开拓一道力学题

由赵景员和王淑贤合编的《力学》中,有一道题是“试证在以角速度ω旋转的圆桶内的液体的自由表面的形状是一抛物面”(426页,第15题).我们试对它进行开拓,使其变成内容很广的综合力学题目.经变化后的题为 “一个充分高的圆柱桶,其底面半径为R,内部装有高度为l,密度为ρ的液体,当它绕其轴(通过桶底中心且平行于桶壁)以角速度ω旋转时,试求(1)其自由液面为抛物面;(2)抛物面的顶点距器底的高度随ω变化的关系图象;(3)ω为何值时桶底才能露出;(4)液体沿器壁上升的高度随ω变化的关系;(5)桶底露出的半径随ω变化的关系;(6)质心高度随ω变化的关系…     

旋转液面的光学性质探究及应用

匀速旋转的圆柱形容器带动其中盛放的液体围绕容器中心轴匀速旋转时,液体的表面在离心力与重力的综合作用下会形成一个抛物面.该抛物面的光学焦距与重力加速度和转速有关,从而利用该装置测量了本地的重力加速度,并利用抛物面聚光的性质制成了一个简易的反射式牛顿焦点系统望远镜,还测定了望远镜的横向放大率与转速之间的关系.     

旋转液体反射抛物面镜

利用光学Mach-Zehnder干涉仪对旋转液体产生的轴对称抛物面的光学反射性能进行了研究.液体抛物面反射镜作为干涉仪的一个反射镜产生的球面波与另一条光路中的平面波干涉形成同心圆的干涉条纹,利用CCD相机采集干涉条纹图像,通过计算机图像处理程序得到旋转液体反射波面的形貌,实现对液体反射镜表面形状的分析.光学干涉技术的高精度特点保证了测量的准确性.     

抛物面反射镜光轴的确定

介绍了一种确定抛物面反射镜光轴的新方法。当抛物面反射镜绕着机械旋转轴旋转时,利用2束平行光(一束与机械旋转轴平行的光和一束与机械旋转轴成一定角度的斜平行光)经抛物面反射镜反射的像点运动,调整抛物面反射镜的位置,使光轴与机械旋转轴重合。理论分析结果表明：其定轴的倾斜误差不大于1′,平移误差不大于5μm。该方法可用于抛物面反射镜检验,也可用于抛物面反射镜的调校工艺中。     

基于室内可见光通信技术的新型两级光学接收天线设计与分析

针对室内可见光通信系统的应用需求,设计了一种新型两级光学接收天线.根据复合抛物面聚光器光学增益随视场增大而减小的聚光特性,将复合抛物面聚光器截面基准曲线旋转设计得到具有一定旋转角与厚度的透镜壁复合抛物面聚光器.进一步结合透镜壁复合抛物面聚光器和半球透镜的优势设计了一种新型两级光学接收天线,在增益保持的情况下视场角增大了近20~?.在一个5 m×5 m×3 m的空旷房间,通过Trace Pro建立光学天线的分析模型,Matlab软件对室内可见光通信系统进行信道建模.计算结果表明,采用这种新型两级光学接收天线,与直接接收的情况相比,平均接收功率增幅为757.2%,是复合抛物面聚光器的5.62倍;信噪比平均值增幅为28.07%,是复合抛物面聚光器的1.67倍;光学增益为11.49,是复合抛物面聚光器的2.81倍.且光斑半径仅为2.5 mm,较复合抛物面聚光器减小了近37.5%,使得能量集中均匀分布,进一步证实该新型两级光学接收天线适用于室内可见光通信系统.     

圆锥形传热面上的薄液膜沸腾

液体在水平传热面上沸腾时,液位越低传热系数越高的现象,见文献[1—3]。液位降到一定限度后,稳定沸腾遭到破坏,传热面上出现的干燥斑因得不到液体的补充逐渐扩大,直到传热面烧毁。为解决零液位附近薄液膜滞腾的稳定性问题,文献[4]研究了倾斜传热面的液膜沸腾。指出:当倾斜传热面的一端保持零液位,沿长度方向液位逐渐增加的状     

