Whispering gallery modes in a conical resonator

A conical closed resonator with perfectly conducting walls is considered. The eigenmodes of the resonator are determined in the first order of perturbation theory, in which the cone angle is a small quantity. A semiclassical approximation is constructed for an arbitrary cone angle; it is shown that the spectrum of whispering gallery modes in this approximation differs insignificantly from the eigenmode spectrum of a cylindrical cavity even for a large cone angle.     

Transition radiation detectors with a dihedral angle or a cone as a radiator

The spectral and angular distributions of the transition radiation produced by a charge crossing an interface shaped like a dihedral angle or a cone are considered. The effects of the variation in the dihedral angle and cone angle, the location of the crossing point on the interface, and the direction of the charge motion on the spatial distribution of the radiation are discussed. The radiation characteristics of the particles that are incident on the interface and those leaving it are given. The features of transition-radiation detectors with dihedral-angle or cone radiators and detectors with plane-surface radiators are compared.     

Quantum phase transition and dynamics induced by atom-pair tunnelling of Bose-Einstein condensates in a double-well potential

We investigate the quantum phase transition (QPT) and dynamics induced by atom-pair tunnelling of Bose-Einstein condensates in a symmetric double well under the mean-field approximation. We find the system undergoes a new QPT towards phase-locking state when atom-pair tunnelling is strong enough, and the critical point of self-trapping QPT is shifted by atom-pair tunnelling. As for the dynamics, the system displays localized dynamical behaviour: phase-locking motion and self-trapping motion. We further study the correlation between this localized dynamics and QPT, and find that the area of the localized trajectories in the phase space can serve as an order parameter for both QPTs. The critical exponent of this order parameter is also discussed.     

Fast quantum,semiclassical and classical dynamics near the conical intersection

The dynamics of wavepacket propagation on a double circular 2-dimensional cone has been studied. The fast transition of the wavepacket from the conical well onto the conical peak is interpreted in terms of the semiclassical picture which uses the notion of the transition probability in the region of closest approach of the packet to the apex of the cone. It is shown that a simple surface hopping approximation predicts correctly the decay probability over times longer than the period of motion in the conical well.     

Electrohydrodynamics of a Cone–Jet Flow at a High Relative Permittivity

We have proposed a new solution of the electrohydrodynamic equations describing a novel cone–jet flow structure formed at a conductive liquid meniscus in an electric field. Focusing on the liquids characterized by a high relative permittivity and using the slender body approximation, the cone–jet transition profiles and their characteristic radii are predicted in relation to the material parameters. The stable value of the cone angle is obtained using the Onsager’s principle of maximum entropy production. Three different regimes of the cone–jet flow behavior are identified depending on the relative importance of capillary, viscous and inertial stress contributions. The presented complete analytical solutions for the cone–jet transition zone and the far jet region yield several different laws of algebraic decrease for the radius, surface charge, and electric field of the jet.     

圆锥边界附近激光空泡溃灭行为的研究

为了研究刚性圆锥边界锥角对激光空泡溃灭行为的影响,文章建立了虚拟平面边界模型, 同时采用阴影摄影术、光偏转法以及数值计算的手段对边界附近空泡溃灭过程进行了研究. 结果表明边界的锥角对空泡的形状、溃灭时间以及液体射流形成均有明显影响. 空泡形状偏离球形的程度和溃灭时间均随锥角的增大而增大,且增大锥角度可以促使射流的形成. 空泡溃灭时间的实验值同理论值具有较高的一致性,验证了虚拟平面边界假设及无量纲距离修正的有效性.     

基于无衍射光莫尔条纹的轴锥透镜锥角测量方法

为了准确地测量轴锥透镜锥角值,根据无衍射光同心圆环间距不随距离改变的特点和莫尔条纹放大的特性,提出了一种基于无衍射光莫尔条纹的轴锥透镜锥角的测量方法。当无衍射光束经分束器分光合束后形成莫尔条纹,平移其中一束光在图像传感器上的位置,实现莫尔条纹数量的变化,通过记录不同莫尔条纹下的中心距离计算出轴锥透镜锥角。实验以锥角为0.5°的轴锥透镜作为被测对象,与CMM测量结果进行比较,该文提出的方法相对测量误差近似为0.54%,重复性为0.86″,验证了该文方法测量轴锥透镜锥角的可行性。     

Modelling of the influence of dihedral angle,volume fractions,particle size and coordination on the driving forces for sintering of dual phase systems

