共轴均匀带电薄圆盘间的相互作用力

本文利用静电场的高斯定律和环路定律巧妙地求出了均匀带电圆盘在空间任一点所产生的电场 ,进而计算出了共轴均匀带电薄圆盘之间的相互作用力     

有限长均匀带电圆柱面电场分布

通过把有限长的圆柱面看成由直线段积分而得,通过有限长均匀带电直线段的电场分布进而求得有限长圆柱面电场分布,其中运用高等数学微积分处理方法,以椭圆积分形式给出电场的柱坐标解析表达式,并通过将圆柱面的高度趋于零,得到圆环电场解析表达式.     

均匀带电细棒和带电圆环电场的计算机模拟

为了可以更直观地观察带电粒子在复杂电场中的运动轨迹以及描述电场的空间分布,本文基于库仑定律和电场叠加原理,应用VPython软件,对均匀带电有限长细直棒和均匀带电圆环的电场的空间分布进行了可视化模拟;并模拟探究了带电粒子在带电圆环电场中的运动形式,对于简单的周期性运动,我们在理论上计算了带电粒子运动周期,并与模拟的结果相比较做了相关的讨论;模拟探究了带电粒子多种复杂的运动形式,预测了带电粒子在圆环电场中运动可能出现的混沌现象。     

均匀带电细圆环电场的计算机模拟

用Matlab程序对均匀带电细圆环在空间激发的电场进行了计算机模拟,可以输出带电圆环附近任意一点的电场强度及电势,做出了过环心与圆环垂直的平面内的等势线,以及三维空间的等势面,实现了电场的可视化,便于形象地理解带电圆环激发电场的空间分布.     

有限长均匀带电直线电场的对称性分析与计算

由椭圆和双曲线的性质得出有限长均匀带电直线的等势面为椭球面.采用椭球面坐标系,利用高斯定理由直接积分法求解了有限长均匀带电直线的电场和电势分布,并进行了必要的讨论.     

微元法研究均匀带电体的电场分布

以均匀无限长带电直线的电场分布为基础,运用微元法和叠加原理研究了无限大均匀带电平面和无限长均匀带电圆柱面在其周围电场分布情况。然后根据均匀带电圆环轴线上的电场分布,进一步讨论均匀圆柱面在其轴线上的电场和均匀带电球面在其周围产生的电场,所得结果与高斯定理完全符合。     

关于均匀带电球面上电场强度的求解

由于均匀带电球面上的电场强度无法用高斯定理求出,现行大部分大学物理基础教材在讨论均匀带电球面产生的场强分布时,只用高斯定理求出了该带电系统内外空间电场的分布,并没有给出球面上场强的计算方法,只是指出在球面上场强值不连续.文章利用叠加原理和电容器能量的变化两种方法分别导出了均匀带电球面上任一点的场强值,验证了均匀带电球面的场强是不连续的,两种方法思路截然不同,但得到的结果完全相同,该结果使得高斯定理求出的均匀带电球面在空间电场分布的结论更加完整.     

均匀外电场中无限长介质圆柱壳的场分布的计算和讨论

用圆柱坐标系中的分离变量法计算了位于均匀外电场中的无限长介质圆柱壳各区域的电势和电场,由计算结果分析了无限长介质圆柱壳对外电场的屏蔽效果,并指出均匀外电场中的无限长导体圆柱壳、无限长介质圆柱体、无限长导体圆柱及无限大均匀电介质中开有一无限长的圆柱形空腔的电势和电场都可以由均匀电场中的无限长介质圆柱壳电势及电场给出.     

对称的非均匀带电球体电势的两种求法

大学物理中求对称的非均匀带电球体在空间任一点产生的电势是静电场中基本问题之一.为了巩固和灵活运用电学基本知识,本文通过两种方法推导出对称的非均匀带电球体在空间任意一点产生的电势,指出求不同带电体电势的基本思路.     

