Two-dimensional spherical oscillator in a constant magnetic field

We study the equations of motion of a spherical oscillator model suggested by Bellucci and Nersessian, in the presence of a constant magnetic field. This model is shown to be exactly solvable classically in contrast to the Higgs oscillator which is not exactly solvable in magnetic fields.     

球几何中子输运保正线性间断有限元格式

针对球几何中子输运方程线性间断有限元方法计算的负中子通量问题,构造了保正线性间断有限元格式,该格式保持中子角通量0阶矩和1阶矩。现有方法计算中子角通量非负时,采用传统的线性间断有限元方法,求解线性方程组;原方法计算出现负通量,则采用构造的保正格式,求解非线性方程组。编制了球几何中子输运问题保正格式程序模块,并集成到应用程序。数值算例表明构造的保正格式计算的中子通量非负,有效降低数值误差,提高数值计算的精度。     

非稳腔傍轴波动方程高斯球面波修正方法的数值研究

在分析用差分方法求解虚共焦非稳腔三维傍轴波动方程,及用数值积分方法与快速付氏变换(FFT)方法求解三维菲涅耳积分方程优缺点的基础上,从激光束在虚共焦非稳腔中以修正高斯球面波形式传输的特征出发,经坐标变换把发散(或会聚)的光束拉直成平行光束,然后用FFT方法求解了在新坐标系中修正函数满足的傍轴波动方程.把相同条件下得到的结果与国内外文献给出的结果进行了比较;计算COIL实验非稳腔给出的近远场结果图象合理正确.     

Normal modes and quality factors of spherical dielectric resonators: I — shielded dielectric sphere

Electromagnetic theoretic analysis of shielded homogeneous and isotropic dielectric spheres has been made. Characteristic equations for the TE and TM modes have been derived. Dielectric spheres of radii of the order of μm size are found suitable for the optical frequency region whereas for the microwave region radii of the order of mm size are found suitable. Parameters suitable for their application in the optical and microwave frequency ranges have been used to compute the frequencies corresponding to the normal modes for the TE and TM modes. Expressions for the quality factors for realistic resonators, i.e., for a dielectric sphere with a non-zero conductivity and a metal shield with a finite conductivity have also been derived for the TE and TM modes. Computations of the quality factors have been made for resonators with parameters suitable for the optical and the microwave regions.     

Anisotropic Spherical Cavity Resonator I. Azimuthally Homogeneous Oscillations

Resonant oscillations are considered in the spherical cavity with the uniform crystal medium and bounded by a non-perfect conductor. The Maxwell equations are reduced to the couple of wave equations each describing the TE and TH modes. We show that the crystal anisotropy affects only the TM modes. The solution of the wave equations satisfies the boundary conditions on the spherical surface that define the spherical characteristics of the resonant oscillations. New types if TM modes appear caused by the anisotropy of the medium. The analytical solution of the dispersion equation is considered in the form of continued fraction. Numerical results are presented demonstrating of natural frequencies of higher mode numbers.     

Self-similar solutions for implosion and reflection of coalesced shocks in a plasma: Spherical and cylindrical geometries

Approximate analytic solutions to the self similar equations of gas dynamics for a plasma, treated as an ideal gas with specific heat ratioγ = 5/3, are obtained for the implosion and subsequent reflection of various types of shock sequences in spherical and cylindrical geometries. This is based on the lowest-order polynomial approximation, in the reduced fluid velocity, for a suitable nonlinear function of the sound velocity and the fluid velocity. However, the method developed here is powerful enough to be extended analytically to higher order polynomial approximations, to obtain successive approximations to the exact self-similar solutions. Also obtained, for the first time, are exact asymptotic solutions, in analytic form, for the reflected shocks. Criteria are given that may enable one to make a choice between the two geometries for maximising compression or temperature of the gas. These solutions should be useful in the study of inertial confinement of a plasma. An erratum to this article is available at .     

A new model for the reformulation of compressible fluid equations

Stimulating the biquaternionic generalization of electric and magnetic fields in electromagnetism, a new model has been proposed to present the Maxwell type equations of compressible fluids. The fluid wave equation has been expressed in a compact and elegant manner. Similarly, the generalized Poynting theorem for fluids has been derived analogous to electromagnetism and linear gravity. Moreover, a brief survey on biquaternionic matrices and the corresponding matrix representations of fluid equations have been given.     