The equilibrium shape of solid particles in an aggregate immersed in a liquid or in a gas results from the minimization of interface energy. A model is developed for expressing the dependence of the solid–solid and solid–second phase interface areas on the system parameters: phase volume fractions, dihedral angle, particle size and coordination. The model aims at allowing quantitative assessment of the role of these parameters on the driving force for sintering. The representative volume element is a cone of which the apex angle accounts for the average particle coordination. In order to comply with the uniformity of interface curvature, the solid–second phase interfaces are described using the mathematics of the Delaunay surfaces. The results are compared with the solutions obtained by approximating the interface shape by the revolution of an arc of circle around the cone axis. This approximation does not involve a significant loss of precision.     

地转动量近似下的Q矢量及其在天气图上的应用

将Hoskins等提出的准地转Q矢量表达式推广到地转动量近似下的Q矢量表达式,并讨论了如何在天气图上用地转动量近似下的Q矢量表达式定性估计垂直运动方向的方法.地转动量近似下的Q矢量与准地转Q矢量相比,表达式中多了与位势高度极值和风速极值相关的两项,分别将地转动量近似下的Q矢量表达式中的每一项写成在天气图上便于判断的表达式.结果表明,在天气图上可以通过以下三种方式定性判断垂直运动方向:一是当等高线呈波状槽脊形式及通过急流的入口和出口区时,使用地转动量近似下的Q矢量的第一项(即准地转Q矢量)加以判断;二是当存在闭合气压系统且等高线与风向有交角时,使用地转动量近似下的Q矢量的第二项加以判断;三是在急流核上使用地转动量近似下的Q矢量的第三项加以判断.     

An angular cutoff composite model for investigation on electromagnetic scattering from two-dimensional rough sea surfaces

Based on the local configuration angle division to select the corresponding method for electromagnetic scattering calculation from rough sea surface,this paper presents an angular cutoff composite model:when the local scattered angle is in the specular region that is given by an approximately 20 degrees cone around the specular direction,the Kirchhoff approximation is applied to evaluate the specular reflection,which dominates the total scattering in this region;the small perturbation method is employed to handle the diffuse reflection which is predominant as the local scattered angle is situated out of the specular region.Numerical results are compared with those of experimental and theoretical models in several configurations as a function of incident angle,wind speed,wind direction.The comparison of numerical results of other experimental and theoretical models in several configurations shows that the new composite model is robust to give accurate numerical evaluations for the sea surface scattering.     

Optical absorption in a narrow-band InSb cylindrical layered nanowire in the presence of strong electrostatic field

On the example of InSb we consider the influence of a strong homogeneous electrostatic field on the state of carriers in a narrow-band quantized cylindrical layer in the case of Kaine dispersion law. Explicit expressions for the energy spectrum and wave function envelopes of charge carriers in the heterolayer are obtained. It is shown that under action of the strong external field the rotational motion, with respect to angular variables, of charge carriers becomes oscillatory in a narrow cone of the azimuth angle. We have obtained corresponding selection rules and calculated the threshold frequencies of absorption for interband and intraband electro-optical transitions in the layer. The threshold frequencies are determined by the geometric sizes of the sample and the magnitude of the external field.     

Cone shape evolution under ion bombardment

The evolution of the profile of a cone developing under ion bombardment on the etch pit bottom has been investigated by computer simulation taking into account sputtering and ion-induced migration of atoms. A twofold increase in the cone apex angle is observed, which is accompanied by the appearance of kinks on its generatrix. A plateau arises on the pit bottom and a circular parapet is formed above the flat surface.     

空心锥状双高斯光束传输特性研究

建立了空心锥状双高斯光束的模型.在空心高斯光束模型的基础上,由初始光场的光强分布,利用柱坐标下的柯林斯公式,导出了空心锥状双高斯光束经过傍轴光学系统的解析传输变换式由传输变换式计算分析了空心锥状双高斯光束在自由空问的可控传输特性,及在1,10和60 m的截面光环的光强分布.用KNbO3双轴晶体进行实验,获得了空心锥状双高斯光束,外锥折射的锥角等于入射光会聚角.实验表明,当空心光束处于锥状发射状态时,空心光束的光环内黑斑面积随传输距离的增加而增加,实验结果与模型吻合较好.该研究为进一步设计制备基于空心锥状舣高斯光束的新型激光元件提供了理论依据和设计参量.     