有限长均匀带电薄圆柱面的电场

由场的叠加原理,导出了有限长均匀带电薄圆柱面电势和电场的级数表达式.     

Stability of the charged radiating cylinder

We discuss the dynamical instability of cylindrically symmetric isotropic geometry under the effect of electromagnetic field. The interior geometry of the dynamical collapse is matched with an exterior geometry through Darmois junction conditions. The perturbation scheme is used to describe the collapse equation and categorize the Newtonian and post-Newtonian regions in radiating as well as non-radiating eras. It is concluded that energy density, pressure, radiation density and electromagnetic field control the stability of the cylinder leading to more unstable configuration.     

Laser generation of surface waves on cylinder and coated cylinder

Analytical models of acoustic field excited by a pulsed-laser line source on a cylinder and a coated cylinder were presented.Surface wave dispersive behaviors for a cylinder with a slow coating were analyzed and compared with that of a bare cylinder.Based on this analysis, the laser-generated transient response of the cylindrical Rayleigh wave on cylinder and the perturbed cylindrical Rayleigh wave on coated cylinder and the higher modes were calculated from the models using residue theory and FFT technique.The theoretical results from the superposed waveform of the cylindrical Rayleigh wave and higher modes for both cylinder and coated cylinder agree well with the waveforms obtained from experiment.The transient response of perturbed Raleigh wave on coated cylinder is quite different with cylindrical Rayleigh wave on cylinder because of the guide of surface coating.The results show that the model and numerical method provide a useful technique for quantitatively characterizing coating parameters of coated cylinder by the laser generated surface waves.     

Use of the wake of a small cylinder to Control unsteady loads on a circular cylinder

Simultaneous measurements of lift and drag forces have been performed in order to study passive control of unsteady loads induced on a circular cylinder. For this purpose, an aerodynamic balance has been developed. The balance, developed for a cylinder of 25.4 mm in diameter, was designed to operate in the subcritical regime (Re=32000). This instrument is characterized by its sensitive element that forms a small central part of the cylinder. The static and dynamic calibrations of the balance show the appropriateness of the present design. Moreover, qualification experiments carried out with a single cylinder gave results (mean and rms values of the lift and drag coefficients) that are in good agreement with those found in the literature. The purpose of this paper is to present a passive control experiment performed by means of the wake of a smaller cylinder interacting with a larger one. Firstly, a parametric study was performed by varying the following: i) the diameterdS of the small cylinder for one large cylinder diameterd (7 values in the range 0.047≤d _S /d≤0.125); ii) the center-to-center spacingS/d (11 values in the range 1.375≤S/d≤2.5); and iii) the stagger anglea(0≤a≤90 with a fine angular stepDa fora≤15). A maximum mean drag reduction of about 48% is achieved. Ata=4 to 8, one can observe a peak of mean lift coefficient. Then unsteady fluid forces, vortex shedding frequency and flow pattern were systematically investigated for the small cylinder having a diameterdS=2.4 mm (0.094d). Reductions of 78% and 56% of the rms lift and drag fluctuations respectively were obtained with the small cylinder placed at a slight stagger angle in the range 6<a<9. This leads to an instantaneous force vector that exhibits more steadiness both in angle and amplitude. Moreover, at these stagger angles, the energy of the lift fluctuations at the shedding frequency is significantly reduced compared to the single cylinder case.     

Domain configurations of the uniaxial infinite cylinder

Models for the possible domain configurations of a uniaxial infinite cylinder are put forward and their theory is developed. For materials having an easy plane and no hexagonal anisotropy either closed flux or helical magnetization configurations are proposed. For non-vanishing hexagonal anisotropy these models are somewhat modified to the partially closed flux configuration and the disc domain structure.

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Part of this paper was presented at the International Conference of Magnetism and Crystallography, Kyoto, Japan 1961.

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In conclusion I should like to thank Z. Frait and Z. roubek for valuable remarks.     