基于改进的迈克尔逊干涉仪的液体折射率测量方法研究

液体折射率是重要光学参数之一，液体折射率参数测量在食品生产鉴定、光学加工等领域都具有重要意义。本文基于便携式迈克尔逊干涉仪，在光学减震台上加装旋转微调载物台，综合考虑旋转后容器器壁、待测液体、空气中光程差的改变量，得到液体折射率的计算公式，与阿贝折射仪测量液体折射率的值进行比较，实验测得水、不同浓度的葡萄糖溶液以及不同浓度的氯化钠溶液，平均相对误差分别为1.1%、3.3%、2.0%,实验过程中测量的最大误差为5.9%,为液体折射率测量提供了一种可行方法，实现液体折射率的测量。本文也可作为迈克尔逊干涉仪的拓展实验，对本科生的创新能力培养有重要意义。     

纳米晶永磁中面缺陷对畴壁钉扎机理的研究

畴壁钉扎模型的矫顽力可以表示为Hc=αpink2K1/μ0Ms-NeffMs，计算了微结构参数αpink随面缺陷内磁性参数A′和K′1的变化情况.结果表明，αpink可以在很宽的范围里取值.结合纳米单相Nd2Fe14B磁体，研究了晶粒边界的磁性参数和晶界厚度对αpink的影响，当A′/A=05，K′1/K1=01，以及晶界厚度r0＝332nm时，αpink最大.同时研究了纳米复相Nd2Fe14B/α-Fe磁体的αpink随α-Fe晶粒尺寸r0的变化情况，当r0＝7nm时，αpink最大. 关键词： 面缺陷 矫顽力 钉扎机理 纳米晶     

二次电子发射系数对含有超广延分布电子的等离子体器壁电势的影响

采用一维模型研究本底电子为麦氏分布的等离子体中存在部分超广延分布的高温电子情况下的二次电子发射系数对器壁电势的影响。数值模拟结果表明：当器壁二次电子发射系数较小时,器壁电势随着超广延分布电子与本底电子的浓度比值、温度比值、以及超广延参量这些参数的增加而减小;当器壁二次电子发射系数较大时,器壁电势则随着超广延分布电子与本底电子的浓度比值、温度比值、以及超广延参量值的增加而增加。     

基于连通器原理的小探头光纤液位传感器研究

介绍了以汞包层光波导为传感探头的光纤液位传感器的原理及信号处理,其工作原理是利用连通器将液位的变化转变为汞包层光波导包层长度的变化。理论分析和实验表明,当光波导直径和光波长一定时,光功率衰减随汞包层光波导长度增加作线性增加。通过对汞包层光波导引起光功率衰减的检测,探头结构的优化设计以及探测器件的选型,可以获得实时性很强的高精度液位测量。实验测得10m液位的最大测量误差为5．2mm,理论分析的相对测量精度可达0．02％。该液位传感器的研制对于油库等易燃、易爆环境中的液位测量具有重要意义。     

Lehmann rotation of cholesteric droplets subjected to a temperature gradient: Role of the concentration of chiral molecules

We present a systematic study of the Lehmann rotation of cholesteric droplets subjected to a temperature gradient when the concentration of chiral molecules is changed. The liquid crystal chosen is an eutectic mixture of 8CB and 8OCB doped with a small amount of the chiral molecule R811. The angular velocity of the droplets strongly depend on their size and on the concentration of chiral molecules. The Lehmann coefficient is estimated by using three different methods. Our results are consistent with a Lehmann coefficient proportional to the concentration of chiral molecules. We additionally show the existence of a critical size of the droplets below which they change texture and stop rotating.     

The change in the sound wave energy due to the scattering by a medium rotating with acceleration

Scattering amplitudes and intensities of partial azimuthal harmonics and the total intensity of the scattered field are calculated for the case of transmission of longitudinal acoustic waves through a liquid rotating with acceleration. It is shown that the intensity of transmitted waves depends on the angular acceleration and does not depend on the angular velocity of the vortex rotation.     

临界转动恒星Achernar的斜压结构与引力昏暗的精细研究

转动和潮汐效应是影响恒星结构和演化的非常重要的物理因素. 根据对Achernar的观测数据, 用扰动理论推导了临界转动恒星Achernar分别作为单星和双星的斜压结构的特征, 给出Achernar等压面上的密度等物理量的分布. 利用考虑转动和潮汐及形变效应的单、双星模型研究了Achernar的引力昏暗现象. 结果表明正剪切增强离心力、减小赤道的重力加速度和温度, 反剪切结果则与之相反. 反剪切和刚性转动情况并不符合对Achernar的引力昏暗观测结果. 发现转动双星模型比单星模型虽更符合Achernar赤道和极半径之比的观测值, 但理论计算的角速度比观测值小. 对比理论计算和观测结果发现, 当Achernar的自转角速度为4.65× 10^-5 s^-1, 正剪切率Ω/Ω_s为0.7851时, Achernar的极点温度为16041 K, 赤道温度为12073 K. 所有理论计算与观测值的相对误差不超过7%.     

