第22届亚洲物理奥林匹克竞赛理论部分第2题试题与解答

第22届亚洲物理奥林匹克竞赛理论试题共三道，其中第二道题为相变的力学模型(A Mechanical Model for Phase Transitions)。该试题以朗道相变理论为背景，研究旋转的环上小球的运动，建立并分析相变的力学模型。本文介绍了该试题内容及解答，并对试题和选手作答情况进行了简要分析。     

用质心运动定理解某些变质量物体运动的问题

在一般理论力学教材中，对变质量物体的运动问题，都采用变质量物体基本运动方程即宿舍尔斯基方程求解．本文提出了用质心运动定理求解该类问题中的一些典型例子，对理论力学教材中缺少质心运动定理某些应用题的情况是个补充．     

对同一运动问题的不同解析

在职高力学中,解决动力学问题最基本、最重要的途径是牛顿运动定律、动能定理、机械能守恒定律和功能原理．要能够熟悉运用以上原理,必须弄清它们之间的相互联系和区别．这样有助于学生对同一力学问题的学习更深入．思路更清晰．下面通过简单运动问题作一示例,应用不同力学原理来解析,一题多     

刚体运动分析中滚动摩阻的影响

在理论力学的教材中,刚性均质圆盘在平面内的直线滚动是运动学和动力学经常研究的对象,该力学模型的工程实例随处可见,例如滚动的车轮及保龄球的运动等．本文以保龄球的刚体平面运动为例,讨论滚动摩阻在运动学和动力学研究中的影响．     

Ni纳米线在旋转磁场下的运动行为研究

本文通过实验及理论分析,对Ni纳米线在旋转磁场下的运动行为进行研究。Ni纳米线的旋转运动分为同步旋转和异步旋转两种形式。通过受力分析结合量纲比较的手段得到,本文研究范围内流体惯性作用、纳米线运动惯性作用的影响可以忽略,而磁场力矩和流体力矩是控制纳米线旋转运动的主要因素。建立了纳米线旋转运动的控制模型,并得到了区分同步旋转和异步旋转运动的判据。分别针对同步旋转运动和异步旋转运动进行分析,对比不同参数对纳米线运动的影响。     

基于特征点跟踪的数字稳像算法

针对图像平移和旋转的数字电子稳像问题,提出了一种新的稳像算法。采用K-R法(Kitchen-Rosenfeld)提取图像特征,根据Similarity变换模型进行运动估计,将图像平移和旋转模型转化为仅绕中心点旋转的单一旋转模型,降低了模型的复杂度和计算量。实验证明,这种算法具有很好的稳像效果。     

质心和质心运动定理应用二例

质心和质心运动定理是力学教学中的一个难点．通过下面对下落弹簧运动规律的分析与研究，不仅可使初学者较深刻地理解和掌握质心和质心运动定理，而且提供了一道运用数学知识处理物理问题的例题．     

旋转冲压发动机冲压压缩分析

旋转冲压发动机是一种没有叶片和活塞的基于冲压压缩技术的新概念发动机,气体的压缩主要是通过运动激波压缩来完成,通过对运动激波压缩过程的理论分析并与发动机冲压转子盘腔冷态流场进行数值模拟结果进行对比,印证了旋转冲压发动机中运动激波压缩假设的正确性．计算结果同时表明,旋转冲压发动机中的运动激波压缩效果和性能良好．     

传送带上的力学问题

以传送带为载体的物理问题，可以考查牛顿运动定律、运动学、功、能方面的知识，涵盖了高中力学的大部分知识点．因此，物体在传送带上的运动，是一种重要的物理模型；同时，这种模型如何应用也是同学们感觉较难把握的问题．希望通过以下几个例题的解析能够对同学们有所帮助．     

涡流管内三维强旋转流场数值模拟与分析

涡流管内可压缩气体的强旋转流动是涡流管能量分离的根本原因和驱动力,因而涡流管内流场研究是揭示涡流管能量分离物理机制的首要关键问题。由于涡流管内可压缩气体的三维强旋转湍流流动,实验测量中存在诸多问题,而CFD数值模拟技术对此具有很大的优势。文中以涡流管内部流场为研究对象,建立了涡流管计算域模型并进行网格划分,讨论了边界条件、湍流模型以及线性方程组求解策略等问题,对不同冷气流率下的涡流管内三维强旋流流场结构特性进行数值模拟,获得了不同冷气流率下的旋转运动、轴向运动、径向运动和循环流的分布特性。研究表明Realizableκ-ε湍流模型能够充分反映强旋流动特点,数值模拟结果与文献中实验值基本吻合。     

Gravitational Faraday Rotation of the Earth and Its Possible Test

It is shown that the rotation of the polarization plane of rays induced by a rotating body can be accumulated by means of a long baseline optical cavity. Theoretical analysis shows that the presently proposal experimental scheme is possible to test this gravitational Faraday rotation effect on the Earth, especially including how to effectively suppress the dominant part of the Sagnac effect due to the rotation of the Earth with a reasonable experimental configuration.     

