耦合系数的有效方法;增大磁芯材料的磁导率可提高耦合系数,但效果随磁导率增大而降低;初级绕组长度与磁芯长度之比约为0.7时,耦合系数达到最大值。     

静轴对称SDYM场的一种新的对称变换

利用静轴对称SDYM场方程的Lax对的解,我们构造出了静轴对称SDYM场的一种新的对称变换.     

静磁外部球谐多极矩展开

本文讨论静磁球谐多极矩展开,包括静磁标势和静磁矢势的外部球谐多极矩展开.在磁矢势外部球谐多极矩分析中介绍了两种不同的方法,方法一基于磁标势外部球谐多极矩展开求惯用磁矢势外部球谐多极矩展开,方法二从电流对远源场点磁矢势场贡献出发借助德拜势直接求得静磁矢势外部球谐多极矩展开的惯用表示.     

静磁场唯一性定理

给出了场内充以线性介质时，多边界面复连通区域内的静磁场唯一性定理，并讨论了在一些特殊情况下定理的表述．     

在柱坐标系中求解轴对称的静电场

提出了求解轴对称静电场的柱函数展开法,推导出用对称轴上的电势分布表示空间电势分布的级数展开式,并给出了求解轴对称静电场的例子.     

利用分离变量法求解轴对称平衡态磁场

分离变量法是一种常用的处理轴对称磁场位型的方法.利用分离变量法甚至可以针对较为复杂的磁场位型,例如含有电流源项的磁场位型,得到较为理想的结果.本文介绍了磁场势函数与流函数的正交关系,并利用分离变量法,考虑双电流源的影响,求解了太阳日冕的无力轴对称平衡态磁场的流函数,并绘制了相应的流函数图像,表明了分离变量法求解较复杂的轴对称平衡态磁场的可行性.     

静磁场的基本规律及其应用

指出在利用安培环路定理计算某些具有特殊对称分布的电流激发的磁场时 ,必须结合磁场中的高斯定理 ,才能帮助我们进一步确定磁场的方向 ,并通过实例加以说明。文章还就安培环路定理与毕奥 萨伐尔定律的关系 ,以及静磁场的基本规律等问题进行了讨论     

对称四振子系统的简正振动的两种解法

用代数法和解耦分析法求解对称四振子系统的简正振动频率.     

两种方法求解外场驱动含时谐振子系统

应用代数动力学规范变换方法和相干态平均的方法,求解外场驱动下含时变频谐振子系统的时间演化算符,比较了两种方法所得的结果.研究结果表明,两种方法所得结果一致.     

轴对称电荷分布非静态轴外场的一种计算方法

利用麦克斯韦方程组和轴对称性,给出了轴对称电荷分布非静态轴外场的一种计算方法.     

轴对称非静态电流分布轴外场的一种计算方法

在轴对称非静态电流分布的情况下,利用麦克斯韦方程组和轴对称性,给出了轴外电磁场的一种计算方法.     

Effect of a weak static magnetic field on nitrogen-14 quadrupole resonance in the case of an axially symmetric electric field gradient tensor

The application of a weak static B₀ magnetic field (less than 1 mT) may produce a well-defined splitting of the ¹⁴N Quadrupole Resonance line when the electric field gradient tensor at the nitrogen nucleus level is of axial symmetry. It is theoretically shown and experimentally confirmed that the actual splitting (when it exists) as well as the line-shape and the signal intensity depends on three factors: (i) the amplitude of B₀, (ii) the amplitude and pulse duration of the radio-frequency field, B₁, used for detecting the NQR signal, and (iii) the relative orientation of B₀ and B₁. For instance, when B₀ is parallel to B₁ and regardless of the B₀ value, the signal intensity is three times larger than when B₀ is perpendicular to B₁. This point is of some importance in practice since NQR measurements are almost always performed in the earth field. Moreover, in the course of this study, it has been recognized that important pieces of information regarding line-shape are contained in data points at the beginning of the free induction decay (fid) which, in practice, are eliminated for avoiding spurious signals due to probe ringing. It has been found that these data points can generally be retrieved by linear prediction (LP) procedures. As a further LP benefit, the signal intensity loss (by about a factor of three) is regained.     

Weak gravitational field and Coriolis potential

In mechanics of the mass point passage from one frame of reference to another moving with velocity consists in subtracting this vector from the velocity of the particle. In general case the vector is not constant, as, for example, when passing through a rotating frame, this operation creates inertial forces. Analysis of this phenomenon from the point of view of Lagrangian and Hamiltonian mechanics is interesting from the general relativistic point of view due to Einstein’s principle of equivalence. We show that the vector plays the role of vector potential which, however, essentially differs from vector potential known in classical electrodynamics. Comparative analysis of the two kinds of vector potentials is completed.      

轴对称非静态电荷电流分布轴外场的交替迭代

在轴对称非静态电荷电流分布的情况下,利用麦克斯韦方程组和轴对称性,给出了计算轴外电磁场的交替迭代法.     

Average vector field methods for the coupled Schr/idinger-KdV equations

The energy preserving average vector field （AVF） method is applied to the coupled Schr6dinger-KdV equations. Two energy preserving schemes are constructed by using Fourier pseudospectral method in space direction discretization. In order to accelerate our simulation, the split-step technique is used. The numerical experiments show that the non-splitting scheme and splitting scheme are both effective, and have excellent long time numerical behavior. The comparisons show that the splitting scheme is faster than the non-splitting scheme, but it is not as good as the non-splitting scheme in preserving the invariants.     

Discrete accidental symmetry for a particle in a constant magnetic field on a torus

A classical particle in a constant magnetic field undergoes cyclotron motion on a circular orbit. At the quantum level, the fact that all classical orbits are closed gives rise to degeneracies in the spectrum. It is well-known that the spectrum of a charged particle in a constant magnetic field consists of infinitely degenerate Landau levels. Just as for the 1/r and r² potentials, one thus expects some hidden accidental symmetry, in this case with infinite-dimensional representations. Indeed, the position of the center of the cyclotron circle plays the role of a Runge-Lenz vector. After identifying the corresponding accidental symmetry algebra, we re-analyze the system in a finite periodic volume. Interestingly, similar to the quantum mechanical breaking of CP invariance due to the θ-vacuum angle in non-Abelian gauge theories, quantum effects due to two self-adjoint extension parameters θ_x and θ_y explicitly break the continuous translation invariance of the classical theory. This reduces the symmetry to a discrete magnetic translation group and leads to finite degeneracy. Similar to a particle moving on a cone, a particle in a constant magnetic field shows a very peculiar realization of accidental symmetry in quantum mechanics.