The sensitive control on the cone angle of hollow beams

The sensitive control on the cone angle of hollow beams was studied in this paper, and the control system consists of positive, negative axicons and telescope zoom system. By analyzing, the condition of sensitive control on the cone angle was obtained. The curve of the cone angle variety against the element shift was given, and the theory we proposed is proved to be correct completely based on experiments. The research of sensitive control on the cone angle can provide a solid foundation in the fields such as fast scan-imaging and remote control etc.     

锥束射线RT扫描大视场三维CT成像方法研究

受探测器尺寸和重建锥角的限制,基于单圆轨道扫描和FDK算法的三维CT成像方法难以对大物体进行三维CT成像。提出了一种基于平板探测器,采用锥束RT扫描方式的成像方法,推导了其三维CT成像算法。首先把对回转物体进行三次锥束平移透照的投影数据重新排成为更大范围的倾斜平行投影数据,然后经过加权滤波和反投影重建,获得物体的三维层析结果。仿真结果表明,该方法在重构大物体图像时,获得了满意的图像质量。水平方向视场是单圆轨道FDK算法视场的2.88倍,在垂直方向减少了锥角过大形成的伪影,提高了物体的重构精度。     

锥体后速度场与压力场的测量与分析

利用全流向十七孔压力探针,测量了Re=1.5×105与Re=3.0×105（基于锥体底面直径）,攻角为0°,锥角为60°的圆锥体后流场速度与压力分布,并用烟线法进行了流场显示对比,得到了所述两种来流条件下锥体后流动速度场与压力场的详细实验测量数据.对速度与压力分布特征进行相关分析后,得到了两种来流条件下流场涡量ω与耗散熵产S_f云图.同时发现在两种来流条件下,锥体后流场可明显划分为3个区域.轴向速度V_z沿锥体轴线分布规律非常相似,均存在3个低速极值点,且锥体后流动驻点位置静压力均基本等于环境静压力.      

关于变摆长的单摆运动与相关的铅直运动的耦合

研究了一个变摆长单摆运动的例子,在平面极坐标系下给出了描述该运动的二阶微分方程组.采用微分方程高精度数值解法得到了随时间变化的摆角、摆长、摆长变化率以及运动轨迹的数值精确解.在小摆角近似下,采用迭代方法推导出摆角、摆角变化率的一级近似解析表达式和摆长、摆长变化率的二级近似解析表达式.由解析表达式得到的数值结果与数值精确解相比较,二者在前几个摆动周期内相吻合.     

Free vibrational characteristics of isotropic coupled cylindrical-conical shells

This paper presents the free vibrational characteristics of isotropic coupled conical-cylindrical shells. The equations of motion for the cylindrical and conical shells are solved using two different methods. A wave solution is used to describe the displacements of the cylindrical shell, while the displacements of the conical sections are solved using a power series solution. Both Donnell-Mushtari and Flügge equations of motion are used and the limitations associated with each thin shell theory are discussed. Natural frequencies are presented for different boundary conditions. The effect of the boundary conditions and the influence of the semi-vertex cone angle are described. The results from the theoretical model presented here are compared with those obtained by previous researchers and from a finite element model.     

Motion of a test particle in a Kerr field with fluctuating perturbations

The motion of a stochastic test particle in the field of a Kerr black hole is discussed in the approximation of Brownian interaction. The probability distribution of the position of orbits with respect to the latitudinal angle is found, and the bifurcation values of their parameters are established. The fluctuational instability of the orbits characteristic of the critical regimes of the motion is investigated, and the properties of some statistical characteristics of the system are determined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 77–82, April, 1982.     

Numerical simulations of laser light guiding and focusing using an open hollow cone

An open hollow cone that can optically guide and focus a laser light into a small beam spot is proposed. The shaping and focusing effects are numerically demonstrated by finite-difference time-domain simulations. The results reveal that the cone-focused laser originates from the multi-beam interference and squeeze of two cone side walls acting like oblique targets. Moreover, the influences of oblique incident angle of laser light, cone angle and cone tip size on the focusing properties are discussed and the optimum cone geometry with cone angle of 16° and tip size of 4.5 wavelengths to achieve high energy concentration at the cone tip is also presented. It is shown that with an open hollow cone a laser light can be focused into a tiny highly localized beam spot of 1 µm diameter and keeps propagating forward for a distance of about 8 wavelengths with a tiny spot diameter remaining almost unchanged. The intensity almost increases up to twentyfold in a 1 µm focal spot.