Analytical solutions for black-hole critical behaviour

Dynamical Einstein cluster is a spherical self-gravitating system of counterrotating particles, which may expand, oscillate and collapse. This system exhibits critical behaviour in its collapse at the threshold of black hole formation. It appears when the specific angular momentum of particles is tuned finely to the critical value. We find the unique exact self-similar solution at the threshold. This solution begins with a regular surface, involves timelike naked singularity formation and asymptotically approaches a static self-similar cluster.     

波束形成后多干扰抵消方法

为解决常规波束形成后干扰抵消方法仅能从目标波束内消除一个干扰影响的局限性,提出了一种可实现多干扰抑制的波束形成后干扰抵消方法,用于解决多干扰条件下的弱目标波束形成问题.该方法通过最小化多个干扰波束对目标波束的影响,获得用于抵消干扰波束的加权值;然后从目标波束中减去加权后的干扰波束,从而获得抑制干扰后的目标波束。该方法继承了常规波束形成方法的稳健性,因此在阵列流型失配等存在误差的条件下可以用于目标波束形成。仿真和海上实验数据表明,与最小方差无失真响应方法和解卷积的常规波束形成方法相比,该方法可以有效抑制干扰的影响,且当目标与任一干扰方位相近时,其方位谱中可以观察到目标波束,而另外两种方法的目标波束均被干扰波束或其旁瓣所掩盖;与设置凹槽的波束图综合方法相比,该方法算法复杂度低,计算速度快,稳健性更好。     

Analytical solutions for laser modes in misaligned resonators

Laser modes of misaligned resonators transversally limited in gain are obtained analytically within the paraxial approximation. The eigenfunctions are shown to be complex Hermite-Gaussian functions, not centered either in intensity or in curvature center. Eigenvalues are also obtained, and the effect of resonator parameters and misalignment is analyzed, revealing the lack of selectivity of misalignment on order mode. The changes in the appearance of the modes are also shown.     

Analytical solutions of the Rayleigh-Plesset equation for N-dimensional spherical bubbles

<正>The behaviors and dynamics of bubbles,usually described by the Rayleigh-Plesset(RP)equation and its generalizations,have been an interesting area in fluid dynamics.Owing to their simplicity and sufficient accuracy,the RP equation for bubble dynamics and its enhanced models remains widely used in science and engineering,see refs.[1-3].In this paper,we consider the RP equation for N-dimensions spheri-     

Analytical solutions of coupled-mode equations for microring resonators

We present a study on analytical solutions of coupled-mode equations for microring resonators with an emphasis on occurrence of all-optical EIT phenomenon, obtained by using a cofactor. As concrete examples, analytical solutions for a 3×3 linearly distributed coupler and a circularly distributed coupler are obtained. The former corresponds to a non-degenerate eigenvalue problem and the latter corresponds to a degenerate eigenvalue problem. For comparison and without loss of generality, analytical solution for a 4×4 linearly distributed coupler is also obtained. This paper may be of interest to optical physics and integrated photonics communities.     

Analytical solutions for a doubly driven two-level atom

We have deduced analytical solutions of an energy level diagram of the doubly driven/dressed atom for a two-level atom exposed to a strong near-resonant bichromatic laser field in a special case, i.e., the bichromatic field with frequencies ω1 and ω2, and Rabi frequencies ?1 and ?2, in which the first coupling field of ?1 acts on the bare atomic levels, and then the resulting singly dressed states are driven by the second coupling field of ?2, thus resulting in the doubly dressed atom.We have measured the probe absorption spectra of a doubly driven two-level atom. The system consists of 52S1/2, F= 2 and 5~2P_(3/2), F'= 3 states of ~(87)Rb atoms in a magneto-optical trap(MOT) as well as the cooling/trapping beams and an additional coupling field. As for the spectroscopic properties of the doubly driven two-level atom, theoretical analytical solutions are in general agreement with the experimental spectrum as a whole.     

Analytical solutions for the spin-1 Bose-Einstein condensate in a harmonic trap

The homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions for the Gross-Pitaevskii equations, a set of nonlinear Schrödinger equation used in simulation of spin-1 Bose-Einstein condensates trapped in a harmonic potential. We investigate the one-dimensional case and get the approximate analytical solutions successfully. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they are in agreement well with each other when the atomic interaction is weakly. We also find a class of exact solutions for the stationary states of the spin-1 system with harmonic potential for a special case.     

Analytical approximate solutions to the Thomas-Fermi equation

The purpose of this paper is to show how to use the Optimal Homotopy Asymptotic Method (OHAM) to solve the nonlinear differential Thomas-Fermi equation. Our procedure does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. An excellent agreement was found between our approximate results and numerical solutions, which prove that OHAM is very efficient in practice, ensuring a very rapid convergence after only one iteration.     

Analytical solutions for two heteronuclear atoms in a ring trap

We consider two heteronuclear atoms interacting with a short-range δ potential in a ring trap. By taking the Bethe-ansatz-type wavefunction and considering the periodic boundary condition properly, we derive analytical solutions for the heteronuclear system. The eigen-energies represented in terms of quasi-momentums can then be determined by solving a set of coupled equations. We present a number of results, which display different features from the case of identical atoms. Our result can be reduced to the well-known Lieb-Liniger solution when two interacting atoms have the same masses.     