Geometrical statistics of the vorticity vector and the strain rate tensor in rotating turbulence

We report results on the geometrical statistics of the vorticity vector obtained from experiments in electromagnetically forced rotating turbulence. A range of rotation rates Ω is considered, from non-rotating to rapidly rotating turbulence with a maximum background rotation rate of Ω = 5 rad/s (with Rossby number much smaller than unity). Typically, the Taylor-scale Reynolds number in our experiments is around Re_λ ≈ 100. The measurement volume is located in the centre of the fluid container above the bottom boundary layer, where the turbulent flow can be considered locally statistically isotropic and horizontally homogeneous for the non-rotating case, see L.J.A. van Bokhoven, H.J.H. Clercx, G.J.F. van Heijst, and R.R. Trieling, Experiments on rapidly rotating turbulent flows, Phys. Fluids 21 (2009) 096601. Based on the full set of velocity derivatives, measured in a Lagrangian way by three-dimensional (3D) particle tracking velocimetry, we have been able to quantify statistically the effect of system rotation on several flow properties. For the range of rotation rates considered, the experimental results show how the turbulence evolves from almost isotropic 3D turbulence (Ω ? 0.2 rad/s) to quasi-two-dimensional turbulence (Ω ≈ 5.0 rad/s), and how this is reflected by several statistical quantities. In particular, we have studied the orientation of the vorticity vector with respect to the three eigenvectors of the local strain rate tensor and with respect to the vortex stretching vector. Additionally, we have quantified the role of system rotation on the self-amplification terms of the enstrophy and strain rate equations and the direct contribution of the background rotation on these evolution equations. The main effect of background rotation is the strong reduction of extreme events and related (strong) reduction of the skewness of PDFs of several quantities, for example, the intermediate eigenvalue of the strain rate tensor and the enstrophy self-amplification term.     

Dynamics of the universe with global rotation

We analyze the dynamics of the FRW models with global rotation in terms of dynamical system methods. We reduce the dynamics of these models to the FRW models with some fictitious fluid which scales like radiation matter. This fluid mimics dynamical effects of global rotation. The significance of the global rotation of the Universe for the resolution of the acceleration and horizon problems in cosmology is investigated. It is found that the dynamics of the Universe can be reduced to the two-dimensional Hamiltonian dynamical system. Then the construction of the Hamiltonian allows for full classification of evolution paths. On the phase portraits we find the domains of cosmic acceleration for the globally rotating universe as well as the trajectories for which the horizon problem is solved. We show that the FRW models with global rotation are structurally stable. This proves that the universe acceleration is due to the global rotation. It is also shown how global rotation gives a natural explanation of the empirical relation between angular momentum for clusters and superclusters of galaxies. The relation J ~ M² is obtained as a consequence of self similarity invariance of the dynamics of the FRW model with global rotation. In derivation of this relation we use the Lie group of symmetry analysis of differential equation.     

Vectorial stimulated Raman scattering resolution on the semi-line

Stimulated Raman scattering between a laser pump pulse and a Stokes pulse is considered in a two-level medium with vectorial optical fields. The model on the semi-line is proved to be solvable by inverse scattering transform scheme. Among solutions, soliton generation is discussed. Then, it is shown how rotation of the Stokes wave leads to a spike of pump radiation in the time domain.     

Self-consistent method for calculation of reflection coefficients of the interface with the dielectric tensor’s rotation

We give an interface between two same media whose orientation of optical axis, however, is rotated, and describe a method in detail to show how to calculate reflectance coefficient in this interface. We also give the theoretical simulation of the reflectance coefficient and discuss the effect of the rotation angle and the direction of electron vector on the reflectance coefficient. For the un-polarized lights the theoretical calculated results show that the reflectance coefficients (r _x1 and r _y1) are very small when the rotated angle is small, and they arrive at the maximum value as the rotation angle is equal to a decided value. For the polarized light, when the rotation angle is small, the reflectance coefficients (r _x1 and r _y1) are also small. Only when the rotation angle increases to a certain extent, they can reach the maximum values and be strongly affected by the direction of electronic vector. However, this effect on the reflectance coefficient in the direction of the maximum refraction is different from that in the direction of minimum refraction.     

Motion and rotation of small glissile dislocation loops in stress fields

We derive here for the first time the equations that describe the combined motion and rotation of small prismatic dislocation loops in stress fields. When the applied torque is balanced by the self-torque of the loop, we show how the solution can be obtained for the loop orientation, and how this orientation affects the glide force on the loop.     

The Q-Effect of the Structures of Three-Body Systems

By making use of two different modes, we made further investigation of how the competition between internal vibration energy and collective rotation energy affects the geometric structures and internal motions of three-body systems.     

Experimental control for initiating and maintaining rotation of parametric pendulum

In this paper, the authors have studied experimentally the control methods of a parametric pendulum excited harmonically to initiate and maintain a period one rotation – the most superior response for energy harvesting. For initiating the period one rotation inherent in the system, first the bang-bang method is applied. Then a new method where velocity is monitored is proposed and applied and finally the time-delayed feedback method with multi-switching is considered. Ultimately the problem of maintaining the rotation of the pendulum is addressed. For first time, robustness and sensitivity of the latter method to change of frequency and amplitude of excitation and added noise are studied. Finally, it has been demonstrated how the delayed feedback method can be applied in a system of two pendula to ensure synchronized rotation.