Rotation and twist regular modes for trapped ghosts

A parameter-independent notion of stationary slow motion is formulated then applied to the case of stationary rotation of massless trapped ghosts. The excitations correspond to a rotation mode with angular momentum J ≠ 0 and twist modes. It is found that the rotation mode, which has no parity, causes excess in the angular velocity of dragged distant coordinate frames in one sheet of the wormhole while in the other sheet the angular velocity of the ghosts is that of rotating stars: 2J/r ³. As to the twist modes, which all have parity, they cause excess in the angular velocity of one of the throat’s poles with respect to the other.     

Destroying superfluidity by rotating a Fermi gas at unitarity

We study the effect of the rotation on a harmonically trapped Fermi gas at zero temperature under the assumption that vortices are not formed. We show that at unitarity the rotation produces a phase separation between a nonrotating superfluid (S) core and a rigidly rotating normal (N) gas. The interface between the two phases is characterized by a density discontinuity n(N)/n(S)=0.85, independent of the angular velocity. The depletion of the superfluid and the angular momentum of the rotating configuration are calculated as a function of the angular velocity. The conditions of stability are also discussed and the critical angular velocity for the onset of a spontaneous quadrupole deformation of the interface is evaluated.     

Centrifugal instability in rotating shallow water and the problem of the spiral structure in galaxies

A new instability predicte by theory to occur in rotating shallow water in which the rotation velocity has a discontinuity, in a regime where the flow velocity exceeds the characteristics velocity of the waves, has been found experimentally. The instability develops when the radial gradient of the angular velocity across the discontinuity is negative; such an instability is likely to be responsible for the formation of the spiral structure in galaxies which have a similar rotational velocity profile.     

Letter: Slowly Rotating, Compact Fluid Sources Embedded in Kerr Empty Space-Time

Spherically symmetric static fluid sources are endowed with rotation and embedded in Kerr empty space-time up to and including quadratic terms in an angular velocity parameter using Darmois junction conditions. The boundary behaviour of the metric tensor and partial derivatives is used to develop a series solution of Einstein's equation's for the rotating fluid. The boundary of the rotating source is expressed explicitly in terms of sinusoidal functions of the polar angle. As an example of the analysis the Schwarzschild interior solution is endowed with rotation and the equation of the fluid boundary is generated together with surface behaviour of the fluid density and angular velocity.     

Robertson-Walker Fluid Sources Endowed with Rotation Characterised by Quadratic Terms in Angular Velocity Parameter

Einstein's equations for a Robertson-Walker fluid source endowed with rotation are presented up to and including quadratic terms in angular velocity parameter. A family of analytic solutions are obtained for the case in which the source angular velocity is purely time-dependent. A subclass of solutions is presented which merge smoothly to homogeneous rotating and non-rotating central sources. The particular solution for dust endowed with rotation is presented. In all cases explicit expressions, depending sinusoidally on polar angle, are given for the density and internal supporting pressure of the rotating source. In addition to the non-zero axial velocity of the fluid particles it is shown that there is also a radial component of velocity which vanishes only at the poles. The velocity four-vector has a zero component between poles.     

Two-dimensional wave propagation in a rotating elastic solid with voids

Two-dimensional wave propagation is studied in an isothermal linear isotropic elastic material with voids rotating with constant angular velocity based on a theory of elastic material with voids developed by Ie?an (1986) in the thermoelastic context. It is found that there exist three coupled plane waves propagating with distinct phase speeds. The presence of voids and the rotation of the medium are responsible for this coupling. In the absence of voids, the classical longitudinal and transverse waves are found to be coupled through the rotation of the medium. At very large frequency or when the angular rotation is very small relative to the wave frequency the waves are decoupled and propagate with distinct phase speeds. These are (i) a longitudinal wave, (ii) a transverse wave and (iii) a longitudinal wave corresponding to the change in void volume fraction. The first two correspond to the waves of classical elasticity, while the third is new and arises from the presence of the voids. The results are illustrated graphically.