球共鸣声学法气体音速的测量原理及实验系统研究

本文阐述了通过音频信号共振频率测量气体音速的原理。同时还分析了实际的球共鸣器的结构对共振频率的影响并给予了相应的修正。据此设计和制作了一套高精度的球共鸣器和低频音频信号测量装置,建立了一套球共鸣声学法测量气体音速的实验系统。本文实验中研究温度、压力、气体音速测量的不准确度分别为±14mK、±2.0kPa和±0.0037％。通过对制冷剂R22饱和蒸气压和氩气低压下音速的测量验证了本实验系统的稳定性和精确性。     

Complex Hyperspherical Equations, Nodal-Partitioning, and First-Excited-State Theorems in ℝ n

Three problems related to the spherical quantum billiard in are considered. In the first, a compact form of the hyperspherical equations leads to their complex contracted representation. Employing these contracted equations, a proof is given of Courant's nodal-symmetry intersection theorem for diagonal eigenstates of spherical-like quantum billiards in . The second topic addresses the first-excited-state theorem for the spherical quantum billiard in . Wavefunctions for this system are given by the product form, ( )Z _q+()Y ⁽ⁿ⁾ , where is dimensionless displacement, is angular-momentum number, qis an integer function of dimension, Z() is either a spherical Bessel function (nodd) or a Bessel function of the first kind (neven) and represents (n– 1) independent angular components. Generalized spherical harmonics are written . It is found that the first excited state (i.e., the second eigenstate of the Laplacian) for the spherical quantum billiard in is n-fold degenerate and a first excited state for this quantum billiard exists which contains a nodal bisecting hypersurface of mirror symmetry. These findings establish the first-excited-state theorem for the spherical quantum billiard in . In a third study, an expression is derived for the dimension of the th irreducible representation (irrep) of the rotation group O(n) in by enumerating independent degenerate product eigenstates of the Laplacian.     

圆柱腔低频声场的球谐函数分解及声场再现

针对圆柱腔低频声场的球谐函数分解,提出了基于移动式球形传声器阵列(简称球阵)测量的空间域直接求解法。利用空间域测量数据,在压缩感知(Compressive Sensing,CS)理论框架下通过一次线性方程组求解,获得整体坐标系下的声场展开系数。首先讨论了感知矩阵的列相关性,比较不同球阵形式及球面采样点数目,不同球谐函数截断阶数以及空间测量位置等的影响。随后在飞机舱室模型内利用文中提出的方法求解声场展开系数,再现腔内水平面的声压分布,并与传统球坐标变换方法做比较。实验结果表明,利用空间域直接求解法,通过球面随机挑选10个采样点的刚性球阵在声腔3个位置进行声场测量,不仅能够有效求解声场展开系数,而且声场再现精度更高,同时计算效率也显著提高。     

An Exact Interior Solution of a Static Charged Sphere in Higher Dimensional Spacetime

By assuming "p = Aρ" and the total intrinsic energy density εr^k (k + D - 1 > 0), we strictly solve the higher dimensional Einstein-Maxwell field equations in a static charged sphere, resulting in an exact interior solution of the equations.     

氦原子1snp组态的塞曼效应

利用塞曼哈密顿的球张量形式,采用将微扰理论与里兹变分方法相结合的方式,导出了氦原子1snp组态塞曼哈密顿矩阵元的一般形式,给出了氦原子1s3p组态塞曼效应之解,并绘出了不同磁场强度下氦原子1s3p组态的塞曼能级分裂图.     

Effect of size and charge on ordering of a highly charged concentrated macroions in suspension

An efficient fast Fourier transform method has been employed to determine correlation function [g(r*)] using the structure factor [S(Q*)] calculated with the rescaled mean spherical approximation (RMSA) and the DLVO potential. Based on this function a parametric (size and charge) study of the ordering in a highly charged and concentrated macroions (an ideal colloid) has been made. The strength of the correlation increases with the increase in the charge on macroions and it saturates after acertain value. Similarly, a critical diameter of the particle depending on the charge on it has been found at which normal feature of the ordering disappears.     

Analysis on diffusion-induced stress for multi-layer spherical core–shell electrodes in Li-ion batteries

Silicon-based carbon composites are believed as promising anodes in the near future due to their outstanding specific capacity and relatively lower volume effect compared to pure silicon anodes. Herein, a multilayer spherical core–shell(MSCS) electrode with a graphite framework prepared with Si@O-MCMB/C nanoparticles is developed, which aims to realize chemically/mechanically stability during the lithiation/delithiation process with high specific capacity. An electrochemical-/mechanical-coupling model for the M-SCS structure is established with various chemical/mechanical boundary conditions.The simulation of finite difference method(FDM) has been conducted based on the proposed coupling model, by which the diffusion-induced stress along both the radial and the circumferential directions is determined. Moreover, factors that influence the diffusion-induced stress of the M-SCS structure have been discussed and analyzed in detail.     