Fluid adsorption at the base of a cylinder

We consider the adsorption of fluid at a cylinder protruding from a flat substrate. For small contact angles θ, a liquid drop condenses at the base, the size of which is determined by macroscopic arguments. The adsorption exhibits scaling behavior related to a number of phase transitions and, for systems with short-ranged forces, shows a remarkable property: for small θ, the height and width of the drop are near identical to expressions for the thickness and parallel correlation length for microscopic wetting films. The only difference is that the bulk correlation length is replaced by the cylinder radius. This geometrical amplification of the microscopic lengths occurs for second-order, first-order, and complete wetting transitions, and is specific to three dimensions. Similar phenomena occurs for long-ranged forces, and shows crossover scaling behavior.     

激光对运动圆柱体加热的几何学研究

 当激光无论从地面或是从空中辐照运动的圆柱体时，都涉及到入射激光相对于圆柱体的辐照方式。在一定假设下，导出了激光对抛射圆柱体表面加热时圆柱表面热加载功率密度分布公式，并结合一理想情况，针对光束入射角度因子、光斑中心的偏移、光斑形状的变化进行了解析计算分析。分析表明，即使圆柱体本身不做自转，圆柱体表面的光强分布中心也会发生偏移，分布也会发生变化，尤其沿圆柱体轴向的分布变化较大，必须结合实际加以细化研究。     

Visualization of the sound scattering by a cylinder

The schlieren method is applied to visualizing the sound scattering ofa cylinder immersed in the liquids.Images of the echoes,caused by normal andoblique incidence from a cylinder,are obtained for two kinds of liquids:(1)theliquid is composed of a transparent liquid;and(2)the liquid is composed of twonon-mixable transparent liquids.It is found experimentally that the echo canbe caused by the discontinaites in the shadow zone.This fact is utilized to dem-onstrate the locus of the helical surface wave creeping along the surface of thecylinder.For such cases the three-dimensional image can be described by thismethod and has not to use the system with special appliances and complexalgorithm.     

Dimer problem on the cylinder and torus

We obtain explicit expressions of the number of close-packed dimers and entropy for three types of lattices (the so-called 8.8.6, 8.8.4, and hexagonal lattices) with cylindrical boundary condition and the entropy of the 8.8.6 lattice with toroidal boundary condition. Our results and the one on 8.8.4 and hexagonal lattices with toroidal boundary condition by Salinas and Nagle [S.R. Salinas, J.F. Nagle, Theory of the phase transition in the layered hydrogen-bonded SnCl²⋅2H₂O crystal, Phys. Rev. B 9 (1974) 4920-4931] and Wu [F.Y. Wu, Dimers on two-dimensional lattices, Inter. J. Modern Phys. B 20 (2006) 5357-5371] imply that the 8.8.6 (or 8.8.4) lattices with cylindrical and toroidal boundary conditions have the same entropy whereas the hexagonal lattices have not. Based on these facts we propose the following problem: under which conditions do the lattices with cylindrical and toroidal boundary conditions have the same entropy?     

Building a cylinder in the topological expansion

Usual cylinder construction neglect planar analyticity and the resulting cylinder is contaminated by j-plane cuts. Beginning with input planar amplitudes that are manifestly consistent with a pole-to-pole planar bootstrap, a three-dimensional cylinder equation is formulated, incorporating planar analyticity. The output cylinder is now free of j-plane cuts. The bare pomeron is a simple pole with trajectory intercept slightly above one.     

柱面镜组的计算机辅助调校

计算机辅助装调技术是通过计算机对理论和实时检测结果的分析计算来有效地指导装调技术。本文通过计算机对由柱面反射镜组成的红外反射扩束系统的各种调整自由度的详细分析 ,以及在检测时对结果的实时分析 ,可确定合理的检测方案 ,有效的减少了调整时间 ,得到了理想的结果