Modeling of the fringe shift in multiple beam interference for glass fibers

A quadratic model is suggested to describe the fringe shift occurred due to the phase variations of uncladded glass fiber introduced between the two plates of the liquid wedge interferometer. The fringe shift of the phase object is represented in the harmonic term which appears in the denominator of the Airy distribution formula of Fabry-Perot’s interferometer. A computer program is written to plot the computed fringe shifts of the described model. An experiment is conducted using liquid wedge interferometer where the fiber of a nearly quadratic thickness variation is introduced between the two plates of the interferometer. The obtained fringe shift shows a good agreement with the proposed quadratic model. Also, it is compared with the previous theoretical shift based on ray optics of semi-circular shape.      

浅水近距离测量声场的干涉结构分析

为指导浅水中水平距离在十倍水深范围内进行的近距离声学测量工作,选取对软底浅水声场产生主要贡献的直达声线和一次水面反射声线,经过合理的近似处理,以射线解析方式给出了中低频信号声场干涉结构的表达式,并将表达式由单频信号推广到宽带信号和线性调频等信号形式。所得到的解析关系式定量给出了浅水中声场干涉结构与信号频率、信号带宽、设备布放深度和水平距离等参数的关系,由此进一步得到浅水条件下中近距离干涉声场的一些特性和规律。通过数值模拟和实际试验数据对上述关系式所进行的检验表明:在浅水的常规测量试验条件下,这些关系式可以较为准确地反映近距离干涉声场的起伏特征,由关系式推论得到的声场特性和规律也得到了初步验证。     

色散渐减光纤中Ginzburg-Landau方程的自相似脉冲演化的解析解

采用对称约简的分析方法，得出了变系数Ginzburg-Landau方程的抛物渐近自相似脉冲解析解的一般表达式.给出了二阶色散系数纵向双曲型变化和纵向指数型变化的色散渐减光纤中自相似脉冲的振幅、啁啾以及脉冲宽度的具体形式，并与数值解进行了对比，其结果符合得很好.从而证实了稀土元素掺杂的色散渐减光纤中，在增益色散因子的影响下，脉冲的演化具有抛物型自相似特性.     

一类Marangoni对流边界层方程的近似解析解

利用Adomain解析拆分和Padé逼近方法对由Marangoni对流诱发的层流边界层问题进行了研究, 提供了一种求解边界层方程的解析分析方法. 得到了问题的近似解析解并对相应的流动及传热特性进行了探讨. 本文所提出的思想方法可以用于解决其他科学和工程技术问题. 关键词： Marangoni对流 非线性 Adomain拆分法 近似解析解     

Controlled decoherence in multiple beam Ramsey interference

We have scattered photons from an interfering path of a multiple beam Ramsey interference experiment realized with a cesium atomic beam. It is demonstrated that in multiple beam interference the decoherence from photon scattering cannot only lead to a decrease but, under certain conditions, also to an increase of the Michelson fringe contrast. In all cases, the atomic quantum state loses information with photon scattering, as "which-path" information is carried away by the photon field. We outline an approach to quantify this which-path information from observed fringe signals, which allows for an appropriate measure of decoherence in multiple path interference.     

Analytical Cartesian solutions of the multi-component Camassa-Holm equations

Here, we give the existence of analytical Cartesian solutions of the multi-component Camassa-Holm (MCCH) equations. Such solutions can be explicitly expressed, in which the velocity function is given by u = b(t)+A(t)x and no extra constraint on the dimension N is required. The advantage of our method is that we turn the process of analytically solving MCCH equations into algebraically constructing the suitable matrix A(t). As the applications, we obtain some interesting results: 1) If u is a linear transformation on , then p takes a quadratic form of x. 2) If A = f (t)I + D with D^T = ?D, we obtain the spiral solutions. When N = 2, the solution can be used to describe “breather-type” oscillating motions of upper free surfaces. 3) If we obtain the generalized elliptically symmetric solutions. When N = 2, the solution can be used to describe the drifting phenomena of the shallow water flow.     

Analytical solutions of the simplified spherical harmonics equations

We derived analytical solutions of the simplified spherical harmonics equations, an approximation of the radiative transfer equation, for infinitely extended scattering media. The derived equations are simple (sum of exponential functions) and quickly evaluated. We compared the solutions with Monte Carlo simulations in the steady-state and time domains and found much better agreement compared to solutions of the diffusion equation, especially for large absorption coefficients, short time values, and small distances from the source.     

Analytical solutions for axisymmetric vibration of loudspeaker cones in transitional range

The loudspeaker cone vibration in the transitional frequency range in which the governing equations have transition or turning points is studied by applying the uniformly valid solutions obtained in a previous paper. The solutions are presented analytically as well as the resonant and anti-resonant frequency equations, the associated patterns and the axial admittance. A new frequency equation for the non-bending effect is obtained. The results agree well with numerical results.     

Analytical solutions of the lattice Boltzmann BGK model

Analytical solutions of the two-dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plane Poiseuille flow and the plane Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time , and the lattice spacing. The analytic solutions are the exact representation of these two flows without any approximation. Using the analytical solution, it is shown that in Poiseuille flow the bounce-back boundary condition introduces an error of first order in the lattice spacing. The boundary condition used by Kadanoffet al. in lattice gas automata to simulate Poiseuille flow is also considered for the triangular lattice Boltzmann BGK model. An analytical solution is obtained and used to show that the boundary condition introduces an error of second order in the lattice spacing.