Systematical study of the trapping forces of optical tweezers formed by different types of optical ring beams

The technique of optical tweezers has been improved a lot since its invention, which extends the application fields of optical tweezers. Besides the conventionally used Gaussian beams, different types of ring beams have also been used to form optical tweezers for different purposes. The two typical kinds of ring beams used in optical tweezers are the hollow Gaussian beam and Laguerre--Gaussian (LG) beam. Both theoretical computation and experiments have shown that the axial trapping force is improved for the ring beams compared with the Gaussian beam, and hence the trapping stability is improved, although the transverse trapping forces of ring beams are smaller than that of Gaussian beam. However, no systematic study on the trapping forces of ring beam has ever been discussed. In this article, we will investigate the axial and transverse trapping forces of different types of ring beams with different parameters systematically, by numerical computation in which the ray optics model is adopted. The spherical aberration caused by the refractive index mismatch between oil and water is also considered in the article. The trapping forces for different objectives that obey the sine condition and tangent condition are also compared with each other. The result of systematical calculation will be useful for the applications of optical tweezers formed by different types of ring beams.     

Analytical static structure factors for the restricted primitive model

The mean static structure for the restricted primitive model formed by m ionic species is presented. Explicit expressions for the partial static structure factors are obtained from the Blum’s solution for the primitive model, which depend on an accumulative parameter, γ, expressed in terms of the Debye length. Additionally, the number-number, number-charge and charge-charge structure factors are provided. An equation to calculate the radial distribution functions which tends to the contact values when r→σ⁺ is also given. Finally, molecular dynamics simulation is performed to assess the accuracy of the theoretical results.     

Spherical reflectors as laser-beam expanders

Lasers emit a narrow beam of light which, for many applications, is often required to be expanded and then collimated. A common type of device used for this purpose is a lens telescope in which a pin-hole is placed at the common focal point of the two lenses. In dye laser cavities, dispersion through a number of prisms gives an expanded beam. The divergence of a laser beam can also be achieved by a convex reflecting surface like a polished steel ball. Here the capability of a small steel ball as an inexpensive, simple and convenient laser-beam expander has been investigated experimentally. It has been shown, with the help of shearing interferograms and Ronchigrams, that the aberrations introduced from on-axis as well as off-axis illumination of the ball are less than 1/4 of a fringe.     

单液滴正碰球面动态行为特性实验研究

在考虑空气阻力影响,确定液滴撞击球面速度的基础上,对较高韦伯数液滴撞击干燥球面动态行为过程进行了实验研究,分析了球面曲率与韦伯数对液滴撞击行为和铺展因子的影响,并与前人撞击平面结果进行了对比.实验表明,靠近撞击球面时,液滴降落速度出现明显波动;球面曲率对液滴撞击后行为影响明显,曲率较大时,液滴撞击后铺展液膜会超出球面直径并滑落,曲率较小时,液滴撞击后在球面上呈现明显的铺展、回缩、震荡、着附动态变化行为,此时最大铺展因子受曲率影响小,随曲率减小,逐渐趋向于撞击平面时的最大铺展因子;韦伯数对液膜铺展速率影响较小,但对液膜回缩时间影响明显,最大铺展因子随韦伯数增加逐渐增大,获得的关联式呈指数变化.     

New Q Matrices and Their Functional Equations for the Eight Vertex Model at Elliptic Roots of Unity

The Q matrix invented by Baxter in 1972 to solve the eight vertex model at roots of unity exists for all values of N, the number of sites in the chain, but only for a subset of roots of unity. We show in this paper that a new Q matrix, which has recently been introduced and is non zero only for N even, exists for all roots of unity. In addition we consider the relations between all of the known Q matrices of the eight vertex model and conjecture functional equations for them.     

Interface Optical Phonon Modes and Frohlich Electron-Phonon Interaction Hamiltonian in a Multi-shell Spherical Nanoheterosystem

Under dielectric continuum approximation, interface optical (IO) phonon modes and the Frohlich electron-IO phonon interaction Hamiltonian in a multi-shell spherical nanoheterosystem were derived and studied. Numericalcalculations on three-layer and four-layer CdS/HgS spherical nanoheterosystems have been performed. Results revealthat there are four IO phonon modes for the three-layer system and six IO phonon modes for the four-layer system.On each interface, there are two IO phonon modes, the frequency of one is between WTO,CdS and WLO,CdS, and that ofthe other is between WTO,HgS and WLO,HgS. With the increasing of quantum number l, the frequency of each IO modeapproaches one of the two frequency values of the single CdS/HgS heterostructure, and the potential for each IO modeis more and more localized at a certain interface, furthermore, the coupling between the electron-lO phonons becomes weaker.